# Spinning up a Daze: TESS Uncovers a Hot Jupiter orbiting the Rapid-Rotator
TOI-778

Jake T. Clark University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Brett C. Addison University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Swinburne University of Technology, Centre for Astrophysics and Supercomputing, John Street, Hawthorn, VIC 3122, Australia  Jack Okumura University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Sydney Vach Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Adriana Errico University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Alexis Heitzmann University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK  Joseph E. Rodriguez Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA  Duncan J. Wright University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Mathieu Clerté University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Carolyn J. Brown University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Tara Fetherolf UC Chancellor’s Fellow  Department of Earth and Planetary Sciences, University of California Riverside, 900 University Avenue, Riverside, CA 92521, USA  Robert A. Wittenmyer University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Peter Plavchan Department of Physics & Astronomy, George Mason University, 4400 University Drive MS 3F3, Fairfax, VA 22030, USA  Stephen R. Kane Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA  Jonathan Horner University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  John F. Kielkopf Department of Physics and Astronomy, University of Louisville, Louisville, KY 40292, USA  Avi Shporer Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  C.G. Tinney Exoplanetary Science at UNSW, School of Physics, UNSW Sydney, NSW 2052, Australia  Liu Hui-Gen School of Astronomy and Space Science, Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University, Nanjing 210046, Jiangsu, China  Sarah Ballard Department of Astronomy, University of Florida, 211 Bryant Space Science Center, Gainesville, FL, 32611, USA  Brendan P. Bowler Department of Astronomy, The University of Texas at Austin, TX 78712, USA  Matthew W. Mengel University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  George Zhou University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Annette S. Lee  The Native Skywatchers Initiative, MN USA  Department of Physics and Astronomy, St. Cloud University, MN USA  Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA  University of Southern Queensland, Centre for Astrophysics, USQ Toowoomba, West Street, QLD 4350 Australia  Avelyn David Department of Physics and Astronomy, St. Cloud University, MN USA  The Native Skywatchers Initiative, MN USA  Jessica Heim  Department of Physics and Astronomy, St. Cloud University, MN USA  The Native Skywatchers Initiative, MN USA  Michele E. Lee  Jeremiah Horrocks Institute, University of Central Lancashire, Preston, PR1 2HE, UK  The Native Skywatchers Initiative, MN USA  Verónica Sevilla  Department of Physics and Astronomy, St. Cloud University, MN USA  The Native Skywatchers Initiative, MN USA  Naqsh E. Zafar  Department of Physics and Astronomy, St. Cloud University, MN USA  The Native Skywatchers Initiative, MN USA  Natalie R. Hinkel Space Science and Engineering Division, Southwest Research Institute, San Antonio, TX 78238, USA  Bridgette E. Allen  NASA Exoplanet Science Institute - Caltech/IPAC, 1200 E. California Blvd, Pasadena, CA 91125 USA  University of Wisconsin Stout, 712 South Broadway Street, Menomonie, WI 54751 USA  Daniel Bayliss Dept. of Physics, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK  Arthur Berberyan  NASA Exoplanet Science Institute - Caltech/IPAC, 1200 E. California Blvd, Pasadena, CA 91125 USA  College of the Canyons, 26455 Rockwell Canyon Rd., Santa Clarita, CA 91355, USA  Perry Berlind  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Allyson Bieryla Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  François Bouchy  Geneva Observatory, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland  Rafael Brahm Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal las Torres 2640, Peñalolén, Santiago, Chile  Millennium Institute for Astrophysics, Chile  Data Observatory Foundation, Chile  Edward M. Bryant Dept. of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK  Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK  Jessie L. Christiansen NASA Exoplanet Science Institute - Caltech/IPAC, 1200 E. California Blvd, Pasadena, CA 91125 USA  David R. Ciardi NASA Exoplanet Science Institute - Caltech/IPAC, 1200 E. California Blvd, Pasadena, CA 91125 USA  Krys N. Ciardi  NASA Exoplanet Science Institute - Caltech/IPAC, 1200 E. California Blvd, Pasadena, CA 91125 USA  Rhode Island College, 600 Mount Pleasant Avenue Providence, RI 02908 USA  Karen A. Collins Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Jules Dallant Geneva Observatory, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland  Allen B. Davis Department of Astronomy, Yale University, 52 Hillhouse Avenue, New Haven, CT 06511, USA  International School of Boston, Cambridge, MA 02140, USA  Matías R. Díaz Las Campanas Observatory, Carnegie Institution of Washington, Colina el Pino, Casilla 601 La Serena, Chile  Departamento de Astronomía, Universidad de Chile, Camino El Observatorio 1515, Las Condes, Santiago, Chile  Courtney D. Dressing Astronomy Department, University of California, Berkeley, CA 94720, USA  Gilbert A. Esquerdo Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Jan-Vincent Harre Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstraße 2, 12489 Berlin, Germany  Steve B. Howell NASA Ames Research Center, Moffett Field, CA 94035, USA  Jon M. Jenkins NASA Ames Research Center, Moffett Field, CA 94035, USA  Eric L. N. Jensen Dept. of Physics & Astronomy, Swarthmore College, Swarthmore PA 19081, USA  Matías I. Jones  European Southern Observatory, Alonso de Córdova 3107, Vitacura, Casilla 19001, Santiago, Chile  Andrés Jordán Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal las Torres 2640, Peñalolén, Santiago, Chile  Millennium Institute for Astrophysics, Chile  Data Observatory Foundation, Chile  David W. Latham Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Michael B. Lund NASA Exoplanet Science Institute - Caltech/IPAC, 1200 E. California Blvd, Pasadena, CA 91125 USA  James McCormac Dept. Physics, University of Warwick, Gibbet Hill Road, CV4 7AL, UK  Louise D. Nielsen Geneva Observatory, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland  Jon Otegi  Geneva Observatory, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland  Samuel N. Quinn Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Don J. Radford Brierfield Observatory, New South Wales, Australia  George R. Ricker Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Richard P. Schwarz Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Sara Seager Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 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  Alexis M. S. Smith Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstraße 2, 12489 Berlin, Germany  Chris Stockdale Hazelwood Observatory, Australia  Thiam-Guan Tan Perth Exoplanet Survey Telescope, Perth, Western Australia  Curtin Institute of Radio Astronomy, Curtin University, Bentley, Western Australia 6102  Stéphane Udry Geneva Observatory, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland  Roland Vanderspek Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Maximilian N. Günther European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands  Songhu Wang Department of Astronomy, Indiana University, Bloomington, IN 47405, USA  Geof Wingham  Mt. Stuart Observatory, New Zealand  Joshua N. Winn Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA

(Received 2022 December 11; Revised 2023 February 22; Accepted 2023 March 8)

###### Abstract

NASA’s Transiting Exoplanet Survey Satellite (TESS) mission, has been
uncovering a growing number of exoplanets orbiting nearby, bright stars. Most
exoplanets that have been discovered by TESS orbit narrow-line, slow-rotating
stars, facilitating the confirmation and mass determination of these worlds.
We present the discovery of a hot Jupiter orbiting a rapidly rotating
($v\sin{(i)}=35.1\pm 1.0$ km s-1) early F3V-dwarf, HD 115447 (TOI-778). The
transit signal taken from Sectors 10 and 37 of TESS’s initial detection of the
exoplanet is combined with follow-up ground-based photometry and velocity
measurements taken from Minerva-Australis, TRES, CORALIE and CHIRON to confirm
and characterise TOI-778 b. A joint analysis of the light curves and the
radial velocity measurements yield a mass, radius, and orbital period for
TOI-778 b of $2.76^{+0.24}_{-0.23}$ $\,M_{\rm J}$, $1.370\pm 0.043$ $\,R_{\rm
J}$, and $\sim 4.63$ days, respectively. The planet orbits a bright ($V=9.1$
mag) F3-dwarf with $M=1.40\pm 0.05$ $\,M_{\odot}$, $R=1.70\pm 0.05$
$\,R_{\odot}$, and $\log g=4.05\pm 0.17$. We observed a spectroscopic transit
of TOI-778 b, which allowed us to derive a sky-projected spin-orbit angle of
$18^{\circ}\pm 11^{\circ}$, consistent with an aligned planetary system. This
discovery demonstrates the capability of smaller aperture telescopes such as
Minerva-Australis to detect the radial velocity signals produced by planets
orbiting broad-line, rapidly rotating stars.

planets and satellites: dynamical evolution and stability — stars: individual
(HD 115447) — techniques: radial velocities – techniques: transits

††journal: The Astronomical Journal††facilities: Minerva-Australis, Euler1.2m
(CORALIE), LCOGT, CHIRON. All of the TESS data used in this paper can be found
in MAST: http://dx.doi.org/10.17909/t9-nmc8-f686 (catalog
10.17909/t9-nmc8-f686).††software:  dynesty (Speagle, 2020), ExoFAST (Eastman,
2017), isochrones (Morton, 2015), Allesfitter (Günther & Daylan, 2019, 2021)

2023 April 19

##  1 Introduction

In the late 1980s, the first exoplanetary candidates around main sequence
stars were discovered orbiting Gamma Cephei (Campbell et al., 1988) and HD
114672 (Latham et al., 1989)111This companion is likely a low-mass star in a
face-on orbit (Kiefer, 2019).. Soon after, Mayor & Queloz (1995) announced the
discovery of 51 Peg b, the first planet found orbiting a Sun-like star –
marking the start of the Exoplanet Era.

In the decade that followed that seminal discovery, the radial velocity
technique dominated the search for exoplanets, revealing a plethora of “hot
Jupiters” – giant planets orbiting their host stars with periods of just a few
days (e.g. Butler et al., 1997; Henry et al., 2000; Tinney et al., 2001).
Based solely on knowledge of the Solar System, it was broadly expected that
planetary systems would feature giant planets on long period orbits, and
small, rocky worlds on short period orbits222For a detailed overview of our
knowledge of the Solar System, and its impact on our understanding of
exoplanetary science, we direct the interested reader to Horner et al. (2020),
and references therein.. Instead, it became obvious that a significant number
of stars ($\sim$1%, e.g. Wittenmyer et al., 2011; Wright et al., 2012;
Kunimoto & Matthews, 2020) host scorching hot giant planets – marking their
planetary systems as being truly exotic when compared to our own.

Such planets (commonly known as “hot Jupiters”) are by far the easiest
exoplanets to detect – a fact made clear by the great success of the Kepler
mission. Kepler launched in 2009 (see, e.g., Borucki et al., 2010), and spent
slightly over four years staring continuously at a single patch of the night
sky – in the northern constellation of Cygnus – monitoring the brightness of
more than 150,000 stars. By recording minuscule dips in brightness exhibited
by some of those stars, Kepler’s primary mission led to the discovery of 3251
planets. However, only a fraction (373, $\sim 11\%$) of those planets have
both mass and radius measurements as the majority of the stars orbited by
those planets are too faint for follow-up radial velocity mass
measurements333As of 8th February, 2023; statistics taken from the NASA
Exoplanet Archive counts page, at
https://exoplanetarchive.ipac.caltech.edu/docs/counts_detail.html..

The successor to Kepler is the Transiting Exoplanet Survey Satellite, TESS
(Ricker et al., 2015). Launched in April 2018, TESS is currently in the
process of scouring the sky, observing hundreds of thousands of the nearest
and brightest stars, in an attempt to find short-period planets around them.
TESS observes the majority of its targets for two consecutive 13.7 day
periods, separated by a short window where the spacecraft pivots to broadcast
data back to Earth. This means that it is particularly well adapted for the
discovery of hot Jupiters as transits of such planets are frequent (multiple
transits likely to occur during the $\sim 27\,\mathrm{day}$ observing window)
and deep. Indeed, the majority of the 291 planets444As of 8th February, 2023;
data courtesy of the NASA Exoplanet Archive’s counts page. confirmed by TESS
are either hot Jupiters or their smaller siblings, the “hot Neptunes” (e.g.
Nielsen et al., 2019; Kossakowski et al., 2019; Jordán et al., 2020; Plavchan
et al., 2020; Addison et al., 2021a, b) and unlike the planets discovered by
Kepler, a majority (271, $\sim 76\%$) of TESS planets have both mass and
radius measurements.

The origin of hot Jupiters and Neptunes have been the source of much debate.
It is widely accepted that such planets cannot have formed on their current
orbits, so close to their host stars. Instead, it is thought that they
originate at much greater distances, beyond the “ice-line” – the location in
the protoplanetary disk around their host at which temperatures were
sufficiently low for water ice to be present (e.g. Pollack et al., 1996; Ida &
Lin, 2004; Wittenmyer et al., 2020).

Several different mechanisms have been proposed to explain this migration –
all of which likely occur in some, but not all, planetary systems. The current
proposals include a smooth process of migration through the protoplanetary
disks of their host stars, as the young planet interacts with the material
from which it is feeding (e.g. Lin et al., 1996; Tanaka et al., 2002); planet-
planet scattering shifting the planet onto an extremely eccentric orbit,
followed by a process of tidal circularisation (e.g. Chatterjee et al., 2008;
Beaugé & Nesvorný, 2012; Li et al., 2019a); and secular perturbations imposed
by a highly inclined unseen massive companion (the Kozai-Lidov mechanism;
Kozai, 1962; Lidov, 1962; Nagasawa et al., 2008a; Nagasawa & Ida, 2011).

For individual hot Jupiters, tell-tale signs of their formation pathways may
still remain. The orbits of planets that migrate purely as a result of
interaction with their host star’s protoplanetary disk are expected to remain
co-planar with the star’s equator, as long as the initial disk isn’t tilted
(as is the case for < 100 Myr close-orbital giants AU Mic b, DS Tuc Ab, HIP
67522 b, V1298 Tau b and c and TOI 942 c Plavchan et al., 2020; Zhou et al.,
2020; Heitzmann et al., 2021; Gaidos et al., 2022), whilst a process of
planet-planet scattering can act to moderately incline a planet’s orbit
relative to that plane. Planets whose migration is driven by the Kozai-Lidov
mechanism can become dramatically misaligned with the equators of their host
stars – sometimes even being injected to polar or retrograde orbits (e.g.
Albrecht et al., 2012; Addison et al., 2018; Siverd et al., 2018; Temple et
al., 2019).

Studies of the inclination of the orbits of hot Jupiters have revealed a
correlation between planetary inclination and host star mass/temperature. The
more massive (and hotter) the host star, the more likely it is that any short-
period planets discovered in orbit will be strongly misaligned to the star’s
equatorial plane (e.g. Collier Cameron et al., 2010; Addison et al., 2013;
Rodríguez Martínez et al., 2020).

Given that more massive stars are more likely to exhibit binarity (Preibisch
et al., 1999; Böhm-Vitense, 2007), it is possible that the increased numbers
of misaligned planets orbiting such stars is a direct result of those stars
having undetected massive companions. Equally, more massive stars tend to form
more massive planets (e.g. Ida & Lin, 2005; Johnson et al., 2007; Bowler et
al., 2010; Jones et al., 2016), and so mechanisms involving planet-planet
scattering are also more likely to play a role in determining the obliquities
of short period planets.

To determine the degree to which these different mechanisms contribute to the
overall population of short-period planets, it is important to discover and
characterise as many such planets, orbiting as wide a variety of stars, as
possible. In this work, we present the discovery of a new hot Jupiter orbiting
HD 115447 (also known as TOI-778), an F3-dwarf with a mass of 1.39$\pm$0.02
$\,M_{\odot}$ and a surface temperature of 6875$\pm$190 K. The candidate
planet was detected by TESS during Sector 10, in the first year of operation
as it surveyed the southern sky. Here, we used follow-up observations from a
variety of ground-based facilities to confirm the existence of TOI-778 b, and
characterise both the planet and its orbit around TOI-778.

In Section 2, we describe the observations of TOI-778 followed by the latest
characterisation of the star in Section 3 from the observations we obtained.
We then present the results of our analysis in Section 4, discuss those
results in Section 5, and then conclude in Section 6.

##  2 Observations and Data Reduction

In this section, we describe the photometric, spectroscopic, and imaging data
sets used to validate the planetary nature of TOI-778 b.

###  2.1 Photometric Observations

####  2.1.1 TESS Light Curve

TOI-778 (TIC 335630746) was observed by TESS during Sector 10 of its primary
mission, from March 26 to April 21, 2019, and extended via Sector 37
observations, taken between April 2 and April 28, 2021. The target star was
identified as a planet host candidate via the analyses of the Science
Processing Observation Center (SPOC, Jenkins et al., 2016), as described by
Jenkins (2002); Jenkins et al. (2010); Twicken et al. (2018); Li et al.
(2019b); Jenkins et al. (2020), using light curves extracted from the two
minute target pixel files. We used the Presearch Data Conditioning Simple
Aperture Photometry flux values from the TESS light curve, removing nonzero
flagged data (such as momentum dumps) that could contaminate the light curve
analysis. The light curves were then normalised by the median flux values and
used in the analysis for TOI-778 b’s confirmation. The resulting light curves
are found in Figure 1.

Figure 1: Full TESS PDCSAP median corrected light curves for TOI-778 from
Sector 10 and Sector 37

####  2.1.2 Next Generation Transit Survey

A transit egress of TOI-778 b was observed using the Next Generation Transit
Survey (NGTS; Wheatley et al., 2018) on UTC 2019 June 22. NGTS is an exoplanet
hunting facility located at the ESO Paranal Observatory in Chile, which
consists of twelve independently operated robotic telescopes. Each telescope
has a 20 cm diameter and an 8 square-degree field-of-view. The NGTS telescopes
use the DONUTS auto-guiding algorithm (McCormac et al., 2013) to achieve sub-
pixel guiding. TOI-778 was observed simultaneously using two NGTS telescopes,
and such multi-telescope observations have been shown to significantly improve
the photometric precision of the observations (Smith et al., 2020; Bryant et
al., 2020). A total of 1486 images were obtained using an exposure time of 10
s and the custom NGTS filter (520 - 890 nm). The airmass of the target was
kept below 2 and the sky conditions were optimal throughout the observations.

The images were reduced using a custom aperture photometry pipeline (Bryant et
al., 2020) which uses the SEP library (Bertin & Arnouts, 1996; Barbary, 2016)
for source extraction and photometry. The pipeline automatically identifies
comparison stars using Gaia DR2 (Gaia Collaboration et al., 2016, 2018),
ranking the stars in the field based on their similarity to TOI-778 in terms
of brightness, colour and CCD position.

####  2.1.3 Perth Exoplanet Survey Telescope

We observed an egress of TOI-778 on UTC 2020 March 31 in V-band from the Perth
Exoplanet Survey Telescope (PEST) near Perth, Australia. The 0.3 m telescope
is equipped with a $1530\times 1020$ SBIG ST-8XME camera with an image scale
of 1$\farcs$2 pixel-1 resulting in a $31\arcmin\times 21\arcmin$ field of
view. A custom pipeline based on
C-Munipack555http://c-munipack.sourceforge.net was used to calibrate the
images and extract the differential photometry, using an aperture with radius
7$\farcs$4\. The images have typical stellar point spread functions (PSFs)
with a full-width-half-maximum (FWHM) of $\sim 4\arcsec$.

####  2.1.4 LCO SAAO

We observed a full transit of TOI-778 in Pan-STARSS $z$-short band on UTC 2020
May 30 from the LCOGT (Brown et al., 2013) 1.0 m network node at South Africa
Astronomical Observatory. We used the TESS Transit Finder, which is 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 0.389$\arcsec$ 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 images were defocused to a FWHM
of $\sim 6\farcs 7$, and circular apertures with radius $8\farcs 2$ were used
to extract the differential photometry.

####  2.1.5 Mount Kent Observatory

On 2020 June 5 at the Mount Kent Observatory, a photometric transit
observation of TOI-778 was taken simultaneously with radial velocity
observations from Minerva-Australis. The observation was performed with the
Shared Skies Partnership’s Planewave CDK700 telescope equipped with an Alta
U16M Apogee camera. All data was taken using a Sloan i’ filter with a
27.3’x27.3’ field of view. All data reduction and analysis was completed using
the AstroImageJ software package.

####  2.1.6 Mt. Stuart

We observed TOI-778 b on UTC 2020 April 28 in Sloan $r^{\prime}$ band from the
Mt. Stuart Observatory near Dunedin, New Zealand. The 0.32 m telescope is
equipped with a $3072\times 2048$ SBIG STXL6303E camera with an image scale of
0$\farcs$88 pixel-1 resulting in a $44\arcmin\times 30\arcmin$ field of view.
The images were calibrated and photometric data were extracted with
AstroImageJ using a circular aperture with radius $3\farcs 5$.

###  2.2 Spectroscopic Observations

In order to obtain precise radial velocity follow-up data and stellar
properties for TOI-778, we carried out observations using four different
facilities. Here we give details about the observations carried out by each
instrument.

Table 1: Radial Velocities for TOI-778

Time | Velocity | Uncertainty | SNRe | Instrument
---|---|---|---|---
[BJD] | [ m s-1] | [ m s-1] |  |
2458662.63164 | 227 | 129 | 46 | Chiron
2458662.63531 | -109 | 142 | 45 | Chiron
2458662.63899 | 32 | 130 | 48 | Chiron
2458664.59022 | -70 | 103 | 61 | Chiron
2458664.59389 | 166 | 110 | 59 | Chiron
2458652.69011 | -6229 | 133 | 7 | Coralie
2458653.67374 | -6090 | 131 | 19 | Coralie
2458654.68544 | -5971 | 106 | 5 | Coralie
2458670.48753 | -5466 | 56 | 53 | Coralie
2458676.51154 | -5935 | 66 | 48 | Coralie
2458647.92621 | -6528 | 149 | 24 | M-A T1
2458647.94762 | -7042 | 228 | 35 | M-A T1
2458654.02680 | -6794 | 189 | 29 | M-A T1
2458665.04743 | -6480 | 249 | 22 | M-A T1
2458673.95523 | -6876 | 96 | 30 | M-A T1
2458647.92621 | -6303 | 179 | 36 | M-A T3
2458647.94762 | -6453 | 200 | 19 | M-A T3
2458654.02680 | -6898 | 177 | 26 | M-A T3
2458662.02455 | -6579 | 229 | 27 | M-A T3
2458662.04596 | -6457 | 318 | 30 | M-A T3
2459004.87332 | -70 | 106 | 18 | M-A T4RM
2459004.88826 | 73 | 82 | 24 | M-A T4RM
2459004.90319 | 85 | 74 | 27 | M-A T4RM
2459004.91813 | 198 | 84 | 23 | M-A T4RM
2459004.93306 | 15 | 66 | 31 | M-A T4RM
2458649.66043 | 182 | 100 | 57 | TRES
2458651.66355 | 336 | 123 | 50 | TRES
2458653.65718 | -36 | 119 | 40 | TRES
2458653.66621 | -29 | 136 | 40 | TRES
2458656.66766 | 615 | 126 | 54 | TRES

Note. — Minerva-Australis is given as M-A. Table 1 is published in its
entirety in machine-readable format online. A portion is shown here for
guidance regarding its form and content.

####  2.2.1 MINERVA-Australis

We carried out the spectroscopic observations of TOI-778 using the Minerva-
Australis facility (Wittenmyer et al., 2018; Addison et al., 2019, 2021a).
Minerva-Australis consists of an array of four independently operated 0.7 m
CDK700 telescopes situated at the Mount Kent Observatory in Queensland,
Australia (Addison et al., 2019). Each telescope simultaneously feeds stellar
light via fiber optic cables to a single KiwiSpec R4-100 high-resolution
($R=80,000$) spectrograph (Barnes et al., 2012) with wavelength coverage from
480 to 620 nm. TOI-778 was observed on 71 epochs with three telescopes
(labelled ‘T1, T3, T4’) between 13 June 2019 and 4 June 2020. Each epoch
consists of two 30-minute exposures and the resulting spectra had a signal-to-
noise per resolution element (SNRe) range between 15 and 36. The resulting
radial velocities and SNRe of each spectrum are given in Table 1. Radial
velocities for the observations are derived for each telescope by cross-
correlation, where the template being matched is the mean spectrum of each
telescope. The instrumental variations are corrected by using simultaneous
Thorium-Argon (ThAr) arc lamp observations. Radial velocities computed from
different Minerva-Australis telescopes are modeled in Section 4 as originating
from independent instruments.

####  2.2.2 TRES

We obtained additional observations of TOI-778 via the Tillinghast Reflector
Echelle Spectrograph (TRES, Fűrész, 2008) on the 1.5 m reflector at the Fred
Lawrence Whipple Observatory in Arizona, USA. TRES is a fiber-fed echelle with
a resolving power of $R\sim 44,000$ over the wavelength range of $390-910$ nm.
Thirteen TRES radial velocities were collected between 15 June 2019 and 29
February 2020 using the standard observing procedure of obtaining a set of
three science observations surrounded by ThAr calibration spectra. The science
spectra are then combined to remove cosmic rays and wavelength calibrated
using the ThAr spectra. The extraction technique follows procedures outlined
in Buchhave et al. (2010). The spectra had a SNRe range between 41-79. The
observation on the night of July 29, 2020 was discarded due to a telescope
issue combined with partly cloudy skies. We derived multi-order radial
velocities using the remaining 12 spectra by cross correlating each spectrum,
order-by-order, against the strongest SNRe spectrum.

Figure 2: Companion sensitivity for the near-infrared adaptive optics imaging.
The black points represent the 5$\sigma$ limits and are separated in steps of
1 FWHM; the purple represents the azimuthal dispersion (1$\sigma$) of the
contrast determinations (see Section 2.3). The inset image is of the primary
target showing no additional close-in companions.

####  2.2.3 CORALIE

The high resolution spectrograph CORALIE (Queloz et al., 2001) is mounted on
the Swiss 1.2m Euler telescope at La Silla, Chile. The instrument is fed with
a 2″ on-sky science fibre and a simultaneous Fabry-Pérot wavelength
calibration fibre, with a resolution of $R=60,000$. A total of 28 spectra of
TOI-778 were obtained between 17 June 2019 and 1 September 2019 by the Swiss
CORALIE team and the WINE-collaboration. One epoch was discarded due to low
S/N, leaving 27 remaining spectra with SNRe 10-50 at a wavelength 550 nm. All
spectra were extracted using the standard CORALIE data reduction pipeline.

Radial velocities were extracted through the cross-correlation technique
(Baranne et al., 1996). We used a weighted binary mask corresponding to an
A0-star dominated by H and Fe lines. This mask highly favours the strongest
1000 absorption lines seen in hot stars (Wyttenbach et al., 2020). TOI-778 is
a rapidly rotating star, resulting in non-Gaussian absorption lines. We
therefore fit a rotational profile to the cross-correlation functions, as done
for WASP-189 in Anderson et al. (2018). Through this method we achieve a
typical radial velocity precision of 80 $\mathrm{m\ s^{-1}}$.

####  2.2.4 CHIRON

We obtained 27 spectra of TOI-778 using the CHIRON spectrograph (Tokovinin et
al., 2013) on the Small and Moderate Aperture Research Telescope System
(SMARTS) 1.5 m telescope at Cerro Tololo, Chile. The CHIRON spectra were
obtained using the $R=80,000$ slicer mode, and each spectrum is bracketed by a
pair of ThAr lamp exposures for wavelength calibration.

This combination allows for higher throughput at the cost of some instrumental
radial velocity precision. For this early-type star, however, the radial
velocity uncertainties are dominated by the broad and sparse spectral lines,
rather than wavelength calibration errors or line-spread function drifts (both
of which are better addressed with the iodine cell, rather than ThAr).
CHIRON’s fiber has an on-sky radius of 1$\farcs$35 with individual exposure
times set to 5 minutes in length. Three back-to-back exposures were taken per
night that we observed TOI-778.

The radial velocities were derived following the procedure described in Jones
et al. (2017); Wang et al. (2019); Davis et al. (2020). To summarise, each set
of observations of TOI-778 during a night was followed by a ThAr exposure, and
the CHIRON pipeline (Paredes et al., 2021) uses this lamp to compute a new
wavelegth solution; this method yields a demonstrated long-term stability of
$\sim$ 15 m s-1, on bright targets. Individual CHIRON spectra are shifted to a
common rest frame and then stacked to form a template. We compute the Cross-
Correlation Function (CCF) between each observed spectrum and this template.
We then fit a Gaussian function plus linear trend to the CCF, and take the
maximum of the fit to be the radial velocity for that observation. This method
is repeated for the 33 echelle orders between ${\sim}$470–650 nm where we have
good wavelength calibration. The final radial velocity at each epoch is
obtained from the median of the individual order velocities, after applying a
3$\sigma$ rejection method. radial velocity uncertainties are computed from
the error in the mean of the non-rejected velocities (as in Jones et al.
2017). For this star, the typical radial velocity error found was about 150
$\mathrm{m\ s^{-1}}$.

###  2.3 High Angular Resolution Imaging

As part of our standard process for validating transiting exoplanets to assess
the possible contamination of bound or unbound companions on the derived
planetary radii (Ciardi et al., 2015), we observed TOI-778 with high-
resolution near-infrared adaptive optics (AO) imaging at Palomar and Keck
Observatories and with optical speckle interferometric imaging at Gemini-
South. The infrared observations provide the deepest sensitivities to faint
companions while the optical speckle observations provide the highest
resolution imaging making the two techniques complementary. Additionally,
since the speckle interferometry overlaps with the TESS band pass, no
assumptions were needed to be made about the SED of possible contaminants.

####  2.3.1 Near-Infrared AO

The Palomar Observatory observations were made with the Palomar High Angular
Resolution Observer (PHARO) instrument (Hayward et al., 2001) behind the
natural guide star AO system P3K (Dekany et al., 2013) on 2020 Jun 12 UT in a
standard 5-point quincunx dither pattern with steps of 5″ in the narrow-band
$Br-\gamma$ filter $(\lambda_{o}=2.1686;\Delta\lambda=0.0326~{}\mu$m). Each
dither position was observed three times, offset in position from each other
by 0.5″ for a total of 15 frames; with an integration time of 10 seconds per
frame, the total on-source time was 150 seconds. PHARO has a pixel scale of
$0.025\arcsec$ per pixel for a total field of view of $\sim 25\arcsec$.

The Keck Observatory observations were made with the NIRC2 instrument on Keck-
II behind the natural guide star AO system (Wizinowich et al., 2000) on June
25, 2019 in the standard 3-point dither pattern that is used with NIRC2 to
avoid the left lower quadrant of the detector which is typically noisier than
the other three quadrants. The dither pattern step size was $3\arcsec$ and was
repeated twice, with each dither offset from the previous dither by
$0.5\arcsec$. NIRC2 was used in the narrow-angle mode with a full field of
view of $\sim 10\arcsec$ and a pixel scale of approximately 10 milliarcsec per
pixel. The Keck observations were made in both the narrow-band $Br-\gamma$
$(\lambda_{o}=2.1686;\Delta\lambda=0.0326~{}\mu$m) and the $J-cont$
$(\lambda_{o}=1.2132;\Delta\lambda=0.0198~{}\mu$m) filters with an integration
time for each filter of 1 second for a total of 9 seconds on target.

The AO data were processed and analyzed with a custom set of IDL tools. The
science frames were flat-fielded and sky-subtracted. The flat fields were
generated from a median average of dark subtracted flats taken on-sky. The
flats were normalised such that the median value of the flats is unity. The
sky frames were generated from the median average of the 15 dithered science
frames; each science image was then sky-subtracted and flat-fielded. The
reduced science frames were combined into a single combined image using a
intra-pixel interpolation that conserves flux, shifts the individual dithered
frames by the appropriate fractional pixels, and median-coadds the frames. The
final resolution of the combined dithers was determined from the full-width
half-maximum of the point spread function; 0.105″ and 0.050″ for the Palomar
and Keck observations respectively.

To within the limits of the AO observations, no stellar companions were
detected. The sensitivities of the final combined AO image were determined by
injecting simulated sources azimuthally around the primary target every
$20^{\circ}$ at separations of integer multiples of the central source’s FWHM
(Furlan et al., 2017; Lund, 2021 submitted). The brightness of each injected
source was scaled until standard aperture photometry detected it with
$5\sigma$ significance. The resulting brightness of the injected sources
relative to TOI-778 set the contrast limits at that injection location. The
final $5\sigma$ limit at each separation was determined from the average of
all of the determined limits at that separation and the uncertainty on the
limit was set by the rms dispersion of the azimuthal slices at a given radial
distance (Figure 2).

###  2.4 Optical Speckle Interferometry

TOI-778 was observed on March 16, 2020, using the Zorro speckle
interferometric instrument mounted on the 8 m Gemini South telescope on the
summit of Cerro Pachon in Chile. Zorro simultaneously obtains diffraction-
limited images at 562 and 832 nm. Our data set consisted of 3 minutes of total
integration time on source taken as sets of 1000 x 0.06 s images plus a
consecutive observation of a Point Spread Function (PSF) standard star.
Following Howell et al. (2011), we combined all images and subjected them to
Fourier analysis to produce speckle reconstructed imagery from which the
5$\sigma$ contrast curves are derived for each passband and nearby companion
stars searched for (Figure 3). Our data reveal TOI-778 to be a single star to
contrast limits of 5–8.5 magnitudes covering a spatial range of $\sim$3 to 196
au at the distance to TOI-778.

Figure 3: Speckle interferometric contrast curves and reconstructed images for
the 562 nm and 832 nm observations. No companion was detected within the
spatial limits of the diffraction limit and 1.2" equaling 3-4 to 196 au at the
distance of TOI-778

##  3 Stellar Properties of HD 115447

The planetary properties of TOI-778 b depend upon the stellar properties of
its host star. We first combine the Minerva-Australis spectra of TOI-778 to
create a median spectrum to input into iSpec (Blanco-Cuaresma et al., 2014;
Blanco-Cuaresma, 2019). iSpec uses a grid-modelling approach to calculate the
effective temperature ($T_{\rm eff}$), surface gravity (${\rm\log}~{}g$) and
overall metallicity ([M/H]) from the input spectra. These spectroscopic
properties are then used along with other photometric and astrometric data as
input for the Bayesian isochrone modelling program isochrones. We used the
Gaia DR2 (Gaia Collaboration et al., 2018) parallax and magnitudes ($G$,
$G_{R}$ and $G_{B}$), 2MASS (Cutri et al., 2003) magnitudes ($J$, $H$ and
$K_{s}$) V-band magnitude ($V$) and colour excess (E(B-V)), with the iSpec
values as input for the isochrones analysis. The resulting derived isochrone
properties for TOI-778, including stellar mass, radius, luminosity, and age
are given in Table 3. Our results are consistent with version 9 of the TESS
Input Catalog (Stassun et al., 2019) and are the parameters used to further
characterise the planetary nature of TOI-778 b. The above procedure of
determining the stellar properties of TOI-778 is similar to that of Addison et
al. (2021a).

We also calculated the rotation period of TOI-778 through the light curve
obtained by TESS (discussed in more detail within Section 2.1). Using SciPy’s
Lomb-Scargle periodogram (Virtanen et al., 2020) on the light curves collected
by TESS (plotted in Figure 1), we performed the analysis in two search ranges:
0.01–1.5 days and 1–13 days. The periodogram analysis was part of a larger
Variability Catalog of TESS light curves (see, Fetherolf et al., 2022), and
TOI-778 did make it into the final Variability Catalog after several careful
vetting steps to remove false positives that could be caused by spacecraft
systematics (e.g., momentum dumps).

A significant signal was found in the 1–13 day periodogram search
corresponding to a stellar rotation period for TOI-778 to be $2.567\pm 0.095$
days. Figure 4 shows a phase-folded plot of TOI-778’s light curve to the
period of 2.567 days. There seems to be no correlation between the light curve
modulation and the momentum dumps of TESS shown in Figure 4 and the normalized
power of the periodogram is sufficiently high, such that we are confident that
this modulation is astrophysical in nature. We include our derived stellar
rotation value in Table 3.

Table 2: Stellar Parameters for HD 115447. Notes.–†Derived using Minerva-
Australis spectroscopic observations. ‡Derived using spectroscopic
observations from TRES. ⋆Preferred solution and used as a prior in the
Allesfitter analysis. ∧Lower limit placed on $v\sin i$ uncertainty of $\pm
1.0$ km s-1 due to contributions of other sources of absorption line-
broadening.

Stellar Parameters | Value | Source
---|---|---
Catalog Information |  |
Right Ascension (h:m:s) | 13:17:20.189 | 1
Declination (d:am:as) | -15:16:24.944 | 1
Parallax (mas) | 6.15415 $\pm$ 0.04231 | 1
$\mu$R.A (mas yr-1) | -60.600 $\pm$ 0.083 | 1
$\mu$Dec. (mas yr-1) | -26.012 $\pm$ 0.065 | 1
Gaia DR2 ID | 3607877948613218304 | 1
2MASS ID | J13172019-1516248 | 2
HD ID | 115447 |
TIC ID | 335630746 | 3
TOI ID | 778 |
Spectroscopic Properties |  |
Spectral type | F2 | 4
| F3V | 5
$T_{\rm eff}$ (K) | $6715\pm 128$ | 3
|  $6875\pm 190$ † | 7
|  $6643\pm 150$ ‡,⋆ | 7
$\log g$ (cgs) | $4.144\pm 0.085$ | 3
|  $4.05\pm 0.17$ † | 7
|  $3.98\pm 0.22$ ‡ | 7
Metallicity, [m/H] |  $0.00\pm 0.08$ † | 7
Metallicity, [m/H] |  $0.03\pm 0.08$ ‡ | 7
$v\sin i$ ( km s-1) |  $28.9\pm 3.7$ † | $7$
|  $35.1\pm 1.0$ ‡,⋆,∧ | $7$
Photometric Properties |  |
$G$ (mag) | 8.9944 $\pm$ 0.0007 | 1
$G_{BP}$ (mag) | 9.226 $\pm$ 0.002 | 1
$G_{RP}$ (mag) | 8.648 $\pm$ 0.002 | 1
$J$ (mag) | 8.25 $\pm$ 0.02 | 2
$H$ (mag) | 8.09 $\pm$ 0.03 | 2
$K_{s}$ (mag) | 8.055 $\pm$ 0.033 | 2
$V$ (mag) | 9.11 $\pm$ 0.02 | 6
$T$ (mag) | 8.690 $\pm$ 0.006 | 3
Derived Stellar Properties |  |
$M_{\star}$ ($M_{\odot}$) | 1.428 $\pm$ 0.094 | 3
|  $1.40\pm 0.05$ ⋆ | 7
$R_{\star}$ ($R_{\odot}$) | 1.677 $\pm$ 0.068 | 3
|  $1.71\pm 0.05$ ⋆ | 7
$\rho_{\star}$ (g cm-3) | 0.40 $\pm$ 0.03 | 7
$L_{\star}$ ($L_{\odot}$) | 5.153 $\pm$ 0.269 | 3
| 5.76 $\pm$ 0.65 | 7
Age (Gyr) | $1.95^{+0.14}_{-0.13}$ | 7
Distance (pc) | $162\pm 1$ | 1
Rotation Period (days) | 2.584$\pm$0.095 | 7

References. — 1. Gaia Collaboration et al. (2018); 2. Cutri et al. (2003) ; 3.
Stassun et al. (2019); 4. Cannon & Pickering (1993); 5. Houk & Smith-Moore
(1988), 6\. Høg et al. (2000), 7. This work.

Figure 4: Left: Relative flux values from TOI-778 during Sector 10 (black
dots). The transit events of TOI-778 b that have been removed for the
periodogram analysis are shown as grey points with the periodic signal of
2.584 days over-plotted in red. Momentum dumps from TESS are shown by the blue
triangles. Centre: The periodogram from the TESS light curve. The transits
have been removed from the light curve for the periodogram analysis such that
the periodogram appears to be near zero at 4.5 days. b. Right: A phase-folded
version of Left figure, with the period and semi-amplitude of the periodic
variations listed at the top of the figure.

##  4 Joint Analysis and Results

Figure 5: Left: A phase-folded radial velocity model of TOI-778 b from our
AllesFitter analysis with the Rossiter-Mclaughlin effect. Each radial velocity
instrument’s data is shown, with CHIRON in violet circles, CORALIE in purple
down arrows, TRES in burgundy triangles, Minerva-Australis Telescope 1 in pink
stars, Minerva-Australis Telescope 3 in orange squares and Minerva-Australis
Telescope 4 in yellow left arrows. 20 randomly drawn posterior radial velocity
models are shown in grey lines while the red line is the best-fit model.
Residual velocities to the best-fit model are shown below. Right: Phase-folded
light curve model for TOI-778 b just from the TESS data with the sectors
(Sectors 10 and 37, respectively) and light curve segments (P1 and P2,
respectively) indicated. Phase-folded light curve models for the ground-based
follow-up is presented in Figure 6.

To determine the planetary nature of TOI-778 b, and its host star’s obliquity,
we used Allesfitter (Günther & Daylan, 2019, 2021) to perform a joint analysis
of the TESS light curve segments, the photometric ground-based light curves,
and the radial velocity measurements. We include both light curves from the
TESS Sectors 10 and 37, keeping them as separate observations with possible
brightness offsets between the sectors. We also split the observations from
each Sector into two parts, since there is a clear break in each sector during
the data download. Thus, we have four independent TESS light curves we use for
the analysis. We use all ground-based photometric observations of TOI-778 that
include at least 50% of the transits of TOI-778 b. These facilities included
the NGTS, PEST, LCO, Mt. Kent, and Mt. Stuart observations. We used all radial
velocity measurements taken from Minerva-Australis, TRES, CORALIE, and CHIRON.
These radial velocities include the data from Minerva-Australis that were
taken during the Rossiter-Mclaughlin observation on June 4, 2020. TOI-778’s
stellar radius, mass and effective temperature are used within the Allesfitter
analysis, as these values are needed for deriving the planetary mass, radius,
and equilibrium temperature.

The priors used for our analysis are given in Tables 3, 3, and 4, and
described below. For each of our light curves, we calculated the quadratic
limb darkening coefficients used by Eastman et al. (2013), an interpolation of
the quadratic limb darkening tables derived by Claret & Bloemen (2011). These
calculated values were then used as the starting values for the limb darkening
coefficient parameters with uniform priors between 0 and 1 within the
Allesfitter analysis. Since NGTS has a unique Band-pass filter, we set its
initial quadratic limb darkening coefficients to 0.5 with a uniform prior
between 0 and 1. We fixed the dilution parameter to 0 since the TESS SPOC
light curves used in the analysis already have any potential blending removed
from the target star’s flux from known sources. For the physical parameters
used in the Allesfitter analysis, we applied uniform priors with starting
values taken from or derived from NASA’s Exoplanet Follow-up Observing Program
database for the orbital period ($P_{p}$), transit mid-time ($T_{0;b}$),
planet-to-star radius ratio ($R_{p}/R_{\star}$), the ratio of the sum of the
planet and star radii to the semi-major axis ($(R_{p}+R_{\star})/a_{p}$),
cosine of the inclination angle ($\cos{i_{p}}$), the radial velocity semi-
amplitude ($K$), and eccentricity ($\sqrt{e_{p}}\cos{\omega_{p}}$ and
$\sqrt{e_{p}}\sin{\omega_{p}}$). Uniform priors were used for the light curves
flux error scaling ($\ln{\sigma_{F_{inst}}}$) as well as on the radial
velocity baseline offsets ($\Delta RV_{inst}$) and jitter terms
($\ln{\sigma_{RV_{inst}}}$) for each instrument. Included in the joint fit was
the Rossiter-McLaughlin effect and for this, we applied a weak ($5\sigma$)
Gaussian prior on the stellar rotational velocity ($v\sin{(i)}$) as derived
using spectroscopic observations from TRES (see Table 3).

We utilise Allesfitter’s nested sampling approach to sample the model
posteriors by implementing the dynesty package (Speagle, 2020). We used a
dynamic nested sampling, with random walk sample, 500 live points and a
tolerance of 0.01. We ran our analysis until a tolerance of 0.01 was achieved
with the derived stellar, planetary and instrumental parameters shown in Table
3 and 4. Median values are shown in Table 3 and 4 along with their associated
1-sigma errors.

Table 3: Astrophysical parameters for TOI-778 b as derived by Allesfitter. Priors are shown as uniform $\mathcal{U}$(a,b) or normal $\mathcal{N}$($\nu$,$\sigma$). Parameters used for the transit and radial velocity fits that are not located in this table can be found in Table 4. Parameter | Prior | Best-Fit
---|---|---
Fitted Planetary Parameters |
$K_{b}$ ( m s-1) |  $\mathcal{U}$(10,1000) | $271\pm 17$
$R_{p}/R_{\star}$ |  $\mathcal{U}$(0.01,0.2) | $0.0825\pm 0.0005$
$(R_{\star}+R_{p})/a_{p}$ |  $\mathcal{U}$(0.05,0.2) | $0.143\pm 0.004$
$\cos{i}$ |  $\mathcal{U}$(0,0.2) | $0.091^{+0.006}_{-0.005}$
$T_{0;b}$ \- 2458000 ($\mathrm{BJD}$) |  $\mathcal{U}$(577.7,579.7) | $578.7161\pm 0.0001$
$P_{b}$ ($\mathrm{d}$) |  $\mathcal{U}$(3.6,5.6) | $4.633611\pm 0.000001$
$\sqrt{e_{b}}\cos{\omega_{b}}$ |  $\mathcal{U}$(-0.9,0.9) | $0.40^{+0.06}_{-0.07}$
$\sqrt{e_{b}}\sin{\omega_{b}}$ |  $\mathcal{U}$(-0.9,0.9) | $0.21\pm 0.07$
Derived Planetary Parameters |
$a_{\mathrm{p}}/R_{\star}$ |  | $7.6\pm 0.2$
$R_{\mathrm{p}}$ ($\mathrm{R_{\oplus}}$) |  | $15.4\pm 0.5$
$M_{\mathrm{p}}$ ($\mathrm{M_{\oplus}}$) |  | $878^{+77}_{-72}$
$i_{\mathrm{p}}$ (deg) |  | $84.7^{+0.3}_{-0.4}$
$e_{\mathrm{p}}$ |  | $0.21\pm 0.04$
$w_{\mathrm{p}}$ (deg) |  | $28_{-10}^{+12}$
$R_{\mathrm{p}}$ ($\mathrm{R_{jup}}$) |  | $1.37\pm 0.04$
$M_{\mathrm{p}}$ ($\mathrm{M_{jup}}$) |  | $2.8\pm 0.2$
$a_{\mathrm{p}}$ (AU) |  | $0.060\pm 0.003$
$b_{\mathrm{tra;p}}$ |  | $0.61\pm 0.02$
$T_{\mathrm{tot;p}}$ (hr) |  | $3.76\pm 0.01$
$T_{\mathrm{full;p}}$ (hr) |  | $2.89\pm 0.01$
$\rho_{\mathrm{p}}$ (cgs) |  | $1.3\pm 0.2$
$T_{\mathrm{eq;p}}$ (K) |  | $1561^{+33}_{-32}$
Stellar Parameters |  |
$v\sin{i}$ ( km s-1) |  $\mathcal{N}$(35.1,5.0) | $39.9^{+4.5}_{-4.3}$
$\lambda$ ($\mathrm{deg}$) |  $\mathcal{U}$(-180,180) | $18\pm 11$
$\rho_{\mathrm{\star}}$ (cgs, derived) |  | $0.38\pm 0.03$
Figure 6: Phase-folded Light curve model for TOI-778 b from the ground-based
observations, the colored symbols are binned observations from Mt. Kent
(violet circles), LCO McDonald (burgundy up triangles), PEST (orange squares),
LCO SAAO (purple down triangles), Mt. Stuart (red stars), and NGTS (yellow
left triangles. The grey points are the unbinned observations from all the
ground-based facilities. 100 randomly drawn posteriors are shown in red, with
the residuals of the fits shown in bottom plot.

The resulting transit light curve model for the TESS and ground-based
photometry can be found in Figure 5 and Figure 6, respectively. Figure 5 also
includes the radial velocity model for TOI-778 b with our Doppler spectroscopy
data. From the global analysis, TOI-778 b’s orbital period is $4.633611\pm
0.000001$ days, in line with the $4.63361\pm 0.00011$ days found by TESS in
Sector 10. It has a relatively large radial velocity semi-amplitude, with a
$16\,\sigma$ detection of $K=271^{+18}_{-17}$ m s-1. Given these parameter
posteriors, and our estimates of the stellar mass, radius and their
uncertainties given in Table 3, we derive a planetary mass, radius, and bulk
density for TOI-778 b to be $2.8\pm 0.2$ $\,M_{\rm J}$, $1.37\pm 0.04$
$\,R_{\rm J}$, and $\rho_{\mathrm{p}}=1.3\pm 0.2$ cgs, respectively. With its
radius, and orbital period, we confirm the planetary nature of TOI-778 b as a
hot Jupiter.

TOI-778 b was found to have a statistically significant non-zero orbital
eccentricity, of $0.21\pm 0.04$. With previous research showing that eccentric
orbits can exist due to hidden planetary companions (e.g. Wittenmyer et al.,
2013; Trifonov et al., 2017; Boisvert et al., 2018; Wittenmyer et al., 2019),
we further inspected the radial velocity residuals using a general Lomb-
Scargle periodograms, but found no significant signals. We also performed an
independent analysis of our radial velocity and photometric data through
EXOFASTv2 (Eastman et al., 2019; Eastman, 2017), and found consistent results
at the 1-$\sigma$ level.

We also conducted a joint analysis of the Rossiter-Mclaughlin observation
(Minerva T4RM) with the global fit to measure the sky-projected spin-orbit
alignment of the system. The resulting effect can clearly be seen in Figures 5
and 7. The global fit analysis yields a sky-projected spin-orbit angle of
$18\pm 11^{\circ}$. In addition, following Masuda & Winn (2020), we find the
stellar inclination to be well aligned to the line of sight, with
$I_{\star}>50^{\circ}$ at $3\sigma$ significance. This result is consistent
with an aligned system and is discussed further in Section 5.

Figure 7: A phase-folded radial velocity model of the Rossiter-McLaughlin
effect of TOI-778. Each radial velocity instrument’s data is shown with CHIRON
in violet circles, CORALIE in purple down arrows, TRES in burgundy triangles,
Minerva-Australis Telescope 1 in pink stars, Minerva-Australis Telescope 3 in
orange squares and Minerva-Australis Telescope 4 in yellow left arrows,
similar to Figure 5. 20 randomly drawn posterior radial velocity models are
shown as grey lines while the best-fit model is plotted as the red line. The
residuals in the velocities from the best-fit model are shown in the bottom
panel.

##  5 TOI-778 b in Context

We have confirmed the planetary nature of TOI-778 b, detected by TESS in
Sector 10 of its primary mission. It is a hot Jupiter with radius
1.37$\pm$0.04 $\,R_{\rm J}$ and mass 2.8$\pm$0.2 $\,M_{\rm J}$ orbiting a
rapidly-rotating early-F star. TOI-778 b appears to be somewhat inflated when
compared to other hot Jupiters of similar masses.

The confirmation and mass measurement of TOI-778 b was challenging due to the
relatively rapid $\sim$35 km s-1 rotation of its early-F type host star.
Figure 8 shows the stellar rotational velocity against the semi-amplitude
radial velocity precision of all known exoplanets with a mass measurement
precision better than 20%.

There are only five other planets that have been discovered with a mass
precision of better than 20%, orbiting around a more rapidly rotating stars.
These include CoRoT-11 b (Gandolfi et al., 2010), HAT-P-69 b (Zhou et al.,
2019a), HATS-70 b (Zhou et al., 2019b), Kepler-1658 b (Chontos et al., 2019)
and WASP-93 b (Hay et al., 2016). In the most extreme case, HAT-P-69 b was
found around the rapidly rotating A star ($v\sin{i}=77.44\pm 0.56$ km s-1),
and achieved a semi-amplitude radial velocity precision of K = 309$\pm$49 m
s-1. Our results demonstrates how a facility like Minerva-Australis, with an
effective telescope radius of 1.20m, can be utilised to follow up and confirm
planetary candidates around such rapidly rotating stars.

Hot Jupiters appear to be less frequent around early type stars than solar-
like stars (Beleznay & Kunimoto, 2022; Sebastian et al., 2022), with Zhou et
al. (2019c) discovering an occurrence rate in TESS data of only 0.43$\pm$0.15%
for hot Jupiters orbiting main-sequence F stars, and 0.26$\pm$0.11% for A-type
stars. These low occurrence rates for earlier-type stars are consistent with
those found for their evolved kin (Grunblatt et al., 2019).

Figure 8: Host-star $v\sin{i}$ as a function of radial velocity amplitude
precision, for 842 planets for which masses have been measured with a
precision of better than 20%.

The rapid rotation, brightness ($V=9.1$ mag), and large radius of the planet
all work in favour of measuring the spin-orbit angle for this system. From
Rossiter-McLaughlin observations of a transit of TOI-778 b, we find the
planet’s orbit to be close to being aligned with the stellar equator, with a
host star sky-projected obliquity of $19\pm 10$ degrees.

An obliquity measurement can aid in better determining the origin and
formation history of exoplanets, especially large and relatively close-in
orbiting ones like TOI-778 b. Since the star’s effective temperature ($T_{\rm
eff}\sim 6700$ K) is beyond the Kraft break temperature of $\sim 6200$ K, it
is unlikely to have realigned from a high obliquity orbit (Kraft, 1967). Thus
we may be seeing the exoplanet’s primordial obliquity, rather than the result
of a secondary realignment. It therefore seems most likely that TOI-778 b
sedately migrated through its host’s disk, rather than reaching its current
location through more chaotic means. Indeed, with a low obliquity angle and a
stellar age of $\sim 2$ Gyr, migration mechanisms such as high-eccentricity,
planet-planet scattering, Kozai–Lidov tidal and secular chaos migrations are
disfavored (Masset & Papaloizou, 2003; Nagasawa et al., 2008b; Dawson &
Johnson, 2018).

While the radial velocity data are limited and noisy, we can also exclude the
presence of perturbing objects more massive than $\sim$6 $\,M_{\rm J}$ within
0.3 AU. Additionally, based on the estimated sensitivity of the high angular
resolution imaging from Gemini, Keck, and Palomar (Section 2.3) and the Pecaut
& Mamajek (2013) table of stellar properties, we can place upper mass limits
for potential stellar companions in this system as $0.73$ $\,M_{\odot}$ at a
distance of 9.2 AU (separation of $0.057$ ″, equivalent to 1 FWHM from the
star for Keck NIRC2), $0.16$ $\,M_{\odot}$ at 40.4 AU ($0.25$ ″), and $0.10$
$\,M_{\odot}$ at 80.9 AU ($0.50$ ″). Combined, the radial velocity and direct
imaging data cannot fully rule out massive planetary, substellar, or low mass
stellar objects with masses $<0.16$ $\,M_{\odot}$ within $\sim 40$ AU,
therefore, planet-planet scattering and Kozai-Lidov tidal migration remain
potentially viable migration mechanisms for TOI-778 b.

Figure 9 shows the planetary obliquity as a function of host star temperature
with TOI-778 b and the sample of known hot Jupiters with obliquity
measurements. From Figure 9, TOI-778 b joins a cohort of other hot Jupiters
with well-aligned orbits, suggesting that disk migration is the likely case of
their evolution to their current positions.

Figure 9: We show all known hot Jupiters (${\rm
R_{p}>0.7~{}R_{J},P_{P}<10~{}days}$) with obliquity measurements and plot
those measurements against their host star’s effective temperature. Points are
coloured by the planet’s orbital eccentricity, albeit planet’s in circular
orbits shown in grey stars. TOI-778 b is shown as the large red filled in
star.

##  6 Conclusion

During Sector 10 of TESS’s primary mission, an exoplanet candidate was
discovered around the rapidly rotating star HD 115447, also known as TOI-778.
This 4.63 day signal was subsequently followed up by the exoplanetary
community through transit observations from PEST, LCO, NGTS, Mount Kent and
Mt. Stuart. Coinciding with these efforts, radial velocity measurements from
TOI-778 were collected from Minerva-Australis, TRES, CORALIE and CHIRON to
then determine the exoplanetary nature of TOI-778 b. From our AllesFitter
global model, we confirm the presence of the hot Jupiter TOI 778 b ($1.37\pm
0.04$ $\,R_{\rm J}$, $2.8\pm 0.2$ $\,M_{\rm J}$). We conducted a Rossiter-
Mclaughlin observation of TOI-778 b and discovered its spin-orbit angle to its
host is $18\pm 11^{\circ}$, which is consistent with an aligned planetary
system. These results also highlight how smaller telescope arrays such as
Minerva-Australiscan lead the charge of confirming and characterising
exoplanets around rapidly rotating stars.

We respectfully acknowledge the traditional custodians of all lands throughout
Australia, and recognise their continued cultural and spiritual connection to
the land, waterways, cosmos, and community. We pay our deepest respects to all
Elders, ancestors and descendants of the Giabal, Jarowair, and Kambuwal
nations, upon whose lands the Minerva-Australis facility at Mt Kent is
situated. Minerva-Australis is supported by Australian Research Council LIEF
Grant LE160100001, Discovery Grants DP180100972 and DP220100365, Mount Cuba
Astronomical Foundation, and institutional partners University of Southern
Queensland, UNSW Sydney, MIT, Nanjing University, George Mason University,
University of Louisville, University of California Riverside, University of
Florida, and The University of Texas at Austin. This paper includes data
collected at the Keck Telescopes. We recognise and acknowledge the cultural
role and reverence that the summit of Maunakea has within the indigenous
Hawaiian community. We are deeply grateful to have the opportunity to conduct
observations from this mountain. Funding for the TESS mission is provided by
NASA’s Science Mission directorate. We acknowledge the use of public TESS
Alert data from pipelines at the TESS Science Office and at the TESS Science
Processing Operations Center. This 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. This paper
includes data collected by the TESS mission, which are publicly available from
the Mikulski Archive for Space Telescopes (MAST). Some of the observations in
the paper made use of the High-Resolution Imaging instrument Zorro. 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. Data were reduced using a software pipeline originally written by
Elliott Horch and Mark Everett. 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).
We thank the Swiss National Science Foundation (SNSF) and the Geneva
University for their continuous support to our planet search programs. This
work has been in particular carried out in the frame of the National Centre
for Competence in Research PlanetS supported by the Swiss National Science
Foundation (SNSF).
This publication makes use of The Data & Analysis Center for Exoplanets
(DACE), which is a facility based at the University of Geneva (CH) dedicated
to extrasolar planets data visualisation, exchange and analysis. DACE is a
platform of the Swiss National Centre of Competence in Research (NCCR)
PlanetS, federating the Swiss expertise in Exoplanet research. The DACE
platform is available at https://dace.unige.ch. This work makes use of
observations from the LCOGT network.
J.T.C would like to thank BC and DN, and is supported by the Australian
Government Research Training Program (RTP) Scholarship. T.F. acknowledges
support from the University of California President’s Postdoctoral Fellowship
Program. A.J. and R.B. acknowledge support from ANID – Millennium Science
Initiative – ICN12_009. A.J. acknowledges additional support from FONDECYT
project 1210718. R.B. acknowledges additional support from FONDECYT Project
1120075.

##  Appendix A Extra Fitting Information

Table 4: Median values and 68% confidence interval of the fitted and derived parameters for TOI-778 from the joint Nested Sampling Allesfitter analysis of the photometry and radial velocity data. Parameter | Description | Prior | Best-Fit
---|---|---|---
Radial Velocity Model Parameters |  |  |
$\ln{\sigma_{\mathrm{jitter}}}$ ($\mathrm{RV_{Chiron}}$) | RV jitter ($\ln$ m s-1) |  $\mathcal{U}$(-3,9) | $1.68^{+1.58}_{-1.61}$
$\ln{\sigma_{\mathrm{jitter}}}$ ($\mathrm{RV_{Coralie}}$) | RV jitter ($\ln$ m s-1) |  $\mathcal{U}$(-3,9) | $4.72_{-3.14}^{+3.09}$
$\ln{\sigma_{\mathrm{jitter}}}$ ($\mathrm{RV_{TRES}}$) | RV jitter ($\ln$ m s-1) |  $\mathcal{U}$(-3,9) | $1.06_{-0.97}^{+0.93}$
$\ln{\sigma_{\mathrm{jitter}}}$ ($\mathrm{RV_{Minerva;T1}}$) | RV jitter ($\ln$ m s-1) |  $\mathcal{U}$(-3,9) | $1.72_{-1.68}^{+1.66}$
$\ln{\sigma_{\mathrm{jitter}}}$ ($\mathrm{RV_{Minerva;T3}}$) | RV jitter ($\ln$ m s-1) |  $\mathcal{U}$(-3,9) | $1.64_{-1.57}^{+1.53}$
$\ln{\sigma_{\mathrm{jitter}}}$ ($\mathrm{RV_{Minerva;T4RM}}$) | RV jitter ($\ln$ m s-1) |  $\mathcal{U}$(-3,9) | $1.56_{-1.50}^{+1.44}$
$\Delta\mathrm{RV_{CHIRON}}$ | RV offset ( m s-1) |  $\mathcal{U}$(-1500,1500) | $54\pm 25$
$\Delta\mathrm{RV_{CORALIE}}$ | RV offset ( m s-1) |  $\mathcal{U}$(-7300,-4300) | $-5788_{-27}^{+26}$
$\Delta\mathrm{RV_{TRES}}$ | RV offset ( m s-1) |  $\mathcal{U}$(-1300,1600) | $206\pm 34$
$\Delta\mathrm{RV_{Minerva_{T1}}}$ | RV offset ( m s-1) |  $\mathcal{U}$(-8300,-5300) | $-6722_{-34}^{+33}$
$\Delta\mathrm{RV_{Minerva_{T3}}}$ | RV offset ( m s-1) |  $\mathcal{U}$(-8300,-5300) | $-6732^{+31}_{-30}$
$\Delta\mathrm{RV_{Minerva_{T4RM}}}$ | RV offset ( m s-1) |  $\mathcal{U}$(-1500,1500) | $-42\pm 29$
Photometric Model Parameters |  |  |
$q_{\mathrm{1;TESS}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.15_{-0.03}^{+0.04}$
$q_{\mathrm{2;TESS}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.46_{-0.18}^{+0.21}$
$q_{\mathrm{1;MtKent}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.06_{-0.04}^{+0.06}$
$q_{\mathrm{2;MtKent}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.43_{-0.28}^{+0.34}$
$q_{\mathrm{1;LCOSAAO}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.16_{-0.06}^{+0.08}$
$q_{\mathrm{2;LCOSAAO}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.30_{-0.21}^{+0.31}$
$q_{\mathrm{1;LCOMcD}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.61_{-0.33}^{+0.25}$
$q_{\mathrm{2;LCOMcD}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.44_{-0.28}^{+0.33}$
$q_{\mathrm{1;MtStuart}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.84_{-0.14}^{+0.11}$
$q_{\mathrm{2;MtStuart}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.39_{-0.17}^{+0.18}$
$q_{\mathrm{1;PEST}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.35_{-0.16}^{+0.19}$
$q_{\mathrm{2;PEST}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.66_{-0.31}^{+0.24}$
$q_{\mathrm{1;NGTS}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.31_{-0.12}^{+0.17}$
$q_{\mathrm{2;NGTS}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.42_{-0.28}^{+0.33}$
$q_{\mathrm{1;Minerva_{T4RM}}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.62_{-0.30}^{+0.25}$
$q_{\mathrm{2;Minerva_{T4RM}}}$ | Transformed limb darkening | $\mathcal{U}(0,1)$ | $0.39_{-0.26}^{+0.33}$
$\ln{\sigma_{\mathrm{TESS}}}$ | Flux error scaling ($\ln{\mathrm{rel.flux.}}$) | $\mathcal{U}(-10,-3)$ | $-7.49\pm 0.01$
$\ln{\sigma_{\mathrm{MountKent}}}$ | Flux error scaling ($\ln{\mathrm{rel.flux.}}$) | $\mathcal{U}(-10,-3)$ | $-6.39\pm 0.04$
$\ln{\sigma_{\mathrm{LCOAAO}}}$ | Flux error scaling ($\ln{\mathrm{rel.flux.}}$) | $\mathcal{U}(-10,-3)$ | $-6.65\pm 0.03$
$\ln{\sigma_{\mathrm{LCOMcD}}}$ | Flux error scaling ($\ln{\mathrm{rel.flux.}}$) | $\mathcal{U}(-10,-3)$ | $-5.10\pm 0.03$
$\ln{\sigma_{\mathrm{MountStuart}}}$ | Flux error scaling ($\ln{\mathrm{rel.flux.}}$) | $\mathcal{U}(-10,-3)$ | $-6.06\pm 0.03$
$\ln{\sigma_{\mathrm{PEST}}}$ | Flux error scaling ($\ln{\mathrm{rel.flux.}}$) | $\mathcal{U}(-10,-3)$ | $-5.58\pm 0.03$
$\ln{\sigma_{\mathrm{NGTS}}}$ | Flux error scaling ($\ln{\mathrm{rel.flux.}}$) | $\mathcal{U}(-10,-3)$ | $-5.34\pm 0.01$
$\delta_{\mathrm{tr;TESS;S10P1}}$ | Transit depth (ppt) | Derived parameter | $7.17\pm 0.04$
$\delta_{\mathrm{tr;TESS;S10P2}}$ | Transit depth (ppt) | Derived parameter | $7.17\pm 0.04$
$\delta_{\mathrm{tr;TESS;S37P1}}$ | Transit depth (ppt) | Derived parameter | $7.17_{-0.04}^{+0.03}$
$\delta_{\mathrm{tr;TESS;S37P2}}$ | Transit depth (ppt) | Derived parameter | $7.17\pm 0.04$
$\delta_{\mathrm{tr;MtKent}}$ | Transit depth (ppt) | Derived parameter | $7.01\pm 0.10$
$\delta_{\mathrm{tr;LCOSAAO}}$ | Transit depth (ppt) | Derived parameter | $7.16\pm 0.09$
$\delta_{\mathrm{tr;LCOMcD}}$ | Transit depth (ppt) | Derived parameter | $7.66_{-0.33}^{+0.29}$
$\delta_{\mathrm{tr;MtStuart}}$ | Transit depth (ppt) | Derived parameter | $7.85_{-0.11}^{+0.12}$
$\delta_{\mathrm{tr;PEST}}$ | Transit depth (ppt) | Derived parameter | $7.46_{-0.22}^{+0.20}$
$\delta_{\mathrm{tr;NGTS}}$ | Transit depth (ppt) | Derived parameter | $7.36_{-0.15}^{+0.16}$

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