# GJ 238 b: A 0.57 Earth radius planet orbiting an M2.5 dwarf star at 15.2 pc

Evan Tey Department of Physics and Kavli Institute for Astrophysics and Space Science, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  Avi Shporer Department of Physics and Kavli Institute for Astrophysics and Space Science, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  Zifan Lin  Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Keivan G. Stassun Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA  Department of Physics, Fisk University, Nashville, TN 37208, USA  Jack J. Lissauer  NASA Ames Research Center, Moffett Field, CA 94035, USA  Coel Hellier  Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK  Karen A. Collins Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Kevin I. Collins George Mason University, 4400 University Drive, Fairfax, VA, 22030 USA  Geof Wingham  Mt. Stuart Observatory, New Zealand  Howard M. Relles  Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Franco Mallia  Campo Catino Astronomical Observatory, Regione Lazio, Guarcino (FR), 03010 Italy  Giovanni Isopi  Campo Catino Astronomical Observatory, Regione Lazio, Guarcino (FR), 03010 Italy  John F. Kielkopf Department of Physics and Astronomy, University of Louisville, Louisville, KY 40292, USA  Dennis M. Conti American Association of Variable Star Observers, 185 Alewife Brook Parkway, Suite 410, Cambridge, MA 02138, USA  Richard P. Schwarz Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Aldo Zapparata  Campo Catino Astronomical Observatory, Regione Lazio, Guarcino (FR), 03010 Italy  Steven Giacalone NSF Astronomy and Astrophysics Postdoctoral Fellow  Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  Elise Furlan  Caltech/IPAC-NASA Exoplanet Science Institute, 770 S. Wilson Avenue, Pasadena, CA 91106, USA  Zachary D. Hartman  Gemini Observatory/NSF’s NOIRLab, 670 A’ohoku Place, Hilo, HI 96720, USA  Steve B. Howell NASA Ames Research Center, Moffett Field, CA 94035, USA  Nicholas J. Scott  NASA Ames Research Center, Moffett Field, CA 94035, USA  Carl Ziegler  Department of Physics, Engineering and Astronomy, Stephen F. Austin State University, 1936 North St, Nacogdoches, TX 75962, USA  César Briceño Cerro Tololo Inter-American Observatory/NSF’s NOIRLab, Casilla 603, La Serena 1700000, Chile  Nicholas Law  Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA  Andrew W. Mann Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA  David Charbonneau Harvard-Smithsonian Center for Astrophysics, 60 Garden St, Cambridge, MA 02138, USA  Zahra Essack Department of Physics and Astronomy, The University of New Mexico, 210 Yale Blvd NE, Albuquerque, NM 87106, USA  Stephanie Striegel NASA Ames Research Center, Moffett Field, CA 94035, USA  SETI Institute, Mountain View, CA 94043, USA  George R. Ricker  Department of Physics and Kavli Institute for Astrophysics and Space Science, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  Roland Vanderspek  Department of Physics and Kavli Institute for Astrophysics and Space Science, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  Sara Seager Department of Physics and Kavli Institute for Astrophysics and Space Science, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Department of Aeronautics and Astronautics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  Joshua N. Winn  Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA  Jon M. Jenkins  NASA Ames Research Center, Moffett Field, CA 94035, USA Avi Shporer<EMAIL_ADDRESS>
###### Abstract

We report the discovery of the transiting planet GJ 238 b, with a radius of
$0.566\pm 0.014$ $R_{\earth}$ ($1.064\pm 0.026$ times the radius of Mars) and
an orbital period of 1.74 day. The transit signal was detected by the TESS
mission and designated TOI-486.01. The star’s position close to the Southern
ecliptic pole allows for almost continuous observations by TESS when it is
observing the Southern sky. The host star is an M2.5 dwarf with $V=11.57\pm
0.02$ mag, $K=7.030\pm 0.023$ mag, a distance of $15.2156\pm 0.0030$ pc, a
mass of $0.4193_{-0.0098}^{+0.0095}$ $M_{\sun}$, a radius of
$0.4314_{-0.0071}^{+0.0075}$$R_{\sun}$, and an effective temperature of
$3{,}485\pm 140$ K. We validate the planet candidate by ruling out or
rendering highly unlikely each of the false positive scenarios, based on
archival data and ground-based follow-up observations. Validation was
facilitated by the host star’s small size and high proper motion, of
$892.633\pm 0.025$ mas per year.

planetary systems, stars: individual (TIC 260708537, TOI 486, GJ 238, LHS
1855)

††facilities: ESO:3.6m (HARPS), Exoplanet Archive, Gemini South 8-m (Zorro),
LCO:1m (Sinistro), SOAR: 4.1m (HRCam), TESS††software:  AstroImageJ (Collins
et al., 2017), TAPIR (Jensen, 2013)

,

##  1 Introduction

The search for small transiting planets – the size of Earth and smaller – is
at the forefront of exoplanet research. Small exoplanets are expected to be
composed primarily of silicates and iron, allowing for comparisons to the
terrestrial planets of the solar system. Of course, the transits of small
planets are difficult to detect, requiring time series photometry precise
enough to detect a relative brightness dip on the order of 10-4. In addition,
the low masses of small planets are challenging to measure, which is why the
mass has not been measured for the majority of known transiting terrestrial
planets. Instead, the planets have been “validated” through statistical
arguments against the known false-positive scenarios in which the transit-like
signal has a non-planetary origin (e.g., Torres et al., 2011; Morton, 2015;
Morton et al., 2016).

The Transiting Exoplanet Survey Satellite (TESS; Ricker et al., 2014) was
designed to detect small transiting planets orbiting bright stars. Especially
advantageous stars are nearby M dwarfs with small sizes and high proper
motion, properties that facilitate validation (e.g., Vanderspek et al., 2019;
Shporer et al., 2020; Gan et al., 2020; Tey et al., 2023).

We present here the discovery of GJ 238 b, the smallest planet detected with
TESS data to this point, with a radius of $0.566\pm 0.014$ $R_{\earth}$
($1.064\pm 0.026$ Mars radii). The planet orbits an M2.5 dwarf with a proper
motion of $892.633\pm 0.025$ mas per year, located in the southern TESS
continuous viewing zone. We have analyzed archival data from other telescopes,
as well as newly acquired data, that allowed us to conclude that the transit
signal seen in the TESS data is indeed due to a transiting planet around the M
dwarf.

Basic information about GJ 238 is listed in Table 1. Section 2 describes the
various data sets we have collected and analyzed. In Section 3 we provide
estimates of the stellar characteristics of GJ 238 and in Section 4 we
describe how we used the available data to reject false positive scenarios. In
Section 5 we discuss the new planet discovery, and we conclude with a brief
summary in Section 6.

Table 1:  Target information and stellar parameters

Parameter | Value | Source
---|---|---
TIC | 260708537 | TIC V8a
R.A. |  06:33:49.146 |  Gaia DR3b
Dec. | -58:31:29.72 |  Gaia DR3b
$\mu_{RA}$ (mas yr-1) | -404.050 $\pm$ 0.018 |  Gaia DR3b
$\mu_{Dec}$ (mas yr-1) | 795.950 $\pm$ 0.018 |  Gaia DR3b
Parallax (mas) | 65.722 $\pm$ 0.013 |  Gaia DR3b
Distance (pc) | 15.2156 $\pm$ 0.0030 |  Gaia DR3b
Epoch | 2016.0 |  Gaia DR3b
$B$ (mag) | 13.11 $\pm$ 0.03 | UCAC4c
$V$ (mag) | 11.57 $\pm$ 0.02 | UCAC4c
$R$ (mag) | 11.22 $\pm$ 0.03 | UCAC4c
$G^{d}$ (mag) | 10.5328 $\pm$ 0.0028 |  Gaia DR3b
$T^{e}$ (mag) | 9.3685 $\pm$ 0.0073 | TIC V8a
$J$ (mag) | 7.898 $\pm$ 0.023 | 2MASSf
$H$ (mag) | 7.312 $\pm$ 0.034 | 2MASSf
$K$ (mag) | 7.030 $\pm$ 0.023 | 2MASSf
$L_{s}$ ($L_{\sun}$) | 0.0242${}_{-0.0028}^{+0.0032}$ | This work
$T_{\rm eff}$ (K) | 3,485 $\pm$ 140 | This work
[Fe/H] | 0.15 $\pm$ 0.10 | This work

eefootnotetext: TESS band.

fffootnotetext: Cutri et al. (2003).

##  2 Observations and data analysis

###  2.1 TESS data

GJ 238 (TIC 260708537) was observed by TESS during the 1st and 3rd years of
TESS operations, in sectors 1–6 (2018 July 25 – 2019 January 7), 8–13 (2019
February 2 – 2019 July 18), and 27–39 (2020 July 4 – 2021 June 24), for a
total of 25 sectors. In the 1st year, also called Cycle 1, it was observed as
one of the targets requested by TESS Guest Investigator programs G011180 (PI:
Courtney Dressing) and G011129 (PI: Wei-Chun Jao). In the 3rd year, also
called Cycle 3, it was observed as one of the targets requested by TESS Guest
Investigator programs G03264 (PI: Jennifer Van Saders), G03278 (PI: Andrew
Mayo), and G03272 (PI: Jennifer Burt).

GJ 238 was initially identified as a transiting planet candidate by the MIT
Quick Look Pipeline (QLP, Huang et al., 2020a, b) which processes the TESS
full frame images (FFIs), using the first six sectors of data. It was
designated TESS object of interest (TOI) 486.01. Later, it was detected as a
transiting candidate by the NASA Science Processing Operations Center (SPOC)
pipeline at NASA Ames Research Center (Jenkins et al., 2016), which analyzes
the pre-selected pixel postage stamps recorded at an effective exposure time
of 2 minutes.

We have examined several diagnostics of TOI 486.01 before initiating the
collection of follow-up data (the latter is described in the following
sections). We compared the odd and even transits when folding the TESS light
curve on twice the candidate orbital period detected by QLP and SPOC, and
found that they show consistent depths. We then compared the transit seen when
folding the TESS light curve on the candidate orbital period to the transit
seen when folding the light curve on half the candidate orbital period. We
noticed that the latter, at half the candidate orbital period, shows a
shallower depth and an increased in-transit scatter. Meaning, the candidate
orbital period is the true period. In addition, the SPOC pipeline provides
difference images, where data taken in transit is subtracted from data taken
out of transit (Twicken et al., 2018). Analysis of the difference signal
position showed it is located $1.65\pm 3.05$ arcsec from GJ 238.

Since GJ 238 was observed in 2-minute cadence during all 25 sectors, we chose
to use SPOC Pre-search Data Conditioning Simple Aperture Photometry (PDCSAP;
Stumpe et al. 2012; Stumpe et al. 2014; Smith et al. 2012) flux for our
analysis. The PDCSAP light curve is plotted in Figure 1.

####  2.1.1 TESS transit light curve fitting

We fit the TESS light curve using exoplanet (Foreman-Mackey et al., 2021),
which uses PyMC3 to conduct No U-turn sampling over the posterior
distribution. In our analysis we ignored data with non-zero quality flags.

For our priors, we used reference parameters from the SPOC Sector 1–39 report.
The orbital period and epoch were given uniform priors centered around the
values from the SPOC report for sectors 1–39, with a range equal to $\pm 10\%$
of the reference period. The ratio of the planet radius to host star radius
$R_{p}/R_{s}$ was given a uniform prior from 0 to 2, and the impact parameter
$b$ was given a uniform prior from 0 to $(1+R_{p}/R_{s})$. For the stellar
mass and radius we used Gaussian priors with means and standard deviations as
derived in Section 3. Finally, we used a quadratic limb darkening model with
parameters $q_{1}$ and $q_{2}$ following the priors from Kipping (2013).

We sampled five independent chains with 2500 tuning steps and 2500 draws, and
confirmed that parameters converged with Gelman & Rubin (1992) statistic $\leq
1.01$.

The fitted and derived posteriors are summarized in Table 2, and the best fit
model can be seen in Figure 2. While we expect a nearly circular orbit for
such a close-orbiting planet (due to tidal dissipation), we conducted an
additional fit without this assumption, and we verified that the resulting
parameters are consistent with our best fit model with $e\equiv 0$. Finally we
conducted one last fit in which the stellar mass and radius were given uniform
priors between 0 and 1 solar mass and radius, respectively. The results for
the stellar mean density were found to be consistent with the mass and radius
estimated independently in Section 3.

Figure 1: TESS PDCSAP 2-minute exposure light curve of GJ 238 plotted in mean-
subtracted relative flux (in parts per thousand, or ppt) as a function of time
in days. The top panel shows the data in sectors 1–6 and 8–13, and the bottom
panel shows data in sectors 27–39. Gaps in the data are primarily due to data
downloads and intervals of bad data (due to, e.g., momentum dumps and
scattered light). The wide gap in the top panel is during a sector when GJ 238
was not observed by TESS.

Figure 2: Left: GJ 238 b TESS phase-folded and binned transit light curve (in
parts per million, ppm) covering an entire orbital period with the transit at
phase zero. Right: Phase-folded and binned transit light curve zoomed-in on
the transit phase. The best fit model is shown with a black solid line. The
lower part of the panel shows the residual flux, after subtracting the model
from the data, and offset by 400 ppm, marked by the dashed black line.  Table
2:  Fitted and derived Parameters

Parameter | Value | Uncertainty
---|---|---
$T_{0}$ (BJD - 2,457,000) | 1326.98222 | ${}_{-0.00070}^{+0.00064}$
$P$ $\mathrm{(d)}$ | 1.7446999 | ${}_{-0.0000018}^{+0.0000019}$
$R_{p}/R_{s}$ | 0.01204 | $\pm 0.00023$
$|b|$ | 0.202 | ${}_{-0.072}^{+0.075}$
$q_{1}$ | 0.66 | $\pm 0.16$
$q_{2}$ | -0.04 | ${}_{-0.17}^{+0.19}$
$M_{s}$ ($M_{\sun}$) | 0.4193 | ${}_{-0.0098}^{+0.0095}$
$R_{s}$ ($R_{\sun}$) | 0.4314 | ${}_{-0.0071}^{+0.0075}$
$i$ (∘) | 89.99 | ${}_{-0.79}^{+0.80}$
$a$ (AU) | 0.02123 | ${}_{-0.00017}^{+0.00016}$
$R_{p}$ ($R_{\earth}$) | 0.566 | $\pm 0.014$
$T_{\mathrm{1,4}}$aaStassun et al. (2018). (h) | 1.239 | $\pm 0.018$
$q_{\mathrm{2,3}}$bbGaia Collaboration et al. (2022). (h) | 0.97510 | ${}_{-0.00109}^{+0.00074}$
$q_{\mathrm{in}}$ccZacharias et al. (2012). (h) | 0.01245 | ${}_{-0.00041}^{+0.00054}$
$T_{\mathrm{eq}}$ddGaia band. (K) | 758 | ${}_{-15}^{+16}$

bbfootnotetext: Duration of the total transit, from 2nd to 3rd contacts, as a
fraction of the entire transit duration ($T_{\mathrm{1,4}}$).

ccfootnotetext: Ingress or egress duration as a fraction of the entire transit
duration ($T_{\mathrm{1,4}}$).

ddfootnotetext: Assuming zero Bond albedo and complete heat circulation from
the planet’s dayside hemisphere (permanently facing the star as the planet is
tidally locked) to its nightside hemisphere (permanently facing away from the
star).

###  2.2 Ground-based photometry

####  2.2.1 Archival imaging

We searched for archival images of GJ 238 and found two exposures taken by the
UK Schmidt Telescope (UKST) using photographic plates and made available
digitally by the STScI Digitized Sky Survey. One was taken on UT 1979 December
21 with the GG395 filter, otherwise known UKST Blue. The second was taken on
UT 1995 January 25 with the RG610 filter, otherwise known as UKST Red. Both
exposures are shown in Figure 3 where GJ 238 is clearly visible. Due to its
high proper motion of $892.633\pm 0.025$ mas per year GJ 238 is seen in
different locations in the sky in the two archival exposures. It also allows
to examine its current location and look for background stars at its position
at the time it was observed by TESS and ground-based observatories (described
in the subsections below), which we discuss in detail in Section 4.3.

Figure 3: The two left panels show the target’s field of view as observed by
the UK Schmidt Telescope (UKST) and processed by the Digitized Sky Survey on
1979 December 21st (leftmost panel) and UT 1995 January 25th (2nd from the
left panel). The 3rd panel from the left shows the target’s field as observed
by an LCO 1 m/Sinistro on UT 2023 February 1st, with the SDSS-$r$ filter. The
three left panels show a 2.5 $\times$ 2.5 arcmin field of view centered on the
target’s position at epoch 2015.5. The motion of the target, which is the
brightest star in the field, is clearly seen. The rightmost panel shows a
Zoomed-in view of the target and the two stars closest to it on the sky,
encircled in green and labeled by their TIC ID. The image is 1.0 $\times$ 1.0
arcmin and the green circles have a 2.0 arcsec radius. In each panel North is
up and East is to the left, and the panel’s title provides its source and the
fractional year when they were obtained.

####  2.2.2 Las Cumbres Observatory

We obtained several ground-based photometric time series covering predicted
transit times at several observatories111Detailed results of each observation
is available on ExoFOP-TESS, including the Las Cumbres Observatory Global
Telescope (LCOGT; Brown et al. 2013) 1m telescopes (on UT 2019 March 3, UT
2019 April 7, UT 2019 December 12, UT 2022 November 11, UT 2022 November 18),
LCO 0.4m (UT 2019 April 7), Mt. Kent Observatory (UT 2019 April 7), and Mt.
Stuart 12.5 inch (UT 2019 April 7). We used the TESS Transit Finder, which is
a customized version of the Tapir software package (Jensen, 2013), to schedule
our transit observations. While the transit is too shallow to be detected in
ground-based data obtained by small telescopes, we obtained these data to look
for deep eclipses of nearby stars. Such eclipses, if they exist, might be
responsible for the shallow transit-like signals seen in the TESS data due to
blending with the target. Differential photometric data were extracted from
the image sequences using AstroImageJ (Collins et al., 2017).

Using the data sets listed above, we were able to rule out eclipses deep
enough to account for the TESS signal, for all the nearby stars. In Figure 4
we show the results of an observation done by an LCO 1m/Sinistro on UT 2022
November 18, where we could rule out a deep eclipse on the two closest stars
to the target, TIC 737377689 ($T$ = 17.62 mag, $G$ = 18.37 mag) and TIC
737377690 ($T$ = 17.61 mag, $G$ = 18.48 mag), marked in Figure 3 rightmost
panel. We used the Pan-STARRS zs filter in that observation, as it covers a
wavelength range fully within that of the TESS band. In that observation TIC
737377689 and TIC 737377690 were well resolved from the target, and the
scatter in their light curves (5.0% and 3.1%, respectively) completely rules
out an eclipse depth of about 25%, which could have resulted in the transit
depth seen in TESS data due to blending with the target in TESS point spread
function (PSF).

Figure 4: Light curves of the two closest stars to the target spanning a
predicted transit time, based on observations with an LCO 1m/Sinistro on UT
2022 November 18, through a Pan-STARRS zs filter (overlapping the TESS band).
Both light curves are plotted in relative flux, and shifted from each other
along the Y-axis for clarity. The seeing during this observation was 2.6
arcsec and a 4.0 arcsec aperture diameter was used to extract the light curves
(for comparison, the distance between TIC 737377690 and the target was close
to 10 arcsec at the time of observation). The two grey points along the X-axis
mark the predicted transit start and end times. The uncertainty on those
values is similar to the size of the markers. The brightness difference
between the target and TIC 737377690 and TIC 737377689 is about 8.2 mag in the
TESS band and 7.9 mag in $G$ (the two nearby stars have similar brightness and
color). Given these brightness differences, to explain the transit seen in
TESS data one of the light curves would have to show a 25% deep eclipse. Such
deep eclipses can be ruled out.

####  2.2.3 WASP

We used photometric data collected by WASP-South (Pollacco et al., 2006)
during 3 observing seasons, 2008–2009, 2010–2011, and 2011–2012, to try
measuring the stellar rotation period using the methods discussed by Maxted et
al. (2011). The period analysis of each observing season is shown in Figure 5.
The strongest period component in the latter two seasons is at $44\pm 2$ days,
while in the first season (2008–2009) it is close to half that period, at
$22\pm 1$ days. We adopt $44\pm 2$ days as an estimate of the star’s rotation
period since it is common for the photometric modulation to lose coherence
across several years, and it is common for the photometric period to
occasionally be one-half of the rotation period due to spots on opposite
hemispheres (e.g., McQuillan et al., 2014).

Figure 5: Period analysis of WASP times-series photometry. The panels show
periodograms of three seasonal data sets (left column panels) and the phase-
folded and binned light curve using the putative 44-d rotational period (right
column panels). The strongest peak of the 2010/11 and 2011/12 seasons
periodogram is at 44 days, while for 2008/09 it is at the 22-day first
harmonic. The horizontal dashed lines are the estimated 1% false-alarm levels.

###  2.3 High resolution spectroscopy

GJ 238 was observed by the High Accuracy Radial velocity Planet Searcher
(HARPS, $R$=120,000; Pepe et al., 2002; Mayor et al., 2003) at the ESO 3.6m
telescope in La Silla, Chile, between December 2008 to March 2012. A total of
eight spectra were obtained, with a signal-to-noise ratio at order 55 ranging
from 15 to 41, under Program IDs 082.C-0718 (PI: Bonfils) and 183.C-0437 (PI:
Bonfils). We use radial velocities (RVs) and uncertainties derived from the
HARPS spectra by Trifonov et al. (2020), who analyzed publicly available HARPS
spectra with the public SpEctrum Radial Velocity AnaLyser (SERVAL) pipeline
(Zechmeister et al., 2018) and corrected for nightly RV zero points. The 8
RVs, with RV uncertainties ranging from 1.0 to 2.9 $\rm m\,s^{-1}$, are
plotted in Figure 6 and listed in Table 3, including the cross correlation
function FWHM, contrast, bisector span, and signal-to-noise ratio at order 55.

Figure 6: Archival HARPS radial velocities (RVs) of GJ 238, from Trifonov et al. (2020). The left panel shows the RVs as a function of time, in BJD. The center panel also shows the RVs as a function of time in BJD but while zooming in on the groups of RVs obtained during the same observing season. The right panel shows the RVs phase folded on the transit ephemeris. Table 3:  HARPS archival differential radial velocitiesaaRVs and RV uncertainties ($\sigma_{RV}$) are taken from Trifonov et al. (2020). Cross correlation function FWHM, Contrast, bisector span (BIS) and signal-to-noise at order 55 (SNR) are taken from the HARPS DRS pipeline. BJD | RV | $\sigma_{RV}$ | FWHM | Contrast | BIS | SNR
---|---|---|---|---|---|---
| $\rm m\,s^{-1}$ | $\rm m\,s^{-1}$ | $\rm km\,s^{-1}$ | $\rm m\,s^{-1}$ | $\rm m\,s^{-1}$ |
2454807.70656 | -8.23 | 2.26 | 3.058 | 23.15 | -10.8 | 19.5
2454830.79427 | -6.99 | 1.25 | 3.046 | 23.17 | -6.2 | 34.3
2455234.61573 | 0.55 | 1.86 | 3.045 | 23.03 | 3.2 | 22.6
2455235.54858 | 2.30 | 1.31 | 3.056 | 23.17 | -2.8 | 31.8
2455275.56181 | 1.33 | 1.42 | 3.045 | 23.27 | -3.3 | 32.3
2455278.54649 | 6.48 | 2.89 | 3.040 | 23.41 | -22.9 | 14.7
2455283.54149 | 3.33 | 1.01 | 3.045 | 23.22 | -7.8 | 40.8
2456012.53361 | -0.12 | 1.12 | 3.042 | 23.03 | -10.4 | 39.7

###  2.4 High angular resolution imaging

We obtained high angular resolution images of the target to look for stars
located close enough to the target to have been unresolved in seeing-limited
ground-based images. In particular, the high angular resolution images can
probe for other stars within the HARPS fiber angular radius (see Section 2.3).
If such nearby stars exist they would reduce the relative brightness dip
observed with TESS, leading to a smaller planet radius estimate (Ciardi et
al., 2015). Deep eclipses of nearby faint stars could also be entirely
responsible for the TESS signal.

We obtained speckle imaging in $I$ band with the high-resolution camera
(HRCam, Tokovinin, 2018) at the 4.1m Southern Astrophysical Research (SOAR)
telescope at Cerro Pachón, Chile, on UT 2020 February 10. This observation was
done as part of the SOAR TESS survey (Ziegler et al., 2021). No nearby stars
were detected within the sensitivity of the data, of $\Delta I$ = 5 mag at 0.5
arcsec and $\Delta I$ = 7 at 3 arcsec, as shown in Figure 7.

We also obtained speckle imaging with the Zorro speckle instrument (Scott et
al., 2021) on the Gemini-South 8m telescope at Cerro Pachón, Chile, on UT 2020
March 13. The Zorro instrument observes simultaneously in two bands, 562 nm
and 832 nm. No nearby stars were detected within the sensitivity of the data,
down to 4 magnitudes fainter than the target at 0.1 arcsec from the target in
562 nm, and in 832 nm down to 4.5 magnitudes at 0.1 arcsec and 7 magnitudes at
1 arcsec, as shown in Figure 7.

Figure 7: Speckle imaging of GJ 238. Each panel shows the contrast curve, in
magnitude difference as a function of angular distance from the target in
arcsec, and the speckle auto-correlation function (ACF) in the inset. Top:
Speckle imaging obtained at SOAR in the $I$ band, on UT 2020 February 10.
Bottom: Speckle imaging obtained with Gemini-South/Zorro, on UT 2020 March 13,
in 562 nm (blue line) and 832 nm (red line and inset).

##  3 Host star characterization

We estimated the host star parameters using the empirical relations of Mann et
al. (2015, 2019), as described below. We first derived the absolute magnitude
in $K$ band based on the observed magnitude and Gaia DR3 parallax, giving
$M_{K}$ = 6.119 $\pm$ 0.023 mag. Next, we used the empirical relation between
$M_{K}$ and stellar mass with the coefficients provided by Mann et al. (2019,
see their Table 6 and Equation 2). This resulted in $M_{s}=0.421\pm 0.021\
M_{\sun}$, adopting a conservative uncertainty of 5% (Tayar et al., 2022). For
comparison, using the empirical relation of Mann et al. (2015, see their Table
1 and Equation 10) results in $0.444\pm 0.022\ M_{\sun}$, which is 5% higher
than the mass estimate above.

To estimate the stellar radius we used the empirical relation between $M_{K}$
and stellar radius derived by Mann et al. (2015, see their Table 1), resulting
in $R_{s}=0.427\pm 0.021\ R_{\sun}$, assuming again a conservative uncertainty
of 5%. For comparison, using the radius-mass empirical relation derived by
Boyajian et al. (2012, their Equation 10) and the mass derived in the previous
paragraph, results in $0.403\pm 0.020\ R_{\sun}$, which is 6% lower than the
radius estimate above.

The preceding estimates of the stellar mass and radius were used as priors
during the transit light curve model fitting, described in Section 2.1.1,
which led to refined values for the stellar mass and radius, listed in Table
2.

To estimate the stellar effective temperature we first calculated the
bolometric correction BCK to $M_{K}$. We did that using the empirical
relations between BCK and the $V-J$ color given by Mann et al. (2015, Table
3). We found BCK = 2.66 $\pm$ 0.13 mag and in turn a bolometric magnitude of
$M_{\rm bol}$ = 8.78 $\pm$ 0.13 mag, which is equivalent to a bolometric
luminosity of $L_{s}$ = $0.0242_{-0.0028}^{+0.0032}$ $L_{\sun}$. Finally,
using the Stefan-Boltzmann law we found $T_{\rm eff}$= $3485_{-135}^{+142}$ K.
That value is consistent with the temperature estimated by Kuznetsov et al.
(2019), based on the HARPS spectra. The stellar parameters derived here
correspond to a spectral type of M2.5 (Pecaut & Mamajek, 2013)222See also:
http://www.pas.rochester.edu/~emamajek/
EEM_dwarf_UBVIJHK_colors_Teff.txt.

We note that our derived stellar mass, radius, and temperature, are well
within $1\sigma$ from the values in TIC V8 (Stassun et al., 2018). And while
they are also consistent with the temperature and radius reported by Muirhead
et al. (2018), the latter reports a stellar mass of 0.473 $\pm$ 0.004
$M_{\sun}$, significantly larger than measured here.

To estimate the stellar metallicity we used the method described in Dittmann
et al. (2016). We first identified stars in the sample listed in Dittmann et
al. (2016) that have similar color and $M_{K}$ to GJ 238, and then calculated
a weighted mean of those stars’ metallicities, with weights based on the
distance from the target position in the color-magnitude parameter space. This
led to a metallicity of [Fe/H] = 0.15 $\pm$ 0.10. We note that that value is
$1.5\sigma$ larger than the metallicity reported by Kuznetsov et al. (2019),
of $-0.05\pm 0.09$, based on the HARPS spectra.

As an alternative estimate of the stellar temperature and radius we performed
an analysis of the entire broadband spectral energy distribution (SED)
together with the Gaia DR3 parallax following the procedures described in
Stassun & Torres (2016); Stassun et al. (2017); Stassun et al. (2018). We use
the 2MASS $JHK_{S}$ magnitudes, the WISE W1–W4 magnitudes, and the Gaia
$G_{\rm BP}$ and $G_{\rm RP}$ magnitudes. We also used the Gaia
spectrophotometry spanning 0.4–1.0 $\mu$m. Altogether, the available
photometry spans the full stellar SED over the wavelength range 0.4–20 $\mu$m,
with the Gaia spectrophotometry providing an especially strong constraint on
the overall absolute flux calibration, as shown in Figure 8.

Figure 8: GJ 238 spectral energy distribution. The red symbols represent the
observed photometric measurements, and the horizontal bars represent the
effective width of the passbands. Blue symbols are the model fluxes from the
best-fit PHOENIX atmosphere model (black). The Gaia spectrophotometry is shown
in gray in both the plot and the inset close-up of the blue end.

We performed a fit using PHOENIX stellar atmosphere models (Husser et al.,
2013) and the metallicity estimated above, with the free parameters being the
effective temperature and the overall flux normalization. We adopted an
extinction $A_{V}\equiv 0$. The resulting fit (Figure 8) has a reduced
$\chi^{2}=1.2$, with $T_{\rm eff}=3440\pm 75$ K. Integrating the model SED
gives the bolometric flux at the Sun, $F_{\rm bol}=3.29\pm 0.12\times 10^{-9}$
erg s-1 cm-2. Taking the $F_{\rm bol}$ and the Gaia parallax together directly
yields the bolometric luminosity, $L_{\rm bol}=0.02374\pm 0.00042$ L⊙, which
from the Stefan-Boltzmann relation gives the stellar radius to be
$R_{s}=0.434\pm 0.020$ R⊙. The results of the SED analysis provide consistent
values for $T_{\rm eff}$ and $R_{s}$ with those provided by the empirical
relations.

The HARPS spectra show absorption in the $H_{\alpha}$ line. According to
Walkowicz, & Hawley (2009), stars of spectral type similar to GJ 238 that show
absorption in $H_{\alpha}$ are either moderately active or inactive, but not
strongly active. This is supported by the lack of flares seen in a visual
examination of the TESS SPOC simple aperture photometry (SAP) light curves. It
is also consistent with the Astudillo-Defru et al. (2017) measurement of $\log
R^{\prime}_{HK}=-5.430\pm 0.089$ based on HARPS spectra, which according to
their study of the correlation between stellar rotation and $\log
R^{\prime}_{HK}$ corresponds to a rotation period of about 80 days (see
Astudillo-Defru et al. 2017 Equation 12).

To directly measure the stellar rotation period we used multi-season time-
series photometry from WASP-South, described in Section 2.2.3 and shown in
Figure 5, and concluded that the rotation period is $44\pm 2$ days. That
rotation period is consistent with a rotation of $51\pm 14$ days measured by
Claytor et al. (2023) using TESS data. The poorer precision of the latter is
expected given the difficulties involved in measured a rotation period longer
than the duration of a TESS sector with TESS data.

A rotation period of $44\pm 2$ days is shorter than predicted by Astudillo-
Defru et al. (2017) based on the spectroscopic $\log R^{\prime}_{HK}$.
However, their data show a large scatter around the relation between $\log
R^{\prime}_{HK}$ and rotation period (see their Figure 6), with one point, Gl
618A, with a mass of 0.38 $M_{\sun}$, having a measured rotation period of
56.5 days and a predicted rotation period based on their fitted relation of 78
days.

##  4 Rejecting false positive scenarios

In the subsections below we consider the various false positive scenarios,
other than a transiting planet orbiting GJ 238, that can lead to a transit-
like signal in the TESS data, and show that they are rejected or found to be
extremely unlikely, based on the data we have accumulated.

We first divided the TESS data into data subsets, and compared the transit
light curve shape in different subsets. We used two 1-year long subsets, and
four 6-months long subsets. In each subset the transit light curve shape was
consistent with that of the other subsets.

###  4.1 Is the M dwarf an eclipsing binary?

In a common false positive scenario the transiting object is in fact a star,
but smaller and cooler than the primary star in the system such that the
secondary eclipse is not detected. To check this possibility we examine
archival radial velocities (RVs) obtained by HARPS, as published by Trifonov
et al. (2020), shown in Figure 6 and listed in Table 3. The available eight
RVs have a span of 15 $\rm m\,s^{-1}$, an RMS of 4.7 $\rm m\,s^{-1}$, and
their MAD $\times$ 1.48 (which equals the standard deviation for a normal
distribution) is 2.7 $\rm m\,s^{-1}$. While the RVs show a long-term RV
variation on a time scale of several hundred days (see Figure 6 left panel),
the RVs within a single observing season show a scatter of only a few $\rm
m\,s^{-1}$ (see Figure 6 center panel). The five HARPS RVs taken during the
second observing season in which this target was observed333Those five RVs
were obtained between UT 2010 February 7 and UT 2010 March 28. span 5.9 $\rm
m\,s^{-1}$, have an RMS of 3.5 $\rm m\,s^{-1}$, and their MAD $\times$ 1.48 is
1.5 $\rm m\,s^{-1}$. Clearly these RVs rule out the possibility of the
transiting object being a star, including a stellar remnant, since a 0.08
$M_{\sun}$ companion would result in a 22.4 $\rm km\,s^{-1}$ semi-amplitude
assuming a circular orbit and given the orbital period and host star mass. We
can also rule out the transiting companion being a massive planet since a
Saturn mass companion ($\approx$0.3 $M_{\rm Jup}$) would result in a 90 $\rm
m\,s^{-1}$ semi-amplitude.

Another way to rule out the transit companion being a star or a brown dwarf is
by looking for orbital phase modulations in the TESS phase folded light curve,
since a massive orbiting companion is expected to induce phase modulations
along the orbit (e.g., Zucker et al., 2007; Shporer, 2017; Shporer et al.,
2019; Wong et al., 2020a, b, 2021a, 2021b). We tested the detectability of
such a signal through injection and recovery of a sine wave signal centered on
phase zero, which corresponds to the expected shape of a Doppler boosting
signal (e.g., Loeb & Gaudi, 2003; Shporer et al., 2010). We ignore other
potential phase modulations since they are expected to be much smaller in
amplitude. When injecting a sinusoidal signal with a semi-amplitude of 9 ppm
to the TESS data we recovered it with $5\sigma$ confidence. Therefore, larger
semi-amplitudes can be detected in the TESS data. An amplitude of 9 ppm
corresponds to a Doppler boosting signal induced by a 1.7 $M_{\rm Jup}$
transiting companion, given the orbital period and the properties of the
primary star. Therefore we conclude that more massive companions would have
induced detectable phase variations. We have also attempted to fit a sine wave
to the phase folded light curve without injection, while ignoring the in-
transit data, and measured an amplitude of $0.3\pm 1.8$ ppm, i.e., a null
result.

Therefore, the above shows that if (1) the transit seen in TESS data
originates from the target, and, if (2) the target is a single star, then the
transiting companion must be an object smaller and less massive than a giant
planet. The suppositions (1) and (2) are investigated in the following
subsections.

###  4.2 Does the transit-like signal originate from an unbounded eclipsing
binary?

The transit signal in the TESS data might originate from a stellar eclipsing
binary that is not associated with the target but whose light is blended with
the target in the TESS PSF, which is roughly an arcminute wide. Although, the
SPOC pipeline difference images show that the transit signal is located
$1.65\pm 3.05$ arcsec from GJ 238 (see Section 2.1). Yet, this angular
distance can still allow for blending with other stars on a similar line of
sight. To investigate this possibility we examined archival images and also
obtained ground-based photometric time series during predicted transit times,
with a typical angular resolution of one or a few arcseconds.

We used archival images to look for stars at the current target location, that
would be blended with the target in ground-based observations. We were able to
do that thanks to the target’s high proper motion, of $892.633\pm 0.025$ mas
per year. We used archival images of the target’s location taken by the UK
Schmidt Telescope (UKST) at 1979 and 1995 and made available by the STScI
Digitized Sky Survey, shown in Figure 3 along with a recent image from 2023
taken by the Las Cumbres Observatory 1m/Sinistro (Brown et al., 2013). The
images show that the current target position does not contain any stars
brighter than 19th mag that will be blended with the target in ground-based
photometric observations. We used that brightness limit since fainter stars
cannot explain the transit depth seen in TESS data even if they undergo a 100%
deep eclipse (full occultation), given the target’s brightness and observed
transit depth. We also checked that all stars brighter than 19th mag in the
vicinity of the target, according to the TIC, are detectable in the archival
images. The two stars closest to the target seen in Figure 3 are at a distance
of about 10 arcsec or more and are investigated below.

We note that it is in principle possible for a distant background star to be
moving at a similar proper motion to that of the target so it is blended with
it in all three epochs shown in Figure 3. However, that possibility is
extremely unlikely.

As described in Section 2.2.2, we collected ground-based light curves of all
stars close to the target and brighter than $T$ = 19.0 mag, and found that
none of them shows a deep eclipse that could result in the shallow transit
seen in TESS data due to blending with the target. This includes the two stars
closest to the target marked in Figure 3 and whose light curves are plotted in
Figure 4. We have also confirmed that all stars brighter than $T$ = 19.0 mag
in the vicinity of the target are detectable in the ground-based photometric
data.

Therefore, we ruled out all stars detected in the data near the target as the
source of an eclipse that can explain the transit seen in TESS data, and,
determined that stars not detected in the data are too faint to be the origin
of the transit even if they undergo a 100% deep eclipse. We are left with the
possibility that the transit seen in TESS data originates from the target
star.

###  4.3 Does the transit-like signal originate from a gravitationally bound
eclipsing binary?

The transit-like feature in TESS light curves might originate from an
eclipsing binary that is gravitationally bound to the target star, so it has
the same proper motion as the target and is not resolved in photometric and
spectroscopic ground-based observations.

To investigate this scenario we observed the target with high angular
resolution imaging using the Gemini-South/Zorro speckle camera, at 562 nm and
832 nm, and using SOAR at the $I$-band, as described in Section 2.4. The
contrast curves are shown in Figure 7. The 832 nm contrast curve places a
$5\sigma$ upper limit showing no stars down to a magnitude difference of about
4.5 mag at 0.1 arcsec, 6.5 mag at 0.5 arcsec, and 7.0 mag at 1.0 arcsec. Given
the properties of the target star, and using the tabulation provided by
Baraffe et al. (2015) of stellar mass, radius, and effective temperature, a
bounded main sequence star that is 4.5 mag fainter than the target at 832 nm
has a mass of about 0.09 $M_{\sun}$. The three angular distances listed above
correspond to sky-projected distances of 1.5 AU, 7.6 AU, and 15.2 AU,
respectively.

Further constraints on the existence of a stellar companion to the target come
from the Gaia DR3 catalog (Gaia Collaboration et al., 2022), although they are
difficult to quantify. The Gaia DR3 catalog does not contain stars near the
target down to a typical angular resolution of 0.4 arcsec and a completeness
brightness beyond 20th magnitude (Riello et al., 2021; Gaia Collaboration et
al., 2023). In addition the target’s Gaia DR3 Re-normalised Unit Weight Error
(RUWE) is 1.12 and the RV error is 0.17 $\rm km\,s^{-1}$, which are typical
for single stars (Katz et al., 2019).

Still, despite all the constraints above there could be a stellar companion to
the target that is fainter than the target and at a sky-projected distance at
the level of 1 AU, which corresponds to an angular distance of 0.066 arcsec
given the distance to the target. We turn to the TESS light curve shape to
further constrain this scenario. Based on our transit fit, we find a $3\sigma$
upper bound on the ratio between the ingress and egress duration and that of
the full transit, $t_{12}/t_{14}$, of 0.13. Since $R_{p}/R_{s}\lesssim
t_{12}/t_{14}$, we can place a $3\sigma$ upper bound on the eclipsing (or
transiting) object radius of $0.13\times
0.43\,R_{\odot}=6.1\,R_{\earth}=0.54\,R_{J}$. In other words, the shape of the
transit light curve – specifically the duration of the ingress/egress relative
to full transit – shows that the eclipsing/transiting object must be smaller
than a star or brown dwarf (e.g., Chabrier & Baraffe, 2000; Sorahana et al.,
2013). This is true whether the transited star is the known M dwarf or a
companion star, since any companion star must be smaller in radius than the
observed M dwarf. Therefore the transit seen in TESS data cannot be due to an
eclipsing binary that is gravitationally bound to the target star.

###  4.4 Does the transiting planet orbit a gravitationally bound star?

We are left with the possibility that a gravitationally bound star hosts the
transiting planet. In this scenario the transiting object has negligible mass
compared to its host star, so we can use our transit fit, and transit
duration, to compute the host star’s mean density. From the fit, we find
$\rho=5.1^{+1.4}_{-1.7}$ g cm-3 with a $3\sigma$ upper bound of $9.4$ g cm-3.
This is consistent with the density of GJ 238 which is $7.64\pm 0.32$ g cm-3,
but inconsistent with the density of most main sequence stars cooler than GJ
238 since stellar density grows larger as stellar mass grows smaller. More
quantitatively, stars smaller than $0.35\,M_{\odot}$ have mean densities
larger than about 11.5 g cm-3. And if the transit host was a gravitationally
bound star more massive than $0.35\,M_{\odot}$ then we would have detected its
spectral lines in the HARPS spectra, since it would be roughly half as bright
as the target star in the optical. Therefore, we can rule out a
gravitationally bound star-planet system as the source of the TESS transit
signal.

###  4.5 Statistical validation

To quantify the probability of the planet candidate being a false positive, we
analyzed the TESS data using the statistical validation tool TRICERATOPS
(Giacalone & Dressing, 2020; Giacalone et al., 2021) while accounting for
follow-up data collected here. TRICERATOPS assesses the reliability of a
planet candidate by simulating an array of astrophysical transit-producing
scenarios, including: (1) a planet transiting the target star, (2) a stellar
companion eclipsing the target star, (3) a planet transiting an unresolved
star that is gravitationally bound to or chance aligned with the target star,
(4) an unresolved pair of eclipsing binary stars that are gravitationally
bound to or chance aligned with the target star, (5) a planet transiting a
nearby star that is spatially resolved from the target star, or (6) a nearby
eclipsing binary star that is spatially resolved from the target star. Using
these simulations, it calculates the false positive probability (FPP) and
nearby false positive probability (NFPP) for the planet candidate. The former
takes into account all false positive scenarios (i.e., scenarios 2–6), whereas
the latter only takes into account false positive scenarios originating from
known nearby stars (i.e., scenarios 5–6).

Because we fully rule out scenarios 5 and 6 with ground-based follow-up
observations (see Section 4.3), we set the NFPP to zero and calculate only the
FPP. As an additional constraint, we fold in the 832 nm speckle contrast curve
shown in Figure 7, which restricts the extent of the parameter space in which
unresolved companions or chance-aligned stars can exist. We ran TRICERATOPS 20
times, resulting in ${\rm FPP}=3.80\pm 0.80\times 10^{-4}$, supporting the
hypothesis that the target is a transiting star-planet system.

##  5 Discussion

We present here the discovery and validation of GJ 238 b, with a radius of
$0.566\pm 0.014$ $R_{\earth}$ ($=1.064\pm 0.026$ Mars radius), making it one
of the smallest known planets, and the smallest discovered by the TESS mission
so far. Figure 9 and Figure 11 show GJ 238 b in the context of currently known
exoplanets. Figure 9 left panel shows the radii of small planets for which the
radius uncertainty is smaller than 25%, as a function of equilibrium
temperature ($T_{\rm eq}$). The equilibrium temperature was computed under the
assumptions that the Bond albedo is zero and there is no heat circulation from
the planet’s dayside and nightside hemispheres, and the dayside has a uniform
temperature. Figure 9 right panel shows the planet radius as a function of the
host star’s distance to the Sun, in log scale. In both panels planets with a
mass measurement uncertainty smaller than 25% are marked in red, and GJ 238 b
is marked by a purple diamond.

The plots show that there are only about a dozen known exoplanets with a
directly measured radius smaller than or similar to that of GJ 238 b. All of
them are validated exoplanets without a measured mass and most are in multi
transiting planet systems (Muirhead et al., 2012; Barclay et al., 2013;
Borucki et al., 2013; Marcy et al., 2014; Campante et al., 2015; Morton et
al., 2016; Cañas et al., 2022). It is interesting to note that most of these
planets have $T_{\rm eq}$ below 1,500 K, as seen in Figure 9 left panel. That
is likely related to the fact that these planets are hosted mostly by K- and
M-type stars, whose lower $T_{\rm eff}$ and small radius compared to G- and
F-type stars leads to a lower planet $T_{\rm eq}$ for planets with similar
orbital periods. And as these are the smallest known exoplanets with a
directly measured radius, the fact that they orbit cool and small stars is
expected.

Figure 9: Left: Planet radius vs. equilibrium temperature at the planet’s
orbit assuming zero bond albedo and no heat circulation. Right: Planet radius
vs. host star distance to the Sun in log scale. In both panels, planets with a
radius measurement better than $4\sigma$ are marked in black, and those which
also have their mass measured to better than $4\sigma$ are marked in red. GJ
238 b is marked by a purple diamond. Solar System terrestrial planets are
marked in blue in the left panel. The figure is based on data from the NASA
Exoplanets Archive downloaded on 2023 December 18.

As mentioned above, most known exoplanets similar in size to GJ 238 b are in
systems where there is at least one other known transiting exoplanet. But,
despite the large amount TESS data collected for GJ 238 only one planet has
been detected so far. It could be that the transit signals of other planets in
the system are too small to be detectable in current data, and might be
detectable with additional data to be collected by TESS in the future. It is
also possible that other planets are not transiting, but might be detectable
with precise radial velocity monitoring. It is interesting to note here that
the SPOC analysis has identified a single transit-like signal close to BJD =
2458364.6, during Sector 2, plotted in Figure 10. The nature of that signal,
whether it is due to a transiting planet, another astrophysical scenario
(false positive), or a residual systematic feature, is still under
investigation.

Figure 10: A single transit-like feature that appears in the TESS light curve
of GJ 238 during Sector 2. The plot shows relative flux, in parts per thousand
(ppt), as a function of time in days (BJD). If this feature is due to a
transiting planet then its depth of bout 0.6 ppt corresponds to a planet
radius of about 3.6 $R_{\earth}$, close to the size of Neptune.

The validation of GJ 238 b motivates further study of the system, explored in
the following subsections.

###  5.1 Planet mass measurement

One natural next step is to attempt measuring the planet’s mass. A planet mass
measurement, combined with the known radius will provide the mean density and
allow to constrain the planet’s composition. Figure 11 shows the radius-mass
diagram for small planets with measured radius and mass better than $4\sigma$,
with the radius of GJ 238 b marked by a horizontal red band. A planet mass
measurement will allow comparisons to the Solar System’s terrestrial planets,
and test whether GJ 238 b is iron-rich like GJ 367 b (Lam et al., 2021).

GJ 238 shows low stellar activity (see Section 3), and the archival HARPS RVs
show high RV stability, especially when examining RVs obtained within the same
observing season (see Figure 6). Therefore, this system seems to be suitable
for intensive high precision RV measurements. Still, the host star’s expected
RV semi-amplitude is only $K_{RV}\approx$ 0.14 $\rm m\,s^{-1}$ for a planet
mass of $M_{p}=0.15$ $M_{\earth}$, which is the expected mass assuming Earth-
like composition (see Figure 11). We have carried out a simple simulation to
estimate the number of RV measurements required for GJ 238 b mass measurement.
In our simulation, we injected an RV circular orbit signal with $K_{RV}$=0.14
$\rm m\,s^{-1}$ into $N$ RVs, each with a precision of $\sigma_{RV}=0.25$ $\rm
m\,s^{-1}$, that are obtained once per night with a jitter of 1.5 hours in the
measurement mid-exposure time. We adopted an RV uncertainty of 0.25 $\rm
m\,s^{-1}$ as that is approximately the RV precision that can be obtained for
stars similar to GJ 238 with state of the art high resolution Echelle
spectrographs, e.g., ESPRESSO (Pepe et al., 2014) and MAROON-X (Seifahrt et
al., 2018, although it cannot observe GJ 238 position).

Figure 11: Planet radius (linear scale) vs. planet mass (log scale) for known
transiting small planets with mass and radius measurement beyond a $4\sigma$
significance. GJ 238 b radius is marked by the red horizontal band whose width
corresponds to the $\pm 1\sigma$ measured radius uncertainty. The dashed lines
are composition models from Zeng et al. (2016), including, from bottom to top,
pure iron (100% Fe; dashed purple line), Earth-like composition (32.5% Fe +
67.5% MgSiO3; dashed blue line), and pure rock (100% MgSiO3; dashed brown
line). A few of the planets are labeled where T1 is an abbreviation for
TRAPPIST-1. Solar System terrestrial planets are marked in blue, where Earth
is labeled by E, Venus by V, Mars by Ma, and Mercury by Me. The figure is
based on data from the NASA Exoplanets Archive downloaded on 2023 December 18.

We repeated the simulation $10^{6}$ times in order to obtain a large sample of
measured $K_{RV}$, and took the mean and RMS of that distribution as the
resulting $K_{RV}$ and its uncertainty. We repeated this exercise while
changing the number of RVs ($N$), and found that $N$=155 RVs are needed for a
$5\sigma$ measurement of the RV signal. While that is a large number, it is
comparable to the number of RVs obtained in order to measure the mass of GJ
367 b (Lam et al., 2021).

The simulation described above is simplistic for several reasons. It assumes
uniform RV precision that is not impacted by observing conditions, and that
the target does not exhibit any other RV signals, due to, e.g., stellar
activity and/or other planets in the system. Although, the star shows low
activity and the stellar rotation is much longer than the orbital period (see
Section 3). On the other hand, scheduling observations close to phases of
quadrature, when the RV is at extrema (assuming a circular orbit) can lead to
a higher RV amplitude measurement SNR. It is also possible that the planet’s
composition is more iron-rich than the Earth-like composition assumed in the
simulation, in which case the number of RVs needed for a $5\sigma$ mass
measurement is reduced, down to $N$=45 RVs for a pure iron composition where
the planet mass is 0.28 $M_{\earth}$.

###  5.2 Planet atmosphere

Here we assess the prospect of studying the atmosphere of GJ 238 b.
Empirically, small and highly irradiated bodies like GJ 238 b tend to lack
substantial atmospheres. Atmospheric retention depends on the balance between
insolation $I$ and a planet’s ability to gravitationally bind its atmosphere,
measured by escape velocity $v_{\rm esc}$. Zahnle & Catling (2017) reported an
empirical $I\propto v_{\rm esc}^{4}$ “cosmic shoreline” dividing between
planets with and without an atmosphere, shown in Figure 12. Given the small
size of GJ 238 b, even under the densest pure-iron composition assumption it
receives excessive insolation relative to its gravitational binding energy,
placing GJ 238 b on the atmosphereless side of the empirical shoreline. M
dwarfs have prolonged high-luminosity pre-main-sequence phase, implying that
GJ 238 b would have been further above the shoreline before landing up in its
current location.

However, planets above the shoreline are not necessary airless. Provided that
abundant high-molecular-weight volatiles are stored in the mantle, survive
from initial loss, and can degas with sufficiently high rate, revival of a
secondary atmosphere is possible (e.g., Kite & Barnett, 2020). Such a high-
molecular-weight atmosphere is resistant to escape. It has been suggested that
the presence of a high-molecular-weight atmosphere on 55 Cnc e, a highly
irradiated super-Earth above the “cosmic shoreline” (Figure 12), is consistent
with observations (e.g., Angelo & Hu, 2017; Jindal et al., 2020).

To investigate whether GJ 238 b can be detected in emission we modeled its
emission spectrum assuming a blackbody with zero heat redistribution (no
atmosphere), a 100 bar CO2 atmosphere, and a 10 bar O2 atmosphere using
petitRADTRANS (Mollière et al., 2019). The relative flux of the emission
signal in these three scenarios is at most $\sim 15$ ppm, which is below the
25 ppm systematic noise floor of the MIRI LRS instrument of JWST reported by
Bouwman et al. (2023). We have also investigated the possibility of detecting
the atmosphere in transmission, and concluded that the signal is smaller than
10 ppm and hence undetectable by JWST. Therefore, we estimate that detecting
the atmosphere of GJ 238 b, if it has any, is not feasible given current
observational capacities.

###  5.3 Astrometry

At a distance of only 15.2 pc, GJ 238 is one the closest stars hosting a small
terrestrial transiting planet, and the closest among planets of similar or
smaller radius, as shown in Figure 9 right panel. This short distance will
allow detection of planets on wide orbits with Gaia time series astrometry
(Perryman et al., 2014), which will become available over the next few years
(Gaia Collaboration et al., 2016, 2022). Given the distance to the system and
the expected astrometric performance described in Perryman et al. (2014), Gaia
astrometry will be sensitive to a $\approx 0.22\,M_{\rm Jup}$ planet at 1 AU,
and a Neptune-mass planet at about 4 AU (although for the latter the Gaia
astrometric time series may not cover a full orbital period).

Figure 12: Stellar insolation at a planet’s orbit as a function of escape
velocity from the planet’s surface, in log-log scale. Based on data from the
NASA Exoplanet Archive downloaded on May 18, 2023. The empirical “cosmic
shoreline” and the water vapor greenhouse runaway threshold (Zahnle & Catling,
2017) are shown in cyan and yellow, respectively. Planets are categorized into
terrestrial planets (magenta), sub-Neptunes (blue), Neptune-like planets
(green), and gas giants (yellow) based on radius, see legend. The red line
shows the possible range of escape velocities of GJ 238 b. Because only
radius, but not mass, is known, the two endpoints represent two extreme
interior scenarios – a 100% iron composition and a 100% silicate composition.

##  6 Summary

We have shown that all false positive scenarios of the transiting planet
candidate TOI-486.01, orbiting GJ 238, are not viable or are extremely
unlikely, making it a real planet, GJ 238 b orbiting the M dwarf GJ 238. The
ability to validate this planet relied critically on its host star’s high
proper motion and small radius and mass. We followed procedures applied to
other similar systems (e.g., Vanderspek et al., 2019; Shporer et al., 2020;
Gan et al., 2020; Tey et al., 2023).

The planet’s radius of $0.566\pm 0.014$ $R_{\earth}$ makes it one of the
smallest planets currently known. Ongoing and future observations by TESS
Extended Missions are expected to lead to detections of increasingly small
transiting planets (Kunimoto et al., 2022), including terrestrial sub-Earth
size planets such as GJ 238 b, which can be studied in further detail thanks
to their proximity to the Sun and host star brightness. This will lead to
gradually putting the solar system terrestrial planets in the context of
exoplanets.

Funding for the TESS mission is provided by NASA’s Science Mission
directorate. We acknowledge the use of public TESS data from pipelines at the
TESS Science Office and at the TESS Science Processing Operations Center. This
paper includes data collected by the TESS mission, which are publicly
available from the Mikulski Archive for Space Telescopes (MAST). 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. This research has made use of the NASA Exoplanet Archive,
which is operated by the California Institute of Technology, under contract
with NASA under the Exoplanet Exploration Program. The Digitized Sky Surveys
were produced at the Space Telescope Science Institute under U.S. Government
grant NAG W-2166. The images of these surveys are based on photographic data
obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK
Schmidt Telescope. The plates were processed into the present compressed
digital form with the permission of these institutions. 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. 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). Some of the
observations in this paper made use of the High-Resolution Imaging instrument
Zorro and were 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 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 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. Z.L. acknowledges funding
from the Center for Matter at Atomic Pressures (CMAP), a National Science
Foundation (NSF) Physics Frontiers Center, under Award PHY-2020249. KAC
acknowledges support from the TESS mission via subaward s3449 from MIT.
SG is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship
under award AST-2303922.

## References

  * (1)
  * Angelo & Hu (2017) Angelo, I., Hu, R. 2017, AJ, 154, 232. doi:10.3847/1538-3881/aa9278
  * Astudillo-Defru et al. (2017) Astudillo-Defru, N., Delfosse, X., Bonfils, X., et al. 2017, A&A, 600, A13
  * Barclay et al. (2013) Barclay, T., Rowe, J. F., Lissauer, J. J., et al. 2013, Nature, 494, 452. doi:10.1038/nature11914
  * Baraffe et al. (2015) Baraffe, I., Homeier, D., Allard, F., et al. 2015, A&A, 577, A42. doi:10.1051/0004-6361/201425481
  * Borucki et al. (2013) Borucki, W. J., Agol, E., Fressin, F., et al. 2013, Science, 340, 587. doi:10.1126/science.1234702
  * Bouwman et al. (2023) Bouwman, J. et al. 2023, PASP, 135, 1045
  * Boyajian et al. (2012) Boyajian, T. S., von Braun, K., van Belle, G., et al. 2012, ApJ, 757, 112
  * Brown et al. (2013) Brown, T. M., Baliber, N., Bianco, F. B., et al. 2013, PASP, 125, 1031
  * Campante et al. (2015) Campante, T. L., Barclay, T., Swift, J. J., et al. 2015, ApJ, 799, 170. doi:10.1088/0004-637X/799/2/170
  * Cañas et al. (2022) Cañas, C. I., Mahadevan, S., Cochran, W. D., et al. 2022, AJ, 163, 3. doi:10.3847/1538-3881/ac3088
  * Chabrier & Baraffe (2000) Chabrier, G. & Baraffe, I. 2000, ARA&A, 38, 337. doi:10.1146/annurev.astro.38.1.337
  * Ciardi et al. (2015) Ciardi, D. R., Beichman, C. A., Horch, E. P., et al. 2015, ApJ, 805, 16
  * Claytor et al. (2023) Claytor, Z. R., van Saders, J. L., Cao, L., et al. 2023, arXiv:2307.05664. doi:10.48550/arXiv.2307.05664
  * Collins et al. (2017) Collins, K. A., Kielkopf, J. F., Stassun, K. G., et al. 2017, AJ, 153, 77
  * Cutri et al. (2003) Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, VizieR Online Data Catalog, II/246
  * Dittmann et al. (2016) Dittmann, J. A., Irwin, J. M., Charbonneau, D., et al. 2016, ApJ, 818, 153
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306
  * Foreman-Mackey et al. (2021) Foreman-Mackey, D., Luger, R., Agol, E., et al. 2021, The Journal of Open Source Software, 6, 3285. doi:10.21105/joss.03285
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1. doi:10.1051/0004-6361/201629272
  * Gaia Collaboration et al. (2022) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2022, arXiv:2208.00211
  * Gaia Collaboration et al. (2023) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1. doi:10.1051/0004-6361/202243940
  * Gan et al. (2020) Gan, T., Shporer, A., Livingston, J., et al. 2020, AAS Journals, submitted
  * Gelman & Rubin (1992) Gelman, A. & Rubin, D. B. 1992, Statistical Science, 7, 457. doi:10.1214/ss/1177011136
  * Giacalone & Dressing (2020) Giacalone, S. & Dressing, C. D. 2020, Astrophysics Source Code Library. ascl:2002.004
  * Giacalone et al. (2021) Giacalone, S., Dressing, C. D., Jensen, E. L. N., et al. 2021, AJ, 161, 24. doi:10.3847/1538-3881/abc6af
  * Huang et al. (2020a) Huang, C. X., Vanderburg, A., Pál, A., et al. 2020a, Research Notes of the American Astronomical Society, 4, 204. doi:10.3847/2515-5172/abca2e
  * Huang et al. (2020b) Huang, C. X., Vanderburg, A., Pál, A., et al. 2020b, Research Notes of the American Astronomical Society, 4, 206. doi:10.3847/2515-5172/abca2d
  * Husser et al. (2013) Husser, T.-O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6. doi:10.1051/0004-6361/201219058
  * Jenkins et al. (2016) Jenkins, J. M., Twicken, J. D., McCauliff, S., et al. 2016, Proc. SPIE, 9913, 99133E
  * Jensen (2013) Jensen, E. 2013, Tapir: A web interface for transit/eclipse observability, ascl:1306.007
  * Jindal et al. (2020) Jindal, A., de Mooij, E., Jayawardhana, R., et al. 2020, AJ, 160, 101, doi:10.3847/1538-3881/aba1eb
  * Katz et al. (2019) Katz, D., Sartoretti, P., Cropper, M., et al. 2019, A&A, 622, A205
  * Kipping (2013) Kipping, D. M. 2013, MNRAS, 435, 2152
  * Kite & Barnett (2020) Kite, E., Barnett, M. 2020, PNAS, 117, 31
  * Kunimoto et al. (2022) Kunimoto, M., Winn, J., Ricker, G. R., et al. 2022, AJ, 163, 290. doi:10.3847/1538-3881/ac68e3
  * Kuznetsov et al. (2019) Kuznetsov, M. K., del Burgo, C., Pavlenko, Y. V., et al. 2019, ApJ, 878, 134. doi:10.3847/1538-4357/ab1fe9
  * Lam et al. (2021) Lam, K. W. F., Csizmadia, S., Astudillo-Defru, N., et al. 2021, Science, 374, 1271. doi:10.1126/science.aay3253
  * Loeb & Gaudi (2003) Loeb, A. & Gaudi, B. S. 2003, ApJ, 588, L117. doi:10.1086/375551
  * Mann et al. (2015) Mann, A. W., Feiden, G. A., Gaidos, E., et al. 2015, ApJ, 804, 64
  * Mann et al. (2019) Mann, A. W., Dupuy, T., Kraus, A. L., et al. 2019, ApJ, 871, 63
  * Maxted et al. (2011) Maxted, P. F. L., Anderson, D. R., Collier Cameron, A., et al. 2011, PASP, 123, 547
  * Marcy et al. (2014) Marcy, G. W., Isaacson, H., Howard, A. W., et al. 2014, ApJS, 210, 20. doi:10.1088/0067-0049/210/2/20
  * Mayor et al. (2003) Mayor, M., Pepe, F., Queloz, D., et al. 2003, The Messenger, 114, 20
  * McQuillan et al. (2014) McQuillan, A., Mazeh, T., & Aigrain, S. 2014, ApJS, 211, 24. doi:10.1088/0067-0049/211/2/24
  * Mollière et al. (2019) Mollière, P. et al. 2019, A&A, 627, A67
  * Morton (2015) Morton, T. D. 2015, Astrophysics Source Code Library. ascl:1503.011
  * Morton et al. (2016) Morton, T. D., Bryson, S. T., Coughlin, J. L., et al. 2016, ApJ, 822, 86. doi:10.3847/0004-637X/822/2/86
  * Muirhead et al. (2012) Muirhead, P. S., Johnson, J. A., Apps, K., et al. 2012, ApJ, 747, 144. doi:10.1088/0004-637X/747/2/144
  * Muirhead et al. (2018) Muirhead, P. S., Dressing, C. D., Mann, A. W., et al. 2018, AJ, 155, 180
  * Pecaut & Mamajek (2013) Pecaut, M. J. & Mamajek, E. E. 2013, ApJS, 208, 9. doi:10.1088/0067-0049/208/1/9
  * Pepe et al. (2002) Pepe, F., Mayor, M., Rupprecht, G., et al. 2002, The Messenger, 110, 9
  * Pepe et al. (2014) Pepe, F., Molaro, P., Cristiani, S., et al. 2014, Astronomische Nachrichten, 335, 8. doi:12.1002/asna.201312004
  * Perryman et al. (2014) Perryman, M., Hartman, J., Bakos, G. Á., et al. 2014, ApJ, 797, 14
  * Pollacco et al. (2006) Pollacco, D. L., Skillen, I., Collier Cameron, A., et al. 2006, PASP, 118, 1407
  * Ricker et al. (2014) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2014, Proc. SPIE, 914320
  * Riello et al. (2021) Riello, M., De Angeli, F., Evans, D. W., et al. 2021, A&A, 649, A3. doi:10.1051/0004-6361/202039587
  * Scott et al. (2021) Scott, N. J., Howell, S. B., Gnilka, C. L., et al. 2021, Frontiers in Astronomy and Space Sciences, 8, 138. doi:10.3389/fspas.2021.716560
  * Seifahrt et al. (2018) Seifahrt, A., Stürmer, J., Bean, J. L., et al. 2018, Proc. SPIE, 10702, 107026D. doi:10.1117/12.2312936
  * Shporer et al. (2010) Shporer, A., Kaplan, D. L., Steinfadt, J. D. R., et al. 2010, ApJ, 725, L200. doi:10.1088/2041-8205/725/2/L200
  * Shporer (2017) Shporer, A. 2017, PASP, 129, 072001
  * Shporer et al. (2019) Shporer, A., Wong, I., Huang, C. X., et al. 2019, AJ, 157, 178
  * Shporer et al. (2020) Shporer, A., Collins, K. A., Astudillo-Defru, N., et al. 2020, ApJ, 890, L7. doi:10.3847/2041-8213/ab7020
  * Smith et al. (2012) Smith, J. C., Stumpe, M. C., Van Cleve, J. E., et al. 2012, PASP, 124, 1000
  * Sorahana et al. (2013) Sorahana, S., Yamamura, I., & Murakami, H. 2013, ApJ, 767, 77. doi:10.1088/0004-637X/767/1/77
  * Stassun & Torres (2016) Stassun, K. G. & Torres, G. 2016, AJ, 152, 180. doi:10.3847/0004-6256/152/6/180
  * Stassun et al. (2017) Stassun, K. G., Collins, K. A., & Gaudi, B. S. 2017, AJ, 153, 136
  * Stassun et al. (2018) Stassun, K. G., Oelkers, R. J., Pepper, J., et al. 2018a, AJ, 156, 102
  * Stassun et al. (2018) Stassun, K. G., Corsaro, E., Pepper, J. A., et al. 2018b, AJ, 155, 22. doi:10.3847/1538-3881/aa998a
  * Stumpe et al. (2012) Stumpe, M. C., Smith, J. C., Van Cleve, J. E., et al. 2012, PASP, 124, 985. doi:10.1086/667698
  * Stumpe et al. (2014) Stumpe, M. C., Smith, J. C., Catanzarite, J. H., et al. 2014, PASP, 126, 100
  * Tayar et al. (2022) Tayar, J., Claytor, Z. R., Huber, D., et al. 2022, ApJ, 927, 31. doi:10.3847/1538-4357/ac4bbc
  * Tey et al. (2023) Tey, E., Huang, C. X., Kunimoto, M., et al. 2023, AJ, 165, 93. doi:10.3847/1538-3881/acaf88
  * Torres et al. (2011) Torres, G., Fressin, F., Batalha, N. M., et al. 2011, ApJ, 727, 24. doi:10.1088/0004-637X/727/1/24
  * Tokovinin (2018) Tokovinin, A. 2018, PASP, 130, 035002. doi:10.1088/1538-3873/aaa7d9
  * Trifonov et al. (2020) Trifonov, T., Tal-Or, L., Zechmeister, M., et al. 2020, A&A, 636, A74. doi:10.1051/0004-6361/201936686
  * Twicken et al. (2018) Twicken, J. D., Catanzarite, J. H., Clarke, B. D., et al. 2018, PASP, 130, 064502. doi:10.1088/1538-3873/aab694
  * Vanderspek et al. (2019) Vanderspek, R., Huang, C. X., Vanderburg, A., et al. 2019, ApJ, 871, L24
  * Walkowicz, & Hawley (2009) Walkowicz, L. M., & Hawley, S. L. 2009, AJ, 137, 3297
  * Wong et al. (2020a) Wong, I., Shporer, A., Kitzmann, D., et al. 2020a, AJ, 160, 88. doi:10.3847/1538-3881/aba2cb
  * Wong et al. (2020b) Wong, I., Shporer, A., Daylan, T., et al. 2020b, AJ, 160, 155. doi:10.3847/1538-3881/ababad
  * Wong et al. (2021a) Wong, I., Kitzmann, D., Shporer, A., et al. 2021a, AJ, 162, 127. doi:10.3847/1538-3881/ac0c7d
  * Wong et al. (2021b) Wong, I., Shporer, A., Zhou, G., et al. 2021b, AJ, 162, 256. doi:10.3847/1538-3881/ac26bd
  * Zahnle & Catling (2017) Zahnle, K., Catling, D. 2017, ApJ, 843, 122. doi:10.3847/1538-4357/aa7846
  * Zacharias et al. (2012) Zacharias, N., Finch, C. T., Girard, T. M., et al. 2012, VizieR Online Data Catalog, I/322A
  * Zechmeister et al. (2018) Zechmeister, M., Reiners, A., Amado, P. J., et al. 2018, A&A, 609, A12. doi:10.1051/0004-6361/201731483
  * Ziegler et al. (2021) Ziegler, C., Tokovinin, A., Latiolais, M., et al. 2021, AJ, 162, 192. doi:10.3847/1538-3881/ac17f6
  * Zeng et al. (2016) Zeng, L., Sasselov, D. D., & Jacobsen, S. B. 2016, ApJ, 819, 127
  * Zucker et al. (2007) Zucker, S., Mazeh, T., & Alexander, T. 2007, ApJ, 670, 1326. doi:10.1086/521389