# Improved Orbital Constraints and H-alpha Photometric Monitoring of the
Directly Imaged Protoplanet Analog HD 142527 B

William O. Balmer William O. Balmer<EMAIL_ADDRESS>Department of Physics &
Astronomy, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD
21218, USA  Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore MD 21218, USA  Katherine B. Follette Department of Physics &
Astronomy, Amherst College, 25 East Drive, Amherst, MA 01002, USA  Laird M.
Close Steward Observatory, University of Arizona, Tucson, 933 N Cherry Ave,
Tucson, AZ 85721, USA  Jared R. Males  Steward Observatory, University of
Arizona, Tucson, 933 N Cherry Ave, Tucson, AZ 85721, USA  Robert J. De Rosa
European Southern Observatory, Alonso de Córdova 3107, Vitacura, Santiago,
Chile  Jéa I. Adams Redai Center for Astrophysics, Harvard & Smithsonian, 60
Garden Street, Cambridge, MA 02138, USA  Alex Watson  Department of Physics &
Astronomy, Amherst College, 25 East Drive, Amherst, MA 01002, USA  Alycia J.
Weinberger Earth & Planets Laboratory, Carnegie Institution for Science,
5241 Broad Branch Rd NW, Washington, DC 20015, USA  Katie M. Morzinski Steward
Observatory, University of Arizona, Tucson, 933 N Cherry Ave, Tucson, AZ
85721, USA  Julio Morales Department of Astronomy, University of
Massachusetts, Amherst, MA, 01003, USA  Kimberly Ward-Duong Department of
Astronomy, Smith College, Northampton MA 01063 USA  Laurent Pueyo Department
of Physics & Astronomy, Johns Hopkins University, 3400 N. Charles Street,
Baltimore, MD 21218, USA  Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore MD 21218, USA

(Received September 2021; Revised May 2022; Accepted May 25th, 2022)

###### Abstract

Companions embedded in the cavities of transitional circumstellar disks have
been observed to exhibit excess luminosity at H$\alpha$, an indication that
they are actively accreting. We report 5 years (2013-2018) of monitoring of
the position and H$\alpha$ excess luminosity of the embedded, accreting low-
mass stellar companion HD 142527 B from the MagAO/VisAO instrument. We use
pyklip, a python implementation of the Karhounen-Loeve Image Processing
algorithm, to detect the companion. Using pyklip forward modeling, we
constrain the relative astrometry to $1-2~{}\mathrm{mas}$ precision and
achieve sufficient photometric precision ($\pm 0.2~{}\mathrm{mag},3\%$ error)
to detect changes in the H$\alpha$ contrast of the companion over time. In
order to accurately determine the relative astrometry of the companion, we
conduct an astrometric calibration of the MagAO/VisAO camera against 20 years
of Keck/NIRC2 images of the Trapezium cluster. We demonstrate agreement of our
VisAO astrometry with other published positions for HD 142527 B, and use
orbitize! to generate a posterior distribution of orbits fit to the relative
astrometry of HD 142527 B. Our data suggest that the companion is close to
periastron passage, on an orbit significantly misinclined with respect to both
the wide circumbinary disk and the recently observed inner disk encircling HD
142527 A. We translate observed H-alpha contrasts for HD 142527 B into mass
accretion rate estimates on the order of $4-9\times
10^{-10}~{}\mathrm{M_{\odot}}\mathrm{yr}^{-1}$. Photometric variation in the
H-alpha excess of the companion suggests that the accretion rate onto the
companion is variable. This work represents a significant step towards
observing accretion-driven variability onto protoplanets, such as PDS 70 b&c.

Direct Imaging(387), Accretion (14)–Stellar accretion(1578), Star formation
(1569), Orbit determination (1175)

††journal: The Astronomical Journal††software: astropy (Astropy Collaboration
et al., 2013, 2018), emcee (Foreman-Mackey et al., 2013), photutils (Bradley
et al., 2020), ptemcee (Vousden et al., 2016), pyklip (Wang et al., 2015),
orbitize! (Blunt et al., 2020)

##  1 Introduction

As the circumstellar environment surrounding young pre-main-sequence stars
evolves, forming planets and binary companions disrupt and shape the
circumstellar disk (e.g. Williams & Cieza, 2011; Dong & Fung, 2017). Embedded
giant planets (protoplanets) and binary companions are expected to play
dramatic roles in the formation of substructures such as cavities, rings, and
spiral features within disks (e.g. Dodson-Robinson & Salyk, 2011; Bae et al.,
2018). In the past two decades, improvements in high-contrast imaging
instrumentation and post-processing techniques have revealed these
morphologically complex disks in striking detail (e.g. Tamura, 2016; Avenhaus
et al., 2018; Esposito et al., 2020; Garufi et al., 2020). Of particular
interest are so-called “transition disks” (Dodson-Robinson & Salyk, 2011;
Espaillat et al., 2014), which host a wide central cavity depleted of dust.
Gas has been observed to flow through these cavities (Casassus et al., 2013),
fueling accretion onto the central star as well as onto the planetary (e.g.
Sallum et al., 2015; Wagner et al., 2018; Haffert et al., 2019; Zhou et al.,
2021) and stellar (Close et al., 2014a) mass companions that may be
responsible for clearing them. This accretion is likely mediated by a
circumsecondary (or circumplanetary) disk, observational evidence of which is
accumulating at NIR (e.g. Lacour et al., 2016) and sub-mm (e.g. Benisty et
al., 2021) wavelengths.

Cleared central cavities and ongoing accretion make transition disks prime
targets for visible light adaptive optics imaging searches for forming
protoplanets. Accreting companions are expected to exhibit substantial
H$\alpha$ excess emission during accretion (Mordasini et al., 2017; Szulágyi &
Ercolano, 2020; Aoyama et al., 2021). This enables their detection at lower
contrasts than non-accreting objects. Taking images through H$\alpha$ and
nearby continuum filters simultaneously and subtracting them allows for
measurement of the H$\alpha$ luminosity of the accreting object through
Simultaneous-Spectral Differential Imaging (S-SDI). So far, few111Aside from
HD 142527 B, there are a total of four candidate accreting objects currently
known to orbit within transitional disk cavities. They include the (disputed)
candidate LkCa 15b: $\mathrm{M_{p}}<5-10\mathrm{M_{J}}$,
$\mathrm{M_{p}\dot{M}}\sim 10^{-6}\mathrm{M_{J}}^{2}\mathrm{yr}^{-1}$ (Sallum
et al., 2015; Currie et al., 2019), confirmed planet PDS 70 b:
$\mathrm{M_{p}}\sim 4-10\mathrm{M_{J}}$, $\mathrm{\dot{M}}\sim 5\times
10^{-7}\mathrm{M_{J}}\mathrm{yr}^{-1}$ (Keppler et al., 2018; Wagner et al.,
2018; Haffert et al., 2019; Hashimoto et al., 2020; Wang et al., 2021),
confirmed planet PDS 70 c: $\mathrm{M_{p}}\sim 4-12\mathrm{M_{J}}$,
$\mathrm{\dot{M}}\sim 1\times 10^{-8}\mathrm{M_{J}}\mathrm{yr}^{-1}$ (Haffert
et al., 2019; Wang et al., 2021), and candidate AB Aur b: $\mathrm{M_{p}}\sim
9-12\mathrm{M_{J}}$ (Currie et al., 2022). embedded, accreting companions have
been directly imaged at H$\alpha$, with recent surveys returning no new
detections (Cugno et al., 2019; Zurlo et al., 2020). This may be a low Strehl
selection effect (Close, 2020) or a reflection of differences in accretion
physics at planetary masses (Aoyama et al., 2021; Marleau et al., 2022).

##  2 HD 142527

HD 142527 is a well-studied transitional disk system at a distance of
$159.3\pm 0.7\mathrm{pc}$ (Gaia Collaboration et al., 2021). The central star,
HD 142527 A, is a young ($5.0\pm 1.5~{}\mathrm{Myr}$; Mendigutía et al., 2014)
F6III-V type Herbig Ae/Be star with an estimated mass of
$\mathrm{M_{A}}=2.0\pm 0.3~{}\mathrm{M_{\odot}}$ (Mendigutía et al., 2014). It
exhibits accretion on the order of
$10^{-7}~{}\mathrm{M_{\odot}}\mathrm{yr}^{-1}$ that is variable by at least a
factor of 7 over $\sim 5$ years (Mendigutía et al., 2014). The system has a
low extinction, ($A_{v}=0.0^{+0.05}_{-0.00}$, Fairlamb et al., 2015). The
outer disk surrounding HD 142527 A is moderately inclined
($\mathrm{i_{disk}}=28.0\pm 0.5^{\circ}$ Perez et al., 2015; Boehler et al.,
2017), hosts spiral arms in both scattered light (e.g. Fukagawa et al., 2006;
Avenhaus et al., 2014; Hunziker et al., 2021) and sub-mm gas emission (e.g.
Garg et al., 2021; Boehler et al., 2021), and exhibits an asymmetrical
‘horseshoe’ of sub-mm thermal emission (e.g. Ohashi, 2008; Boehler et al.,
2017). The central cavity of the disk is heavily depleted of dust (Avenhaus et
al., 2017) and extends to $\sim 140$au (Avenhaus et al., 2014). Gas emission
within the cavity exhibits a complex morphology, with a possible warp in the
innermost region (Casassus et al., 2013, 2015; Perez et al., 2015) and non-
Keplerian motion throughout (Garg et al., 2021).

The inner thermally-emitting disk component was first inferred by SED modeling
of NIR excess and unresolved sub-millimeter observations (Verhoeff et al.,
2011; Boehler et al., 2017). Narrow “shadow” features have been observed along
the outer disk cavity wall, suggesting that this inner disk may be inclined
with respect to the outer disk (Marino et al., 2015). Bohn et al. (2021)
provided the first resolved measurements of the inner disk using VLTI/GRAVITY
observations, which they used to investigate the mutual alignments of the
inner and outer disk components. They found that the K-band complex
visibilities of their data were best fit by an inner disk model with an
inclination of $\mathrm{i_{d,inn}}=23.76\pm 3.18^{\circ}$ and a longitude of
ascending node of $\Omega\mathrm{{}_{d,inn}}=15.44\pm 7.44^{\circ}$. Refitting
ALMA CO data to derive outer disk geometry, they found an outer disk
inclination of $\mathrm{i_{d,out}}=38.21\pm 1.38^{\circ}$ and a longitude of
ascending node of $\Omega\mathrm{{}_{d,out}}=162.72.44\pm 1.38^{\circ}$. From
these measurements they inferred that the inner and outer disks of HD142527
are statistically significantly misaligned by $59^{\circ}$. This difference in
inclination is consistent with the inner disk generating the shadows observed
in scattered light and is suggestive of dynamical disruption, namely a
companion on an inclined orbit (Facchini et al., 2018).

In 2012, a companion candidate to HD 142527 A was detected with the VLT/NACO
instrument (Lenzen et al., 2003; Rousset et al., 2003) using Sparse Aperture
Masking (SAM) at $88~{}\mathrm{mas}$ separation, with an estimated mass of
$0.1-0.4~{}\mathrm{M_{\odot}}$ (Biller et al., 2012). Subsequently, the
Magellan Adaptive Optics (MagAO) team used the Visible Light Adaptive Optics
(VisAO) instrument to confirm the companion by directly imaging HD 142527 B in
H$\alpha$ ($\Delta\mathrm{mag}=6.33\pm 0.20~{}\mathrm{mag}$) and in 643nm
continuum ($\Delta\mathrm{mag}=7.50\pm 0.25~{}\mathrm{mag}$) with a
combination of classical Angular Differential Imaging (cADI) and S-SDI
(referred to hereafter as ASDI, Close et al., 2014a). The presence of
H$\alpha$ excess in the VisAO detection indicated that the companion was
actively accreting at a rate of $\sim\mathrm{\dot{M}}=5.9\times
10^{-10}~{}\mathrm{M_{\odot}}\mathrm{yr}^{-1}$ (Close et al., 2014a).

The companion was also imaged using the Gemini Planet Imager (GPI, Macintosh
et al., 2014) in total intensity at Y-band with Angular Differential Imaging
(ADI)/ Principle Component Analysis (PCA) and polarized intensity light with
Polarized Differential Imaging (PDI) and ADI/PCA (Rodigas et al., 2014).
Interestingly, the polarized light detection was marginally spatially
inconsistent with the total intensity source by $\sim 20~{}\mathrm{mas}$ at
$2\sigma$ confidence in their reduction, which they interpret either as
scattered light from the disk around the companion, or a clump of dust
separated from the companion222It should be noted that Avenhaus et al. (2017)
do not detect a compact polarized source in their SPHERE/ZIMPOL images of the
circumprimary environment..

The companion was subsequently characterized using VLT/NACO and Gemini/GPI
SAM; it was confirmed to exhibit infrared excess indicative of a 1700K
circumsecondary environment and was found to be significantly younger ($1.0\pm
1\mathrm{Myr}$) than A (Lacour et al., 2016). Lacour et al. (2016) fit a mass
of $\mathrm{M_{B}}=0.13\pm 0.03~{}\mathrm{M_{\odot}}$ and a temperature of
$\mathrm{T_{B}}=3000\pm 100\mathrm{K}$ to the SED of the object. Using the
SPHERE/SINFONI instrument (Eisenhauer et al., 2003), Christiaens et al. (2018)
find $\mathrm{T_{B}}=3500\pm 100$ K, a spectral type of M2.5, and therefore an
age of $0.75\pm 0.25\mathrm{Myr}$ and mass of
$\mathrm{M_{B}}=0.35~{}\mathrm{M_{\odot}}$ with a recovered spectrum that is
significantly brighter than that found in Lacour et al. (2016). They do not
investigate this discrepancy333This may be due to a distance scaling error;
see discussion in Greenbaum et al. (2019)..

The SPHERE IFS and IRDIS instruments were used to examine the companion via
NIR direct imaging and SAM (Claudi et al., 2019). Their results suggest best
fit temperatures in the range of $2600-2800\mathrm{K}$, closer to those fit in
Lacour et al. (2016), and a spectral type M5-6. They also demonstrate
variability in the differential flux of B with respect to the brightness of A
on the order of half a magnitude between $1-1.6\mu$m. While this could be due
to the variability of the primary star, Claudi et al. (2019) quantified the
variability of the primary and found it was insufficient to explain the
variability in the continuum flux of HD 142527 B. They place dynamical
constraints on the mass of HD 142527 B, finding
$\mathrm{M_{B}}=0.26^{+0.16}_{-0.14}~{}\mathrm{M_{\odot}}$.

Cugno et al. (2019) observed HD 142527 B using SPHERE/ZIMPOL in H$\alpha$ with
ADI+S-SDI in a similar fashion to Close et al. (2014a). They recovered the
companion in three filters – a broad H$\alpha$ filter, a narrow H$\alpha$
filter, and a continuum filter. They confirmed H$\alpha$ excess emission from
the companion and estimated an accretion rate of
$\sim\mathrm{\dot{M}}=1-2\times
10^{-10}~{}\mathrm{M_{\odot}}\mathrm{yr}^{-1}$, marginally lower than that
derived by Close et al. (2014a).

Further study of HD 142527 B informs a number of open questions in the fields
of star and planet formation. The extreme mass ratio ($\sim 20:1$) between the
primary and secondary in this system, the fact that HD 142527 B is orbiting
within a transition disk cavity, and its ongoing accretion make the system a
higher mass analog to protoplanetary systems such as PDS 70 b&c, allowing for
the refinement of techniques used to image these systems in visible light.

The HD 1425257 system itself is also an important probe of the processes of
planet formation in binary systems. Improved orbital constraints can place
limits on the mutual inclinations between the HD 142527 AB binary orbit and
the inner and outer disk segments (Czekala et al., 2019). Recent VLTI/GRAVITY
observations of the inner disk are especially important to consider, as it is
likely that HD 142527 B is responsible for the inclination of the misinclined
inner disk. Orbit fits to the HD 142527 binary allow mutual inclinations of
all three components of the system (the inner disk, binary, and outer disk) to
be determined and compared to hydrodynamical models.

The nature of the HD 142527 B companion itself is also broadly informative of
star and planet formation processes, as its young age relative to HD 142527 A
might indicate that it formed from the disk via disk instability. It could
also be that HD 142527 B formed at the lower end of the IMF, was dynamically
captured, and is disrupting planet formation around HD 142527 A. In either
scenario, its motion necessarily drives the dynamical evolution of the disk
(e.g. Aly et al., 2021).

Observations of the companion to date have only covered a $60-70^{\circ}$
orbital arc. The nature of HD 142527 B’s orbit and its relationship to both
the wide observed cavity in the circumbinary disk and the inner circumprimary
disk is still an area of ongoing study that can be improved by further
constraining the orbital elements, particularly the eccentricity and
inclination of the binary orbit and the mutual inclinations of the various
components. Until the orbit is very well characterized, it cannot be certain
whether the companion can be held solely responsible for the massive cavity.

Additionally, relatively little is known about the density and dynamics of gas
flow through transitional disk cavities or the reprocessing of material in
circumsecondary accretion disks. Accretion rates and epoch-to-epoch variations
in accretion rate can inform accretion processes for companions in these
actively planet-forming systems.

In this work, we build upon previous detections of H$\alpha$ excess emission
from HD 142527 B. We monitor the companion’s astrometric motion in visible
light and provide the most complete orbital solution to date, enabling a more
precise comparison between the mutual inclinations of system components. We
leverage additional epochs of observation at H$\alpha$ to argue that the
accretion onto the companion is likely variable on (at least) yearly
timescales.

##  3 Observations & Data Reduction

###  3.1 VisAO observations

We observed HD 142527 with the Magellan Adaptive Optics (Close et al., 2013;
Morzinski et al., 2016) VisAO (Males et al., 2014) instrument in H$\alpha$ SDI
mode (Close et al., 2014b) on 7 nights between 2013 and 2018. Table 1 records
general information about the VisAO observations of HD 142527. During
observations, the telescope rotator was turned off, resulting in rotation of
the FOV, which enables ADI. More field rotation allows for more reference
images to be used in constructing the PSF model, improving its quality; this
is especially important for tightly-separated companions like HD 142527 B. The
total field rotation for each observation is noted in Table 1. HD 142527 A was
dithered across the CCD throughout the observing night to mitigate the effects
of near-focus dust spots in the images. MagAO uses a Natural Guide Star (NGS)
to conduct wavefront corrections, and in all datasets the NGS used was the on-
axis science target, HD 142527 A. The SDI observing mode splits the incoming
light using a Wollaston beamsplitter, and results in simultaneous continuum
($\lambda_{c}=656\mathrm{nm}$, $\Delta\lambda=6.32\mathrm{nm}$) and H$\alpha$
($\lambda_{c}=643\mathrm{nm}$, $\Delta\lambda=6.20\mathrm{nm}$) images
($512\times 1024$ pixels in size) on the top and bottom of the CCD,
respectively.

We conducted a revised calibration of the absolute astrometric solution for
the VisAO instrument, which is documented in detail in Appendix A. We
determined an updated platescale and North Angle offset by tying observations
of the $\theta^{1}$ Ori B multiple system over 6 years to observations of the
same system taken over 20 years with the precisely astrometrically calibrated
Keck/NIRC2 instrument (Yelda et al., 2010; Service et al., 2016). The updated
VisAO platescale is $7.95\pm 0.010~{}\mathrm{mas}$ $\mathrm{pix}^{-1}$ and the
updated North Angle offset is $0.497\pm 0.192^{\circ}$ counterclockwise. This
new solution does not necessitate a revision of previously published results,
as both values agree with previous calibrations within errorbars (Close et
al., 2013; Males et al., 2014). However, the updated calibration improves the
accuracy of VisAO astrometry, and validates the stability of the North Angle
offset between instrument mountings, which occur every semester.

Table 1: VisAO observations of HD 142527

Date | $\mathrm{N_{ims}}$ | Exposure | Total integration | Total rotation | FWHM | Saturation radius | Avg. Seeing | Stellar H$\alpha$/Cont.
---|---|---|---|---|---|---|---|---
(YY/MM/DD) |  | (s) | (m) | (∘) | (mas) | (pix) | (”) |
2013-04-11 | 1961 | 2.27 | 74.2 | 65.3 | 25.0 |  $\cdots$ |  $\cdots$ | $0.83\pm 0.03$
2014-04-08 | 1758 | 2.27 | 66.5 | 101.7 | 38.9 |  $\cdots$ |  $\cdots$ | $1.11\pm 0.10$
2015-05-15 | 2387 | 2.27 | 90.3 | 117.4 | 37.8 |  $\cdots$ | 0.55 | $1.19\pm 0.23$
2015-05-16 | 1143 | 2.27 | 43.2 | 34.8 | 33.8 | 2 | 0.80 | $1.17\pm 0.07$
2015-05-18 | 159 | 30 | 79.5 | 76.8 | 30.7 | 9 | 0.66 | $1.16\pm 0.08$
2017-02-02 | 242 | 12 | 48.4 | 16.1 | 43.7 | 2 | 0.72 | $1.13\pm 0.02$
2018-04-27 | 580 | 5 | 48.3 | 49.2 | 28.5 | 3 |  $\cdots$ | $1.31\pm 0.10$

Note. — The average seeing was determined by measurements taken from the DIMM,
Magellan Baade, or both (in which case the two are averaged). For datasets
where no external seeing information exists, the column is left blank. The
stellar H$\alpha/$Cont. ratios are calculated by performing aperture
photometry on every image in both wavelengths for each dataset. We extract
photometry from the central star in the case of unsaturated datasets and from
the instrumental ghost in the case of saturated data. We report the median
ratio for each dataset in the table above. A ratio $<1$ indicates a relatively
quiescent phase in the accretion onto the primary.

###  3.2 Preprocessing

VisAO data were reduced and preprocessed with the GAPlanetS data reduction
pipleline described in detail in Follette et al. (2017) and Follette et al.
(2022, in prep.). In short, images were dark subtracted, flat fielded (except
for the 2013-04-11 dataset, for which no flatfields exist), split between
H$\alpha$ and continuum channels, and registered using a Fourier cross-
correlation algorithm, which yields errors on the position of the central star
of $\sim 0.1\mathrm{pix}$ (Follette et al. 2022, in prep.).

In half of our observations (3 of 7, see Table 1), the central star was
allowed to saturate in order to improve SNRs in the search for additional
companions within the system. A stable instrumental ghost appears in VisAO
images to the right of the natural guide star (NGS). We investigated the
stability of the ghost as a photometric and astrometric calibrator for
saturated data, and found it to be suitable for both purposes (see Appendix
B).

Following alignment, images with cosmic rays within $50\mathrm{pix}$ ($\approx
0\farcs 04$) of the central star were rejected by hand. Images were then
cropped to a 451 pixel ($\sim$3$\farcs$5) square surrounding the central star.

We then measured the “H$\alpha$ scale factor” by conducting aperture
photometry on the central star (or ghost, for saturated images) for each image
in the sequence. We adopt the median of the ratios between the H$\alpha$ flux
and the continuum flux for each image in the sequence as the best estimate of
the scale factor ($F_{*,H\alpha}/F_{*,Cont}$), and the standard deviation as
the uncertainty, and these values are recorded in Table 1. This scale factor
is an estimate of the H$\alpha$ excess of the primary star, and allows us to
quantify the accretion variability of the host star itself and to correct for
the effect of stellar accretion on measured contrasts for the companion (see
Section 5).

###  3.3 PSF Subtraction

Figure 1: Gallery of post-KLIP images showing the detections of HD 142527 B in
H$\alpha$ (top) and continuum (bottom). The colorbar normalized to the peak
pixel value of the companion in each image. The cyan circle indicates the
nearest in time position of HD 142527 B reported in previous literature
(Lacour et al., 2016; Claudi et al., 2019). The cyan star indicates the
position of HD 142527 A. The innermost pixels have been masked to $r\sim
1\times$FWHM for each dataset.

We conducted PSF subtraction using the python implementation of Karhunen-Loeve
Image Processing, pyklip444https://pyklip.readthedocs.io (Wang et al., 2015).
The pyklip input parameters movement, annuli, and numbasis were chosen based
on the optimization techniques described in Adams Redai et al. (2022, in prep)
as developed for the the Giant Accreting Protoplanets Survey (Follette et al.
2022, in prep). In brief, the pyklip movement parameter is an exclusion
parameter that removes images from the reference library in which a companion
at a given separation from the star would have shifted (rotated with the sky)
by fewer than the specified number of pixels relative to the image for which
the PSF model is being constructed. The annuli parameter describes the size of
annular zones that pyklip treats separately, where the width of the annulus is
$\Delta r=(\mathrm{OWA-IWA})/\texttt{annuli}$. Generically, the inner edge of
each annulus is defined as $r_{in}=\textrm{IWA}+\Delta r\times n$, but for HD
142527 B, the companion always lies within the inner annulus, so n=1 and
$r_{in}=IWA$, while $r_{out}=IWA+\Delta r$. Our images are non-coronagraphic,
so do not have a hardware-determined inner working angle. However, we found
that applying one in software generally improves our detections and we have
adopted a fixed value of $1\times\mathrm{FWHM}$ here. The numbasis parameter
controls the number of principle components, or KL modes, included in the
constructed PSF. We chose to fix the maximum number of KL basis vectors used
to construct the PSF at 100 and applied a pre-KLIP highpass filter of
$1\times\mathrm{FWHM}$ in all analyses to match the broader GAPlanetS Survey
strategy.

We refer the reader to Adams Redai et al. (2022, in prep) for additional
information on the optimization of pyklip parameters for GAPlanetS data. To
briefly summarize the optimization method used here, we:

  1. 1.

conduct a grid search in pyKLIP’s movement, annuli, and numbasis (KL mode)
parameters and generate KLIP images for each combination

  2. 2.

compute six “image quality metrics” for each movement, annuli, and numbasis
combination. These metrics are: peak SNR of the companion(s), average SNR of
the companion(s), the “neighbor quality” of the previous two metrics (computed
by smoothing their metric maps), false positive ($>$5$\sigma$) pixels, and
contrast, normalized so that their best (highest for SNRs, lowest for contrast
and false positive pixels) values are 1.

  3. 3.

Sum or average across a desired choice of metrics, companion(s), and KL modes
to select “optimal” values for each of the three KLIP parameters.

For this work, the target of the optimization for most datasets were “false
planets” inserted into into the continuum images. In these datasets, we
optimized on the sum of all 6 normalized image quality metrics averaged
between 5 and 20 KL modes and across 4 to 8 false planets (as many as would
fit with a radial spacing of 0.5$\times$FWHM and an azimuthal spacing of 85o
between the IWA and control radius of each dataset) to select the optimal
movement and annuli parameters. We then selected a single optimal numbasis
value by maximizing the sum of the 6 normalized metrics for the optimal
combination of annuli and movement. The optimal values for all three
parameters are reported in Table 2.

Although the companion is recovered in all epochs using this parameter
selection method, which optimizes for robust recovery of companions throughout
the region between the IWA and control radius, it’s not necessarily the best
choice of parameters for the specific location of the companion. In the case
of a robust known companion like HD 1425257 B, optimization can also be done
on the location of the companion itself in H$\alpha$ images, and we utilize
this method to achieve higher SNR recoveries of the companion in the May 16,
2015 and April 27, 2018 datasets. For these epochs, we optimize on the sum of
the peak and average SNR metrics for the companion, and select the annuli,
movement, and numbasis parameters that maximize this sum. Since each epoch of
VisAO data for HD 142527 B has a corresponding near-in-time NIR detection, we
optimized the KLIP parameters on the known NIR location of the companion.
Contrast curves and limits on additional companions in the HD 142527 cavity
appear in the upcoming GAPlanetS survey paper, Follette et al. (2022, in
prep).

Table 2: Adopted pyklip starlight subtraction parameters Date | Movement | Annuli | KL mode
---|---|---|---
2013-04-11 | 1 | 14 | 20
2014-04-08 | 1 | 25 | 100
2015-05-15 | 2 | 20 | 20
2015-05-16 | 12 | 1 | 12
2015-05-18 | 7 | 2 | 5
2018-04-27 | 1 | 25 | 20

##  4 Results

Using pyklip, we detect the companion in both filters in all epochs of
observation except 2017-02-02, where the total field rotation was too small
($16.1^{\circ}$) to achieve the necessary contrast to detect the very tightly
separated companion555At the expected separation in this epoch (50mas, Claudi
et al., 2019), the highest contrast observable within this dataset was
$0.5\times 10^{-2}$, whereas our brightest detection of HD 142527 B across all
epochs was at a contrast of $0.3\times 10^{-2}$.. As expected, the
observations with the greatest total field rotation (2015-05-15) and best
atmospheric quality (2013-04-11) yielded the highest SNR recoveries of the
companion. Figure 1 shows each recovery in H$\alpha$ and continuum. We
quantify the quality of each recovery using the forward modeling capabilities
of pyKLIP.

###  4.1 Bayesian Forward Modeling

To determine the astrometry of the imaged companion, we implement KLIP forward
modeling (Pueyo, 2016) and conduct Bayesian Klip Astrometry (BKA, Wang et al.,
2016). This technique involves the projection of a companion PSF estimate onto
the basis vectors used to construct the primary KLIP PSF model to synthesize a
forward-modeled PSF. This forward-model is fit to the post-KLIP data using an
affine-invariant MCMC with emcee (Foreman-Mackey et al., 2013). This produces
a posterior distribution of model fits that yields robust uncertainties on
astrometry and photometry. We take the median of the posterior distribution of
a given parameter as its measured value and the 16th and 84th percentiles as
uncertainties on that median. The strength of KLIP forward modeling when
compared to negative planet injection grid searches is the speed and precision
of model fitting and convergence, which enables the application of a Bayesian
analysis framework as well as the capability to model correlated noise within
the images using a gaussian process.

For unsaturated data, we find that using a 2D Gaussian PSF with the FWHM of
the median stellar PSF produces excellent forward model fits (see discussion
in Appendix B).

For saturated datasets, we do not have a direct measure of the stellar FWHM.
In Appendix B, we investigate the suitability of a range of forward models in
extracting astrometry and photometry for the tight HD42527B companion in
saturated datasets. In short, we find that the ghost is suitable as a
photometric calibrator (see Appendix B), and determine that the ratio of the
peak value of a Moffat fit to the ghost to the peak value of a Moffat fit to
the unsaturated NGS PSF in unsaturated data is a stable quantity. We also find
that the ghost is slightly out of focus, and that its FWHM is $\sim 7\%$ wider
than the stellar FWHM in unsaturated datasets. This result matches our
expectations: as the ghost is produced by a reflection off of the MagAO 50/50
beamsplitter, it has a longer path than the 0th order source, and is therefore
slightly out of focus. We assume that both the star-to-ghost brightness
scaling and the FWHM discrepancy holds in the case where the NGS is saturated,
and estimate the FWHM of our saturated datasets by taking
$0.93\times\mathrm{FWHM_{ghost}}$. We find that the optimal forward model for
saturated data is a Gaussian PSF whose FWHM was set to the
$0.93\times\mathrm{FWHM_{ghost}}$ to match the expected FWHM of the image
plane PSF.

In order to further quantify the strength of our detections, we utilize the
PlanetEvidence class (Golomb et al., 2019) within pyklip to conduct a Bayesian
model comparison and determine the SNR of HD 142527 B for a given detection.
PlanetEvidence uses the nested sampling implementation pyMultiNest (Buchner et
al., 2014; Feroz et al., 2009) to compare two models: $\mathrm{H_{0}}$, where
the image contains only speckle noise, and $\mathrm{H_{1}}$, where the image
contains a source at the position of HD 142527 B. PlanetEvidence returns
marginal distributions of the parameters for the source and null cases, and
calculates the SNR of the detection within the fitting region and the evidence
values for $\mathrm{H_{0}}$ and $\mathrm{H_{1}}$ ($\mathrm{Z_{0}}$ and
$\mathrm{Z_{1}}$). The log-ratio of these evidence values,
$\log{B_{10}}=\log{Z_{1}/Z_{0}}$, enables us to quantify the confidence with
which one model can be favored over the other.666See Golomb et al. (2019) for
definitions of the evidence values, discussion of log-ratios, and an example
involving quantifying the detection of $\beta$ Pictoris b. This framework
provides a more robust estimate of the quality of the detection, better
capturing asymmetric speckle noise that can dominate at very close separations
than SNR computed within an annulus. The SNR values reported in Table 4 are
calculated from the residuals within the fitting region as described in Golomb
et al. (2019).

For example, values for $\log{B_{10}}>5$ are considered “strong” evidence
against the null hypothesis. We achieved strong evidence ($\log{B_{10}}>10$)
in all cases, and unambiguous detections ($\log{B_{10}}>20$) in eleven out of
tweleve datasets. While the evidence is not strong for the detection in the
continuum for the 2018-04-27 epoch, the search for the companion in this epoch
is not a “blind” search. We can be reasonably certain that signal at this
location is due to the real companion due to the near-in-time observations in
the NIR (Claudi et al., 2019). Nevertheless, the continuum detection in 2018
should be approached with some skepticism.

###  4.2 Forward Model Results

Our Bayesian forward modeling returns posterior distributions of the x and y
positions (in pixels) of the fit model, a flux scaling parameter $\alpha$, and
a length scale $l$ of correlated noise within the image. We transform $\alpha$
into contrast by multiplying it by a constant $10^{-2}$ (a pyklip input term
setting the initial contrast of the forward model) and by the peak counts of
the forward model (which in our case is 1 as the PSF model is normalized
before it is passed to pyklip).

We calculate the astrometry given in Table 3 by applying the updated
platescale and north angle offset (described in detail in Appendix A) to the
separation and position angle measurements of the companion from the posterior
distributions of forward model fits. We propagate $0.1\mathrm{pix}$
uncertainties on the position of the host star from the image registration
process, $1\sigma$ uncertainties on the position of the companion from the
posterior distribution of forward model fits, and estimated uncertainties on
our absolute astrometry (see Appendix A for details) into our calculations to
obtain final uncertainty estimates on separation and PA measurements for the
companion.

Figure 2: Representative pyklip forward model fits for HD 142527 B. Shown are the 2013-04-11 H$\alpha$ (top row) and continuum (bottom row) detections. Based on the PlanetEvidence analysis, the evidence ratios $\log{Z_{1}/Z_{0}}$ are 266.30 and 75.89 in H$\alpha$ and continuum, respectively. Both are considered extremely strong evidence in favor of the existence of the companion at this location. Table 3: Results of Forward Model fitting and companion SNR  Date | Separation | PA | $\Delta\mathrm{mag}$ | $\log{Z_{1}/Z_{0}}$ | SNR
---|---|---|---|---|---
(DD/MM/YY) | (mas) | (∘) | (mag) |  |
Continuum |  |  |  |  |
2013-04-11 | $82.74\pm 1.51$ | $128.07\pm 0.68$ | $7.3\pm 0.2$ | 75.89 | 5.24
2014-04-08 | $78.25\pm 3.39$ | $116.00\pm 2.45$ | $7.2\pm 0.3$ | 22.33 | 5.82
2015-05-15 | $70.63\pm 1.95$ | $112.28\pm 1.38$ | $7.4\pm 0.2$ | 22.77 | 7.85
2015-05-16 | $70.59\pm 4.36$ | $107.33\pm 2.10$ | $7.4\pm 0.3$ | 37.14 | 5.37
2015-05-18 | $73.70\pm 3.92$ | $110.97\pm 2.24$ | $7.3\pm 0.3$ | 77.43 | 5.98
2018-04-27 | $42.75\pm 3.22$ | $58.53\pm 2.95$ | $7.3\pm 0.4$ | 13.55 | 2.64
H$\alpha$ |  |  |  |  |
2013-04-11 | $82.30\pm 1.36$ | $127.91\pm 0.61$ | $6.29\pm 0.13$ | 266.30 | 10.53
2014-04-08 | $77.57\pm 1.86$ | $118.21\pm 1.04$ | $6.59\pm 0.17$ | 32.67 | 8.02
2015-05-15 | $69.89\pm 1.50$ | $109.68\pm 0.98$ | $6.88\pm 0.16$ | 51.26 | 12.03
2015-05-16 | $72.64\pm 2.29$ | $107.98\pm 1.09$ | $6.73\pm 0.19$ | 75.94 | 8.11
2015-05-18 | $69.96\pm 1.36$ | $110.02\pm 0.76$ | $7.11\pm 0.16$ | 131.84 | 7.90
2018-04-27 | $44.29\pm 2.57$ | $58.14\pm 2.20$ | $6.9\pm 0.3$ | 24.31 | 3.47

We determine the H$\alpha$ contrast of the companion relative to the primary
star reported in Table 3 as follows. First, we take the median and standard
deviation on the forward model fit to the contrast ($C_{B-A}$) as the derived
value and uncertainty, respectively. For the continuum filter, this value can
be converted to a contrast in magnitudes via a simple magnitude
transformation, namely $\Delta\mathrm{mag}=-2.5\log{\mathrm{C_{B-A}}}$.
However, at H$\alpha$, the star itself is actively accreting, influencing the
H$\alpha$ contrast extracted from BKA. In order to measure the H$\alpha$
contrast of the companion with respect to the stellar continuum, we multiply
the BKA-derived contrast of the companion at H$\alpha$
($F_{comp,H\alpha}/F_{*,H\alpha}$) by the stellar H$\alpha$ to continuum scale
factor for the observations ($F_{*,H\alpha}/F_{*,Cont}$, determined as
described in Section 3 and given in Table 1). This leaves us with the contrast
of the companion at H$\alpha$ relative to the stellar continuum
($F_{comp,H\alpha}/F_{*,Cont}$) and allows us to compare the brightness of the
companion at H$\alpha$ over time without being influenced by stellar H$\alpha$
variability. We propagate errors on the BKA-derived contrast and scale factor
through the logarithmic transformation to magnitude.

Table 3 records the results of our forward model fits to the astrometry and
photometry of continuum and H$\alpha$ images for each epoch. Figure 2
illustrates a representative model fit and residuals for the 2013-04-11
dataset, and galleries of forward model fits to other epochs can be found in
Appendix C.

##  5 Analysis & Discussion

We calculate the separation and PA of the companion on each night of
observation as the weighted mean of the x and y positions in the H$\alpha$ and
continuum filters, where the weights are the uncertainties in each filter
(calculated as described in Section 4). The final uncertainty on the H$\alpha$
and continuum averaged position is then the square root of the sum of the
uncertainties on the individual measurements. Table 4 records the final VisAO
astrometry together with previous astrometry from the literature, and these
positions are plotted in Figure 3.

Figure 3: Astrometric measurements of HD 142527 B relative to HD 142527 A
(black star) from NACO, GPI, SPHERE, SINFONI, and VisAO (this work) between
2012 and 2018. The crosses represent the reported uncertainties on each
measurement. The companion experiences significant orbital motion
($\Delta\theta\approx 65^{\circ}$) and decreases substantially in separation
($\Delta\rho\approx 30~{}\mathrm{mas}$) from 2016 to 2018. The VisAO values
(yellow circles) agree well with astrometry from other instruments. Error bars
on our measurements reflect the 1-2mas accuracy achievable using pyklip
forward modeling. Table 4: HD 142527 B astrometry

Date | Separation | Position Angle | Instrument | Source
---|---|---|---|---
(DD/MM/YY) | (mas) | (∘) |  |
2012/3/11 | $89.70\pm 2.60$ | $133.10\pm 1.90$ | NACO | B12
2013/3/17 | $82.00\pm 2.10$ | $126.30\pm 1.60$ | NACO | L16
2013/4/11 | $82.50\pm 1.01$ | $127.98\pm 0.46$ | VisAO | This work
2013/7/14 | $82.50\pm 1.10$ | $123.80\pm 1.20$ | NACO | L16
2014/4/8 | $77.73\pm 1.63$ | $117.87\pm 0.96$ | VisAO | This work
2014/4/25 | $88.10\pm 10.10$ | $123.00\pm 9.20$ | GPI | R14
2014/5/10 | $78.00\pm 1.80$ | $119.10\pm 1.00$ | SINFONI | Ch18
2014/5/12 | $77.20\pm 0.60$ | $116.60\pm 0.50$ | GPI | L16
2015/5/13 | $69.00\pm 2.00$ | $110.20\pm 0.50$ | IFS/IRDIS | Cl19
2015/5/15 | $70.16\pm 1.19$ | $110.56\pm 0.80$ | VisAO | This work
2015/5/16 | $72.19\pm 2.02$ | $107.84\pm 0.97$ | VisAO | This work
2015/5/18 | $70.00\pm 1.35$ | $110.12\pm 0.72$ | VisAO | This work
2015/7/3 | $65.50\pm 0.40$ | $106.20\pm 0.40$ | IFS/IRDIS | Cl19
2016/3/26 | $60.00\pm 2.00$ | $97.10\pm 0.50$ | IFS/IRDIS | Cl19
2016/3/31 | $62.80\pm 2.70$ | $98.70\pm 1.80$ | ZIMPOL | Cu19
2016/6/13 | $61.00\pm 2.00$ | $96.30\pm 0.50$ | IFS/IRDIS | Cl19
2017/5/16 | $48.50\pm 0.50$ | $77.80\pm 0.20$ | IFS/IRDIS | Cl19
2018/4/14 | $44.00\pm 1.00$ | $55.40\pm 0.40$ | IFS/IRDIS | Cl19
2018/4/27 | $43.69\pm 2.01$ | $58.28\pm 1.76$ | VisAO | This work

Note. — Sources for the listed astrometry in order of appearance are B12 =
Biller et al., L16=Lacour et al., R14=Rodigas et al., Ch18=Christiaens et al.,
Cl19=Claudi et al., Cu19=Cugno et al..

###  5.1 Orbit Fitting

By combining our derived astrometry with compiled results from the literature,
we compute orbits fit to the motion of HD 142527 B with orbitize! (Blunt et
al., 2020), an open-source python package that performs Bayesian orbit fitting
for directly imaged companions777https://orbitize.info. We use the parallel
tempered (Vousden et al., 2016) affine-invariant (Foreman-Mackey et al., 2013)
MCMC sampler in orbitize!, in order to determine the posterior probabilities
for 8 orbital parameters: semi-major axis ($a$), eccentricity ($e$),
inclination angle ($i$), argument of periastron of the companion’s orbit
($\omega$), longitude of ascending node ($\Omega$), epoch of periastron
passage ($\tau$), system parallax ($\pi$), and total mass of the binary system
($\mathrm{M_{tot}}$).

We assume default orbitize! priors except on the total mass of the system and
the system parallax. We set a Gaussian prior on the system parallax,
$\mathcal{N}(\mu=6.356,\,\sigma=0.047)$, following the measured Gaia eDR3
parallax (Gaia Collaboration et al., 2021). We adopt a Gaussian prior on the
total system mass ($\mathrm{M_{tot}}$) of
$\mathcal{N}(\mu=2.3~{}\mathrm{M_{\odot}},\,\sigma=0.3~{}\mathrm{M_{\odot}})$
based on the results of Mendigutía et al. (2014) and Claudi et al. (2019). We
refer the reader to Blunt et al. (2020) for information about orbitize!
default priors, as well as more detailed descriptions of the variables
involved in the orbital solution. Posterior distributions are computed by
first initializing an MCMC with 50 walkers and 20 temperatures for a 100,000
step burn-in phase per walker; the walker samples are discarded before a total
of 5,000,000 additional samples are recorded to approximate the posterior.

Table 5 records our estimates of the orbital elements for HD 142527 B. Figure
4 shows 100 randomly drawn orbits from our posterior distribution of orbit
fits overplotted on the astrometry compiled in Table 4. The full corner plot
visualizing the posterior distributions of all eight orbital parameters
(Figure 14) can be found in Appendix D. Our additional VisAO astrometry
provides marginally tighter constraints relative to previous orbital
solutions. We note, however, that our MCMC approach is likely more robust
under poorly-constrained posterior distributions than previous Least Squares
Monte Carlo approaches (See discussion in §2.3.2 of Blunt et al., 2020).

Figure 4: 100 randomly drawn orbitize! orbits fit to the motion of HD 142527
B. Astrometry from Figure 3 is overplotted. Left: the orbits projected in RA
and Dec, relative to HD 142527 A (black star). Right: the orbits in
separation/position angle versus time. The new VisAO astrometry does not add
new coverage of the orbital arc, but the 2018 recovery adds more weight to the
near-in-time SPHERE NRM astrometry.

Our orbitize! orbit fitting yields well-converged unimodal distributions in
all parameters except $\omega$ and $\Omega$, which show bimodal distributions
with peaks spaced $180^{\circ}$ apart. This a known degeneracy in visual
orbits with a lack of RV constraints888HD 142527 A is a pre-main-sequence F
type star, which makes RV measurements particularly challenging. RV
measurements for the system have been included in large pipeline surveys, such
as the HARPS-RVBANK, but we choose not to consider these RVs for our orbital
fitting, because they are likely dominated by stellar jitter which is outside
of the scope of this paper to treat properly.. To avoid confusion, we report
values of the first ($0-180^{\circ}$) modes of $\omega$ and $\Omega$ in Table
5, noting that solutions with values 180∘ higher are equally likely.

Previous orbital solutions to the motion of HD 142527 B have have shown it to
be both inclined ($\mathrm{i}\sim 125\pm 5^{\circ}$ Lacour et al., 2016) and
eccentric ($\mathrm{e}>$0.2 Lacour et al., 2016; Claudi et al., 2019). Our
unimodal eccentricity distribution ($\mathrm{e}=0.24\pm 0.15$) agrees with the
first family of eccentricities fit by Claudi et al. (2019) ($\mathrm{e}\sim
0.2-0.45)$; we do not reproduce their additional family of eccentricities
($\mathrm{e}\sim 0.45-0.7$). This could be due to the increased weight our
additional astrometry places on the position of the companion in 2018, or due
to differences in the exploration of parameter space between the LSMC and MCMC
frameworks. We further constrain the system inclination to $\mathrm{i}=126\pm
2^{\circ}$.

The longitude of ascending node ($\Omega$) and time of periastron passage of
an orbit are more difficult to constrain with limited azimuthal coverage.
Claudi et al. (2019) placed constraints of $124-135^{\circ}$ and 2020–2022 on
these values. Our value of time of periastron passage,
$2021.07^{+0.82}_{-0.72}$ agrees with their estimate within errorbars, but our
refined $\Omega=142.38^{+5.51}_{-6.12}$ marginally disagrees; our solutions
preferring a somewhat higher value. According to our orbital fits, periastron
passage has likely already occurred for HD 142527 B.

HD 142527 B’s orbit is interesting in the context of star and planet formation
in that its eccentricity might indicate a stellar formation history. Directly
imaged brown dwarf companions have been found to have a distribution of
eccentricities that favor higher values when compared to directly imaged
planets (Bowler et al., 2020), suggesting that they form independent of the
system and are captured, rather than arising from within the circumplanetary
disk. HD 142527 may therefore be more analogous to objects like GQ Lup B (Wu
et al., 2017; Stolker et al., 2021), a captured, accreting Very Low Mass
object that is dynamically truncating/disrupting its circumprimary
environment, than to accreting protoplanets.

Table 5: HD 142572B Orbital Elements a (au) | $14.71^{+8.18}_{-2.33}$
---|---
e | $0.28^{+0.22}_{-0.10}$
i $(^{\circ})$ | $126.27^{+2.13}_{-2.28}$
$\omega(^{\circ})$ | $86.02^{+52.31}_{-42.59}$
$\Omega(^{\circ})$ | $142.38^{+5.51}_{-6.12}$
Time of periastron passage (yr) | $2021.07^{+0.82}_{-0.72}$
$\mathrm{M_{total}}(M_{\odot})$ | $2.49^{+0.27}_{-0.27}$
Parallax (mas) | $6.36\pm 0.05$
$\theta_{in-\star}(^{\circ})$ | $56.55^{+2.93}_{-2.79},66.38^{+1.84}_{-1.36}$
$\theta_{\star-out}(^{\circ})$ | $45.87^{+2.05}_{-1.53},76.49^{+2.66}_{-2.72}$

###  5.2 Mutual Inclinations

Figure 5: The orbit of HD 142527 B in context. The position of HD 142527 A is
marked with a cyan star, and 250 randomly drawn orbits from fits to the
astrometry of HD 142527 B are plotted with colors corresponding to their
mutual inclination with the outer disk ($\theta_{\star-out}$). The outer image
of the circumbinary disk is a Gemini/GPI scattered light polarized intensity
H-band image reprocessed with an updated GPI pipeline and interpolated to
VisAO’s platescale. The inner image is the post-KLIP 2015/05/15 H$\alpha$
detection from VisAO (also shown in Figure 1). Both images are normalized to
their respective maximum pixel values before combination.

In order to contextualize our results within the broader HD142527 system
architecture, Figure 5 superimposes (a) 50 randomly drawn orbits from the
posterior distribution of orbit fits, (b) a single epoch VisAO detection of
the H$\alpha$ point source, and (c) an H-band polarized intensity observation
of the HD142527 outer disk. The image of the circumbinary disk was obtained by
re-reducing GPI polarimetric data first published in Rodigas et al. (2014)
using the updated GPI DRP described in De Rosa et al. (2020); these data were
then interpolated to VisAO’s platescale to facilitate comparison with VisAO
observations of the companion (shown for all epochs in Figure 1).

The “mutual inclination” between the orbit of a binary star and its
circumbinary disk is expected to inform the evolution of the circumbinary and
circumstellar environments, and has wide-ranging implications for planet
formation in binary systems (Czekala et al., 2019). While external binary
companions may significantly truncate a circumstellar disk, perhaps
suppressing planet occurrence (Kraus et al., 2016), circumbinary disks around
tighter binary systems result in circumbinary planets (e.g. Kostov et al.,
2020, 2021). The HD 142527 system is interesting to consider in this context
because it is one of a handful of systems with direct imaging measurements of
both inner and outer disk components as well as the binary orbit.

The mutual inclination between the disk plane and binary orbit, $\theta$, is
defined as

$\displaystyle\cos{\theta}=\cos{i_{\mathrm{d}}}\cos{i_{\star}}+\sin{i_{\mathrm{d}}}\sin{i_{\star}}\cos{\left(\Omega_{\mathrm{d}}-\Omega_{\star}\right)},$

where $\theta$ is the angle between the angular momentum vector of the binary
orbit and the midplane of the disk (Czekala et al., 2019).

We determine the posterior distribution of mutual inclinations between the
binary orbit and both the inner and outer disk components (shown in Figure 15)
by drawing random samples from the posterior distribution of $i_{\star}$ and
$\Omega_{\star}$ produced by orbitize!, and assuming a gaussian distribution
for the disk orientation centered on the values most recently inferred from
ALMA gas kinematic data for the outer disk ($i_{\mathrm{disk,outer}}=38.21\pm
1.38^{\circ}$, $\Omega_{\mathrm{disk,outer}}=162.72\pm 1.38^{\circ}$, Perez et
al., 2015; Boehler et al., 2017; Bohn et al., 2021), and VLTI/GRAVITY
observations for the inner disk ($i_{\mathrm{disk,inner}}=23.76\pm
3.18^{\circ}$, $\Omega_{\mathrm{disk,inner}}=15.44\pm 7.44^{\circ}$, Bohn et
al., 2021).

Regardless of the $180^{\circ}$ ambiguity in $\Omega_{\star}$, the current
orbital solution for HD 142527 B yields large mutual inclinations throughout
the system. We find $\theta_{\star-out}=45.87^{+2.05}_{-1.53}(^{\circ})$ or
$76.49^{+2.66}_{-2.72}(^{\circ})$ (due to the mutual inclination’s dependence
on the bimodal $\Omega_{\star}$). These values are not consistent with those
reported previously ($35\pm 5^{\circ}$) by Czekala et al. (2019), who adopted
the $\Omega_{\star}$ solution from Claudi et al. (2019).

Our best fit to the mutual inclination of the binary with respect to the inner
disk is $\theta_{in-\star}=56.55^{+2.93}_{-2.79}(^{\circ})$ or
$66.38^{+1.84}_{-1.36}(^{\circ})$.

Taken together, our mutual inclination fits present a system where each
component of the system is dramatically misinclined with respect to the
others.

Modeling the interaction of the binary companion and the circumbinary disk,
Price et al. (2018) demonstrated that the morphological features of the
circumbinary disk (wide cavity, asymmetric dust horseshoe, and spiral arms)
can be qualitatively reproduced solely through interaction with the binary
companion under orbits representative of those found in Lacour et al. (2016).
To best reproduce the observed morphology, Price et al. (2018) favor a
narrower family of eccentric orbits ($\mathrm{e}=0.6-0.7$) with nearly
perpendicular mutual inclinations with respect to the outer disk.

Our work lends some support to this hypothesis, as one of the equal,
symmetrically-distributed peaks in $\theta$ (resulting from the degeneracy in
$\Omega_{\star}$) from our orbit fits centers on $\theta=79.93\pm
3.04^{\circ}$, suggestive of the near perpendicular configuration they
describe. Our orbit fitting has not produced a distribution suggestive of such
high eccentricities, however.

###  5.3 Photometry

Figure 6 plots the contrast of the companion relative to the stellar continuum
over time, derived as described in Section 4. $\Delta\mathrm{mag}$
measurements from Cugno et al. (2019) are overplotted to demonstrate
consistency with our measurements. Between 2013-04-11 and 2015-05-15, the
H$\alpha$ contrast of the companion decreased by $0.68~{}\mathrm{mag}$. This
is suggestive of a moderately variable accretion rate onto the companion on
yearly timescales. Over the same baseline, the continuum did not vary within
uncertainties. As there is not significant variability in the continuum
contrast of the companion between epochs, this suggests that the extinction
towards HD 142527 B is constant to $\pm 0.2~{}\mathrm{mag}$. Accretion-driven
variability in the stellar continuum flux at our cadence is similarly limited
to at or below this value, though it likely occurs on shorter timescales (e.g.
Stauffer et al., 2014).

Figure 6: The visible-light contrast of HD 142527 B with respect to the
continuum of HD 142527 A over time. Brown and green diamonds mark our
H$\alpha$ and continuum contrast measurements, respectively. The grey shaded
region represents the $1\sigma$ standard deviation of our measurements of
continuum contrast, centered on the median. The red and blue squares mark the
contrasts measured in nearly equivalent filters by Cugno et al. (2019) using
VLT/SPHERE/ZIMPOL. The amount of H$\alpha$ excess appears to vary between many
of the epochs, while the continuum contrast varies minimally and is consistent
with uniformity within error bars.

The Close et al. (2014a) contrast measurements
($\Delta\mathrm{mag_{H\alpha}}=6.33\pm 0.20~{}\mathrm{mag}$,
$\Delta\mathrm{mag_{cont}}=7.50\pm 0.25~{}\mathrm{mag}$), derived from the
same dataset, agree with our measurements within error bars, and we note our
slightly higher continuum brightness estimate is likely due to improved PSF
subtraction and forward modeling, which allows us to better quantify flux lost
to this process. While taken in marginally different filters, the Cugno et al.
(2019) contrast measurements (shown with square symbols in Figure 6) agree
well with our results; their continuum contrast measurement falls along our
median continuum contrast and their H$\alpha$ contrast lies within the range
of values we have measured, with similar uncertainties.

Our method for calculating the contrast of the companion with respect to the
stellar continuum should should be insenstitive to stellar H$\alpha$
variability, leaving only stellar continuum variability as a potential
contaminant. The star has a known periodicity of $\sim 6$ days, with a peak-
to-valley amplitude of $0.09~{}\mathrm{mag}$ in the R-band (Claudi et al.,
2019), too small to account for the observed variation in the H$\alpha$
channel. If stellar continuum variability were contaminating the observed
H$\alpha$ variation, we would expect to see it directly in our measurements of
the companion’s continuum contrast, and we do not observe such variation. We
note that the companion’s infrared continuum has been observed to vary on the
order of 0.5mag (Claudi et al., 2019) but we do not observe a similar
variability at visible wavelengths.

Our data are therefore suggestive of variability in the H$\alpha$ emission of
this directly imaged accreting companion, resulting in the observed time
variability in the H$\alpha$ excess. This variability has implications for
future direct imaging protoplanet surveys. If accretion onto less massive
companions is similarly variable, detection limits will need to be interpreted
with some caution, as companions will be more quiescent at certain times.

###  5.4 Accretion Rate

We estimate the mass accretion rate onto HD 142527 B using H$\alpha$ contrast
measurements following a standard set of assumptions for accreting objects.
First, we convert our contrast into a line luminosity measurement via

$\mathrm{L_{H\alpha}}=4\pi D^{2}\times\mathrm{Z_{pt}}\times d\lambda\times
10^{((\mathrm{mag_{\star}}+\Delta\mathrm{mag_{B}})/-2.5)},$

where $D$ is the distance to the system, $\mathrm{Z_{pt}}=2.339\times
10^{-5}\mathrm{erg}/\mathrm{cm}^{2}/\mathrm{s}/\mu\mathrm{m}$ is the Vega
zeropoint of the H$\alpha$ filter (Males et al., 2014),
$d\lambda=0.006\mu\mathrm{m}$ is the width of the H$\alpha$ filter, and
$\mathrm{mag_{\star}}=8.1-A_{R}$ is the R-band apparent magnitude of the
central star (8.1, Cugno et al., 2019), corrected for extinction
($A_{R}=0.05$, Fairlamb et al., 2015; Cugno et al., 2019).

We convert line luminosity to an estimate of the total accretion luminosity of
the star using the Rigliaco et al. (2012) empirical relationship between
$L_{H\alpha}$ and $L_{acc}$ derived for T-Tauri stars, namely:

$\log{L_{\mathrm{acc}}}=b+a\log{\left(L_{H\alpha}/L_{\odot}\right)},$

where $a=1.25\pm 0.07$ and $b=2.27\pm 0.23$. From the accretion luminosity, we
derive the mass accretion rate via the standard relation:

$\dot{M}=\left(1-\frac{R_{\star}}{R_{in}}\right)^{-1}\frac{L_{acc}R_{\star}}{GM_{\star}}\sim
1.25\frac{L_{acc}R_{\star}}{GM_{\star}},$

(Gullbring et al., 1998) assuming $R_{in}\sim 5R_{\star}$, as in Rigliaco et
al. (2012). We adopt the dynamical mass of the companion
($M_{\mathrm{B}}=0.26M_{\odot}$) and best fit BHAC evolutionary model radius
($R_{\mathrm{B}}=1.2R_{\odot}$) from Claudi et al. (2019) to compute our final
accretion rate estimate from this equation.

Table 6 records the line luminosities and mass accretion rates for each epoch
calculated following these assumptions. The peak H$\alpha$ excess, which
occurs in the 2014-04-08 epoch, corresponds to a mass accretion rate estimate
of $6\times 10^{-10}~{}\mathrm{M_{\odot}}\mathrm{yr}^{-1}$.

Table 6: HD 142572B Accretion estimates Date | $L_{H\alpha}$ | $\dot{M}$
---|---|---
MM/DD/YY | $L_{\odot}$ | $\mathrm{M_{\odot}yr}^{-1}$
2013-04-11 | 2.12E-04 | 8.78E-10
2014-04-08 | 1.56E-04 | 5.99E-10
2015-05-15 | 1.14E-04 | 4.02E-10
2015-05-16 | 1.28E-04 | 4.67E-10
2015-05-18 | 1.36E-04 | 5.04E-10
2018-04-27 | 1.10E-04 | 3.84E-10

These mass accretion rate estimates differ from those calculated by Cugno et
al. (2019, $\mathrm{\dot{M}}=1-2\times
10^{-10}~{}\mathrm{M_{\odot}}\mathrm{yr}^{-1}$), who assumed a smaller radius
($0.9\mathrm{R_{\odot}}$ given by Lacour et al., 2016). We assert that the
larger radii inferred from the evolutionary model fit (Claudi et al., 2019) is
more appropriate given the purported age of the system, and this yields a
slight increase in mass accretion rate estimate. The values still agree within
an order of magnitude.

Our derived values are consistent with the value of $5.9\times
10^{-10}~{}\mathrm{M_{\odot}}\mathrm{yr}^{-1}$ reported by Close et al.
(2014a); although they adopted a lower radius of $0.29\mathrm{R_{\odot}}$ and
a mass of $0.25~{}\mathrm{M_{\odot}}$, they did not conduct the same
accounting for the H$\alpha$ excess of the primary, which makes up the
difference. Regardless of radius assumption, all derived accretion rates lie
in a range consistent with observations of accretion rates onto low mass
T-Tauri stars of similar masses and ages as HD 142527 B (e.g.
$10^{-9}-10^{-11}$, Rigliaco et al., 2012).

Variability in mass accretion rates onto the primary stars of transitional
disks has been observed previously. For example, the mass accretion rate of HD
142527 A changed by a factor of 7 over five years (Mendigutía et al., 2014).
Variations in mass accretion rate on the order of factors of 2-10 on week-to-
day long timescales have also been observed for accreting low mass stars more
generally (e.g. Robinson & Espaillat, 2019). We detect only marginally
significant variability in the H$\alpha$ contrast of HD 142527 B given our
conservative uncertainties. To our knowledge, however, this is the first
detection of accretion variability in a secondary companion within a
transitional disk gap.

HD 142527 B is likely surrounded by a circumsecondary disk (Lacour et al.,
2016) through which accreting material is processed. This circumsecondary disk
is embedded within the cavity of the larger circumbinary disk, similar to the
circumplanetary disk recently observed around PDS 70 c (Benisty et al., 2021).
The non-detection results from Avenhaus et al. (2017) covered in §2 suggest
that, if circumsecondary signal exists at the position of the companion, its
contribution is much smaller than our photometric errors derived from Bayesian
KLIP forward modeling. This motivates the need for a high-resolution ALMA
search for circumsecondary material, as was recently done in the PDS 70 system
(Benisty et al., 2021).

If the observed variability of HD 142527 B was due to the rotation of an
accretion hotspot in and out of view, we would expect to see detectable
continuum variability, similar to that observed in the NIR, but we do not. The
observed variability could also be due to an accretion column rotating in and
out of view. If that was the case, we might expect to observe large amplitude
day-to-day variations between the 2015 observations, which we do not. The
simplest explanation is that the accretion rate itself is variable over time,
but more data are needed to verify this and to fully understand the degree and
timescale of the variability of HD 142527 B.

Observations of accretion variability in planetary mass companions embedded
within transition disk cavities have been difficult to date. The H$\alpha$
lightcurve for PDS 70 b, for example, does not support large amplitude
($>30\%$) variability on month-long timescales (Zhou et al., 2021). Does this
indicate that accretion onto objects orbiting within transition disk cavities
is relatively stable when compared to accretion onto young stars? Recent
modeling suggests that accretion onto a protoplanet from a circumplanetary
disk may occur at a quasi-steady rate when averaged over week-long timescales,
but should exhibit daily variability (Takasao et al., 2021).

The difficulty in obtaining accurate photometry of accretion emission onto
planetary mass companions limits our ability to detect variations in their
H$\alpha$ excess. The next generation of instruments (e.g. MagAO-X, Males et
al., 2020), which can achieve higher Strehl ratios in the visible, may be able
to observe such variability for a wider range of embedded companions using
similar methods. Our result could indicate that accretion onto companions
within cavities is variable at a measurable level, at least for the highest
mass companions. The caveat to this interpretation is that HD 142527 B is a
stellar mass companion, whose accretion variability may be best understood in
the domain of very-low-mass stellar accreting objects, rather than embedded
planetary mass accretors.

##  6 Conclusions

In this paper, we present a five year monitoring campaign of the accreting
companion HD 142527 B. We used the unique forward modeling capabilities of the
Karhunen-Loeve Image Processing (KLIP) algorithm to achieve 1-2 mas precision
on astrometric measurements taken over a 6 year time baseline, and validate an
updated VisAO astrometric calibration solution (using the $\theta^{1}$ Ori
B2-B3 binary, see Appendix A) by demonstrating good agreement between VisAO
observations of HD 142527 B and the literature. We combine literature
astrometry and multi-epoch MagAO/VisAO observations to fit the orbit of HD
142527 B using orbitize! and derive a posterior distribution of orbital
elements. We verify that the companion is on an inclined
($\mathrm{i}=124.85\pm 4.56^{\circ}$), eccentric ($\mathrm{e}=0.24\pm 0.15$)
orbit and is near periastron passage. We find that the HD142527 binary has a
mutual inclination with respect to the outer disk of $\theta_{\star-
out}=45.87^{+2.05}_{-1.53}(^{\circ})$ or $76.49^{+2.66}_{-2.72}(^{\circ})$
(depending on the degenerate position of the ascending node, $\Omega$). We
also find a dramatic mutual inclination with respect to the newly directly
detected inner disk, $\theta_{in-\star}=56.55^{+2.93}_{-2.79}(^{\circ})$ or
$66.38^{+1.84}_{-1.36}(^{\circ})$. These newly derived inclinations could be
used to guide hydrodynamical models of this system, in the context of disk
warping, tearing, and precession in the presence of a disruptive companion.

While HD 142527 B may be too tightly separated at the time of writing to be
detected without interferometric techniques, astrometry of the companion
following periastron passage ($\sim 2021$) will be crucial in further
constraining its orbit and therefore its mass. An improved mass estimate and
updated characterization can yield, among other things, more precise accretion
rate estimates. A single observation with the VLTI/GRAVITY interferometer, for
instance, could track the companion’s periastron passage, provide an improved
mass constraint, and even place estimates (or upper limits) on the Br-$\gamma$
emission from HD 142527 B. With an improved mass constraint, the companion
could be better compared to evolutionary models, yielding an improved age
determination and a better understanding of the companion’s formation. GRAVITY
observations could also detect or place additional constraints on the size of
the circumsecondary disk around HD 142527 B, as was done for the PDS 70
planets (Wang et al., 2021). High resolution ALMA observations could directly
detect the presence of a circumsecondary disk around B, provide constraining
astrometry, and explore the inner disk surrounding A. In the future, fiber-fed
spectroscopy of the companion with an instrument such as KPIC may allow for
the measurement of the radial velocity, absorption, and accretion signatures
of the companion at high spectral resolution, which could help constrain its
currently uncertain age and spectral type (M2.5-M7).

Leveraging careful optimization of the pyKLIP algorithm, we achieved the most
finely separated detection of a faint ($\Delta\mathrm{mag}>6$) directly imaged
companion using a non-coronagraphic, non-interferometric instrument to date.
We observe clear H$\alpha$ excess in all epochs of observation, corresponding
to mass accretion rates similar to those observed in young, isolated M-dwarfs.
We observe tentative signs of variability in the H$\alpha$ excess of the
companion, suggestive of accretion variability. We estimate accretion rates
for the HD 142527 B companion on the order of $4-9\times
10^{-10}~{}\mathrm{M_{\odot}}\mathrm{yr}^{-1}$, assuming a radius based on
evolutionary models.

Our results demonstrate that careful, long time-baseline observations from the
current generation of high-contrast imaging instruments, combined with
improvements in post-processing techniques, are able to place substantial
constraints on both orbital motion and photometric variability, even for very
tightly-separated directly imaged companions, provided a self-consistent data
reduction and post-processing methodology. In the future, similar observations
of systems such as PDS 70, LkCa 15, and AB Aur b (and other, newly discovered
accreting protoplanets) with instruments such as MagAO-X will open new windows
into the time variability of protoplanetary accretion and the process by which
substellar companions form and evolve.

## Acknowledgements

We sincerely thank the anonymous reviewer for their thoughtful, rigorous, and
supportive review that contributed immensely to the improvement of this paper.
Special thanks to Gabriel-Dominique Marleau and Yuhiko Aoyama for their
fruitful discussions of accretion physics. We thank Sarah Blunt for her
tremendous help with our orbit fitting, Jason Wang for his pyklip expertise,
as well as Connor Robinson for his encouragement. Special thanks to David Sing
for his encouragement (and for letting WOB use his server to run last minute
orbits). WOB would like to thank Yevaud, Kalessin, and Morgoth, as well as
Benjamina, Martin, Luke, Emmett, Jack, and Kate Balmer.

WOB and KBF acknowledge funding from NSF-AST-2009816. WOB thanks the LSSTC
Data Science Fellowship Program, which is funded by LSSTC, NSF Cybertraining
Grant #1829740, the Brinson Foundation, and the Moore Foundation; their
participation in the program has benefited this work. KBF’s work on this
project was also supported by a NASA Sagan fellowship. LMC’s work was
supported by NASA Exoplanets Research Program (XRP) grants 80NSSC18K0441 and
80NSSC21K0397. KMM’s work has been supported by the NASA XRP by cooperative
agreement NNX16AD44G.

This paper includes data gathered with the 6.5 meter Magellan Telescopes
located at Las Campanas Observatory, Chile. Some of the data presented herein
were obtained at the W.M. Keck Observatory, which is operated as a scientific
partnership among the California Institute of Technology, the University of
California and the National Aeronautics and Space Administration. The
Observatory was made possible by the generous financial support of the W.M.
Keck Foundation.

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

WOB and KBF would like to acknowledge the land that the images used in this
paper were observed from. Las Campanas Observatory, and the Magellan Clay
Telescope, are built on Diaguita land. More on the Diaguita is available from
the Museo Chileno de Arte Precolombino: http://precolombino.cl/en/culturas-
americanas/pueblos-originarios-de-chile/diaguita/, and additional information
from Diagutia activists can be found: https://upndsalta.blogspot.com.
Astrobites has written an informative article, “Astronomical Observatories and
Indigenous Communities in Chile,” which can be found here:
https://astrobites.org/2019/09/10/astronomical-observatories-and-indigenous-
communities-in-chile/. The W. M. Keck Observatory, and the Keck II Telescope,
are built on Native Hawaiian land. We are honored to be given the opportunity
to conduct astronomy using data taken from this sacred place and would like to
point to the informative Astrobites articles (“Mauna Kea and Modern
Astronomy,” https://astrobites.org/2018/11/09/mauna-kea-and-modern-astronomy/,
“Maunakea, Western Astronomy, and Hawai‘i,”
https://astrobites.org/2019/08/02/maunakea-western-astronomy-and-hawaii/. We
would like to encourage our colleagues to seek out additional information
about the on-going protests against additional construction on the mountain
and the historical precedent for these protests.

The authors would like to acknowledge the land they have conducted research
from during the course of this investigation. WOB and KBF would like to
acknowledge the Nonotuck land Amherst College occupies, the Nonotuck
ancestors, their descendants, and the neighboring Indigenous nations: the
Nipmuc and the Wampanoag to the East, the Mohegan and Pequot to the South, the
Mohican to the West, and the Abenaki to the North. WOB would also like to
acknowledge the Piscataway community, their elders and ancestors, as well as
their future generations. WOB acknowledges that Johns Hopkins was founded upon
the exclusions and erasures of many Indigenous peoples, including those on
whose land this institution is located.

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##  Appendix A Astrometric Calibration of VisAO

Given the precision ($\lesssim 1~{}\mathrm{mas}$) afforded by BKA and other
methods, the dominant source of error on the astrometry of directly imaged
companions is often the absolute astrometric calibration of the instrument. In
order to ensure our astrometric measurements of HD 142527 B were accurate when
compared to literature astrometry, it was necessary to conduct an epoch to
epoch calibration to determine the stability of the absolute astrometry of
VisAO over time.

The astrometric calibration of an instrument such as VisAO is non-trivial due
to the instrument’s small FOV (8” x 8”), and because MagAO is a natural guide
star adaptive optics system, which requires a bright target
($\mathrm{R_{mag}}<15$) within the field to make effective wavefront
corrections. This significantly limits the number of viable calibration fields
available to the observer.

Previous astrometric solutions for VisAO (Males et al., 2014; Close et al.,
2013) have been calculated by cross-referencing MagAO/VisAO images with
LBT/PISCES images of the dense Trapezium cluster (Close et al., 2012). The
astrometric solution of PISCES was itself derived from cross-referencing
against HST/ACS images of the cluster (Ricci et al., 2008). There is non-
negligible orbital motion in these systems (Close et al., 2013) that needs to
be accounted for in images taken months to years apart.

Additionally, VisAO is removed and remounted between observing runs, which
introduces epoch to epoch uncertainty in its calibration. Until now, VisAO
users have operated under the assumption that the astrometric calibration has
remained stable between mountings since 2013, adopting the most recent
published calibration of the instrument from Males et al. (2014), who find a
platescale of $7.8596\pm 0.0019~{}\mathrm{mas}$ $\mathrm{pix}^{-1}$ and an
offset from north of $0.59^{\circ}\pm\sim 0.^{\circ}3$ clockwise based on
Trapezium data collected in the Ys filter.

We measured the VisAO astrometric solution by cross comparing VisAO astrometry
with an orbit fit to Keck/NIRC2 images999These data are available from the
Keck Observatory Archive (KOA) at koa.ipac.caltech.edu. of the $\theta^{1}$
Ori B2-B3 binary obtained between 2001 and Jan. 2020. The data were corrected
for non-linearity, dark subtracted, flat fielded, and bad-pixel corrected
before being corrected for geometric distortion, as described in De Rosa et
al. (2020). The NIRC2 astrometric solution is tied to precise HST/ACS
observations of SiO masers in the Galactic Center (Yelda et al., 2010; Service
et al., 2016).

Our calibration method follows De Rosa et al. (2020), who conducted a similar
calibration of the Gemini Planet Imager (GPI) using the same Keck/NIRC2
images. We measure the position of the $\theta^{1}$ Ori B2-B3 binary across
more than 20 years of NIRC2 imagery using photutils PSF photometry (Bradley et
al., 2020). We used the PSF of $\theta^{1}$ Ori B1 to conduct PSF photometry,
fitting both components of the binary jointly with orbitize!, which allows us
to determine the expected position of the binary at arbitrary epochs and
accounts for non-linear orbital motion over time. Our observations of HD
142527 and our VisAO calibration images of the $\theta^{1}$ Ori B system fall
within the NIRC2 baseline of observations, meaning that each comparison is
made within a well-constrained orbital fit. Figure 7 shows two representative
images of $\theta^{1}$ Ori B2-B3 from NIRC2 and MagAO respectively.

Figure 7: Representative images of $\theta^{1}$ Ori B2-B3 from NIRC2 (left,
NB2.108 band) and MagAO (right, z’ band). All relative astrometry herein is
conducted with respect to $\theta^{1}$ Ori B2, which is centered at (0,0).

We initialized an oribitze! MCMC with 50 walkers, which each took 100,000
steps after 100,000 “burn-in” steps were discarded, for a total of 5 million
accepted fit orbits. We set the initial total system mass to be $5.5\pm
0.5M_{\odot}$ (Close et al., 2013) and the initial system parallax to
$2.655\pm 0.042$ (Gaia Collaboration et al., 2021). We then determined the
platescale and North Angle offset in each dataset by comparing the separation
and Position Angle of the B2-B3 binary in VisAO images of the system to the
expected separation and Position Angle of the NIRC2 orbital fit. The VisAO
images of the $\theta^{1}$ Ori B system were reduced and registered following
the methods described in Section 3, and the positions measured using photutils
PSF photometry.

We determined the platescale and North Angle offset for each dataset, then
took the average of each dataset weighted by the measurement uncertainty. We
observe no significant variations in platescale or North Angle offset over
time or between filters, and conclude that both have remained stable across
instrument mountings. Our measurements of each therefore represent
observations of a constant over time, and we take the weighted average of
measurements from individual epochs to be the most precise estimate of the
true platescale and North Angle for VisAO.

We find the updated VisAO platescale to be $7.95\pm 0.010~{}\mathrm{mas}$
$\mathrm{pix}^{-1}$ and the North Angle offset to be $0.497\pm 0.192^{\circ}$
counterclockwise. Our updated calibration yields updated errors, and we find
(similar to De Rosa et al.) slightly larger errors on the platescale than
previous calibrations, and smaller errors on the North Angle offset. It would
appear that by measuring the platescale in only one filter with a limited
number of observations, previous calibrations underestimated the platescale
error, and that a longer baseline of observations allows improved precision in
determination of the North Angle offset.

Figure 8 plots measurements of the VisAO platescale over time and across
multiple filters. Figure 9 shows the orbital fit to the NIRC2 observations of
$\theta^{1}$ Ori B2-B3 and updated VisAO astrometry of the binary pair.

Figure 8: VisAO platescale as measured in various VisAO filters over time. The
orange shaded region, centered on the horizontal orange dash-dot line,
represents the previous astrometric solution of Males et al. (2014) using data
taken in the Ys filter in 2014. Note the agreement between our measurement of
the same Ys data (red diamond) and their value. We note that the H$\alpha$
observations suffered from poor observing conditions and an unfavorable
observing strategy for astrometry which resulted in very low signal-to-noise
on the B2-B3 pair. No obvious trend in platescale with wavelength or time is
present, and therefore we adopt the weighted average and standard deviation on
the weighted average (represented by the blue dashed line and shaded region,
respectively) as the updated platescale and platescale error for the
instrument. Figure 9: 500 orbital fits to the NIRC2 astrometry of $\theta^{1}$
Ori B2-B3 randomly drawn from the posterior distribution. Astrometry compiled
in Table 7 is overplotted. Only the NIRC2 astrometry (orange triangles) was
used to fit the orbit of the binary, and the corrected VisAO astrometry (red
diamonds) falls along the fit orbits by design.

As a byproduct of this astrometric calibration, we have obtained astrometric
measurements of the $\theta^{1}$ Ori B2-B3 over nearly 20 years, as well as an
updated, well-defined orbital solution for the binary. We record the
astrometry from both NIRC2 and VisAO with other literature astrometry in Table
7. We record the orbital elements as drawn from the posterior distribution of
fits to the NIRC2 astrometry in Table 8.

Table 7: $\theta^{1}$ Ori B2-B3 astrometry

Epoch | Separation | Position Angle | Instrument | PI
---|---|---|---|---
(MJD) | (mas) | (∘) |  |
50735 | $114.000\pm 0.050$ | $204.300\pm 4.000$ | SAOa | Weigelt et al. 1999
51120 | $117.000\pm 0.005$ | $205.700\pm 4.000$ | SAOa | Weigelt et al. 1999
52171 | $118.200\pm 0.004$ | $207.800\pm 1.000$ | GEMINI | Close et al. 2003
52263 | $115.600\pm 4.766$ | $210.212\pm 0.595$ | NIRC2 | This work
52659 | $116.000\pm 0.003$ | $209.700\pm 1.000$ | MMT | Close et al. 2003
53281 | $116.329\pm 6.831$ | $211.649\pm 0.768$ | NIRC2 | This work
53417 | $115.919\pm 0.444$ | $212.922\pm 0.165$ | NIRC2 | This work
53426 | $116.109\pm 0.112$ | $212.840\pm 0.030$ | NIRC2 | This work
55850 | $115.600\pm 0.001$ | $220.390\pm 0.300$ | LBT | Close et al. 2012
55598 | $117.249\pm 4.133$ | $219.128\pm 0.543$ | NIRC2 | This work
55598 | $116.936\pm 1.880$ | $218.154\pm 0.943$ | NIRC2 | This work
56265 | $116.000\pm 0.000$ | $221.500\pm 0.300$ | MagAO | Close et al. 2013
56388 | $115.914\pm 1.223$ | $221.989\pm 1.584$ | MagAO | This work
56389 | $115.914\pm 1.015$ | $221.992\pm 1.047$ | MagAO | This work
56990 | $115.648\pm 0.550$ | $223.931\pm 2.079$ | MagAO | This work
56903 | $114.453\pm 0.557$ | $223.776\pm 0.860$ | NIRC2 | This work
56997 | $115.012\pm 4.235$ | $223.980\pm 1.871$ | NIRC2 | This work
57322 | $114.090\pm 5.086$ | $224.290\pm 0.694$ | NIRC2 | This work
57367 | $115.447\pm 1.301$ | $225.152\pm 2.603$ | MagAO | This work
57405 | $115.318\pm 3.311$ | $224.424\pm 0.662$ | NIRC2 | This work
57405 | $115.318\pm 3.311$ | $224.424\pm 0.662$ | NIRC2 | This work
57439 | $115.296\pm 2.548$ | $225.253\pm 1.120$ | NIRC2 | This work
57620 | $114.498\pm 2.178$ | $226.040\pm 1.549$ | NIRC2 | This work
57709 | $115.239\pm 2.008$ | $226.264\pm 2.108$ | MagAO | This work
57788 | $115.188\pm 0.116$ | $226.521\pm 0.498$ | MagAO | This work
57790 | $115.187\pm 0.117$ | $226.527\pm 0.526$ | MagAO | This work
57798 | $115.182\pm 0.673$ | $226.554\pm 1.218$ | MagAO | This work
58162 | $115.067\pm 4.193$ | $227.458\pm 0.558$ | NIRC2 | This work
58234 | $114.875\pm 1.121$ | $227.979\pm 1.218$ | MagAO | This work
58790 | $114.316\pm 2.814$ | $229.360\pm 0.561$ | NIRC2 | This work
58852 | $114.130\pm 2.234$ | $229.690\pm 0.003$ | NIRC2 | This work

. Note that the MagAO measurements presented here are not independent
measurements, as they were tied to the orbit fit to NIRC2 observations in
order to determine the platescale and North Angle offset.

Note. — SAOa speckle interferometry from Weigelt et al. (1999), and GEMINI,
MMT, and LBT direct imaging from Close et al. (2003, 2012, 2013)

Table 8: $\theta^{1}$ Ori B2-B3 orbital elements a (au) | $42.23_{-1.38}^{+2.83}$
---|---
e | $0.72_{0.02}^{+0.02}$
i $(^{\circ})$ | $53.64_{-0.90}^{+0.98}$
$\omega(^{\circ})$ | $91.09\pm 2.26,271.05\pm 2.31$
$\Omega(^{\circ})$ | $114.18\pm 13.00,293.07\pm 13.36$
Periastron (yr) | $2059.17_{-4.07}^{+5.11}$
Parallax (mas) | $2.65_{-0.04}^{+0.04}$
$\mathrm{M_{total}}(M_{\odot})$ | $5.44_{-0.46}^{+0.48}$

##  Appendix B Forward Model choice and VisAO ghost calibration

The VisAO CCD saturates at $\sim 16,000$ counts, and because of its small FOV,
there are no other stars within the field that can be used as a PSF to forward
model. There are no artificial satellite spots injected as astrometric or
photometric calibrators, but there is an instrumental ‘ghost’ PSF that appears
to the right of the natural guide star in each image (see Figure 10). We
investigated the stability of the ghost and the scaling relationships between
the ghost and central PSF using 10 unsaturated datasets taken as part of the
GAPlanetS survey (Follette et al., 2017, and Follette et al. 2022, in prep.).

We find that peak of the ghost varies consistently with the peak of the
central PSF. We adopt the empirical scaling relationships
$\mathrm{F_{c,H\alpha}}=179.68\pm 4.59\times\mathrm{F_{g,H\alpha}}$ and
$\mathrm{F_{c,cont.}}=196.31\pm 3.56\times\mathrm{F_{g,cont.}}$ However, we
find that when fit with a Moffat distribution, the FWHM of the ghost is on
average 7% larger than that of the central PSF. We therefore adopt the
relationship $\mathrm{FWHM_{c}}=0.93\times\mathrm{FWHM_{ghost}}$ in
determining the FWHM of saturated images.

This ghost calibration was conducted in part because we had initially used the
instrumental ghost as a forward model PSF, and found it to be a poor fit. We
then investigated the best choice of forward model for saturated data by
comparing sum-of-squares residuals for the ghost itself, a Moffat distribution
fit to the ghost, a Gaussian distribution fit to the ghost, and both
distributions (Moffat and Gaussian) with reduced FWHM equal to
$0.93\times\mathrm{FWHM_{ghost}}$. For each PSF, we conducted the same
procedure as in Section 4, forward modeling the PSF through KLIP and fitting
it to the known companion, resulting in a posterior distribution of fits and a
residual map. We found that for the majority of our images of HD 142527 B,
Gaussian PSFs yielded the smallest residuals. We assume that, scaling by the
above relationships, the counts under the Gaussian are equivalent to those
under the unsaturated central PSF. This then enables us to conduct photometry
using BKA.

Figure 10: A saturated image of HD 142527. The position of the instrumental
ghost is marked with a black arrow. The Y axis is in pixels, and the X axis is
labeled in milliarcseconds to illustrate the spatial extent of the 451 pixel
crop and the position of the ghost.

##  Appendix C Forward Model Fits

Optimized post-KLIP images for each detection epoch, best fit BKA models, and
the residuals between them are shown for HD 142527 B in the H$\alpha$ and
continuum filters in Figures 11 and 12, respectively. The marginal posterior
distributions for the BKA fits, an example of which is shown in Figure 13, are
distributed normally for all epochs. The most common correlation is a slight
linear correlation between X and Y position (as seen in Figure 13).

Figure 11: A gallery of BKA forward model best fits to HD 142527 B in the
H$\alpha$ filter, in chronological order from top to bottom. Data (left) is
fit by BKA, yielding a best fit forward model (center), and their difference
(right). Figure 12: A gallery of BKA forward model best fits to HD 142527 B in
the continuum filter, in chronological order from top to bottom. Data (left)
is fit by BKA, yielding a best fit forward model (center), and their
difference (right). Figure 13: A corner plot illustrating the posterior
distribution of BKA forward model fits to the 2013-04-11 H$\alpha$ data, which
is representative of all other epochs. Note that all marginal parameters are
normally distributed, and the only correlation is a slight linear correlation
between X and Y position.

##  Appendix D Orbit fit posteriors

This appendix details posterior distributions of orbital elements for our
astrometric fits, computed using orbitize!. Figure 14 illustrates the
posterior distribution of orbital elements for the HD 142527 AB binary. Figure
15 plots the mutual inclination parameters $\mathrm{i_{\star}},\Omega_{\star}$
from Figure 14, computed as described in Section 5, along with
$\mathrm{i_{d}},\Omega\mathrm{{}_{d}}$ drawn from gaussian distributions
specified by the disk parameters fit by Bohn et al. (2021), and the resultant
distribution of mutual inclinations $\theta$. Figure 16 illustrates the
posterior distribution for the orbit of the $\theta^{1}$ Ori B2-B3 derived
from Keck NIRC2 observtions, as described in Appendix A.

Figure 14: Posterior distribution of orbital elements fit to the astrometry of
HD 142527 B. $\omega$ and $\Omega$ show bimodal distributions with peaks
spaced $180^{\circ}$ apart; this a known degeneracy in visual orbits with a
lack of RV constraints. Figure 15: Posterior distribution of fit
($\mathrm{i_{\star}},\Omega_{\star}$) and randomly sampled
($\mathrm{i_{disk}},\Omega\mathrm{{}_{disk}}$) for both inner and outer disks
yields a posterior distribution of $\theta$, the mutual inclination angle
between the binary orbit and the disk component. As in Czekala et al. (2019),
the mutual inclination of the outer disk for this system is multimodal, but
dramatically misaligned ($\theta\gg 3^{\circ}$) no matter choice of
$\Omega_{\star}$. Interestingly, one family of $\theta_{\star-\mathrm{out}}$
is nearly perpendicular, similar to the configuration described in Price et
al. (2018). Figure 16: Posterior distribution of orbital elements fit to NIRC2
astrometry of $\theta^{1}$ Ori B2-B3. The fit displays a posterior
distribution typical of short-arc visual orbit fits, with the same bimodal
$\omega$ and $\Omega$ noted previously, normally distributed $\pi$ and
$\mathrm{M_{tot}}$, correlated semi-major axis, eccentricity, and inclinations
that are otherwise relatively constrained. This orbit is so satisfyingly
typical, I have petitioned for it act as the unofficial mascot of orbitize!
but I have not yet been humored thusly.

  *[S-SDI]: Simultaneous-Spectral Differential Imaging
  *[SAM]: Sparse Aperture Masking
  *[MagAO]: Magellan Adaptive Optics
  *[VisAO]: Visible Light Adaptive Optics
  *[cADI]: classical Angular Differential Imaging
  *[ADI]: Angular Differential Imaging
  *[PCA]: Principle Component Analysis
  *[PDI]: Polarized Differential Imaging