# Separated twins or just siblings? A multi-planet system around an M dwarf
including a cool sub-Neptune

Mallory Harris Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA  Diana Dragomir Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA  Ismael Mireles  Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA  Karen A. Collins Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Solène Ulmer-Moll  Observatoire de Genève, Université de Genève, Chemin Pegasi 51, CH-1290 Sauverny, Switzerland  Physikalisches Institut, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland  Steve B. Howell  NASA Ames Research Center, Moffett Field, CA 94035, USA  Keivan G. Stassun Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA  George Zhou Centre for Astrophysics | University of Southern Queensland, Toowoomba, QLD, AU  Carl Ziegler Department of Physics, Engineering and Astronomy, Stephen F. Austin State University, 1936 North St, Nacogdoches, TX 75962, USA  François Bouchy Observatoire de Genève, Université de Genève, Chemin Pegasi 51, CH-1290 Sauverny, Switzerland  César Briceño  Cerro Tololo Inter-American Observatory, Casilla 603, La Serena, Chile  David Charbonneau Harvard-Smithsonian Center for Astrophysics, 60 Garden St, Cambridge, MA 02138, USA  Kevin I. Collins George Mason University, 4400 University Drive, Fairfax, VA, 22030 USA  Gábor Fűűrész  Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Natalia M. Guerrero Department of Astronomy, University of Florida, Gainesville, FL, 32611, USA  Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Jon M. Jenkins NASA Ames Research Center, Moffett Field, CA 94035, USA  Eric L. N. Jensen Department of Physics & Astronomy, Swarthmore College, Swarthmore PA 19081, USA  Martti H. K. Kristiansen Brorfelde Observatory, Observator Gyldenkernes Vej 7, DK-4340 Tølløse, Denmark  Nicholas Law  Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA  Monika Lendl Observatoire de Genève, Université de Genève, Chemin Pegasi 51, CH-1290 Sauverny, Switzerland  Andrew W. Mann Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA  Hugh P. Osborn Physikalisches Institut, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland  Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Samuel N. Quinn Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  George R. Ricker Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Richard P. Schwarz Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Sara Seager Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Eric B. Ting NASA Ames Research Center, Moffett Field, CA 94035, USA  Roland Vanderspek Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  David Watanabe Planetary Discoveries, Fredericksburg, VA 22405, USA  Joshua N. Winn Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA

###### Abstract

We report the discovery of two TESS sub-Neptunes orbiting the early M dwarf
TOI-904 (TIC 261257684). Both exoplanets, TOI-904 b and c, were initially
observed in TESS sector 12 with twin sizes of 2.49R⊕ and 2.31R⊕, respectively.
Through observations in five additional sectors in the TESS primary mission
and the first and second extended missions, the orbital periods of both
planets were measured to be 10.887$\pm$0.001 and 83.999$\pm$0.001 days,
respectively. Reconnaissance radial velocity measurements (taken with
EULER/CORALIE) and high resolution speckle imaging with adaptive optics
(obtained from SOAR/HRCAM and Gemini South/ZORRO) show no evidence of an
eclipsing binary or a nearby companion, which together with the low false
positive probabilities calculated with the statistical validation software
TRICERATOPS establish the planetary nature of these candidates. The outer
planet, TOI-904 c, is the longest-period M dwarf exoplanet found by TESS, with
an estimated equilibrium temperature of 217K. As the three other validated
planets with comparable host stars and orbital periods were observed by Kepler
around much dimmer stars (Jmag $>$ 12), TOI-904 c, orbiting a brighter star
(Jmag $=$ 9.6), is the coldest M dwarf planet easily accessible for
atmospheric follow-up. Future mass measurements and transmission spectroscopy
of the similar sized planets in this system could determine whether they are
also similar in density and composition, suggesting a common formation
pathway, or whether they have distinct origins.

††facilities: LCOGT, Gemini South/ZORRO, EULER/CORALIE, SOAR/HRCAM††software:
AstroImageJ (Collins et al., 2017), TAPIR (Jensen, 2013), astropy (Astropy
Collaboration et al., 2013, 2018, 2022), triceratops (Giacalone & Dressing,
2020), juliet (Espinoza et al., 2019), emcee (Foreman-Mackey et al., 2013),
batman (Kreidberg, 2015), wotan (Hippke et al., 2019), eleanor (Feinstein et
al., 2019), dynesty (Speagle, 2020), LDTK (Parviainen & Aigrain, 2015; Husser
et al., 2013), SpecMatch-Emp (Yee et al., 2017)

tablenum SIXtablenum

##  1 Introduction

The past decade of exoplanet exploration has revealed that M dwarf stars
typically host multiplanet systems of small, rocky planets with orbital
periods P$<$20 days (Dressing & Charbonneau, 2015; Hardegree-Ullman et al.,
2019). As these cool, low-mass stars allow for easier detections and
characterizations of exoplanets than larger hosts, whether via deeper transits
or more significant radial velocity reflex motion, these short-period planets
have been prioritized for in-depth study by the exoplanet community. Yet few
planets have been found at greater distances from M dwarf hosts to date.
Indeed, the Kepler mission only discovered $\sim$30 M dwarf planets at
distances $>0.15$ AU (periods P$>$25 days) (Muirhead et al., 2012; Barclay et
al., 2015; Torres et al., 2015; Dressing & Charbonneau, 2015; Morton et al.,
2016; Torres et al., 2017; Berger et al., 2018), all of which orbit stars
dimmer than Vmag$=$15 and thus are not easily accessible for ground-based
observations. By prioritizing M dwarf stars and focusing on stars in the solar
neighborhood, the Transiting Exoplanet Survey Satellite (TESS) now has the
potential to populate this under-explored region of parameter space and
provide targets for future characterization.

TESS is conducting a full-sky survey of nearby, bright stars, 75$\%$ of which
are M dwarfs (Ricker et al., 2015). Unlike Kepler, which observed one region
of the sky for four years, the TESS primary mission observed both hemispheres
by cycling through 26 sectors observed for $\sim$27 day intervals, and it is
continuing to re-observe the hemispheres (as well as the ecliptic) in the same
fashion through its extended missions. While this observation strategy makes
TESS most sensitive to planets with P$\lesssim$10 days, there exists the
potential to observe planets with longer orbital periods in overlapping
sectors near the ecliptic poles. Further, TESS is projected to observe many
planets with P$\gtrsim$25 days as single-transit events (Villanueva et al.,
2019) that could be recovered in later extended missions. Since its launch in
2018, TESS has found 28 confirmed planets with periods $>$25 days, 5 of which
(Cañas et al., 2020; Rodriguez et al., 2020; Fukui et al., 2022; Mann et al.,
2022; Schanche et al., 2022) orbit low-mass stars.

In this Letter, we introduce and statistically validate TESS Object of
Interest (TOI) 904 c, a sub-Neptune with a period of 84 days that was observed
to produce a single transit event in four different sectors of the TESS
primary mission and its first and second extended missions. We also introduce
another planet in the same system (TOI-904 b) with a period of 10.87 days.
Orbiting an early M dwarf (TIC 261257684, TOI-904) at Tequil$\approx$200K,
TOI-904 c is the coldest M dwarf planet discovered by TESS to date. Only three
other transiting planets have been observed around low-mass stars with similar
orbital periods: Kepler-186 f (P=129.94 days; Quintana et al., 2014),
Kepler-1229 b (P=86.83 days; Morton et al., 2016) and Kepler-1628 b (P=76.38
days; Morton et al., 2016). Unlike these planets, TOI-904 c orbits an M dwarf
bright enough (Jmag = 9.61) for future mass measurements and atmospheric
characterization. Through these additional observations, this system embodies
a (currently) unique opportunity to test theories of planet formation around
low-mass stars. Further, by measuring the densities and constraining the
composition of both planets in this system, we can determine whether these
similarly sized planets also have twin compositions and formation histories,
or if they evolved through distinct formation pathways while orbiting the same
host star.

##  2 Observations

###  2.1 TESS Observations

TESS observed TOI-904 in Sectors 12 and 13 (2019 May 21 to 2019 July 17) of
its primary mission (PM), Sectors 27, 38 and 39 (2020 July 05 to 2020 July 30,
2021 April 29 to 2021 June 24) of its first extended mission (EM1) and Sector
61 (2023 January 18 to 2023 February 12) of its second extended mission (EM2).
TOI-904 was included in the TESS Candidate Target List (Stassun et al., 2019)
and was monitored in both the 2-minute postage stamps (PS) and longer cadence
(30-minutes in PM, 10-minutes in EM1, 200-seconds in EM2) Full-Frame Images
(FFI) during both missions (see Fig. 1). The transit signatures of TOI-904 b
and c were initially detected by the Science Processing Operations Center,
(SPOC; Jenkins et al., 2016) located at the NASA Ames Research Center, in a
transit search of Sector 12 with a noise-compensating matched filter (Jenkins,
2002; Jenkins et al., 2010, 2020) on 2019 July 01. This filter originally
folded a single transit of TOI-904 c onto the second transit of TOI-904 b.
Both the SPOC and the Visual Survey Group (VSG; Kristiansen et al., 2022)
working in conjunction with the TESS Single Transit Planet Candidate Working
Group (TSTPC) flagged these transit events and attributed both to a single
planet candidate with an orbital period of $18.35\pm 0.005$ days. The correct
period of TOI-904 b, $10.877\pm 0.001$ days, was identified by the SPOC via a
transit search of Sector 13 conducted on 2019 July 27. The transit signature
passed all the diagnostic tests presented in the resulting Data Validation
report (Twicken et al., 2018) and was fitted with an initial limb-darkened
transit model (Li et al., 2019). The difference image centroiding test located
the source of the transit signature to within 1.3$\pm$2.9 arcsec. The TESS
Science Office reviewed the diagnostic results and issued an alert for
TOI-904.01 on 2019 June 23 (Guerrero et al., 2021), and it was then recognized
as a TESS Object of Interest on 2019 July 15 on the TESS data alerts web
portal at the Massachusetts Institute of
Technology111https://doi.org/10.17909/t9-wx1n-aw08.

Figure 1: TESS observations of TOI-904. Panel (a): Raw observations of each
TESS sector, with 2-minute data shown in light grey and 10-minute binned data
shown in dark grey. We show the Tukey biweight trend calculated with the wotan
(Hippke et al., 2019) library of the variability is shown in dark blue. Each
planet transit is denoted by an arrow at the bottom of the graph, with blue
denoting transits of TOI-904 b and gold denoting transits TOI-904 c. Panel
(b): TESS data detrended by the same fit, with each transit high-lighted in
the same color as the arrows in the previous figure. Panel (c): The phase
folded light curves of transits of TOI-904 b with the transit fit including a
shaded region denoting $1\sigma$ uncertainty. Panel (d): The phase-folded
light curves of TOI-904 c with the transit fit including a shaded region
denoting $1\sigma$ uncertainty.

The SPOC conducted a subsequent multisector search of Sectors 12, 13, 27, 38
and 39 on 2021 July 25, where they recovered 12 transits of TOI-904 b and the
signature of TOI-904 c at 4$\times$ the true period (see Appendix B). The SPOC
found the difference imaging centroiding test located the source of the
transit signature to within 3.4$\pm$3.4 arcsec. In August 2021, a member of
the TSTPC working group (Hugh Osborn) found an undetected additional transit
of TOI-904 c in SPOC-produced light curves near the end of TESS Sector 39,
which together with the Sector 12 transit constrained the period of this
planet to a discrete set of possible aliases. We proceeded to search all
previous TESS observations of this star for additional transits of this outer
planet, and discovered a third clear transit in TESS Sector 27 from which we
were able to derive a unique period of $83.999\pm 0.001$ days. This planet was
registered as a community TOI on 2021 September 01, and the TESS Science
Office issued an alert for it on 2022 April 20. We searched the TESS
observations of TOI-904 for any additional transit signals and found no
evidence of additional planets in this system from the transit method.

To investigate possible false positive scenarios of the planets that were
observed in this system, we visually inspected the background of each
individual light curve that included a transit of the outer planet to rule out
false positives due to asteroids or other anomalies. We also used the Gaia DR3
(Gaia Collaboration et al., 2022) to investigate the possibility for blended
objects in the aperture and whether the Re-normalised Unit Weight Error
(RUWE), a measure of the normalized chi-square of the Gaia observations to the
astronometric single-star fit corrected for color and magnitude dependencies
(Lindegren et al., 2018; Pearce et al., 2020), indicated that the host star
existed in a binary that could be responsible for the observed transits. With
a RUWE metric $\approx$0.999, TOI-904 showed no obvious indication of being a
stellar binary (Pearce et al., 2020). As our preliminary inspection gave no
indication that either planet candidates’ transits were false positives, we
looked to follow-up observations (as described in the following Sections) to
further validate this system.

###  2.2 Ground-Based Photometry

The TESS pixel scale is $\sim 21\arcsec$ pixel-1, and photometric apertures
typically extend out to roughly 1 arcminute, which generally results in
multiple stars blending in the TESS aperture. An eclipsing binary in one of
the nearby blended stars could thus mimic a transit-like event in the large
TESS aperture. With additional ground-based photometric observations, we can
attempt to (1) rule out or identify nearby eclipsing binaries (NEBs) as
potential sources of the detection in the TESS data, (2) check for the
transit-like event on-target using smaller photometric apertures than in the
TESS images to confirm that the event is occurring on-target, or in a star so
close to TOI-904 that it was not detected by Gaia DR3 (which is unlikely as
such a star would be too faint unless it is perfectly aligned with the target
star, but which is accounted for in the triceratops transit probability
calculation in Section 3.2), and (3) refine the TESS ephemeris.

####  2.2.1 Las Cumbres Observatory

We acquired ground-based transit follow-up photometry of TOI-904 b as part of
the TESS Follow-up Observing Program Sub Group 1 (TFOP SG1; Collins,
2019)222https://tess.mit.edu/followup. We used the TESS Transit Finder, which
is a customized version of the Tapir software package (Jensen, 2013), to
schedule our transit observations and AstroImageJ (Collins et al., 2017) to
extract differential photometry.

We observed predicted transit windows of TOI-904 b in Pan-STARRS $z$-short
band from the Las Cumbres Observatory Global Telescope (LCOGT; Brown et al.,
2013) 1.0 m network nodes at Siding Spring Observatory and South Africa
Astronomical Observatory on UTC 2020 October 15 and 2020 December 19,
respectively. The 1 m telescopes are equipped with $4096\times 4096$ SINISTRO
cameras having an image scale of $0\farcs 389$ per pixel, 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).

We used circular photometric apertures of radius $1\farcs 9$ and $5\farcs 8$
to check for possible NEBs that could be contaminating the SPOC photometric
apertures, which generally extend $\sim 1\arcmin$ from the target star. To
account for possible contamination from the wings of neighboring star PSFs, we
searched for NEBs in all known Gaia EDR3 and TIC version 8 nearby stars out to
$2\farcm 5$ from TOI-904 that are possibly bright enough in TESS band to
produce the TESS detection (assuming a 100% eclipse and 100% contamination of
the TESS aperture). To attempt to account for possible delta-magnitude
differences between TESS-band and the follow-up Pan-STARRS $z$-short band, we
checked stars that are an extra 0.5 magnitudes fainter in TESS-band than
needed. We consider a star cleared of an NEB if the RMS of its 10-minute
binned light curve is more than a factor of 5 smaller than the adjusted
expected NEB depth in the star (adjusted to allow for the potential TESS-band
delta-magnitude difference). We then visually inspect each neighboring star’s
light curve to ensure no obvious eclipse-like signal. The NEB check light
curve data are available at ExoFOP-
TESS333https://exofop.ipac.caltech.edu/tess/target.php?id=261257684. We rule
out an NEB as the source of the TOI-904 b signal in the TESS data.

Photometry of TOI-904 was extracted using circular apertures with radius
$5\farcs 8$, which exclude flux from the nearest known Gaia EDR3 and TIC
neighbor (TIC 724109412) $25\farcs 4$ Southwest. We detect the transit event
within the TOI-904 photometric apertures in the two $z$-short band light
curves and include the data in the analyses of this work (see Fig. 2).

We attempted to observe an additional transit of TOI-904 c on UTC 2022
February 27 with the South Africa Astronomical Observatory, resulting in a
tentative partial transit detection. This detection, however, lacked a
sufficient out-of-transit baseline to be conclusive and is not included in the
analyses of this work.

###  2.3 Spectroscopic Follow-up

Figure 2: Follow-up observations of the planetary system around TOI-904. Left:
CORALIE observations phase-folded on the periods of both TOI-904 b (Panel (a),
dark blue) and TOI-904 c (Panel (b), gold). The best fit radial velocity
trends for both phase-folded data sets are shown in light blue. Neither figure
shows evidence of a stellar or brown dwarf mass companion. Panel (c): high-
resolution imaging taken at 562 nm and 832 nm (blue and gold, respectively).
There is no clear flux from another object between 0.1 and 1.2 arcsec down to
4 and 8 magnitude differences, respectively, and thus no evidence of a
blending or binary star. Panel (d): Ground based photometric observations of
TOI-904 b taken with the LCOGT Siding Spring Observatory (Panel (d) left) and
the South Africa Astronomical Observatory (Panel (d) right). Observations were
taken in 36 second intervals (light blue) and were binned to 5 minutes (dark
blue). The best-fit transit model is overlaid in black, showing that both
observations recover full transits of the planet at a comparable depth to the
TESS observations.

Brown dwarf or grazing stellar binaries are frequent sources of false positive
transit signals. While few instruments are capable of confirming the exoplanet
nature of transits by measuring the masses of small extrasolar planets, many
more are equipped to detect the Doppler signal caused by a stellar or brown
dwarf mass companion. Reconnaissance radial velocity measurements of the host
star are thus able to rule out a false positive due to a bound stellar (or
brown dwarf) binary while also providing key observations to refine the
spectroscopic parameters of the host star.

####  2.3.1 SMARTS/CHIRON Spectroscopy

We obtained four observations of TOI-904 with the CHIRON facility on the
SMARTS 1.5-meter telescope at Cerro Tololo Inter-American Observatory, Chile
(Tokovinin et al., 2013). CHIRON is a high resolution spectrograph with a
resolving power of $R=80,000$ over the wavelength range of $4100-8700$ Å with
‘slicer’ mode observations. The spectra were extracted via the standard
pipeline as per Paredes et al. (2021).

We attempted to derive a line broadening velocity from the CHIRON
observations. We performed a least-squares deconvolution between each spectrum
and a non-rotating synthetic spectrum generated via the ATLAS9 model
atmospheres grid (Castelli & Kurucz, 2004) at the stellar effective
temperature and surface gravity of our target star. We then modeled the line
broadening profile via a combination of the rotational, radial-tangential
macroturbulent, and instrumental broadening kernels (as per Gray & Corbally,
1994). We find the rotational broadening component to have width of
$<2\,\mathrm{km\,s}^{-1}$ ($1\sigma$) when the additional broadening terms are
considered, consistent with expectations from the photometric modulation
derived rotation period of the target star.

####  2.3.2 EULER/CORALIE Spectroscopy

TOI-904 was observed by the Swiss 1.2m Euler telescope with the CORALIE
instrument installed at its Nasmyth focus. CORALIE is a fiber-fed high-
resolution spectrograph with a spectral resolution of 60,000 (Queloz et al.,
2001). CORALIE has a 3 pixel sampling per resolution element. Five spectra of
TOI-904 were taken between 2020 February 2 and April 14 (see Figure 2). The
observations have an exposure time of 2400 s and reach a signal-to-noise ratio
varying between 11 and 16. The observations are targeting the extreme phases
of the estimated radial velocity signal (see Fig. 2 Panels a and b). The
radial velocity is extracted by cross-correlating a M2 stellar mask with each
spectrum (Pepe et al., 2002). The radial velocity data has an RMS of 15 m/s
over the time span of the observations.

###  2.4 High Angular Resolution Imaging

Close stellar companions (bound or line of sight) can confound exoplanet
discoveries in a number of ways. The detected transit signal might be a false
positive due to a background eclipsing binary and even real planet discoveries
will yield incorrect stellar and exoplanet parameters if a close companion
exists and is unaccounted for (Furlan & Howell, 2017, 2020). Additionally, the
presence of a bound companion star leads to the non-detection of small planets
residing with the same exoplanetary system (Lester et al., 2021).

####  2.4.1 SOAR/HRCAM High-Resolution Imaging

We searched for stellar companions to TOI-904 with speckle imaging on the
4.1-m Southern Astrophysical Research (SOAR) telescope (Tokovinin, 2018) on
2022 January 07 UT, observing in Cousins I-band, a similar visible bandpass as
TESS. This observation was sensitive to a 5.4-magnitude fainter star at an
angular distance of 1 arcsec from the target. No nearby stars were detected
within 3″of TOI-904 in the SOAR observations.

####  2.4.2 Gemini South/ZORRO High-Resolution Imaging

TOI-904 was observed on 2021 October 21 UT and 2022 January 13 UT using the
Zorro speckle instrument on the Gemini South 8-m telescope (Scott et al.,
2021; Howell & Furlan, 2022). Zorro provides simultaneous speckle imaging in
two bands (562nm and 832 nm) with output data products including a
reconstructed image with robust contrast limits on companion detections. While
both observations had consistent results that TOI-904 is a single star to
within the angular and contrast levels achieved, the January 2022 observation
had better seeing which led to deeper contrast levels. Seven sets of 1000 X
0.06 second images were obtained and processed in our standard reduction
pipeline(Howell et al., 2011). Figure 2 Panel c shows our final contrast
curves and the 832 nm reconstructed speckle image. We find that TOI-904 is a
single star with no companion brighter than 5-8 magnitudes below that of the
target star from the 8-m telescope diffraction limit (20 mas) out to 1.2”. At
the distance of TOI-904 (d=46 pc) these angular limits correspond to spatial
limits of 0.9 to 55 AU.

##  3 Analysis

Stellar Parameters | Planet Parameters
---|---
Catalogue Data† | Model Properties
TIC ID | 261257684 | Fixed Initial Parameters |
TOI | 904 |  $q_{1,TESS}$∗ | 0.336
R.A. | 05:57:29.11 |  $q_{2,TESS}$∗ | 0.208
Dec | -83:07:47.02 |  $q_{1,zs}$∗ | 0.281
pmRA (mas yr-1) | $-28.941\pm 0.032$ |  $q_{2,zs}$∗ | 0.192
pmDec (mas yr-1) | $110.858\pm 0.033$ | eccentricity | 0.0
Parallax (mas) | 21.697$\pm$0.016 |  $\omega$ (deg) | 90.0
Distance (pc) | 46.089$\pm$0.035 | Dilution† | 0.994
|  | Planet b | Planet c
|  | Modeled Parameters |
Photometric Properties† | (SPOC individual fits)⋄ |
TESS mag | 10.846$\pm 0.007$ | T0 (BJD-TDB) | 2366.621${}^{+0.001}_{-0.002}$ | 2386.349${}^{+0.003}_{-0.004}$
GAIA mag | 11.8559$\pm$0.0004 | Period (days) | 10.8772${}^{+0.0003}_{-0.0003}$ | 83.9997${}^{+0.0006}_{-0.0007}$
V mag | 12.588$\pm$0.069 | R${}_{p}/$R∗ | 0.039${}^{+0.001}_{-0.001}$ | 0.038${}^{+0.001}_{-0.001}$
J mag | 9.607$\pm$0.022 |  $\rho_{*}$ (cgs) | 1.878${}^{+2.710}_{-0.960}$ | 5.545${}^{+1.304}_{-2.535}$
K mag | 8.766$\pm$0.021 |  $i$ (deg) | 88.19${}^{+1.26}_{-0.876}$ | 89.83${}^{+0.13}_{-0.20}$
Stellar Properties | Derived Properties |
M∗∙ (M⊙) | 0.557$\pm 0.028$ | Rp (R⊕) | 2.426${}^{+0.163}_{-0.152}$ | 2.167${}^{+0.130}_{-0.118}$
R∗∙ (R⊙) | 0.527$\pm$0.021 | R${}_{*}/$a | 0.043${}^{+0.015}_{-0.009}$ | 0.0078${}^{+0.0005}_{-0.0014}$
L∗∙ (L⊙) | 0.051$\pm 0.012$ | a (AU) | 0.056${}^{+0.019}_{-0.012}$ | 0.312${}^{+0.023}_{-0.058}$
$\rho_{*}$⋄ (cgs) | 5.360$\pm$0.296 | b | 0.714${}^{+0.124}_{-0.422}$ | 0.373${}^{+0.288}_{-0.280}$
Teff‡ (K) | 3770.2$\pm$70.0 | tduration (hours) | 3.65${}^{+1.27}_{-0.78}$ | 5.04${}^{+0.37}_{-0.93}$
$[$Fe$/$H$]$‡ (dex) | 0.022$\pm$0.090 | Teq (K) | 429.43$\pm$32.61 | 217.26$\pm$9.10
$v\,sin\,i^{\Join}$ (km $s^{-1}$) | $<2$ |  |  |
Age∙ (Gyr) | 1.5$\pm$0.2 |  |  |
| (or 0.8$\pm$0.1) |  |  |
Table 1: Table of TOI-904 stellar parameters as well as the fitted and derived
parameters of TOI-904 b and c.
$\dagger$: Taken from TESS Input Catalog (Stassun et al., 2019).
$\ddagger$: Derived from CORALIE observations (section 2.3.2) using SpecMatch-
Emp (Yee et al., 2017).
$\Join$ Derived from CHIRON observations discussed in Section 2.3.1
$\ast$: Calculated using LDTK (Parviainen & Aigrain, 2015; Husser et al.,
2013).
$\diamond$: Calculated using juliet (Espinoza et al., 2019) on SPOC (Jenkins
et al., 2016) observations.
$\bullet$: Section 3.1 analysis.

###  3.1 Host Star Parameters

As an independent determination of the basic stellar parameters from those in
the TESS Input Catalog (TIC; Stassun et al., 2019), we performed an analysis
of the broadband spectral energy distribution (SED) of the star together with
the Gaia EDR3 (Gaia Collaboration et al., 2016, 2018) parallax (with no
systematic offset applied; see, e.g., Stassun & Torres, 2021), in order to
determine an empirical measurement of the stellar radius, following the
procedures described in Stassun & Torres (2016); Stassun et al. (2017, 2018).
We pulled the $JHK_{S}$ magnitudes from 2MASS (Skrutskie et al., 2006), the
W1–W4 magnitudes from WISE (Wright et al., 2010), the $G_{\rm BP}G_{\rm RP}$
magnitudes from Gaia (Riello et al., 2021) a̧nd the NUV flux from GALEX
(Martin et al., 2003, 2005). Together, the available photometry spans the
stellar SED over the wavelength range 0.2–22 $\mu$m.

We performed a fit using NextGen stellar atmosphere models, with the effective
temperature ($T_{\rm eff}$) and metallicity ([Fe/H]) adopted from the
spectroscopic analysis using the SpecMatch-Emp software tool (Yee et al.,
2017) on the CORALIE spectra (the surface gravity, $\log g$, has very little
influence on the broadband SED). We limited the extinction, $A_{V}$, to the
full line-of-sight value from the Galactic dust maps of Schlegel et al.
(1998). The resulting fit has a reduced $\chi^{2}$ of 2.3 (not including the
NUV flux which suggests the presence of chromospheric activity), with best-fit
$A_{V}=0.03\pm 0.03$. Integrating the model SED gives the bolometric flux at
Earth, $F_{\rm bol}=7.62\pm 0.45\times 10^{-10}$ erg s-1 cm-2. Taking the
$F_{\rm bol}$ together with the Gaia parallax gives the stellar radius,
$R_{\star}=0.527\pm 0.021$ R⊙. The stellar mass can also be estimated via the
empirical $M_{K}$ based relations of Mann et al. (2019), giving
$M_{\star}=0.557\pm 0.028$ M⊙.

Finally, we can use the star’s rotation period, $P_{\rm rot}$, to estimate its
age via empirical gyrochronology relations. We use the full TESS light curve
and a Lomb-Scargle periodogram as implemented in astropy (Press & Rybicki,
1989) to obtain a rotation period of 8.55 days, with a False Alarm Probability
on the order of 10-181. However, similar spot coverage on opposite hemispheres
can cause aliasing at half the true rotation period, meaning the real rotation
period could be 17.1 days. If in fact the period is 8.55 d, then using
empirical relations for M-dwarfs from Engle & Guinan (2018), this suggests
that the stellar age is approximately 1 Gyr. This relatively young age would
be consistent with chromospheric activity suggested by the NUV flux in the
SED, however our current constraints on $v\,sin\,i$ from radial velocity
observations of this target favor the 17.1 day period. Precise
characterization of the star’s $v\,sin\,i$ and other activity indicators such
as log $R^{\prime}_{\text{HK}}$ is needed to better constrain the age of the
host star.

These and additional stellar parameters are shown in Table 1.

###  3.2 Planet Validation

Figure 3: Plots of all known transiting multi-planet systems (Left) and cold
planets (Right; T${}_{eq}<$300 K) around M dwarf stars. Each system is shown
as a function of system name (left y-axis), stellar mass (right y-axis), semi-
major axis (x-axis) planet equilibrium temperature (color) and planet radius
(point size). TOI-904 is shown at the bottom of each panel with a gold
horizontal line.

In this section we discuss and rule out false-positive scenarios that could
explain the transit signals we have detected in our observations of TOI-904.
Our radial velocity observations taken with the CORALIE instrument sampled the
expected times of radial velocity maxima and minima for both planets and
detected no signal indicating a stellar or brown dwarf mass companion to the
host star. Using the radvel package (Fulton et al., 2018) under the assumption
of circular orbits, we obtain 3$\sigma$ mass limits of 238.85 $M_{\oplus}$ and
350.34 $M_{\oplus}$ for TOI-904 b and c, respectively, which precludes a
stellar mass object at these orbital periods. The high angular resolution
images of TOI-904 taken with SOAR and ZORRO show no nearby stars brighter than
5-8 magnitudes less than the host star to distances as close as 0.9 AU, from
which we can rule out the possibilities that the transits are located on a
nearby star or that a nearby star is diluting our observations. Together, the
reconnaissance radial velocities and imaging observations lead us to rule out
the possibility that a blended eclipsing binary could be causing either of the
observed transiting planet candidates.

Our ground-based photometric observations of TOI-904 b further allow us to
eliminate the possibility that the TESS observations of TOI-904 b occurred on
another star in the TESS pixel. Both observed transits had a strong
significance of detection of 11$\sigma$ (see Figure 2 Panel d). Although we
have yet to recover a complete transit of TOI-904 c from ground-based
instruments, statistical analyses from the Kepler survey (Lissauer et al.,
2012; Rowe et al., 2014; Morton et al., 2016) and recent calculations based on
TESS observations from Guerrero et al. (2021) indicate that multi-planet
transiting systems are nearly always true planets, especially those with
planets smaller that $6R_{\oplus}$, adding validity to the planetary nature of
TOI-904 c.

Finally, we used the triceratops (Giacalone & Dressing, 2020) software library
to statistically validate both planet candidates. triceratops begins by using
the MAST module of astroquery (Ginsburg et al., 2019) to obtain the TIC
properties for each star within 10 pixels of the target star. Using the TESS
magnitudes, each neighboring star is considered for its flux contribution in
the target pixel and as a possible source of the transit signal. The tool then
creates models of transiting planet and eclipsing binary light curves which
are used to calculate the probability of each scenario using a Bayesian
framework. These probabilities are then used to determine whether or not a
planet candidate can be classified as “validated” (has a False Positive
Probability $<1.5\%$ and Nearby False Positive Probability $<0.1\%$).
Previously, in their work statistically validating several hundred TOIs,
Giacalone & Dressing (2020) found the False Positive Probability (FPP; defined
as the summed probability of all scenarios in which a planet sized object is
located on the give host star subtracted from unity) for TOI-904 b to be 3%,
and designated the planet as a “Likely Planet”. By doing a joint fit using the
new Gemini South/ZORRO observations discussed in Section 2.4 and incorporating
all TESS transit detections of both planets, we find that for TOI-904 b,
3$\sigma$ upper limit on the FPP = $0.049\%$. Doing the same calculation for
TOI-904 c, we calculate the 3$\sigma$ upper limit to be 0.0011%, allowing us
to statistically validate both planets with $>$99% certainty. With the added
validity from the planet multiplicity of this system (Lissauer et al., 2012),
we can confidently state that both objects observed around this star are
planets.

###  3.3 Fitting Planet Parameters

We conducted our analysis on the raw 2-minute Simple Aperture Photometry (SAP)
light curves produced by the SPOC pipeline (Twicken et al., 2010; Morris et
al., 2020). We obtained all available data using the Mikulski Archive for
Space Telescope (MAST) portal. We removed long-timescale correlated noise
(caused by stellar variability) by applying the wotan software library’s Tukey
biweight algorithm (Hippke et al., 2019) to each sector of TESS observations
after masking known transit signals. To conduct a transit analysis of both
signals in each light curve, we use the juliet software library (Espinoza et
al., 2019) built on the batman (Kreidberg, 2015) transit modeling software and
the dynesty (Speagle, 2020) nested sampling algorithm for calculating Bayesian
posteriors and evidences. We used the LDTK (Parviainen & Aigrain, 2015; Husser
et al., 2013) software to calculate the limb-darkening parameters in the TESS
passband based on the stellar properties given in Table 1. We assumed linear
ephemerides, circular orbits, and quadratic limb-darkening while fitting the
following parameters: $R_{p}/R_{*}$, b, $T_{0}$, P and the stellar density
$\rho_{*}$. We performed both a joint multi-planet fit and individual fits for
each planet (in which we masked out all transits of the other planet). We also
did an independent check of the juliet individual planet fit analyses using
the batman modeling package with the emcee (Foreman-Mackey et al., 2021)
python package. The emcee software was used to perform an invariant Markov
chain Monte Carlo (MCMC) sampling, initializing 100 walkers and having each
fit take 10,000 steps with 8,000 burn-in steps. Using the same limb-darkening
values, we fitted the parameters $T_{0}$, P,$R_{p}$/$R_{*}$, $\cos{i}$ and
$a/R_{*}$. Our single-planet analysis was consistent with the results from the
juliet analysis (see Appendix A: Table 2).

As an additional cross check, we repeated this analysis for light curves
produced by different pipelines to check if the transit signals were not
affected by different methods of aperture selection and background
subtraction. We repeated our analysis for the 30-minute light curves created
by the TESS-SPOC, QLP and eleanor (Feinstein et al., 2019) pipelines (see
Appendix A). As with the 2-minute observations, we used the raw un-detrended
data before repeating the analysis detailed above using the emcee and juliet
single and multi-planet fits. We found that the transit fits created from the
eleanor, QLP, 2-minute and 30-minute SPOC data were in agreement within
1$\sigma$.

We fit the LCO observations described in Section 2.2.1 of TOI-904 b using the
juliet software library and our own emcee fit as described above and using
LDTK package to calculate the star’s limb-darkening parameters in the
SLOAN/SDSS.z passband. We found that the transit depths for the TESS were
within 1$\sigma$ of the fit we performed on the 2-minute SPOC data, as shown
in Appendix A: Table 2.

##  4 Discussion

Figure 4: Created using the dynamite (Dietrich & Apai, 2020) the relative
likelihood of the most probable locations of unseen planets orbiting TOI-904
in log-period space. The yellow circle indicate the period of the two known
planets in the system, while the dark blue lines show the probability density
function (PDF) calculated for this system and the light blue histogram
represents the stable Monte Carlo iterations sampled from the PDF. These
scenarios were calculated using the dynamite Exoplanets Systems Simulator
model (syssim; He et al., 2019). By incorporating the location of known
planets and the stellar type, the dynamite software finds that additional non-
transiting planets are most likely to have periods of 6.74, 18.5, 50.7, and
139.05 days.

In this Letter we have announced the discovery and validation of TOI-904 c, a
cool sub-Neptune (T${}_{eq}\approx 217.26\pm 10.22$ K;
$R_{p}=2.310^{+0.155}_{-0.147}R_{\oplus}$; P $=83.999\pm 0.001$ days) that is
the coldest planet discovered by TESS orbiting an M dwarf star to date. We
also report on TOI-904 b, another sub-Neptune
($R_{p}=2.490^{+0.203}_{-0.150}R_{\oplus}$; P$=10.8772\pm 0.0003$ days)
located much closer to the early M dwarf host star.

M dwarfs are known to host a number of Earth to Neptune sized planets (see
Figure 3). These planetary systems are generally very compact, and tend to
exist within $\sim$0.2 AU of their host star. By contrast, TOI-904 is an
extended system with $\sim$0.23 AU between the two planets. While distant
planets have been found around other M dwarfs, all these planets were found
either on the periphery of a compact system comprised of several other small
planets (e.g. Kepler-186) or as the lone planet in their systems (e.g.
Kepler-1628, Kepler-1229). As this is already a multi-planet system, we
searched for indications of any other planets orbiting TOI-904 to determine if
this system belongs in the former category. One way in which we looked for
non-transiting planets was by searching for Transit-Timing Variations (TTVs)
in the TESS and LCO observations of TOI-904 b and the TESS observations of
TOI-904 c. We found that the maximum TTV amplitude of a sine wave fit with
periods from 0.1-100 days to be 5-10 minutes for the inner planet and 25-30
minutes for the outer planet. We found no current evidence of a non-transiting
planet in the TTVs of the observed transits for TOI-904 b or c.

We also used the dynamite software library created by Dietrich & Apai (2020)
to statistically calculate the potential periods and probabilities of unseen
planets in multi-planet systems. dynamite calculates these probabilities by
implementing a triple integral over the probability density function (PDF) of
planet inclination, period and radius based on the occurrence rates calculated
by Mulders et al. (2018), assuming each variable is independent (Dietrich &
Apai, 2020). This PDF is then sampled using the Monte Carlo method before
producing all dynamically stable results based on calculations using Dietrich
& Apai (2020) Eq. 6 (see Fig. 4). Our implementation of dynamite predicted
four potential planets in the TOI-904 system, with orbital periods of 6.74,
18.5, 50.7, and 139.05 days (see Fig. 4). These additional planets may be
detectable using extreme-precision radial velocity observations (EPRVs) or
potential TTVs in future observations of TOI-904 b and c, both of which will
be re-observed by TESS in sectors 65, 66 and 67.

Especially in the absence of another planet, the planets orbiting TOI-904
represent an interesting case-study for exoplanet formation scenarios around
low-mass stars. TOI-904 c is one of three known transiting M dwarf planets
that orbit beyond 0.2 AU and have R${}_{p}>$ 1.8 REarth, implying that they
could have a gaseous envelope. The other two, (Berger et al., 2018; Morton et
al., 2016) however, are Kepler systems with J${}_{mag}>$12, while TOI 904 has
Jmag= 9.6. This system thus provides an unprecedented opportunity to constrain
planet formation at larger distances from M dwarfs by probing its atmosphere.
Assuming a predicted mass of 6.1 M⊕ (based on the mass-radius relations of
Chen & Kipping 2017), the transmission spectroscopy metric (TSM; Kempton et
al. 2018) of TOI-904 c is 23. Thanks mainly to its higher equilibrium
temperature, the TSM of TOI-904 b (assuming a mass of 6.9 M⊕) is 50. By
comparison, the TSM values of Kepler-1628 b and Kepler-1229 b are 13 and 4,
respectively.

Additional study of this system could resolve the currently ambiguous
composition of the two planets. Simulations conducted by Burn et al. (2021)
and Pan et al. (2022) of planet formation via core accretion around low-mass
stars both predict that planets with radii $\sim$2.3R⊕ could have a range of
densities, spanning the ultra-dense sub-Neptune, water world and puffy sub-
Neptune paradigms described by Luque & Pallé (2022). Both studies expect that
in any case, planets of this size are likely to have some atmosphere, so it is
not realistic to expect these planets to be rocky in composition. The mass
limits we obtained using radvel on our CORALIE measurements rule out none of
these scenarios, with 2$\sigma$ upper limits of 174 and 244 $M_{\oplus}$ on
the mass of TOI-904 b and c, respectively. With follow-up mass and atmospheric
measurements, we can resolve this degeneracy for the outer planet and gain
insight into planet formation of cold planets around low-mass stars. With the
predicted masses mentioned above, we expect radial velocity semi-amplitude of
2.9 and 1.3 m/s for TOI-904 b and c, respectively. Based on Luque & Pallé
(2022)’s analysis of M dwarf small planets, the three different regimes of
planet density differ in scale by a factor of two (0.25, 0.5 and
1$\rho_{\oplus}$ for puffy, water and rocky planets, respectively). The masses
for planets in each regime would similarly differ, resulting in detectable
differences in the expected semi-amplitudes of radial velocity measurements.
We find that the three compositions would result in masses (semi-amplitudes)
of 3.3 M⊕ (1.4 m/s), 6.5 M⊕ (2.9 m/s) and 13.1 M⊕ (5.8 m/s), respectively, for
the inner planet; for the outer planet, the masses (semi-amplitudes) would be
2.6 M⊕ (1.1 m/s), 5.2 M⊕ (2.3 m/s) and 10.4 M⊕ (4.6 m/s), respectively. While
a 5$\sigma$ mass measurement (Batalha et al., 2019) could be achieved with
HARPS (Mayor et al., 2003) or Magellan II/PFS (Crane et al., 2010; Teske et
al., 2016), particularly for TOI-904 b, the mass precision needed to
distinguish between different bulk compositions is realistically only within
reach of VLT-ESPRESSO (Pepe et al., 2021). Indeed, ESPRESSO was used to
measure a semi-amplitude of 2.2 m/s for the candidate planet LHS 1140d, which
has a period of 79 days and orbits a star five times fainter than TOI 904
(Lillo-Box et al., 2020).

If TOI-904 c is an ultra-dense Neptune, and is thus most easily detectable for
mass measurements, both planets may have formed in situ (Kennedy et al., 2006;
Hansen & Murray, 2012; Hansen, 2015). This case would have resulted in TOI-904
c forming as a rocky, ultra-dense Neptune (similar to K2-110 b; Osborn et al.
2017) if the snow-line of the M dwarf receded towards the star on planet
formation timescales causing a late stage of mass accretion for planets
located near the snow line (Kennedy et al., 2006). In situ formation seems
unlikely for this system, however, as the larger inner planet TOI-904 b could
not have reached its size at its current location due to the high temperature
($>$2000 K; Ali-Dib et al. 2020) of a forming protoplanet at this distance
from the host star, precluding the accretion of any gaseous envelope. In situ
formation also often predicts 4-10 rocky planets on co-planar orbits (Hansen &
Murray, 2012; Pan et al., 2022), for which there is currently no evidence in
this system.

It is more probable that TOI-904 c migrated to its current location from a
greater distance via type-I migration (Burn et al., 2021; Luque & Pallé, 2022;
Pan et al., 2022). If the planet did form further in the disk, its core was
likely formed of both rock and ice materials before the planet migrated
inward. In this case, this planet’s density could allow us to differentiate
between a ‘water world’ with $\sim 50\%$ ice/rock ratios and little to no
envelope (Burn et al., 2021; Luque & Pallé, 2022) and a planet with a lower
ice/rock ratio and a larger atmosphere (Pan et al., 2022). In this model, the
inner planet’s core could be made up of rocky materials or an ice/rock
mixture. If the latter, Bitsch et al. (2019) state that the hot inner water
world would be considerable evidence for the planet migration model, and
TOI-904 b’s overall water content could inform the exact migration history of
that planet. If instead planet b has a large gaseous envelope, its water
content could still inform which formation path this system followed and where
it acquired its envelope, either as it did so beyond the snow line (Burn et
al., 2021) or after being trapped in inner regions of the protoplanetary disk,
where little water is available to accrete (Pan et al., 2022).

Type-I migration is a very efficient process, however, and models of this
theory predict very compact multi-planet systems, unlike the widely separated
planets orbiting TOI-904. One possibility to resolve this discrepancy is that
TOI-904 c formed at a significantly greater distance from the host star than
TOI-904 b, which would explain why the inner planet migrated in so much
further and why the mutual separation of the planets has persisted. This could
also result from lower disk density at greater distances, where type-I
migration could be triggered for smaller planets like TOI-904 c (Burn et al.,
2021). This theory could be tested by determining if TOI-904 c has a larger
C/O ratio than TOI-904 b, which would indicate that TOI-904 c may have formed
beyond the methane ice line and that TOI-904 b did not.

Given that the planets are so similar in size, a final alternate theory could
be that they followed the same formation path by forming sequentially,
following the inside-out formation theory suggested by Chatterjee & Tan
(2014). In this theory, pebbles form in outer regions of this disk before
migrating inward and stalling at a high pressure region (potentially at the
water ice line) before forming a planet at that location. The planet would
then migrate inward and cause the high pressure zone to move outward, allowing
the process to repeat and form another planet. Pan et al. (2022) conducted the
first simulations of this type of formation around M dwarfs, and found that it
is likely to result in systems of 2-4 sub-Neptune sized planets located at
greater distances and separations than type-I migration would produce, and
thus more closely resemble the TOI-904 system. If both planets have a high
water content, TOI-904 b’s larger size could be explained by an inflated
hydrosphere caused by its closer proximity to the star (Luque et al., 2019).
If the compositions of these planets are similar, the TOI-904 system could
strongly support this relatively new theory of planet formation. Whatever
theory of formation dominates in these systems, through investigating the mass
and atmospheric composition of both planets we can determine whether they have
twin compositions or are only sibling planets orbiting the same star.

## Acknowledgements

We thank the anonymous reviewer for their feedback and suggestions which have
helped improve this paper.

We would also like to acknowledge Rebekah Dawson at the Center for Exoplanets
and Habitable Worlds at Pennsylvania State University for her advice in
regards to the TTV analysis conducted in this paper.

Some of the data presented in this paper were obtained from the Mikulski
Archive for Space Telescopes (MAST) at the Space Telescope Science Institute.
The specific observations analyzed can be accessed via
https://doi.org/10.17909/73w3-v751 (catalog DOI: 10.17909/73w3-v751 ).

This research has made use of the NASA Exoplanet Archive, which is operated by
the California Institute of Technology, under contract with the National
Aeronautics and Space Administration under the Exoplanet Exploration Program.
The data described here may be obtained from
https://dx.doi.org/10.17909/T9RP4V. We acknowledge the use of public TESS data
from pipelines at the TESS Science Office and at the TESS Science Processing
Operations Center. 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. Some of the observations in the paper made use of the High-
Resolution Imaging instrument Zorro obtained under Gemini LLP Proposal Number:
GN/S-2021A-LP-105. Zorro was funded by the NASA Exoplanet Exploration Program
and built at the NASA Ames Research Center by Steve B. Howell, Nic Scott,
Elliott P. Horch, and Emmett Quigley. Zorro was mounted on the Gemini North
(and/or South) telescope of the international Gemini Observatory, a program of
NSF’s OIR Lab, which is managed by the Association of Universities for
Research in Astronomy (AURA) under a cooperative agreement with the National
Science Foundation on behalf of the Gemini partnership: the National Science
Foundation (United States), National Research Council (Canada), Agencia
Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia,
Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia,
Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science
Institute (Republic of Korea). This work makes use of observations from the
LCOGT network. Part of the LCOGT telescope time was granted by NOIRLab through
the Mid-Scale Innovations Program (MSIP). MSIP is funded by NSF. This research
has made use of the Exoplanet Follow-up Observation Program (ExoFOP444DOI:
10.26134/ExoFOP5) website, which is operated by the California Institute of
Technology, under contract with the National Aeronautics and Space
Administration under the Exoplanet Exploration Program. This work was based in
part on observations obtained at the Southern Astrophysical Research (SOAR)
telescope, which is a joint project of the Ministério da Ciência, Tecnologia e
Inovações (MCTI/LNA) do Brasil, the US National Science Foundation’s NOIRLab,
the University of North Carolina at Chapel Hill (UNC), and Michigan State
University (MSU). 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. This publication makes use
of data products from the Two Micron All Sky Survey, which is a joint project
of the University of Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the National Aeronautics
and Space Administration and the National Science Foundation. This publication
makes use of data products from the Wide-field Infrared Survey Explorer, which
is a joint project of the University of California, Los Angeles, and the Jet
Propulsion Laboratory/California Institute of Technology, funded by the
National Aeronautics and Space Administration. D. D. acknowledges support from
the TESS Guest Investigator Program grants 80NSSC22K0185 and , and NASA
Exoplanet Research Program grant 18-2XRP18_2-0136. The contributions of S. U.,
M .L. and H. O. have been carried out within the framework of the NCCR PlanetS
supported by the Swiss National Science Foundation under grants 51NF40_182901
and 51NF40_205606. M. L. further acknowledges support of the Swiss National
Science Foundation under grant number PCEFP2_194576.

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APPENDIX A

| Pipelines | Planet b | Planet c
---|---|---|---
|  | R${}_{p}/$R⋆ | b |  $i$ (deg) | Rp (R⊕) | R${}_{p}/$R⋆ | b |  $i$ (deg) | Rp (R⊕)
|  SPOC | 0.042${}^{+0.002}_{-0.002}$ | 0.71${}^{+0.12}_{-0.42}$ | 88.19${}^{+1.26}_{-0.88}$ | 2.42${}^{+0.16}_{-0.15}$ | 0.037${}^{+0.002}_{-0.001}$ | 0.37${}^{+0.29}_{-0.28}$ | 89.83${}^{+0.13}_{-0.20}$ | 2.17${}^{+0.13}_{-0.12}$
|  TESS-SPOC | 0.042${}^{+0.003}_{-0.002}$ | 0.79${}^{+0.10}_{-0.24}$ | 87.73${}^{+1.11}_{-1.17}$ | 2.46${}^{+0.18}_{-0.17}$ | 0.037${}^{+0.002}_{-0.002}$ | 0.42${}^{+0.29}_{-0.31}$ | 89.80${}^{+0.15}_{-0.23}$ | 2.20${}^{+0.27}_{-0.18}$
|  QLP | 0.037${}^{+0.003}_{-0.002}$ | 0.49${}^{+0.35}_{-0.37}$ | 88.94${}^{+0.83}_{-1.89}$ | 2.15${}^{+0.20}_{-0.12}$ | 0.036${}^{+0.003}_{-0.002}$ | 0.57${}^{+0.30}_{-0.36}$ | 89.70${}^{+0.21}_{-0.43}$ | 2.07${}^{+0.21}_{-0.15}$
|  eleanor | 0.038${}^{+0.003}_{-0.002}$ | 0.55${}^{+0.31}_{-0.34}$ | 88.84${}^{+0.78}_{-1.77}$ | 2.23${}^{+0.22}_{-0.14}$ | 0.042${}^{+0.005}_{-0.003}$ | 0.57${}^{+0.32}_{-0.22}$ | 89.72${}^{+0.12}_{-1.50}$ | 2.42${}^{+0.33}_{-0.20}$
juliet |  LCO | 0.036${}^{+0.003}_{-0.003}$ | 0.47${}^{+0.28}_{-0.30}$ | 89.11${}^{+0.61}_{-0.97}$ | 2.10${}^{+0.20}_{-0.19}$ |  |  |  |
(10/15/2020) |  |  |  |  |  |  |  |
LCO | 0.039${}^{+0.003}_{-0.003}$ | 0.36${}^{+0.23}_{-0.25}$ | 89.38${}^{+0.44}_{-0.52}$ | 2.23${}^{+0.18}_{-0.19}$ |  |  |  |
| (12/19/2020) |  |  |  |  |  |  |  |
|  SPOC | 0.040${}^{+0.001}_{-0.001}$ | 0.24${}^{+0.25}_{-0.17}$ | 89.55${}^{+0.32}_{-0.56}$ | 2.29${}^{+0.10}_{-0.10}$ | 0.038${}^{+0.001}_{-0.001}$ | 0.485${}^{+0.13}_{-0.08}$ | 89.77${}^{+0.04}_{-0.08}$ | 2.19${}^{+0.11}_{-0.11}$
|  TESS-SPOC | 0.039${}^{+0.001}_{-0.001}$ | 0.24${}^{+0.25}_{-0.17}$ | 89.55${}^{+0.32}_{-0.56}$ | 2.29${}^{+0.10}_{-0.11}$ | 0.035${}^{+0.002}_{-0.001}$ | 0.39${}^{+0.19}_{-0.19}$ | 89.82${}^{+0.09}_{-0.11}$ | 2.03${}^{+0.12}_{-0.12}$
|  QLP | 0.038${}^{+0.001}_{-0.001}$ | 0.21${}^{+0.25}_{-0.15}$ | 89.61${}^{+0.28}_{-0.55}$ | 2.19${}^{+0.11}_{-0.11}$ | 0.034${}^{+0.002}_{-0.002}$ | 0.44${}^{+0.16}_{-0.16}$ | 89.79${}^{+0.08}_{-0.10}$ | 1.96${}^{+0.14}_{-0.13}$
juliet two- planet fit |  eleanor | 0.039${}^{+0.003}_{-0.002}$ | 0.66${}^{+0.15}_{-0.24}$ | 88.43${}^{+0.76}_{-0.90}$ | 2.25${}^{+0.17}_{-0.14}$ | 0.043${}^{+0.004}_{-0.003}$ | 0.76${}^{+0.11}_{-0.18}$ | 89.54${}^{+0.16}_{-0.22}$ | 2.50${}^{+0.23}_{-0.20}$
SPOC | 0.041${}^{+0.003}_{-0.002}$ | 0.65${}^{+0.18}_{-0.43}$ | 88.48${}^{+1.11}_{-1.11}$ | 2.38${}^{+0.20}_{-0.15}$ | 0.037${}^{+0.002}_{-0.001}$ | 0.35${}^{+0.26}_{-0.24}$ | 89.84${}^{+0.11}_{-0.17}$ | 2.14${}^{+0.19}_{-0.10}$
TESS-SPOC | 0.040${}^{+0.002}_{-0.001}$ | 0.46${}^{+0.31}_{-0.31}$ | 89.09${}^{+0.65}_{-1.19}$ | 2.34${}^{+0.17}_{-0.12}$ | 0.037${}^{+0.002}_{-0.002}$ | 0.43${}^{+0.30}_{-0.29}$ | 89.81${}^{+0.13}_{-0.24}$ | 2.14${}^{+0.15}_{-0.13}$
|  QLP | 0.039${}^{+0.003}_{-0.002}$ | 0.47${}^{+0.31}_{-0.32}$ | 89.02${}^{+0.69}_{-1.31}$ | 2.25${}^{+0.17}_{-0.13}$ | 0.036${}^{+0.003}_{-0.002}$ | 0.48${}^{+0.34}_{-0.33}$ | 89.77${}^{+0.16}_{-0.36}$ | 2.07${}^{+0.19}_{-0.15}$
|  eleanor | 0.040${}^{+0.003}_{-0.002}$ | 0.49${}^{+0.31}_{-0.34}$ | 88.96${}^{+0.74}_{-1.44}$ | 2.32${}^{+0.19}_{-0.16}$ | 0.043${}^{+0.003}_{-0.002}$ | 0.48${}^{+0.31}_{-0.32}$ | 89.76${}^{+0.17}_{-0.33}$ | 2.47${}^{+0.20}_{-0.16}$
emcees |  LCO Transits | 0.037${}^{+0.003}_{-0.004}$ | 0.46${}^{+0.31}_{-0.31}$ | 89.16${}^{+0.59}_{-1.21}$ | 2.14${}^{+0.19}_{-0.25}$ |  |  |  |
(joint fit) |  |  |  |  |  |  |  |
Table 2: Parameters derived from the juliet, emcee and joint juliet planet
fits for each pipelines’ data products used in this study and the LCO
observations of TOI-904 b. The fits createdfrom the eleanor light curves
generally show a deeper transit depth the outer planet TOI-904 c. QLP light
curves presented shallower transits but within an uncertainty of the SPOC and
TESS-SPOC observations, as did the fits made from eleanor observations of the
inner planet. The LCO observations both show the inner planet to be smaller
than expected, and very comparable with the TESS-found sizes of the outer
planet. Ground-based observations of TOI-904 c are needed to further elucidate
the difference in the two planets’ radii. Figure 5: Graphic depictions of the
juliet fits of TOI-904 created using the different pipelines’ data products.
Top: data from each pipeline (pale points, overlaid with darker points when
binning was applied) with the joint and individual planet fits over-plotted.
Source of data products from left to right: SPOC 2-minute pipeline, TESS-SPOC
30-minute pipeline, MIT Quicklook pipeline, eleanor pipeline). Bottom Left:
Comparison of each joint planet fit of TOI-904 b created from the different
pipelines, with the SPOC 2-minute data in light blue, the 30-minute TESS-SPOC
data in red, the QLP data in dark blue and the eleanor data in yellow. Bottom
Right: Same as Bottom Left figure for the individual planet fits of TOI-904 b.
Figure 6: Same as Figure 5, fitting for TOI-904 c.

APPENDIX B

Planet | Transit Time (BJD-TDB)
---|---
TOI-904 b | 1637.847${}^{+0.005}_{-0.005}$
| 1648.716${}^{+0.006}_{-0.006}$
| 1659.599${}^{+0.009}_{-0.006}$
| 1670.478${}^{+0.009}_{-0.003}$
| 1681.374${}^{+0.010}_{-0.015}$
| 2040.301${}^{+0.003}_{-0.004}$
| 2051.181${}^{+0.003}_{-0.004}$
| 2344.870${}^{+0.003}_{-0.005}$
| 2355.746${}^{+0.004}_{-0.004}$
| 2366.630${}^{+0.006}_{-0.008}$
| 2377.510${}^{+0.004}_{-0.004}$
| 2388.369${}^{+0.006}_{-0.007}$
| 2964.869${}^{+0.005}_{-0.006}$
| 2986.621${}^{+0.005}_{-0.010}$
TOI-904 c | 1630.353${}^{+0.003}_{-0.004}$
| 2050.349${}^{+0.005}_{-0.006}$
| 2386.358${}^{+0.006}_{-0.011}$
| 2974.345${}^{+0.007}_{-0.009}$
Table 3: The transit times for all TESS transits of TOI-904 b and c as they
were observed in Sectors 12, 13, 27, 38, 39 and 61. Two transits of TOI-904 b
were excluded due to poor quality data, near 2333.999 and 2975.741.