11institutetext:  Instituto de Astrofísica de Canarias (IAC), E-38200 La
Laguna, Tenerife, Spain 22institutetext: Dept. Astrofísica, Universidad de La
Laguna (ULL), E-38206 La Laguna, Tenerife, Spain 33institutetext: Centro de
Astrobiologia (CSIC-INTA), Carretera de Ajalvir km 4, 28850 Torrejon de Ardoz,
Madrid, Spain 44institutetext: Department of Earth and Planetary Science, The
University of Tokyo, Tokyo, Japan 55institutetext: Komaba Institute for
Science, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan
66institutetext: Japan Science and Technology Agency, PRESTO, 3-8-1 Komaba,
Meguro, Tokyo 153-8902, Japan 77institutetext: Astrobiology Center, 2-21-1
Osawa, Mitaka, Tokyo 181-8588, Japan 88institutetext: National Astronomical
Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
99institutetext: Department of Physics and Astronomy, Vanderbilt University,
Nashville, TN 37235, USA 1010institutetext: Department of Astronomy, The
University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
1111institutetext: Center for Astrophysics ${\rm\mid}$ Harvard & Smithsonian,
60 Garden Street, Cambridge, MA 02138, USA 1212institutetext: Rheinisches
Institut für Umweltforschung an der Universität zu Köln, Abteilung
Planetenforschung, Aachener Str. 209, 50931 Köln, Germany 1313institutetext:
Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese
Academy of Sciences, Nanjing 210023, China 1414institutetext: European Space
Agency (ESA), European Space Research and Technology Centre (ESTEC),
Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands 1515institutetext: Institute
of Planetary research, German Aerospace Center, Rutherfordstrasse 2, 12489,
Berlin, German 1616institutetext: Department of Astronomical Science, The
Graduated University of Advanced Studies, SOKENDAI, 2-21-1, Osawa, Mitaka,
Tokyo, 181-8588, Japan 1717institutetext: Department of Astronomy and Tsinghua
Centre for Astrophysics, Tsinghua University, Beijing 100084, China
1818institutetext: George Mason University, 4400 University Drive, Fairfax,
VA, 22030 USA 1919institutetext: Dept. of Physics & Astronomy, Swarthmore
College, Swarthmore PA 19081, USA 2020institutetext: University of Maryland,
Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
2121institutetext: NASA Ames Research Center, Moffett Field, CA 94035, USA
2222institutetext: SETI Institute, 189 Bernardo Avenue, Suite 100, Mountain
View, CA 94043, USA 2323institutetext: Noqsi Aerospace Ltd., 15 Blanchard
Avenue, Billerica, MA 01821, USA 2424institutetext: Harvard-Smithsonian Center
for Astrophysics, 60 Garden St., Cambridge, MA, 02138, USA 2525institutetext:
Department of Physics and Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2626institutetext: Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA 2727institutetext: Department of Aeronautics and
Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2828institutetext: Department of Earth, Atmospheric, and Planetary Sciences,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2929institutetext: Department of Astrophysical Sciences, Princeton University,
Princeton, NJ 08544, USA 3030institutetext: 51 Pegasi b Fellow

# TOI-519 b: a short-period substellar object around an M dwarf validated
using multicolour photometry and phase curve analysis

H. Parviainen  TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysisTOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysis E. Palle
TOI-519 b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysis M.R. Zapatero-Osorio  TOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysis G. Nowak TOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysisTOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysis A. Fukui  TOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysis F. Murgas  TOI-519 b: a short-
period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysisTOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysis N. Narita  TOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysis K.G. Stassun  TOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysisTOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysis J.H.
Livingston  TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysis K.A. Collins  TOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis D.
Hidalgo Soto TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysisTOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysis V.J.S. Béjar
TOI-519 b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysis J. Korth  TOI-519 b: a short-
period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysis M. Monelli TOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis P.
Montanes Rodriguez TOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis N.
Casasayas-Barris TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysisTOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysis G. Chen
TOI-519 b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysis N. Crouzet TOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysisTOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysis J.P. de Leon
TOI-519 b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysis A. Hernandez TOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysisTOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysis K. Kawauchi TOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysis P. Klagyivik TOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysis N. Kusakabe TOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis R. Luque
TOI-519 b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysis M. Mori TOI-519 b: a short-
period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysis T. Nishiumi TOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis J.
Prieto-Arranz TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysisTOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysis M. Tamura
TOI-519 b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis N.
Watanabe TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysis T. Gan TOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis K.I.
Collins TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysis E.L.N. Jensen TOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis T.
Barclay  TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysis J.P. Doty TOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis J.M.
Jenkins  TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysis D.W. Latham  TOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis M.
Paegert  TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysis G. Ricker  TOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysis D.R.
Rodriguez  TOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysis S. Seager  TOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysis A. Shporer  TOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysis R. Vanderspek  TOI-519 b: a short-period substellar object around an
M dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysis J. Villaseñor TOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysis J.N. Winn  TOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysis B. Wohler  TOI-519 b: a short-
period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysisTOI-519 b: a short-period substellar object
around an M dwarf validated using multicolour photometry and phase curve
analysisTOI-519 b: a short-period substellar object around an M dwarf
validated using multicolour photometry and phase curve analysisTOI-519 b: a
short-period substellar object around an M dwarf validated using multicolour
photometry and phase curve analysis I. Wong  TOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysisTOI-519 b: a short-period substellar object around an M
dwarf validated using multicolour photometry and phase curve analysisTOI-519
b: a short-period substellar object around an M dwarf validated using
multicolour photometry and phase curve analysisTOI-519 b: a short-period
substellar object around an M dwarf validated using multicolour photometry and
phase curve analysis

(Received September 15, 1996; accepted March 16, 1997)

###### Abstract

Context. We report the discovery of TOI-519 b (TIC 218795833), a transiting
substellar object ($R=1.07\,R_{\mathrm{Jup}}$) orbiting a faint M dwarf
($V=17.35$) on a 1.26 d orbit. Brown dwarfs and massive planets orbiting M
dwarfs on short-period orbits are rare, but more have already been discovered
than expected from planet formation models. TOI-519 is a valuable addition
into this group of unlikely systems, and adds towards our understanding of the
boundaries of planet formation.

Aims. We set out to determine the nature of the Transiting Exoplanet Survey
Satellite (TESS) object of interest TOI-519 b.

Methods. Our analysis uses a SPOC-pipeline TESS light curve from Sector 7,
multicolour transit photometry observed with MuSCAT2 and MuSCAT, and transit
photometry observed with the LCOGT telescopes. We estimate the radius of the
transiting object using multicolour transit modelling, and set upper limits
for its mass, effective temperature, and Bond albedo using a phase curve model
that includes Doppler boosting, ellipsoidal variations, thermal emission, and
reflected light components.

Results. TOI-519 b is a substellar object with a radius posterior median of
1.07 $R_{\mathrm{Jup}}$ and 5th and 95th percentiles of 0.66 and 1.20
$R_{\mathrm{Jup}}$, respectively, where most of the uncertainty comes from the
uncertainty in the stellar radius. The phase curve analysis sets an upper
effective temperature limit of 1800 K, an upper Bond albedo limit of 0.49, and
a companion mass upper limit of 14 $M_{\mathrm{Jup}}$. The companion radius
estimate combined with the $T_{\mathrm{eff}}$ and mass limits suggests that
the companion is more likely a planet than a brown dwarf, but a brown-dwarf
scenario is more likely a priori given the lack of known massive planets in
$\approx 1$ day orbits around M dwarfs with $T_{\mathrm{eff}}<3800$ K, and the
existence of some (but few) brown dwarfs.

###### Key Words.:

Stars: individual: TIC 218795833 - Planet and satellites: general - Methods:
statistical - Techniques: photometric

##  1 Introduction

Current planet formation models predict a very low probability for a low-mass
star to harbour a brown dwarf or a massive planet on a short-period orbit
(Mordasini et al., 2012), and M dwarf planet occurrence rate studies based on
the Kepler data have corroborated this paucity (Dressing & Charbonneau, 2015).
However, against the expectations, a set of such objects have been discovered
during the last years. Five brown dwarfs111TOI 263.01 by Parviainen et al.
2020, NGTS-7 A b by Jackman et al. 2019, LP 261-75b by Irwin et al. 2018, AD
3116 by Gillen et al. 2017, and NLTT 41135 b by Irwin et al. 2010. and four
gas-giant planets222Kepler-45b by Johnson et al. 2012, HATS-6b by Hartman et
al. 2015, HATS-71b by Bakos et al. 2018, and NGTS-1b by Bayliss et al. 2018.
are currently known to orbit M dwarf hosts cooler than 4000 K with orbital
periods smaller than five days. The formation and subsequent evolution of
these systems is an open question, as is their actual prevalence. A larger
sample is required to find out whether the currently known systems are all
rare objects, born from random formation accidents, or whether these systems
belong to a family with a common formation path.

The _Transiting Exoplanet Survey Satellite_ (TESS) (Ricker et al., 2014)
recently completed the second half of its two-year primary mission, and has
discovered to date over two thousand transiting planet candidates (_TESS
objects of interest_ , or _TOI_ s). However, since various astrophysical
phenomena can lead to a photometric signal mimicking an exoplanet transit
(Cameron, 2012), only a fraction of the candidates are legitimate planets
(Moutou et al., 2009; Almenara et al., 2009; Santerne et al., 2012; Fressin et
al., 2013), and the true nature of each individual candidate needs to be
resolved by follow-up observations (Cabrera et al., 2017; Mullally et al.,
2018). A mass estimate based on radial velocity (RV) measurements is the most
reliable way to confirm a planet candidate, but RV observations are practical
only for a subset of candidates (Parviainen et al., 2019).

We recently reported the validation of TOI-263.01, a substellar companion
orbiting an M dwarf on an extremely short-period orbit of 0.56 days
(Parviainen et al., 2020). The validation was based on ground-based
multicolour photometry following a multicolour transit modelling approach
described in Parviainen et al. (2019). This approach models transit light
curves observed in different passbands (filters) jointly, and yields posterior
estimates for the usual quantities of interest (QOIs) in transiting planet
light curve analysis, such as orbital period, impact parameter, stellar
density, and an estimate for the _true companion radius ratio_. The true
radius ratio is a conservative radius ratio estimate333Here a ”conservative
radius ratio estimate” means that it should not underestimate the radius
ratio, but rather give its reliable upper limit when assuming complete
ignorance about the possible third light contamination. that accounts for
possible light contamination from unresolved objects inside the photometry
aperture. The true radius ratio combined with a stellar radius estimate gives
the absolute (conservative) radius of the companion, and if this is securely
below the theoretical lower radius limit for a brown dwarf ($\sim
0.8\,R_{\mathrm{Jup}}$, Burrows et al. 2011), the candidate can be considered
a validated planet. If the true radius is $\sim 1\,R_{\mathrm{Jup}}$, the
nature of the companion is ambiguous due to the mass-radius degeneracy for
objects with masses in gas giant planet and brown dwarf regime, and for radii
larger than $1\,R_{\mathrm{Jup}}$ the probability that the object is a brown
dwarf or a low-mass star increases rapidly.

We report the discovery of TOI-519 b, a transiting substellar object
($0.66\,R_{\mathrm{Jup}}<R<1.20\,R_{\mathrm{Jup}}$, where the lower and upper
limits correspond to 5th and 95th percentiles, respectively) orbiting a faint
M dwarf (TIC 218795833, see Table 1) on a 1.27 d orbit. The object was
originally identified in the TESS Sector 7 photometry by the TESS _Science
Processing Operations Center_ (SPOC) pipeline (Jenkins et al., 2016), and was
later followed up from the ground using multicolour transit photometry and
low-resolution spectroscopy. The planet candidate passes all the SPOC Data
Validation tests (Twicken et al., 2018), but the faint host star ($V=17.35$)
makes radial velocity follow up challenging. However, the large transit depth
makes the system amenable to validation using multicolour transit photometry,
although the uncertainties in estimating M dwarf radii complicate the
situation by allowing solutions with $R>1.2\,R_{\mathrm{Jup}}$. In this case,
a radius estimate is not sufficient for validation, and we turn to phase-curve
modelling to further constrain the companion’s mass and effective temperature.

Table 1: TOI-519 identifiers, coordinates, properties, and magnitudes. The
stellar properties are based on a spectrum observed with ALFOSC, and their
derivation is described in detail in Sect. 3 _Main identifiers_
---
TIC |  | 218795833
2MASS |  | J08182567-1939465
WISE |  | J081825.63-193946.2
_Equatorial coordinates_
RA (J2000) |  | $8^{h}\,18^{m}\,25\aas@@fstack{s}62$
Dec (J2000) |  | $-19\degr\,39\arcmin\,46\aas@@fstack{\prime\prime}05$
_Stellar parameters_
Eff. temperature | $T_{\mathrm{eff}}$ | [K] | $3350^{+100}_{-200}$
Bolometric flux | $F_{\mathrm{bol}}$ | [erg s-1cm-2] | $(3.13\pm 0.11)\times 10^{-11}$
Mass | $\mathrm{M_{\star}}$ | [$M_{\odot}$ ] | $0.369_{-0.097}^{+0.026}$
Radius | $\mathrm{R_{\star}}$ | [$R_{\odot}$ ] | $0.373_{-0.088}^{+0.020}$
Parallax |  | [mas] | 8.626 $\pm$ 0.069
Spectral type |  |  | M3.5${}^{+1.0}_{-0.5}$
_Magnitudes_
Filter |  | Magnitude | Uncertainty
TESS |  | 14.4347 | 0.0074
$B$ |  | 17.869 | 0.175
$V$ |  | 17.350 | 0.200
Gaia DR2 |  | 15.7067 | 0.0004
$J$ |  | 12.847 | 0.027
$H$ |  | 12.226 | 0.027
$K$ |  | 11.951 | 0.024

##  2 Observations

###  2.1 TESS photometry

Figure 1: TOI-519 and its surroundings observed by DSS with the TESS aperture
used by the SPOC pipeline shown in pink and TOI-519 marked with a square. The
nearest star lower-right from TOI-519 introduces a significant amount of flux
contamination in the TOI-519 light curve.

TESS observed TOI-519 b during Sectors 7 and 8. Sector 7 was observed for 24.4
days covering 18 transits with a two-minute cadence. Sector 8 was observed for
for 24.6 days covering 13 transits (some of the transits occur during useless
sections of the light curve), but the two-minute time cadence is not
available, and the light curve must be created from the Full Frame Image (FFI)
data.

We chose to use the Sector 7 Presearch Data Conditioning (PDC) light curve
(Stumpe et al., 2014, 2012; Smith et al., 2012), produced by the SPOC
pipeline, for the analysis. We add back the crowding correction
(”CROWDSAP”)444The PDC crowding metric, $C$, corresponds to the ratio of the
target flux to the total aperture flux, and the contamination defined in this
paper, $c$, to the ratio of the contaminating flux to the total flux, and the
two are related as $c=1-C$. removed by the pipeline, since the crowding
correction can introduce a bias into our parameter estimation if the crowding
is overestimated by the SPOC pipeline.555As is the case here, see Discussion
for details. The TOI-519 light curve can be expected to contain a significant
amount of flux contamination from a nearby star with a similar brightness (see
Fig. 1), and our parameter estimation approach leads to an independent TESS
contamination estimate based on the differences in transit depths between the
TESS and ground-based transit observations.

The TESS photometry used in the transit analysis consists of 18 3.6 hour-long
windows of SPOC data from Sector 7 centred around each transit based on the
linear ephemeris, and each subset was normalised to its median out-of-transit
(OOT) level assuming a transit duration of 2.4 h. The photometry has an
average point-to-point (ptp) scatter of 18.7 parts per thousand (ppt). We do
not detrend the photometry, but model the baseline in the transit analysis.

The phase curve analysis uses all the SPOC Sector 7 data except the transits.
We also created long-cadence light curves for Sectors 7 and 8 using the
Eleanor package (Feinstein et al., 2019), since while the short transit
duration makes long-cadence less-than-optimal for transit modelling, having
two sectors of data instead of one could still be beneficial for the phase
curve modelling. However, we were not able to produce light curves with
Eleanor that would have matched the SPOC-produced light curve in quality. The
long-cadence light curves show significantly higher systematics that led them
to be useless in the phase curve analysis.

###  2.2 MuSCAT2 photometry

We observed four full transits of TOI-519 b simultaneously in $g$, $r$, $i$,
and $z_{\mathrm{s}}$ bands with the MuSCAT2 multicolour imager (Narita et al.,
2019) installed at the 1.52 m Telescopio Carlos Sanchez (TCS) in the Teide
Observatory, Spain, on the nights of 22.11.2019, 8.1.2020, 13.1.2020, and
29.2.2020. The exposure times were optimised on per-night and per-CCD basis,
but were generally between 60 and 90 s. The observing conditions were
excellent through all the nights (see Fig. 2 for an example frame).

Figure 2: MuSCAT2 field observed in $r$ band. TOI-519 is marked with a cross,
and the dotted circle marks the $2.5\arcmin$-radius region centred around
TOI-519.

The photometry was carried out using standard aperture photometry calibration
and reduction steps with a dedicated MuSCAT2 photometry pipeline, as described
in Parviainen et al. (2020). The pipeline calculates aperture photometry for
the target and a set of comparison stars and aperture sizes, and creates the
final relative light curves via global optimisation of a model that aims to
find the optimal comparison stars and aperture size, while simultaneously
modelling the transit and baseline variations modelled as a linear combination
of a set of covariates.

###  2.3 MuSCAT photometry

We also observed one full transit of TOI-519 b simultaneously in $g$, $r$, and
$z_{\mathrm{s}}$ bands with the multicolour imager MuSCAT (Narita et al.,
2015) mounted on the 1.88 m telescope at Okayama Astro-Complex on Mt.
Chikurinji, Japan, on 30.11.2019. The observation was conducted for 3.4 hours
covering the transit, during which the sky condition was excellent. The
telescope focus was slightly defocused so that the full width at half maximum
(FWHM) of stellar point-spread function (PSF) was around 3″. The exposure
times were set at 60, 40, and 60 s in $g$, $r$, and $z_{\mathrm{s}}$ bands,
respectively.

Image calibration (dark correction and flat fielding) and standard aperture
photometry were performed using a custom pipeline (Fukui et al., 2011), with
which the aperture size and comparison stars were optimised so that the point-
to-point dispersion of the final light curve was minimised. The adopted
aperture radius was 10 pixels (3.6″) for all bands.

###  2.4 LCOGT photometry

Three full transits of TOI-519 b were observed using the Las Cumbres
Observatory Global Telescope (LCOGT) 1 m network (Brown et al., 2013) in $g$,
$i$, and $z_{\mathrm{s}}$ bands on the nights of 29.03.2019, 01.04.2019, and
16.04.2019, respectively. We used the TESS Transit Finder, which is a
customised version of the Tapir software package (Jensen, 2013), to schedule
our transit observations. The $g$ and $z_{\mathrm{s}}$ transits were observed
from the LCOGT node at Cerro Tololo Inter-American Observatory, Chile, and
used 60 s and 150 s exposures, respectively. The $i$ transit was observed from
the LCOGT node at South Africa Astronomical Observatory, South Africa, and
used 150 s exposures. The 1 m telescopes are equipped with $4096\times 4096$
pixel LCO SINISTRO cameras having an image scale of
0$\aas@@fstack{\prime\prime}$389 pixel-1 resulting in a $26\arcmin\times
26\arcmin$ field of view.

The images were calibrated by the standard LCOGT BANZAI pipeline (McCully et
al., 2018) and the photometric data were extracted using the AstroImageJ (AIJ)
software package (Collins et al., 2017). The $g$ and $z_{\mathrm{s}}$ images
have PSFs with FWHM $\sim 1\aas@@fstack{\prime\prime}8$, and the $i$ images
were defocused resulting in FWHMs $\sim 3\aas@@fstack{\prime\prime}2$.
Circular apertures with radius 11, 15, and 10 pixels were used to extract
differential photometry in the $g$, $i$, and $z_{\mathrm{s}}$ bands,
respectively.

###  2.5 Spectroscopy

On 16.3.2020, we obtained the optical low-resolution spectrum of TOI-519 with
the Alhambra Faint Object Spectrograph and Camera (ALFOSC) mounted at the 2.56
m Nordic Optical Telescope (NOT) on the Roque de los Muchachos Observatory.
ALFOSC is equipped with a 2048$\times$2064 CCD detector with a pixel scale of
0.2138 ″pixel-1. We used grism number 5 and an horizontal long slit with a
width of 1.0″, which yield a nominal spectral dispersion of 3.53 Å pixel-1
and a usable wavelength space coverage between 5000 and 9400 Å. Two spectra of
1800 s each were acquired at parallactic angle and airmass of 1.51. ALFOSC
observations of the white dwarf G191–B2B were acquired with the same
instrumental setup as TOI-519, with an exposure time of 120 s, and at an
airmass of 1.65. Raw images were reduced following standard procedures at
optical wavelengths: bias subtraction, flat-fielding using dome flats, and
optimal extraction using appropriate packages within the IRAF666Image
Reduction and Analysis Facility (IRAF) is distributed by the National Optical
Astronomy Observatories, which are operated by the Association of Universities
for Research in Astronomy, Inc., under contract with the National Science
Foundation. environment. Wavelength calibration was performed with a precision
of 0.65 Å using He i and Ne i arc lines observed on the same night. The
instrumental response was corrected using observations of the
spectrophotometric standard star G191–B2B. Because the primary target and the
standard star were observed close in time and at a similar airmass, we
corrected for telluric lines absorption by dividing the target data by the
spectrum of the standard normalised to the continuum. The two individual
spectra of TOI-519 were combined and the final spectrum, which has a spectral
resolution of 16 Å ($R\approx 450$ at 7100 Å), is depicted in Fig. 3.

##  3 Stellar characterisation

We used the ALFOSC telluric-free spectrum to determine the spectral type of
TOI-519 by measuring various spectroscopic indices, or colour ratios, suitable
for M dwarfs. Some of these indices are nearly insensitive to the instrumental
correction errors and their sensitivity to low and moderate extinction is also
reduced, which makes them reliable indicators of spectral type. Other indices
are useful as luminosity and metallicity discriminants. We obtained the flux
ratios A, B/A, D/A, and TiO5 defined by Kirkpatrick et al. (1991) and Gizis
(1997), all of which explore strong atomic lines and molecular bands present
in M-type stars. Derived values and a short description of the features
covered by the flux ratios are given in Table 7. All of these indices show
very little dispersion in terms of spectral type and indicate that TOI-519 is
an M3.0–M3.5 dwarf. This spectral type is fully consistent with the absolute
magnitudes of TOI-519 in the optical through mid-infrared wavelengths (see
next subsection).

However, spectral indices covering widely separated pseudo-continuum and
feature regions yield later spectral types. The PC3 index defined by Martin et
al. (1996), which measures the spectroscopic slope between two pseudo-
continuum points of the optical data, delivers M5 spectral type (Table 7). The
best match to the ALFOSC spectrum among the data set of spectroscopic
templates of Kesseli et al. (2017) is provided by M4.0 spectral type as
illustrated in Fig. 3. This discrepancy of about one spectral type may be
explained by the presence of a moderate extinction or a higher metallicity.
The former scenario, although feasible given the low Galactic latitude of our
target ($b\approx+9$ deg), is less likely because of the close distance to
TOI-519. Also, $GJHK$ and WISE colours are compatible with one single spectral
type, which is a signpost of no or very little extinction towards TOI-519.
Nevertheless, to explore the high metallicity scenario in detail, higher
resolution spectra would be needed. To be conservative, we will adopt a
spectral type M3.0–M4.5 for TOI-519.

From the ALFOSC spectrum, H$\alpha$ is not seen in emission and we can impose
a lower limit of 0.5 Å to the pseudo-equivalent width of any emission feature
around 6563 Å. Potasium and sodium atomic lines, which are features rather
sensitive to temperature and surface gravity, are seen in absorption with
strengths similar to those of the M3.0–M4.5 standard stars. This suggests that
TOI-519 has a high surface gravity, thus discarding the idea that our target
is a very young or a giant star (and the atomic and molecular indices of Table
7 also reject our target being a giant or a subdwarf star).

From the spectral type—$T_{\rm eff}$ relationship given in Houdebine et al.
(2019), we derived $T_{\rm eff}=3350^{+100}_{-200}$ K for TOI-519, where the
quoted errors account for spectral types in the interval M3–M4.5. Houdebine et
al. (2019) claimed that their temperature calibration is valid for solar and
near-solar metallicities (only strongly metal-depleted M dwarfs deviate from
this calibration). TOI-519 does not show obvious absorption features due to
hydrides ( e.g., CaH) in the optical spectrum, which indicates that it is not
a subdwarf (Kirkpatrick et al., 2014). Using various $T_{\rm
eff}$—mass—stellar radii relationships available in the literature (e.g.,
Schweitzer et al. 2019; Houdebine et al. 2019; Cifuentes et al., submitted),
we obtained that TOI-519 has a radius of $R_{*}=0.373^{+0.020}_{-0.088}$ R⊙
and a mass of $M_{*}=0.369^{+0.026}_{-0.097}$ M⊙. This mass determination is
only slightly larger than that derived from Mann et al. (2019) relations,
$M_{\star}=0.36\pm 0.03\;M_{\odot}$, and both values are consistent at the 1
$\sigma$ level.

Table 2: Spectroscopic indices and color ratios.

Index | Feature | Value | SpT
---|---|---|---
A | CaH $\lambda$6975 Å | 1.24 | M3.0
B/A | Ti i $\lambda$7358 Å | 0.85 | M3.5
D/A | Ca ii $\lambda$8542 Å | 0.87 | M3.5
TiO5 | TiO $\lambda\lambda$7042–7135 Å | 0.48 | M3.0
PC3 | pseudo-continuum $\lambda\lambda$7569, 8250 Å | 1.21 | M5.0

777The uncertainty of the indices is 5% or less. All spectral types have been
rounded to the nearest half subtype.

Figure 3: The ALFOSC, telluric-free optical spectrum of TOI-519 is shown in
red (spectral resolution of 16 Å). For comparison purposes, the solar-
metallicity M4.0 spectral standard template from Kesseli et al. (2017) is also
plotted as the grey line (this spectrum has been degraded to the resolution of
our target and it is also corrected for the telluric lines absorption). The
most significant spectral features are labelled. The spectra are normalised to
unity at around 7500 Å.

###  3.1 Spectral Energy Distribution

As an independent determination of the stellar parameters, in particular the
stellar radius, we performed an analysis of the broadband spectral energy
distribution (SED) together with the Gaia DR2 parallax following the
procedures described in Stassun & Torres (2016) and Stassun et al. (2017a, b).
We pulled the $grizy$ magnitudes from the Pan-Starrs database, the $JHK_{S}$
magnitudes from 2MASS, and the $W1$–$W3$ magnitudes from WISE. Together, the
available photometry spans the full stellar SED over the wavelength range
0.4–10 $\mu$m (see Fig. 4).

Figure 4: Spectral energy distribution of TOI 519. Red symbols represent the
observed photometric measurements, where the horizontal bars represent the
effective width of the passband. Blue symbols are the model fluxes from the
best-fit NextGen atmosphere model (black).

We performed a fit using NextGen stellar atmosphere models, adopting the
effective temperature from the spectroscopically determined value. The
extinction ($A_{V}$) was set to zero due to the star being very near. The
metallicity was left as a free parameter. The resulting fit, shown in Fig. 4,
has a reduced $\chi^{2}$ of 2.5 and a best-fit metallicity of $0.0\pm 0.5$.
Integrating the model SED gives the bolometric flux at Earth of $F_{\rm bol}=$
$(3.20\pm 0.11)\times 10^{-11}$ erg s-1 cm-2. Taking the $F_{\rm bol}$ and
$T_{\rm eff}$ together with the Gaia DR2 parallax, adjusted by $+0.08$ mas to
account for the systematic offset reported by Stassun & Torres (2018), gives
the stellar radius as $0.342\pm 0.031\leavevmode\nobreak\ R_{\odot}$. Finally,
we estimate a mass of $0.36\pm 0.03$ $M_{\odot}$ via Mann et al. (2019)
empirical M-dwarf relations based on the absolute K-band magnitude. These
values are in agreement with the values estimated from the low-resolution
spectrum.

##  4 Light curve analysis

###  4.1 Overview

We modelled the TESS light curves simultaneously with the MuSCAT2, MuSCAT, and
LCOGT light curves following the approach described in Parviainen et al.
(2020) and Parviainen et al. (2019) to characterise the system and obtain a
robust ”true radius ratio” estimate for the companion. Next, we carried out a
phase curve analysis using the TESS light curve to constrain the companion’s
effective temperature and mass. As a double-check, we also carried out
separate analyses using only the TESS or the ground-based data, but we do not
detail those here. We have assumed zero eccentricity in all the analyses given
the short circularisation time scales for a one-day period (Dawson & Johnson,
2018).

The analyses were carried out with a custom Python code based on PyTransit
v2888https://github.com/hpparvi/pytransit (Parviainen, 2015; Parviainen et
al., 2019), which includes a physics-based contamination model based on the
PHOENIX-calculated stellar spectrum library by Husser et al. (2013). The limb
darkening computations were carried out with LDTk
999https://github.com/hpparvi/ldtk (Parviainen & Aigrain, 2015), and Markov
Chain Monte Carlo (MCMC) sampling was carried out with emcee (Foreman-Mackey
et al., 2013; Goodman & Weare, 2010). The code relies on the existing Python
packages for scientific computing and astrophysics: SciPy, NumPy (van der Walt
et al., 2011), AstroPy (The Astropy Collaboration et al., 2013; Price-Whelan
et al., 2018), photutils (Bradley et al., 2019), astrometry.net (Lang et al.,
2010), IPython (Perez & Granger, 2007), Pandas (Mckinney, 2010), xarray (Hoyer
& Hamman, 2017), matplotlib (Hunter, 2007), and seaborn. The analyses are
publicly available from
GitHub101010https://github.com/hpparvi/parviainen_2020_toi_519 as Jupyter
notebooks.

###  4.2 Multicolour transit analysis

The final multicolour photometry dataset consists of the 18 transits in the
TESS data from Sector 7, four transits observed simultaneously in four
passbands ($g$, $r$, $i$, and $z_{\mathrm{s}}$) with MuSCAT2, one transit
observed in three passbands ($g$, $r$, and $z_{\mathrm{s}}$) with MuSCAT, and
two transits observed in two passbands ($i$ and $z$) with the LCOGT
telescopes. This sums up to five passbands (we consider $z$ and
$z_{\mathrm{s}}$ the same), 25 transits, and 39 light curves.

The analysis follows standard steps for Bayesian parameter estimation
(Parviainen, 2018). First, we construct a flux model that aims to reproduce
the transits and the light curve systematics. Next, we define a noise model to
explain the stochastic variability in the observations not explained by the
deterministic flux model. Combining the flux model, the noise model, and the
observations gives us the likelihood. Finally, we define the priors on the
model parameters, after which we estimate the joint parameter posterior
distribution using Markov Chain Monte Carlo (MCMC) sampling.

The posterior estimation begins with a global optimisation run using
Differential Evolution (Storn & Price, 1997; Price et al., 2005) that results
with a population of parameter vectors clumped close to the global posterior
mode. This parameter vector population is then used as a starting population
for the MCMC sampling with emcee, and the sampling is carried out until a
suitable posterior sample has been obtained (Parviainen, 2018). The model
parametrisation, priors, and the construction of the posterior function follow
directly Parviainen et al. (2020).

###  4.3 Phase curve analysis

While multicolour transit analysis allows us to securely estimate the
companion’s radius ratio, modelling variations in the TESS light curve over
its orbital phase gives us a tool to estimate the companion’s effective
temperature, Bond albedo, and mass (Loeb & Gaudi, 2003; Mislis et al., 2012;
Shporer, 2017; Shporer et al., 2019). Phase curve modelling is a well-
established method for companion mass estimation, and has been widely used to
study planets and brown dwarfs found by the CoRoT and Kepler missions (i.e,
CoRoT-3b Mazeh & Faigler 2010; TrES-2b Barclay et al. 2012; Kepler-13b Shporer
et al. 2011 and Mislis & Hodgkin 2012; Kepler-91b Lillo-Box et al. 2014 and
Barclay et al. 2015; and Kepler-41b Quintana et al. 2013, to name a few, and
homogeneous phase-curve studies have been also reported by Esteves et al.
2013; Angerhausen et al. 2015; and Esteves et al. 2015).

The main four components contributing to the phase curve are Doppler boosting,
ellipsoidal variations, reflection, and thermal emission, as illustrated in
Fig. 5. The relative importance of the different effects depends on the
orbital geometry, the host star, and the companion properties. For example,
the effects of Doppler boosting (Loeb & Gaudi, 2003) are expected to be
significantly more important than ellipsoidal variations for TOI-519 b, as
visible from Fig. 6 depicting the peak-to-peak expected amplitudes for TOI-519
b.

Figure 5: Schematic showing Doppler boosting (DB), ellipsoidal variations
(EV), thermal emission (TE), and reflection (RF) and all the phase curve
components combined as a function of orbital phase. Figure 6: Amplitudes of
the four phase curve components for TOI-519 b as a function of the unknown
companion mass, Bond albedo ($A_{\mathrm{b}}$), and effective temperature.

Phase curve analysis can be useful in distinguishing between low-mass stars
and substellar objects orbiting low-mass stars on short-period orbits, and can
also be used to distinguish between brown dwarfs and planets if the
photometric precision is sufficiently high. In our case, the host star is
faint by TESS standards, and we do not expect to detect significant phase
variability if the companion is a planet or a low-mass brown dwarf. If the
companion was a low-mass star, however, Doppler boosting should give rise to a
clearly detectable signal. Our goal here is to derive upper limits for the
amplitudes of the different components, which can then be translated into
upper limits for the effective temperature, companion mass, and Bond albedo.

We model the TESS out-of-transit light curve with a phase curve model
combining reflection, thermal emission, Doppler boosting, and ellipsoidal
variations. The TESS data are prepared the same way as for the main transit
light curve analysis, but we exclude the transits from the light curve. We
also simplify the model slightly and fix the radius ratio, zero epoch, orbital
period, orbital inclination, and semi-major axis to their median posterior
values derived by the multicolour transit analysis (the uncertainties left in
these quantities after the multicolour modelling have a very minor effect on
the phase curve model), and assume a circular orbit.

The phase curve model is parameterised by the companion’s Bond albedo,
$A_{\mathrm{B}}$, log companion mass, $\log M_{\mathrm{p}}$, host star mass,
$M_{\star}$, and the effective temperatures of the host and the companion,
$T_{\star}$ and $T_{c}$, respectively. In its most abstract form, the model is
a sum of a constant baseline level $C$ ($\approx 1$) and the four components
multiplied by their amplitudes

$F(\phi)=C+A_{\mathrm{r}}F_{\mathrm{r}}+A_{\mathrm{t}}F_{\mathrm{t}}+A_{\mathrm{b}}F_{\mathrm{b}}+A_{\mathrm{e}}F_{\mathrm{e}},$
(1)

where $\phi\in[0,2\pi]$ is the orbital phase ($\phi=0$ for a transit),
$A_{\mathrm{r}}F_{\mathrm{r}}$ is the reflected light,
$A_{\mathrm{t}}F_{\mathrm{t}}$ is thermal emission,
$A_{\mathrm{b}}F_{\mathrm{b}}$ is the Doppler boosting, and
$A_{\mathrm{e}}F_{\mathrm{e}}$ is the ellipsoidal variation signal.

We approximate the planet as a Lambertian sphere111111Lambertian reflectance
is admittedly rather a poor reflectance model for a gas giant or a brown
dwarf, but sufficient for our purposes here. (Russell, 1916; Madhusudhan &
Burrows, 2012), for which the phase function is given as

$A_{\mathrm{r}}F_{\mathrm{r}}=k^{2}\frac{2}{3}\frac{A_{\mathrm{B}}}{a_{\mathrm{s}}^{2}}\times\frac{(\sin\alpha+(\pi-\alpha)\cos\alpha)}{\pi}\;\mathcal{E}(\phi),$
(2)

where $k$ is the planet-star radius ratio, $a_{\mathrm{s}}$ the scaled semi-
major axis, $\alpha$ the phase angle $\alpha=|\phi-\pi|$ , and $\mathcal{E}$
is the eclipse function that is modelled as a transit over an uniform disk but
with depth scaled from 0 (full eclipse) to 1 (out of eclipse).

The thermal emission is simplified to give a constant contribution to the
observed flux over the whole orbital phase except when the companion is
occulted by the star. The contribution is a product of planet-star area ratio
and planet-star flux ratio calculated by approximating the host star and the
companion as black bodies,

$A_{\mathrm{t}}F_{\mathrm{t}}=k^{2}\frac{\int
T(\lambda)\,P(T_{\mathrm{p}},\lambda)\,\mathrm{d}\lambda}{\int
T(\lambda)\,P(T_{\star},\lambda)\,\mathrm{d}\lambda}\times\mathcal{E}(\phi),$
(3)

where $T$ is the TESS passband transmission, $P$ is Planck’s law, and
$\lambda$ the wavelength.

The expected Doppler boosting is calculated following Loeb & Gaudi (2003)

$A_{\mathrm{b}}F_{\mathrm{b}}=\frac{\beta}{c}\left(\frac{2\pi
G}{p}\right)^{1/3}\frac{M_{p}\sin i}{M_{\star}^{2/3}}\times\sin\phi,$ (4)

where $c$ is the speed of light, $G$ is the gravitation constant, $p$ is the
orbital period, and $\beta$ is the photon-weighted passband-integrated beaming
factor (Bloemen et al., 2010), described as

$\beta=\frac{\int T(\lambda)\,\lambda F_{\lambda}\,B\,\mathrm{d}\lambda}{\int
T(\lambda)\,\lambda F_{\lambda}\,\mathrm{d}\lambda},$ (5)

where $F_{\lambda}$ is the stellar flux at wavelength $\lambda$, and
$B=5+\mathrm{d}\log F_{\lambda}/\mathrm{d}\log\lambda$ is the beaming factor
(Loeb & Gaudi, 2003).121212Methods to calculate the photon-weighted passband-
integrated beaming factor and the different phase curve components can be
found from PyTransit. The beaming factor is calculated based on a stellar
spectrum modelled by Husser et al. (2013) rather than a black body
approximation.

The ellipsoidal variation model follows from Pfahl et al. (2008) assuming a
circular orbit, and is

$A_{\mathrm{e}}F_{\mathrm{e}}=\frac{0.15(15+u)(1+g)}{3-g}\frac{M_{p}}{M_{\star}}\left(\frac{R_{\star}}{a}\right)^{3}\times\sin^{2}i\left(-\cos
2\phi\right),$ (6)

where $u$ is the linear limb darkening coefficient, $g$ is the gravity
darkening coefficient, $a$ is the semi-major axis, and $R_{\star}$ is the
stellar radius.

We model the correlated noise in the light curve as a Gaussian process (GP)
following an approximate Matern 3/2 kernel using the celerite package
(Foreman-Mackey et al., 2017). This is because the expected phase curve signal
amplitudes are very small, and correlated noise could either lead to a false
detection or mask an existing real signal, and, especially, affect the
posterior density tails. The flexibility from a GP model leads to a
conservative analysis where we can be secure we do not underestimate the
component amplitudes allowed by the data, and that the derived upper limits
are robust. The GP noise model is parametrised by log white noise, log input
scale and log output scale, all of which are kept free in the optimisation and
posterior estimation.

We set a normal prior on the host star effective temperature of
$\mathcal{N}(3300,100)$ K and uniform priors on the log companion mass (from
0.3 to 300$\,M_{\mathrm{Jup}}$, see also discussion about the posterior
sensitivity on the prior and parametrisation in Sect. 6), effective
temperature (from 500 to 3000 K), and Bond albedo (from 0 to 1). We set a
normal prior on the log white noise standard deviation,
$\mathcal{N}(\hat{s},0.15)$, where $\hat{s}$ is a white noise estimate
calculated from the flux point-to-point scatter. The log GP input scale has a
uniform prior $\mathcal{U}(-8,8)$, and the log output scale a wide normal
prior $\mathcal{N}(-6,1.5)$.

##  5 Results

Figure 7: The phase folded and binned TESS light curve, MuSCAT2 light curves,
MuSCAT light curves, and LCOGT light curves together with the posterior median
models and the residuals. The median baseline model has been removed from the
observed and modelled photometry for clarity.

We show the photometry used in the multicolour analysis with the transit model
in Fig. 7, the posterior densities for the true radius ratio, contaminant
effective temperature, impact parameter, and stellar density in Fig. 8, and
the final marginal posterior densities for the apparent and true radius ratio,
and the apparent and true absolute radius in Fig. 9. The multicolour analysis
gives a TESS contamination estimate of $0.31_{-0.02}^{+0.04}$, allows us to
exclude significant flux contamination from sources of different spectral type
than the host in the ground-based photometry, and also allows us to constrain
the contamination from sources with a same spectral type as the host star to
$<15\%$ in the ground-based photometry. This leads to median true radius ratio
of 0.298 with a 5th percentile posterior lower limit of 0.290 and a 95th
percentile posterior upper limit of 0.315.

The posterior densities for the companion mass, effective temperature, and
Bond albedo from the phase curve analysis are shown in Fig. 10. The phase
curve analysis leads to a $T_{\mathrm{eff,C}}$ posterior that is uniform
between $0$ K and $1750$ K and then quickly slopes to zero. A tentative mode
can be seen near 1700 K, but this is not statistically significant, and both
the companion mass and Bond albedo have their modes at lower prior limit. The
analysis allows us to set an upper limit of 1800 K (corresponding to the 95th
posterior percentile) for the companion $T_{\mathrm{eff}}$, an upper albedo
limit of 0.49, and upper companion mass limit of 14 $M_{\mathrm{Jup}}$. The
companion mass posterior has a long tail, with a 99th percentile at $\sim
22\,M_{\mathrm{Jup}}$.

The companion mass posterior derived from the Doppler boosting and ellipsoidal
variation signals can be sensitive on the prior set on the mass. We
parameterise the companion mass using log mass on which we set a uniform prior
(which translates to a non-uniform prior on the mass), since the companion
mass is a ”scale” parameter with an unknown magnitude (Gelman et al., 2013;
Parviainen, 2018). We tested the posterior sensitivity on the
parameterisation, and while the body of the posterior changes, the 95th
posterior percentile is not affected significantly.

Figure 8: Marginal and joint posterior distributions for a set of parameters
of interest from the joint light curve analysis. Figure 9: Marginal posterior
distributions for the apparent and true radius ratios (top), and the apparent
and true absolute planet radii (bottom). The true radius ratio posterior has a
long tail towards large values due to possible flux contamination. However,
its effect on the absolute radius estimate is minor due to the large
uncertainties in the stellar radius estimate. Figure 10: Marginal posterior
distributions for the companion mass, effective temperature, and Bond albedo.
The orange shading shows a set of posterior percentile limits. Table 3:
Relative and absolute estimates for the stellar and companion parameters
derived from the multicolour transit analysis.

_Ephemeris_
---
Transit epoch | $T_{0}$ | [BJD] | $2458491.8771169\pm 1.3\times 10^{-4}$
Orbital period | $P$ | [days] | $1.2652328\pm 5\times 10^{-7}$
Transit duration | $T_{14}$ | [h] | $1.2332\pm 0.0097$
_Relative properties_
Apparent radius ratio | $k_{\mathrm{app}}$ | $[R_{\star}]$ | $0.2939\pm 0.0037$
True radius ratio | $k_{\mathrm{true}}$ | $[R_{\star}]$ | $0.30\;(-0.0058)\;(+0.0091)$
Scaled semi-major axis | $a_{\mathrm{s}}$ | $[R_{\star}]$ | $10.11\pm 0.14$
Impact parameter | $b$ |  | $0.19\;(-0.09)\;(+0.06)$
_Absolute properties_
Apparent companion radiusa | $R_{\mathrm{p,app}}$ |  [$R_{\mathrm{Jup}}$ ] | $0.73\pm 0.20$
True companion radiusa | $R_{\mathrm{p,true}}$ |  [$R_{\mathrm{Jup}}$ ] | $0.75\pm 0.21$
Semi-major axisa | $a$ | [AU] | $0.012\pm 0.004$
Eq. temperatureb | $T_{\mathrm{eq}}$ | [K] | $760\pm 54$
Stellar density | $\rho_{\star}$ | $[\mathrm{g\,cm^{-3}}]$ | $12.20\;(-0.44)\;(+0.55)$
Inclination | $i$ | [deg] | $88.9\pm 0.4$

131313 The estimates correspond to the posterior median ($P_{50}$) with
$1\sigma$ uncertainty estimate based on the 16th and 84th posterior
percentiles ($P_{16}$ and $P_{84}$, respectively) for symmetric, approximately
normal posteriors. For asymmetric, unimodal posteriors, the estimates are
$P_{50}{}^{P_{84}-P_{50}}_{P_{16}-P_{50}}$. $a$$a$footnotetext: The semi-major
axis and planet candidate radius are based on the scaled semi-major axis and
true radius ratio samples, and the stellar radius estimate shown in Table 1.
$b$$b$footnotetext: The equilibrium temperature of the planet candidate is
calculated using the stellar $T_{\mathrm{eff}}$ estimate, scaled semi-major
axis distribution, heat redistribution factor distributed uniformly between
0.25 and 0.5, and planetary albedo distributed uniformly between 0 and 0.4.

##  6 Discussion and Conclusions

Figure 11: TOI-519 b in the context of currently known transiting planet and
brown dwarf systems. First (top), we show the radius as a function of orbital
period for transiting planets and brown dwarfs (BDs) with a focus on
companions around cool ($T_{\mathrm{eff}}<4000$ K) host stars. Transiting
planets around cool hosts are shown as orange-rimmed stars, transiting BDs
around cool hosts as orange-rimmed circles, transiting BDs around hot host
($T_{\mathrm{eff}}>4000$ K) as dark-blue-rimmed circles, and transiting
planets around hot hosts as blue shading. Next (bottom), we show the radius as
a function of the effective temperature of the host star for transiting
planets (stars) and brown dwarfs (circles). Objects with $P<1$ d are coloured
as dark blue, $1<P<5$ d as orange, and $P>5$ d as light grey. Figure 12:
TOI-519 b in the context of currently known transiting planet and brown dwarf
systems and eclipsing M dwarf binaries marked as dark red circles. Otherwise
as in Fig. 11.

The reliability of transiting planet candidate validation based on
constraining the size of the transiting object depends crucially on the
reliability of the stellar radius estimate. Large ($\sim 1R_{\mathrm{Jup}}$)
companions around low-mass stars are especially problematic due to the mass-
radius degeneracy for objects in this radius regime and uncertainties in the
low-mass star radii. For TOI-519 b, while the radius ratio is well-
constrained, the companion’s absolute radius depends on the stellar radius
estimate based on M dwarf mass-radius relations and stellar classification
based on low-resolution spectroscopy template matching. The companion radius
posterior ranges from 0.66 $R_{\mathrm{Jup}}$ (certainly a planet) to 1.20
$R_{\mathrm{Jup}}$ (low-mass star or young brown dwarf). Only with the
effective temperature and companion mass limits from the phase curve analysis
can we assess if the object is substellar.

The radius, effective temperature, and mass constraints from the multicolour
and phase curve analyses validate TOI-519 b as a substellar object. That is,
with $R\sim 1\,R_{\mathrm{Jup}}$, $M<14\,M_{\mathrm{Jup}}$, and
$T_{m}athrm{p}<1800$ K, TOI-519 b is either a very low mass brown dwarf or a
massive planet located in a very sparsely populated region in the period-
radius space for substellar objects around M dwarfs. Here, the mass limit from
the Doppler boosting creates a stronger constrain on the nature of the
companion than the temperature limit, since the system is likely old enough
that even a low-mass star could have cooled down below our detection
threshold. Further, the upper mass limit favours the hypothesis that TOI-519 b
is a planet rather than a brown dwarf, but a brown dwarf scenario is strongly
favoured a priori. The currently known hot Jupiters around M dwarfs generally
orbit hosts hotter than 3700 K with periods larger than 2 days, with the
exception of Kepler-45b (see Fig. 11), and the (period, radius, host
$T_{\mathrm{eff}}$) space TOI-519 b falls in is dominated by brown dwarfs.

We caution that, in the case of TOI-519, the TESS crowding metric appears to
be overestimated by the PDC pipeline. The CROWDSAP value that corresponds to
the ”ratio of target flux to the total flux in optimal aperture” is 0.51,
corresponding to a contamination of 0.49, while our derived TESS contamination
posterior median is 0.31. Our TESS contamination estimate can be considered
secure since it is directly related to the differences in the apparent transit
depths measured from the TESS and ground-based light curves. The ground-based
transits are shallower than expected based on the crowding-corrected (PDC)
TESS-observations, and this can only happen if the crowding is overestimated.
Overestimated crowding leads to an overestimated radius ratio, and, thus,
overestimated absolute radius. While this may be a rare occurrence, it is
recommended to check for discrepancies between the TESS and ground-based
photometry when carrying out a transit analysis, and include a free
contamination factor for the TESS photometry if a joint transit analysis can
be carried out with ground-based photometry.

Figure 11 shows TOI-519 b in the context of all currently known planets and
brown dwarfs transiting cool host stars, and Fig. 12 extends these to include
eclipsing M dwarf binaries. While the small number of objects does not allow
to make any statistically significant inferences, we can recognise some
curious features whose significance will be uncovered in the future. First,
all large ($R>0.5\,R_{\mathrm{Jup}}$) objects orbiting cool
($T_{\mathrm{eff}}<4000$ K) dwarfs with periods shorter than 2 d are brown
dwarfs. If TOI-519 b is confirmed to be planet it will be the only inhabitant
of this parameter space. However, this feature is not very significant in the
current context of low-number statistics, since all four of the known hot
Jupiters orbiting M dwarfs have periods from 2 to 4 d (i.e also relatively
short). More significant is the lack of large objects around cool dwarfs in
the period range of 4 to 200 d, but this can be largely due to observational
biases (the figure includes only transiting objects with measured radii).

The lower panel of Figure 11 shows a radius versus host stellar temperature.
We note that giant planets and brown dwarfs seem to be found orbiting distinct
spectral types. All large objects ($R>0.5\,R_{\mathrm{Jup}}$) around the
coolest dwarfs ($T_{\mathrm{eff}}<3400$ K) are brown dwarfs, except for
HATS-71 A b, and these transiting brown dwarfs seem to be clustered orbiting
cool dwarfs with $T_{\mathrm{eff}}\sim 3100-3400$ K. On the contrary, giant
planets are found around spectral types with $T_{\mathrm{eff}}>3700$ K. For
the spectral types with $T_{\mathrm{eff}}\sim 3400-3700$ K there is a desert
of any companions with a $R>0.5\,R_{\mathrm{Jup}}$. Whether this apparent
clustering is of any significance needs to be verified by more hot Jupiter and
brown dwarf discoveries around cool dwarfs.

###### Acknowledgements.

We thank the anonymous referee for their helpful and constructive comments. We
acknowledge financial support from the Agencia Estatal de Investigación of the
Ministerio de Ciencia, Innovación y Universidades and the European FEDER/ERF
funds through projects ESP2013-48391-C4-2-R, AYA2016-79425-C3-2-P,
AYA2015-69350-C3-2-P, and PID2019-109522GB-C53, and PGC2018-098153-B-C31. This
work is partly financed by the Spanish Ministry of Economics and
Competitiveness through project ESP2016-80435-C2-2-R. We acknowledge supports
by JSPS KAKENHI Grant Numbers JP17H04574, JP18H01265, and JP18H05439, and JST
PRESTO Grant Number JPMJPR1775. JK acknowledges support by Deutsche
Forschungsgemeinschaft (DFG) grants PA525/18-1 and PA525/19-1 within the DFG
Schwerpunkt SPP 1992, Exploring the Diversity of Extra-solar Planets. MT is
supported by JSPS KAKENHI grant Nos. 18H05442, 15H02063, and 22000005. This
work was partly supported by Grant-in-Aid for JSPS Fellows, Grant Number
JP20J21872. This article is partly based on observations made with the MuSCAT2
instrument, developed by ABC, at Telescopio Carlos Sánchez operated on the
island of Tenerife by the IAC in the Spanish Observatorio del Teide. We
acknowledge the use of public TESS Alert data from pipelines at the TESS
Science Office and at the TESS Science Processing Operations Center. This work
makes use of observations from the LCOGT network. Resources supporting this
work were provided by the NASA High-End Computing (HEC) Program through the
NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the
production of the SPOC data products. This work makes use of observations from
the LCOGT network.

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