A High-Contrast Search for Variability in HR 8799bc with VLT-SPHERE
B.A. Biller, D. Apai, M. Bonnefoy, S. Desidera, R. Gratton, M. Kasper, M. Kenworthy, A.M. Lagrange, C. Lazzoni, D. Mesa, A. Vigan, K. Wagner, J.M. Vos, A. Zurlo
MMNRAS , 1–27 (0000) Preprint 22 January 2021 Compiled using MNRAS L A TEX style file v3.0
A High-Contrast Search for Variability in HR 8799bc with VLT-SPHERE
B.A. Biller, , ★ D. Apai , M. Bonnefoy , S. Desidera , R. Gratton , M. Kasper ,M. Kenworthy , A.M. Lagrange , C. Lazzoni , , D. Mesa , A. Vigan ,K. Wagner , , J.M. Vos , A. Zurlo , SUPA, Institute for Astronomy, University of Edinburgh, Blackford Hill, Edinburgh EH9 3HJ, UK Centre for Exoplanet Science, University of Edinburgh, Edinburgh, UK Steward Observatory, The University of Arizona, Tucson, AZ 85721, USA Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France INAF - Osservatorio Astronomico di Padova, Vicolo della Osservatorio 5, 35122, Padova, Italy European Southern Observatory (ESO), Karl-Schwarzschild-Str. 2,85748 Garching, Germany Leiden Observatory, Leiden University, PO Box 9513, 2300 RA, Leiden, The Netherlands Dipartimento di Fisica a Astronomia "G. Galilei", Universita’ di Padova, Via Marzolo, 8, 35121 Padova, Italy Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France NASA Hubble/Sagan Fellow Department of Astrophysics, American Museum of Natural History, Central Park West at 79th Street, New York, NY 10024, USA Escuela de Ingeniería Industrial, Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejercito 441, Santiago, Chile
22 January 2021
ABSTRACT
The planets HR8799bc display nearly identical colours and spectra as variable young exoplanet analogues such as VHS 1256-1257ABb and PSO J318.5-22, and are likely to be similarly variable. Here we present results from a 5-epoch SPHERE IRDISbroadband- 𝐻 search for variability in these two planets. HR 8799b aperture photometry and HR 8799bc negative simulated planetphotometry share similar trends within uncertainties. Satellite spot lightcurves share the same trends as the planet lightcurvesin the August 2018 epochs, but diverge in the October 2017 epochs. We consider Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 to trace non-sharedvariations between the two planets, and rule out non-shared variability in Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 to the 10-20% level over 4-5hours. To quantify our sensitivity to variability, we simulate variable lightcurves by inserting and retrieving a suite of simulatedplanets at similar radii from the star as HR 8799bc, but offset in position angle. For HR 8799b, for periods <
10 hours, we aresensitive to variability with amplitude > >
25% for similar periods.
Key words: planets and satellites: atmospheres – Planetary Systems, planets and satellites: gaseous planets – Planetary Systems,infrared: planetary systems – Resolved and unresolved sources as a function of wavelength, (stars:) brown dwarfs – Stars
Over the last 15 years, a small but growing cohort of young, widely-separated giant planets, such as HR 8799bcde (Marois et al. 2008,2010) and 𝛽 Pic b (Lagrange et al. 2010), have been directly imagedvia their own thermal emission in the infrared (see e.g. Bowler 2016).Instruments such as SPHERE at the VLT (Beuzit et al. 2019), GPIat Gemini (Macintosh et al. 2014), SCExAO-Charis at Subaru (Jo-vanovic et al. 2015; Currie et al. 2019), and Gravity at the VLT (Grav-ity Collaboration et al. 2019) have enabled spectroscopy and deepcharacterization of the atmospheres of these planets (Konopacky et al.2013; Snellen et al. 2014; Barman et al. 2015; Bonnefoy et al. 2014,2016; Zurlo et al. 2016; De Rosa et al. 2016; Ingraham et al. 2014;Rajan et al. 2015; Lavie et al. 2017; Wang et al. 2018b; Greenbaumet al. 2018; Ruffio et al. 2019; Gravity Collaboration et al. 2019).However, most of these studies have captured only a snapshot of theplanet’s atmospheric state, taken over a 1-3 hour long observation, or ★ E-mail: [email protected] have combined multiple observations taken at different points in theplanet’s rotation, creating essentially an "integrated" spectrum. Onlyone directly imaged exoplanet has a measured rotation period, 𝛽 Picb, which is a fast rotator, with a 7-9 hour period (Snellen et al. 2014),assuming a similar inclination as the disc. Top-of-atmosphere asym-metric structure (e.g. from spots, patchy clouds and various othermechanisms) could cause significant changes in flux as a functionof time and wavelength, as different structures rotate in and out ofview. These structures may also evolve dynamically over multiplerotation periods, producing longer-term changes in planet bright-ness. To determine if either of these phenomena are present requirestime-resolved observations of exoplanets, preferably covering mul-tiple rotation periods. Detecting and characterizing such features,especially as a function of wavelength, will provide strong tests foratmospheric models of these planets.Studies of field brown dwarfs, the more massive cousins ofthese young planets, suggest that we would expect to find signif-icant changes in the flux of young planets with time. Quasiperi-odic variability is commonly found in field L and T type brown © a r X i v : . [ a s t r o - ph . E P ] J a n B.A. Biller et al. dwarfs, with periods from 1.5-30 hours, and amplitudes rangingfrom 0.01-27% (Radigan et al. 2012, 2014; Radigan 2014; Wilsonet al. 2014; Metchev et al. 2015; Eriksson et al. 2019). These objectsare fast rotators (3-20 hours, see e.g. Zapatero Osorio et al. 2006)with silicate clouds expected in their atmospheres (e.g. horizon-tal banded clouds recently detected in Luhman 16A via linear polar-ization by Millar-Blanchaer et al. 2020). These potentially inhomoge-neous cloud features likely drive the observed variability, modulatedby the fast rotation of these objects. Spectroscopic variability moni-toring has shown, for instance, that the variability in high amplitudeL/T transition brown dwarfs such as 2MASS J21392676+0220226(henceforth 2M2139) and SIMP J013656.5+093347 (henceforthSIMP 0136) is best reproduced by inhomogeneous coverage of boththin and thicker cloud components (Apai et al. 2013).Directly imaged young, giant exoplanets share similar effectivetemperatures and compositions as these L and T dwarfs, and likelypossess comparable or even higher amplitude variability. One keyphysical difference between brown dwarfs and young giant exoplan-ets is the much lower surface gravity of the young planets compared tomore massive, older brown dwarfs. Surface gravity strongly affectsthe placement of clouds in these atmospheres, with ramificationsfor the variability properties of younger, lower mass objects (Mar-ley et al. 2012). The variability amplitudes of young, free-floatingplanetary mass objects appear to be significantly boosted relativeto older, higher mass brown dwarf counterparts with similar spec-tral types. Vos et al. (2019) find that 30% of low surface-gravityL dwarfs are variable, compared to 11% of field L dwarfs. Thenear-IR variability detections in the L6-L7 exoplanet analogues VHSJ125601.92-125723.9 (henceforth VHS 1256-1257ABb, Gauza et al.2015; Bowler et al. 2020; Zhou et al. 2020), PSO J318.5338-22.8603(henceforth PSO J318.5-22 , ∼ 𝑀 𝐽𝑢 𝑝 𝛽 Pic moving group memberLiu et al. 2013; Allers et al. 2016), WISEPJ004701.06+680352.1(henceforth W0047, AB Dor moving group, Gizis et al. 2015),and 2MASS J2244316+204343 (henceforth 2M2244, AB Dor mov-ing group, Vos et al. 2018) have peak-to-trough amplitudes > highest-amplitude variability detections for any L spectral type object, with VHS 1256-1257ABb potentially themost variable planetary mass or substellar object yet observed( ∼
25% variability observed over an 8-hour HST observation, Bowleret al. 2020). These objects have spectra that are nearly identicalto those of the outer two HR 8799 planets (Zurlo et al. 2016;Bonnefoy et al. 2016) and HIP 65426b (Chauvin et al. 2017).Given their close spectral match, the HR 8799 planets are poten-tially equally intrinsically variable (although the observable variabil-ity amplitude is likely smaller, as the HR 8799 planets are proba-bly viewed close to pole-on, Ruffio et al. 2019; Wang et al. 2018a).The extreme contrast difference between star and planet has hin-dered studies of variability in exoplanet companions such as HR8799bcde. Planet imagers such as SPHERE at the VLT (Beuzit et al.2019) and GPI at Gemini (Macintosh et al. 2014) now enable shortcadence observations of bright giant planets – previous generationsof imagers required ≥ < 𝐻 -band single exposures. Apai et al. (2016) conducted a pilot vari-ability study ( < > The star HR 8799 is a F0V member of the 42 + − Myr Columba mov-ing group (Torres et al. 2008; Zuckerman et al. 2011; Bell et al.2015), with an estimated mass of ∼ 𝛾 Doradus pulsating variable. As in all 𝛾 Doradus stars, manypulsation modes are excited; the mode with highest amplitude hasa period of ∼ ∼ ∼ 𝛾 Dor variables with TESS suggest this is the case,Antoci et al. 2019), the red optical or near-IR variability of HR 8799has not been directly measured. Thus, the fact that SPHERE enablesmonitoring of the multiple HR 8799 planets simultaneously as wellas the ability to produce artificial "satellite spots" as photometric ref-erences (Langlois et al. 2013) crucially allow us to disentangle anyintrinsic variability of the star from variability of the planets. As wedo not expect the planets to have the same rotational period, phase orvariability amplitude, any variability with the same period and phaseshared by multiple planets would then probably either be intrinsicto the star or caused by changing observing conditions. Similarly,the satellite spot light curves should follow the trend produced bythe changing conditions as well as any astrophysical variability fromthe star, providing a reference lightcurve that can be used to detrendsingle planet lightcurves. Detrending using a lightcurve from a pho-tometric reference has been successfully implemented in numerousground-based variability monitoring campaigns for isolated objects(Radigan et al. 2014; Vos et al. 2019), building a "calibration curve"from other stars in the field to remove variations due to changingconditions; here we will attempt a similar detrending using both thesatellite spot lightcurves and the other planets as the photometricreferences.The HR 8799 system also hosts a 3-component debris disk (awarm inner belt separated by the orbits of the planets from a coldplanetesimal belt and an outer halo of small grains) imaged at mid-IR, submillimeter, and mm wavelengths (Su et al. 2009; Matthewset al. 2014; Booth et al. 2016; Wilner et al. 2018). The disk is viewednearly face-on (Matthews et al. 2014). Current orbital fits suggestthat the planet orbits are close to coplanar with the disk, with a smallinclination of ∼ ◦ (Ruffio et al. 2019; Wang et al. 2018a; Konopackyet al. 2016; Pueyo et al. 2015; Maire et al. 2015). If the 4 planetsindeed share a similar inclination with the disk, they are likely viewedclose to pole-on. This is a non-ideal viewing angle for variabilitydetection. The brown dwarfs with the highest observed variabilityamplitudes are generally those which are observed at or close toequator-on (90 ◦ inclination, Vos et al. 2017), as inhomogeneousfeatures on objects observed at lower inclinations will appear smallerdue to projection effects. Thus, given the probable pole-on viewingangle of the HR 8799 planets, any variability amplitude we potentiallymeasure is likely only a fraction of the intrinsic variability amplitude.With the current generation of near-IR extreme adaptive optics(AO) planet-finding cameras, high-contrast ground-based variabilitymonitoring is feasible at wavelengths of 1-4 𝜇 m. After correcting forinclination effects, field brown dwarfs (Radigan et al. 2014; Metchevet al. 2015) display a monotonic decrease in variability amplitude MNRAS , 1–27 (0000)
R 8799 variability across this wavelength range, with the highest amplitude variabilityin 𝐽 band ( ∼ 𝜇 m), decreasing somewhat through the rest of thenear-IR, and with considerably lower mid-IR (3-5 𝜇 m) amplitudes;thus, SPHERE’s near-IR capabilities are ideal for a first search forvariability in the HR 8799 planets, which share similar atmosphericproperties to these objects. In our initial July 2015 observation, wechose to observe in the SPHERE 𝐽
23 filter, as close as possible to theexpected 𝐽 -band peak of variability for similar objects. However, asHR 8799bcde are intrinsically fainter at 𝐽 than in 𝐻 or 𝐾 , we foundthat the planets were not detected with sufficient S/N in the July 2015data to enable variability studies, hence for the rest of the epochs, thebroadband 𝐻 filter was chosen as the best compromise. From July 2015 to August 2018, we obtained 7 epochs of SPHERE-IRDIS variability monitoring for the HR 8799 planets (programs095.C-0689(A), 099.C-0588(A), and 0101.C-0315(A)). A summaryof the observations is provided in Table 1. SPHERE-IRDIS is a dual-band imaging (DBI) camera, enabling coronagraphic observationsin two wavelength bands simultaneously (Dohlen et al. 2008; Vi-gan et al. 2010; Beuzit et al. 2019). In July 2015, we collected oneepoch of simultaneous imaging in the SPHERE dual-band 𝐽
23 fil-ters ( 𝐽 𝜆 𝑐 =1189.5 nm, Δ 𝜆 =47.6 nm, 𝐽 𝜆 𝑐 =1269.8 nm, Δ 𝜆 =50.8nm) and a second epoch of simultaneous imaging in the 𝐾
12 filters( 𝐾 𝜆 𝑐 =2102.5 nm, Δ 𝜆 =102 nm, 𝐾 𝜆 𝑐 =2255 nm, Δ 𝜆 =109 nm).All other epochs were obtained using the SPHERE broadband 𝐻 filter ( 𝜆 𝑐 =1625.5 nm, Δ 𝜆 =291 nm) in both of IRDIS’ wavelengthchannels . HR 8799 is relatively far north for the VLT, thus we wereonly able to observe for 4-6 hours per epoch with airmass < 𝑁 _ 𝐴𝐿𝐶 _ 𝑌 𝐽𝐻 _ 𝑆 corona-graphic configuration (inner working angle of 0.0925") of SPHERE’sapodized pupil Lyot coronagraph (Carbillet et al. 2011; Guerri et al.2011) in all epochs except for the 𝐾
12 observations taken on 31 July2015, which utilized the 𝑁 _ 𝐴𝐿𝐶 _ 𝐾𝑠 coronagraphic configurationinstead (inner working angle of 0.12"). The 2015 epochs were taken indesignated visitor modes for full half nights, enabling longer overallobservations (albeit sometimes at higher airmasses). All other epochswere taken in service mode. Conditions on 20 August 2018 were ex-cellent, leading the service observer to adjust the base exposure time(DIT) on the fly to reduce saturation of HR 8799. Unfortunately, thenumber of exposures (NEXP) taken was not also adjusted to com-pensate for the decreased DIT, leading to a significant loss in timecoverage at this epoch. On some nights, initial exposures were takenwith different DIT values or satellite spot illumination; these frameshave been removed from the subsequent analysis.To ensure a simultaneous photometric reference at all epochs,observations were conducted using the star center template that pro-vides satellite spots. Adding an additional periodic modulation tothe deformable mirror (above and beyond that used to correct theincoming wavefront) produces 4 satellite spots in a cross pattern onthe detector (Langlois et al. 2013). These satellite spots appear rela-tively circular when using a narrow-band filter and elongated when We report results from IRDIS channel 1 here, as the data obtained fromchannel 2 is functionally identical to the channel 1 data. using a wide-band filter. They share the spectra of the star and canpotentially be used as both photometric and astrometric references(Langlois et al. 2013; Wang et al. 2014). In the July 2015 observa-tions, off-axis point spread function (PSF) images were also inter-spersed every 20-30 minutes throughout the observation to use as aphotometric reference. We found that this compromised the stabilityof the observations, so in later epochs we only obtained off-axis PSFimages at the start and finish of each 4-5 hour observing sequence.Conditions varied considerably between epochs. Obtained H -bandStrehl ratio, seeing, and coherence time 𝜏 over each observation areplotted in Fig. 1 and wind speed and precipitable water vapor are plot-ted in Fig. 2. The H -band Strehl ratio and wind speeds are estimatesfrom the SPARTA AO real-time computer (Beuzit et al. 2019); seeing(from the observatory Differential Image Motion Monitor measure-ments), coherence time 𝜏 and precipitable water vapor are drawnfrom the raw data file headers. Most epochs had quite good condi-tions and AO performance, with seeing <
1" and Strehl ratios between0.8 and 0.9. The K band epoch taken on 31 July 2015, however, wasobtained in considerably worse conditions (seeing > J band epoch taken on2015-07-30 was obtained in reasonably good conditions, but, unlikeother epochs, HR 8799b is not apparent in single frame images asthe planet is fainter in 𝐽 than in 𝐻 or 𝐾 band. Thus, the 2015 epochseither do not have sufficient photometric stability or sufficiently highsignal-to-noise detection per planet to enable variability monitoringand are excluded from further variability analysis.When the wind speed at 10 m or 30 m drops below 3 m/s,SPHERE observations can be affected by the "Low Wind Effect"(LWE) (Sauvage et al. 2016; Milli et al. 2018), causing a highlydistorted PSF shape. For most of our observations, measured windspeed remained above 3 m/s, dropping below this speed for mostof the observation on 2018-08-18 and a portion of the observationon 2017-10-13. We visually inspected PSF images for these epochsobtained via the SPARTA AO data handling system to determine ifthese observations were affected by LWE and found that this effectwas mild or non-existent in our observations.Data were reduced and aligned by the SPHERE Data Center usingthe standard SPHERE pipeline. For details on the SPHERE DataCenter and the pipeline, please see Delorme et al. (2017) and Pavlovet al. (2008). We adopted standard values for pixel scale of 12.25 mas/ pixel and true north orientation of -1.75 ◦ in these reductions (Maireet al. 2016). Fully reduced images for the full observing sequencesfor the October 2017 and August 2018 data are presented in Fig. 3;these were processed using the Vortex Image Processing PrincipleComponent Analysis (VIP-PCA) pipeline (Gomez Gonzalez et al.2017). This PCA analysis utilizes the library of frames composingthe full observing sequence to build a series of principal componentimages (henceforth PCA modes), with the majority of the specklepattern well-modeled with the first few components. Subtracting outan image built from these PCA modes will then remove the specklepattern, with an increasing number of modes further improving themodeling of the speckle pattern, at the expense of subtracting outsome planet light as well. For the full observing sequence, we foundthat removing 25 principal components provided the best balancebetween fully suppressing the speckle pattern without causing sig-nificant planet self-subtraction. Our observations were acquired with satellite spots present in allframes. The standard SPHERE pipeline uses images taken with satel-
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Figure 1. 𝐻 -band Strehl ratio, seeing, and coherence time as a function of time during each of our 7 variability monitoring observations. Ranking observationsin order of observing conditions: the 2015 observations were taken in the worst conditions among those probed by our variability search and are excluded fromour variability analysis. The October 2017 observations were taken in very good conditions and the August 2018 observations were taken in excellent conditions. lite spots before and after the main observing sequence (in most cases,without satellite spots) as astrometric references to measure the stel-lar position behind the coronagraph and finely centre images, whilephotometric calibration is performed relative to unsaturated imagesof the star taken before and after the main observing sequence. Sincevariations in seeing, Strehl, and airmass over an observation willcause brightness fluctuations in the stellar PSF, the planets, and the speckle pattern, establishing a photometric reference free of vari-ability from the planets is vital for detrending and interpreting ourexoplanet observations. As the star is behind the coronagraph dur-ing our observations, it is unfeasible to obtain unsaturated images ofthe star to use as a photometric reference. Hence, here we establishwhether or not the satellite spots serve as appropriate photomet- MNRAS , 1–27 (0000)
R 8799 variability Figure 2.
Windspeed and precipitable water vapor as a function of time during each of our 7 variability monitoring observations. Precipitable water vapormeasurements were not available for the 2015 epochs, and thus are shown here only for the October 2017 and August 2018 observations. The windspeedmeasurement presented here is estimated from the SPARTA AO real-time computer. In the 2015-07-31 epoch, this windspeed value is likely an overestimate ofthe actual windspeed, as telescopes on Paranal cease operations at windspeeds above 18 m/s. ric references and a proxy for measurements of unsaturated stellarimages.While satellite spots appear relatively circular when using anarrow-band filter, with the broadband 𝐻 filter they appear as roughlyelliptical spots. Thus, to determine satellite spot position in eachframe in our time series data, we fit a 2-dimensional elliptical Gaus- sian to each of the four satellite spots using the astropy photutilsmodeling package (Bradley et al. 2019). We then extracted aper-ture photometry using the astropy photutils aperphot package in anelliptical aperture with semi-major and semi-minor axes of 4 and2 pixels, rotated to the correct angle to recover the flux from eachsatellite spot, and centered on the satellite spot positions from the 2-d MNRAS000
Windspeed and precipitable water vapor as a function of time during each of our 7 variability monitoring observations. Precipitable water vapormeasurements were not available for the 2015 epochs, and thus are shown here only for the October 2017 and August 2018 observations. The windspeedmeasurement presented here is estimated from the SPARTA AO real-time computer. In the 2015-07-31 epoch, this windspeed value is likely an overestimate ofthe actual windspeed, as telescopes on Paranal cease operations at windspeeds above 18 m/s. ric references and a proxy for measurements of unsaturated stellarimages.While satellite spots appear relatively circular when using anarrow-band filter, with the broadband 𝐻 filter they appear as roughlyelliptical spots. Thus, to determine satellite spot position in eachframe in our time series data, we fit a 2-dimensional elliptical Gaus- sian to each of the four satellite spots using the astropy photutilsmodeling package (Bradley et al. 2019). We then extracted aper-ture photometry using the astropy photutils aperphot package in anelliptical aperture with semi-major and semi-minor axes of 4 and2 pixels, rotated to the correct angle to recover the flux from eachsatellite spot, and centered on the satellite spot positions from the 2-d MNRAS000 , 1–27 (0000)
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Figure 3.
Full sequence reduced images for data taken in October 2017 and August 2018. Data were processed using the VIP PCA pipeline (Gomez Gonzalezet al. 2017), removing 25 principal component modes. All four planets are easily detected; the image scale runs from -10 to 10 ADU and has been adjusted tohighlight the residual speckle noise remaining after subtraction of the principal modes. elliptical Gaussian fits. We also extracted aperture photometry from"background" elliptical apertures placed 6 pixels away on either sideof each satellite spot. The background as a function of time was thencalculated as the average of these two background elliptical apertures.The geometry of the extraction apertures and the numbering conven-tion for satellite spots is shown in Fig. 4. In Fig. 5, we plot photometry(normalized by the median value across the whole observation foreach satellite spot) as a function of time for each satellite spot for theepoch of 2018-08-18 (taken in excellent conditions), for the variouscases of: 1) the amplitude of the 2d-gaussian fit (shown as crosses),2) elliptical aperture photometry (shown as filled circles), and 3)elliptical aperture photometry, with the background subtracted fromthe background elliptical apertures (shown as filled squares). We plotas well the median of the normalized satellite spot curves for eachcase. Photometry for the other epochs of observations can be foundin Appendix A. In all cases, we find that the 2-d Gaussian fit and theelliptical aperture photometry yield similar results, as expected. Wefound amplitudes for the 2-d Gaussian fits of 200-300 counts for the2017-10-08 epoch and 2000-3000 counts for the other epochs. Likelyowing to better observing conditions, the satellite spot photometryfor the August 2018 epochs is notably more stable and less variablethan that for the October 2017 epochs.In most cases, subtracting the background photometry did not sig-nificantly change the shape of the satellite spot light curves. Notably,however, for the 2017-10-08 epoch, where the satellite spots wereunder-illuminated, the satellite spot photometry seemed to followthat of the background regions and was significantly flattened and"detrended" via the background subtraction. Also, for satellite spot4 in the 2017-10-13 epoch, background subtraction appears to havecorrected a linear trend seen in this satellite spot but not in the other3 satellite spots during this epoch. We extracted photometry from aset of 5 circular "background regions" for comparison as well, withone region centered on the core of the star PSF, and the other fourspaced evenly around the image. Backgrounds extracted from eachof these regions were similar as a function of time and resembledthe background photometry obtained in the elliptical backgroundregions selected close to the satellite spots. In Appendix B, we over-plot the median flux in the satellite spots, measured background flux, obtained Strehl ratio and seeing, to search for correlations in thesatellite spot lightcurves as a function of ambient conditions. Otherthan the 2017-10-08 epoch (when, as noted previously, the satellitespots were under-illuminated), the satellite spot light curves do notappear to be strongly correlated to the Strehl ratio or anti-correlatedwith the background level.
Following Apai et al. (2016), we calculate the degree of correlationbetween individual satellite spots using the Spearman’s correlationtest. The Spearman’s correlation test ranks two sets of data in order ofascending data values, and then assesses how correlated the rankedsets of data are – this is the Spearman 𝜌 value. If the datasets areperfectly correlated (a higher data value in one dataset always corre-sponds to a higher value in the other), this will produce a 𝜌 value of1. Perfectly anti-correlated datasets will produce a 𝜌 value of -1. TheSpearman’s correlation test requires that the relationship betweentwo variables follows a monotonic function, unlike a Pearson corre-lation test which specifically requires a linear relationship. We usedspearmanr from from scipy.stats in python to calculate the Spearman 𝜌 values between different normalized satellite spot lightcurves. TheSpearman 𝜌 values between different satellite spots are shown inFig. 6.We find that the satellite spots are mildly correlated in the October2017 data, but at a low level and with a wide spread, with correlationsranging from 0.23 to 0.90, but generally around 0.5. This is signif-icantly lower than the typical correlations of 0.7-0.9 found by Apaiet al. (2016). In our August 2018 data, we find much smaller corre-lations between satellite spots, even though these data were taken inconsiderably better conditions, with correlations ranging from 0.03to 0.71, with values of around 0.3-0.4 for most of the pairs of satellitespots. These low Spearman 𝜌 values likely stem from the very smallspread in satellite spot photometric values for these data, due to theexcellent conditions, causing the Spearman’s correlation test to be animperfect proxy for observation quality in this case. This can be seenmore clearly if we examine the correlation plots between satellitespots directly – an example of which is given in Fig. 7, and the rest MNRAS , 1–27 (0000)
R 8799 variability Figure 4.
Satellite spots aperture photometry extraction regions and naming convention, overplotted on a single frame of data from 2018-08-18. of which appear in Appendix C. Due to larger changes in observingconditions and poorer Strehl values overall, values for satellite spotphotometry varied more over the October 2017 observations com-pared to the August 2018, leading to higher values of the Spearman 𝜌 value (in other words, the greater range of values sampled allowsa seemingly larger correlation between values).Following Apai et al. (2016), we also calculate Spearman 𝜌 valuesafter dividing through by the mean satellite spot lightcurve. Thisremoves shared variations between satellite spots, thus highlightingthe difference in behavior between the individual satellite spots. TheSpearman 𝜌 values between different satellite spots after division bythe mean are shown in Fig. 8, with the corresponding correlationplots shown in Appendix C. Apai et al. (2016) found a fairly constantpattern of no or weak anti-correlation between most of the satellitespots, with relatively strong anti-correlations between one set ofdirectly opposite spots, and two sets of adjacent spots. We find morenight-by-night diversity in our results, which are discussed in detail inAppendix C – however, given the small range of flux values coveredin our observations, we do not consider these Spearman 𝜌 values tobe robust. To minimize self-subtraction and ensure sufficient speckle suppres-sion, coverage of a sufficient range in parallactic angle is necessarywithin each temporal bin within the full observation to move eachplanet off of itself over the course of that segment of the observation. We fit a 2-dimensional Gaussian to the PSF images taken before andafter each temporal sequence. On all 5 nights, the FWHM of the PSFwas measured to be roughly 4 pixels. Thus, ideally, we would cover atleast 20 pixels of on-sky rotation ( ≥ > ◦ of skyrotation for HR 8799, over 4-5 hours; the parallactic angle coveragenecessary for 20 pixels of on-sky rotation will vary according to theplanet-star separation.For HR 8799b, we adopt 10 ◦ of rotation on sky per temporal binas this minimum coverage; at a planet-star separation of ∼ ◦ of sky rotation corresponds to a shift of 24 pixels on sky, sufficient toshift the planet > ◦ in each bin.For HR 8799c at a planet-star separation of ∼ ◦ of sky rotationcorresponds to a shift of 14 pixels on sky ( ∼ MNRAS000
Satellite spots aperture photometry extraction regions and naming convention, overplotted on a single frame of data from 2018-08-18. of which appear in Appendix C. Due to larger changes in observingconditions and poorer Strehl values overall, values for satellite spotphotometry varied more over the October 2017 observations com-pared to the August 2018, leading to higher values of the Spearman 𝜌 value (in other words, the greater range of values sampled allowsa seemingly larger correlation between values).Following Apai et al. (2016), we also calculate Spearman 𝜌 valuesafter dividing through by the mean satellite spot lightcurve. Thisremoves shared variations between satellite spots, thus highlightingthe difference in behavior between the individual satellite spots. TheSpearman 𝜌 values between different satellite spots after division bythe mean are shown in Fig. 8, with the corresponding correlationplots shown in Appendix C. Apai et al. (2016) found a fairly constantpattern of no or weak anti-correlation between most of the satellitespots, with relatively strong anti-correlations between one set ofdirectly opposite spots, and two sets of adjacent spots. We find morenight-by-night diversity in our results, which are discussed in detail inAppendix C – however, given the small range of flux values coveredin our observations, we do not consider these Spearman 𝜌 values tobe robust. To minimize self-subtraction and ensure sufficient speckle suppres-sion, coverage of a sufficient range in parallactic angle is necessarywithin each temporal bin within the full observation to move eachplanet off of itself over the course of that segment of the observation. We fit a 2-dimensional Gaussian to the PSF images taken before andafter each temporal sequence. On all 5 nights, the FWHM of the PSFwas measured to be roughly 4 pixels. Thus, ideally, we would cover atleast 20 pixels of on-sky rotation ( ≥ > ◦ of skyrotation for HR 8799, over 4-5 hours; the parallactic angle coveragenecessary for 20 pixels of on-sky rotation will vary according to theplanet-star separation.For HR 8799b, we adopt 10 ◦ of rotation on sky per temporal binas this minimum coverage; at a planet-star separation of ∼ ◦ of sky rotation corresponds to a shift of 24 pixels on sky, sufficient toshift the planet > ◦ in each bin.For HR 8799c at a planet-star separation of ∼ ◦ of sky rotationcorresponds to a shift of 14 pixels on sky ( ∼ MNRAS000 , 1–27 (0000)
B.A. Biller et al.
Figure 5.
Satellite spot photometry for 2018-18-18 (normalized by the median value across the whole observation for each satellite spot) as a function of timefor each satellite spot, with an offset in flux included between each satellite spot lightcurve for clarity. Results with background subtraction are shown on the tophalf of the plot, while results without background subtraction are plotted on the bottom half of the plot. The amplitudes from a 2-d gaussian fit to each satellitespot are plotted as black crosses, elliptical aperture photometry is plotted as filled circles, and elliptical aperture photometry with an additional backgroundsubtraction is plotted as filled squares. The mean of the elliptical aperture photometry for all 4 satellite spots are plotted in the middle of the figure, with magentacircles for the elliptical aperture photometry without background subtraction, and cyan square for elliptical aperture photometry with background subtraction. for HR 8799c, we adopt 14 ◦ of rotation per sky per temporal bin,corresponding to 5 equal parallactic angle bins and a shift of ∼ ∼ ∼ ∼ ∼ ◦ of sky rotation corresponds to shifts of ∼ ∼ ◦ of rotation on sky per temporal bin as the minimum coverage,and hence only consider a total of 3 equal parallactic angle bins perobservation. At ∼ MNRAS , 1–27 (0000)
R 8799 variability Figure 6.
Spearman 𝜌 coefficients between satellite spots, with no division by the mean lightcurve. A 𝜌 value of 1 implies perfect correlation; a 𝜌 value of -1implies perfect anti-correlation. Conditions were particularly excellent for our August 2018 datasets; our satellite spot photometry thus covered a limited rangeof values, meaning that correlation between satellite spots is not a particularly good proxy for the quality of the observation. (10 pixel width) at the planet radial separation to estimate the back-ground at this position and also the median in a circular annulusaperture from 3-5 pixels around the 2-d Gaussian best fit position toremove any remaining trend in the background. Aperture photometryfor HR 8799b as well as negative simulated planet photometry forHR 8799bc are presented in Figure 9. We must robustly remove speckle noise while preserving a photo-metric reference in order to determine well-calibrated time-seriesphotometry for the HR 8799 planets. To do so, we adopt the standardtechnique of negative simulated planet subtraction. We first dividethe observation into a number of temporal bins, which vary accordingto the planet considered (see Section 5.1). For each temporal bin, wethen inserted negative simulated planets at the approximate positionsof each of the four planets in a grid of radius, planet position angle(henceforth 𝜃 ), and Δ (magnitude) into each frame. Three unsaturatedpoint-spread function (PSF) images were taken before and after thetime-series data. Planets were simulated by median combining theseunsaturated PSF images and scaling them according to the Δ ( 𝑚𝑎𝑔 ) of the planet.We performed the insertion in two steps:
1) Coarse Grid – in order to precisely determine the position of each planet, we ran an initial grid in radius and 𝜃 , with planet Δ (mag) kept fixed and set to literature values. After inserting thenegative simulated planets, the VIP PCA pipeline (Gomez Gonzalezet al. 2017) was used to remove 10 principal modes, de-rotate, andstack data from each bin. From the de-rotated and stacked data, wethen calculated the 𝜒 residual for each planet at each grid point.Over the full grid, we then find the minimum 𝜒 and hence the bestsolution for planet position. The 𝜒 value for each grid point wascalculated as the square of the sum of the counts in a circular regionwith radius of 5 pixels centered on the planet divided by the standarddeviation in a circular noise annulus around the planet (5-10 pixels).For the negative simulated planet subtraction, the inhomogeneousbackground due to the PSF of the star is removed via the PCAanalysis, so we chose a larger aperture size in comparison to thedirect aperture photometry of HR 8799b described in Section 5.2, inorder to obtain better statistics for evaluating the quality of our PSFsubtraction. In radius, we ran the wide grid over a radial offset of -4to +4 pixels from the initial radius guess, in steps of 0.2 pixels. Inangle, we ran the wide grid over an angular offset of -2 to +2 degreesfrom the initial angle guess, in steps of 0.1 degrees.
2) Fine Grid – after estimating planet position with the coarse grid,we ran a finer grid in position as well as Δ (mag), centered on the bestposition found during the coarse grid step. From the fine-grid 𝜒 grid,we then converted to likelihood (e.g. 𝑒𝑥 𝑝 (− 𝜒 ) ) and renormalized MNRAS000
2) Fine Grid – after estimating planet position with the coarse grid,we ran a finer grid in position as well as Δ (mag), centered on the bestposition found during the coarse grid step. From the fine-grid 𝜒 grid,we then converted to likelihood (e.g. 𝑒𝑥 𝑝 (− 𝜒 ) ) and renormalized MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure 7.
Correlation plots for satellite spots 3 vs. 4 and 4 vs. 1. The satellite spot photometry covers a much more limited range of values on nights withexcellent conditions (August 2018) compared to nights with more moderate conditions (October 2017), leading to lower Spearman 𝜌 values for August 2018 vs.August 2017, despite the higher quality of the August 2018 data. the posterior probability distribution function (henceforth PDF) to1, assuming that we had estimated planet position and Δ ( 𝑚𝑎𝑔 ) withsufficient accuracy to ensure that each planet was within our finegrid. We then marginalized over radius and 𝜃 , and fit a 1-d Gaussianto the 1-d posterior. The peak and width of the best-fit Gaussianwas adopted as the best Δ ( 𝑚𝑎𝑔 ) and error on Δ ( 𝑚𝑎𝑔 ) respectively;in fact, this ability to robustly estimate errors is why we chose tocalculate the posterior across the full fine grid, instead of using e.g.an amoeba downhill optimization procedure to select the highestprobability set of parameters. In radius, we ran the fine grid over aradial offset from the best radius found by the wide grid, runningfrom -1 to +1 pixel, in steps of 0.1 pixels. We ran the fine grid over anangular offset running from -1 to +1 degrees from the best angularposition found by the wide grid, in steps of 0.1 degrees. In Δ ( 𝑚𝑎𝑔 ) ,we ran over a grid of offsets from -0.5 to 0.5 mag, in steps of 0.05mag for the October 2017 epochs and from -0.333 to 0.333, in stepsof 0.033 mag for the August 2018 epochs.We selected 10 PCA modes as the ideal choice to best subtractspeckles while preserving planet flux – we motivate this choice fur-ther in Sections 5.4 and 5.7. For HR 8799b and HR8799c, we thencalculated best Δ ( 𝑚𝑎𝑔 ) values for 6 and 5 temporal bins respec-tively, evenly spaced in parallactic angle across the observation. Forthe night of 18 August 2018, we show a zoomed-in view of HR 8799b or c respectively in Figures 10 and 11, before and after removing thebest-fit negative simulated planet. The image scale in these figuresruns from -10 to 10 ADU; while at the position of HR 8799b, specklenoise has been fully removed and noise statistics can be assumed tobe Gaussian, a considerable amount of speckle noise remains at theseparation of HR 8799c even after subtraction of 10 PCA modes.Negative simulated planet photometry as a function of time (andconverted to flux units) for HR 8799bc are presented in Figure 9.For each photometric measurement, to convert errors calculated in Δ ( 𝑚𝑎𝑔 ) to flux units, we drew 100000 samples from a Gaussiancentered on the best Δ ( 𝑚𝑎𝑔 ) value and with 𝜎 given by the erroron Δ ( 𝑚𝑎𝑔 ) , then converted to flux units and adopted the standarddeviation of the 100000 samples as our error in flux.From Figure 9, it is clear that some nights yielded considerablybetter data than others – specifically, compared to the October 2017epochs, the August 2018 epochs have much less spread in satellitespot measurements and correspondingly smaller spread in planetphotometry measurements. Unsurprisingly, the two August 2018epochs had the longest coherence times and highest Strehl ratiosacross all epochs (see Fig. 1). For the August 2018 epochs, the planetand satellite spots measurements generally agree. This implies that inthese epochs, all or at least the bulk of the variation in planet flux wemeasure here is simply systematic trends as seeing, Strehl, etc., vary MNRAS , 1–27 (0000)
R 8799 variability Figure 8.
Spearman 𝜌 coefficients between satellite spots, after division by the mean lightcurve (thus removing common variations). A 𝜌 value of 1 impliesperfect correlation; a 𝜌 value of -1 implies perfect anti-correlation. across the observation. In October 2017, however, we find significantdivergence between planet and satellite spot lightcurves. Measure-ments for HR 8799b and HR 8799c also appear to be in agreement,except for epoch 2018-08-18, where the first and last measurementsfor HR 8799c are divergent from the HR 8799b and satellite spotlightcurves. However, we do not believe this is a bonafide detectionof variability, as this result appears to be PCA-mode dependent andthese two time bins were taken right at the beginning and end of theobservation, where the airmass was at its highest and sky rotation atits lowest. We discuss this further in Sections 5.4 and 5.7. Obtaining accurate photometry for planets embedded in speckle noiserequires balancing the number of PCA modes utilized with the ac-ceptable level of planet self-subtraction. Utilizing a greater numberof PCA modes will more fully remove the speckle noise, but at theexpense of removing flux from the planet itself. We tested the effectof using different numbers of PCA modes with the 18 August 2018dataset (which appears by eye to be the highest-quality and moststable of the datasets) by re-running the fine-grid planet photometrypipeline with 4, 6, 10, and 16 modes. We used 6 equally spaced par-allactic angle temporal bins for both b and c (as opposed to 5 for c)so we could directly compare results for the same sets of input dataframes. Lightcurves are plotted in Fig. 12. Negative simulated planetphotometry gives similar results for HR 8799b, independent of the number of PCA modes used. However, we found that the negativesimulated planet photometry for c varies more strongly with numberof PCA modes chosen. For the most part, the retrieved photometryfor HR 8799c is still consistent using a wide range of number of PCAmodes, with the exception that the first and last parallactic angle binsdiverge by ∼ 𝜎 from the trend given by the satellite spots if thenumber of PCA modes used is ≥
10. However, these two points doagree with the satellite spot trend within 2 𝜎 . Given that they weretaken at the extrema of the observation, at high airmasses and witha slow rate of sky rotation, they simply may not be reliable or mayhave true uncertainties higher than the uncertainty estimated here. InSection 5.7, we further consider the ideal number of PCA modes toadopt in this case, using simulated planet tests. Even with 4-5 hour long observations spanning > ◦ degrees inparallactic angle, we do not achieve sufficient sky-rotation to obtainhigh-sensitivity variability measurements for the innermost HR 8799planets. Binning the observation into 3 equal parallactic angle binswill ensure ≥ ◦ degrees of sky rotation. For the inner two planets,HR 8799d and HR8799e, at separations of ∼ ∼ ◦ of sky rotation corresponds to shifts of ∼
20 pixels and ∼
14 pixelson sky. Examples of final images after negative simulated planetremoval for 2018-08-18 are presented in Figures 13. Like with HR
MNRAS000
MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure 9.
Satellite spot aperture photometry (with and without background subtraction), planet b aperture photometry, and planet b and c psf-fitting photometryas a function of time during the observation for October 2017 and August 2018 broadband- 𝐻 datasets. Each lightcurve has been normalized using its mean fluxvalue. Planet b aperture and psf-fitting photometry have been slightly offset in time to improve error bar legibility. Planets b and c almost always display thesame trends as a function of time; in the August 2018 data these trends are also well-correlated with the trends seen in the satellite spot photometry.MNRAS , 1–27 (0000) R 8799 variability Figure 10.
Best negative simulated planet subtractions for HR 8799b on 18 August 2018. The full ∼ Figure 11.
Best negative simulated planet subtractions for HR 8799c on 18 August 2018. The full ∼ >
30% level on 4-5hour-long timescales.
We note that the lightcurves of HR 8799bc are almost always similarto each other, but in the October 2017 epochs, diverge significantlyfrom the satellite spot lightcurves. Thus, while we initially considereddetrending the planet photometry using the satellite spot photometry,it is clear that the satellite spot lightcurves do not provide an appro-priate photometric reference for the planet photometry at all epochs.Instead, we follow the approach of Apai et al. (2016) and calculated Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 – essentially detrending the b lightcurve usingthat of c, or vice versa. This traces non-shared variations betweenthe two planets. We considered five temporal bins here, to assure 20pixels of movement on the sky for HR 8799b and c, with differencelightcurves presented in Fig. 15. Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 measured byApai et al. (2016) is overplotted as a purple horizontal line. Withinerrors, our results are in agreement with those from Apai et al. (2016).The uncertainty on the measurement is dominated by the uncertainty in our measurement of Δ ( 𝑚𝑎𝑔 ) 𝑐 . Depending on epoch, we rule outnon-shared variability in Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 to the 10-20% levelover 4-5 hours. To quantify our sensitivity to variability in the 2018-08-18 epoch(the best quality data of our search), we simulate variable and non-variable lightcurves by inserting and retrieving a suite of simulatedplanets at a similar radius from the star as HR 8799bc, but offset inposition angle from the true planet position angle. Thus, we sample asimilar region of the speckle pattern, but place each simulated planetsufficiently far from its real counterpart that they do not interfere witheach other during the PCA analysis. In the simulated lightcurves, weestimate systematic noise sources to first order (e.g. varying Strehlratio, seeing, etc) expected in the data by scaling the simulated planetflux by the normalized satellite spot aperture photometry (averagedacross all 4 satellite spots) after background subtraction. While thisis not a rigorous attempt to model all potential noise sources, it issufficient to set constraints on the amplitudes and periods of variablesignals that we can potentially detect. Note the satellite spot aperturephotometry is only an appropriate noise model for the August 2018epochs (and not for the October 2017 epochs), as in August 2018,planet photometry and satellite spot photometry largely followedsimilar trends. We then simulate either a constant planet flux or asinusoidal variability signal. Since the positions of the simulatedplanets are known a priori, we do not run the full 3-d planet retrievalgrid, but only consider a 1-d grid of Δ mag at the a priori planetposition.We first consider the effect of using different numbers of PCA MNRAS000
We note that the lightcurves of HR 8799bc are almost always similarto each other, but in the October 2017 epochs, diverge significantlyfrom the satellite spot lightcurves. Thus, while we initially considereddetrending the planet photometry using the satellite spot photometry,it is clear that the satellite spot lightcurves do not provide an appro-priate photometric reference for the planet photometry at all epochs.Instead, we follow the approach of Apai et al. (2016) and calculated Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 – essentially detrending the b lightcurve usingthat of c, or vice versa. This traces non-shared variations betweenthe two planets. We considered five temporal bins here, to assure 20pixels of movement on the sky for HR 8799b and c, with differencelightcurves presented in Fig. 15. Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 measured byApai et al. (2016) is overplotted as a purple horizontal line. Withinerrors, our results are in agreement with those from Apai et al. (2016).The uncertainty on the measurement is dominated by the uncertainty in our measurement of Δ ( 𝑚𝑎𝑔 ) 𝑐 . Depending on epoch, we rule outnon-shared variability in Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 to the 10-20% levelover 4-5 hours. To quantify our sensitivity to variability in the 2018-08-18 epoch(the best quality data of our search), we simulate variable and non-variable lightcurves by inserting and retrieving a suite of simulatedplanets at a similar radius from the star as HR 8799bc, but offset inposition angle from the true planet position angle. Thus, we sample asimilar region of the speckle pattern, but place each simulated planetsufficiently far from its real counterpart that they do not interfere witheach other during the PCA analysis. In the simulated lightcurves, weestimate systematic noise sources to first order (e.g. varying Strehlratio, seeing, etc) expected in the data by scaling the simulated planetflux by the normalized satellite spot aperture photometry (averagedacross all 4 satellite spots) after background subtraction. While thisis not a rigorous attempt to model all potential noise sources, it issufficient to set constraints on the amplitudes and periods of variablesignals that we can potentially detect. Note the satellite spot aperturephotometry is only an appropriate noise model for the August 2018epochs (and not for the October 2017 epochs), as in August 2018,planet photometry and satellite spot photometry largely followedsimilar trends. We then simulate either a constant planet flux or asinusoidal variability signal. Since the positions of the simulatedplanets are known a priori, we do not run the full 3-d planet retrievalgrid, but only consider a 1-d grid of Δ mag at the a priori planetposition.We first consider the effect of using different numbers of PCA MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure 12.
The effect of utilizing different numbers of PCA modes on HR8799b and c lightcurves for 18 August 2018. The lightcurve for planet b is consistentindependent of the number of modes used. The retrieved photometry for HR 8799c is largely self-consistent using a wide range of number of PCA modes, withthe exception that the first and last parallactic angle bins diverge by ∼ 𝜎 from the trend given by the satellite spots if the number of PCA modes used is ≥ , 1–27 (0000) R 8799 variability Figure 13.
Best negative simulated planet subtractions for HR 8799d and HR 8799e on 18 August 2018. The full ∼ modes when retrieving simulated planets. Retrieved lightcurves (us-ing 4, 10, or 16 PCA modes) for simulated constant-flux versionsof HR 8799bc are presented in Fig. 16. The simulated HR 8799blightcurve is robustly retrieved using 4, 10, or 16 modes, but the4 and 16 mode retrievals look considerably noisier than the 10mode retrieval, further justifying our adoption of 10 modes as stan-dard. The retrieved lightcurves for HR 8799c are noisier than thosefor HR 8799b. Using 4 or 10 modes, the HR 8799c simulatedlightcurves match the satellite spot lightcurve within errors. The 16mode lightcurve is extremely noisy and is clearly oversubtracting theplanet flux, resulting in significantly higher uncertainties. In all cases,the final photometric point in the HR 8799c simulated lightcurve isbrighter than the satellite spot lightcurve at the same bin; this mirrorswhat is found in the actual HR 8799c lightcurve. At this radius fromthe star and this temporal point in the observations, we suspect thatspeckle residuals remain that are not accounted for in the satellitespot lightcurves. In other words, the satellite spot lightcurve does notserve as an appropriate photometric reference for this particular datapoint.In Fig. 17, we present simulated lightcurves for HR 8799bc with aperiod of 8.6 hours, similar to the period of the variable free-floatingplanetary mass object PSO J318.5-22 (Biller et al. 2018), a phaseof 40 ◦ , and with variability amplitudes of 0%, 5%, 10%, and 20%.As before, we use 6 and 5 equal parallactic angle bins for HR 8799band c respectively, to ensure at least 5 FWHMs of motion on the skyin each parallactic angle bin. Variability is clearly apparent in thesimulated HR 8799b lightcurves with amplitudes ≥ ◦ to 330 ◦ (insteps of 30 ◦ ). We then detrend each simulated HR8799bc lightcurveby dividing through by the mean satellite spot lightcurve, with er-rors on the detrended lightcurve given as the sum in quadrature ofthe errors on the simulated planet and satellite spot lightcurves. For each detrended simulated lightcurve at a specific value of period,amplitude, and phase, we set up a metric for the detection of vari-ability in the detrended lightcurve as follows: If (maximum(flux) -minimum(flux)) / maximum(error) >
2, we consider variability to bedetected (e.g. a 2- 𝜎 variability detection). This metric was tested byeye for a significant number of simulated lightcurves, and generallyagrees with visual assessment. To build the detection map, we assigneach combination of period, amplitude, and phase the value 1 if vari-ability is detected, and 0 if variability is not detected. We then sumalong the phase axis and divide by the number of phases simulatedto produce a fractional detection map as a function of period andamplitude. Detection maps for HR 8799bc in the 2018-08-18 epochare presented in Fig. 18. For HR 8799b, for periods <
10 hours, we aregenerally quite sensitive to variability with amplitude > >
25% forsimilar periods.
In this section, we present epoch-by-epoch astrometry and photome-try, and compare to literature values. For this purpose, we used onlythe data frames from the hour approaching meridian crossing and thehour after meridian crossing, thus covering the time period duringeach observation with the most field rotation and best airmass. Weagain ran our full negative simulated planet code to retrieve the best Δ (mag), radius, and position angle value for each planet.Astrometric results are plotted compared to literature astrometryin the left panel of Fig. 19. A zoomed-in plot on our epochs ofastrometry is presented in right panel of Fig. 19 and the epoch-by-epoch astrometry for each planet is presented in Tab. 2. To convertthe uncertainties derived from the negative simulated planet codefrom radius and position angle values to Δ RA and Δ DEC, we drew100000 samples from Gaussians centered on the best radius andposition angle values and with 𝜎 given from the respective errorson from the negative simulated planet subtraction, converted thesevalues to Δ RA and Δ DEC, then adopted the mean and standarddeviations of these distributions as the corresponding Δ RA, Δ DEC
MNRAS , 1–27 (0000) B.A. Biller et al.
Figure 14.
Satellite spot aperture photometry (with and without background subtraction), planet b aperture photometry, and planet d and e psf-fitting photometryas a function of time during the observation for October 2017 and August 2018 broadband- 𝐻 datasets. Planets d and e are consistent within errors with thesatellite spot photometry, however, our uncertainties are much higher for HR 8799de relative to HR 8799b, as this region of our images still show considerablespeckle residuals even after removing 10 PCA modes. values and 1- 𝜎 uncertainties. In this case, we conservatively adoptthe 2- 𝜎 values for uncertainties, which gives us the uncertainty onthe relative planet position 𝜎 PP at this epoch. However, we mustconsider further astrometric uncertainties in our full error budget.Following Zurlo et al. (2016), we adopt a plate scale uncertainty 𝜎 PS of 2 mas and star center position 𝜎 SC uncertainty of 1.2 mas; the fulluncertainty is then given as the sum in quadrature of 𝜎 PP , 𝜎 PS , and 𝜎 SC . Our astrometric points are consistent with the already-observedorbital motion of these planets, however, we defer orbital fitting ofthese points and further epochs of SPHERE orbital monitoring toZurlo et al. in prep.Our epoch-by-epoch values of the absolute 𝐻 magnitude of eachplanet are compared to literature photometry in the 𝐻 band in Figs. 20to 22 and presented in tabular form in Table 3. To convert from Δ magto absolute magnitude in 𝐻 , we adopt a parallax of 24.2175 ± 𝐻 -band magnitude of 5.280 ± Δ (mag) toabsolute mag prevent a meaningful epoch-to-epoch comparison inabsolute H, however, our photometry is constant to within error barsboth between our own epochs and with 𝐻 Δ (mag) to absolute mag, Apai et al. (2016) instead opt to con-sider Δ (mag) 𝑏 - Δ (mag) 𝑐 , etc., in other words, the relative difference MNRAS , 1–27 (0000)
R 8799 variability Figure 15. Δ (mag) of HR 8799b - Δ (mag) of HR 8799c as a function of time during each broadband- 𝐻 observation, compared to the results from Apai et al.(2016) (purple line and shaded rectangle). Δ (mag) of HR 8799b - Δ (mag) is consistent with being constant within errors. in contrast between different planets in the system. We plot our mea-surements of this value in comparison to those from Apai et al. (2016)in Fig. 23 and present our measurements in tabular form in Table 4;our values all agree within 1- 𝜎 with those from Apai et al. (2016),with no compelling evidence of epoch-to-epoch variability. As noted in Section 2, HR 8799 is a 𝛾 Doradus pulsating variable,with a dominant periodicity of ∼ ∼ 𝐻 exoplanet lightcurves; this seems to becorrelated to the observing conditions and may be due to the fact thatthe planet spectra are similar to each other, but much redder than thespectrum of the star (which is shared by the satellite spots). To testwhether this is the case, it would be interesting to observe a binary MNRAS000
R 8799 variability Figure 15. Δ (mag) of HR 8799b - Δ (mag) of HR 8799c as a function of time during each broadband- 𝐻 observation, compared to the results from Apai et al.(2016) (purple line and shaded rectangle). Δ (mag) of HR 8799b - Δ (mag) is consistent with being constant within errors. in contrast between different planets in the system. We plot our mea-surements of this value in comparison to those from Apai et al. (2016)in Fig. 23 and present our measurements in tabular form in Table 4;our values all agree within 1- 𝜎 with those from Apai et al. (2016),with no compelling evidence of epoch-to-epoch variability. As noted in Section 2, HR 8799 is a 𝛾 Doradus pulsating variable,with a dominant periodicity of ∼ ∼ 𝐻 exoplanet lightcurves; this seems to becorrelated to the observing conditions and may be due to the fact thatthe planet spectra are similar to each other, but much redder than thespectrum of the star (which is shared by the satellite spots). To testwhether this is the case, it would be interesting to observe a binary MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure 16.
The effect of utilizing different numbers of PCA modes on simulated constant-flux HR8799b and c lightcurves for 18 August 2018 (noise simulatedusing the satellite spot lightcurve, inserted at the same radius but differing PA compared to the actual planets). The planet b simulated lightcurve is consistentindependent of the number of modes used. The retrieved photometry for HR 8799c is much noisier, with the 10 mode lightcurve providing the best trade-offbetween preserving planet flux and suppressing speckles. The final photometric point in HR 8799c simulated lightcurve is considerably brighter than the satellitespot lightcurve at the same bin using 4, 10, or 16; this mirrors what is seen in the actual HR 8799c lightcurve. At this radius from the star and this temporal pointin the observations, speckle residuals remain that affect our negative simulated planet subtraction, but are not accounted for in the satellite spot lightcurves. companion with a more similar (e.g. bluer) spectrum to its host, alongwith the satellite spots. If the binary companion displays the sametrends as the satellite spots in a range of different observing condi-tions, the divergence between planet and satellite spot lightcurves wemeasure here would likely be due to the red colours of the planetsrelative to the star. In this case, a narrow band or integral field spec-troscopic search for variability would not have to contend with thisparticular issue, but would rather be limited by the brightness of theplanet in a narrow bandpass.However, the source of the divergence may instead be that the satel-lite spots are artificially introduced and do not fully share propertiesof imaged astrophysical objects. The satellite spots for SPHEREare generated by introducing a waffle pattern onto the SPHERE de-formable mirror, producing 4 artificial sources in a cross-pattern (Langlois et al. 2013). In contrast, GPI uses a square grid in the pupilplane of the telescope to produce a similarly shaped cross-patternof 4 first-order diffraction spots (Sivaramakrishnan & Oppenheimer2006; Wang et al. 2014). It would be interesting to investigate whetherthese different methods to produce artificial references cause differ-ences in the behaviours of these references; note however, that Figure7 of Wang et al. (2014) seems to show similar correlations / anticor-relations between different satellite spots as we found in Section 4.1and Appendix C. Unlike a real companion or stellar image, satellitespots in SPHERE and GPI are not incoherent with stellar residuals.The coherent satellite spots suffer from pinning effects (interferencebetween the satellite spots and PSF residuals) and provide only re-duced accuracy for photometry and astrometry. Recently, Sahoo et al.(2020) has experimented with introducing fiducial incoherent faint
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R 8799 variability Figure 17.
Simulated lightcurves for HR 8799bc with sinusoidal variability with a period of 8.6 hours, and amplitudes of 5%, 10%, and 20%. Variabilityis apparent by eye in the simulated HR 8799b lightcurves with amplitudes ≥ Figure 18.
Simulated planet fractional detection maps for HR 8799bc in our 2018-08-18 data. The color scale is set by the fraction of simulated lightcurvesdetected at each combination of period and amplitude. For HR 8799b, for periods <
10 hours, we are generally quite sensitive to variability with amplitude > >
25% for similar periods. MNRAS000
25% for similar periods. MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure 19.
Left:
Astrometric comparison between our epochs, Marois et al. (2008), and Zurlo et al. (2016). The error bars are smaller than the plot symbols; allfour planets show significant on-sky motion even between our 2017 and 2018 epochs.
Right : Planet-by-planet view of astrometry from our October 2017 andAugust 2018 epochs. copies of the host star in the image plane of Subaru ScEXAO and thenalternating the pattern of these copies between exposures. This pro-duces an incoherent photometric reference and may solve some of theissues of using satellite spots as photometric references encounteredin this study.
HR 8799bcde share very similar spectra and colours to highly vari-able mid-to-late-L variable planetary mass objects such as VHS1256-1257ABb (Bowler et al. 2020; Zhou et al. 2020) and PSOJ318.5-22 (Liu et al. 2013; Biller et al. 2015, 2018). Although vari-ability amplitude can vary between epochs for these objects, theseobjects are always highly variable in the near-IR, and particularlyin 𝐽 -band – VHS 1256-1257ABb has been observed to be variableby 24.7% over ∼ 𝜇 m (Bowler et al. 2020) and PSOJ318.5-22 has been observed to be 7-10% variable over ∼ 𝐽 𝑆 band (Biller et al. 2015). These two objects are observedat high inclinations; Zhou et al. (2020) find that the 𝑣𝑠𝑖𝑛𝑖 and pe-riod of VHS 1256-1257ABb is most consistent with an equator-onviewing inclination and Biller et al. (2018) measure an inclinationfor PSO J318.5-22 of 56.2 ± ◦ . Field brown dwarfs (Radigan et al.2014; Metchev et al. 2015) display the highest amplitude variabilityin 𝐽 band ( ∼ 𝜇 m), decreasing somewhat through the rest ofthe near-IR, and with considerably lower mid-IR (3-5 𝜇 m) ampli-tudes; VHS 1256-1257ABb shows a similar trend to the field browndwarfs at all wavelengths, with the mid-IR amplitude less than halfthe near-IR amplitude (Zhou et al. 2020), while PSO J318.5-22 isa rare exception to this rule, with nearly equal near-IR vs. mid-IRamplitudes. As the HR 8799bcde planets share comparable atmo-spheric properties to these objects, they may also have high intrinsicvariability amplitudes in the near-IR.In our best epoch on 18 August 2018, for periods less than 10hours, we were sensitive to 5-10% variability in HR 8799b and to ≥
25% variability in HR 8799c in the broadband H filter. However, PSO J318.5-22 is also notably one of few brown dwarfs or exoplanetanalogues with simultaneously measured near-IR and mid-IR amplitudes. the measured variability amplitude will be less than the intrinsic vari-ability amplitude due to geometric dilution effects and attenuationof flux within the line-of-sight through the planet’s own atmosphere.Vos et al. (2017) estimate the contributions of geometric effects andatmospheric attenuation as: 𝐴 = 𝐴 𝑂 𝑠𝑖𝑛𝑖 − 𝜅 𝑑𝑥𝑠𝑖𝑛𝑖 (1)where 𝐴 is the measured variability amplitude, 𝐴 𝑂 is the intrin-sic variability amplitude, 𝑖 is the inclination of the planet, 𝑑𝑥𝑠𝑖𝑛𝑖 isthe path length of the light through the atmosphere of the planet,and 𝜅 is the degree of attenuation through the atmosphere per unitlength (see also Fig. 4 in Vos et al. 2017). The first term gives thegeometric dilution due to projection. The HR 8799 disk is inclinedby ∼ ◦ (based both on disk studies and orbital fits for the indi-vidual planets, see e.g. Matthews et al. 2014; Ruffio et al. 2019;Wang et al. 2018a; Konopacky et al. 2016; Pueyo et al. 2015; Maireet al. 2015). For brown dwarfs with measured inclination angles, Voset al. (2017, 2020) find a relationship between inclination angle and ( 𝐽 − 𝐾 ) colour anomaly (object 𝐽 − 𝐾 - average 𝐽 − 𝐾 forother objects with the same spectral type and gravity class). Theyfind that objects viewed at high inclination (equator-on) are redderthan the average object of the same spectral type and objects viewedat low inclination (pole-on) are comparatively bluer. Assuming thatHR 8799b shares the inclination of the disk (but noting that the incli-nation of the planet has not been measured), adopting an L7 spectraltype, and calculating colour anomaly using photometry from Maroiset al. (2008); Currie et al. (2011) converted from MKO into 2MASSfilters using the conversion from Stephens & Leggett (2004), we plotHR 8799b alongside field and low-gravity brown dwarfs on the sameinclination vs. colour anomaly plot in Fig. 24. The colour anomaly isconsistent with a wide range of possible inclinations for this planet.However, assuming the planets do share the inclination of the diskand ignoring additional attenuation from the atmospheres of the plan-ets themselves implies that the intrinsic variability amplitude for theHR 8799 planets will be at least a factor of 2.2 greater than any mea-sured variability amplitude. Thus, if the planets are observed nearlypole-on, we are sensitive to intrinsic variability amplitudes of 11-22% for HR 8799b, and >
55% for HR 8799c. Assuming that VHS1256-1257ABb and PSO J318.5-22 are observed nearly equator-
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R 8799 variability Figure 20.
Our broadband- 𝐻 epoch-by-epoch photometry compared to SPHERE 𝐻 𝐻 on (hence measured variability amplitude is nearly the same as theintrinsic variability amplitude), we could potentially have detectedvariability if HR 8799b was a VHS 1256-1257ABb analogue, buta PSO J318.5-22 analogue would have remained undetected (as wefound from our simulated planet tests). Taking atmospheric attenua-tion into account as well (second term in Equation 1) further reducesthe measured variability amplitude as a function of decreasing in-clination. This term is sensitive to the wavelength being monitored;we expect light at near-IR wavelengths to be produced deeper in agiven object than light at mid-IR wavelengths, thus, near-IR lightwill traverse a longer path length and will be more attenuated as afunction of inclination.While the observed photometric variability for brown dwarfs andplanetary mass objects to date is consistent with inhomogeneous top-of-atmosphere features (e.g. quasiperiodic variability that evolves ontimescales of a few rotational periods), a transiting companion toan exoplanet would provide another potential source of variability.The geometry of the HR 8799 system is not ideal for this scenario– assuming the planet and the companion to the planet are coplanar and have inclinations similar to that of the system, observable transitswould be unlikely for this face-on system. However, a companion toone of the HR 8799 planets with an orbit inclined perpendicularlyto the inclination of the system could potentially produce transitsin this system. Lazzoni et al. in prep simulate transits due to com-panions to known planets for a range of planetary systems, focusingprimarily on the edge-on 𝛽 Pic system. For HR 8799b, simulating anensemble of satellites around HR 8799 b with masses in the range[0.001,0.39] × M 𝐽𝑢 𝑝 and semi-major axis in the range [0.001, 𝑅 ℎ ],where 𝑅 ℎ is the Hill radius of the planet yields numerous transitevents with depths greater than 10%. However, the transit durationsare often quite long – up to tens of hours, with only a minority ofsimulated transits shorter than 10 hours. Thus, it is likely that ground-based observations with durations <
10 hours, such as those reportedhere, would simply be too short to realistically detect such a transit.
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Figure 21.
Our broadband- 𝐻 epoch-by-epoch photometry compared to LBT 𝐻 -band photometry from Skemer et al. (2012). Here we summarize the main results of this study:(i) The satellite spots were well-illuminated ( ∼ ∼
200 counts at peak). Forthese well-illuminated epochs, background subtraction did not no-ticeably affect the mean satellite spot lightcurve, as the backgroundlevel was so much lower than the satellite spot peak. For 2017-10-08,subtracting the background noticeably detrended the mean satellitespot lightcurve.(ii) The degree of excursion (maximum vs. minimum satellite spotlightcurve value) varies strongly for different epochs of observations– the August 2018 epochs are considerably more stable and havenoticeably smaller ranges of values in the satellite spot lightcurvesthan the October 2017 epochs. This leads to overall better sensitivityto variability and improved ability to detrend planet lightcurves.(iii) In contrast to Apai et al. (2016), we do not find a night-by-night stable pattern of correlations / anti-correlations betweensatellite spots. In particular, for our best datasets (August 2018), we find low levels of correlation / anti-correlation between satellite spots,because the satellite spot photometry is very stable on those nightsand do not cover a wide range of values (in other words, the satellitespot lightcurves are quite flat in these epochs, so do not appear verycorrelated at all).(iv) Ensuring 5 × FWHM sky rotation at the exoplanet radius tooptimize speckle suppression but minimize self-subtraction, our ∼ Δ mag, position of each planet ineach raw data frame, for 6 temporal bins for b and 5 temporal binsfor c. As HR 8799b is sufficiently far from the core of the specklepattern, we were able to also retrieve direct aperture photometry forthis planet. In all epochs, HR 8799b aperture photometry and HR8799bc negative simulated planet photometry share similar trendswithin uncertainties, except for the final temporal bin on 2018-08-18, where HR 8799c appears bright compared to HR 8799b. This is MNRAS , 1–27 (0000)
R 8799 variability Figure 22.
Our broadband- 𝐻 epoch-by-epoch photometry compared to Palomar 𝐻 -band photometry from Oppenheimer et al. (2013) and Keck 𝐻 -bandphotometry from Marois et al. (2008). likely due to uncorrected speckle noise at the radius of HR 8799c inthis temporal bin, and is recreated in simulated planet injection testsusing the satellite spots as the noise model. The fact that HR8799bcgenerally show the same trends means that they are appropriate touse to detrend each other, to search for non-shared variations.(vi) Satellite spot lightcurves share the same trends as the planetlightcurves in the August 2018 epochs, however, the planets divergesignificantly from the lightcurve trends in the October 2017 epochs.The divergence may be due to the much redder colors of the planetsrelative to the satellite spots (which should share the spectrum of thestar). This means that the satellite spot lightcurves are only appropri-ate to detrend planet lightcurves for the August 2018 epochs, not theOctober 2017 epochs.(vii) We found that the number of PCA modes removed had noreal effect on our ability to retrieve photometry for HR 8799b, but HR8799c is significantly affected by the number of modes subtracted,especially in the first and last temporal bin (also when conditions wereworst / airmasses were highest). For HR 8799c, removing 16 modes oversubtracts light from the exoplanet, but with 4 modes removed,obvious speckle noise remains in the residual images, thus we choseto subtract 10 modes as the best compromise.(viii) Considering results for HR 8799de using 3 temporal bins,these planets appear to follow satellite spot trends to within error bars,but too much speckle noise remains at these radii to meaningfullyconstrain variability to high precision.(ix) Since the satellite spot lightcurves are not appropriate todetrend planet lightcurves at all epochs, we consider Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 as a function of time during each observation – essentiallydetrending the b lightcurve using that of c, or vice versa. This tracesnon-shared variations between the two planets. We used five tempo-ral bins, to assure 20 pixels of movement on the sky for HR 8799band c, with difference lightcurves presented in Fig. 15. Within errors,our results are in agreement with those from Apai et al. (2016). Theuncertainty on the measurement is dominated by the uncertainty inour measurement of Δ ( 𝑚𝑎𝑔 ) 𝑐 . Depending on epoch, we rule out MNRAS000
Our broadband- 𝐻 epoch-by-epoch photometry compared to Palomar 𝐻 -band photometry from Oppenheimer et al. (2013) and Keck 𝐻 -bandphotometry from Marois et al. (2008). likely due to uncorrected speckle noise at the radius of HR 8799c inthis temporal bin, and is recreated in simulated planet injection testsusing the satellite spots as the noise model. The fact that HR8799bcgenerally show the same trends means that they are appropriate touse to detrend each other, to search for non-shared variations.(vi) Satellite spot lightcurves share the same trends as the planetlightcurves in the August 2018 epochs, however, the planets divergesignificantly from the lightcurve trends in the October 2017 epochs.The divergence may be due to the much redder colors of the planetsrelative to the satellite spots (which should share the spectrum of thestar). This means that the satellite spot lightcurves are only appropri-ate to detrend planet lightcurves for the August 2018 epochs, not theOctober 2017 epochs.(vii) We found that the number of PCA modes removed had noreal effect on our ability to retrieve photometry for HR 8799b, but HR8799c is significantly affected by the number of modes subtracted,especially in the first and last temporal bin (also when conditions wereworst / airmasses were highest). For HR 8799c, removing 16 modes oversubtracts light from the exoplanet, but with 4 modes removed,obvious speckle noise remains in the residual images, thus we choseto subtract 10 modes as the best compromise.(viii) Considering results for HR 8799de using 3 temporal bins,these planets appear to follow satellite spot trends to within error bars,but too much speckle noise remains at these radii to meaningfullyconstrain variability to high precision.(ix) Since the satellite spot lightcurves are not appropriate todetrend planet lightcurves at all epochs, we consider Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 as a function of time during each observation – essentiallydetrending the b lightcurve using that of c, or vice versa. This tracesnon-shared variations between the two planets. We used five tempo-ral bins, to assure 20 pixels of movement on the sky for HR 8799band c, with difference lightcurves presented in Fig. 15. Within errors,our results are in agreement with those from Apai et al. (2016). Theuncertainty on the measurement is dominated by the uncertainty inour measurement of Δ ( 𝑚𝑎𝑔 ) 𝑐 . Depending on epoch, we rule out MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure 23.
Our broadband-H epoch-by-epoch photometry compared to Apai et al. (2016). non-shared variability in Δ ( 𝑚𝑎𝑔 ) 𝑏 − Δ ( 𝑚𝑎𝑔 ) 𝑐 to the 10-20% levelover 4-5 hours.(x) To fully quantify our sensitivity to variability in the 2018-08-18 epoch (the best quality data of our search), we simulate variableand non-variable lightcurves by inserting and retrieving a suite ofsimulated planets at a similar radius from the star as HR 8799bc, butoffset in position angle from the true planet position angle. Simu-lated planets are assumed to have sinusoidal lightcurves, with noiseestimated using the mean satellite spot lightcurve. We ran a completegrid of simulated planet lightcurves with periods from 2 to 20 hours,amplitudes from 3% to 30%, and phases from 0 ◦ to 330 ◦ . For HR8799b, for periods <
10 hours, we are generally quite sensitive to vari-ability with amplitude > >
25% for similar periods. Taking intoaccount that these planets are likely observed nearly pole-on (incli-nation < ◦ ) and correcting for geometric dilution, these measuredlimits on variability amplitudes correspond to sensitivity to intrinsic variability amplitudes of 11-22% for HR 8799b, and >
55% for HR8799c for periods of <
10 hours, in the broadband H filter. (xi) We derive epoch-by-epoch astrometry and photometry, andcompare to literature values, using the data frames from the hourapproaching meridian crossing and the hour after meridian cross-ing, thus covering the time period during each observation with themost field rotation and best airmass. We again ran our full negativesimulated planet code to retrieve the best Δ mag, radius, and posi-tion angle value for each planet. Our epoch-by-epoch photometryagrees within uncertainties to literature values which employ similarnegative simulated planet subtraction techniques. Unfortunately, theuncertainties inherent in converting from relative photometry withinan epoch to Δ (mag) for an entire epoch (i.e. variability of the star,error on the brightness of the star) prevent an epoch-by-epoch searchfor variability.While 8-m telescopes with extreme AO systems have the sensitivityto detect HR 8799bc with high S/N in a reasonably small amount ofobserving time, for the inner planets, the varying speckle noise flooreffectively precluded variability studies at the required accuracy fora plausible detection. This changing speckle background is driven MNRAS , 1–27 (0000)
R 8799 variability -1.0 -0.5 0.0 0.5 1.0(J-K) Colour Anomaly020406080 I n c li na t i on ( ° ) HR8799b M08HR8799b C11Field brown dwarfsLow-g brown dwarfs
Figure 24.
Inclination vs. colour anomaly for HR 8799b as well as field and low surface gravity brown dwarfs from Vos et al. (2020). HR 8799b has been plottedassuming it shares the same 27 ◦ inclination as the HR 8799 disk(Matthews et al. 2014; Ruffio et al. 2019; Wang et al. 2018a; Konopacky et al. 2016; Pueyo et al.2015; Maire et al. 2015), however, the inclination of this planet has not been directly measured. Adopting a spectral type of L7, we calculate the colour anomaly(object 𝐽 − 𝐾 - average 𝐽 − 𝐾 for other objects with the same spectral type and gravity class) for HR 8799b using photometry from Marois et al. (2008); Currieet al. (2011) converted into the 2MASS filter set using the conversion from Stephens & Leggett (2004). The colour anomaly for HR 8799b is consistent with awide range of possible inclinations for this planet, including a nearly pole-on 27 ◦ inclination. by the fundamental instability of working from the ground; we mustcontend with light that has already traversed the atmosphere of theEarth and is only imperfectly corrected by our adaptive optics system.The limits of ground-based studies are also apparent in variabilitystudies of field brown dwarfs and isolated planetary mass objects;ground-based variability monitoring is only sensitive to variationsof > > DATA AVAILABILITY STATEMENT
The raw data underlying this article were accessed from the ESOarchive facility at http://archive.eso.org/cms.html and processed atthe SPHERE Data Centre, jointly operated by OSUG/IPAG (Greno-ble), PYTHEAS/LAM/CESAM (Marseille), OCA/Lagrange (Nice),Observatoire de Paris/LESIA (Paris), and Observatoire de Lyon. Thederived data generated in this research will be shared on reasonablerequest to the corresponding author.
ACKNOWLEDGEMENTS
We thank the anonymous referee for useful suggestions which im-proved this work. B.B acknowledges funding by the UK Scienceand Technology Facilities Council (STFC) grant no. ST/M001229/1.
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J.M.V. acknowledges support by NSF Award Number 1614527 andSpitzer Cycle 14 JPL Research Support Agreement 1627378. Sup-port for this work was provided by NASA through the NASAHubble Fellowship grant HST-HF2-51472.001-A awarded by theSpace Telescope Science Institute, which is operated by the Associa-tion of Universities for Research in Astronomy, Incorporated, underNASA contract NAS5-26555. A.Z. acknowledges support from theFONDECYT Iniciación en investigación project number 11190837Based on observations collected at the European Organisation forAstronomical Research in the Southern Hemisphere under ESOprogrammes 095.C-0689(A), 099.C-0588(A), and 0101.C-0315(A).This work has made use of the SPHERE Data Centre, jointly oper-ated by OSUG/IPAG (Grenoble), PYTHEAS/LAM/CESAM (Mar-seille), OCA/Lagrange (Nice), Observatoire de Paris/LESIA (Paris),and Observatoire de Lyon. This research made use of Astropy, acommunity-developed core Python package for Astronomy (AstropyCollaboration et al. 2013, 2018). This research made use of Photu-tils, an Astropy package for detection and photometry of astronomicalsources (Bradley et al. 2019). REFERENCES
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APPENDIX A: SATELLITE SPOT PHOTOMETRY
We present here satellite spot lightcurves for the epochs of 2017-10-07, 2017-10-12, 2017-10-13, and 2018-08-20 (Figs. A1 through A4).The satellite spot photometry for the August 2018 epochs is notablymore stable and less variable than that for the October 2017 epochs;note the smaller plot range used for the August 2018 epochs.
APPENDIX B: EFFECT OF CONDITIONS ON SATELLITESPOT PHOTOMETRY
To search for correlations in the satellite spot lightcurves as a functionof ambient conditions, we overplot the median flux in the satellitespots, measured background flux, obtained Strehl ratio and seeingfor the 2017-10-12 (average conditions) and 2018-08-18 (excellentconditions) epochs in Figs. B1 through B5. All satellite spot andbackground lightcurves have been normalized to themselves; thebackground levels are generally quite a bit lower than the flux in thesatellite spots, but here we consider variations relative to the nor-malization of the component in question. As expected, backgroundlevel is anti-correlated with the Strehl ratio; as Strehl ratio decreases,more starlight is lost from the core of the PSF and instead appearsas a higher background level. Seeing is also roughly anti-correlatedwith Strehl ratio, commensurate with the expectation of poorer adap-tive optics correction during poorer seeing conditions. Other than the2017-10-08 epoch (when, as noted previously, the satellite spots wereunder-illuminated), the satellite spot light curves do not appear to beobviously anti-correlated with the background level. However, thismay be because the AO residual background scales as (1 - Strehl ra-tio), whereas the satellite spots should scale directly with the Strehlratio. Thus, for instance, a drop in Strehl ratio from 90% to 80%would have a factor of 2 effect on the AO residual background, butonly a 10% effect on the satellite spot brightness.
APPENDIX C: SATELLITE SPOT CORRELATION PLOTS
We present additional satellite spot correlation plots. Correlationplots without the mean lightcurve removed are shown in Fig. C1and C2. Plots with the mean lightcurve removed are shown in Fig-ures C3 through C5. The goal of measuring satellite spot photometryis to eventually remove trends due to non-astrophysical variability(i.e. changes in AO correction, seeing, flexure) as well as astrophys-ical trends from the star. Thus, we measure two different types oftrends in our satellite spot data: how much the satellite spots followa monotonic function between each other (i.e. smooth trends in timedue to changes in observing conditions) – and how much inherentspread is left in the satellite spots after removing common variations.Larger trends with time in the satellite spot data shared betweenspots follow major changes in Strehl, seeing, coherence time, etc –better data, such as those from August 2018 show smaller trends overthe observation compared to data from October 2017, as conditionswere inherently more stable. Plotting satellite spots against each otherthen mostly highlights the inherent scatter in the data, as for the bestdatasets, we covered only a small range of different star spot values.This produces a smaller Spearman 𝜌 value, even though the data isof better quality.On 2018-10-18, and 2018-08-20, we find the strongest anti-correlations between adjacent satellite spots 1-4 and 2-3, weakeranti-correlations between satellite spots 1-2 and 3-4, and no or slightpositive correlation between the two opposite sets of satellite spots.On 2017-10-08, we find that adjacent satellite spots 1-4 and 2-3show relatively strong anti-correlation (but not much correlation be-tween other adjacent satellite spots). On 2017-10-12, we find anti-correlation between adjacent spots 1-2 and 3-4. On 2017-10-13,adjacent spots 1-2 and 3-4 are somewhat anti-correlated, as well asopposite spots 1-3 and 2-4. These anti-correlations are directly vis-ible in the satellite spot lightcurves in most cases, especially in theAugust 2018 data. These results differ from Apai et al. (2016), whofound a fairly constant pattern of no or weak anti-correlation betweenmost of the satellite spots, with relatively strong anti-correlations be-tween one set of directly opposite spots, and two sets of adjacentspots. However, given the small range of flux values covered in ourobservations, we do not consider these Spearman 𝜌 values to berobust. Additionally, in this study we have considered observationstaken only in a fairly narrow range of observing conditions – thus,we have not considered Spearman 𝜌 for a sufficient range of differ-ent conditions to justify strong conclusions regarding satellite spotbehavior. It would be interesting to consider correlation plots forall archival SPHERE-IRDIS sequences using satellite spots through-out the sequence, to search for overarching trends as a function ofobserving conditions. This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS000
We present additional satellite spot correlation plots. Correlationplots without the mean lightcurve removed are shown in Fig. C1and C2. Plots with the mean lightcurve removed are shown in Fig-ures C3 through C5. The goal of measuring satellite spot photometryis to eventually remove trends due to non-astrophysical variability(i.e. changes in AO correction, seeing, flexure) as well as astrophys-ical trends from the star. Thus, we measure two different types oftrends in our satellite spot data: how much the satellite spots followa monotonic function between each other (i.e. smooth trends in timedue to changes in observing conditions) – and how much inherentspread is left in the satellite spots after removing common variations.Larger trends with time in the satellite spot data shared betweenspots follow major changes in Strehl, seeing, coherence time, etc –better data, such as those from August 2018 show smaller trends overthe observation compared to data from October 2017, as conditionswere inherently more stable. Plotting satellite spots against each otherthen mostly highlights the inherent scatter in the data, as for the bestdatasets, we covered only a small range of different star spot values.This produces a smaller Spearman 𝜌 value, even though the data isof better quality.On 2018-10-18, and 2018-08-20, we find the strongest anti-correlations between adjacent satellite spots 1-4 and 2-3, weakeranti-correlations between satellite spots 1-2 and 3-4, and no or slightpositive correlation between the two opposite sets of satellite spots.On 2017-10-08, we find that adjacent satellite spots 1-4 and 2-3show relatively strong anti-correlation (but not much correlation be-tween other adjacent satellite spots). On 2017-10-12, we find anti-correlation between adjacent spots 1-2 and 3-4. On 2017-10-13,adjacent spots 1-2 and 3-4 are somewhat anti-correlated, as well asopposite spots 1-3 and 2-4. These anti-correlations are directly vis-ible in the satellite spot lightcurves in most cases, especially in theAugust 2018 data. These results differ from Apai et al. (2016), whofound a fairly constant pattern of no or weak anti-correlation betweenmost of the satellite spots, with relatively strong anti-correlations be-tween one set of directly opposite spots, and two sets of adjacentspots. However, given the small range of flux values covered in ourobservations, we do not consider these Spearman 𝜌 values to berobust. Additionally, in this study we have considered observationstaken only in a fairly narrow range of observing conditions – thus,we have not considered Spearman 𝜌 for a sufficient range of differ-ent conditions to justify strong conclusions regarding satellite spotbehavior. It would be interesting to consider correlation plots forall archival SPHERE-IRDIS sequences using satellite spots through-out the sequence, to search for overarching trends as a function ofobserving conditions. This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS000 , 1–27 (0000) B.A. Biller et al.
Date MJD at start filter set obs. length field rotation seeing airmass median Strehl DIT NEXP(UTC) of observation (hours) (degrees) (arcsec) (s)2015-07-30 57233.2178 J2/J3 4.99 83.4 0.96 1.43 - 2.04 0.83 16 9602015-07-31 57234.1999 K1/K2 5.96 90.9 1.30 1.43 - 2.54 0.69 16 11212017-10-08 58033.9927 BB-H 4.70 76.3 0.64 1.43 - 2.12 0.83 16 4762017-10-12 58038.0299 BB-H 4.50 75.8 0.60 1.43 - 2.03 0.87 16 8822017-10-13 58038.9936 BB-H 4.91 80.0 0.67 1.43 - 1.90 0.85 8 18562018-08-18 58348.1795 BB-H 4.50 73.9 0.65 1.43 - 2.02 0.89 16 8962018-08-20 58350.1367 BB-H 4.39 72.6 0.35 1.43 - 1.99 0.90 4 896
Table 1.
Log of IRDIS ObservationsEpoch Planet Δ RA (mas) Δ Dec (mas)17-10-08 HR8799b 1616.72 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 2.
Epoch-by-Epoch AstrometryMNRAS , 1–27 (0000)
R 8799 variability Epoch Planet H 𝑎𝑏𝑠 ( 𝑚𝑎𝑔 ) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 3.
Epoch-by-Epoch PhotometryEpoch b -c (mag) b - d (mag) b - e (mag)17-10-08 1.01 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 4.
Epoch-by-Epoch subtracted Photometry MNRAS000
Epoch-by-Epoch subtracted Photometry MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure A1.
Satellite spot photometry for 2017-10-07 (normalized by the median value across the whole observation for each satellite spot) as a function of timefor each satellite spot, with an offset in flux included between each satellite spot lightcurve for clarity. Results with background subtraction are shown on the tophalf of the plot, while results without background subtraction are plotted on the bottom half of the plot. The amplitudes from a 2-d gaussian fit to each satellitespot are plotted as black crosses, elliptical aperture photometry is plotted as filled circles, and elliptical aperture photometry with an additional backgroundsubtraction is plotted as filled squares. The mean of the elliptical aperture photometry for all 4 satellite spots are plotted in the middle of the figure, with magentacircles for the elliptical aperture photometry without background subtraction, and cyan square for elliptical aperture photometry with background subtraction.MNRAS , 1–27 (0000)
R 8799 variability Figure A2.
Satellite spot photometry for 2017-10-12, plot axes and labels are the same as in Fig. A1. MNRAS000
Satellite spot photometry for 2017-10-12, plot axes and labels are the same as in Fig. A1. MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure A3.
Satellite spot photometry for 2017-10-13, plot axes and labels are the same as in Fig. A1.MNRAS , 1–27 (0000)
R 8799 variability Figure A4.
Satellite spot photometry for 2018-08-20, plot axes and labels are the same as in Fig. A1. MNRAS000
Satellite spot photometry for 2018-08-20, plot axes and labels are the same as in Fig. A1. MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure B1.
Mean satellite spot photometry, background photometry, strehl ratio, and seeing vs. time for 2017-10-08.MNRAS , 1–27 (0000)
R 8799 variability Figure B2.
Mean satellite spot photometry, background photometry, strehl ratio, and seeing vs. time for 2017-10-12.MNRAS000
Mean satellite spot photometry, background photometry, strehl ratio, and seeing vs. time for 2017-10-12.MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure B3.
Mean satellite spot photometry, background photometry, strehl ratio, and seeing vs. time for 2017-10-13.MNRAS , 1–27 (0000)
R 8799 variability Figure B4.
Mean satellite spot photometry, background photometry, strehl ratio, and seeing vs. time for 2018-08-18.MNRAS000
Mean satellite spot photometry, background photometry, strehl ratio, and seeing vs. time for 2018-08-18.MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure B5.
Mean satellite spot photometry, background photometry, strehl ratio, and seeing vs. time for 2018-08-20.MNRAS , 1–27 (0000)
R 8799 variability Figure C1.
Correlation plots for satellite spots across from each other.
Figure C2.
Correlation plots for satellite spots on the sides. MNRAS000
Correlation plots for satellite spots on the sides. MNRAS000 , 1–27 (0000) B.A. Biller et al.
Figure C3.
Correlation plots for satellite spots across from each other, mean satellite spot lightcurve removed.
Figure C4.
Correlation plots for satellite spots on the sides, mean satellite spot lightcurve removed.MNRAS , 1–27 (0000)
R 8799 variability Figure C5.
Correlation plots for satellite spots on the sides, mean satellite spot lightcurve removed. MNRAS000