# A Second Planet Transiting LTT 1445A and a Determination of the Masses of
Both Worlds

Jennifer G. Winters Center for Astrophysics $|$ Harvard & Smithsonian, 60
Garden Street, Cambridge, MA 02138, USA  Ryan Cloutier Banting Fellow  Center
for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA
02138, USA  Amber A. Medina Center for Astrophysics $|$ Harvard & Smithsonian,
60 Garden Street, Cambridge, MA 02138, USA  Jonathan M. Irwin  Center for
Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138,
USA  David Charbonneau Center for Astrophysics $|$ Harvard & Smithsonian, 60
Garden Street, Cambridge, MA 02138, USA  Nicola Astudillo-Defru Departamento
de Matemática y Física Aplicadas, Universidad Católica de la Santísima
Concepción, Alonso de Rivera 2850, Concepción, Chile  Xavier Bonfils
Université Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France  Andrew W.
Howard Department of Astronomy, California Institute of Technology, Pasadena,
CA 91125, USA  Howard Isaacson Department of Astronomy, University of
California Berkeley, Berkeley CA 94720, USA  Centre for Astrophysics,
University of Southern Queensland, Toowoomba, QLD, Australia  Jacob L. Bean
Department of Astronomy & Astrophysics, University of Chicago, 5640 S. Ellis
Avenue, Chicago, IL 60637, USA  Andreas Seifahrt Department of Astronomy &
Astrophysics, University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637,
USA  Johanna K. Teske  Earth & Planets Laboratory of the Carnegie Institution
for Science, 5241 Broad Branch Road, NW, Washington, DC 20015, USA  Jason D.
Eastman Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street,
Cambridge, MA 02138, USA  Joseph D. Twicken SETI Institute, Moffett Field, CA
94035, USA  NASA Ames Research Center, Moffett Field, CA 94035, USA  Karen A.
Collins Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street,
Cambridge, MA 02138, USA  Eric L. N. Jensen Department of Physics & Astronomy,
Swarthmore College, Swarthmore PA 19081, USA  Samuel N. Quinn Center for
Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138,
USA  Matthew J. Payne Center for Astrophysics $|$ Harvard & Smithsonian, 60
Garden Street, Cambridge, MA 02138, USA  Martti H. Kristiansen Brorfelde
Observatory, Observator Gyldenkernes Vej 7, DK-4340 Tølløse, Denmark  DTU
Space, National Space Institute, Technical University of Denmark, Elektrovej
327, DK-2800 Lyngby, Denmark  Alton Spencer  Western Connecticut State
University, Danbury CT 06810, USA  Andrew Vanderburg Department of Physics and
Kavli Institute for Astrophysics and Space Research, Massachusetts Institute
of Technology, Cambridge, MA 02139, USA  Mathias Zechmeister Institut für
Astrophysik, Georg-August-Universität, Friedrich- Hund-Platz 1, D-37077
Göttingen, Germany  Lauren M. Weiss Department of Physics, University of Notre
Dame, Nieuwland Science Hall, Notre Dame, IN 46556, USA  Sharon Xuesong Wang
Department of Astronomy, Tsinghua University, Beijing 100084, People’s
Republic of China  Gavin Wang Tsinghua International School, Beijing 100084,
China  Stanford Online High School, 415 Broadway Academy Hall, Floor 2, 8853,
Redwood City, CA 94063, USA  Stéphane Udry  Observatoire de Genève, Université
de Genève, Chemin Pegasi 51, 1290 Sauverny, Switzerland  Ivan A. Terentev
Citizen Scientist, Planet Hunter, Petrozavodsk, Russia  Julian Stürmer
Landessternwarte, Zentrum für Astronomie der Universität Heidelberg,
Königstuhl 12, D-69117 Heidelberg, Germany  Guðmundur Stefánsson Princeton
University, Department of Astrophysical Sciences, 4 Ivy Lane, Princeton, NJ
08540, USA  Henry Norris Russell Fellow  Avi Shporer Department of Physics and
Kavli Institute for Astrophysics and Space Research, Massachusetts Institute
of Technology, Cambridge, MA 02139, USA  Stephen Shectman  The Observatories
of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena,
CA 91101, USA  Ramotholo Sefako South African Astronomical Observatory, P.O.
Box 9, Observatory, Cape Town 7935, South Africa  Hans Martin Schwengeler
Citizen Scientist, Planet Hunter, Bottmingen, Switzerland  Richard P. Schwarz
Patashnick Voorheesville Observatory, Voorheesville, NY 12186, USA  Nicholas
Scarsdale Department of Astronomy and Astrophysics, University of California,
Santa Cruz, CA 95060, USA  Ryan A. Rubenzahl NSF Graduate Research Fellow
Department of Astronomy, California Institute of Technology, Pasadena, CA
91125, USA  Arpita Roy Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore, MD 21218, USA  Department of Physics and Astronomy, Johns
Hopkins University, 3400 N Charles St, Baltimore, MD 21218, USA  Lee J.
Rosenthal  Department of Astronomy, California Institute of Technology,
Pasadena, CA 91125, USA  Paul Robertson Department of Physics & Astronomy,
University of California Irvine, Irvine, CA 92697, USA  Erik A. Petigura
Department of Physics & Astronomy, University of California Los Angeles, Los
Angeles, CA 90095, USA  Francesco Pepe  Observatoire de Genève, Université de
Genève, Chemin Pegasi 51, 1290 Sauverny, Switzerland  Mark Omohundro  Citizen
Scientist, c/o Zooniverse, Department of Physics, University of Oxford, Denys
Wilkinson Building, Keble Road, Oxford, OX1 3RH, UK  Joseph M. Akana Murphy
NSF Graduate Research Fellow  Department of Astronomy and Astrophysics,
University of California, Santa Cruz, CA 95064, USA  Felipe Murgas Instituo de
Astrofísica da Canarias (IAC), 38205 La Laguna, Tenerife, Spain  Departamento
de Astrofísica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife,
Spain  Teo Močnik Gemini Observatory/NSF’s NOIRLab, 670 N. A’ohoku Place,
Hilo, HI 96720, USA  Benjamin T. Montet School of Physics, University of New
South Wales, Sydney, NSW 2052, Australia  UNSW Data Science Hub, University of
New South Wales, Sydney, NSW 2052, Australia  Ronald Mennickent Departamento
de Astronomía, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Andrew W. Mayo Department of Astronomy, University of California Berkeley,
Berkeley, CA 94720, USA  Centre for Star and Planet Formation, Natural History
Museum of Denmark & Niels Bohr Institute, University of Copenhagen, Øster
Voldgade 5-7, DK-1350 Copenhagen K., Denmark  Bob Massey Villa ’39
Observatory, Landers, CA 92285, USA  Jack Lubin Department of Physics &
Astronomy, University of California Irvine, Irvine, CA 92697, USA  Christophe
Lovis  Observatoire de Genève, Université de Genève, Chemin Pegasi 51, 1290
Sauverny, Switzerland  Pablo Lewin The Maury Lewin Astronomical Observatory,
Glendora, CA 91741, USA  David Kasper Department of Astronomy & Astrophysics,
University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637, USA  Stephen
R. Kane Department of Earth and Planetary Sciences, University of California,
Riverside, CA 92521, USA  Jon M. Jenkins NASA Ames Research Center, Moffett
Field, CA 94035, USA  Daniel Huber Institute for Astronomy, University of
Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA  Keith Horne SUPA
Physics and Astronomy, University of St. Andrews, Fife, KY16 9SS Scotland, UK
Michelle L. Hill Department of Earth and Planetary Sciences, University of
California, Riverside, CA 92521, USA  Paula Gorrini Institut für Astrophysik,
Georg-August-Universität, Friedrich- Hund-Platz 1, D-37077 Göttingen, Germany
Steven Giacalone Department of Astronomy, University of California Berkeley,
Berkeley, CA 94720, USA  Benjamin Fulton NASA Exoplanet Science
Institute/Caltech-IPAC, MC 314-6, 1200 E. California Blvd., Pasadena, CA
91125, USA  Thierry Forveille Université Grenoble Alpes, CNRS, IPAG, F-38000
Grenoble, France  Pedro Figueira  European Southern Observatory, Alonso de
Córdova 3107, Vitacura, Región Metropolitana, Chile  Instituto de Astrofísica
e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762
Porto, Portugal  Tara Fetherolf Earth and Planetary Sciences Department,
University of California, Riverside, CA 92521, USA  UC Chancellor’s Fellow
Courtney Dressing Department of Astronomy, University of California Berkeley,
Berkeley CA 94720, USA  Rodrigo F. Díaz International Center for Advanced
Studies (ICAS) and ICIFI (CONICET), ECyT-UNSAM, Campus Miguelete, 25 de Mayo y
Francia, (1650) Buenos Aires, Argentina  Xavier Delfosse Université Grenoble
Alpes, CNRS, IPAG, F-38000 Grenoble, France  Paul A. Dalba NSF Astronomy and
Astrophysics Postdoctoral Fellow  Department of Astronomy and Astrophysics,
University of California, Santa Cruz, CA 95064, USA  Department of Earth and
Planetary Sciences, University of California, Riverside, CA 92521, USA  Fei
Dai Division of Geological and Planetary Sciences, California Institute of
Technology, Pasadena, CA 91125, USA  C.C.Cortés  Departamento de Física,
Facultad de Ciencias, Universidad del Bío-Bío, Avenida Collao 1202, Casilla
15-C, Concepción, Chile  Departamento de Astronomía, Universidad de
Concepción, Casilla 160-C, Concepción, Chile  Ian J. M. Crossfield  Department
of Physics & Astronomy, University of Kansas, 1082 Malott, 1251 Wescoe Hall
Dr., Lawrence, KS 66045, USA  Jeffrey D. Crane The Observatories of the
Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, CA
91101, USA  Dennis M. Conti American Association of Variable Star Observers,
49 Bay State Road, Cambridge, MA 02138, USA  Kevin I. Collins George Mason
University, 4400 University Drive, Fairfax, VA 22030 USA  Ashley Chontos NSF
Graduate Research Fellow  Institute for Astronomy, University of Hawai‘i, 2680
Woodlawn Drive, Honolulu, HI 96822, USA  R. Paul Butler Earth & Planets
Laboratory, Carnegie Institution for Science, 5241 Broad Branch Road, NW,
Washington, DC 20015, USA  Peyton Brown Department of Physics and Astronomy,
Vanderbilt University, 6301 Stevenson Center Ln., Nashville, TN 37235, USA
Madison Brady  Department of Astronomy & Astrophysics, University of Chicago,
5640 S. Ellis Avenue, Chicago, IL 60637, USA  Aida Behmard NSF Graduate
Research Fellow  Division of Geological and Planetary Sciences, California
Institute of Technology, Pasadena, CA 91125, USA  Corey Beard Department of
Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA
Natalie M. Batalha Department of Astronomy and Astrophysics, University of
California, Santa Cruz, CA 95060, USA  Jose-Manuel Almenara Université
Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France

###### Abstract

LTT 1445 is a hierarchical triple M-dwarf star system located at a distance of
6.86 parsecs. The primary star LTT 1445A (0.257 M☉) is known to host the
transiting planet LTT 1445Ab with an orbital period of 5.36 days, making it
the second closest known transiting exoplanet system, and the closest one for
which the host is an M dwarf. Using TESS data, we present the discovery of a
second planet in the LTT 1445 system, with an orbital period of 3.12 days. We
combine radial velocity measurements obtained from the five spectrographs
ESPRESSO, HARPS, HIRES, MAROON-X, and PFS to establish that the new world also
orbits LTT 1445A. We determine the mass and radius of LTT 1445Ab to be
$2.87\pm 0.25$ M⊕ and $1.304^{+0.067}_{-0.060}$ R⊕, consistent with an Earth-
like composition. For the newly discovered LTT 1445Ac, we measure a mass of
$1.54^{+0.20}_{-0.19}$ M⊕ and a minimum radius of 1.15 R⊕, but we cannot
determine the radius directly as the signal-to-noise of our light curve
permits both grazing and non-grazing configurations. Using MEarth photometry
and ground-based spectroscopy, we establish that star C (0.161 M☉) is likely
the source of the 1.4-day rotation period, and star B (0.215 M☉) has a likely
rotation period of 6.7 days. Although we have not yet determined the rotation
period of star A, we estimate a probable rotation period of 85 days. Thus,
this triple M-dwarf system appears to be in a special evolutionary stage where
the most massive M dwarf has spun down, the intermediate mass M dwarf is in
the process of spinning down, while the least massive stellar component has
not yet begun to spin down.

††facilities: TESS, MEarth, LCOGT, ESO:3.6m (HARPS), Gemini:Gillett
(MAROON-X), Keck (HIRES), Magellan:Clay (PFS), VLT (ESPRESSO)††software:
AstroImageJ (Collins et al., 2017), astropy (Astropy Collaboration et al.,
2013, 2018), celerite (Foreman-Mackey et al., 2017), ExoFASTv2 (Eastman et
al., 2013; Eastman, 2017), exoplanet (Foreman-Mackey et al., 2019), george
(Ambikasaran et al., 2015), IDL, IRAF, LcTools II (Schmitt & Vanderburg,
2021), PYMC3 (Salvatier et al., 2016), python, serval (Zechmeister et al.,
2018), starry (Luger et al., 2019), TAPIR (Jensen, 2013), Time Utilities
(Eastman et al., 2010), todcor (Zucker & Mazeh, 1994)

##  1 Introduction

Terrestrial exoplanets are difficult to study. Whether one is seeking to
measure their bulk densities, search for attendant satellites, or probe their
atmospheres, the task is made easier by two factors: First, the stars must be
nearby, so that we might mitigate the cruel dictates of the inverse square
law. Second, the stellar mass and radius should be small, so that the ratio of
the planetary and stellar quantities is maximized. It is for these reasons
that nearby M-dwarf systems are the darlings of the exoplanet menagerie.
Fortunately, M dwarfs are abundant, making up approximately 72% of all stars
in the stellar neighborhood (Henry et al., 2018). Their dominance among nearby
planetary hosts is likewise in evidence: Indeed, of the 16 stars within 15
parsecs that are known to host transiting exoplanets, all but 4 are M dwarfs.

At a distance of 6.53 pc, the closest star known to host transiting exoplanets
is HD 219134 (Motalebi et al., 2015; Gillon et al., 2017). Although the two
transiting worlds have had their densities measured, they are otherwise
largely inaccessible because the parent star is a K dwarf with a radius of
0.778 R☉. But the star in second place is much more diminutive in stature: LTT
1445A, with a radius of 0.268 R☉ and a mass of 0.257 M☉. At a distance of 6.86
pc (Gaia Collaboration et al., 2016; Lindegren et al., 2021), it is the
closest M dwarf known to host a transiting planet. Using data from the
Transiting Exoplanet Survey Satellite ($TESS$) (Ricker et al., 2015) and a
host of ground-based telescopes, Winters et al. (2019, hereafter W19),
published the discovery of LTT 1445Ab, a planet with an orbital period of 5.36
days. Although that planet was presumed to be terrestrial owing to its radius,
no measurement of its mass has yet been presented. A mass measurement is
crucial for at least two reasons: First, it would constrain the bulk
composition of the planet. If the planet proves to be terrestrial, the mass
measurement would allow for the determination of the ratio of its iron-and-
nickel core to its magnesium-silicate mantle, which in turn could be compared
to elemental abundances of the stellar photosphere. Second, future atmospheric
studies require a direct estimate of the surface gravity to enable an
unambiguous interpretation of data gathered in transmission, since the
atmospheric scale height is a combination of the surface gravity, temperature,
and mean molecular weight. Intriguingly, LTT 1445A is the most massive member
of a resolved triple M-dwarf system. The three stars fall on a line (see Fig.
1 from W19) and the stellar orbital plane of stars B and C is viewed edge-on,
and hence the entire system may be co-planar.

In pursuit of the mass of LTT 1445Ab, we set out to gather multi-epoch radial
velocity (RV) measurements with five high-resolution spectrographs. While that
activity was underway, we found a second periodic transit-like signal in the
TESS data. Combining the RV and TESS data with ground-based photometric
monitoring, we established that indeed a second planet transits LTT 1445A, and
orbits interior to the known world. In what follows, we describe these
findings, along with our measurements of the masses of both worlds.

We briefly summarize the host star system in §2, before turning to a
description of our photometric and spectroscopic data in §3. We present our
analysis of these data in §4, and their implications in §5.

##  2 Description of the Host Stellar System

The host system, LTT 1445ABC111Other names for A: TIC 98796344, TOI 455, L
730-18, BD-17 588A, RST 2292A, WDS J03019-1633A, 2MASS J03015142-1635356, Gaia
DR2 5153091836072107136, GJ 3193; other names for BC: TIC 98796342, BD-17
588B, RST 2292BC, WDS J03019-1633B, 2MASS J03015107-1635306, Gaia DR2
5153091836072107008. (Luyten, 1957, 1980), is a nearby, hierarchical trio of
mid-to-late M dwarfs. The preliminary astrometric orbit for LTT 1445BC,
presented in W19, indicates an orbital period of $36.2\pm 5.3$ yrs and a semi-
major axis $1.159\pm 0.076$ arcseconds, which corresponds to an average
physical separation of $8.1\pm 0.5$ AU. As noted in W19, the separation
between the A and BC appears to have recently begun decreasing, with the most
recent value of 7$\farcs$10 obtained in 2017, according to data available in
the Washington Double Star (WDS)
Catalog222https://www.usno.navy.mil/USNO/astrometry/optical-IR-prod/wds/WDS
(Mason et al., 2009). Considering the total mass of the three stellar
components and an average angular separation of 5″ (corresponding to 34 AU,
calculated using the weighted mean of the parallaxes of A and BC: $145.6917\pm
0.0244$ mas), we estimate the period of the A-BC orbit to be roughly 250
years. We refer the reader to Figure 1 in W19, which presents a resolved image
of the 3 stars in the system. We also refer the reader to Table 1 in W19,
which lists the astrometry, photometry, and stellar parameters of LTT 1445.

##  3 Observations

###  3.1 Photometric Time Series Data

We describe here the photometric time series observations of LTT 1445 by
$TESS$, the MEarth-South telescope array, and the Las Cumbres Observatory
telescope network.

####  3.1.1 TESS Observations

$TESS$ observed LTT 1445 in the first year of its prime mission, which
resulted in the discovery of LTT 1445Ab, as described in W19. We included this
system in our $TESS$ Guest Investigator program (PI Winters; G03250) target
list to gather short-cadence (two-minute) data of the volume-complete sample
of M dwarfs with masses $0.1\leq{\rm M/M_{\odot}}\leq 0.3$ within 15 parsecs
(Winters et al., 2021). LTT 1445A and BC were also included in the $TESS$
Input Catalog (TIC) and Candidate Target List (CTL) (Stassun et al., 2018) via
the Cool Dwarf Sample (Muirhead et al., 2018). The LTT 1445 system was re-
observed at two-minute cadence in sector 31 from UT 2020 October 22 to
November 16, in spacecraft orbits 69 and 70. The system fell on CCD 4 of
Camera 2.

As described in the data release
notes333https://archive.stsci.edu/missions/tess/doc/tess_drn/tess_sector_31_drn47_v02.pdf
for sector 31, data collection was paused for 1.4 days between the two orbits
to download data, a single momentum dump was conducted halfway through each
orbit, and a star tracker anomaly caused the data collection in orbit 70 to
end 2.08 days early.

The two-minute cadence data were reduced with the NASA Ames Science Processing
Operations Center (SPOC) pipeline (Jenkins et al., 2015, 2016) that was
repurposed from the $Kepler$ reduction pipeline (Jenkins et al., 2010). A
planet candidate with an approximate radius of 1.5$\pm$0.4 R⊕ was again
detected in four transits during sector 31 to have a period of 5.36 days and a
transit depth of 2750$\pm$191 ppm with a signal-to-noise ratio of 15.2.

A second planet with a 3.12-day period and a transit duration of roughly 45
min was identified in the sector 4 light curve of LTT 1445 by several of us
(MHK, IAT, HMS, MO, AS). After the release of the sector 31 light curve data,
we recovered a very shallow transit signal with a period of P = 3.12 days.
This second planet has not been identified by the $TESS$ planet-vetting team,
and thus is not assigned a TOI designation; however, the $TESS$ SPOC algorithm
recovered signals at periods of 1.5623 days and 1.5616 days, half that of the
expected period, with a multiple event statistic (MES, Jenkins et al., 2002,
equivalent to the signal to noise of the transit in the folded light curve) of
6.77 and 5.36 for the sector 4 and 31 data, respectively. To advance to the
vetting process, planet candidates must have a SPOC MES larger than 7.1. The
SPOC team manually re-ran their data validation algorithm (Twicken et al.,
2018; Li et al., 2019), allowing for both the 1.56- and 3.12-day periods.
While the 1.56-day signal was strong, the candidate failed the odd/even
transit test at this period. The 3.12-day signal passed the odd/even transit
test. The 3.12-day signal consisted of six observed transits in the sector 4
light curve yielding a transit depth of $1554\pm 187$ ppm, and eight transits
in the sector 31 light curve, yielding a transit depth of $1607\pm 192$ ppm.
However, the SNR of the light curve was insufficient to use the $TESS$ pixel-
level diagnostics to identify which star in LTT 1445 was the origin of the
3.12-day transit signal.

There is no background star from which the transit could originate. W19
compared the position of the system in archival images taken in 1953 to its
position at the time the TESS data were taken in 2018. The system’s high
proper motion (roughly half an arcsecond per year) and the sixty-five year
difference in the images permitted W19 to eliminate the hypothesis that the
transit signal originates from a background star coincident with the position
of LTT1445 at the $TESS$ epochs. The system has moved only roughly 1″ between
the 2018 and 2020 data, so this conclusion remains valid. We are thus
confident that the transit signal originates in the LTT 1445 system.

####  3.1.2 MEarth-South Photometric Monitoring

For the purpose of determining the rotation periods of A and BC, we gathered
photometric monitoring observations using MEarth-South (Nutzman & Charbonneau,
2008; Irwin et al., 2015) telescope 6 at Cerro Tololo Inter-American
Observatory (CTIO), Chile, beginning UT 2019 February 14; observations are
ongoing at the time of writing. The dataset used in the present analysis
includes 330 nights of data ending 2021 October 7. We gathered no observations
between 2020 March 10 and 2020 November 4, when CTIO was closed due to the
COVID-19 pandemic.

We gathered data in visits of $5\times 4$ seconds at a cadence of
approximately 20 minutes between visits while the target was above 2 airmasses
and there were no higher priority observations such as transit followup. We
obtained a total of 17,987 exposures.

The delivered image quality of the MEarth telescopes can be highly variable
over long time baselines, predominantly due to wind shake. Wind at the
location of MEarth-South on Cerro Tololo shows a seasonal variation, with
stronger and more gusty winds during the winter and spring seasons in
particular. FWHM values ranging from approximately 1.7 to 5.3 pixels were
recorded during the time series, where the pixel scale is $0.84$ arcsec/pixel.
Consequently while the BC pair is always blended, there is variable blending
between A and BC, requiring specialized photometric extraction procedures.

As described in W19, separate apertures of 4.2 pixel radius were placed on the
A and BC components, using a global (full-field) astrometric solution for
aperture positioning to avoid drift in the relative positions of the A and BC
apertures as a function of image quality. For the present purpose we require
separate light curves of A and BC, so external comparison stars elsewhere in
the field were used rather than the procedure used for the transit followup
observations in our previous work. The LTT 1445 system is in a sparse field so
there were relatively few of these available, and they are fainter than the
target stars. Thus, the resulting photometric solutions exhibit higher noise
levels and systematic errors than are typical for MEarth data.

The comparison star solutions are unable to correct the effect of variable
blending between A and BC, which causes fairly severe systematic errors in the
resulting light curves. In order to partly correct this effect we modified our
standard techniques used for periodogram analysis of MEarth data detailed in
Newton et al. (2016) to use simultaneous linear decorrelation against both the
standard “common mode” term (to correct variable atmospheric precipitable
water vapor) and against full-width-half-maximum (FWHM).

The resulting periodograms are shown in Figure 1, where we compare results for
the TESS light curve containing all three components with the separate MEarth
light curves for A and BC. We also show the periodogram of the observational
window function in each case.

The periodogram is plotted in terms of the F-test statistic for the nested
model comparison between the null hypothesis of only the baseline detrending
with no rotation signal, and the alternate hypothesis where there is also a
sinusoidal signal of the given period (further details of this procedure are
given in Newton et al. 2016). At fixed period, this statistic would follow an
$F$ distribution $F(2,\nu)$ where the number of degrees of freedom $\nu$ is
large. Standard results for this distribution show the 1.4 day signal in the
MEarth light curve of LTT 1445 BC is highly significant with an $F$ value
several hundred above the baseline level in the periodogram.

Figure 1: Periodograms and Window Functions of $TESS$ and MEarth data of LTT
1445. The $TESS$ data (top two panels), which include all three stellar
components, exhibit a 1.4-day period. This signal is also seen in the
periodogram of the MEarth data for LTT 1445BC (fourth panel), confirming that
either the B or C component is the origin of the 1.4-day signal in the TESS
data. The peak at 3.5 days represents an alias of the 1.4-day period. The
cluster of peaks between 50 and 100 days likely indicate the rotation period
of A (middle two panels), but more data are needed for a robust detection of
the expected period of $85\pm 22$ days. A marginal 6.7-day signal is also seen
in both the $TESS$ data and the MEarth data of LTT 1445BC, which we discuss
further in §4.5 .

The 1.4-day signal detected in TESS data and reported previously by W19 is
found to originate from BC, as expected based on stellar activity and
rotational broadening results presented in the previous paper, but this has
now been resolved observationally. The $1\ {\rm day}^{-1}$ alias of this
signal is also seen close to 3.5 days. No clear rotational modulation signal
meeting our quality criteria (see Newton et al. 2016) is yet detected in LTT
1445A, but the periodogram shows power at long periods between approximately
40 and 150 days and the corresponding alias period close to 1 day. Based on
the observed activity level and mass of this star, a rotation period around
$85\pm 22$ days would be expected (calculated using the empirical relation in
Newton et al. 2017), but has yet to be detected in the observations. We show
the MEarth light curves for LTT 1445A and BC in Figure 2.

####  3.1.3 MEarth-South Transit Follow-Up Observations

We also performed follow-up observations with MEarth-South spanning times of
the transit of planet b. Because MEarth is able to spatially resolve star A
from stars BC, these data serve to confirm that planet b indeed transits star
A. As discussed above in §3.1.2, MEarth observations of the LTT 1445 system
are extremely sensitive to image quality due to the components being barely
resolved in the data. Additionally, due to the short exposure time,
atmospheric scintillation noise is severe and increases with airmass.
Consequently, although we observed several transits of LTT 1445Ab for
followup, the majority of these were of poor quality, and all but one were
rejected for the final analysis.

Our analysis includes a single full transit observed on UT 2019 September 2
using 7 telescopes. Otherwise, the observational strategy and reduction
techniques were identical to those described in W19 and are not repeated here.
A total of 3935 data points were gathered during this time series and the
resulting light curve is shown in the top panel of Figure 3.

Because the expected transit depth of the 3.12-day planet candidate was below
the detection limits of the MEarth array, we did not attempt observations to
confirm it with MEarth.

Figure 2: MEarth light curves of LTT 1445A (top) and BC (bottom), phase-folded
to the 1.4-day stellar rotation period. The data have been corrected for
precipitable water vapor, and outliers have been rejected. The gray points and
errorbars indicate the individual measurements, while the black points
indicated the binned data. The red curve in the bottom panel illustrates the
1.4-day rotation period model for LTT 1445BC. The top panel illustrates that
we do not yet have enough data for a robust rotation period detection of LTT
1445A.

###  3.2 LCOGT Transit Follow-up Observations

We observed three full transits of LTT 1445Ab from the Las Cumbres Observatory
Global Telescope (LCOGT) (Brown et al., 2013) 1.0 m network. We observed a
full transit on UT 2019 August 16 in Pan-STARRS Y-band from the CTIO node
using 30 second exposures, and a full transit on UT 2020 October 8 in Pan-
STARRS $z$-short band from the McDonald Observatory node using 10 second
exposures. A full transit was observed on UT 2019 July 16 from the South
Africa Astronomical Observatory node in Pan-STARRS Y-band using 30 second
exposures. However, we ultimately chose not to include this observation in the
analysis because only a few minutes of nominal post-transit baseline were
observed, resulting in an unclear time of egress and thus a depth measurement
that is not well constrained. We used the TESS Transit Finder, a customized
version of the Tapir software package (Jensen, 2013), to schedule our transit
observations. The $4096\times 4096$ LCOGT SINISTRO cameras have 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), and photometric data were extracted with AstroImageJ
(Collins et al., 2017). The UT 2019 August 16 images were (unintentionally)
mildly defocused and have typical stellar point-spread-functions with a FWHM
of roughly $3\farcs 8$. Circular apertures with radius of roughly $2\farcs 7$
were used to extract the differential photometry. We estimate that about $2\%$
of the flux in the target star aperture is from the nearby pair LTT 1445BC.
The UT 2020 October 8 images were very slightly defocused and have typical
stellar point-spread-functions with a FWHM of roughly $2\farcs 1$. Circular
apertures with radius about $3\farcs 5$ were used to extract the differential
photometry. We estimate that about $1.3\%$ of the flux in the target star
aperture is from the nearby pair LTT 1445BC. For all observations, we used a
single comparison aperture around the nearby pair LTT 1445BC to extract the
light curve of LTT 1445Ab. The light curves are presented in the bottom panel
of Figure 3.

Figure 3: Transits of LTT 1445Ab measured from ground-based data. The top
panel shows the transit of LTT 1445Ab as observed by MEarth-South on UT 2019
September 2 using 7 telescopes. The bottom panel shows two transits of LTT
1445Ab as observed by LCOGT.

Using the LCOGT 1.0 m network and an ephemeris extracted from $TESS$ sector 4
data, we attempted to recover the 3.12-d transit signal on 6 epochs in 2019
and 2020. However, the updated ephemeris based upon the combination of the
sector 4 and 31 data shows that those observations were typically 5 hours late
and do not span the times of transit.

###  3.3 Spectroscopic Data

We combined 136 RVs of LTT 1445A from five high-resolution spectrographs taken
over roughly two years. Here we describe the instruments in alphabetical
order, as well as the methods used to measure the RVs and their uncertainties.
We list the RVs and their uncertainties in Table 1.

####  3.3.1 ESPRESSO

We acquired 19 spectra of the LTT 1445A with the Echelle SPectrograph for
Rocky Exoplanets and Stable Spectroscopic Observations (ESPRESSO) spectrograph
(Pepe et al., 2021) on the VLT from UT 2020 July 04 to September 03. ESPRESSO
is an ultra-stable, fiber-fed echelle spectrograph with resolving power $R=$
140,000 in the high-resolution (1-UT) configuration and a wavelength range of
$378.2-788.7$ nm. We used integration times of 900 sec and we employed the
slow (100 kpx s-1), $2\times 1$ binning readout mode. We elected not to use
the simultaneous wavelength calibration; thus, the calibration fiber was set
on sky. The signal-to-noise ratios (SNR) of the spectra range between 58 and
142 at 650 nm, with an average of 104.

We derived the RVs using the $\chi^{2}$-minimization template-matching method
described in Astudillo-Defru et al. (2015). The stellar template was built
from the median of the individual spectra, accounting for the ESPRESSO design
that creates two individual images (slices) of the same spectral order. To
compute the RVs, we discarded echelle orders below order 15 (30 slices) due to
the low flux, as well as zones containing telluric features. RV uncertainties
were computed following the methods described in Bouchy et al. (2001) and
range between 0.15 m s-1 and 0.32 m s-1, with an average uncertainty of 0.20 m
s-1.

####  3.3.2 HARPS

We acquired 45 spectra of LTT 1445A with the High Accuracy Radial Velocity
Planet Searcher (HARPS) spectrograph (Mayor et al., 2003) on the La Silla
3.6-m telescope from UT 2019 March 04 to October 21. HARPS is a fiber-fed
echelle spectrograph with resolving power $R=$ 115,000 and a wavelength range
of 378-691 nm. We employed integrations times of 900 sec and the spectra were
read out in slow mode (104 kpx s-1), except for one spectrum acquired on 2019
September 12, which had an exposure time of 1500 sec. We found that for seven
of our spectra we had inadvertently observed the BC component, as evidenced by
the H$\alpha$ emission. We discarded these from the RV analysis, but these
spectra later proved to be a blessing in disguise, as they allowed us to
investigate the rotational broadening of the B and C components (see §4.5).
The calibration fiber was set on sky. The science fiber provides SNRs between
26 and 60 at 650 nm, with an average of 48. As with ESPRESSO, we derived the
RVs by template matching and we estimated the uncertainties following the
methods of Bouchy et al. (2001); these range between 1.06 m s-1 and 2.86 m
s-1, with an average uncertainty of 1.44 m s-1. We allowed for a separate RV
zero point offset for the 2019 February data because of the roughly four month
time span between those data and the later observations.

We also measure the Ca II H and K emission (S activity index) and proceed to
calculate a value of log(R’HK)=$-5.413\pm 0.118$. Following Astudillo-Defru et
al. (2017), we estimate a rotation period of $79\pm 15$ days, in agreement
with the estimated rotation period of $85\pm 22$ days noted above.

####  3.3.3 HIRES

We acquired 39 spectra of LTT 1445A with the High Resolution Echelle
Spectrometer (HIRES) on the 10-m Keck telescope on Maunakea, Hawaii, on nights
between UT 2019 August 14 and 2020 February 28. HIRES is an optical echelle
spectrograph with resolving power $R\approx 55,000$ (Vogt et al., 1994). We
used the standard procedures of the California Planet Search (CPS; Howard et
al., 2010) to make the observations and reduce the spectra. This includes the
use of an iodine cell to calibrate the wavelength solution and point spread
function of HIRES, as well as a long slit (the “C2” decker) to measure and
subtract contemporaneous sky spectra. We used an image rotator to orient the
field so that light from LTT 1445A went through the slit and light from LTT
1445BC did not. The HIRES spectra span the wavelengths 364–790 nm with our CPS
setup, but the RVs were computed from the wavelength range 500–630 nm because
that region is calibrated by the iodine. We used integration times of 900 s,
which resulted in SNRs of 100–170 per pixel on blaze near 550 nm. We computed
relative RVs using the method descended from Butler et al. (1996). The HIRES
RVs have internal uncertainties between 1.3 m s-1 and 2.0 m s-1, with an
average uncertainty of 1.5 m s-1.

####  3.3.4 MAROON-X

We used the MAROON-X spectrograph (Seifahrt et al., 2016, 2018, 2020) on the
8.1-m Gemini-North telescope to measure RVs of LTT 1445A during three
observing runs of two weeks each between December 2019 and November 2020.
MAROON-X is a stabilized, fiber-fed echelle spectrograph with resolving power
$R\simeq$ 85,000 and a wavelength range of $500-920$ nm in two camera arms.
MAROON-X has demonstrated an RV stability of at least 30 cm s-1 over the span
of a few weeks during its first year of operations (Seifahrt et al., 2020) and
has recently been used to determine a precise mass of the nearby transiting
rocky planet Gl 486b (Trifonov et al., 2021).

We acquired 27 spectra of LTT 1445A over 8 nights during the science
verification and commissioning phase of the instrument in December 2019. The
simultaneous calibration was not operational during these first observations,
so bracketing wavelength calibration exposures were taken to track the
instrumental drift. The lack of simultaneous calibration likely limits the
instrumental precision of these data to approximately 1 m s-1. Moreover, we
found that 7 of the 27 spectra in two consecutive nights in 2019 had low SNR
and also showed abnormal chromatic index and differential line widths in
MAROON-X’s blue arm. Some of these spectra lead to RV outliers and thus all 7
spectra were subsequently dropped from the RV analysis. Due to their low SNR
and thus larger individual RV uncertainty, their contribution to the nightly
mean was small and did not significantly change the final RV data point for
the night.

We gathered an additional 20 spectra over 17 nights in September and November
2020. We find only a single night with notable stellar activity in this
dataset. Because the RV measurement from this one night does not present as a
clear outlier, we included this datapoint in the RV analysis.

We used integration times of 600 sec in 2019 and 300 sec in 2020. In 2019, the
peak SNR per 1D pixel ranges between 60 and 190 at 640 nm in the blue arm and
between 140 and 430 at 800 nm in the red arm, with a widespread distribution
depending on seeing conditions. In 2020, we find peak SNRs ranging between 50
and 95 at 640 nm in the blue arm and between 130 and 250 at 800 nm in the red
arm.

We reduced the MAROON-X raw data using a custom Python 3 pipeline based on
tools previously developed for the CRIRES instrument (Bean et al., 2010). The
wavelength and instrumental drift solution of MAROON-X is based on a
stabilized Fabry Perot etalon (Stürmer et al., 2017) in conjunction with a
ThAr lamp for the initial measurement of the gap size and chromatic dispersion
of the etalon. In early 2020, the simultaneous calibration fiber of MAROON-X
became operational, allowing for a robust order-by-order drift correction at
the sub-m s-1 level. Barycentric corrections were computed using the
barycorrpy code (Kanodia & Wright, 2018) from weighted averages based on
MAROON-X’s white light exposure meter.

We computed the RVs using serval (Zechmeister et al., 2018), which employs a
$\chi^{2}$-minimization algorithm based on matching an empirical template to
each order at each epoch. The template is constructed from the data itself as
a weighted average of all observations. A telluric mask is used to exclude
telluric absorption features deeper than about 1%, both in the construction of
the template and in each epoch. Typical uncertainties derived by serval are
based on the inter-order dispersion of the RVs and range from 0.25 m s-1 for
the highest SNR of 430 in the red channel to 1.6 m s-1 for the lowest SNR of
60 in the blue channel. To increase the SNR for robust RV calculations, we
combined blue and red arm observations as well as multiple back-to-back
observations per night into nightly epoch means and propagated uncertainties
based on the spread of the individual measurements. These final uncertainties
range from 0.4 to 1.4 m s-1 in 2019 and 0.4 to 1.0 m s-1 in 2020, with an
average uncertainty of 0.8 and 0.6 m s-1, respectively.

Because of an instrument intervention that took place after the 2019
commissioning run, which introduced changes to both the etalon as well as the
spectral format of the blue arm, we treat the data from 2019 and 2020 as
independent data sets with distinct RV offset parameters.

####  3.3.5 PFS

We acquired 25 spectra (15 when binned by night) of LTT 1445A with the Planet
Finder Spectrograph (PFS, Crane et al., 2006, 2008, 2010), mounted on the
6.5-m Magellan II telescope at Las Campanas Observatory in Chile, from UT 2019
July 20 to 2020 November 4. PFS covers $391-734$ nm and the subsequent RVs are
calibrated using the iodine method. The default 0$\farcs$3 slit provides a
resolving power $R\simeq 127,000$. Integration times ranged from 960 to 1500 s
resulting in SNRs between 40 and 70 at the peak of the blaze around 600 nm.
All PFS spectra are reduced and analyzed using a custom IDL pipeline based on
Butler et al. (1996) that regularly delivers sub-1 m s-1 precision. We binned
observations taken sequentially to improve the SNR for robust RV calculations.
The RV uncertainties in our nightly-binned RVs ranged between 0.48 m s-1 and
0.83 m s-1, with an average uncertainty of 0.63 m s-1.

Table 1: Radial Velocities for LTT 1445A

BJDaaBarycentric Julian Date of mid-exposure, in the TDB time-system. |  $v_{\rm rad}$bbBarycentric radial velocity. | $\sigma$ | Spectrograph
---|---|---|---
(days) | (${\rm m\ s^{-1}}$) | (${\rm m\ s^{-1}}$) |
2458546.500296 | -5457.74 | 1.31 | HARPS
2458547.501338 | -5463.53 | 1.16 | HARPS
2458548.500633 | -5460.85 | 1.36 | HARPS
2458555.506869 | -5455.18 | 1.29 | HARPS
2458556.505906 | -5453.54 | 1.16 | HARPS

Note. — This table is available in its entirety in machine-readable form.

##  4 Analysis

Because of the complex nature of the $TESS$ light curve, we used a combination
of exoplanet (Foreman-Mackey et al., 2017) and ExoFASTv2 (Eastman et al.,
2019) for our light curve modeling: We first used exoplanet to fit and remove
the photometric modulation in the $TESS$ light curve using a Gaussian
Processes (GP) regression model via celerite while preserving the transit
signals of the two planets. We then used ExoFASTv2, which does not use GPs, to
simultaneously fit the RV data and the de-trended transit data from exoplanet.
We also performed an independent RV-only analysis that included a GP
regression to account for stellar activity that could affect the uncertainties
of the planetary masses.

We will know the masses and radii of these planets only as well as we know
these values for their host star. We estimate a mass of $0.257\pm 0.014$ M⊙
for the host star using the mass-luminosity relation in the $K-$band by
Benedict et al. (2016) and then use a single-star mass-radius relation
(Boyajian et al., 2012) to estimate a stellar radius of $0.268\pm 0.027$ R⊙.
We calculate the bolometric corrections in $K$ (Mann et al., 2015, erratum)
and in $V$ (Pecaut & Mamajek, 2013), along with their respective bolometric
luminosities. We adopt the mean of the two bolometric luminosities and then
use the Stefan-Boltzmann Law to calculate an effective temperature $T_{\rm
eff}$ of $3337\pm 150$ K for LTT 1445A. We adopt the metallicity [Fe/H] of
$-0.340\pm 0.090$ dex from Neves et al. (2014), which is measured using HARPS
data. We updated the parallax of LTT 1445A to that of the Gaia EDR3 (Gaia
Collaboration et al., 2016; Lindegren et al., 2021) for our estimates of the
star’s mass, radius, and effective temperature, but these values did not
change significantly from those reported in W19. We use these stellar
parameters of LTT 1445A as priors for the light curve and RV modeling
described below.

###  4.1 Light Curve Modeling with exoplanet

The presence of other objects in the $TESS$ aperture can dilute the transit
depth of the planet, which is measured from the light curve. If the additional
objects have identifiers and $TESS$ magnitudes in the $TESS$ Input Catalog
(TICv8.1; Stassun et al., 2019), the SPOC pipeline calculates a dilution
(i.e., contamination) factor and performs a correction to the final light
curve (Stumpe et al., 2012). For the sector 4 data, the SPOC contamination
value of 0.4849 is very close to our estimated value of $0.480\pm 0.013$,
which is calculated from $T$ mags estimated from an M-dwarf-specific relation
(W19). For the sector 31 light curve, the SPOC contamination value is 0.42003,
which is significantly different. The difference is partly due to an updated
$T$ mag for LTT 1445A of $T=8.843$ mag in the TICv8.1, compared to $T=8.64$
mag from an earlier TIC version. However, the TICv8.1 also appears to have a
duplicate entry for LTT 1445BC, one from the 2MASS cross-match (TIC 98796342)
with $T=8.554$ mag and the other from the Gaia DR2 cross-match (TIC 651819442)
with $T=11.558$ mag. Thus, the SPOC dilution value in the sector 31 light
curve is an overestimate of the amount of contaminating light from the BC
components. As in W19, we removed the SPOC dilution value and imposed our own.

As in W19, we did not include the third transit of LTT 1445Ab in sector 4 in
our analysis because the light curve baseline showed a strong slope at egress;
we note that this transit was also omitted from the results in the SPOC DV
report. The third transit of LTT 1445Ac in the sector 4 light curve was not
observed, as it occurred during the communication failure. The fourth transit
occurred during the brief chunk of light curve right before the data download.
Our GP did not fit properly over such a small span of data, so in the interest
of working with uniformly processed data, we omitted this transit from our
analysis. The third transit of the 5.36-day planet in the sector 31 data
occurred during the pause in data collection while the data were being
downloaded and was thus not observed. The star tracker anomaly reported for
sector 31 did not affect the transits of either planet.

We used the python package exoplanet (Foreman-Mackey et al., 2019), which
employs probabilistic methods to model exoplanet transit and radial velocity
data sets. It has the additional capability to incorporate Gaussian Processes
(GP) with celerite (Foreman-Mackey et al., 2017) and limb-darkened light
curves with starry (Luger et al., 2018). We used the SPOC-generated Pre-Search
Data Conditioning Simple Aperture Photometry (PDCSAP) light curve (Smith et
al., 2012; Stumpe et al., 2012, 2014), corrected with our calculated dilution
factor. Before fitting, we removed positive outliers (flares) that deviated by
more than three times the median absolute deviation of the PDCSAP light curve.
While we do not know from which star the flares originate, recent work on
nearby mid-to-late M dwarfs (see, e.g., Medina et al. 2020) indicates that
rapidly rotating stars flare far more frequently. Thus, we suspect that many
of the flares originate from either or both of the B or C components.

We model the stellar rotational modulation, as well as any other possible
systematics, with a GP. The GP kernel is the sum of two simple harmonic
oscillators, which has been shown to be an appropriate kernel for data that
are quasi-periodic in nature (Angus et al., 2018), such as the observed
rotational modulation in the light curve of LTT 1445ABC. To model the
planetary transits, we used a limb-darkened transit model and a Keplerian
orbit. We used the same model, priors, GP hyper-parameters, and methods for
the fit as described in W19. We measure planet-to-star radius ratios of
$0.037\pm 0.005$ and $0.047\pm 0.006$ for LTT 1445Ac and LTT 1445Ab in the
$TESS$ sector 4 light curve data and ratios of $0.035\pm 0.009$ and $0.042\pm
0.007$ for the respective planets in the $TESS$ sector 31 light curve data.

We note that the 1.4-day rotation signal has evolved in the two years that
elapsed between sector 4 and 31. While the period of the modulation is the
same, the semi-amplitude of the variability has roughly doubled from $1.475\pm
0.302$ ppt in the sector 4 light curve to $3.027\pm 0.401$ ppt in the sector
31 light curve. This increase in the semi-amplitude is likely due to a change
in the morphology of the starspot groups leading to a larger hemisphere-
integrated asymmetry in sector 31. We show our GP fit to the $TESS$ light
curve data for both sector 4 and 31 in Figure 4.

###  4.2 Global Modeling with ExoFASTv2

We perform a simultaneous global fit of the $TESS$ light curve and radial
velocity data using ExoFASTv2 (Eastman et al., 2019). ExoFASTv2 is a suite of
IDL routines that simultaneously fits exoplanetary transit and radial velocity
data using a differential Markov Chain Monte Carlo (MCMC) code. We include the
$TESS$ light curves from sectors 4 and 31, and we use 134 RVs from the five
spectrographs. We used as input for the ExoFASTv2 the output light curve data
from exoplanet with the stellar variability removed. In order to allow for the
propagation of the uncertainty in the dilution that was corrected by the
exoplanet fit, we allow for a residual dilution, with a prior centered on zero
with $\sigma=0.013$.

Because we derived the stellar parameters as described in §2, we did not
include a spectral energy distribution in the fit, and we disabled the default
MIST stellar evolutionary models that use isochrones to constrain the stellar
parameters. We placed Gaussian priors on the stellar mass, radius, effective
temperature, and metallicity that were equal to the uncertainties noted above
in §4. We interpolated the quadratic limb darkening coefficients in Table 15
of Claret (2017) to the effective temperature of LTT 1445A, which we imposed
with a Gaussian prior with a standard deviation of 0.10. While the atmospheric
models used to derive the limb darkening tables are questionable for low-mass
stars such as LTT 1445A, the impact is likely to be negligible due to the low
precision of the $TESS$ light curve.

We include a slope term to account for a change in the RVs of LTT 1445A due to
the stellar A-BC orbit. We estimated the magnitude of the RV slope as follows.
Because the maximum change in RVs over the 643-day timespan of our data is
dependent upon the eccentricity of the orbit, we explored which eccentricities
would result in a stable configuration for the A-BC orbit. The stability
criterion for hierarchical triple star systems from Harrington (1972) requires
the eccentricity of the outer (A-BC) orbit and the ratio of the semi-major
axes of the inner (B-C) and outer orbits. We investigated eccentricites 0 to
0.9 and semi-major axes of 1″ (from the preliminary astrometric orbit for LTT
1445BC reported in Winters et al. (2019)) and 5″ (the mean separation noted
for LTT 1445A-BC in §2), respectively, to estimate that retrograde motion
orbits with eccentricities less than 0.45 would be stable. Therefore, we
estimate that a orbital period of 253 yr for LTT 1445A-BC would result in a
drift in our RV data with values between 0.0002 m s-1 day-1 for a circular
orbit to 0.25 m s-1 day-1 for an eccentric ($e=0.45$) orbit. We ran two
separate ExoFASTv2 fits, one that included the term for the slope, and one
that did not. ExoFASTv2 provides statistical metrics, such as the Bayesian
Information Criterion (BIC) (Schwarz, 1978) and Akaike Information Criterion
(AIC) (Akaike, 1974), for model fits. Both metrics are functions of the number
of parameters being fit and the maximum ln(likelihood) from the MCMC sample,
while the BIC also considers the number of data points being fit. The better
model has the smallest algebraic value of AIC or BIC. The fit that included
the slope term for the RVs was slightly preferred over the flat RV fit, with
BIC and AIC values of $-22202$ and $-22424$, respectively, for the model with
no slope, compared to values of $-22209$ and $-22437$ for the model with the
slope. We thus included the RV slope term in all of our models.

We rejected flat models (i.e., any instances where an expected transit was not
found) in order to prevent the fit from running away, which can happen in the
hotter chains when using parallel tempering. We required the number of
independent draws to be greater than 1000 and determined that, with a Gelman-
Rubin statistic (Gelman & Rubin, 1992) of 1.0090 in the worst case, the chains
were well-mixed.

We initially allowed the radius of the 3.12-day planet to be unconstrained,
but found that grazing geometries were permitted, indicating that the light
curve can set only a lower limit on the planet’s radius and an upper limit on
its inclination. Similar to Rodriguez et al. (2018), we imposed a constraint
on the radius of the 3.12-day planet based on the mass-radius relations by
Chen & Kipping (2017). The impact is that this prior sets an upper limit on
the planet radius (resulting from the measured planetary mass, informed by the
RVs), while the lower limit on the planet radius is set from the observed
depth of the transit. We emphasize that our data do not permit us to directly
determine the radius of the 3.12-day planet: Although we state the value we
determine by employing the Chen & Kipping (2017) prior, the planet radius
could be much larger and should be determined by gathering data of greater
precision, which would permit the determination of the four points of contact
(if they exist). In Table 3, we have flagged all quantities that are affected
by this prior.

In principle, if the radius from the Chen & Kipping (2017) relation were
inconsistent with the lower limit from the transit, using this relation could
bias the mass of the 3.12-day planet. To ensure that was not the case, we used
ExoFASTv2 to run a 2-planet fit to only the RV data. We found that the
resulting RV semi-amplitude of LTT 1445Ac is in agreement with both that from
our ExoFASTv2 global model fit with the radius constraint imposed, and the
separate RV$+$GP fit we describe in §4.4.

Finally, we note that ExoFASTv2 rejects any samples where the planets’
projected orbits cross into each other’s Hill spheres, with the intention of
constraining both planets’ eccentricity by rejecting unstable configurations.
While this is a reasonable approximation, it is not a substitute for a
detailed analysis of the long-term stability of the system, which is beyond
the scope of this work.

Figure 4: The $TESS$ PDCSAP light curves from sector 4 (top 3 panels) and 31
(bottom 3 panels) data. The top panels of each plot are the non-detrended
light curves from each sector of data, which show evidence of flares and
rotational modulation due to stellar spots on either the B or C component. The
purple lines indicates the fits to the modulations. The middle panels of each
plot show the residual data after the removal of the stellar variability with
Gaussian Process (GP) regression; the planetary transit models for the
5.36-day planet (purple line) and 3.12-day planet (orange line) are
overplotted. The dotted lines indicate transits that occurred during a data
download, and which were not observed. The bottom panels of each plot
illustrate the light curves with planetary transits and stellar variability
removed.

###  4.3 Confirmation of the 3.12-day Planet

Because our only detection of the transits of the 3.12-day planet is from the
$TESS$ light curve data in which the light from all three stars is blended
together, the light curve itself does not prove that the planet orbits star A.
Instead the proof comes from our RVs of LTT 1445A: We first ran a global
ExoFASTv2 fit using both sectors of $TESS$ data and all of the RVs, accounting
for only the confirmed 5.36-day planet. We added the RV jitter output from the
global model in quadrature with the uncertainties on the RV residuals to
properly weight the uncertainties from each instrument. We then created a
Lomb-Scargle (L-S) periodogram using the L-S tool (VanderPlas & Ivezić, 2015)
in astropy (Astropy Collaboration et al., 2013, 2018), which we show in Figure
5. There is a peak at 3.12195 days with maximum L-S power at 0.298. The L-S
False Alarm Probability (FAP) of a peak at this power is $1.06\times
10^{-5}$%, indicating high significance of the signal and indicating that
indeed the 3.12-day planet also transits the primary star of LTT 1445.

Figure 5: Lomb-Scargle periodogram of the residuals from the 5.36-day planet
fit to the RV data of LTT 1445A. False alarm probabilities of 10%, 1% and
$1\times 10^{-5}$% are noted (black dashed lines), as are the orbital periods
for the 3.12- and 5.36-day period planets (dotted and solid orange and purple
lines, respectively). A highly significant peak at 3.12 days is evident, which
confirms that the 3.12-day planet also orbits LTT 1445A.

We included the second planet in our global model to explore whether the
addition of the second planet to our model would improve the fit to the data,
under the assumption that it transits the primary star. The results indicate
that the two-planet model is preferred over a single-planet model via the BIC
and AIC metrics (BIC: $-21981$ vs. $-22209$; AIC: $-22169$ vs. $-22437$ for
the one- and two-planet model, respectively). In §4.4 we conduct an
independent analysis of the RV data using a Gaussian Process to account for
stellar activity, and similarly find that the two-planet model is strongly
preferred.

We thus adopt the two-planet model as the most appropriate description of the
data and list the median values of the fit parameters from our global
ExoFASTv2 model for both planets in Table 3. We show the resulting transit and
RV plots for each planet in Figures 6 and 7.

Figure 6: Transits of LTT 1445Ac (top) and LTT 1445Ab (bottom) observed with
$TESS$. The data have been deblended to remove any signal from the stellar BC
components, and are shown in gray, while the orange and purple lines indicate
the models for LTT 1445Ac and LTT 1445Ab.

Figure 7: RV orbital plots and residuals from the global ExoFASTv2 2-planet
fit. In the top panel we show the RV data folded at the 3.12-day period (and
corrected for the 5.36-day planet, and the slope), with the model for the
3.12-day planet overplotted in gray; residuals to the fit of both planets are
shown underneath, phase-folded to the 3.12-day planet period. Similarly, in
the third panel we show the RV data folded at the 5.36-day period (and
corrected from the 3.12-day planet, and the slope), with the model for the
5.36-day overplotted in gray; residuals to the fit of both planets are shown
underneath, phase-folded to the 5.36-day planet period. The data from ESPRESSO
are plotted as orange squares, HARPS as blue circles, HIRES as pale red stars,
MAROON-X as purple diamonds, and PFS as green triangles. The bottom panel
illustrates the unphased RV data, where the gray curve indicates the
combination of the 3.12-day and 5.36-day planet models and the linear slope
due to the orbit of LTT 1445A about BC.

###  4.4 Radial Velocity Modeling with a Gaussian Process

Active regions on the surface of a rotating star may produce non-orbital RV
signals due to both the magnetic suppression of the net convective blueshift
of the photosphere, and through the effect of spots downweighting portions of
the stellar velocity field on the visible hemisphere of the star (Meunier et
al., 2010). The temporal evolution of these activity signals can be
detrimental to the recovery of accurate planetary signals if not properly
accounted for. Here we assess the impact of stellar activity in our RV data by
explicitly treating stellar activity with a GP regression model component
(e.g., Haywood et al., 2014; Rajpaul et al., 2015). Specifically, we model
temporal correlations from rotationally-modulated magnetic activity using a
quasi-periodic GP following the methodology of Cloutier et al. (2017, 2020a,
2020b). To summarize, we adopt a separate quasi-periodic GP for each RV
spectrograph due to their unique noise properties and the inherently chromatic
nature of stellar activity. For each spectrograph indexed by $s$, the quasi-
periodic covariance kernel is

$k_{sij}=a_{s}^{2}\exp{\left[-\frac{(t_{i}-t_{j})^{2}}{2\lambda^{2}}-\Gamma^{2}\sin^{2}{\left(\frac{\pi|t_{i}-t_{j}|}{P_{\rm
GP}}\right)}\right]},$ (1)

where $a_{s}$ is the covariance amplitude for spectrograph $s$, $\lambda$ is
the exponential timescale related to the lifetime of active regions, $\Gamma$
is the coherence parameter, and $P_{\rm GP}$ is the periodic timescale related
to the stellar rotation. We also fit an additive scalar jitter
$\sigma_{s,\text{RV}}$ for each spectrograph to account for any excess
uncorrelated noise. The hyperparameters $\\{\lambda,\Gamma,P_{\rm GP}\\}$ are
all directly related to the active regions themselves and are therefore
independent of the spectrograph. As such, these hyperparameters are shared
among each spectrograph’s GP model.

We proceed with modeling our full RV dataset with a Keplerian model for each
transiting planet, plus a GP activity model for each spectrograph. We use a
custom-build python package, as described in Cloutier et al. (2021), to sample
the joint posterior of our complete RV model that incorporates the affine-
invariant MCMC sampler emcee (Foreman-Mackey et al., 2013) and the george
package (Ambikasaran et al., 2015) to evaluate the marginalized likelihood of
our GP activity model components. We adopt the model parameter priors reported
in Table 2. We recover the median a-posteriori GP hyperparameters and
construct the predictive GP distributions for each spectrograph. We treat the
mean function of each predictive distribution as the best-fit activity model
for that spectrograph.

Table 2: $RV+GP$ Priors  Parameters | Prior |
---|---|---
_GP hyper-parameters_ |
$\rm{log}~{}a_{s}/\rm{(m/s)}$ | $\mathcal{U}(-5,5)$ |
$\rm{log}~{}\lambda/\rm{days}$ | $\mathcal{U}(\log{1},\log{1000})$ |
$\rm{log}~{}\Gamma$ | $\mathcal{U}(-3,3)$ |
$P_{GP}$ [days] | $\mathcal{N}(85,22)$ |
_LTT 1445Ab RV Parameters_ |
$P_{b}$ [days] | $\mathcal{N}(5.358766,0.000004)$ |
$T_{0,b}$ [BJD] | $\mathcal{N}(2458412.7085,0.0004)$ |
$\rm{log}~{}K_{b}/\rm{(m/s)}$ | $\mathcal{U}(-3,3)$ |
$h_{b}=\sqrt{e}~{}\cos{\omega}$ | $\mathcal{U}(-1,1)$ |
$k_{b}=\sqrt{e}~{}\sin{\omega}$ | $\mathcal{U}(-1,1)$ |
_LTT 1445Ac RV Parameters_ |
$P_{c}$ [days] | $\mathcal{N}(3.123904,0.000004)$ |
$T_{0,c}$ [BJD] | $\mathcal{N}(2458412.5816,0.0006)$ |
$\rm{log}~{}K_{c}/\rm{(m/s)}$ | $\mathcal{U}(-3,3)$ |
$h_{c}=\sqrt{e}~{}\cos{\omega}$ | $\mathcal{U}(-1,1)$ |
$k_{c}=\sqrt{e}~{}\sin{\omega}$ | $\mathcal{U}(-1,1)$ |
_Spectrograph Parameters_ |
$\gamma_{i}$ [m/s] | $\mathcal{U}(-20,20)+\rm{median}(\textbf{rv})$ |
$\rm{log}~{}s_{i}/(m/s)$ | $\mathcal{U}(-5,5)$ |

We use this analysis to evaluate the evidence for a second planet:
Specifically, we calculate the Perrakis estimator (Perrakis et al., 2014), as
used by Díaz et al. (2016), as an importance sampler to estimate the Bayesian
model evidences for the one and two-planet RV+GP models. We find that the
evidence ratio $\mathcal{Z}_{2}/\mathcal{Z}_{1}=1202$, which supports the
confirmation of the 3.12-day planet in our RV time series (Nelson et al.,
2020). We conclude that a two-planet model is heavily favored over a one-
planet model when including an explicit activity model in the form of a quasi-
periodic GP.

###  4.5 Rotational Velocities and RVs of LTT 1445BC

We have determined with our MEarth photometry that the 1.4-day rotational
modulation we see in the $TESS$ data originates from LTT 1445BC, as discussed
in §3.1.2. But we are not able to determine from the photometric time series
alone whether the B or C component is the source of that signal. Very high
resolution spectra of LTT 1445BC might permit the measurement of the
rotational velocities of each component, which would allow us to determine the
source. We noted in §3.3.2 that seven of our initial HARPS spectra of LTT 1445
were of the blended BC component. We downloaded these publicly available data
and analyzed them using todcor (Zucker & Mazeh, 1994) and the methods
described in Winters et al. (2020) to extract individual RVs and rotational
velocities ($v\sin i$) for the B and C components.

We used an observation of Barnard’s Star taken UT 2017 September 22 as the
template for our analysis. We searched for the nonlinear least-squares maximum
likelihood value for three parameters: flux ratio $\alpha$ and the two values
of $v\sin i$. We calculate $\alpha$, the ratio of the flux of C relative to
that of B, to be 0.31 at wavelengths $6760-6836$ Å (echelle aperture 71 of the
HARPS data), roughly equivalent to filter $R_{\rm KC}$. While this seems a bit
low when compared to the $\alpha$ value of 0.50 we expect from photometry
($\Delta$ $R_{\rm KC}$ $=0.75\pm 0.03$ mag; Henry et al. 2006), the angular
separation between B and C at the time of these observations is comparable to
the HARPS 1″ fiber diameter. Thus, it is reasonable that there is less light
from LTT 1445C landing in the fiber.

With this caveat in mind, we measure an average rotational broadening of 7.1
km s-1 for LTT 1445C and 1.9 km s-1 for LTT 1445B from the six spectra taken
in September. These measurements suggest that the 1.4-day rotation period
comes from the C component and the 6.7-day marginal peak we see in the
residual periodograms of the $TESS$ and MEarth photometry in Figure 1 is
probably the rotation period of the B component. (We note that these results
are not completely conclusive, due to $\sin i$ degeneracy: If the 6.7-day
photometric period is spurious, then B could be the origin of the 1.4-day
period, if we simply haven’t detected the photometric period of C. But we view
this possibility as unlikely.) Furthermore, we note that while we have not
robustly detected rotational broadening in B, our solutions do slightly prefer
some.

As part of our analysis, we measure individual RVs for LTT 1445B and LTT 1445C
of $-3.98\pm 0.01$ km s-1 and $0.24\pm 0.20$ km s-1. We use the least-squares
deconvolution (Donati et al., 1997) to visualize the rotational broadening
profiles of LTT 1445B and C in Figure 8.

Figure 8: Least-squares deconvolution profiles of LTT 1445B (green dashed
line) and C (blue dashed line) from HARPS data (gray lines), which indicate
the rotational broadening for each of the B and C components. The solid red
line shows the joint fit of the broadened spectra.

###  4.6 Check of Consistency Across Fits

We performed a number of quality checks to ensure that our results are robust.
We investigate three sets of parameters to check for consistency between model
fits: We first compare the radius ratios we determine for each of the transit
datasets. We then turn to the RV data, and compare both the RV semi-amplitude
and the eccentricities from different analyses.

We made separate adjustments to the PDCSAP light curves from both sectors of
$TESS$ data to correct the excess light from other stars in the optimal
aperture. To ensure that we performed this correctly, we compare the results
from fitting the transits of LTT 1445Ab from each sector of $TESS$ data and
find consistent planet-to-star radius ratios $Rp/R_{*}$: From sector 4 data,
we measure the radius ratio to be $0.0465\pm 0.0015$, compared to that from
sector 31, which is $0.0436^{+0.0015}_{-0.0014}$. We also compare the transit
depth measurement results of LTT 1445Ab from our ground-based data to those
from our global model. The measured radius ratio of the planet to the host
star from ground-based data from MEarth and LCO are $0.0435\pm 0.0021$ and
$0.049^{+0.004}_{-0.003}$ (68.3% interval), respectively. These are both in
agreement with the measured $Rp/R_{*}$ of $0.0451^{+0.0014}_{-0.0013}$ from
our global model. The agreement between all three measurements of the radius
ratio of LTT 1445Ab indicates that we correctly adjusted the $TESS$ dilution
factor. We are not able to perform a radius ratio comparison for LTT 1445Ac
because we do not yet have an independent ground-based detection of it.

We compare the results from our global model to the results from our modeling
of the RVs with a GP. The measured RV semi-amplitudes from the RV$+$GP model
for planets c and b are $1.49\pm 0.17$ m s-1 and $2.28\pm 0.17$ m s-1, while
they are $1.67\pm 0.20$ m s-1, and $2.60\pm 0.21$ m s-1 from our global model
for planets c and b, respectively. All measurements are in agreement.

From the RV$+$GP model, the 95% confidence intervals for the eccentricities of
the orbits of c and b are $<0.165$ and $<0.089$, respectively. These are in
agreement with the results from our global model, which are $<0.223$ and
$<0.110$, respectively.

Because the results from our RV$+$GP model and our global ExoFASTv2 model are
in agreement, we determined that the inclusion of a GP to model any periodic
stellar variability in our RVs is unnecessary. Thus, we adopt the median
values from our global ExoFASTv2 model as our preferred results.

Figure 9: Transit mid-times of the LTT 1445A planets. We show the measured
transit mid-times for LTT 1445Ac (orange points, top panel) and for LTT 1445Ab
(purple points, bottom panel). The transit mid-times for LTT 1445Ab from
$TESS$, LCO, and MEarth data are noted as filled points, squares, and a star,
respectively; transit mid-times for LTT 1445Ac are from TESS data only. As
illustrated, the transit times for each planet are consistent with zero
(dotted lines), when considering the uncertainties.  Figure 10: Masses and
radii for small planets transiting M dwarfs and with precisely ($\geq
3\sigma$) measured masses. The solid curves are illustrative interior
structure models of 100% water, 100% magnesium silicate rock, 33% iron plus
67% rock (i.e., Earth-like), and 100% iron from Zeng & Sasselov (2013). LTT
1445Ab and c are depicted by the square markers. LTT 1445Ab falls exactly on
the composition curve corresponding to the Earth’s ratio of iron (and nickel)
to a magnesium-silicate. Although we measure the mass of LTT 1445Ac, we have
deduced only a lower limit on its radius (green arrow), corresponding to the
configuration where the transits are not grazing. If indeed they are not
grazing, then the radius of LTT 1445Ac would be the minimum value depicted by
the square marker here, and would lie on the same composition curve as LTT
1445Ab.

###  4.7 Search for Transit Timing Variations

Multi-planet systems sometimes exhibit transit timing variations (TTVs) (Agol
et al., 2005; Holman & Murray, 2005), and we might expect them in the LTT 1445
system because the orbital periods of the two planets are not too dissimilar.
Using the case of two planets not in resonance on circular orbits from Agol et
al. (2005), we calculate that TTVs for the LTT 1445A planets are expected to
be on the order of 1 min for each planet. We utilized ExoFASTv2’s TTV
capability to search for variations in each planet’s transit mid-times, but
did not detect any. We ran 213 chains for 3000 steps, thinned by 300, for a
total number of 191.7 million simulations. For LTT 1445Ac, the shallow transit
depth, grazing geometry, and low SNR of the light curves thwarted our efforts
to reach a Gelman-Rubin value of less than 1.05 for the TTV parameters, except
for LTT 1445Ac’s transit epoch 239, which has two solutions. Therefore, for
this TTV analysis only, we adopt the criterion of convergence at a Gelman-
Rubin value less than 1.1 Gelman et al. (2004). We omit transit 239 from our
TTV analysis and provide the mid-transit times for each planet’s transit from
all of the time series photometry in Table 4. We show in Figure 9 that the
transit mid-times of both planets are consistent with a linear solution when
considering the uncertainties.

##  5 Discussion and Conclusions

We have measured the mass and radius of LTT 1445Ab to a precision of 9% and
5%, respectively. These precise mass and radius measurements permit the
investigation of the planetary core mass fraction (cmf), which provides a
probe for the planetary composition. Using the semi-empirical relation from
Zeng et al. (2016), we calculate a cmf of $0.425\pm 0.283$ for LTT 1445Ab.
This is illustrated in the radius vs. mass diagram in Figure 10, which
includes composition curves from Zeng & Sasselov (2013). The planet falls
squarely on the rocky compositional curve of 33% iron plus 67% magnesium-
silicate. In the near future we hope to determine the abundances of key
elements in the stellar photosphere, and see if they match the ratios we have
inferred for the planet for its bulk composition.

We have detected a second planet transiting LTT 1445A. The presence of
additional planets orbiting LTT 1445A is not surprising, given the previously
known existence of LTT 1445Ab (W19) and the recent result that
$90^{+5}_{-21}$% of mid-M dwarfs host multiple planets less massive than 10 M⊕
and with orbital periods less than 50 days (Cloutier et al., 2021). LTT 1445A
joins the growing list of mid-M dwarf systems in which additional planets have
been revealed via follow-up observations of the original discovered planet.
Some examples include GJ 357cd (Luque et al., 2019), GJ 1132c (Bonfils et al.,
2018), GJ 3473c (Kemmer et al., 2020), and LHS 1140c (Ment et al., 2019).

While we have measured the mass of LTT 1445Ac to a precision of 13%, the
$TESS$ data do not permit us to determine if all four points of contact are
present in the transit curve of LTT 1445Ac, and hence whether the planetary
transits are grazing. While the measured depth provides a minimum value for
the radius of LTT 1445Ac, a grazing configuration allows acceptable solutions
of arbitrarily large radii for the transiting object. If we impose a prior
based on the mass-radius relation of Chen & Kipping (2017), then we find an
acceptable, non-grazing fit to the light curve, and the resulting planet
radius is $1.147^{+0.055}_{-0.053}$ R⊕. This would correspond to a cmf of
$0.235\pm 0.297$, again consistent with the telluric value. Ultimately this
question requires a more precise light curve, and we eagerly await the
observations scheduled with $HST$ (HST-GO-16503, PI: J. Winters).

Intriguingly, our results indicate that the two planets have circular (or low-
eccentricity) orbits that are misaligned by at least $-2.25_{-0.29}^{+0.28}$
degrees (as inferred from the posterior of the global model fit). This value
is a lower limit for several reasons: First, it results from the inclusion of
the mass-radius relation of Chen & Kipping (2017), which results in non-
grazing transits. Grazing transits by a larger planet would result in an even
larger misalignment. Second, even if this solution is correct and the transits
are not grazing, we observe only a projection onto the line-of-sight of the
true misalignment between the planetary orbits. Third, there is an ($i,180-i$)
degeneracy and if the two orbits are on opposite sides of the central
crossing, the mutual inclination would be $-2.91_{-0.45}^{+0.34}$ degrees,
larger than the value presented above. For reference, the mutual inclination
of the orbits of Venus and the Earth is 3.4 degrees.

We confirmed that the 1.4-day rotational modulation seen in the $TESS$ data
originates from LTT 1445BC. We have calculated the $v\sin i$ and RV values for
LTT 1445B and C individually, and find that the 1.4-day signal is likely the
rotation period of LTT 1445C, while the less statistically significant 6.7-day
signal may be the rotation period of LTT 1445B. From the activity and mass of
LTT 1445A, we expect its rotation period to be $85\pm 22$ days, based on the
empirical relation in Newton et al. (2017). We have not yet detected the
rotation period with MEarth, but our observations are ongoing. If our
estimated rotation rates are correct, it implies that this triple star system
is in a special evolutionary state, where A has spun down, B is in the process
of spinning down, and C has not yet begun to spin down. LTT 1445 could be an
important benchmark system for rotational evolution because it directly
samples the mass dependence of the rapid spin-down phase discussed in the
context of mid-to-late field M dwarfs by Newton et al. (2017). Intriguingly,
the dynamical masses of the stars B and C can eventually be estimated
directly, although this may take some time given the moderately long orbital
period of $36.2\pm 5.3$ yrs (W19).

LTT 1445 is the second closest known transiting exoplanet system, and the
closest one with an M-dwarf host star. Due to the efforts of MEarth (Nutzman &
Charbonneau, 2008; Irwin et al., 2015), TRAPPIST (Gillon et al., 2016, 2017),
and $TESS$ (Ricker et al., 2015), there are currently ten systems among the M
dwarfs within 15 pc with masses $\leq 0.35~{}{\rm M}/\hbox{M${}_{\odot}$}$
that are known to host transiting planets: GJ 1214b (Charbonneau et al.,
2009), GJ 1132bc (Berta-Thompson et al., 2015; Bonfils et al., 2018),
TRAPPIST-1 (Gillon et al., 2016, 2017; Grimm et al., 2018), LHS 1140bc
(Dittmann et al., 2017; Ment et al., 2019), LHS 3844b (Vanderspek et al.,
2019), LTT 1445Abc (W19, this work), L 98-59bcd (Kostov et al., 2019; Cloutier
et al., 2019), GJ 357b (Luque et al., 2019), 2MA 0505-4756b (TOI-540b; Ment et
al., 2021), and GJ 486b (Trifonov et al., 2021). Although challenging, these
planets are among the very best available for near-future studies of their
atmospheres. Kempton et al. (2018) provide empirical relations that allow for
a quantitative comparison of the SNR of spectra acquired with $JWST$, based on
the stellar and planetary properties. For LTT 1445Ab, we calculate a
transmission spectroscopy metric (TSM) of 30 for LTT 1445Ab and an emission
spectroscopy metric (ESM) of 5.7. If LTT 1445Ac is indeed terrestrial with the
values listed in Table 3, then it would have an even higher TSM of 46 and an
ESM of 8.7. For reference, Kempton et al. (2018) recommend minimum TSM and ESM
values of 10 and 7.5, respectively, for planets that should be prioritized for
future atmospheric studies. Furthermore, the proximity of LTT 1445A makes it a
good candidate for stellar wind and mass-loss-rate measurements, as recently
detailed in Wood et al. (2021), to determine their effect on the planetary
atmospheres, should those be present.

W19 noted that, given the transit probability and number of nearby mid-to-late
M dwarfs, $TESS$ might find one more planet that is as accessible to follow-up
study as LTT 1445Ab. LTT 1445Ac would appear to satisfy that criterion. As
$TESS$ has observed roughly 80% of the sky, the LTT 1445 system may remain the
closest small star with transiting exoplanets. Then again, perhaps the
remaining 20% of the sky will hold some as-yet undiscovered jewels.

Table 3: ExoFASTv2 Median Values and 68% Confidence Intervals for LTT 1445Ac &
LTT 1445Ab

Parameter | Units | Values
---|---|---
Host Star Parameters: | LTT 1445A |
$M_{*}$ | Stellar Mass (M⊙) | $0.257\pm 0.014$ |
$R_{*}$ | Stellar Radius (R⊙) | $0.265^{+0.011}_{-0.010}$ |
$T_{eff}$ | Stellar Effective Temp. (K) | $3340\pm 150$ |
[Fe/H] | Stellar Metallicity | $-0.34\pm 0.09$ |
$\dot{\gamma}$ | RV slope1 (m s-1day-1) | $-0.0081^{+0.0026}_{-0.0029}$ |
Planetary Parameters: | LTT 1445Ac | LTT 1445Ab
$P$ | Period (days) | $3.1239035^{+0.0000034}_{-0.0000036}$ | $5.3587657^{+0.0000043}_{-0.0000042}$
$R_{P}$ | Radius6 ($\,R_{\rm E}$) | $1.147^{+0.055}_{-0.054}$ | $1.305^{+0.066}_{-0.061}$
$M_{P}$ | Mass ($\,M_{\rm E}$) | $1.54^{+0.20}_{-0.19}$ | $2.87^{+0.26}_{-0.25}$
$T_{C}$ | Time of conjunction2 ($\rm{BJD_{TDB}}$) | $2458412.58159^{+0.00059}_{-0.00057}$ | $2458412.70851^{+0.00040}_{-0.00039}$
$T_{T}$ | Time of min. proj. sep.3 ($\rm{BJD_{TDB}}$) | $2458412.58156^{+0.00059}_{-0.00057}$ | $2458412.70851^{+0.00040}_{-0.00039}$
$i$ | Inclination6 (Degrees) | $87.43^{+0.18}_{-0.29}$ | $89.68^{+0.22}_{-0.29}$
$e$ | Eccentricity4 | $<0.223$ | $<0.110$
$K$ | RV semi-amplitude (m s-1) | $1.67^{+0.21}_{-0.20}$ | $2.60\pm 0.21$
$\delta$ | Transit depth (fraction) | $0.00157^{+0.00015}_{-0.00014}$ | $0.00203\pm 0.00012$
$T_{14}$ | Total transit duration (days) | $0.0201\pm 0.0011$ | $0.05697^{+0.00071}_{-0.00068}$
$a$ | Semi-major axis (AU) | $0.02661^{+0.00047}_{-0.00049}$ | $0.03813^{+0.00068}_{-0.00070}$
$R_{P}/R_{*}$ | Radius of planet in stellar radii6 | $0.0396^{+0.0018}_{-0.0017}$ | $0.0451^{+0.0014}_{-0.0013}$
$a/R_{*}$ | Semi-major axis in stellar radii | $21.56^{+0.78}_{-0.82}$ | $30.9^{+1.1}_{-1.2}$
$b$ | Transit Impact parameter6 | $0.937^{+0.012}_{-0.016}$ | $0.17^{+0.15}_{-0.12}$
$b_{S}$ | Eclipse impact parameter6 | $0.977^{+0.20}_{-0.089}$ | $0.17^{+0.14}_{-0.12}$
$\rho_{P}$ | Density6 (g cm-3) | $5.57^{+0.68}_{-0.60}$ | $7.1^{+1.2}_{-1.1}$
$log(g_{P})$ | Surface gravity6 | $3.057^{+0.042}_{-0.043}$ | $3.217^{+0.050}_{-0.053}$
$\langle F\rangle$ | Incident Flux (109 erg s-1 cm-2) | $0.0149^{+0.0032}_{-0.0027}$ | $0.0073^{+0.0016}_{-0.0013}$
$T_{eq}$ | Equilibrium temperature5 (K) | $508\pm 25$ | $424\pm 21$
Wavelength Parameters: | TESS |
$u_{1}$ | Linear limb-darkening coeff | $0.156^{+0.079}_{-0.076}$ |
$u_{2}$ | Quadratic limb-darkening coeff | $0.396\pm 0.093$ |
$A_{D}$ | Dilution from neighboring stars | $-0.012^{+0.048}_{-0.049}$ |
Spectrograph Parameters: |  | Relative RV Offset1 | RV Jitter
|  | (m s-1) | (m s-1)
ESPRESSO |  | $-5460.28^{+0.50}_{-0.53}$ | $0.96^{+0.23}_{-0.17}$
HARPS (2019) |  | $-5458.7^{+1.4}_{-1.5}$ | $1.9^{+1.7}_{-1.0}$
HARPS (2020) |  | $-5453.51^{+0.63}_{-0.64}$ | $2.30^{+0.45}_{-0.38}$
HIRES |  | $-1.75\pm 0.45$ | $2.29^{+0.45}_{-0.39}$
MAROON-X (2019) |  | $-0.14^{+0.58}_{-0.53}$ | $1.16^{+0.74}_{-0.49}$
MAROON-X (2020) |  | $1.84^{+0.78}_{-0.72}$ | $0.93^{+0.29}_{-0.22}$
PFS |  | $0.41^{+0.58}_{-0.54}$ | $1.87^{+0.60}_{-0.43}$
$TESS$ Transit Parameters: |  | Added Variance $\sigma^{2}$ | Baseline flux $F_{0}$
2018 |  | $0.000000170^{+0.000000039}_{-0.000000036}$ | $0.999954\pm 0.000031$
2020 |  | $-0.000000009^{+0.000000038}_{-0.000000036}$ | $1.000084\pm 0.000030$

††footnotetext: See Table 3 in Eastman et al. (2019) for a detailed
description of all parameters.

11footnotetext: Reference epoch = 2458868.217394

22footnotetext: Time of conjunction is commonly reported as the ”transit
time.”

33footnotetext: Time of minimum projected separation is a more correct
”transit time.”

44footnotetext: $2-\sigma$ (95%) upper limits.

55footnotetext: Assumes no albedo and perfect redistribution.

66footnotetext: The value for planet c was derived using the measured mass,
the lower limit on the radius from the light curve, and Chen & Kipping (2017)
exoplanet mass-radius relation to estimate the planetary radius.

Table 4: Median values and 68% confidence interval for planet transit mid-times Transit | Planet | Epoch | $T_{T}$
---|---|---|---
TESS UT 2018-10-21 (TESS) | c | 0 | $2458412.5815^{+0.0014}_{-0.0015}$
TESS UT 2018-10-24 (TESS) | c | 1 | $2458415.7050^{+0.0023}_{-0.0020}$
TESS UT 2018-11-02 (TESS) | c | 4 | $2458425.0776\pm 0.0015$
TESS UT 2018-11-05 (TESS) | c | 5 | $2458428.2012^{+0.0014}_{-0.0016}$
TESS UT 2018-11-08 (TESS) | c | 6 | $2458431.3244^{+0.0024}_{-0.0018}$
TESS UT 2018-11-11 (TESS) | c | 7 | $2458434.4493^{+0.0015}_{-0.0014}$
TESS UT 2020-10-24 (TESS) | c | 235 | $2459146.6968^{+0.0017}_{-0.0015}$
TESS UT 2020-10-27 (TESS) | c | 236 | $2459149.8248^{+0.0010}_{-0.0011}$
TESS UT 2020-10-30 (TESS) | c | 237 | $2459152.9482^{+0.0018}_{-0.0015}$
TESS UT 2020-11-02 (TESS) | c | 238 | $2459156.0701\pm 0.0011$
TESS UT 2020-11-08 (TESS) | c | 240 | $2459162.3186^{+0.0013}_{-0.0012}$
TESS UT 2020-11-11 (TESS) | c | 241 | $2459165.4436^{+0.0017}_{-0.0016}$
TESS UT 2020-11-15 (TESS) | c | 242 | $2459168.5643^{+0.0015}_{-0.0014}$
TESS UT 2018-10-21 (TESS) | b | 0 | $2458412.70898^{+0.00099}_{-0.00093}$
TESS UT 2018-10-26 (TESS) | b | 1 | $2458418.06643^{+0.00080}_{-0.00076}$
TESS UT 2018-11-06 (TESS) | b | 3 | $2458428.78545^{+0.00099}_{-0.0010}$
TESS UT 2018-11-11 (TESS) | b | 4 | $2458434.14368^{+0.00075}_{-0.00065}$
LCO UT 2019-08-16 (z’) | b | 56 | $2458712.7997^{+0.0030}_{-0.0027}$
MEarth UT 2019-09-02 (TESS) | b | 59 | $2458728.87397^{+0.00096}_{-0.0011}$
LCO UT 2020-10-08 (z’) | b | 134 | $2459130.7844^{+0.0018}_{-0.0028}$
TESS UT 2020-10-24 (TESS) | b | 137 | $2459146.85959^{+0.00092}_{-0.00090}$
TESS UT 2020-10-29 (TESS) | b | 138 | $2459152.21770^{+0.00080}_{-0.0013}$
TESS UT 2020-11-09 (TESS) | b | 140 | $2459162.93558^{+0.00089}_{-0.00077}$
TESS UT 2020-11-14 (TESS) | b | 141 | $2459168.2972^{+0.0019}_{-0.0023}$

.

Acknowledgments

We thank the referee for a thoughtful and prompt review that improved the
manuscript. This work is made possible by a grant from the John Templeton
Foundation. The opinions expressed in this publication are those of the
authors and do not necessarily reflect the views of the John Templeton
Foundation. The MEarth Team gratefully acknowledges funding from the David and
Lucile Packard Fellowship for Science and Engineering (awarded to D.C.). This
material is based upon work supported by the National Science Foundation under
grant AST-1616624, and work supported by the National Aeronautics and Space
Administration under Grant No. 80NSSC18K0476 issued through the XRP Program.

This paper includes data collected by the TESS mission that are publicly
available from the Mikulski Archive for Space Telescopes (MAST). We
acknowledge the use of public TESS data from pipelines at the TESS Science
Office and at the TESS Science Processing Operations Center. This research has
made use of the Exoplanet Follow-up Observation Program website, which is
operated by the California Institute of Technology, under contract with the
National Aeronautics and Space Administration under the Exoplanet Exploration
Program. 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.
Funding for the $TESS$ mission is provided by the NASA’s Science Mission
Directorate.

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 work was enabled by observations
made from the Gemini-North telescope, located within the Maunakea Science
Reserve and adjacent to the summit of Maunakea. The authors wish to recognize
and acknowledge the very significant cultural role and reverence that the
summit of Maunakea has always had within the indigenous Hawaiian community. We
are grateful for the privilege of observing the Universe from a place that is
unique in both its astronomical quality and its cultural significance. The
international Gemini Observatory, a program of NSF’s NOIRLab, 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 Observatory 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).
The MAROON-X spectrograph was funded by the David and Lucile Packard
Foundation, the Heising-Simons Foundation, the Gemini Observatory, and the
University of Chicago. This paper includes data gathered with the 6.5 meter
Magellan Telescopes located at Las Campanas Observatory, Chile. Some of the
data presented herein were obtained at the W. M. Keck Observatory, which is
operated as a scientific partnership among the California Institute of
Technology, the University of California and the National Aeronautics and
Space Administration. The Observatory was made possible by the generous
financial support of the W. M. Keck Foundation.

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. 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 (NASA) and the NSF have been used in this publication. This
work has made use of the Washington Double Star Catalog maintained at the U.S.
Naval Observatory. This work has made use of the Smithsonian Astrophysical
Observatory/NASA Astrophysics Data System.

R.C. acknowledges support from the Banting Postdoctoral Fellowship program,
administered by the Government of Canada. N.A.-D. acknowledges the support of
FONDECYT project 3180063. J.M.A.M. is supported by the NSF Graduate Research
Fellowship, grant No. DGE-1842400. J.M.A.M. also acknowledges the LSSTC Data
Science Fellowship Program, which is funded by LSSTC, NSF Cybertraining Grant
No. 1829740, the Brinson Foundation, and the Moore Foundation; his
participation in the program has benefited this work. D.H. acknowledges
support from the Alfred P. Sloan Foundation, the National Aeronautics and
Space Administration (80NSSC21K0652), and the National Science Foundation
(AST-1717000). K.H. acknowledges support from STFC grant ST/R000824/1. T.F.
acknowledges support from the University of California President’s
Postdoctoral Fellowship Program. P.D. acknowledges support from a National
Science Foundation Astronomy and Astrophysics Postdoctoral Fellowship under
award AST-1903811.

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