A survey of the linear polarization of directly imaged exoplanets and brown dwarf companions with SPHERE-IRDIS. First polarimetric detections revealing disks around DH Tau B and GSC 6214-210 B
R.G. van Holstein, T. Stolker, R. Jensen-Clem, C. Ginski, J. Milli, J. de Boer, J.H. Girard, Z. Wahhaj, A.J. Bohn, M.A. Millar-Blanchaer, M. Benisty, M. Bonnefoy, G. Chauvin, C. Dominik, S. Hinkley, C.U. Keller, M. Keppler, M. Langlois, S. Marino, F. Ménard, C. Perrot, T.O.B. Schmidt, A. Vigan, A. Zurlo, F. Snik
AAstronomy & Astrophysics manuscript no. polarization_companions_arxiv © ESO 2021January 12, 2021
A survey of the linear polarization of directly imaged exoplanetsand brown dwarf companions with SPHERE-IRDIS (cid:63)
First polarimetric detections revealing disks around DH Tau B andGSC 6214-210 B
R. G. van Holstein , , T. Stolker , , R. Jensen-Clem , C. Ginski , , J. Milli , J. de Boer , J. H. Girard , Z. Wahhaj ,A. J. Bohn , M. A. Millar-Blanchaer , , M. Benisty , , M. Bonnefoy , G. Chauvin , , C. Dominik , S. Hinkley ,C. U. Keller , M. Keppler , M. Langlois , S. Marino , F. Ménard , C. Perrot , , , T. O. B. Schmidt , A. Vigan ,A. Zurlo , , and F. Snik (A ffi liations can be found after the references) Received 30 August 2020 / Accepted 18 December 2020
ABSTRACT
Context.
Young giant planets and brown dwarf companions emit near-infrared radiation that can be linearly polarized up to several percent.This polarization can reveal the presence of an (unresolved) circumsubstellar accretion disk, rotation-induced oblateness of the atmosphere, or aninhomogeneous distribution of atmospheric dust clouds.
Aims.
We aim to measure the near-infrared linear polarization of 20 known directly imaged exoplanets and brown dwarf companions.
Methods.
We observed the companions with the high-contrast imaging polarimeter SPHERE-IRDIS at the Very Large Telescope. We reducedthe data using the IRDAP pipeline to correct for the instrumental polarization and crosstalk of the optical system with an absolute polarimetricaccuracy < .
1% in the degree of polarization. We employed aperture photometry, angular di ff erential imaging, and point-spread-function fittingto retrieve the polarization of the companions. Results.
We report the first detection of polarization originating from substellar companions, with a polarization of several tenths of a percentfor DH Tau B and GSC 6214-210 B in H -band. By comparing the measured polarization with that of nearby stars, we find that the polarizationis unlikely to be caused by interstellar dust. Because the companions have previously measured hydrogen emission lines and red colors, thepolarization most likely originates from circumsubstellar disks. Through radiative transfer modeling, we constrain the position angles of the disksand find that the disks must have high inclinations. For the 18 other companions, we do not detect significant polarization and place subpercentupper limits on their degree of polarization. We also present images of the circumstellar disks of DH Tau, GQ Lup, PDS 70, β Pic, and HD 106906.We detect a highly asymmetric disk around GQ Lup and find evidence for multiple scattering in the disk of PDS 70. Both disks show spiral-likefeatures that are potentially induced by GQ Lup B and PDS 70 b, respectively.
Conclusions.
The presence of the disks around DH Tau B and GSC 6214-210 B as well as the misalignment of the disk of DH Tau B with the diskaround its primary star suggest in situ formation of the companions. The non-detections of polarization for the other companions may indicate theabsence of circumsubstellar disks, a slow rotation rate of young companions, the upper atmospheres containing primarily submicron-sized dustgrains, and / or limited cloud inhomogeneity. Key words.
Methods: observational - Techniques: high angular resolution - Techniques: polarimetric - Planets and satellites: formation - Planetsand satellites: atmospheres - Protoplanetary disks
1. Introduction
Understanding the formation and evolution of young, self-luminous exoplanets and brown dwarf companions is one ofthe main goals of high-contrast imaging at near-infrared wave-lengths (e.g., Nielsen et al. 2019; Vigan et al. 2020). Only afew of these directly imaged substellar companions have beendetected close to the parent star and within a circumstellardisk (e.g., Lagrange et al. 2010; Keppler et al. 2018; Ha ff ert et al.2019); most companions are found at much larger separations( (cid:38)
100 au; see e.g., Bowler 2016). Close-in planets and compan-ions are generally believed to form through core accretion (Pol-lack et al. 1996; Alibert et al. 2005) or gravitational instabilities (cid:63)
Based on observations collected at the European Southern Obser-vatory under ESO programs 098.C-0790, 0101.C-0502, 0101.C-0635,0101.C-0855, 0102.C-0453, 0102.C-0466, 0102.C-0871, 0102.C-0916,and 0104.C-0265. in the circumstellar disk (Cameron 1978; Boss 1997). Compan-ions at larger separations may form through direct collapse in themolecular cloud (Bate 2009) or disk gravitational instabilities atan early stage (Kratter et al. 2010). Alternatively, companionsmay form close to the star and subsequently scatter to wide or-bits through dynamical encounters with other companions (e.g.,Veras et al. 2009).In all formation scenarios, the companion is generally ex-pected to form its own circumsubstellar accretion disk (e.g., Sta-matellos & Whitworth 2009; Szulágyi et al. 2017). Indeed, ahandful of substellar companions show evidence for the pres-ence of an accretion disk through hydrogen emission lines, rednear-infrared colors, and excess emission at mid-infrared wave-lengths (e.g., Seifahrt et al. 2007; Bowler et al. 2011; Baileyet al. 2013; Kraus et al. 2014; Zhou et al. 2014; Ha ff ert et al.2019). Interestingly, whereas ALMA and other radio interferom-eters have been successful at detecting the dust and gas of disks Article number, page 1 of 29 a r X i v : . [ a s t r o - ph . E P ] J a n & A proofs: manuscript no. polarization_companions_arxiv around isolated substellar objects (e.g., Ricci et al. 2014; van derPlas et al. 2016; Bayo et al. 2017), attempts to detect such disksaround substellar companions have almost exclusively yieldednon-detections (Bowler et al. 2015; MacGregor et al. 2017; Wuet al. 2017a,b; Wol ff et al. 2017; Ricci et al. 2017; Pérez et al.2019; Wu et al. 2020). The only detection of a disk around a sub-stellar companion at mm-wavelengths is that of PDS 70 c withALMA by Isella et al. (2019). ALMA has also detected a diskaround FW Tau C (Kraus et al. 2015; Caceres et al. 2015), but,from models of the Keplerian rotation of the gas, the companionappears to be a ∼ . M (cid:12) star (Wu & Sheehan 2017; Mora et al.2020). To explain their non-detections, Wu et al. (2017a) andWu et al. (2020) suggest that the disks around substellar com-panions must be very compact ( (cid:46) R Jup or (cid:46) . ffi ciently low for refractory mate-rial to condense (Allard et al. 2001; Ackerman & Marley 2001).This atmospheric dust scatters the thermal radiation emanatingfrom within the object, linearly polarizing the light. Whereasthe spatially integrated polarization signal of a spherical, hori-zontally homogeneous dusty atmosphere is zero, a net polariza-tion remains when this symmetry is broken (Sengupta & Kris-han 2001). Examples of these asymmetries are rotation-inducedoblateness and an inhomogeneous distribution of atmosphericdust clouds (Sengupta & Marley 2010; de Kok et al. 2011; Mar-ley & Sengupta 2011; Stolker et al. 2017), or even a large transit-ing moon (Sengupta & Marley 2016). Based on the models, thedegree of linear polarization due to circumsubstellar disks andatmospheric asymmetries can be several tenths of a percent upto several percent in favorable cases.Spatially unresolved polarimetric observations have alreadybeen used to study disks around pre-main sequence stars (e.g.,Rostopchina et al. 1997; Bouvier et al. 1999; Grinin 2000; Mé-nard et al. 2003). In addition, optical and near-infrared polariza-tion has been detected for dozens of field brown dwarfs (Ménardet al. 2002; Zapatero Osorio et al. 2005; Tata et al. 2009; Zap-atero Osorio et al. 2011; Miles-Páez et al. 2013, 2017). In mostcases, the polarization of these brown dwarfs is interpreted asbeing caused by rotation-induced oblateness or circumsubstel-lar disks, whereas an inhomogeneous cloud distribution has ap-peared harder to prove. However, Millar-Blanchaer et al. (2020)recently measured the near-infrared polarization of the two L / Ttransition dwarfs of the Luhman 16 system and found evidencefor banded clouds on the hotter, late-L-type object. With the adaptive-optics-fed high-contrast imaging instru-ments Gemini Planet Imager (GPI; Macintosh et al. 2014) andSPHERE-IRDIS (Beuzit et al. 2019; Dohlen et al. 2008) at theVery Large Telescope (VLT), we now have access to the spatialresolution and sensitivity required to measure the near-infraredpolarization of substellar companions at small separations. Aftercorrection for instrumental polarization e ff ects, the polarimetricmodes of both instruments can reach absolute polarimetric accu-racies of (cid:46) .
1% in the degree of polarization (Wiktorowicz et al.2014; Millar-Blanchaer et al. 2016; van Holstein et al. 2020).Early attempts to measure the polarization of substellar compan-ions by Millar-Blanchaer et al. (2015) and Jensen-Clem et al.(2016) with GPI and by van Holstein et al. (2017) with SPHERE-IRDIS have been unsuccessful. Nevertheless, van Holstein et al.(2017) showed that SPHERE-IRDIS can achieve a polarimetricsensitivity close to the photon noise limit at angular separations > . (cid:48)(cid:48) . Ginski et al. (2018) detected a companion to CS Cha us-ing SPHERE-IRDIS and measured the companion’s polarizationto be 14%, suggesting that it is surrounded by a highly inclinedand vertically extended disk. However, recent optical spectro-scopic observations with MUSE show that the companion is notsubstellar in nature, but is a mid M-type star that is obscured byits disk (Ha ff ert et al. 2020).In this paper, we present the results of a survey of 20 plane-tary and brown dwarf companions with SPHERE-IRDIS, aimingto detect linear polarization originating from both circumsub-stellar disks and atmospheric asymmetries. Our study is comple-mented by a similar survey of seven companions using GPI andSPHERE by Jensen-Clem et al. (2020).The outline of this paper is as follows. In Sect. 2 we presentthe sample of companions and the observations. Subsequently,we describe the data reduction in Sect. 3 and explain the extrac-tion of the polarization signals in Sect. 4. In Sect. 5 we discussour detections of polarization and the upper limits on the polar-ization for the non-detections. In the same section, we presentimages of five circumstellar disks that we detected in our sur-vey. Because the most plausible explanation for the polarizationof the companions is the presence of circumsubstellar disks, weperform radiative transfer modeling of a representative exampleof such a disk in Sect. 6. Finally, we discuss the implications ofour measurements in Sect. 7 and present conclusions in Sect. 8.
2. Target sample and observations
The sample of this study consists of 20 known directly im-aged planetary and brown dwarf companions, out of the approxi-mately 140 such companions that are currently known . Becausethe expected polarization of the companions is around a fewtenths of a percent or less, our primary selection criterion waswhether SPHERE-IRDIS can reach a high signal-to-noise ratio(S / N) in total intensity without requiring an excessive amountof observing time. Therefore, the selected companions are rela-tively bright, are at a moderate companion-to-star contrast, are ata large angular separation from the star, and / or have a bright starfor good adaptive-optics (AO) performance (see van Holsteinet al. 2017). Our sample contains the majority of the approxi-mately two dozen known companions that match these require-ments. Three of the remaining companions have been observedby Jensen-Clem et al. (2020) in their survey of seven compan-ions. From The Extrasolar Planets Encyclopaedia, http://exoplanet.eu , (Schneider et al. 2011), consulted on January 5, 2021.Article number, page 2 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions
An overview of the properties of the companions of our sam-ple is shown in Fig. 1, with the full details presented in Table 1 .The sample is diverse, with the companions spanning spectraltypes from T5.5 to M7, masses between approximately 6 and70 M Jup , and ages between approximately 2 Myr and 11 Gyr. Thecompanions orbit stars of spectral types A5 to M1. Six compan-ions show evidence of hosting a circumsubstellar disk, mostlyin the form of red near-infrared colors, excess emission at mid-infrared wavelengths, and hydrogen emission lines that revealongoing accretion. As can be seen particularly well from Fig. 1,the overall sample ranges from young, hot, accreting compan-ions with spectral types between late M and early L, to old, cold,and massive companions of later spectral types. For the six com-panions that show evidence of hosting a circumsubstellar disk,we expect any polarization to be primarily due to this (spatiallyunresolved) disk, whereas for the other companions polarizationwould most likely be due to an inhomogeneous cloud distribu-tion or rotation-induced oblateness. Age (Myr)M5L0L5T0T5 Sp e c t r a l t y p e E ff e c t i v e t e m p e r a t u r e ( K ) M Jup
HD 19467 BHR 7672 BHD 4747 BHR 8799 deHR 8799 bcPDS 70 b HD 206893 BGQ Lup B PZ Tel BCD-35 2722 B1RXS J1609 B AB Pic bDH Tau B I: GSC 6214 B
II: TYC 8998 bIII:
HD 106906 bBeta Pic bGSC 8047 B
IIIIII
Fig. 1: Properties of the companions of our sample showing theage, spectral type, mass (surface area of data points), e ff ectivetemperature, and possible existence of a circumsubstellar disk(thick border). The data points of HR 8799 b and c, and ofHR 8799 d and e, overlap. All our observations were performed with the dual-beam polari-metric imaging (DPI) mode of SPHERE-IRDIS (de Boer et al.2020; van Holstein et al. 2020). In this mode, linear polarizersare inserted in the left and right optical channels of IRDIS tosimultaneously create images of the two orthogonal linear polar-ization states on the detector. A rotatable half-wave plate (HWP)modulates the incident linear polarization with switch angles 0 ◦ ,45 ◦ , 22 . ◦ , and 65 . ◦ (a HWP cycle) to measure Stokes Q and U . The observations were carried out between October 10, 2016,and February 16, 2020, under generally good to excellent atmo-spheric conditions. An overview of the observations is shown inTable 2. Throughout this paper we use the short names GSC 8047, GSC 6214,1RXS J1609, and TYC 8998 for the stars GSC 08047-00232,GSC 06214-00210 (or GSC 6214-210), 1RXS J160929.1-210524, andTYC 8998-760-1, respectively.
The observation strategy was as follows. We generally ob-served each target multiple times with typically over 30 min ofon-source exposure time per visit. However, for some targets asingle visit was enough to detect the companion with high S / N intotal intensity. We mainly observed in broadband H , but some-times used broadband J or K s when we wanted to obtain data inan additional filter or in the case the companion was brighter in K s than H . We used the apodized Lyot coronagraph with a maskdiameter of 185 mas (for J and H ) or 240 mas (for K s ) to sup-press the starlight (Carbillet et al. 2011; Guerri et al. 2011). Thisallowed us to use longer integration times per frame to minimizethe e ff ects of read noise. However, we did not use integrationtimes longer than 64 s to limit the e ff ect of changing atmosphericconditions during a HWP cycle. In addition to the polarimetricscience frames, we took star center frames to accurately deter-mine the position of the star behind the coronagraph and starflux frames to measure the total stellar flux. We also took skyframes with the same instrument setup as the science and starflux frames to subtract the sky background from the respectiveframes.For the majority of the observations, we used the pupil-tracking mode (van Holstein et al. 2017). In this mode the imagederotator (K-mirror) rotates such that the telescope pupil is keptfixed with respect to the detector while the on-sky field of viewrotates with the parallactic angle. The pupil-tracking mode hasnumerous advantages. With su ffi cient parallactic rotation we canapply angular di ff erential imaging (ADI; Marois et al. 2006) tosuppress speckle noise and accurately determine the total inten-sity of the companions located at small angular separations fromthe star. Furthermore, because the speckles are quasistatic, theyare more e ff ectively removed in the polarimetric data-reductionsteps (and can be further suppressed by applying ADI to the po-larimetric images). In addition, the di ff raction spikes created bythe support structure of the telescope’s secondary mirror are sup-pressed by a mask added to the Lyot stop. Finally, the loss of sig-nal due to the crosstalk produced by the image derotator is lim-ited (see van Holstein et al. 2020). As a result, the polarimetrice ffi ciency, that is, the fraction of the linearly polarized light in-cident on the telescope that is actually measured, is always high(typically (cid:38) ff set the derotator position angle and control the orientationof the image on the detector. For instance, the companions ofAB Pic and HD 106906 are at such large angular separations(see Table 1) that we needed to place them in one of the cornersof the 11 (cid:48)(cid:48) × (cid:48)(cid:48) field of view to make them visible. In the caseof 1RXS J1609 and DH Tau we switched to field-tracking modeafter we discovered that both companions crossed a cluster ofbad pixels during the pupil-tracking observations. In all cases,we chose the orientation of the image derotator such that thepolarimetric e ffi ciency was high (see de Boer et al. 2020).
3. Data reduction
We reduced the data with the publicly available and highly au-tomated pipeline
IRDAP (IRDIS Data reduction for AccuratePolarimetry), version 1.2.2 (van Holstein et al. 2020). IRDAPpreprocesses the raw data by subtracting the sky background,flat fielding, correcting for bad pixels, extracting the images ofIRDIS’ left and right optical channels, and centering using thestar center frames. It then subtracts the right images from theleft images (the single di ff erence) for each of the measurements https://irdap.readthedocs.io Article number, page 3 of 29 & A proofs: manuscript no. polarization_companions_arxiv
Table 1: Properties of the companions of our sample.
Target d (pc) SpTstar Age ρ ( (cid:48)(cid:48) ) Mass( M Jup ) SpTcomp. T e ff (K) log g Evid.CSD ReferencesHR 8799 b 41.2 A5 42 + − Myr 1.7 5.8 ± ∼ L / T 1175 ± ∼ . + − Myr 0.9 7 . + . − . ∼ L / T 1225 ±
125 3.5 - 3.9 - 1,2,3HR 8799 d 41.2 A5 42 + − Myr 0.7 7 . + . − . L7 ± ±
100 3.0 - 4.5 - 1,2,3HR 8799 e 41.2 A5 42 + − Myr 0.4 7 . + . − . L7 ± ±
50 4.3 ± ± ± ± < . . + . − . Gyr 0.8 68 . + . − . L4.5 ± ∼
30 Myr 3.2 22 + − M9.5 ± ±
100 4.0 ± ± . + . − . T5.5 ± + − ∼ ∼
10 - 40 L1 ± ±
100 4.0 ± + − Myr 0.3 15 - 40 L3 - L5 1300 - 1700 3.5 - 5.0 - 7,21,22HD 4747 B 18.8 G9 11 ± . + . − . T1 ± + − . + . − . - 15,23,24CD-35 2722 B 22.4 M1 100 ±
50 Myr 3.1 31 ± ± ± ∼
30 Myr 5.5 13 + − L0 ± + − ± ± ± ± ± ∼ . + − Myr 2.2 14.5 ± ± ±
100 . . . H,N,M 19,31PDS 70 b 113.0 K7 5 . ± . ∼ ∼ L 1500 - 1600 ∼ ∼
10 Myr 2.2 14.0 ± ± ± ∼ A V ∼ + − M9.25 ± ±
100 3.5 ± β Pic b 19.7 A6 18 . + . − . Myr 0.3 13 ± ± ±
40 4 . + . − . - 40,41,42,43,44TYC 8998 b 94.6 K3 16 . ± . ± ∼ L0 1727 + − . + . − . - 32,45 Notes. d is the distance from Earth, SpT stands for spectral type, ρ is the approximate angular separation of the companion from the hoststar at the time of observation, T e ff is the e ff ective temperature, and log g is the surface gravity. The second column from the right indicatesthe evidence for the existence of a circumsubstellar disk (CSD), which includes hydrogen emission lines (H), red near-infrared colors (N),excess emission at mid-infrared wavelengths (M), a radially extended point spread function in Hubble Space Telescope images (P), andsignificant extinction by dust ( A V ). HR 7672 B, HD 19467 B, HD 4747 B, and β Pic b have also been observed by Jensen-Clem et al.(2020).
References.
Distances from Gaia DR2 (Gaia Collaboration et al. 2018; Bailer-Jones et al. 2018). Other properties from: (1) Gray et al.(2003), (2) Wang et al. (2018), (3) Bonnefoy et al. (2016), (4) Gravity Collaboration et al. (2019), (5) Torres et al. (2006), (6) Maireet al. (2016a), (7) Gray et al. (2006a), (8) Crepp et al. (2012), (9) Liu et al. (2002), (10) Boccaletti et al. (2003), (11) Chauvin et al.(2005a), (12) Ginski et al. (2014), (13) Bonnefoy et al. (2014), (14) Crepp et al. (2014), (15) Wood et al. (2019), (16) Crepp et al. (2015),(17) Kharchenko & Roeser (2009), (18) Donati et al. (2012), (19) Wu et al. (2017a) and references therein, (20) Wu et al. (2017b) andreferences therein, (21) Delorme et al. (2017), (22) Milli et al. (2017), (23) Montes et al. (2001), (24) Crepp et al. (2018), (25) Wahhaj et al.(2011), (26) Bonnefoy et al. (2010), (27) Chauvin et al. (2005b), (28) Houk & Cowley (1975), (29) Kalas et al. (2015), (30) Daemgen et al.(2017), (31) Pearce et al. (2019), (32) Pecaut & Mamajek (2016), (33) Müller et al. (2018), (34) Keppler et al. (2018), (35) Christiaenset al. (2019), (36) Ha ff ert et al. (2019), (37) Rizzuto et al. (2015), (38) Wu et al. (2015), (39) Herbig (1977), (40) Gray et al. (2006b),(41) Miret-Roig et al. (2020), (42) Stolker et al. (2020), (43) Chilcote et al. (2017), (44) Dupuy et al. (2019), (45) Bohn et al. (2020). taken at HWP switch angles equal to 0 ◦ , 45 ◦ , 22 . ◦ , and 67 . ◦ toobtain the Q + -, Q − -, U + -, and U − -images, respectively. IRDAPalso adds these same left and right images (the single sum) toobtain the total-intensity I Q + -, I Q − -, I U + -, and I U − -images. Sub-sequently, IRDAP computes cubes of Q - and U -images from thedouble di ff erence and the corresponding cubes of total-intensity I Q - and I U -images from the double sum, as: Q = (cid:0) Q + − Q − (cid:1) , (1) I Q = (cid:0) I Q + + I Q − (cid:1) , (2)and similar for U and I U . For the two data sets of HD 4747 andthe data set of PZ Tel in J -band, strongly varying atmosphericseeing prevents the double di ff erence from fully removing thesignal created by transmission di ff erences between the two or-thogonal polarization directions downstream of the image dero- tator. To remove this spurious polarization, we used the normal-ized double di ff erence (see van Holstein et al. 2020) instead ofthe conventional double di ff erence for these three data sets.After computing the double di ff erence and double sum,IRDAP uses a fully validated Mueller matrix model to correctfor the instrumental polarization (created upstream of the imagederotator) and crosstalk of the telescope and instrument with anabsolute polarimetric accuracy of (cid:46) .
1% in the degree of po-larization. IRDAP also derotates the images and corrects themfor true north (see Maire et al. 2016b). This results in a totalof four images: Q , U , I Q , and I U , that constitute our best esti-mate of the linear polarization state incident on the telescope.Finally, IRDAP computes images of the linearly polarized in-tensity PI = √ ( Q + U ), and, following the definitions of deBoer et al. (2020), images of Q φ and U φ . Positive (negative) Q φ indicates linear polarization in the azimuthal (radial) direction,and U φ shows the linear polarization at ±
45° from these direc-
Article number, page 4 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions
Table 2: Overview of the observations performed.Target Date Trackingmode Filter DIT (s) NDIT t exp (min) Parallacticrotation (°) Seeing (") Coherencetime (ms)HR 8799 2016-10-11 Pupil BB_H 16 3 137.6 50.5 0.41 - 0.93 2.4 - 6.1PZ Tel 2016-10-10 Pupil BB_H 12 4 32.0 14.3 0.57 - 1.21 3.6 - 6.42016-10-12 Pupil BB_J 12 4 32.0 12.9 0.86 - 1.24 2.8 - 6.1HR 7672 2018-06-08 Pupil BB_H 4 1 12.8 9.8 0.51 - 0.68 3.5 - 5.92018-07-13 Pupil BB_H 4 1 12.8 11.0 0.36 - 0.46 7.2 - 11.02018-07-14 Pupil BB_H 4 1 12.8 10.9 0.44 - 0.56 11.7 - 15.2GSC 8047 2018-08-07 Pupil BB_H 64 1 42.7 13.0 0.40 - 0.65 3.9 - 6.82018-08-09A Pupil BB_H 64 1 42.7 13.7 0.43 - 0.82 3.1 - 7.32018-08-09B Pupil BB_H 32 2 38.4 17.7 0.39 - 0.56 4.0 - 9.2HD 19467 2018-08-07 Field BB_H 12 1 25.6 0.47 - 0.66 2.2 - 3.92018-08-10A Field BB_H 12 1 25.6 0.42 - 0.53 6.4 - 11.22018-08-10B Field BB_H 12 1 32.0 0.52 - 0.78 4.3 - 9.5GQ Lup 2018-08-15 Pupil BB_H 32 1 38.4 6.0 0.48 - 0.72 3.9 - 7.9HD 206893 2018-09-06 Pupil BB_K s
32 1 36.3 31.6 0.46 - 0.64 6.5 - 10.42018-09-08 Pupil BB_K s
32 1 40.5 39.3 0.48 - 0.84 11.2 - 19.5HD 4747 2018-09-10 Pupil BB_K s
12 1 25.6 1.1 1.19 - 1.77 2.0 - 3.52018-09-11 Pupil BB_K s
12 1 25.6 1.2 0.53 - 0.75 2.2 - 4.4CD-35 2722 2018-11-22 Pupil BB_H 16 1 16.0 3.3 0.56 - 0.68 2.7 - 5.1AB Pic 2019-01-12 Field BB_H 32 1 46.9 0.59 - 0.91 2.7 - 5.3HD 106906 2019-01-17 Field BB_H 32 1 29.9 0.40 - 0.86 5.1 - 11.82019-01-18 Field BB_H 32 1 29.9 0.40 - 0.96 8.4 - 14.42019-01-20 Field BB_H 32 1 29.9 0.44 - 0.78 11.5 - 16.72019-01-26 Field BB_H 32 1 29.9 0.36 - 0.48 13.9 - 20.1GSC 6214 2019-02-22 Pupil BB_H 32 1 29.9 1.3 0.43 - 0.99 11.2 - 21.02019-08-06 Pupil BB_H 32 1 33.1 1.6 0.34 - 0.53 5.1 - 11.42019-08-07 Pupil BB_H 32 1 29.9 0.8 0.43 - 0.58 5.8 - 8.8PDS 70 2019-07-12 Pupil BB_K s
64 1 135.5 85.2 0.37 - 0.79 2.8 - 5.42019-08-09 Pupil BB_H 64 1 38.4 13.5 1.28 - 1.67 1.8 - 2.51RXS J1609 2019-08-06 Pupil BB_H 32 1 29.9 1.5 0.33 - 0.50 8.0 - 13.22019-08-29 Field BB_H 64 1 46.9 0.55 - 0.81 2.6 - 3.62019-08-31 Field BB_H 64 1 11.7 0.89 - 1.13 2.2 - 3.02019-09-17A Field BB_H 64 1 12.8 0.58 - 0.73 3.4 - 4.12019-09-17B Field BB_H 64 1 38.4 0.52 - 0.80 2.7 - 3.92019-09-23 Field BB_H 64 1 38.4 0.71 - 1.03 3.0 - 5.1DH Tau 2019-08-17 Pupil BB_H 32 1 14.9 4.3 0.48 - 0.56 3.9 - 4.82019-09-16 Field BB_H 64 1 38.4 0.90 - 1.60 1.6 - 2.92019-10-24 Field BB_H 64 1 38.4 0.20 - 0.32 5.5 - 12.02019-10-25A Field BB_H 64 1 38.4 0.50 - 0.99 5.9 - 10.42019-10-25B Field BB_H 64 1 38.4 0.47 - 0.64 5.3 - 11.7 β Pic 2019-10-29 Pupil BB_H 4 8 29.9 20.9 0.34 - 0.60 3.3 - 5.82019-11-26 Pupil BB_H 4 8 29.9 19.8 0.37 - 0.53 2.9 - 7.8TYC 8998 2020-02-16 Pupil BB_H 32 4 34.1 12.8 0.46 - 0.75 7.1 - 11.2
Notes.
The date is in the format year-month-day, DIT stands for detector integration time, NDIT is the number of detector integra-tions per HWP switch angle and t exp is the total on-source exposure time. The parallactic rotation is only indicated for observationsperformed in pupil-tracking mode. The seeing and coherence time are retrieved from measurements by the DIMM (Di ff erentialImage Motion Monitor) and from the MASS-DIMM (Multi-Aperture Scintillation Sensor), respectively. Article number, page 5 of 29 & A proofs: manuscript no. polarization_companions_arxiv tions. In Sect. 5.5 we use the polarized intensity and Q φ - and U φ -images to show the five circumstellar disks that we detected.The model-corrected Q - and U -images often contain a haloof polarized light from the star. This polarization can originatefrom interstellar dust, (unresolved) circumstellar material, andspurious or uncorrected instrumental polarization. With IRDAPwe can therefore determine the stellar polarization from the I Q -, I U -, and model-corrected Q - and U -images by measuring theflux in these images in a user-defined region that contains onlystarlight and no signal from a companion, background star, orcircumstellar disk. For most data sets we measured the stellarpolarization using a star-centered annulus placed over the AOresiduals, or in the case that region contains little flux, a largeaperture centered on the star. IRDAP then determines the cor-responding uncertainty by measuring the stellar polarization foreach HWP cycle individually and computing the standard errorof the mean over the measurements. Finally, IRDAP creates anadditional set of Q - and U -images with the stellar polarizationsubtracted. To this end, it scales the I Q - and I U -images with themeasured fractional stellar polarization and subtracts the result-ing images from the model-corrected Q - and U -images. When-ever discussing data in this paper, we always mean the reduc-tion without the stellar polarization subtracted, unless explicitlystated.For the observations taken in pupil-tracking mode, IRDAPadditionally performs classical ADI and ADI with principalcomponent analysis (PCA; Soummer et al. 2012; Amara &Quanz 2012) to suppress the stellar speckle halo and detect thecompanions in total intensity. IRDAP also processes the starflux frames by performing sky subtraction, flat fielding, bad-pixel correction, and registering through fitting the frames to a2D Gaussian function. We obtained the final images of the stel-lar point spread function (PSF) by mean-combining the left andright processed star flux frames and scaling the pixel values tothe integration time and system transmission (i.e., due to neutral-density filters) of the science frames. We separately reduced thedata sets of targets that we observed multiple times and then usedIRDAP to mean-combine the final images produced in each re-duction.The final Q - and U -images of most data sets still containa small amount of speckle noise close to the star. For the datasets of HR 8799, HD 206893 and β Pic, which have com-panions at small separations from the star, we therefore per-formed additional reductions in which we apply classical ADI onthe polarimetric images to further suppress these speckles (seevan Holstein et al. 2017). To this end, we added a reductionstep to IRDAP in which we median-combine the instrumental-polarization-subtracted Q -frames (and U -frames) and subtractthe resulting median image from each of the frames before dero-tating them. In these reductions we skip the later step of deter-mining and subtracting the stellar polarization because the ADIstep has already removed the halo of polarized starlight.
4. Extraction of polarization of companions:Detection of polarization of DH Tau B
With the data of all targets reduced, we can determine the polar-ization of the companions, or, in the case we do not detect signifi-cant polarization, place upper limits on the degree of polarizationof the companions. For this we have developed a method similarto that employed by Jensen-Clem et al. (2020), which, in turn, isbased on the method used by Jensen-Clem et al. (2016). In thismethod, we use aperture photometry to estimate the probabil-ity distributions of the companion signals in the I Q -, I U -, Q -, and U -images. We then use these distributions to calculate the proba-bility distributions of the degree and angle of linear polarization,from which we retrieve the median values, uncertainties, and up-per limits. We applied this method to the data sets of GSC 8047,CD-35 2722, AB Pic, HD 106906, GSC 6214, 1RXS J1609,DH Tau, and TYC 8998. In this section, we demonstrate themethod using the 2019-10-24 H -band data set of DH Tau and ex-emplify the detection of the polarization of DH Tau B, a compan-ion at a large angular separation from its star. For companions atclose separations or with large star-to-companion contrasts, wehave slightly adapted the method and determine the distributionsin I Q and I U through ADI with negative PSF injection or fittingof the companion PSF. In Appendices C and D we demonstratethe two respective methods and show how we set upper limits onthe polarization of β Pic b and HD 19467 B.To start the analysis of the 2019-10-24 data set of DH Tau,we determine the center coordinates of the companion DH Tau Bby mean-combining the I Q - and I U -images and fitting a 2D Mof-fat function to the resulting image at the position of the com-panion. We then make a cosmetic correction to the Q - and U -images (if necessary) to remove spurious structures that resultfrom imperfect relative centering of the images, image motion,and parallactic rotation (see Appendix A). The I Q -, Q -, and U -images (after the cosmetic correction) at the companion positionare shown in Fig. 2. The signals in Q and (in particular) in U areclear indications that DH Tau B is polarized. I Q Counts
Q U -60 -40 -20 0 20 40 60Counts
Fig. 2: Reduced I Q -, Q -, and U -images (after applying thecosmetic correction described in Appendix A) at the position ofthe companion DH Tau B of the 2019-10-24 data set ofDH Tau, showing an aperture of radius 8 pixels centered on thecompanion. The I U -image, which is not shown, is very similarto the I Q -image.To determine the probability distributions of the companionsignals in I Q , I U , Q , and U , we define a range of aperture radiifrom 1 to 10 pixels to be used for the photometry. For each aper-ture radius we perform the following five steps, after which weselect the final aperture radius to be used for our results. Be-cause at the end of this section we select a final aperture radiusof 8 pixels, we use this radius in the examples of the five stepsbelow.As the first step, we place an aperture of the given radiusat the position of the companion in each of the I Q -, I U -, Q -,and U -images (see Fig. 2) and sum the flux in the aperture. Inthe same images we then place a ring of comparison aperturesaround the star at the same separation as the companion to sam-ple the background. We exclude those apertures that contain thefirst Airy ring of the companion, di ff raction spikes from the starand the companion, and clusters of bad pixels. The resulting ringof apertures for an aperture radius of 8 pixels is shown super-imposed on the I Q -image in Fig. 3. In this figure the first Airy Article number, page 6 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions ring and the di ff raction spikes created by the Lyot stop maskare clearly visible at the companion position, which is evidenceof the extremely good atmospheric conditions during the obser-vations (see Table 2). Finally, we sum the flux in each of thecomparison apertures and compute the mean background as themean of the aperture sums. d e c () C o un t s Fig. 3: Reduced I Q -image of the 2019-10-24 data set ofDH Tau, showing an aperture of radius 8 pixels at the positionof the companion DH Tau B (red) and the ring of comparisonapertures of the same radius around the star (white).In step two, we calculate the probability density function(PDF) of the companion signal in I Q , I U , Q , and U , taking intoaccount only the photon noise of the companion. To this end,we compute the companion signals in I Q , I U , Q , and U by sub-tracting the mean background from the summed flux of the com-panion aperture. We then compute the PDFs of I Q and I U from aGaussian distribution with the mean and variance equal to the re-spective companion signals, while accounting for the conversionfrom counts to total number of detected photoelectrons and backto counts (using a detector gain of 1.75 e − / count). The resultingPDF of I Q for an aperture radius of 8 pixels is shown in Fig. 4(left). For large number of photons, the photon noise in Q and U is the same as that in I Q and I U . We therefore construct the PDFsof Q and U from a Gaussian distribution with the mean equal tothe companion signals in Q and U , but the variance equal to thatof the PDFs of I Q and I U . Figure 4 (right) shows the resultingPDF in Q .For the third step, we estimate the PDF of the background in I Q , I U , Q , and U using the comparison aperture sums obtainedin the first step. To not a priori assume a specific functional formof the PDF, we use kernel density estimation (KDE). In thismethod, the PDF is obtained by placing a Gaussian kernel of agiven bandwidth (i.e., a Gaussian distribution with a given stan-dard deviation) at each data point of the sample and summingthe resulting kernels. We compute the bandwidth of the Gaus-sian kernel using Scott’s rule (Scott 2015), in this case yield-ing a bandwidth of ∼
84 counts for I Q and I U , and ∼
18 countsfor Q and U . Histograms of the background samples and thePDFs as estimated via KDE for an aperture radius of 8 pixelsare shown in Fig. 5. We note that for very close-in companionssuch as PDS 70 b, the number of comparison apertures is low I Q (counts)0.0000.0010.0020.0030.0040.005 P r o b a b ili t y d e n s i t y ±
80 counts 750 500 250 0 Q (counts)0.0000.0010.0020.0030.0040.005 393 ±
80 counts
Fig. 4: PDF of the signal of DH Tau B in I Q (left) and Q (right)from the 2019-10-24 data set of DH Tau, using an apertureradius of 8 pixels and taking into account only the photon noiseof the companion. The mean and standard deviation of thedistributions are shown above the graphs, with the latter alsoindicated by the light-blue shaded area.enough that KDE does not produce accurate results. When thereare fewer than 21 comparison apertures, we therefore accountfor the small-sample statistics by fitting the background sampleswith a Student’s t -distribution with the empirical standard devia-tion equal to s = s bg √ (1 + / n ), with s bg the standard deviation ofthe comparison aperture sums and n the number of comparisonapertures (see Mawet et al. 2014).
500 750 1000 1250 I Q (counts)0.02.55.07.510.012.5 N u m b e r o f a p e r t u r e s I U (counts)051015 887.2 ± 183.3 counts100 0 Q (counts)051015 N u m b e r o f a p e r t u r e s U (counts)0.02.55.07.510.012.5 13.9 ± 36.9 counts KDEGaussian
Fig. 5: Histograms of the background in I Q , I U , Q , and U of the2019-10-24 data set of DH Tau, as obtained through summingthe flux in the 8-pixel-radius comparison apertures of Fig. 3.The mean and standard deviation of the samples are shownabove the histograms. The blue curves show the PDFs asestimated through KDE and the red curves show the best-fitGaussian distributions for comparison.In step four, we compute the final probability distributionsin I Q , I U , Q , and U that include both the photon noise of the Article number, page 7 of 29 & A proofs: manuscript no. polarization_companions_arxiv I Q (counts)0.00000.00050.00100.00150.0020 P r o b a b ili t y d e n s i t y I U (counts)0.00000.00050.00100.00150.0020 201432 ± 216 counts (931) 800 600 400 200 0 Q (counts)0.0000.0010.0020.0030.004 393 ± 91 counts (4.3) 600 800 1000 1200 U (counts)0.0000.0010.0020.0030.004 943 ± 89 counts (10.5)0.4 0.3 0.2 0.1 0.0 q (%)02468 P r o b a b ili t y d e n s i t y u (%)02468 0.47 ± 0.04 % (10.6) 0.3 0.4 0.5 0.6 0.7 P (%)02468 0.51 ± 0.04 % (11.5) 45 50 55 60 65 70 ( )0.0000.0250.0500.0750.1000.1250.150 56 ± 3 Fig. 6: Final probability distributions of the signals of DH Tau B in I Q , I U , Q , and U (top row), and in normalized Stokes q and u ,degree of linear polarization, and angle of linear polarization (bottom row) from the 2019-10-24 data set of DH Tau, using anaperture radius of 8 pixels. The median values of the distributions, as well as the uncertainties computed from the two-sided68.27% equal-tailed interval around the median, are shown above the graphs. The S / N, i.e., the median value divided by the largestuncertainty, is shown within parentheses. The 68.27% intervals are also indicated by the light-blue and light-red shaded areas.companion and the uncertainty of the background. For this, wedraw 10 random samples from the previously constructed PDFsof the companion signal (step two) and the background (stepthree). Because we already subtracted the background whencomputing the PDF of the companion signal, we first subtract themean background from the drawn background samples. We thencompute the final distribution by subtracting the resulting back-ground samples from the samples of the companion signal. Next,we compute the median values of the final distributions anddetermine the uncertainties from the two-sided 68.27% equal-tailed interval around the median, corresponding to the 1 σ (onestandard deviation) confidence interval of the Gaussian distribu-tion. The resulting probability distributions for an aperture ra-dius of 8 pixels, including the median values, uncertainties, andS / Ns (i.e., the median value divided by the largest uncertainty),are shown in Fig. 6 (top row). The data are clearly photon-noiselimited in Q and U because the distributions are nearly Gaussianand the uncertainties are close to the standard deviation shownin Fig. 4 (right). It follows that we detect DH Tau B with a veryhigh S / N in total intensity and also have significant detections ofpolarization, especially in Stokes U .As the fifth and final step, we use the I Q -, I U -, Q -, and U -samples to compute the distributions of normalized Stokes q = Q / I Q , normalized Stokes u = U / I U , the degree of linearpolarization P = √ ( q + u ), and the angle of linear polarization χ = / arctan( u / q ). We compute the median values and uncer-tainties in the same way as we did for I Q , I U , Q , and U . Theresults of these computations for an aperture radius of 8 pixelsare shown in Fig. 6 (bottom row).After performing the five steps above for each defined aper-ture radius, we plot the median values and uncertainties of q , u , the degree and angle of polarization, and the S / N in q , u , and thedegree of polarization as a function of aperture radius in Fig. 7.From this figure we see that, within the uncertainties, the po-larization of the companion is constant with changing apertureradius. We select a final aperture radius of 8 pixels, as indicatedby the vertical dashed lines in Fig. 7, because at this radius theS / N in q and u is maximized and the aperture is su ffi ciently largeto suppress (average out) the spurious signals resulting from in-completely removed bad pixels (see Appendix B). We concludethat for this 2019-10-24 data set, we measure DH Tau B to havea degree of polarization of 0 . ± .
04% and an angle of polar-ization of 56 ± ◦ (east of north) in H -band.
5. Results
After careful analysis of our data with the methods as describedin Sect. 4 and Appendices C and D, we detected unresolved po-larization originating from DH Tau B and GSC 6214 B. We con-sider these measurements detections because the measured po-larization signals are significant (i.e., have an S / N of at least5 in q or u ) and are very likely intrinsic to the companions(i.e., are not due to interstellar dust). We present these results inSects. 5.1 and 5.2. We also marginally detected polarization from1RXS J1609 B, but we show in Sect. 5.3 that this polarization isbest explained by interstellar dust. For the other 17 companionswe do not detect significant polarization. In Sect. 5.4, we placeupper limits on the degree of polarization of 1RXS J1609 B andthese other companions. Finally, in Sect. 5.5, we briefly describefive circumstellar disks that we detected in our survey and ofwhich two had not been imaged in polarized scattered light be-fore. Article number, page 8 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions P o l a r i z a t i o n s i g n a l ( % ) q u P A n g l e o f li n e a r p o l a r i z a t i o n () S i g n a l - t o - n o i s e r a t i o Q U P
Fig. 7: Normalized Stokes parameters q and u and degree oflinear polarization (top), angle of linear polarization (center),and S / N in q , u , and the degree of linear polarization (bottom)of DH Tau B as a function of aperture radius for the 2019-10-24data set of DH Tau. The uncertainties of the measured valuesare shown with error bars. The final selected aperture radius of8 pixels is indicated with the dashed vertical lines. In this section we present the detection of polarization originat-ing from DH Tau B. Table 3 shows the measured H -band de-gree and angle of polarization of DH Tau B, including the un-certainties and the attained S / Ns, for each of the various datasets and the data set created by mean-combining the final imagesof the three data sets taken at favorable atmospheric conditions(i.e., the 2019-10-24, 2019-10-25A, and 2019-10-25B data sets;see Table 2). For each data set the measured q - and u -signals arewithin the uncertainties constant with aperture radius. We de-termined the final values of the polarization signals using aper-tures of radius 8 pixels, which is at, or close to, the radius wherethe S / N in q and u is maximized for the various data sets (seeSect. 4). As shown in Table 3, we detect significant polariza-tion from DH Tau B, reaching S / Ns of around 10 for the threedata sets taken at favorable atmospheric conditions. The mea-sured degree and angle of polarization for the di ff erent data setsare overall consistent. From visual inspection of the images, wefind that the small di ff erences among the data sets are primarilydue to small biases caused by incompletely removed bad pixels(see Appendix B). These di ff erences can additionally be causedby time-varying atmospheric conditions and AO performance,the limited accuracy of the Mueller matrix model with which thedata have been corrected (see van Holstein et al. 2020), and otherunknown systematic e ff ects. From the mean-combined images,we measure DH Tau B to have a degree and angle of polarizationof 0 . ± .
03% and 58 ± ◦ (east of north), respectively, with anS / N of 7.7 in q and 16.1 in u . Table 3 also lists the stellar degrees and angles of polar-ization as measured with an annulus at the location of the AOresiduals (see Sect. 3). For the mean-combined data set we de-termined the uncertainty on the stellar polarization by propagat-ing the uncertainties from the individual data sets using a MonteCarlo calculation and assuming Gaussian statistics. The mea-surements of the stellar polarization are very likely a ff ected bysome systematic e ff ects because the signals are less consistentthan those of the companion and show di ff erences among thedata sets that are much larger than the calculated (statistical) un-certainties. The most likely explanation for these di ff erences isthat time-varying atmospheric conditions and AO performancecause the e ff ective coronagraphic extinction to vary from frameto frame. Because the companion is not a ff ected by the coron-agraph, this can also explain why the polarization measured forthe companion is more consistent among the data sets. The stel-lar polarization measurements show that the star could be trulypolarized because the angles of polarization for the three datasets taken at favorable conditions (2019-10-24, 2019-10-25A,and 2019-10-25B) are quite similar. Importantly, the measuredpolarization of the companion di ff ers significantly from that ofthe star in all data sets, with the companion having a significantlylarger degree of polarization and a very di ff erent angle of polar-ization.DH Tau, at a distance of 135 pc , is located at the frontside of the Taurus molecular cloud complex that extends from atleast 126 pc to 163 pc (Galli et al. 2018). To determine whetherDH Tau B is intrinsically polarized, we therefore need to deter-mine the contribution of interstellar dust to the measured polar-ization. The interstellar polarization is a result of dichroism byelongated dust grains that are aligned with the local (galactic)magnetic field. Because interstellar dust creates the same polar-ization for the companion and the star, this contribution can oftenbe determined from the measured stellar polarization (e.g., for1RXS J1609, see Sect. 5.3, and ROXs 42B, see Jensen-Clemet al. 2020). However, we cannot do that in this case becausethe star hosts a disk that we spatially resolve in our images (seeSect. 5.5 and Fig. 12, top left) and therefore the stellar polariza-tion is likely a combination of intrinsic and interstellar polariza-tion.To investigate the contribution of interstellar dust to the po-larization of DH Tau B, we show in Fig. 8 a map of the polariza-tion of DH Tau A and B and a few dozen nearby stars. The mapis superimposed on a Herschel-SPIRE (Pilbratt et al. 2010) im-age at 350 µ m that shows the concentrations of interstellar dustin the region. White lines show optical measurements of starsat the periphery of the B216-B217 dark cloud from Heyer et al.(1987). Yellow lines display measurements from Moneti et al.(1984) of the three nearest bright stars to DH Tau. Of these stars,HD 283704 (58 pc) is unpolarized as it is located in front of theclouds, whereas HD 283705 (170 pc) and HD 283643 (396 pc)are located behind the clouds and are both polarized with an an-gle of polarization of 26 ± ◦ . Because the stars from Heyer et al.(1987) and Moneti et al. (1984) are generally much older thanDH Tau and are therefore not expected to have a circumstel-lar disk that significantly polarizes their light, their polarizationmust primarily originate from interstellar dust. Comparing theangles of polarization of DH Tau A (128 ± ◦ ) and B (58 ± ◦ )with those of the reference stars in Fig. 8, we conclude that thepolarization of both DH Tau A and B must include an intrinsiccomponent. All distances in this paper are retrieved from Bailer-Jones et al.(2018). Article number, page 9 of 29 & A proofs: manuscript no. polarization_companions_arxiv
Table 3: Degree and angle of linear polarization, including the uncertainties, of the parent star DH Tau A and the companionDH Tau B as measured in H -band for each of the five data sets and the data set created by mean-combining the final images of the2019-10-24, 2019-10-25A, and 2019-10-25B data sets.Data set P star (%) χ star ( ◦ ) P com (%) χ com ( ◦ ) S / N q com S / N u com . ± .
01 83 ±
10 0 . ± . ± . ± .
01 114 ± . ± . ± . ± .
01 119 ± . ± .
04 56 ± . ± .
01 145 ± . ± .
05 51 ± . ± .
02 123 ± . ± .
05 66 ± . ± .
009 128 ± . ± .
03 58 ± Notes. P star and χ star are the degree and angle of linear polarization of the parent star DH Tau A, re-spectively, and P com and χ com are the degree and angle of polarization of the companion DH Tau B.S / N q com and S / N u com are the S / Ns with which the q - and u -signals of DH Tau B are detected. h m m m D e c ( J ) B216-B217HD 283705HD 283704 HD 283643DH Tau A IQ TauDK Tau A DF TauDH Tau B 1 % optical 1 % H -bandSPHERE-IRDIS DH Tau B H -bandSPHERE-IRDIS T Tauri stars H -bandHeyer et al. (1987) opticalMoneti et al. (1984) H -band Fig. 8: Map of the linear polarization of DH Tau B and nearby stars superimposed on a Herschel-SPIRE map at 350 µ m. The lengthand orientation of the lines indicate the degree and angle of linear polarization, respectively. The black line shows the H -bandpolarization we measure for DH Tau B, and the orange lines display the SPHERE-IRDIS H -band measurements of DH Tau A andthree other nearby T Tauri stars whose archival data we analyzed. White lines show optical measurements by Heyer et al. (1987).Yellow lines indicate the H -band polarization of three bright stars closest to DH Tau as derived from optical measurementsby Moneti et al. (1984). The length of the H -band vectors are scaled by a factor of four with respect to the optical vectors.We now set limits on the interstellar degree of polariza-tion of the DH Tau system. To this end, we convert the optical measurements of the degree of polarization of the nearby stars Article number, page 10 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions
HD 283705 and HD 283643 (2.48% and 1.27%) from Monetiet al. (1984) to H -band. For this conversion we use Serkowski’slaw of interstellar polarization (Serkowski et al. 1975): P = P max exp (cid:104) − K ln ( λ max /λ ) (cid:105) , (3)where λ is the wavelength of the light, P max is the maximumdegree of polarization, and λ max is the wavelength at which thismaximum occurs. The parameter K is computed following Whit-tet et al. (1992): K = . + . λ max , (4)with λ max in micrometers. Because the observations were takenwithout color filter, we retrieve the spectral response of a Ga-As photomultiplier tube similar to that used for the measure-ments and multiply it with the transmission of the Earth’s atmo-sphere. With the resulting spectral transmission, we can computethe degree of polarization that the instrument measures from thetransmission-weighted average over the curve from Serkowski’slaw. Assuming λ max = . µ m, which is the average value forthe 16 bright stars in Taurus observed by Whittet et al. (1992),we fit P max for both stars. From the fitted curves we then com-pute the degree of polarization at H -band, yielding 0.9% forHD 283705 and 0.5% for HD 283643. Because DH Tau is lo-cated at the front side of the clouds (rather than behind theclouds as are the comparison stars), the interstellar polarizationof DH Tau is most likely below 0.9%, probably below 0.5%.This is in agreement with the H -band degrees of polarization ofthree nearby T Tauri stars whose archival SPHERE-IRDIS po-larimetric data we analyzed (see Fig. 8). Of these stars, DF Tau(125 pc) is unpolarized, and DK Tau A (128 pc), which does nothave a disk, and IQ Tau (131 pc), which has a very faint disk, are0.33% and 0.34% polarized, respectively, both with an angle ofpolarization of ∼ ◦ .Although we do not know the exact interstellar degree of po-larization for DH Tau, the angle of polarization is likely close to26 ◦ , which is the angle of both HD 283705 and HD 283643. Tosee whether DH Tau B is intrinsically polarized, we take the po-larization signal that we measured in the mean-combined images(0 . ± .
03% at 58 ± ◦ ; see Table 3) and subtract interstellar po-larization signals with an angle of polarization of 26 ◦ and a rangeof degrees of polarization. The resulting intrinsic degree and an-gle of polarization of DH Tau B versus the interstellar degreeof polarization is shown in Fig. 9 (top). We see that the intrin-sic polarization decreases for interstellar degrees of polarizationbetween 0% and 0.2% and increases for larger interstellar po-larizations. The intrinsic polarization increases because an everlarger interstellar polarization needs to be canceled to producethe measured polarization. For the range plotted, the intrinsicangle of polarization increases from 60 ◦ to 100 ◦ . Most impor-tantly, the intrinsic degree of polarization is always higher than0.4%, showing that DH Tau B should be intrinsically polarizedif the interstellar polarization indeed has an angle of polarizationof 26 ◦ .From the measurements by Heyer et al. (1987) (white linesin Fig. 8), we see that there are slight variations in the angle ofpolarization of the stars in the region. Goodman et al. (1992) de-termined that the angles of polarization of these stars are Gaus-sian distributed with a mean of 27 ◦ and a standard deviation of15 ◦ . Using this distribution of angles, we take a more probabilis-tic approach and perform a Monte Carlo simulation in which RCA Photomultiplier Manual, , consulted on June 2, 2020. I n t r i n s i c d e g r ee o f li n e a r p o l a r i z a t i o n ( % ) Degree of linear polarizationAngle of linear polarization0.0 0.2 0.4 0.6 0.8 1.0Interstellar degree of linear polarization (%)0.00.20.40.60.81.0 I n t r i n s i c d e g r ee o f li n e a r p o l a r i z a t i o n ( % ) I n t r i n s i c a n g l e o f li n e a r p o l a r i z a t i o n () P r o b a b ili t y d e n s i t y n o r m a li z e d b y c o l u m n Fig. 9: Intrinsic polarization of DH Tau B after subtractinginterstellar polarization signals from the measured polarizationof the companion. Top: Intrinsic degree and angle of linearpolarization of DH Tau B as a function of the degree ofpolarization due to interstellar dust, assuming an angle of 26 ◦ for the interstellar polarization. The bands around the curvesshow the uncertainties of our measurements. Bottom:Probability distributions of the intrinsic degree of polarizationof DH Tau B for a range of degrees of polarization due tointerstellar dust, assuming the angle of the interstellarpolarization to have the same distribution as that determinedby Goodman et al. (1992) for the B216-B217 dark cloudadjacent to DH Tau. The probability distribution of eachcolumn is normalized to one.we compute for a range of interstellar degrees of polarizationthe probability distribution of the intrinsic polarization. The his-tograms of the resulting distributions for each value of the in-terstellar degree of polarization are displayed in Fig. 9 (bottom).In this figure we have normalized the distribution of each col-umn to one. It follows that the curves of Fig. 9 (top) are in factamong the most probable scenarios. We also see that DH Tau Bmust be at least 0.2% intrinsically polarized for interstellar de-grees of polarization between 0% and 0.3% or higher than 0.7%,regardless of the interstellar angle of polarization. Only for in-terstellar degrees of polarization between 0.3% and 0.7% thereis a small possibility ( ∼ In this section we present the likely detection of intrinsic po-larization originating from GSC 6214 B. Figure 10 shows thereduced I Q -, Q -, and U -images in H -band at the position of the Article number, page 11 of 29 & A proofs: manuscript no. polarization_companions_arxiv companion of the data set created by mean-combining the finalimages of the three data sets. Table 4 shows the measured polar-ization of GSC 6214 B for the three individual data sets and themean-combined one. Similar to the DH Tau data, the measuredpolarization signals of each data set are within the uncertaintiesconstant with aperture radius. We select a final aperture radiusof 4 pixels, corresponding to the (approximate) radius where theS / N in q and u is maximized in each of the data sets. Overallthe measured degree and angle of polarization of the data setsare consistent within the uncertainties. The slightly di ff erent re-sults of the 2019-02-22 data set compared to the other two datasets could be caused by the relatively strong time-varying atmo-spheric conditions that the observations were taken under (seeTable 2). Whereas the q - and u -measurements of the three datasets individually do not reach the required 5 σ -limit for a detec-tion, the mean-combined measurement does, reaching an S / N of5.2 in u . From the mean-combined data we therefore concludethat we detect significant polarization from GSC 6214 B, with adegree and angle of polarization of 0 . ± .
04% and 138 ± ◦ ,respectively. I Q Counts
Q U -15 -10 -5 0 5 10 15Counts
Fig. 10: Reduced mean-combined I Q -, Q -, and U -images (afterapplying the cosmetic correction described in Appendix A) atthe position of the companion GSC 6214 B, showing anaperture of radius 4 pixels centered on the companion. The I U -image, which is not shown, is very similar to the I Q -image.Table 4 also shows the stellar degrees and angles of po-larization. Because we do not spatially resolve a disk aroundGSC 6214 A, we used a star-centered aperture extending up toand including the AO residuals to maximize the S / N. The mea-sured signals show significant di ff erences and are overall incon-sistent among the data sets. The signals average to a degree ofpolarization of only 0.10%. The measurements of the stellar po-larization are therefore most likely dominated by spurious sig-nals. To determine whether the companion is truly polarized, weneed to investigate the potential origins of these spurious signalsand the e ff ect they have on the measurement of the companionpolarization.If the stellar polarization primarily results from uncorrectedinstrumental polarization, which to first order equally a ff ects thestar and the companion, we would need to subtract these sig-nals from the images. Using the mean-combined images with thestellar polarization subtracted, we measure for the companion adegree and angle of polarization of 0 . ± .
04% and 141 ± ◦ , re-spectively, with an S / N of 1.4 in q and 7.2 in u . This polarizationsignal is larger and more significant than that measured fromthe images without the stellar polarization subtracted (see Ta-ble 4). However, the measured signals are less consistent amongthe data sets, suggesting that uncorrected instrumental polariza-tion may not be the principal cause of the stellar polarization. A more likely scenario seems that the stellar polarization sig-nals are dominated by systematic e ff ects due to time-varying at-mospheric conditions and AO performance in combination withthe coronagraph, similar to the case of DH Tau (see Sect. 5.1).Also in the case of GSC 6214, the systematic e ff ects do not af-fect (as much) the companion measurements because those mea-surements are overall consistent among the data sets. This sug-gests that the measurements of the companion are more reliablethan those of the star. Because the companion polarization is sig-nificantly di ff erent from the stellar polarization in all data sets,particularly in the angle of polarization (see Table 4), and wemeasure significant polarization from the companion for boththe reduction with and without the stellar polarization subtracted(reaching S / Ns of 7.2 and 5.2 in u , respectively), we concludethat the companion is most likely truly polarized.To determine whether the polarization of GSC 6214 B is in-trinsic to the companion or caused by interstellar dust, we showin Figure 11 a map of the angles of polarization of nearby brightstars from the catalog by Heiles (2000). The map is displayedover an IRAS (Neugebauer et al. 1984) 100 µ m map that showsthe dust concentrations in the region of the Ophiuchus molecularcloud complex where GSC 6214 is located. Comparing the an-gle of polarization of GSC 6214 B and the nearby stars, it mayseem that the companion is polarized by interstellar dust. How-ever, GSC 6214 is located at 109 pc, whereas estimates for thedistance of the Ophiuchus molecular cloud complex range fromapproximately 120 to 150 pc (e.g., Mamajek 2008; Lombardiet al. 2008; Ortiz-León et al. 2017; Yan et al. 2019). Indeed, thethree stars closest to GSC 6214 in Fig. 11 are located at 128 to131 pc. We therefore consider it more likely that GSC 6214 islocated in front of the main concentrations of dust. In addition,if the companion were polarized by interstellar dust, we wouldexpect to measure in all data sets a stellar polarization with thesame angle of polarization as the companion (which is the casefor 1RXS J1609; see Sect. 5.3). In principle it is possible thatGSC 6214 A is not significantly polarized because the inter-stellar polarization is canceled by intrinsic polarization due toan unresolved circumstellar disk. However, this scenario seemsvery unlikely because Bowler et al. (2015) do not detect a diskwith ALMA and put an upper limit on the disk’s mass as lowas 0.0015% of the mass of the star. Taking into account all con-siderations, we conclude that it is likely that the polarization wemeasure for GSC 6214 B is intrinsic to the companion, but westress that we are less confident than for DH Tau B. In this section we present the detection of polarization in the1RXS J1609 system. In all six data sets of 1RXS J1609, weconsistently measure within the uncertainties the same degreeand angle of polarization for the central star 1RXS J1609 A. Inthe mean-combined data set, which uses the four highest-qualitydata sets (2019-08-06, 2019-08-29, 2019-09-17B, and 2019-09-23), we measure for the star a degree and angle of polarizationof 0 . ± .
01% and 97 ± ◦ , respectively. In the same data set,we measure for the companion 0 . ± .
1% and 95 ± ◦ , usingan aperture radius of 5 pixels. Although the measurement of thecompanion polarization is not a significant detection, it is strik-ing that it is within the uncertainties the same as the measuredstellar polarization. In the six individual data sets we also mea-sure the polarization of the companion to be consistent with thatof the mean-combined data, although with higher uncertainties.Finally, using the mean-combined data, we measure for the rel-atively bright background object that is also visible in the field Article number, page 12 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions
Table 4: Degree and angle of linear polarization, including the uncertainties, of the parent star GSC 6214 A and the companionGSC 6214 B as measured in H -band for each of the three data sets and the data set created by mean-combining the final images ofthe three data sets. Data set P star (%) χ star ( ◦ ) P com (%) χ com ( ◦ ) S / N q com S / N u com . ± .
05 27 ± . ± .
07 143 ±
16 0.5 1.92019-08-06 0 . ± .
06 72 ±
13 0 . ± .
07 137 ± . ± .
04 70 ±
17 0 . ± .
07 139 ± . ± .
03 54 ± . ± .
04 138 ± Notes.
The meaning of the column headers is described in the notes of Table 3. h m m m m m -19°-20°-21°-22° RA (J2000) D e c ( J ) Ophiuchus ridge Ophiuchus coreHD 147700 (61 pc)GSC 6214 B (109 pc) 1RXS J1609 AHD 144470HD 14421761 pc / 109 pc128 - 186 pc186 pc
Fig. 11: Map of the angle of linear polarization of thecompanion GSC 6214 B, the star 1RXS J1609 A, and othernearby bright stars superimposed on an IRAS map at 100 µ m.The angles of GSC 6214 B and 1RXS J1609 A are from theSPHERE-IRDIS H -band measurements from this work,whereas for the other stars the angles are taken from the catalogof optical measurements by Heiles (2000). The length of thelines is arbitrary and contrary to Fig. 8 does not indicate thedegree of polarization. HD 147700 in unpolarized. White linesindicate stars at a distance between 128 pc and 142 pc, and blueand orange lines show objects closer or farther away,respectively. We note that the region shown is much larger thanthat of Fig. 8, and therefore the angular separation among thestars is much larger as well.of view a degree and angle of polarization of 0 . ± .
1% and103 ± ◦ , respectively. Because all three objects have withinthe uncertainties the same degree and angle of polarization, theirpolarization likely originates from the same source, that is, frominterstellar dust.To confirm this scenario, we turn to Fig. 11, which shows that1RXS J1609 is located in the Ophiuchus molecular cloud com-plex a few degrees west from GSC 6214. Contrary to GSC 6214,1RXS J1609, at a distance of 139 pc, is definitely located withinthe dust clouds that are located at a distance of approximately120 to 150 pc (see Sect. 5.2). Indeed, the measured angles of po-larization of 1RXS J1609 A, 1RXS J1609 B and the backgroundobject agree well with those of the nearby bright stars locatedat a similar distance (see Fig. 11). Serkowski et al. (1975) havefitted their multiwavelength optical measurements of the starsHD 144470 and HD 144217 (142 and 129 pc; see Fig. 11) toSerkowski’s law of interstellar polarization (see Eq. (3)) and de- termined the values of P max and λ max for both stars. Using thesevalues, we find that in H -band the degrees of polarization areequal to approximately 0.4% and 0.3%, respectively. These val-ues are similar to the degree of polarization we measure for thestar, the companion, and the background object in our images of1RXS J1609, where the slight di ff erences are likely due to theinhomogeneous spatial distribution of the interstellar dust. Weconclude that the polarization we measure for 1RXS J1609 Boriginates from interstellar dust and therefore set an upper limiton the degree of polarization in Sect. 5.4. In this section we present upper limits on the degree of polariza-tion of the 18 companions for which we do not reach the 5 σ -limitin q or u to claim a detection. For the majority of the compan-ions, the S / N in q and u is typically (cid:46) / N in q or u reachesa value of almost 4. However, in these four cases the signals inthe Q - and U -images (after the cosmetic correction described inAppendix A) do not resemble scaled-down positive or negativeversions of the total-intensity PSF as one would expect for realsignals, but show strong pixel-to-pixel variations caused by in-completely removed bad pixels (see Appendix B).Table 5 shows for each target the upper limits determinedfrom the 68.27% and 99.73% intervals, as described in Ap-pendix C. For targets for which we obtained multiple data sets,we computed the upper limits from the mean-combined im-ages. For the majority of the companions, which are generallythe fainter ones, we determined the upper limits using an aper-ture radius equal to half times the full width at half maximum(FWHM) of the stellar PSF. This aperture radius is on average1.9 pixels in H -band and 2.6 pixels in K s -band, and is at, orclose to, the radius at which the upper limit is minimized. Forseven, generally brighter companions (CD-35 2722 B, AB Pic b,HD 106906 b, GQ Lup B, GSC 8047 B, PZ Tel B in J -band, and1RXS J1609 B) we used an aperture radius of 5 pixels to averageout and suppress the spurious signals created by incompletelyremoved bad pixels (see Appendix B). However, the bad pixelsgenerally still create a bias in the q - and u -signals, and so wehave to accept that this increases the upper limits. For the datasets where this bias is really strong (i.e., CD-35 2722, PZ Telin J -band, and TYC 8998), we excluded from the data reduc-tion those frames that contribute strong bad pixels at the positionof the companion in the final images. Because HD 106906 b islocated at an angular separation of 7 . (cid:48)(cid:48) from the central star,which is larger than the isoplanatic angle during the observa-tions, its PSF is strongly elongated in the radial direction fromthe star. To account for this, we used an elliptically shaped aper- Article number, page 13 of 29 & A proofs: manuscript no. polarization_companions_arxiv ture. Finally, for the companions of HR 8799, HD 206893, and β Pic, we computed the upper limits using the polarimetric im-ages from the reduction with the added classical ADI step (seeAppendix C).Table 5 also shows for each target the stellar degree and an-gle of polarization. For the majority of the stars the degree ofpolarization is around 0.1%. To be conservative and because wegenerally do not know the origin of these low polarization sig-nals (intrinsic, interstellar dust or spurious), we interpret the sig-nals as biases. For these targets we therefore computed the upperlimits on the companion polarization from both the reductionswith and without the stellar polarization subtracted, and showthe highest values in Table 5. For three targets we measure astellar polarization higher than approximately 0.1%. In the caseof GQ Lup and PDS 70 this stellar polarization is caused by a cir-cumstellar disk (see Keppler et al. 2018 and Sect. 5.5). AlthoughGQ Lup is located in the Lupus I cloud, the contribution of inter-stellar dust is likely small because HD 141294, the nearest brightstar to GQ Lup (at 14 . (cid:48) and a distance of 153 pc compared to151 pc for GQ Lup), is unpolarized at optical wavelengths (Rizzoet al. 1998; Alves & Franco 2006). For PDS 70 and GQ Lupwe therefore determined the upper limits using only the imageswithout the stellar polarization subtracted. For 1RXS J1609 onthe other hand, the stellar polarization is caused by interstellardust (see Sect. 5.3), and we therefore used the reduction wherethe stellar polarization is subtracted.Examining the upper limits in Table 5, we see that for 11companions the 68.27% upper limits are ≤ . H -band. Theselow upper limits are in almost all cases dominated by the pho-ton noise from the companion in the Q - and U -images or thebias due to incompletely removed bad pixels. The upper lim-its are still larger than the (minimum) polarimetric accuracy ofthe Mueller matrix model with which the data have been cor-rected (see van Holstein et al. 2020). For the companions ofHR 8799, HD 19467, and HD 206893, which are fainter or lo-cated at a much smaller separation than the other companions,the 68.27% upper limits are dominated by the uncertainty of thebackground in Q and U and have values between 0.4% and 0.8%.For the very close-in planet PDS 70 b we reach upper limits of5.0% in K s -band and 9.2% in H -band. These upper limits areso high because the comparison apertures contain signal fromthe inner circumstellar disk of PDS 70 A (see Fig. 12) and theStudent’s t -distribution imposes a large statistical penalty for thelow number of available comparison apertures (see Appendix C).We note that for PDS 70 c (Ha ff ert et al. 2019), the circumstel-lar disk prevents us from measuring the polarization altogether.Finally, we reach the highest polarimetric point-source contrastin the mean-combined data set of β Pic, with a 1 σ -contrast of3 · − at a separations of 0 . (cid:48)(cid:48) and a contrast below 10 − forseparations > . (cid:48)(cid:48) (see Appendix E). Overall, it follows that ourmeasurements are sensitive to polarization signals of around afew tenths of a percent. β Pic, and HD 106906
In our survey we also detected the five circumstellar disks dis-played in Fig. 12. Although the disks of DH Tau and GQ Luphave already been detected at mm-wavelengths (Wol ff et al.2017; MacGregor et al. 2017; Wu et al. 2017b), here we presentthe first images in polarized scattered light, revealing variousinteresting features. For PDS 70, HD 106906, and β Pic near-infrared polarimetric images already exist (Keppler et al. 2018; Hashimoto et al. 2012; Kalas et al. 2015; Millar-Blanchaer et al.2015), but our images are generally deeper, reveal new features,or confirm features that were previously observed. In this sec-tion, we therefore briefly discuss these disks, although we con-sider a detailed analysis beyond the scope of this paper.Figure 12 (top left) shows the polarized intensity image ofthe DH Tau system, with the circumstellar disk visible in the topright corner of the panel. The relatively small disk has a diameterof approximately 0 . (cid:48)(cid:48) or 67 au at 135 pc. From ALMA mea-surements of the Keplerian rotation of the disk, Sheehan et al.(2019) have determined an inclination of 48 ◦ and a position an-gle of 2 . ◦ (east of north), with the northern side of the diskrotating toward us (i.e., blue shifted). In our images the disk hasa smooth intensity profile with no visible disk gap, rings, or spi-rals. A strong brightness asymmetry is visible between the east-ern and western sides of the disk, which could be related to theviewing angle of the disk and the dust scattering properties. Thisasymmetry is compatible with the position angle derived fromALMA: if the side inclined toward the Earth appears bright-est due to enhanced forward scattering, then the eastern side isthe forward-scattering near side of the disk. Alternatively, thisbrightness asymmetry could result from shadowing by an un-resolved inner disk component because the brightness changesquite abruptly with azimuth. The brightness asymmetry mightextend toward the inner (coronagraphically masked) parts of thedisk because the angle of polarization that we measure for theaverage stellar polarization (128 ◦ , see Table 3) agrees well withthe angle of polarization one obtains when integrating over thenon-obscured parts of the disk. In the bottom left corner of thepanel the polarization signal of DH Tau B is visible, where theangle of polarization is indicated with the two lines protrudingfrom the circle around the companion.Figure 12 (top row, second column) shows the polarizedintensity image of the circumstellar disk and companion ofGQ Lup. From ALMA images (MacGregor et al. 2017; Wu et al.2017b), which show a rather featureless disk, the disk inclinationand position angle are known to be 60 ◦ and 346 ◦ , respectively.Our scattered light images show a remarkable north-south asym-metry in the circumstellar disk, with the southern part of the diskextending out to 0 . (cid:48)(cid:48) (127 au at 151 pc) and the northern partonly out to 0 . (cid:48)(cid:48) (74 au). Two spiral-like features can be seenprotruding eastward from the southern part of the disk. The diskasymmetry and spiral-like features are reminiscent of those ofthe disk around RY Lup (Langlois et al. 2018) and could be theresult of periodic close passes of GQ Lup B (see e.g., Dong et al.2016; Cuello et al. 2019, 2020). The orbital analyses presentedby Schwarz et al. (2016) and Wu et al. (2017b) indeed show thatthe orbit of GQ Lup B is almost certainly eccentric and that itis quite likely that the inclinations of the orbit and the disk aresimilar. However, Wu et al. (2017b) argue that although the incli-nations may be similar, the disk and companion orbit are likelynot in the same plane. We also find that the starlight of GQ Lupis polarized due to the unresolved part of the circumstellar disk,with an angle of polarization (83 ± ◦ ; see Table 5) approximatelyperpendicular to the position angle of the disk. GQ Lup B ap-pears to be polarized in Figure 12 (top row, second column), butthis polarization is spuriously created by subtracting the stellarpolarization from the image. We will present a dynamical anal-ysis of the complete system and detailed radiative transfer andhydrodynamical modeling of the circumstellar disk in a futurepaper (van Holstein et al. in prep.).Figure 12 (top row, third and fourth columns) show the H -band Q φ - and U φ -images of the circumstellar disk aroundPDS 70. The disk is seen at a position angle of 159 ◦ and an Article number, page 14 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions
Table 5: 68.27% and 99.73% upper limits on the degree of linear polarization of the companions ( P com ), as well as the measureddegree and angle of linear polarization of the central star ( P star and χ star ), for the targets for which we do not detect significantpolarization. Target Filter P star (%) χ star ( ◦ ) 68.27% upper 99.73% upperlimit on P com (%) limit on P com (%)HR 8799 b BB_H 0 . ± .
006 126 ± . . . ± .
006 126 ± . . . ± .
006 126 ± . . . ± .
006 126 ± . . . ± .
03 17 ±
24 0 .
06 0 . . ± .
01 159 ± . . . ± .
007 138 ± . . . ± .
02 160 ±
39 0 . . . ± .
005 7 ± . . . ± .
02 83 ± . . s . ± .
06 107 ±
15 0 . . s . ± .
02 71 ± . . . ± .
03 66 ± . . . ± .
01 6 ± .
07 0 . . ± .
008 68 ± . . s . ± . ± . . ± .
02 65 ± . . ± .
01 97 ± . . β Pic b BB_H 0 . ± .
008 163 ± . . . ± .
09 0 ± . . ◦ , with the southwestern side being the nearside (Hashimoto et al. 2012). The Q φ -image clearly shows theknown azimuthal brightness variations of the outer disk ring,as well as bright features close to the coronagraph’s inner edgethat most likely originate from the inner disk (see Keppler et al.2018). The U φ -image contains significant signal, with the maxi-mum value equal to ∼
49% of the maximum in the Q φ -image, re-vealing the presence of non-azimuthal polarization. The patternin U φ agrees well with the radiative transfer models by Canovaset al. (2015), indicating that part of the photons are scatteredmore than once. The Q φ -image also shows a weak spiral-like fea-ture extending toward the east from the northern ansa of the diskand perhaps a similar feature at the southern ansa. With thesefeatures the disk resembles the model images by Dong et al.(2016) for the inclination and position angle of the PDS 70 disk.We may therefore be seeing the e ff ect of two spiral arms in theouter disk ring, potentially induced by PDS 70 b.Figure 12 (top right) shows the Q φ -image of the debris diskof HD 106906, which is viewed close to edge-on. The forward-scattering near side of the disk can be seen passing slightly tothe north of the star. The image clearly shows the known east-west brightness asymmetry of the disk, which had until now onlybeen detected in total intensity (Kalas et al. 2015; Lagrange et al.2016). Because our data are particularly deep (i.e., 120 min totalon-source exposure time), we detect the backward-scattering farside of the disk to the west of the star, just south of the brighternear side of the disk (see Kalas et al. 2015). Finally, Fig. 12 (center) shows the Q φ -image of the nearlyedge-on-viewed debris disk of β Pic. The disk extends fromone side of the 11 (cid:48)(cid:48) × (cid:48)(cid:48) IRDIS field of view to the other.Earlier near-infrared scattered light images reported by Millar-Blanchaer et al. (2015) show the disk only to ∼ . (cid:48)(cid:48) or 33 au at20 pc due to the smaller field of view of GPI. In our images wesee the disk extending to at least 5 . (cid:48)(cid:48) or 115 au on both sidesof the star. The disk midplane is seen slightly o ff set to the north-west of the star (up in Fig. 12 center) due to the disk’s smallinclination away from edge-on. Our image also shows the ap-parent warp in the disk (see Millar-Blanchaer et al. 2015, andreferences therein) that extends eastward (to the bottom left) inthe northeastern (left) part of the disk and westward (to the up-per right) in the southwestern (right) part of the disk. This warp isparticularly well visible in Fig. 12 (bottom), which shows a total-intensity image after applying ADI with PCA using IRDAP.
6. Modeling of polarization from circumsubstellardisks
As discussed in Sects. 5.1 and 5.2, we (very) likely detected in-trinsic polarization from DH Tau B and GSC 6214 B, with adegree of polarization of several tenths of a percent in H -band.The host stars of these two companions are among the youngestin our sample ( (cid:46)
20 Myr) and the companions have indicators forthe presence of circumsubstellar disks through hydrogen emis-sion lines, red near-infrared colors, and excess emission at mid-infrared wavelengths (see Fig. 1 and Table 1). Therefore, the
Article number, page 15 of 29 & A proofs: manuscript no. polarization_companions_arxiv
DH Tau ( PI ) GQ Lup ( PI ) β Pic ( Q ϕ ) HD 106906 ( Q ϕ )PDS 70 ( Q ϕ )NE NE NENE N E DH Tau B GQ Lup B β Pic (ADI-PCA total intensity) N E PDS 70 ( U ϕ ) NE Disk far sideDisk warpDisk warp β Pic b Position of PDS 70 b
Fig. 12: H -band images of the five circumstellar disks detected in our sample, showing the linearly polarized intensity ( PI ) forDH Tau and GQ Lup, Q φ and U φ for PDS 70, and Q φ for HD 106906 and β Pic. A total-intensity image after applying ADI withPCA (subtracting four principal components) is additionally shown for β Pic. The U φ -image of PDS 70 is shown on a linear scale,whereas all other images are shown on a logarithmic scale. All polarimetric images have the polarized stellar halo subtracted. Theangular scale and sky orientation are indicated in each image. Gray circles mask regions obscured by the coronagraph.most plausible explanation for the polarization in these cases isscattering of the companion’s thermal emission by dust withina spatially unresolved circumsubstellar disk. However, we notethat the late M to early L spectral types of these low-mass com-panions (see Fig. 1 and Table 1) suggest their atmospheres couldbe dusty. As a result, the polarization could also originate fromrotation-induced oblateness, an inhomogeneous cloud distribu-tion, or a combination of these atmospheric asymmetries and adisk (see Stolker et al. 2017). Still, it seems reasonable to as-sume that the polarization is solely caused by a disk becausethe companions have low projected rotational velocities (Bryanet al. 2018; Xuan et al. 2020), and out of the 20 companions ob-served, we only detect intrinsic polarization for the companionsthat have hydrogen emission lines.In this section we perform (spatially resolved) radiativetransfer modeling of a representative example of a circumsub-stellar disk to investigate whether our detections of polarizationof several tenths of a percent can really be explained by suchdisks. To this end, we first describe the setup of the radiativetransfer model in Sect. 6.1. We then examine the generation ofan integrated (i.e., spatially unresolved) polarization signal inSect. 6.2 and the dependence of the polarization on the proper-ties of the disk in Sect. 6.3. We stress that we consider an isolatedcircumsubstellar disk (i.e., it is not embedded in a circumstellardisk) and that our models are general and not tailored to eitherDH Tau B or GSC 6214 B. Because we only study the degree andangle of polarization produced by the disk, the exact spectrum ofthe companion has little e ff ect on the results. In Sects. 7.1 and 7.2 we use the results of our modeling to interpret and discuss ourmeasurements. To quantify the expected near-infrared polarization from a self-luminous atmosphere with a circumsubstellar disk, we computeda radiative transfer model with
MCMax (Min et al. 2009), whichis a Monte Carlo radiative transfer code for axisymmetric disksthat is optimized for the high optical depths in protoplanetarydisks. The model considers a passive, irradiated disk around aself-luminous substellar atmosphere (the contribution from thelight of the central star is negligible). We selected a syntheticspectrum from the
BT-Settl atmospheric models (Allard et al.2012) at an e ff ective temperature T e ff = g = . − L (cid:12) by assuming a radius for the atmosphereof 2 R Jup at an age of ∼
10 Myr (e.g., Bara ff e et al. 2015). Wethen modeled the circumsubstellar disk as a scaled down versionof a circumstellar disk (see e.g., Williams & Cieza 2011). Weparametrized the structure of the circumsubstellar disk with aprofile for the dust surface density that is inversely proportionalto the radius, Σ ∝ r − . Using a surface density at the inner ra-dius of Σ in = .
07 g cm − and an inner and outer disk radius of R in = .
003 au and R out = .
01 au, we computed the total massresiding in the solids. For the pressure scale height, we used alinear dependence with the disk radius, h ∝ r , with a (constant)aspect ratio of h / r = .
1. The dust opacities contain by vol-
Article number, page 16 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions ume 60% silicates, 15% amorphous carbon, and 25% porosity(Woitke et al. 2016). Furthermore, we used a maximum hollowvolume ratio of 0.8 for the distribution of hollow spheres, whichapproximates the irregularity of the dust grains (Min et al. 2016).The size distribution of the grains was chosen in the range of0.05–3000 µ m with a power-law exponent of − .
5. Dust settlingis included with the prescription from Dubrulle et al. (1995),which assumes an equilibrium between turbulent mixing andgravitational settling. In this way, the dust scale height is a func-tion of disk radius and grain size, which is controlled by the vis-cosity parameter α = − . After setting up the disk and dust properties, we can now per-form the radiative transfer computations to study the generationof a spatially integrated polarization signal from the disk. Wepropagate the Monte Carlo photons through the disk to computethe thermal structure and the local source function. We then run amonochromatic ray tracing at 1 . µ m (the central wavelength ofthe IRDIS H -band filter) to compute the synthetic total-intensityand Stokes Q - and U -images. Figure 13 displays an exampleimage of the total-intensity surface brightness for a disk incli-nation of 70 ◦ . In this figure, the length and orientation of thelines indicate the local degree and angle of polarization, respec-tively. Finally, we compute the spatially integrated polarizationusing the sum of the pixel values in each of the Stokes images.In Fig. 13, this results in an integrated degree and angle of polar-ization of 0.24% and 0 ◦ , respectively. Indeed, the polarized fluxis largest along the major axis of the disk, where scattering an-gles are closest to 90 ◦ , yielding a net polarization that is orientedperpendicular to the major axis of the disk. In fact, the angle ofpolarization is always perpendicular to the position angle of thedisk, independent of the disk inclination.For the interpretation of a nonzero integrated polarization,we need to consider various e ff ects that are visible in the spa-tially resolved image of the disk in Fig. 13. To produce a mea-surable degree of polarization, the linearly polarized intensityshould have a nonzero value while lowering the total intensitywill further enhance the degree of polarization. In the exampleof Fig. 13, most of the polarized flux comes from the inner edgeof the disk, where the flux in total intensity is about 10 to 100times lower than the atmospheric emission. Part of the polariza-tion signal is canceled because there is both horizontally and ver-tically polarized flux, but a net vertically polarized flux remains.The local degree of polarization increases along the major axisof the disk toward larger separations because of reduced multi-ple scattering. However, the total intensity is also lower in theseregions such that the polarized intensity is also low there. Thismeans that the integrated polarization depends primarily on theinner radius and the surface density, whereas the outer radius,and therefore the total disk mass, are much less relevant. Be-cause the inner radius of the disk is at ∼ R Jup and the inclinationis 70 ◦ , part of the photosphere of the central object is obscuredby the near side of the disk. This reduces the total intensity ofthe system such that the net degree of polarization is enhancedcompared to a situation in which the full atmosphere would bevisible. We now investigate the dependence of the spatially integrateddegree of polarization on the inner radius and the surface den- sity at the inner radius. To this end, we run a grid of 10 × R Jup )and dust surface density at the inner radius (10 − –10 g cm − ).All other parameters are the same as in Sect. 6.1, except for theouter radius which we changed from 0.01 au to 0.4 au. In thisway, the disk remains radially su ffi ciently extended even thoughthe outer radius of the disk has a negligible impact on integrateddegree of polarization because most of the polarized flux comesfrom the inner edge. Because the total disk mass depends on theinner radius and surface density, it is di ff erent for each model.We note that the estimated polarization may rely on additionalproperties of both the disk structure and the dust grains.As discussed in Sect. 6.2, the integrated degree of polariza-tion depends strongly on the fractional occultation of the substel-lar atmosphere by the disk. This e ff ect occurs at a high enoughinclination if the projected disk reaches close to the atmosphereand / or the vertical extend of the disk (which scales with the dustsurface density) is su ffi ciently large. To resolve with a high pre-cision the obscuration of the atmosphere, we perform the raytracing at su ffi cient spatial resolution. We set the disk inclina-tion i to 70 ◦ and 80 ◦ because for geometry reasons detectionsare biased toward highly inclined disks and, more importantly, anonzero polarization from a circumsubstellar disk is only to beexpected if the disk is su ffi ciently inclined. For example, we findthat for i < ◦ and i < ◦ , the degree of polarization is < . < . ◦ (see Fig. 14, top), the polarizationreaches a maximum value of 0.4–0.5% when the inner radius is5–10 R Jup and the surface density is (cid:38) − . At small innerradii, there is a correlation with the surface density because in-creasing the inner radius can be counteracted by an increase insurface density in order to maintain the same integrated degreeof polarization. At a given surface density, the degree of polar-ization converges to a constant value at larger inner radii becausethe atmosphere is no longer obscured and most of the polarizedflux originates from the cavity edge. For higher surface densi-ties, this turnover point occurs at larger disk radii because thescattering surface is higher.A more extreme picture emerges when the inclination is in-creased to 80 ◦ (see Fig. 14, bottom). Whereas for surface densi-ties (cid:46) − the correlation with the inner radius is compara-ble to the i = ◦ case, at higher surface densities the substellaratmosphere becomes fully obscured by the disk. There is a peakin the degree of polarization when the vertically extended diskobscures the atmosphere along the minor axis of the disk whilethere is still some disk surface visible close to the major axis. Asa result, the total intensity of the atmosphere is strongly reducedwhile the polarized flux at scattering angles close to 90 ◦ is lessattenuated, leading to a degree of polarization as high as ∼ ∼
8% because boththe substellar atmosphere and the cavity edge are obscured bythe vertical extent of the disk. In this case, only light that scat-ters through the surface layer of the disk will reach the observer,which is therefore no longer dependent on the surface densityand the inner radius.
7. Discussion
In Sect. 6 we performed radiative transfer modeling of a genericcircumsubstellar disk to study the origin of the integrated po-
Article number, page 17 of 29 & A proofs: manuscript no. polarization_companions_arxiv d e c ( m a s )
20 % P com = 0.24 % 10 T o t a l i n t e n s t y ( W m m m a s ) Fig. 13: Synthetic image of a self-luminous companion ( T e ff = ◦ , that is, the spatiallyunresolved light is linearly polarized along the minor axis of the disk. R Jup )10 S u r f a c e d e n s i t y ( g c m ) . . . D e g r ee o f li n e a r p o l a r i z a t i o n ( % ) R Jup )10 S u r f a c e d e n s i t y ( g c m ) . . . . . . D e g r ee o f li n e a r p o l a r i z a t i o n ( % ) Fig. 14: Dependence of the integrated degree of linearpolarization on the inner radius of the circumsubstellar disk andthe surface density of the dust at the inner radius. The grid ofradiative transfer models is shown for a disk inclination of 70 ◦ (top) and 80 ◦ (bottom).larization and the dependence of this polarization on the disk properties. We use the results of our modeling in Sect. 7.1 to in-terpret our likely detections of polarization from DH Tau B andGSC 6214 B and our non-detection for GQ Lup B. In Sect. 7.2we then briefly examine the non-detections of polarization for1RXS J1609 B, HD 106906 b, and PDS 70 b, which also have ev-idence for the existence of a circumsubstellar disk. Subsequently,we outline the implications of our upper limits on the polariza-tion of the other companions with respect to the presence of at-mospheric asymmetries in Sect. 7.3. Finally, in Sect. 7.4, we dis-cuss potential measurements with various instruments to confirmand further characterize the circumsubstellar disks of DH Tau Band GSC 6214 B. As discussed in Sect. 6, the most plausible explanation for thepolarization of DH Tau B and GSC 6214 B is the presence ofa circumsubstellar disk. From the radiative transfer modeling inthat same section, we see that the integrated degree of polariza-tion of such a disk depends on many parameters and that esti-mating disk properties is therefore a degenerate problem. Nev-ertheless, we can still put constraints on the dust grain sizes andthe disk’s inclination and position angle, and through that con-strain the rotational periods and formation mechanisms of thecompanions.Whereas we most likely detect polarization from the disksof DH Tau B and GSC 6214 B, no emission has been detectedfrom these companions at mm-wavelengths (Bowler et al. 2015;Wu et al. 2017a; Wol ff et al. 2017; Wu et al. 2020). It is there-fore possible that these disks contain mostly micrometer-sizeddust grains and only little mm-sized grains, or, as suggestedby Wu et al. (2017a), that the disks are compact and opticallythick at mm-wavelengths. From our polarimetric measurementswe cannot determine whether the disks are really compact be-cause most of the polarized flux originates from the inner edgeof the disk (see Sect. 6.2). Because we do not spatially resolve Article number, page 18 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions the disks, we can put a limit on the disk size from the measuredFWHM of the PSF. The FWHM corresponds to a maximum diskradius of ∼ ff e & Bate 2009; Martin & Lubow2011; Shabram & Boley 2013). However, it is possible that thedisks extend beyond 3 au, but that we do not reach the sensitivityand contrast to detect the flux at the outer regions.From the measured degree of polarization we can put con-straints on the inclination of the disks. With degrees of polariza-tion of a few to several tenths of a percent, the disks of DH Tau Band GSC 6214 B must have a high inclination because a low-inclination disk will have a very low, nearly zero degree of po-larization below the sensitivity that we reach with our measure-ments (see Sect. 6.3). In fact, it could be that GQ Lup B hostssuch a low-inclination disk because we do not detect signifi-cant polarization although the measured hydrogen emission linesare stronger than those of DH Tau B and GSC 6214 B (Zhouet al. 2014). We also see that the inclination of the disks ofDH Tau B and GSC 6214 B cannot be close to edge-on so thatdisk completely obscures the companion’s atmosphere becausein that case we would measure polarization degrees of several toeven ten percent. Such a high degree of polarization of 14% hasbeen measured for CS Cha B in J - and H -band by Ginski et al.(2018), which the authors indeed interpret as being caused by ahighly inclined and vertically extended disk. This interpretationwas recently confirmed by Ha ff ert et al. (2020) using medium-resolution optical spectroscopy with MUSE.The projected rotational velocity, v sin i , has been measuredfor DH Tau B, GSC 6214 B and GQ Lup B through high-resolution spectroscopic observations (Xuan et al. 2020; Bryanet al. 2018; Schwarz et al. 2016), finding values of 9 . ± . − , 6 . + . − . km s − , and 5 . + . − . km s − , respectively. As-suming that the spin axes of the companions are perpendicular tothe plane of their disks (the regular moons of our solar system’sgiant planets, which are believed to have formed in circumsub-stellar disks, orbit near the equatorial plane of the planets) andtaking the companion radii and uncertainties from Xuan et al.(2020) and Schwarz et al. (2016), we constrain the rotational pe-riod of the companions using a Monte Carlo calculation. We as-sume the inclination to be uniformly distributed in cos i , with val-ues between 60 ◦ and 80 ◦ for DH Tau B and GSC 6214 B and be-tween 0 ◦ and 45 ◦ for GQ Lup B. We find rotational periods equalto 29–37 h for DH Tau B, 22–77 h for GSC 6214 B, and 19–64 hfor GQ Lup B, within the 68% confidence interval. These esti-mates of the rotational periods are roughly an order of magnitudelarger than the average periods expected from the period-massrelation as determined from observations of free-floating low-mass brown dwarfs of similar ages (e.g., Rodríguez-Ledesmaet al. 2009; Scholz et al. 2015, 2018). This discrepancy can beexplained by the companions hosting circumsubstellar accretiondisks. The estimated slow rotation of the companions, which isat ∼ .
1% of their break-up velocities (see Xuan et al. 2020), isconsistent with a scenario in which the companions lose angu-lar momentum to their disks during accretion and should stillspin up as they contract (see Takata & Stevenson 1996; Bryanet al. 2018; Xuan et al. 2020). The long rotational periods wefind also show that rotation-induced oblateness does not signif-icantly contribute to the measured polarization because polar-ization > .
1% is generally expected only for rotational periodsof ∼ ◦ and 190 ◦ (seeFig. 9), whereas that of the disk of GSC 6214 B is around 48 ◦ (see Table 4). Because we already found that both disks likelyhave large inclinations, we have strong constraints on the 3Dorientation of the disks. The disk of DH Tau B is most likelymisaligned with the circumstellar disk of DH Tau A, which hasan inclination and position angle of 48 ◦ and 2 . ◦ , respectively(see Sect. 5.5 and Fig. 12), although the position angles couldpossibly be aligned. Such a misalignment of disks is also foundfor CS Cha A and B (Ginski et al. 2018). Although GSC 6214 Ais not known to host a circumstellar disk, orbital motion hasbeen detected for GSC 6214 B (Pearce et al. 2019). However,the orbital elements are not su ffi ciently constrained to concludeon possible (mis)alignments of the disk and the orbit. If a low-inclination disk exists around GQ Lup B, it would be misalignedwith the circumstellar disk that has an inclination of 60 ◦ (seeSect. 5.5 and Fig. 12) and the orbit of GQ Lup B that likely has asimilar inclination. However, the circumsubstellar disk could bealigned with the spin axis of GQ Lup A that has an inclinationof ∼ ◦ (Donati et al. 2012).The misalignment of the disks of DH Tau A and B, and pos-sibly also of GQ Lup A and B, suggests that the companionsmay have formed in situ through direct collapse in the molecularcloud, akin to the formation mechanism of binary stars. Indeed,CS Cha B, with its misaligned disk, was initially thought to beof substellar nature (Ginski et al. 2018), but was recently foundto actually be a low-mass star (Ha ff ert et al. 2020). However,formation through gravitational instabilities in the circumstellardisk is also possible because this mechanism can form compan-ions at separations of up to at least 300 au (Tobin et al. 2016).Although one might expect the circumstellar and circumsubstel-lar disks to be coplanar in this scenario, misalignments can resultif the companion formed away from the midplane of the originaldisk, the original disk was asymmetric, or the circumstellar diskor other objects disturbed the circumsubstellar disk (Stamatel-los & Whitworth 2009; Bryan et al. 2020). It seems unlikely,however, that DH Tau B, GSC 6214 B, and GQ Lup B formedclose to their stars and were subsequently scattered to a higherorbit through dynamical encounters with massive inner bodies.This is because tidal interactions would most likely severely dis-turb or even destroy the circumsubstellar disks (see Stamatellos& Whitworth 2009; Bailey et al. 2013; Bowler et al. 2011), andno massive objects at small separations, nor the gaps they wouldcreate in the circumstellar disks, have been detected (see Fig. 12;Pearce et al. 2019; Wu et al. 2017b). There is also evidence for disks around 1RXS J1609 B,HD 106906 b, and PDS 70 b (see Table 1), but we do not detectintrinsic polarization from these companions (see Sect. 5.4). Itcould be that these companions host a disk but that the propertiesand geometry of these disks is such that they do not produce ameasurable degree of polarization. However, for 1RXS J1609 Bno hydrogen emission lines are detected. Instead, the evidencefor the existence of a disk is based on red near-infrared col-ors, weak mid-infrared excess that is spatially unresolved be-tween the primary star and the companion, and a moderate ex-tinction (Bailey et al. 2013; Wu et al. 2015). Because we find thatthe companion is polarized by interstellar dust (see Sect. 5.3), it
Article number, page 19 of 29 & A proofs: manuscript no. polarization_companions_arxiv seems more likely that these properties are caused by interstellardust rather than a circumsubstellar disk.As discussed in Sect. 5.4, we placed an upper limit of 0.2%on the degree of polarization of HD 106906 b, with a 68.27%confidence level. Because also no hydrogen emission lines aredetected for this companion, a possible explanation for the non-detection is that the companion simply does not host a circum-substellar disk. In the case of PDS 70 b we do not reach a veryhigh sensitivity and placed a 68.27% upper limit of 5.0% on thedegree of polarization in K s -band. Therefore, we can concludethat if PDS 70 b hosts a disk, the inclination is probably notso high that it completely obscures the planet’s atmosphere. Be-cause we only detected polarization for companions with hydro-gen emission lines, it seems that these lines are the best non-polarimetric indicators for the existence of a circumsubstellardisk. Of the 18 companions for which we do not detect significantpolarization, 14 show no clear evidence of hosting a circum-substellar disk (see Fig. 1 and Table 1). Because the majorityof the companions have late-M to mid-L spectral types and aretherefore expected to have dusty atmospheres, we could expectto detect polarization due to rotation-induced oblateness or aninhomogeneous cloud distribution. Indeed, polarization betweenseveral tenths of a percent to a percent has been detected at near-infrared wavelengths (in particular in J -, Z -, and I -band) formore than a dozen late-M to mid-L field brown dwarfs (Miles-Páez et al. 2013, 2017). In our survey, we reached sensitivities(upper limits) ≤ .
3% for 11 companions (see Sect. 5.4 and Ta-ble 5), and so we might have expected to detect polarization fora few of the companions. Because we do not detect polariza-tion due to atmospheric asymmetries for any of the compan-ions, these asymmetries either do not exists for the compan-ions observed or they produce polarization below the sensitivityreached.In the majority of cases, the polarization of field browndwarfs is interpreted to be caused by rotation-induced oblate-ness. In that sense our non-detections are particularly surpris-ing because the companions observed are generally young andhave a low surface gravity (see Table 1), which should result ina more oblate atmosphere for a given rotation rate and there-fore more polarization (Sengupta & Marley 2010; Marley &Sengupta 2011). It is important to note, however, that the fieldbrown dwarfs observed by Miles-Páez et al. (2013) are old (ages0.5–5 Gyr) and have measured projected rotational velocities v sin i >
30 km s − . Indeed, in their sample of several dozenfield brown dwarfs, Zapatero Osorio et al. (2006) found thatabout half of the very young field brown dwarfs (1–10 Myr) have v sin i ≤
10 km s − whereas all old brown dwarfs ( ≥ v sin i ≈
30 km s − . Very young brown dwarfs rotate slowly be-cause they are still in the process of spinning up as they cool andcontract. Looking at Fig. 1, we can divide our sample roughlyinto a large group of young, high-temperature companions withlate-M to mid-L spectral types, and a smaller group of older,lower-temperature companions of mid-L to T spectral types.A possible explanation for our non-detections is that while thecompanions of the first group may have dusty atmospheres, theyrotate too slowly to produce a measurable level of polarization.And on the other hand the second group may rotate faster, butdue to their later spectral types their upper atmospheres may lackthe scattering dust to produce polarization (Allard et al. 2001;Sengupta & Marley 2009). A more in-depth analysis of the de- grees of polarization produced due to rotation-induced oblate-ness is presented in Jensen-Clem et al. (2020).There could also be other explanations for our non-detections. It could be that the dust grains in the upper atmo-sphere are submicron sized, as also suggested by studies of theemission spectra of (field) brown dwarfs and planets (Hiranakaet al. 2016; Bonnefoy et al. 2016), and that we therefore needto observe at shorter wavelengths than H -band (i.e., in Y - or J -band). Miles-Páez et al. (2017) observed one of the field browndwarfs in Z -, J -, and H -band and found that the degree of polar-ization decreases strongly with increasing wavelength, with themaximum polarization in Z -band and no detection in H -band.Another possibility, as suggested by Miles-Páez et al. (2017), isthat the low-gravity atmospheres of young objects have thickerdust clouds, resulting in strong multiple scattering and there-fore a low integrated degree of polarization. Finally, our non-detections may also indicate that the atmospheric dust cloudsare homogeneously distributed, or that the inhomogeneities donot produce a measurable degree of polarization. Indeed, Millar-Blanchaer et al. (2020) recently detected polarization that islikely due to cloud banding on Luhman 16 A, but the measureddegree of polarization is only 0.03% in H -band. To confirm that the polarization from DH Tau B and GSC 6214 Bis truly intrinsic and not caused by interstellar dust, we shouldperform follow-up observations. For this we can use the re-cently implemented star-hopping technique for SPHERE-IRDISto quasi-simultaneously measure the stellar polarization fromnearby diskless reference stars. As a reference for DH Tau wecan observe DI Tau, a very close neighbor to DH Tau located ata separation of only 15 . (cid:48)(cid:48) and at the same distance from Earth,and whose spectral-energy distribution (classified as class III;Luhman et al. 2010) and very low mass-accretion rate (Alonso-Martínez et al. 2017) indicate it very likely does not host a cir-cumstellar disk that creates significant intrinsic stellar polariza-tion. For GSC 6214 we can observe BD-20 4481, which is ofsimilar spectral type as GSC 6214 A and is located at a separa-tion of 13 . (cid:48) and at a distance of 113 pc (compared to 109 pcfor GSC 6214). We can use the measurements of the stellar po-larization of the reference stars to subtract the interstellar com-ponent of the companions’ polarization, and with that accuratelydetermine the intrinsic polarization of the companions. We canalso measure the polarization of DH Tau A and GSC 6214 Awith a di ff erent instrument than SPHERE, for example with theWIRC + Pol near-infrared spectropolarimeter (Tinyanont et al.2019) on the Hale Telescope at Palomar Observatory. UsingWIRC + Pol we can determine the stellar polarization as a func-tion of wavelength, enabling us to quantify the interstellar polar-ization by comparing the measurements with Serkowski’s law ofinterstellar polarization.We can further characterize the circumsubstellar disks ofDH Tau B and GSC 6214 B, as well as the companions them-selves, by performing measurements with various current andfuture instruments. We can perform IRDIS polarimetric mea-surements in multiple filters to constrain the distribution of par-ticle sizes in the disks. By combining these measurements withoptical and near-infrared medium-resolution spectroscopy usingMUSE and ERIS on the VLT, we can constrain the fundamen-tal parameters of the companions. If we are able to detect thedisks with ALMA, we can derive their dust mass from the con-tinuum emission, their gas mass from the CO spectral-line emis-
Article number, page 20 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions sion, and their e ff ective temperature from the emission in twodi ff erent wavelength bands. Similar to ALMA observations, thedust mass and e ff ective temperature of the disk can be deter-mined from mid-infrared photometric and spectroscopic obser-vations, for example with MIRI on board the James Webb SpaceTelescope (JWST), METIS on the Extremely Large Telescope(ELT), or even VISIR on the VLT. Finally, with the sensitivity ofMIRI and METIS we could detect silicate emission features at10 and 18 µ m.
8. Summary and conclusions
We measured the near-infrared linear polarization of 20 youngplanets and brown dwarf companions using SPHERE-IRDIS.We reduced the data using the IRDAP pipeline to correct forthe instrumental polarization and crosstalk of the optical systemwith an absolute polarimetric accuracy < .
1% in the degree ofpolarization. To retrieve the polarization of the companions, weemployed a combination of aperture photometry, ADI, and PSFfitting. We achieved a best 1 σ polarimetric contrast of 3 · − atan angular separation of 0 . (cid:48)(cid:48) from the star and a contrast < − for separations > . (cid:48)(cid:48) .We report the first detection of polarization originating fromsubstellar companions, with a measured degree of polarizationof several tenths of a percent for DH Tau B and GSC 6214 Bin H -band. By comparing the measured polarization with thatof nearby stars, we find that this polarization is unlikely to becaused by interstellar dust. Because the companions have pre-viously measured hydrogen emission lines and red colors, weconclude that the polarization most likely originates from cir-cumsubstellar accretion disks. Through radiative transfer mod-eling we constrain the position angles of the disks and find thatthe disks must have high inclinations to produce these measur-able levels of polarization. For GQ Lup B, which has strongerhydrogen emission lines than DH Tau B and GSC 6214 B,we do not measure significant polarization. This implies thatif GQ Lup B hosts a disk, this disk has a low inclination. As-suming that the spin axes of the companions are perpendicu-lar to the plane of their disks, we use previously measured pro-jected rotational velocities to constrain the rotational periods ofDH Tau B, GSC 6214 B, and GQ Lup B to be 29–37 h, 22–77 h,and 19–64 h, respectively, within the 68% confidence interval.Finally, we find 1RXS J1609 B to be marginally polarized by in-terstellar dust, which suggests that the red colors and extinctionthat are thought to indicate the presence of a disk are more likelycaused by interstellar dust.The disk of DH Tau B, and possibly that of GQ Lup B, aremisaligned with the disks around the primary stars. These mis-alignments suggest that these wide-separation companions haveformed in situ through direct collapse in the molecular cloud,although formation through gravitational instabilities in the cir-cumstellar disk cannot be excluded. Formation at close separa-tions from the star followed by scattering to a higher orbit isunlikely because dynamical encounters with other bodies wouldmost likely severely disturb or even destroy the circumsubstellardisks.For 18 companions we do not detect significant polarizationand place upper limits of typically < .
3% on their degree of po-larization. These non-detections may indicate that young com-panions rotate too slowly to produce measurable polarizationdue to rotation-induced oblateness, or that any inhomogeneitiesin the atmospheric clouds are limited. Another possibility isthat the upper atmospheres of the companions contain primarilysubmicron-sized dust grains. This implies that we should per- form future measurements in Y - or J -band, although these bandsare more challenging in terms of companion-to-star contrast andcontrast performance of the instrument.In our survey, we also detected the circumstellar disks ofDH Tau, GQ Lup, PDS 70, β Pic, and HD 106906, which forDH Tau and GQ Lup are the first disk detections in scatteredlight. The disk of DH Tau is compact and has a strong bright-ness asymmetry that may reveal the forward- and backward-scattering sides of the disk or may be caused by shadowing by anunresolved inner disk component. The disk of GQ Lup shows apronounced asymmetry and two spiral-like features that could bethe result of periodic close passes of GQ Lup B. The PDS 70 diskshows significant non-azimuthal polarization indicating multiplescattering. We also detect one or two weak spiral-like featuresprotruding from the ansae of the disk that may be the result oftwo spiral arms in the outer disk ring, potentially induced byPDS 70 b.Our measurements of the polarization of companions arereaching the limits of the instrument and the data-processingtechniques. We find that incompletely corrected bad pixels cancause systematic errors of several tenths of a percent in the mea-sured polarization. To minimize this e ff ect, we recommend touse the field-tracking mode without dithering for future observa-tions that aim to measure the polarization of companions. How-ever, for companions at close separations or with large star-to-companion contrasts, pupil-tracking observations are still pre-ferred to retrieve the companions’ total intensity with ADI.These close-in companions can alternatively be observed infield-tracking mode when using the recently implemented star-hopping technique to enable reference star di ff erential imaging.We also find that the measurements of the stellar polarizationare a ff ected by systematic errors related to the use of the corona-graph in combination with time-varying atmospheric conditions.We therefore recommend to take additional stellar polarizationmeasurements without coronagraph.To further characterize the circumsubstellar disks ofDH Tau B and GSC 6214 B, as well as the companions them-selves, we can perform follow-up observations with SPHERE-IRDIS, ALMA, JWST-MIRI, MUSE and ERIS on the VLT, andMETIS on the ELT. Our polarimetric detections of the disks ofDH Tau B and GSC 6214 B are a first step in building a com-plete picture of the companions, their formation, and evolution,and pave the way to detecting polarization of young planets withfor example SPHERE + (Boccaletti et al. 2020) and the futureplanet-characterization instrument EPICS (or PCS) on the ELT. Acknowledgements.
RGvH thanks ESO for the studentship at ESO Santiago dur-ing which part of this project was performed. TS acknowledges the support fromthe ETH Zurich Postdoctoral Fellowship Program. The research of FS, JdB, andAJB leading to these results has received funding from the European ResearchCouncil under ERC Starting Grant agreement 678194 (FALCONER). CP ac-knowledges financial support from Fondecyt (grant 3190691) and from the ICM(Iniciativa Científica Milenio) via the Núcleo Milenio de Formación Planetariagrant, from the Universidad de Valparaíso. This research has made use of theSIMBAD database, operated at CDS, Strasbourg, France; NASA’s AstrophysicsData System Bibliographic Services; Scipy, a free and open-source Python li-brary used for scientific computing and technical computing (Virtanen et al.2020); and Astropy, a community-developed core Python package for Astron-omy (Astropy Collaboration et al. 2013; Price-Whelan et al. 2018).
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L. 2014, ApJ,783, L17 Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Lei-den, The Netherlandse-mail: [email protected] European Southern Observatory, Alonso de Córdova 3107, Casilla19001, Vitacura, Santiago, Chile Institute for Particle Physics and Astrophysics, ETH Zurich,Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland University of California, Santa Cruz, 1156 High Street, Santa Cruz,CA 95064, USA Anton Pannekoek Institute for Astronomy, University of Amster-dam, Science Park 904, 1098 XH Amsterdam, The Netherlands Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France Space Telescope Science Institute, Baltimore 21218, MD, USA Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA91109, USA Department of Astronomy, California Institute of Technology, 1200East California Boulevard, Pasadena, CA 91125, USA Unidad Mixta Internacional Franco-Chilena de Astronomía (CNRS,UMI 3386), Departamento de Astronomía, Universidad de Chile,Camino El Observatorio 1515, Las Condes, Santiago, Chile University of Exeter, Physics Building, Stocker Road, Exeter, EX44QL, UK Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidel-berg, Germany Université de Lyon, Université Lyon1, ENS de Lyon, CNRS, Cen-tre de Recherche Astrophysique de Lyon UMR 5574, 69230 Saint-Genis-Laval, France Institute of Astronomy, University of Cambridge, Madingley Road,Cambridge CB3 0HA, UK LESIA, Observatoire de Paris, Université PSL, CNRS, SorbonneUniversité, Université Paris Diderot, Sorbonne Paris Cité, 5 placeJules Janssen, 92195 Meudon, France Instituto de Física y Astronomía, Facultad de Ciencias, Universidadde Valparaíso, Av. Gran Bretaña 1111, Valparaíso, Chile Núcleo Milenio Formación Planetaria – NPF, Universidad de Val-paraíso, Av. Gran Bretaña 1111, Valparaíso, Chile Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg,Germany Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France Núcleo de Astronomía, Facultad de Ingeniería, Universidad DiegoPortales, Av. Ejercito 441, Santiago, Chile Escuela de Ingeniería Industrial, Facultad de Ingeniería y Ciencias,Universidad Diego Portales, Av. Ejercito 441, Santiago, ChileArticle number, page 23 of 29 & A proofs: manuscript no. polarization_companions_arxiv
Appendix A: Cosmetic correction of spuriousstructure in Q - and U -images If a companion is polarized, we would expect the polarizationsignals in the Q - and U -images to resemble scaled-down positiveor negative versions of the corresponding total-intensity images I Q and I U . However, for many data sets the Q - and U -imagesshow spurious structure with adjacent positive and negative sig-nals. For example, for the 2019-10-24 data set of DH Tau, asshown in Fig. A.1 (first column), we see that the Q -image con-tains positive and negative signals and that the signal in U iso ff set from the center coordinates of the companion. These spu-rious structures result from imperfect relative centering of theimages of IRDIS’ left and right optical channels and image mo-tion during the observations. For pupil-tracking observations thespurious structures can additionally originate from image rota-tion between the two measurements of the double di ff erence. Q reduced Q model Q corrected-60 -40 -20 0 20 40 60Counts U reduced U model U corrected Fig. A.1: Reduced Q - and U -images (first column), modelimages of the spurious structures in Q and U (second column),and Q - and U -images corrected for the spurious structures(third column) at the position of the companion DH Tau B ofthe 2019-10-24 data set of DH Tau. An aperture of radius8 pixels centered on the companion is shown superimposed onthe images.In the case these spurious structures are visible in the Q - and U -images of a data set, we make to each image individuallya (cosmetic) correction similar to that described in Snik et al.(2010). For this we retrieve a positive and negative copy of the I Q - or I U -image at the companion position and create a modelimage in which the two copies are symmetrically shifted in op-posite directions from the center coordinates of the companion.We then subtract this model image from the Q - or U -image andfit the shifts in the x - and y -directions by minimizing the sum ofsquared residuals in an aperture of radius 8 pixels in the result-ing image. Because the aperture sum in the model images is zero,subtracting these images only suppresses the spurious structuresand does not alter the net polarization signals in Q and U .For the data set of DH Tau, we find a total relative shift equalto 0.015 pixels for Q and 0.013 pixels for U . Only small rela-tive shifts are needed because the maximum values of the total-intensity PSFs are more than 100 times larger than the maxi- mum values of the positive and negative signals of the spuriousstructure. The model images and the corrected Q and U -imagesare shown in Fig. A.1 (second and third column). The spuriousstructure has clearly disappeared in the corrected images, withthe Q -image only having negative signal and the signal in U be-ing positioned at the companion’s center coordinates. Appendix B: Systematic errors due to bad pixels
A few percent of the pixels of the IRDIS Hawaii 2RG detectorare bad, that is, they are dead, nonlinearly responding, or hot pix-els. When preprocessing the raw frames with IRDAP, bad pixelsare identified with a bad pixel map followed by sigma-filteringand then replaced by the median value of the surrounding pixels.These data-reduction steps correct the majority of the bad pix-els, but some bad pixels remain uncorrected or are replaced by avalue that is not accurate. This results in systematic errors of thepixel values. Whereas these small errors are not a real problemfor photometry of point sources in total intensity or imaging ofcircumstellar disks in polarized light, they become quite prob-lematic when trying to measure the polarization of point sourcesat a level as low as a few tenths of a percent of the total intensity.Incomplete correction of bad pixels only marginally a ff ectsdata taken in field-tracking mode. This is because in field-tracking mode the PSF of the companion is approximately sta-tionary on the detector and only moves very slightly due tovariations in AO performance. The bad pixels, which are at afixed position on the detector, are therefore replaced by approx-imately the same (median) value in consecutive frames, and soare strongly suppressed when computing the double di ff erence.In addition, any uncorrected or incompletely corrected bad pix-els that remain are further averaged out over the various HWPcycles. However, this averaging over HWP cycles only partiallyapplies for our data because we generally observed in field-tracking mode with dithering in which case the detector movesby one to a few pixels each HWP cycle. We note that for total-intensity imaging, for which we compute the median over manyexposures rather than di ff erences of exposures, dithering doeshelp suppress bad pixels.Data taken in pupil-tracking mode are typically morestrongly a ff ected by incomplete correction of bad pixels. Inpupil-tracking observations the companion moves over the de-tector, and so in each frame the bad pixels are at a di ff erent lo-cation with respect to the companion PSF. Therefore, the badpixels are replaced by very di ff erent median values, and rela-tively large systematic errors remain after the double di ff erence.For data sets with fast parallactic rotation (e.g., the data sets ofGSC 8047 and TYC 8998), the bad pixels are more problematicthan for data sets with only little rotation (e.g., GSC 6214). Fordata sets with many HWP cycles the bad pixel e ff ect averages outsomewhat, but the systematic errors are still much larger than forfield-tracking data.We attempted to remove the systematic errors due to bad pix-els by creating a more aggressive bad pixel map from the darkand flat frames, performing aggressive sigma-filtering, locallyreplacing the bad-pixel values with cubic spline interpolationrather than with the median filter, and computing the medianover the Mueller-matrix-model-corrected Q - and U -images ofeach HWP cycle. Unfortunately, we were not able to identify allbad pixels in the data and completely remove the e ff ect. Thisis primarily because part of the bad pixels cause systematic er-rors of only several percent or less of the total intensity. Suchsmall deviations from the true value are practically impossible Article number, page 24 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions to detect in the images and only become evident when comput-ing di ff erences of images as we do in polarimetry.Although we were not able to completely correct for the badpixels, we can mitigate their e ff ect by excluding those framesthat contribute strong bad pixels to the final images or that showbad pixels at the position of the companion in the bad pixel map.In addition we can average out the systematic error due the badpixels by mean-combining several data sets. We can also uselarge apertures to perform the photometry with, such that thebad pixels values (which are both positive and negative in polari-metric images) average out and sum to a lower spurious signal.Future observations aimed at measuring the polarization of com-panions should preferably be performed in field-tracking modewithout dithering. Appendix C: Retrieval of total intensity throughADI: Upper limit on polarization of β Pic b
Companions at small separations or at large star-to-companioncontrasts are swamped in the halo of starlight in total intensity.For data sets that were taken in pupil-tracking mode and havesu ffi cient parallactic rotation, we have therefore slightly adaptedthe method described in Sect. 4 and determine the probabilitydistribution of the total intensity of the companion by perform-ing ADI with negative PSF injection. We still determine the dis-tributions of Q and U using aperture photometry because thestellar speckle halo is almost completely removed in the po-larimetric data-reduction steps, in particular for the reductionswith the added classical ADI step (see Sect. 3). We appliedthis adapted method to the data sets of HR 8799, HD 206893,PDS 70, and β Pic. In this section we demonstrate the methodwith the 2019-11-26 H -band data set of β Pic and show how wecalculate upper limits on the degree of polarization of the com-panion β Pic b. A total-intensity image of the data after applyingclassical ADI with IRDAP is shown in Fig. C.1 (left). d e c () Classical ADI total intensity200 100 0 100 200Counts 0.40.20.00.20.4 RA ( ) Q with classical ADI20 10 0 10 20Counts Fig. C.1: Reduced images of the 2019-11-26 data set of β Pic.Left: Total-intensity image after applying classical ADI withIRDAP to reveal the companion β Pic b. Right: Q -image aftercombining polarimetry with classical ADI, showing theaperture of radius 1.85 pixels at the position of the companion(yellow) and the ring of comparison apertures of the sameradius around the star (black).To perform the ADI with negative PSF injection, we usethe PynPoint pipeline, version 0.8.2 (Amara & Quanz 2012; https://pynpoint.readthedocs.io Stolker et al. 2019), and closely follow the steps describedin Stolker et al. (2020). In short, we fetch the preprocessed sci-ence frames and the stellar PSF image from the reduction withIRDAP in Sect. 3. Subsequently, we iteratively subtract scaledcopies of the stellar PSF from the preprocessed science framesat the approximate position of the companion and apply ADIwith PCA (in this case subtracting three principal components)to minimize the residuals at that same location. Using Markovchain Monte Carlo (MCMC) we then sample the posterior dis-tributions of the companion’s angular separation, position angleand contrast with respect to the star. We take the median of theposterior distribution of the contrast as the final contrast valueand determine the corresponding statistical uncertainties fromthe 16th and 84th percentiles. We also estimate the systematicuncertainty on the contrast by injecting fake companions at var-ious position angles (but the same separation and contrast as thereal companion), retrieving them, and computing the distributionof the di ff erence between the retrieved and injected contrasts.This systematic uncertainty accounts for the azimuthal variationsof the noise around the central star and is generally 1 to 5 timeslarger than the statistical uncertainty (similar to the results ofWertz et al. 2017). Finally, we compute the overall uncertaintyas the quadratic sum of the statistical and systematic uncertain-ties.After these steps, we determine the probability distributionof the companion’s total intensity (expressed in counts) for arange of aperture radii from 1 to 10 pixels. To this end, we draw10 samples from a Gaussian distribution with the mean andstandard deviation equal to the companion-to-star contrast anduncertainty we retrieved with PynPoint. We then sum the flux inthe stellar PSF image using an aperture of the given radius andmultiply the Gaussian samples by this summed flux. The result-ing total-intensity distribution of the companion, which we usefor both I Q and I U , is shown in Fig. C.2 (left) for an apertureradius of 1.85 pixels. This radius is the final aperture radius weselect at the end of this section and corresponds to half times thefull width at half maximum (FWHM) we measure on the stellarPSF. P r o b a b ili t y d e n s i t y P r o b a b ili t y d e n s i t y I Q (counts)0.000000.000250.000500.000750.001000.001250.001500.00175 P r o b a b ili t y d e n s i t y +240239 counts (108) 25000 25500 26000 26500 27000 I U (counts)0.000000.000250.000500.000750.001000.001250.001500.00175 25978 +240239 counts (108) 100 50 0 50 100 Q (counts)0.00000.00250.00500.00750.01000.01250.0150 3 +2426 counts (0.1) 100 50 0 50 U (counts)0.0000.0050.0100.0150.020 -37 +/- 19 counts (1.9)0.4 0.2 0.0 0.2 q (%)01234 P r o b a b ili t y d e n s i t y +0.0940.099 % (0.1) 0.4 0.2 0.0 0.2 u (%)012345 0.142 +0.0720.073 % (2.0) 0.0 0.2 0.4 P (%)0123456 68.27 % upperlimit = 0.2 %99.73 % upperlimit = 0.4 % 0.0 0.2 0.4 P (%)0.00.20.40.60.81.0 C u m u l a t i v e d i s t r i b u t i o n Upper limit = 0.205 %, 0.386 %68.27 %99.73 %
Fig. C.2: Final probability distributions of the signal of β Pic bfrom the 2019-11-26 data set of β Pic, using an aperture radiusof 1.85 pixels. Left: Probability distribution of the totalintensity. The mean and 68.27% uncertainties of the distributionare shown above the graph, with the latter also indicated by thelight-blue shaded area. The S / N is shown within parentheses.Right: Probability distribution of the degree of linearpolarization. The upper limits computed from the one-sided68.27% and 99.73% intervals are indicated by the light-red anddarker red shaded areas, respectively.
Article number, page 25 of 29 & A proofs: manuscript no. polarization_companions_arxiv
To determine the probability distributions in Q and U , we usethe images from the reduction with the added classical ADI step.In the case of β Pic, the classical ADI step does not only furthersuppress the speckle noise, but also removes most of the signalfrom the nearly edge-on-viewed circumstellar disk that crossesthe position of β Pic b (see Fig. 12, center and bottom). Theclassical ADI step suppresses the disk signal because the diskis broad and the parallactic rotation of the observations in only19 . ◦ . Indeed, as can be seen in Fig. C.1 (right) for the Q -image,the disk is almost completely removed and there are only fewspeckles left at the separation of the companion. Any polariza-tion originating from the companion should still be visible in the Q - and U -images because point sources are much less a ff ectedby ADI-induced self-subtraction.We analyze the Q - and U -images by following the exactsteps as described in Sect. 4, but with one exception. Beforeperforming the aperture photometry, we quantify the through-put of the ADI procedure by performing a simulation in whichwe inject and retrieve an artificial source at the separation of theactual companion. We then correct the Q - and U -images for theself-subtraction by dividing them by the calculated throughput,which for this data set is 49%. After performing all the steps,we determine the companion’s polarization for each of the de-fined aperture radii (as in Fig. 7 for DH Tau B). Contrary to thedata of DH Tau, for this data set of β Pic we detect no signalswith an S / N higher than 0.9 in Q and 1.9 in U for any apertureradius. Indeed, the reduced Q -image (see Fig. C.1, right) and U -image contain only noise at the position of the companion. Wetherefore conclude that we do not detect significant polarizationoriginating from the companion β Pic b.We now proceed to set limits on the degree of polarization ofthe companion. To this end, we determine, for each defined aper-ture radius, two upper limits from the probability distribution ofthe degree of polarization. We compute these upper limits fromthe 68 .
27% and 99 .
73% intervals, which for a Gaussian distri-bution would correspond to the 1 σ and 3 σ confidence intervals,respectively. These intervals are calculated one-sided and start-ing at zero because the degree of linear polarization is computedas P = √ ( q + u ) and therefore can only have positive values (seeSparks & Axon 1999). Figure C.2 (right) shows the distributionof the degree of polarization for an aperture radius of 1.85 pixelswith the two intervals indicated. Figure C.3 shows the two upperlimits as a function of aperture radius. From this figure we seethat the upper limits are relatively constant for an aperture radiussmaller than approximately 3.5 pixels. For larger apertures, theupper limits increase as more noise is included in the companionaperture and the uncertainty of the background due to the lownumber of background samples increases. We select our finalaperture radius to be 1.85 pixels, equal to half times the FWHMof the stellar PSF, and conclude that the 68.27% and 99.73% up-per limits on the degree of polarization of β Pic b are equal to0.2% and 0.4%, respectively. We note that while for this particu-lar data set the upper limits monotonically increase with apertureradius, for several other data sets this is not the case due to in-completely removed bad pixels (see Sect. 5.4 and Appendix B).
Appendix D: Retrieval of total intensity through PSFfitting: Upper limit on polarization of HD 19467 B
Several observations of faint or close-in companions were notexecuted in pupil-tracking mode (i.e., they were executed infield-tracking mode) or have little parallactic rotation. For theseobservations we cannot retrieve the probability distribution of U pp e r li m i t o n P ( % ) Fig. C.3: Upper limits on the degree of linear polarization of β Pic b computed from the one-sided 68.27% and 99.73%intervals as a function of aperture radius from the 2019-11-26data set of β Pic. The final selected aperture radius of 1.85pixels, equal to half times the FWHM of the stellar PSF, isindicated with the dashed vertical line.the companion’s total intensity through ADI with negative PSFinjection as described in Appendix C. We also cannot use aper-ture photometry with comparison apertures as outlined in Sect. 4because the spatially varying stellar halo at the separations ofthese companions prevents accurate determination of the back-ground. We therefore use MCMC to fit the stellar PSF imageto the I Q - and I U -images at the companion position and deter-mine the corresponding probability distributions. We applied thismethod to the data sets of PZ Tel, HR 7682, HD 19467, GQ Lup,and HD 4747. To confirm that the PSF fitting is accurate, we alsoused the method to retrieve the total intensities of HR 8799 b, c,and d, and find that the results di ff er only 0.03 to 0.07 mag withthose obtained with PynPoint (see Appendix C). In this sectionwe demonstrate the PSF fitting method with the 2018-08-07 H -band data set of HD 19467 and set upper limits on the degree ofpolarization of the companion HD 19467 B. Figure D.1 showsthe I Q -image of this data set. d e c () C o un t s Fig. D.1: Reduced I Q -image of the 2018-08-07 data set ofHD 19467, showing the position of the companion HD 19467 Bin the white circle. The asymmetric wind-driven halo and thestellar di ff raction spikes are clearly visible.As the first step in our analysis, we obtain a rough estimateof the companion’s contrast and x - and y -coordinates. To thisend, we fit a model consisting of a 2D Mo ff at function and aninclined plane to the reduced I Q -image at the companion posi-tion. The inclined plane accounts for the (approximately) lin-early varying local background due to the stellar PSF and thestellar di ff raction spikes (see Fig. D.1) and is described by a con-stant (the z -intercept) and slopes in the x - and y -direction. We Article number, page 26 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions then fit a model containing the stellar PSF and an inclined planeto cropped versions of the I Q and I U -images, using the resultsfrom the Mo ff at fit for the initial estimates of the fit parameters.We use the Nelder-Mead method as implemented in the Pythonfunction scipy.optimize.minimize to minimize the sum ofsquared residuals ( SSR ): SSR = N (cid:88) i = (cid:20)(cid:16) I Q , i − ˆ I Q , i (cid:17) + (cid:16) I U , i − ˆ I U , i (cid:17) (cid:21) , (D.1)where I Q , i and I U , i are the flux values in the i -th pixel of thecropped I Q - and I U -images, ˆ I Q , i and ˆ I U , i are the correspondingmodeled flux values, and N is the total number of pixels in eachof the cropped images. We minimize the residuals in the I Q -and I U -images simultaneously to obtain a single set of x - and y -coordinates for the companion position. For the other parame-ters we fit separate values for I Q and I U .We now repeat the PSF fitting using MCMC to obtain thefinal values of the fit parameters and the corresponding poste-rior distributions. We use the MCMC sampler from the Pythonpackage emcee (Foreman-Mackey et al. 2013) and let 32 walkersexplore the probability space with 20,000 steps each (resultingin a total of 640,000 samples). We randomly generate the start-ing values of the walkers from Gaussian distributions centeredon the best-fit parameter values from our previous fit. We use aGaussian distribution for the log-likelihood function:ln L ∝ − (cid:34) N ln (cid:16) πσ (cid:17) + SSR σ (cid:35) , (D.2)where SSR is computed from Eq. (D.1) and σ is the standard de-viation that accounts for the noise in the images. Because there isno region in the I Q and I U -images from which we can determinea representative value for σ , we include it among the parametersto be fitted (i.e., we treat σ as a nuisance parameter). We set theprior for σ proportional to 1 /σ , that is, Je ff rey’s prior, to makesure it is non-informative. For the other parameters we use uni-form priors. We remove the first 822 steps of each walker, equalto five times the maximum autocorrelation time, and check by vi-sual inspection that the chains of all parameters have converged.The cropped I Q - and I U -images and the best-fit model and resid-ual images are shown in Fig. D.2. Figure D.3 shows the resulting1D- and 2D-projections of the posterior distribution of the fittedparameters. The distributions in Fig. D.3 are visually very closeto being Gaussian and show correlations only between the com-panion’s contrast in I Q or I U and the corresponding z -interceptof the background.We now determine the companion’s probability distributionsin I Q and I U (expressed in counts) for a range of aperture radiifrom 1 to 10 pixels. Similarly to the method described in Ap-pendix C, we sum the flux in the stellar PSF image using anaperture of the given radius and multiply the MCMC contrastsamples in I Q and I U by this flux. For the remainder of the anal-ysis we follow the steps described in Sects. 4 and Appendix C,with the only exception that we sample the PDFs in Q and U with the same number of samples as used for the MCMC analy-sis. After performing the complete analysis, we detect no signalswith an S / N higher than 1.4 in Q and 2 in U for any apertureradius. Finally, using an aperture radius of 1.86 pixels, equalto half times the FWHM of the stellar PSF, we determine the68.27% and 99.73% upper limits on the degree of polarizationof HD 19467 B to be equal to 1.0% and 2.0%, respectively. I Q data I Q model150 175 200 225 250 275 300Counts I Q residuals -10 -5 0 5 10Counts I U data I U model I U residuals Fig. D.2: Data, best-fit model and residual images of theMCMC fitting of the stellar PSF at position of HD 19467 B tothe reduced I Q - and I U -images of the 2018-08-07 data set ofHD 19467. Appendix E: Contrast curve of β Pic data
Figure E.1 shows the 1 σ and 5 σ point-source contrast in Q and U as a function of angular separation from the star for the mean-combined data set of β Pic as constructed with IRDAP. Thecurves are computed by summing the flux in rings of aperturesaround the star, computing the standard deviation over the aper-ture sums, and normalizing the result with the total stellar fluxretrieved from the star flux frames. At small separations the cor-rection for small-sample statistics is applied (see Mawet et al.2014). For comparison the figure also shows the azimuthally av-eraged flux in the total-intensity I Q - and I U -images and the cor-responding photon noise. At angular separations between ∼ . (cid:48)(cid:48) and 2 . (cid:48)(cid:48) the polarimetric sensitivity is close to the photon-noiselimit, with a 1 σ -contrast of 7 · − to 1 · − and a 5 σ -contrastof 5 · − to 5 · − . At separations larger than 2 . (cid:48)(cid:48) the sensi-tivity is limited by read noise or background noise and the 1 σ -and 5 σ -contrast are < · − and < · − , respectively. Article number, page 27 of 29 & A proofs: manuscript no. polarization_companions_arxiv x com (px) = 625.98 +0.020.02 . . . . . y c o m ( p x ) y com (px) = 443.60 +0.020.02 . . . . c o n t r a s t I Q contrast I Q = 1.13 +0.020.02 . . . . c o n t r a s t I U contrast I U = 1.14 +0.020.02 . . . . z - i n t e r c e p t I Q ( c o un t s ) z -intercept I Q (counts) = 159.30 +0.570.58 . . . . x - s l o p e I Q ( c o un t s / p x ) x -slope I Q (counts/px) = 4.27 +0.170.17 . . . . y - s l o p e I Q ( c o un t s / p x ) y -slope I Q (counts/px) = 1.23 +0.170.17 . . . z - i n t e r c e p t I U ( c o un t s ) z -intercept I U (counts) = 159.21 +0.570.57 . . . . x - s l o p e I U ( c o un t s / p x ) x -slope I U (counts/px) = 4.15 +0.170.17 . . . . . y - s l o p e I U ( c o un t s / p x ) y -slope I U (counts/px) = 1.25 +0.170.17 .
90 625 .
95 626 .
00 626 . x com (px) . . . . ( c o un t s ) .
50 443 .
55 443 .
60 443 .
65 443 . y com (px) .
08 1 .
12 1 .
16 1 . contrast I Q .
08 1 .
12 1 .
16 1 . contrast I U . . . . z -intercept I Q (counts) . . . . x -slope I Q (counts/px) . . . . y -slope I Q (counts/px) . . . z -intercept I U (counts) . . . . x -slope I U (counts/px) . . . . . y -slope I U (counts/px) . . . . (counts) (counts) = 4.55 +0.360.32 Fig. D.3: Posterior distributions after using MCMC to fit the stellar PSF at the position of the companion HD 19467 B to thereduced I Q - and I U -images of the 2018-08-07 data set of HD 19467. The fitted parameters are the companion position in x and y ,the companion-to-star contrast in I Q and I U , the background’s z -intercept and slopes in the x - and y -direction in I Q and I U , and thestandard deviation σ that accounts for the noise in the images. The diagonal panels show the marginalized 1D distributions of thefitted parameters and the o ff -diagonal panels show the 2D projections of the posterior, revealing the covariance of the parameterpairs. The median and uncertainties (computed as the 18th and 84th percentiles) of the distributions are shown above thehistograms and are indicated with the dashed vertical lines. The contours superimposed on the o ff -diagonal panels indicate the 1 σ ,2 σ and 3 σ confidence levels assuming Gaussian statistics. The figure is created using the Python package corner (Foreman-Mackey 2016). Article number, page 28 of 29. G. van Holstein et al.: A survey of the linear polarization of young, directly imaged planets and brown dwarf companions )10 P o i n t - s o u r c e c o n t r a s t I Q and I U Q and U Q and U Photon noise
Fig. E.1: 1 σ and 5 σ point-source contrast in Q and U as afunction of angular separation from the star for themean-combined data set of β Pic. The azimuthally averagedflux in the total-intensity I Q - and I U -images and thecorresponding photon noise are shown for comparison.-images and thecorresponding photon noise are shown for comparison.