The evidence of radio polarization induced by the radiative grain alignment and self-scattering of dust grains in a protoplanetary disk
Akimasa Kataoka, Takashi Tsukagoshi, Adriana Pohl, Takayuki Muto, Hiroshi Nagai, Ian W. Stephens, Kohji Tomisaka, Munetake Momose
DDraft version October 6, 2018
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THE EVIDENCE OF RADIO POLARIZATION INDUCED BY THE RADIATIVE GRAIN ALIGNMENT ANDSELF-SCATTERING OF DUST GRAINS IN A PROTOPLANETARY DISK
Akimasa Kataoka,
1, 2, ∗ Takashi Tsukagoshi, Adriana Pohl,
4, 2
Takayuki Muto, Hiroshi Nagai, Ian W. Stephens, Kohji Tomisaka, and Munetake Momose National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan Zentrum f¨ur Astronomie der Universit¨at Heidelberg, Institut f¨ur Theoretische Astrophysik, Albert-Ueberle-Str. 2, D-69120 Heidelberg,Germany College of Science, Ibaraki University, 2-1-1 Bunkyo, Mito, Ibaraki 310-8512 Max Planck Institute for Astronomy, K¨onigstuhl 17, D-69117 Heidelberg, Germany Division of Liberal Arts, Kogakuin University, 1-24-2 Nishi-Shinjuku, Shinjuku-ku, Tokyo 163-8677 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA (Received; Revised; Accepted)
Submitted to ApJLABSTRACTThe mechanisms causing millimeter-wave polarization in protoplanetary disks are under debate. To disentangle thepolarization mechanisms, we observe the protoplanetary disk around HL Tau at 3.1 mm with the Atacama LargeMillimeter/submillimeter Array (ALMA), which had polarization detected with CARMA at 1.3 mm. We successfullydetect the ring-like azimuthal polarized emission at 3.1 mm. This indicates that dust grains are aligned with themajor axis being in the azimuthal direction, which is consistent with the theory of radiative alignment of elongateddust grains, where the major axis of dust grains is perpendicular to the radiation flux. Furthermore, the morphologyof the polarization vectors at 3.1 mm is completely different from those at 1.3 mm. We interpret that the polarizationat 3.1 mm to be dominated by the grain alignment with the radiative flux producing azimuthal polarization vectors,while the self-scattering dominates at 1.3 mm and produces the polarization vectors parallel to the minor axis of thedisk. By modeling the total polarization fraction with a single grain population model, the maximum grain size isconstrained to be 100 µ m, which is smaller than the previous predictions based on the spectral index between ALMAat 3 mm and VLA at 7 mm. Keywords: polarization — protoplanetary disks
Corresponding author: Akimasa [email protected] ∗ NAOJ fellowformer Humboldt Research Fellow a r X i v : . [ a s t r o - ph . E P ] J u l Kataoka et al. INTRODUCTIONThe millimeter-wave polarization of circumstellardisks is a powerful tool to investigate the grain prop-erties. However, the mechanisms that produce themillimeter-wave polarization are under debate.There have been two mechanisms proposed that canexplain millimeter-wave polarization in protoplanetarydisks: the alignment and scattering of dust grains. Thepolarized thermal dust emission has been used as atracer of magnetic fields in scales of molecular clouds andstar-forming regions (e.g., Lai et al. 2001, 2002; Girartet al. 2006, 2009; Rao et al. 2009; Stephens et al. 2013;Hull et al. 2013, 2014; Cortes et al. 2016; Planck Collab-oration et al. 2016; Ward-Thompson et al. 2017) or cir-cumstellar disks around Class 0-I protostars (Rao et al.2014; Segura-Cox et al. 2015). It is considered that themajor axis of elongated dust grains is aligned with thedirection perpendicular to magnetic fields with a helpof radiative torque (e.g., Lazarian & Hoang 2007). Inprotoplanetary disks, if the dust grains are aligned withmagnetic fields, the polarization fraction is expected tobe high enough to detect with interferometers (Cho &Lazarian 2007; Bertrang et al. 2017). However, therewere many attempts to detect polarized emission fromprotoplanetary disks around Class II or III protostars,which resulted in non-detections (Hughes et al. 2009,2013). It has recently been pointed out that dust grainsin disks may not align with magnetic fields but withradiation fields (Tazaki et al. 2017).The other possibility of the polarization mechanisms isthe self-scattering of the thermal dust emission (Kataokaet al. 2015). If the grain size is comparable to the wave-lengths, scattering-induced polarization can produce 2-3 % polarization from protoplanetary disks. If it is thecase, we can constrain the grain size from the polariza-tion fraction. Together with dust coagulation theory,we can test the grain growth theory with polarizationobservations (Pohl et al. 2016).There have been two resolved detections of mm-wavepolarization for disks that are Class I or older. The firstdetection was made on the protoplanetary disk aroundHL Tau with CARMA at 1.3 mm and SMA at 0.87 mm(Stephens et al. 2014). The polarization vectors are par-allel to the direction of the minor axis of the disk. Thismorphology has been first interpreted as complex mag-netic fields dominated by toroidal components (see alsoMatsakos et al. 2016). However, the polarimetric imagecan also be interpreted with the self-scattering (Kataokaet al. 2016a; Yang et al. 2016). The other polarizationdetection is from the disk around HD 142527, whichhas conspicuous asymmetric ring emission of dust con-tinuum at the wavelength of 0.87 mm (Kataoka et al.2016b). The polarization vectors are mainly directedradially, but are directed azimuthally in the outer re-gion of the disk. The flip of the polarization vectors areexpected from the self-scattering theory (Kataoka et al. 2015). This confirms that the self-scattering is work-ing on the protoplanetary disk. However, it does notexclude the possibility of the grain alignment.To disentangle the mechanisms between the grainalignment and self-scattering, multi-wave polarizationobservations are essential. The wavelength dependenceof the polarization fraction is not strong in the case ofthe grain alignment while it is strong in the case of theself-scattering because the scattering-induced polariza-tion is efficient only when the maximum grain size isaround λ/ π where λ is the wavelengths (Kataoka et al.2015).To obtain the wavelength-dependent polarimetric im-ages, we observe the HL Tau disk with Atacama LargeMillimeter/submillimeter Array (ALMA) with usingBand 3. HL Tau is a young star in Taurus molecularcloud with the distance of 140 pc (Rebull et al. 2004).The circumstellar disk is around in ∼
100 AU scale(Kwon et al. 2011). The disk has several ring and gapstructures with tens of AU scales (ALMA Partnershipet al. 2015). The observed band corresponds to wave-lengths of 3.1 mm, which is sufficiently longer than theprevious CARMA polarimetric observations at 1.3 mm(Stephens et al. 2014). OBSERVATIONSHL Tau was observed by ALMA on October 12,2016 during its Cycle 4 operation (2016.1.00115.S, PI:A.Kataoka). The antenna configuration was C40-6, and41 antennas were operating. The correlater processedfour spectral windows centered at 90 . , . , . , and104 . . . (cid:48)(cid:48) × . (cid:48)(cid:48) , corresponding to ∼ × µ Jy, respectively. RESULTSThe top panel of Fig. 1 shows the polarized inten-sity in color scale overlaid with polarization vectors ,and the contour represents the continuum emission. Thebottom panel of Fig. 1 shows the polarization fraction We plot the polarization vectors not scaling with the polariza-tion fraction but written with the same length because this allowsfor the polarization morphology to be more obvious. However,the reliability depends not on the polarization fraction but on thepolarized intensity.
ASTEX wavelength-dependent polarization ∆ RA [arcsec]1.51.00.50.00.51.01.5 ∆ D E C [ a r c s e c ]
100 AU
Polarized Intensity [ m J y / b e a m ] ∆ RA [arcsec]1.51.00.50.00.51.01.5 ∆ D E C [ a r c s e c ]
100 AU
Polarization fraction [ % ] Figure 1.
ALMA Band 3 observations of the HL Tau disk. The wavelength is 3.1 mm. The top panel shows the polarizedintensity in color scale, the polarization direction in red vectors, and the continuum intensity in the solid contour. The vectorsare shown where the polarized intensity is larger than 5 σ PI . The contours corresponds to (10 , , , , , , , × the rms of 9.6 µ Jy. The bottom panel shows that the polarization fraction in color scale, polarization vectors in red, and thesame continuum intensity contours as the top.
Kataoka et al. in color scale and the others are the same as the toppanel. Due to the lower spatial resolution than the longbaseline campaign (ALMA Partnership et al. 2015), themultiple ring and gap structure of the continuum is notresolved. The total flux density is 75.1 mJy, which isconsistent with the previous ALMA observations withBand 3 (74.3 mJy; ALMA Partnership et al. 2015).We successfully detect the ring-like polarized emis-sion at 3.1 mm. The polarized intensity has a peakof 145 µ Jy/beam, which corresponds to 21 sigma detec-tion with the rms of 6.9 µ Jy. The peak of the polarizedintensity is not located at the central star but on thering. We see three blobs on the ring but it may be dueto the interferometric effects. The polarized intensity atthe location of the central star is lower than the otherregions. We interpret this structure as beam dilutionof the central region where polarization is expected tobe azimuthal and thus canceled out to each other. Thepolarization fraction is around 1.8 % on the ring.The flux densities of the entire disk are − . µ Jy forStokes Q and − . µ Jy for Stokes U. Therefore, the in-tegrated polarized intensity is
P I = (cid:112) Q + U − σ =56 . µ Jy. Dividing the total polarized intensity by thetotal Stokes I, we obtain 0.08 % for the total polarizationfraction. The instrumental polarization contaminationof the ALMA interferometers is the polarization fractionof 0.1 % for a point source in the center of the field or0.3 % within up to the inner 1/3 of the FWHM (seethe technical handbook of ALMA. More discussion isfound in Nagai et al. 2016). The derived polarizationfraction of the integrated flux corresponds to the case ofthe point source. Therefore, the upper limit of the in-tegrated polarization fraction of the HL Tau disk at 3.1mm by our observations is 0.1 %. The low total polar-ization fraction means that we could not have detectedpolarization if we had not resolved the target. DISCUSSIONS4.1.
Comparison with the previous observations
To interpret the polarization emission from HL Tau,we compare the ALMA results with the previous ob-servations. We show the CARMA polarization obser-vations by Stephens et al. 2014 in Fig. 2(a), wherewe show the polarization vectors, while the original pa-per presents vectors rotated by 90 degrees to show in-ferred magnetic fields (i.e., if polarization is due to grainsaligned with the magnetic field). For the comparison, wesmooth the ALMA observations with the beam size of0 . (cid:48)(cid:48) × . (cid:48)(cid:48) and PA of 79.5 degrees, which is the beamsize of the CARMA observations (Stephens et al. 2014),as shown in Fig. 2(b).The 3.1-mm polarization morphology with our ALMAobservation is completely different from that at 1.3 mm.At 1.3 mm, the polarization vectors show the directionparallel to the minor axis. At 3.1 mm, however, thepolarization vectors show the circular pattern. To interpret the strong dependence of the polariza-tion on the wavelengths, we consider three possibilities:alignment by magnetic fields, alignment by radiationanisotropy, and self-scattering of thermal dust emission.Figure 3 shows the schematic illustration of the polariza-tion vectors with the three different mechanisms. Figure3 (a) shows the case of the grain alignment with toroidalmagnetic fields (e.g., Cho & Lazarian 2007). As we ex-pect the major axis of the grains is aligned perpendicularto the magnetic fields. In the existence of the toroidalmagnetic fields (e.g., Brandenburg et al. 1995), the po-larization vectors are in the radial direction. Figure 3(b) shows the case of the grain alignment with radia-tion anisotropies (e.g., Tazaki et al. 2017). The fluxgradient is in general in the outgoing radial direction.Considering that the major axis of the grains is per-pendicular to the flux gradient, the polarization vectorsshould be in the azimuthal direction. Figure 3 (c) showsthe case of self-scattering (Kataoka et al. 2015, 2016a;Yang et al. 2016). The flux coming parallel to the ma-jor axis is much stronger than that parallel to the minoraxis. This leads to the polarization vectors parallel tothe minor axis .In the case of HL Tau, the 3.1 mm polarimetric im-age is consistent with case (b), which is the alignmentwith the radiation anisotropy. The polarization vectorsare essentially perpendicular to that expected for case(a), and thus we can rule out grain alignment with thetoroidal magnetic fields at 3.1 mm. However, we cannotrule out the grain alignment with the poloidal magneticfields. In the case of 1.3 mm image, however, we inter-pret it with (c) the self-scattering of the thermal dustemission, which provides the polarization vectors paral-lel to the minor axis. However, there could be also somecontributions of (b) the alignment with the radiationfields to the polarization, which enhances the polariza-tion vectors at the north-west and south-east regions(along the major axis) while decreases the polarizationfraction at the north-east and south-west regions (alongthe minor axis).The wavelength dependence in the polarization frac-tion in the case of the self-scattering is strong (Kataokaet al. 2015) while it is weaker in the case of the grainalignment. Therefore, the most natural interpretationis that the alignment with the radiation fields providesthe axisymmetric azimuthal polarization vectors on bothwavelengths while the self-scattering dominates at 1.3mm. 4.2. Modeling the scattered components While we plot the polarization vectors at the central part ofthe disk (Kataoka et al. 2016a), the polarization vectors mightbecome azimuthal at the outer edge of the disk because the fluxgradient is stronger than the quadrupole components (Pohl et al.2016; Yang et al. 2016)
ASTEX wavelength-dependent polarization ∆ RA [arcsec]1.51.00.50.00.51.01.5 ∆ D E C [ a r c s e c ]
100 AU
PI (CARMA, 1.3 mm) [ m J y / b e a m ] ∆ RA [arcsec]1.51.00.50.00.51.01.5 ∆ D E C [ a r c s e c ]
100 AU
PI (ALMA, 3.1 mm) [ m J y / b e a m ] Figure 2.
Comparison of the polarization images between λ = 1 . λ = 3 . . (cid:48)(cid:48) × . (cid:48)(cid:48) with the PA of 79.5 degrees. The color scale represents the polarized intensity while the grey contours representthe continuum emission. The levels of the grey contours are (10 , , , , , , , × σ I where σ I = 2 . σ I = 0 .
017 mJy/beam ALMA data. (a) alignment with toroidal magnetic fields (b) alignment with radiation fields (c) self-scattering
Figure 3.
Schematic illustrations for the differences of polarization vectors of each mechanism of polarization of thermal dustemission. The major axis is in the horizontal direction. Note that each panel represents E-vectors. (a) Grain alignment withthe toroidal magnetic fields. (b) Grain alignment with the radiation fields. (c) Self-scattering of the thermal dust emission
By modeling the scattered components of the polariza-tion, we can constrain the grain size in the HL Tau disk.To model the scattering components in polarization, weconsider the total polarization fraction across HL Tau.If we integrate the polarization all over the disk, theaxisymmetric vectors are canceled out. The scattering-induced polarization provides the vectors parallel to theminor axis, which resides as the total polarization frac-tion. However, the alignment with the radiative flux isalmost axisymmetric and thus does not contribute somuch on the integrated polarization fraction. We esti-mate the contribution of the radiative flux alignment tothe total polarization fraction assuming that the disk isgeometrically and optically thin, the local alignment ef-ficiency p is the same in the entire disk (Fiege & Pudritz 2000; Tomisaka 2011), and there is no wavelength depen-dence. The contribution is calculated to be 0 . × p andthe polarization vectors are parallel to the major axis.We have already discussed that the upper limit ofthe total polarization fraction is 0.1 % at 3.1 mm withour ALMA observations. The polarization fraction withSMA is reported to be 0 . ± .
4% at 0.87 mm (Stephenset al. 2014). Note that the detection was 2 sigma signifi-cance, which might be an upper limit of the polarizationfraction while we use the reported value in Stephenset al. 2014 in this paper. We calculate the total de-gree of polarization observed with CARMA at 1.3 mmwith the data reported by Stephens et al. 2014, which is0 . ± . Kataoka et al. wavelength [ µ m ]0.00.20.40.60.81.01.21.41.61.8 t o t a l p o l a r i z a t i o n f r a c t i o n [ % ] CARMASMA ALMA (Band 3) scat ( a max = 50 µ m ) + alignscat ( a max = 70 µ m ) + alignscat ( a max = 100 µ m ) + alignscat ( a max = 150 µ m ) + align Figure 4.
The total polarization fraction as a function of the observed wavelengths. The total polarization fraction is derivedby integrating each Stokes I, Q, and U component. The curves represent the prediction of the HL Tau disk with the self-scattering model where the maximum grain sizes are a max = 50, 70, 100, and 150 µ m (Kataoka et al. 2016a) and with theradiative alignment model. The dashed, solid, and dotted lines represent the models with the local alignment efficiency of p = 0 , . , . Figure 4 compares that the theoretical prediction andthe observational results of the total polarization frac-tion. The contribution of the self-scattering is estimatedas P = CP ω , where C is the calibration factor set tobe 2.0 %, P is the polarization efficiency for the scat-tering angle of 90 degrees in a single scattering, and ω isthe albedo (Kataoka et al. 2015, 2016a). This predictionis confirmed to match the results radiative transfer cal-culations of the polarization due to the self-scatteringwithin the error of 50 % (Kataoka et al. 2016a). Thedust grains are assumed to be spherical and have apower-law size distribution of n ( a ) ∝ a − . . We varythe maximum grain size a max for a max = 50, 70, 100 and150 µ m. The contribution of the radiative alignmentis estimated in three cases where the local polarizationfraction is p = 0 , .
8, and 3 . p = 1 . . × p = 0 , . , and 0 . a max = 50 µ m,the expected polarization fraction is too low to explain the observations because the albedo is too small atthe wavelengths of 0.87 and 1.3 mm. In the case of a max = 150 µ m, on the other hand, the polarizationfraction is too high to explain the SMA, CARMA, andALMA observations. In the case of a max = 70 µ m, ifthe contribution from the radiative alignment is smallin the range of 0 < p < . p > . a max = 100 µ m, the combination of the self-scatteringand the radiative alignment greatly explains the wholeobservations. Therefore, we conclude that the maxi-mum grain size is constrained to be a max = 100 µ mfrom the polarimetric observations of SMA, CARMA,and ALMA.4.3. Dust grains in the HL Tau disk
The opacity index of dust grains with a max = 100 µ mis the same as the interstellar medium or higher, whichcorresponds to β ∼ . ASTEX wavelength-dependent polarization . β ∼ . µ m in size)that dominate the polarization in the disk. The seconddust population primarily consists of large grains ( (cid:29) µ m in size) that produce significant continuum emissionbut negligible scattering at these wavelengths.Introducing porosity does not solve the problem. Theabsorption opacity at millimeter wavelengths is deter-mined by mass-to-area ratio (Kataoka et al. 2014). Toexplain the small opacity index, we need more massiveaggregates if we consider porous dust aggregates. Onthe other hand, the scattering properties at long wave-lengths are determined by the size of the whole aggre-gates (Tazaki et al. 2016; Min et al. 2016). Therefore,the dust aggregates larger than a max = 100 µ m pro-duces much more degree of polarization emission at 3.1mm, which is not consistent with our observations.Another possibility is to change the constituent mate-rials that determine the refractive index at the millime-ter wavelengths. The grain size constraints from thepolarization are mainly determined by the wavelengthdependence of the albedo, which is determined by thecombination of the grain size and observed wavelengths,which does not so much change even if the refractive in-dex is changed. On the other hand, the opacity slope ofthe dust grains is proportional to the imaginary part ofthe refractive index at the observed wavelengths. There-fore, it is possible to reconcile the problem by consider-ing a different mixture of grains than those commonlyassumed (e.g., Woitke et al. 2016). There are still plenty of parameters that could affectthe total polarization fraction: wavelength dependenceof the alignment efficiency, optical depth effects, or verti-cal structure of the disk, etc. Further detailed modelingshould be done in future papers.The small grain sizes that are required to produce thepolarization by scattering has huge implications on themechanisms to form the ring and gap structures of theHL Tau disk (ALMA Partnership et al. 2015). The in-ferred grain size suggests that the grains are more cou-pled with the gas than grains with size of 1 mm or larger.For example, the disk turbulence should be extremelyweak because the dust settling is required to reproducethe geometrically thin dust disk (e.g., Pinte et al. 2016).Furthermore, there are some scenarios that requires thedust to be decoupled from the gas such as trapping dustgrains at gas pressure bumps produced by planets (Dip-ierro et al. 2015) and the secular gravitational instabilityof the gas and dust disk (Takahashi & Inutsuka 2014).In the case of the sintering-induced fragmentation ataround snowlines, the grain size is determined by thefragmentation properties (Okuzumi et al. 2016), whichis not tested with various parameters. The mm-wavepolarization requests these scenarios to produce 100 µ mgrains.We appreciate the discussions with Cornelis P. Dulle-mond, Tomoyuki Hanawa, Satoshi Okuzumi, andBenjamin Wu. This work is supported by JSPSKAKENHI Grant Numbers JP15K17606, JP26800106,JP17H01103, JP15H02074. T.M. is supported by NAOJALMA Scientific Research Grant Numbers 2016-02A.This paper makes use of the following ALMA data:ADS/JAO.ALMA ALMA Partnership, Brogan, C. L., P´erez, L. M., et al.2015, ApJL, 808, L3Bertrang, G. H.-M., Flock, M., & Wolf, S. 2017, MNRAS,464, L61Brandenburg, A., Nordlund, A., Stein, R. F., & Torkelsson,U. 1995, ApJ, 446, 741Carrasco-Gonz´alez, C., Henning, T., Chandler, C. J., et al.2016, ApJL, 821, L16Cho, J., & Lazarian, A. 2007, ApJ, 669, 1085Cortes, P. C., Girart, J. M., Hull, C. L. H., et al. 2016,ApJL, 825, L15 Dipierro, G., Price, D., Laibe, G., et al. 2015, MNRAS, 453,L73Fiege, J. D., & Pudritz, R. E. 2000, ApJ, 544, 830Girart, J. M., Beltr´an, M. T., Zhang, Q., Rao, R., &Estalella, R. 2009, Science, 324, 1408Girart, J. M., Rao, R., & Marrone, D. P. 2006, Science,313, 812Hughes, A. M., Hull, C. L. H., Wilner, D. J., & Plambeck,R. L. 2013, AJ, 145, 115Hughes, A. M., Wilner, D. J., Cho, J., et al. 2009, ApJ,704, 1204