# The discovery of three hot Jupiters, NGTS-23b, 24b and 25b, and updated
parameters for HATS-54b from the Next Generation Transit Survey

David G. Jackson1, Christopher A. Watson1, Ernst J. W. de Mooij1, Jack S.
Acton2, Douglas R. Alves3, David R. Anderson,4,5 David J. Armstrong4,5, Daniel
Bayliss4,5, Claudia Belardi2, François Bouchy6, Edward M. Bryant7, Matthew R.
Burleigh2, Sarah L. Casewell2, Jean C. Costes8, Phillip Eigmüller9, Michael R.
Goad2, Samuel Gill4,5, Edward Gillen,10,11, Maximilian N. Günther12,13, Faith
Hawthorn4,5, Beth A. Henderson2, James A. G. Jackman14,4,5, James S.
Jenkins15,16, Monika Lendl6, Alicia Kendall2, James McCormac4,5, Maximiliano
Moyano17, Louise. D. Nielsen18, Ares Osborn4,5, Ramotholo R. Sefako19, Alexis
M. S. Smith9, Rosanna H. Tilbrook2, Oliver Turner6, Stéphane Udry6, Jose I.
Vines3, Richard G. West4,5, Peter J. Wheatley4,5 and Hannah Worters19
1Astrophysics Research Centre, School of Mathematics and Physics, Queen’s
University Belfast, BT7 1NN Belfast, UK
2School of Physics and Astronomy, University of Leicester, University Road,
Leicester, LE1 7RH, UK
3Departamento de Astronomia, Universidad de Chile, Casilla 36-D, Santiago,
Chile
4Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill
Road, Coventry, CV4 7AL, UK
5Dept. of Physics, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL,
UK
6Observatoire de Genève, Université de Genève, Chemin Pegasi 51, 1290
Sauverny, Switzerland
7Mullard Space Science Laboratory, University College London, Holmbury St
Mary, Dorking, Surrey, RH5 6NT, UK
8Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France
9Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse
2, 12489 Berlin, Germany
10Astronomy Unit, Queen Mary University of London, Mile End Road, London E1
4NS, UK
11Astrophysics Group, Cavendish Laboratory, J.J. Thomson Avenue, Cambridge,
CB3 0HE, UK
12European Space Agency (ESA), European Space Research and Technology Centre
(ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, Netherlands
13ESA Research Fellow
14School of Earth and Space Exploration, Arizona State University, Tempe, AZ,
85287, USA
15Núcleo de Astronomía, Facultad de Ingeniería y Ciencias, Universidad Diego
Portales, Av. Ejército 441, Santiago, Chile
16Centro de Astrofísica y Tecnologías Afines (CATA), Casilla 36-D, Santiago,
Chile
17 Instituto de Astronomía, Universidad Católica del Norte, Angamos 0610,
1270709, Antofagasta, Chile
18European Southern Observatory (ESO), Karl-Schwarzschild-Straße 2, 85748
Garching bei München, Germany
19South African Astronomical Observatory, P.O Box 9, Observatory 7935, Cape
Town, South Africa
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We report the discovery of three new hot Jupiters with the Next Generation
Transit Survey (NGTS) as well as updated parameters for HATS-54b, which was
independently discovered by NGTS. NGTS-23b, NGTS-24b and NGTS-25b have orbital
periods of 4.076, 3.468, and 2.823 days and orbit G-, F- and K-type stars,
respectively. NGTS-24 and HATS-54 appear close to transitioning off the main-
sequence (if they are not already doing so), and therefore are interesting
targets given the observed lack of hot Jupiters around sub-giant stars. By
considering the host star luminosities and the planets’ small orbital
separations (0.037 – 0.050 au), we find that all four hot Jupiters are above
the minimum irradiance threshold for inflation mechanisms to be effective.
NGTS-23b has a mass of 0.61 $M_{\rm{J}}$ and radius of 1.27 $R_{\rm J}$ and is
likely inflated. With a radius of 1.21 $R_{\rm J}$ and mass of 0.52 $M_{\rm
J}$, NGTS-24b has a radius larger than expected from non-inflated models but
its radius is smaller than the predicted radius from current Bayesian
inflationary models. Finally, NGTS-25b is intermediate between the inflated
and non-inflated cases, having a mass of 0.64 $M_{\rm J}$ and a radius of 1.02
$R_{\rm J}$. The physical processes driving radius inflation remain poorly
understood, and by building the sample of hot Jupiters we can aim to identify
the additional controlling parameters, such as metallicity and stellar age.

###### keywords:

planetary systems – planets and satellites: detection – stars: individual:
NGTS-23 (CTOI-77287067), NGTS-24 (TOI-4270), NGTS-25 and HATS-54

††pubyear: 2022††pagerange: The discovery of three hot Jupiters, NGTS-23b, 24b
and 25b, and updated parameters for HATS-54b from the Next Generation Transit
Survey–D

##  1 Introduction

Although hot Jupiters have a low occurrence rate of <1% (Mayor et al., 2011;
Hsu et al., 2019; Zhou et al., 2019), they still represent one of the most
common categories of planets found due to biases inherent in exoplanet
discovery techniques. Understanding the structure, composition and evolution
of these planets is of fundamental importance in understanding the processes
of formation, evolution and migration acting on the wider exoplanet
population. Increasing the sample of known hot Jupiters continues to help
constrain and parameterize planetary models. For example, there are models
that attempt to explain the evolution of planetary radii whilst accounting for
the effects of stellar irradiation and heavy element cores (Fortney et al.,
2007; Baraffe et al., 2008) but they struggle to explain the observed radii of
highly-irradiated gas giants.

There are a number of proposed mechanisms to explain inflation in hot Jupiters
such as kinetic heating (Guillot & Showman, 2002), Ohmic heating through
magnetohydrodynamic effects (Batygin & Stevenson, 2010; Perna et al., 2010;
Ginzburg & Sari, 2016), double diffusive convection (Chabrier & Baraffe, 2007)
and tidal dissipation (Bodenheimer et al., 2001, 2003; Jermyn et al., 2017).
In order to distinguish between such models, a robust sample of well-
characterised hot Jupiters is required to enable statistical studies to
constrain these models (such as that by Sestovic et al. 2018). Of particular
interest are planets irradiated by fluxes greater than approximately $2\times
10^{5}$ $\rm{W\,m^{-2}}$, which appear to be preferentially inflated (Demory &
Seager, 2011; Miller & Fortney, 2011). However, it is still unclear what
impact additional parameters, such as metallicity, have on whether the planet
will appear inflated.

We present the discovery of three new hot Jupiters from the Next Generation
Transit Survey (NGTS; Wheatley et al., 2018). We also refine the parameters
for HATS-54b, which was independently discovered by NGTS. In Section 2, the
initial NGTS photometry is described as well as the follow-up observations
(both photometry and spectroscopy). Section 3 describes how both the stellar
and planetary parameters were derived. The results will be discussed in
Section 4 including investigations into the orbital decay timescales (Section
4.1) and the potential inflation (Section 4.2) of these planets. Our final
conclusions are given in Section 5.

##  2 Observations

The planets presented in this work were confirmed using both photometric and
spectroscopic observations. These observations are outlined in this section.

###  2.1 Photometry

All planets presented in this paper were detected using photometry from NGTS.
To confirm the planetary nature of the stellar companions, and to further
constrain the system parameters, additional photometry was obtained using the
Transiting Exoplanet Survey Satellite (TESS; Ricker et al., 2014), EulerCam
(Lendl et al., 2012) and the 1-/1.9 m telescopes at the South African
Astronomical Observatory (SAAO; Coppejans et al., 2013). A summary of the
photometric observations is given in Table 2.1, and the phase-folded transit
lightcurves can be seen in Figure 1. Lightcurves not used in the global
fitting can be found in the appendix (Figure 7).

Table 1: Summary of photometric observations.

Target | Instrument | Nights Observed | Nimages | Exptime (s) | Filter | Comments
---|---|---|---|---|---|---
NGTS-23 | NGTS | 2017/08/16 – 2018/03/18 | 187,478 | 10 | NGTS |
TESS | 2018/10/19 – 2018/11/14 | 1027 | 1800 | TESS | Sector 4
TESS | 2018/11/15 – 2018/12/11 | 1176 | 1800 | TESS | Sector 5
TESS | 2020/10/22 – 2020/11/16 | 3445 | 600 | TESS | Sector 31
TESS | 2020/11/20 – 2020/12/16 | 3589 | 600 | TESS | Sector 32
EulerCam | 2018/12/27 | 171 | 90 | VG |
SAAO 1.0 m | 2018/12/15 | 300 | 60 | V |
SAAO 1.9 m | 2018/12/19 | 295 | 60 | V |
NGTS-24 | NGTS | 2017/12/10 – 2018/06/26 | 235,369 | 10 | NGTS |
TESS | 2019/02/28 – 2019/03/25 | 1084 | 1800 | TESS | Sector 9
TESS | 2019/03/26 – 2019/04/22 | 1103 | 1800 | TESS | Sector 10
TESS | 2021/03/07 – 2021/04/01 | 3467 | 600 | TESS | Sector 36
NGTS-25 | NGTS | 2018/03/24 – 2018/11/01 | 208,001 | 10 | NGTS |
TESS | 2020/07/05 – 2020/07/30 | 2898 | 600 | TESS | Sector 27
SAAO 1.0 m | 2019/10/03 | 940 | 20 | V |
HATS-54 (NGTS-22) | NGTS | 2015/12/18 – 2016/09/01 | 124,203 | 10 | NGTS |
TESS | 2019/04/23 – 2019/05/20 | 1145 | 1800 | TESS | Sector 11
TESS | 2021/04/02 – 2021/04/28 | 3461 | 600 | TESS | Sector 37
EulerCam | 2019/03/25 | 130 |  $\sim$80 | VG |
EulerCam | 2019/04/27 | 136 | 75 | VG |
SAAO 1.0 m | 2018/07/09 | 700 | 20 | I |
SAAO 1.0 m | 2019/04/30 | 360 | 60 | V |

####  2.1.1 NGTS

NGTS is a wide-field photometric survey located at ESO’s Paranal Observatory
in Chile. NGTS has a fully robotic array of twelve 20cm Newtonian telescopes
operating using the unique NGTS filter band (520-890nm). Each telescope is
equipped with a 2K$\times$2K e2V deep-depleted Andor IKon-L CCD camera. It is
optimised to detect and characterise transiting exoplanets around K and early
M-type stars and has achieved sufficient precision to discover exoplanets as
small as 3$R_{\oplus}$ (Wheatley et al., 2018; West et al., 2019; Smith et
al., 2021).

NGTS-23 (CTOI-77287067; V=14.010), NGTS-24 (TOI-4270; V=13.192) and
NGTS-25(V=14.266) were observed with NGTS during the 2018 campaign for a total
of 162 nights, 158 nights and 147 nights, respectively. HATS-54 (TOI-1920,
NGTS-22; V=13.914) was observed during the 2016 campaign for a total of 119
nights and was detected by NGTS independently of its discovery by Espinoza et
al. (2019). All the objects were observed with a 10s exposure time and over
120,000 images were collected for each object. The data were reduced and
aperture photometry performed via the CASUTools
111http://casu.ast.cam.ac.uk/surveys-projects/software-release package, before
nightly trends were removed using an adapted version of the SysRem algorithm
(Tamuz et al., 2005).

The data was then searched for transit-like events by ORION, a custom
implementation of the box-fitting least-squares (BLS) fitting algorithm
(Kovács et al., 2002; Collier Cameron et al., 2006; Wheatley et al., 2018).
ORION identified nine partial and one full transit for HATS-54b (NGTS-22b);
ten partial and one full transit for NGTS-23b; nine partial and seven full
transits for NGTS-24b; and eleven partial and eight full transits for
NGTS-25b. The initial fits to the NGTS data provided by ORION revealed that
the depths, widths and shapes of the transits for each object were compatible
with transiting hot Jupiters.

Further checks were performed to ensure that the nature of the signal was
planetary and not stellar or a false positive. These included comparing the
transit depth of consecutive odd and even transits, which can show a depth
difference that can demonstrate an eclipsing binary system has been mis-folded
on half the true period. Also, secondary eclipses around 0.5 phase in the
phase-folded lightcurves were searched for as this could also indicate that
the orbiting companion is stellar in nature. All candidates passed this
vetting and thus follow-up observations were taken.

####  2.1.2 SAAO

Between 2018 July and 2019 October, we took follow-up photometry for each
target (except for NGTS-24) using either the 1.0 m or 1.9 m telescope at SAAO
(Coppejans et al., 2013). The 1.0 m telescope was equipped with the full-frame
transfer CCD Sutherland High-speed Optical Camera (SHOC), “SHOC’n’awe", that
has a 2.85′$\times$2.85′field of view. The 1.9 m telescope was equipped with
the “SHOC’n’disbelief” optical camera, that had a slightly narrower field of
view of 1.3′$\times$1.3′. We were able to simultaneously observe at least one
comparison star of similar brightness for each object. All observations were
taken using either the I band or V band filters.

Two lightcurves were obtained for NGTS-23 one each on the 1.0 m and 1.9 m
telescopes, on the 2018 December 15 and 2018 December 19, respectively. Both
observations used an exposure time of 60 seconds with the V band filter. Both
observations ended early due to high humidity however, we obtained 300 images
and 295 images, respectively.

A single V-band light curve was taken for NGTS-25b on the 2019 October 3 using
the 1.0 m telescope. 940 images were obtained using an exposure time of 20
seconds. However, the middle of these observations were affected by bad
seeing.

Two observations of HATS-54b were conducted using the 1.0 m telescope on the
nights of the 2018 July 9 and the 2019 April 30. The 2018 observation obtained
700 images with an exposure time of 20s using the I band filter. This
observation was ended early due to high humidity. The 2019 observation
obtained 360 images with an exposure time of 60s using the V band filter.

Each lightcurve was bias and flat-field corrected using the local Python-based
SAAO SHOC pipeline, which uses IRAF (Tody, 1986) photometry tasks (PyRAF\-
Science Software Branch at STScI, 2012) and facilitates the extraction of raw
and differential lightcurves. We used the Starlink package autophotom (Currie
et al., 2014) to perform aperture photometry on both our target and comparison
stars, and chose apertures that gave the maximum signal-to-noise ratio.
Background apertures were adjusted to account for changes in the stellar
point-spread function over the night as the atmospheric conditions varied.
Finally, the measured fluxes of the comparison stars for each object were used
for differential photometry of our targets.

####  2.1.3 EulerCam

We also observed NGTS-23 and HATS-54 with EulerCam (Lendl et al., 2012) on the
1.2 m Euler Telescope at La Silla Observatory. All observations presented in
this work were done through a _Geneva V_ filter (Rufener & Nicolet, 1988).
NGTS-23 was observed on the 2018 December 27, with 171 images being acquired
with an exposure time of 90 s and a 0.1 mm defocus.

HATS-54 was observed twice with EulerCam. The first observation was performed
on the 2019 March 5, with 130 images being acquired with an exposure time of
approximately 80 seconds. No defocus was applied for this observation. The
second observation was carried out on the 2019 April 27. 136 images were
acquired with an exposure time of 75 seconds and a defocus of 0.5 mm. Only a
partial transit of NGTS-23 was observed, whereas the observations of HATS-54b
covered one full transit and one partial transit.

For both targets, the data were reduced using the standard procedure of bias
subtraction and flat field correction. The aperture photometry as well as x-
and y-positions, full width half-maximum (FWHM), airmass and sky background of
the target star were extracted using the PyRAF-based routines. The comparison
stars and the photometric aperture radius were carefully chosen in order to
reduce the RMS in the out-of-transit lightcurve parts.

####  2.1.4 TESS

TESS is a space-based NASA survey telescope that searches for transiting
planets around bright stars (Ricker et al., 2014). It has a wide field of
view, with four 24$\times$24° cameras, each equipped with four 2k$\times$2k
CCDs. Its typical observing baseline of $\approx$27 days makes it well-suited
to detecting short-period transiting exoplanets. We searched for our
candidates in the TESS full frame images (FFIs) using the TESSCut
222https://mast.stsci.edu/tesscut/ tool and found that all four stars were
observed by TESS, with observations between the 2018 October 19 and the 2021
April 28. NGTS-23 was observed in Sectors 4, 5, 31 and 32; NGTS-24 was
observed in Sectors 9, 10 and 36; HATS-54 was observed in Sectors 11 and 37
and NGTS-25 was observed in Sector 27. HATS-54b falls onto a CCD in TESS
Sector 38 but we do not use it as it appears to be in the overscan region of
the camera. A summary of this information can be found in Table 2.1.

Observations before 2020 July were within the primary mission of TESS, so the
TESS FFIs for these sectors were observed at 30 minute cadence. For
observations that are in the first extended mission of TESS (which is set to
finish in 2022 September) the TESS FFIs were observed at 10 minute cadence.
This means that all of the stars were observed at both 10 minute and 30 minute
cadence with TESS apart from NGTS-25, which was only observed with 10 minute
cadence. For each of our candidates we used an automatically determined
optimal aperture to exclude neighbouring stars, ranging from three to eight
pixels. However, the large pixel scale of TESS (21″) meant that there was
still some slight dilution of the FFI lightcurves.

For each candidate, we found that the best BLS period from TESS was consistent
with the ORION value for the NGTS photometry. TESS detected six full transits
for NGTS-25, eighteen full transits for NGTS-24, two partial and twenty full
transits for NGTS-23 and seventeen full transits for HATS-54.

For all four objects, the transits observed with TESS, as well as the other
photometric follow-up, was consistent with planetary companions. Therefore,
all objects were subsequently followed up with spectroscopy to determine the
mass of the companions.

(a) NGTS-23

(b) NGTS-24

(c) NGTS-25

(d) HATS-54 (NGTS-22)

Figure 1: NGTS discovery photometry (blue points) and follow up photometry for
each planet. The lighter points show the original photometry except for NGTS,
which has been binned to 10 minute intervals. The darker datapoints have been
binned to 0.002 phase. Photometry from HATS is shown in red while the HATS
follow-up photometry that was also used in our combined fits are shown in
yellow. The solid black line shows the lightcurve model for the planet.
Residuals are shown to the right of the lightcurves. Lightcurves offset for
clarity.

###  2.2 Spectroscopy

In addition to the photometric follow-up, spectroscopy was also used to obtain
radial velocity measurements for all of the systems. This allowed for the
mass, and therefore the density, of the respective transiting companion to be
determined. A summary of the spectroscopic observations is given in Table 2.2
and phase-folded radial-velocity curves can be seen in Figure 2.

The three different échelle spectrographs used are all located at La Silla
Observatory in Chile. The High Accuracy Radial velocity Planet Searcher
(HARPS; Mayor et al., 2003) has a resolving power of R=115,000 and is mounted
on the ESO 3.6 m telescope. The R=60,000 CORALIE spectrograph (Queloz et al.,
2001a) is installed on the Swiss 1.2 m Leonhard Euler telescope while the
Fibre-fed Extended Range Optical Spectrograph (FEROS; Kaufer & Pasquini, 1998)
is mounted on the MPG/ESO 2.2 m telescope and has R=48,000. All four systems
were observed by a minimum of two spectrographs and have at least 11
datapoints (see Table 2.2).

The HARPS data was reduced via the offline data reduction system (DRS) before
being cross-correlated with a binary mask to extract radial velocities
(Baranne et al., 1996). For NGTS-24 and NGTS-23 a G2 mask was used whereas a
G9 mask and a K0 mask were used for HATS-54 and NGTS-25, respectively. This
procedure was also employed for the CORALIE data, for which the spectra were
reduced using the standard CORALIE DRS. For the data collected with FEROS, the
CERES reduction pipeline (Brahm et al., 2017) performed a radial velocity
extraction by the same method.

All four targets had semi-amplitudes consistent with a Jupiter-mass companion
($K$ $\sim$ 100 $\rm{m\,s^{-1}}$) and had variations in phase with the derived
period from the photometric data. We investigated whether there were any
correlations between the line bisector (BIS) of the CCF to ensure that the
signals were of planetary origin and did not arise from stellar activity (e.g.
stellar spots) or a blended eclipsing binary (Queloz et al., 2001b). No
evidence was found to contradict the existence of a planetary companion.

Table 2: Summary of the spectroscopic observations.
$\mathrm{SNR_{\rm{combined}}}$ is the SNR of the co-added spectra that were
used in the analysis outlined in Section 3.

Target | Instrument | Nights Observed | Nspectra | $\mathrm{SNR}_{\mathrm{combined}}$ | Programme
---|---|---|---|---|---
NGTS-23 | HARPS | 2019/09/12 – 2020/01/20 | 7 | 29.13 | 0104.C-0588
FEROS | 2018/12/24 – 2020/01/04 | 8 | - | 0102.A-9011 & 0103.A-9004
& 0103.C-0719 & 0104.A-9012
CORALIE | 2018/10/27 – 2018/11/06 | 3 | - | N/A
NGTS-24 | FEROS | 2019/12/30 – 2020/01/04 | 6 | - | 0104.A-9012
CORALIE | 2019/04/22 – 2019/12/26 | 5 | - | N/A
NGTS-25 | HARPS | 2021/06/12 – 2021/09/13 | 12 | 20.92 | 105.20G9
CORALIE | 2019/08/09 – 2021/08/22 | 2 | - | N/A
HATS-54 (NGTS-22) | HARPS | 2019/05/10 – 2019/06/08 | 5 | 26.45 | 0103.C-0719
FEROS | 2019/04/18 – 2019/04/26 | 8 | - | 0103.A-9004
CORALIE | 2019/02/23 – 2019/04/28 | 6 | - | N/A

(a) NGTS-23

(b) NGTS-24

(c) NGTS-25

(d) HATS-54 (NGTS-22)

Figure 2: Phase-folded radial velocity measurements for NGTS-23, NGTS-24,
NGTS-25, and HATS-54 (NGTS-22). These include data obtained from HARPS (blue
points), FEROS (green points) and CORALIE (orange points). HARPS spectroscopy
used by the HATS team is shown in peak while the FEROS spectroscopy used by
HATS is shown in brown. The radial velocity model is shown by the solid black
line. The residuals are shown below the radial velocity measurements.

##  3 Analysis

The measured planetary parameters are dependent on the characterisation of the
host star. Therefore, accurately constraining the properties of the host star
is vital to determine accurate planetary parameters.

###  3.1 Stellar Analysis

Most of our stellar parameters were obtained by fitting the spectral energy
distributions (SEDs). However, to obtain suitable priors to constrain the SED
fits, we first analysed spectra for each object. For the spectral analysis we
used the open source framework iSpec (Blanco-Cuaresma et al., 2014; Blanco-
Cuaresma, 2019). iSpec allows users to choose from a list of models for
spectral synthesis. We chose to employ the spectrum (Gray & Corbally, 1994)
radiative transfer code and the solar abundance model from Asplund et al.
(2009). Additionally, we use the Gaia-ESO Survey (GES) line list (version 6.0
- Heiter et al., 2021), which covers most of the wavelength range of our
spectra (420-920nm), and the MARCES.GES model atmosphere (Gustafsson et al.,
2008).

We used our high-resolution HARPS data for the analysis of NGTS-23, NGTS-25
and HATS-54. For each object, we shift the spectra to the laboratory frame of
reference before co-adding them to produce a high signal-to-noise ratio (SNR)
combined spectrum. The SNRs of these spectra are reported in Table 2.2. For
NGTS-24, we attempted to follow a similar procedure using the CORALIE/FEROS
spectra. However, the SNR of the co-added CORALIE spectra were too low to
obtain meaningful results. For FEROS, the Th-Ar lamp used for calibration
appears to have contaminated the stellar spectrum. Therefore, we are unable to
use the FEROS spectra for spectral analysis but they still yield reliable
results for the radial velocity measurements.

We determined the stellar effective temperature, (${T_{\rm{eff}}}$) and the
surface gravity (${log\,g}$), via fits to the the H$\alpha$, NaI D and MgI b
lines whereas FeI and FeII lines were used to determine the metallicity
(${[Fe/H]}$), alpha enhancement ($[\alpha/Fe]$), microscopic velocity
(${v_{\rm{mic}}}$), macroscopic velocity (${v_{\rm{mac}}}$) and the rotational
line-of-sight broadening (${v{sini}_{*}}$).

####  3.1.1 Gaia DR3

For all four objects, we obtained additional photometric and astrometric data
from Gaia DR3 (Gaia Collaboration et al., 2016; Gaia Collaboration, 2022).

Our host stars show no evidence of being unresolved binaries, with all four
targets having an astrometric excess noise of approximately zero as well as a
low astrometric goodness of fit in the along-scan direction (GOF_AL) in Gaia
DR3 (Evans, 2018) and RUWE (re-normalised unit weight error) of approximately
one. They also pass the photometric filtering processes outlined by Arenou et
al. (2018) to identify blended stars.

The Gaia positions, proper motions, and absolute radial velocities of each
star were used to determine the Galactic velocity components ($U_{\rm
LSR},V_{\rm LSR},W_{\rm LSR}$), assuming a Local Standard of Rest of
UVW=(11.1, 12.14, 7.25 $\rm km\,s^{-1}$ \- Schönrich et al. 2010). By using
the selection criteria for kinematically thin-disk ($v_{\rm tot}$ < 50 $\rm
km\,s^{-1}$) and kinematically thick-disk (70 < $v_{\rm tot}$ < 180 $\rm
km\,s^{-1}$) objects (Gaia Collaboration et al., 2018), we conclude that three
of the stars belong to the thin disk population while NGTS-23 is in-between
the two populations. This appears consistent with our determination that
NGTS-23 is the only metal-poor star out of our systems (see Table 4).

Table 3: The galactic velocity components and total space velocities for the four systems presented in this paper. Target | $\mathrm{U_{LSR}},\mathrm{V_{LSR}},\mathrm{W_{LSR}}({km\,s^{-1}})$ | ${v_{\rm{tot}}}({km\,s^{-1}})$
---|---|---
NGTS-23 | -54.39, 19.95, -1.52 | 57.95
NGTS-24 | 5.11, 25.74, 2.54 | 26.37
NGTS-25 | -14.40, 27.52, 11.98 | 33.29
HATS-54 (NGTS-22) | 31.40, -38.39, -4.24 | 49.78

####  3.1.2 SED fitting

We performed fits to the SEDs of each object to obtain the stellar parameters
for each system. For this, we employed the Python tool ARIADNE (Vines &
Jenkins, 2022). ARIADNE fits catalogue photometry to different atmospheric
model grids such as Phoenix V2 (Husser et al., 2013), BT-Settl, BT-Cond, BT-
NextGen (Allard et al., 2012; Hauschildt et al., 1999), Castelli & Kurucz
(2004), and Kurucz (1993).

The SEDs were modelled by interpolating the model grids in ${T_{\rm{eff}}}$ –
${\log\,g}$ – ${[Fe/H]}$ space. Any underestimated uncertainties in the
photometry were accounted for by including an excess noise term. Gaussian
priors for ${T_{\rm{eff}}}$, ${\log\,g}$, and ${[Fe/H]}$ were taken from our
stellar analysis with iSpec (see Table 4), whilst Gaussian priors for the
stellar radius and distance were obtained from the Gaia DR2/DR3 values,
although we used an inflated value for the radius error. For NGTS-24b, we used
values from Gaia but with inflated errors as were were not able to obtain
results using iSpec. Inflated errors were chosen so as not to unnecessarily
bias the results from ARIADNE. In addition, $A_{V}$ was limited to the maximum
line-of-sight value taken from galactic dust maps (Schlegel et al., 1998;
Schlafly & Finkbeiner, 2011). The priors for the excess noise parameters were
set to a normal distribution with a mean of zero and a variance equal to five
times the associated uncertainty. The mass value was estimated from MIST
isochrones (Choi et al., 2016) using the previously derived values. The
derived stellar parameters are listed in Table 4.

Table 4: Stellar properties of the four systems. The second last column contains the stellar parameters for HATS-54 from the discovery paper (Espinoza et al., 2019). The final column gives the data source, for which the following references are given: 2MASS (Skrutskie et al., 2006); APASS (Henden & Munari, 2014); Gaia (Gaia Collaboration et al., 2016, 2018; Gaia Collaboration, 2022); WISE (Wright et al., 2010); TIC8 (Stassun et al., 2019). ∗ denotes that, for NGTS-24b, ARIADNE was used instead of iSpec for reasons outlined in Section 3.1. Property |  NGTS-23 |  NGTS-24 |  NGTS-25 | HATS-54 (NGTS-22) |  Source
---|---|---|---|---|---
|  |  |  |  Updated |  Discovery |
|  |  |  |  |  |
2MASS ID |  J04414374-4002404 |  J11141533-3754365 |  J20294038-3901565 |  J13223237-4441196 |  – |  2MASS
GAIA Source ID |  4816462091938129408 |  5397086969654628864 |  6682513094425008640 |  6087996849371141248 |  – |  Gaia DR2
TIC ID |  77287067 |  151920165 |  290742484 |  363851359 |  – |  TIC8
R.A. |  $04^{h}41^{m}43.6^{s}$ |  $11^{h}14^{m}15.3^{s}$ |  $20^{h}29^{m}40.3^{s}$ |  $13^{h}22^{m}32.4^{s}$ |  – |  Gaia DR3
DEC |  $-40^{\circ}02^{\prime}41.0"$ |  $-37^{\circ}54^{\prime}36.5"$ |  $-39^{\circ}01^{\prime}55.5"$ |  $-44^{\circ}41^{\prime}20.0"$ |  – |  Gaia DR3
$\mu_{RA}({mas\,y^{-1}})$ |  0.86±0.01 |  -0.69±0.01 |  5.17±0.02 |  -3.50±0.02 |  – |  Gaia DR3
$\mu_{DEC}({mas\,y^{-1})}$ |  12.27±0.02 |  0.57±0.01 |  6.03±0.02 |  -7.96±0.02 |  – |  Gaia DR3
Parallax (mas) |  0.95±0.01 |  1.39±0.01 |  1.90±0.02 |  1.36±0.02 |  – |  Gaia DR3
|  |  |  |  |  |
|  |  |  |  |  |
V (mag) |  14.010±0.062 |  13.192±0.063 |  14.266±0.048 |  13.914±0.027 |  – |  APASS
B (mag) |  14.578±0.024 |  13.948±0.053 |  15.146±0.052 |  14.710±0.070 |  – |  APASS
g (mag) |  14.291±0.028 |  13.561±0.014 |  14.656±0.048 |  14.258±0.045 |  – |  APASS
r (mag) |  13.940±0.049 |  13.007±0.011 |  14.000±0.049 |  13.694±0.041 |  – |  APASS
i (mag) |  13.845±0.043 |  12.799±0.051 |  13.844±0.092 |  13.497±0.074 |  – |  APASS
G (mag) |  13.9406±0.0002 |  13.0410±0.0002 |  14.0742±0.0003 |  13.7621±0.0003 |  – |  Gaia DR3
J (mag) |  13.056±0.023 |  11.879±0.019 |  12.818±0.019 |  12.611±0.021 |  – |  2MASS
H (mag) |  12.797±0.024 |  11.577±0.022 |  12.417±0.020 |  12.273±0.024 |  – |  2MASS
K (mag) |  12.730±0.035 |  11.510±0.019 |  12.324±0.022 |  12.170±0.017 |  – |  2MASS
W1 (mag) |  12.710±0.024 |  11.455±0.023 |  12.287±0.023 |  12.157±0.023 |  – |  WISE
W2 (mag) |  12.744±0.023 |  11.505±0.020 |  12.328±0.024 |  12.165±0.023 |  – |  WISE
T (mag) |  13.586±0.006 |  12.570±0.006 |  13.546±0.006 |  13.276±0.006 |  – |  TIC8
|  |  |  |  |  |
|  |  |  |  |  |
Spectral Type |  F9V |  G2IV |  K0V |  G6V |  – |  ARIADNE
${T_{\rm{eff}}}$ |  6057±64 |  5820${}^{+93}_{-8}$ |  5321±58 |  5621±70 |  5702±26 |  iSpec∗
${log\,g}$ |  4.04±0.15 |  4.09${}^{+0.05}_{-0.04}$ |  4.48±0.14 |  4.20±0.20 |  4.240±0.023 |  iSpec∗
$[Fe/H]$ |  -0.26±0.11 |  0.27${}^{+0.18}_{-0.03}$ |  0.12±0.05 |  0.37±0.07 |  0.396±0.031 |  iSpec∗
$[\alpha/Fe]$ |  0.07±0.17 |  – |  -0.08±0.10 |  -0.15±0.10 |  – |  iSpec
$v\sin i$ (km$\,\rm{s}^{-1}$) |  1.46±1.08 |  – |  1.96±0.68 |  <2.50 |  3.83±0.42 |  iSpec
${v_{\rm{mic}}}$ (km$\,\rm{s}^{-1}$) |  1.24±0.20 |  – |  0.89±0.21 |  0.88±0.23 |  0.948±0.034 |  iSpec
${v_{\rm{mac}}}$ (km$\,\rm{s}^{-1}$) |  5.71±0.84 |  – |  3.24±0.78 |  4.49±0.68 |  3.61±0.11 |  iSpec
$R_{*}(R_{\odot})$ |  1.24±0.03 |  1.64${}^{+0.03}_{-0.09}$ |  0.86${}^{+0.02}_{-0.05}$ |  1.23±0.02 |  1.317±0.036 |  ARIADNE
$M_{*}(M_{\odot})$ |  1.01${}^{+0.06}_{-0.07}$ |  1.26${}^{+0.05}_{-0.21}$ |  0.91${}^{+0.03}_{-0.04}$ |  1.05±0.05 |  1.097±0.022 |  ARIADNE
$\rho_{*}(\rm{g\,cm^{-3}})$ |  0.755${}^{+0.027}_{-0.034}$ |  $0.406\pm 0.059$ |  2.219${}^{+0.085}_{-0.110}$ |  $0.795\pm 0.052$ |  0.678±0.054 |  Joint Model
$L_{*}(L_{\odot})$ |  1.920${}^{+0.093}_{-0.106}$ |  2.792${}^{+0.215}_{-0.289}$ |  0.511${}^{+0.045}_{-0.052}$ |  1.302${}^{+0.049}_{-0.055}$ |  1.631${}^{+0.114}_{-0.076}$ |  ARIADNE
$d$ (pc) |  991${}^{+19}_{-23}$ |  725${}^{+33}_{-28}$ |  517${}^{+18}_{-22}$ |  720${}^{+11}_{-12}$ |  769±21 |  ARIADNE
$A_{v}$ (mag) |  0.019${}^{+0.029}_{-0.016}$ |  0.249${}^{+0.035}_{-0.067}$ |  0.077${}^{+0.061}_{-0.054}$ |  0.114${}^{+0.042}_{-0.038}$ |  0.279±0.018 |  ARIADNE
Age (Gyrs) |  6.39${}^{+1.93}_{-1.60}$ |  4.77${}^{+3.56}_{-0.91}$ |  3.49${}^{+3.49}_{-3.37}$ |  7.96${}^{+2.97}_{-2.26}$ |  6.60±0.76 |  ARIADNE

####  3.1.3 Stellar Rotation

As well as modelling the stellar parameters, we also wished to constrain the
stellar rotation period. Coupled to a knowledge of the stellar radius and
${v\rm{sini}_{*}}$, determination of the stellar rotation period can then
allow constraints to be placed on the inclination angle of the stellar
rotation axis. This can enable misaligned star-planet systems to be identified
(Watson et al., 2010).

The first method used to constrain the rotation period was to
spectroscopically measure the chromospheric activity of the star. Using the
formulae described in Lovis et al. (2011), the log$\,\rm{R^{\prime}_{HK}}$ was
measured from the co-added HARPS spectra used in Section 3.1. Therefore, the
only system we were not able to obtain a log$\,\rm{R^{\prime}_{HK}}$ value for
was NGTS-24b. From these co-added spectra, we found
log$\,\rm{R^{\prime}_{HK}}$ values of -5.43, -4.61 and -4.74 for NGTS-23,
NGTS-25 and HATS-54, respectively. Using the relation from Noyes et al.
(1984), the most probable stellar rotation periods are predicted to be 27 days
for NGTS-23, 24 days for NGTS-25 and 29 days for HATS-54.

Our second approach used the ${v\,{\sin i}_{*}}$ of the star measured from
iSpec. By assuming that the stellar inclination angle, $i_{*}$, is 90° (i.e.
$\sin i_{*}$=1), an upper limit can be placed on the stellar rotation period
when the stellar radius is known. NGTS-23 and NGTS-25 were found to have a
${v\,{\sin i}_{*}}$ of 1.46±1.08 km$\,\rm{s}^{-1}$ and 1.96±0.68
km$\,\rm{s}^{-1}$ respectively, which correspond to upper limits of the
rotation periods of 43±32 days and 22±8 days. We were only able to obtain an
upper-limit to the ${v\,{\sin i}_{*}}$ for HATS-54, finding it to be <2.50
km$\,\rm{s}^{-1}$. This corresponds to an upper limit of 25 days. However, if
the value of ${v\,{\sin i}_{*}}$ is lower then this upper limit will increase,
which means that HATS-54 is likely a slow rotator. These are consistent with
the previous estimates from the log$\,\rm{R^{\prime}_{HK}}$ and appear
consistent with the age and spectral types of the stars.

Finally, we searched the Generalised Lomb-Scargle periodograms (Lomb, 1976;
Scargle, 1982; Zechmeister & Kürster, 2009) of the NGTS photometry after the
transits were removed (see appendix 8 for plots). NGTS-23 has significant
peaks at approximately 15 days and 33 days. The 33 day peak is more consistent
with the previous estimate of 27 days from the log$\,\rm{R^{\prime}_{HK}}$.
The most significant peak for NGTS-24 is at approximately 30 days. However, it
is possible that this peak is indicative of the moon contaminating the
photometry. However, given that the next most significant peak is about 47
days, it appears likely that NGTS-24 is slowly rotating. NGTS-25 has peaks in
the periodogram at approximately 14 days and 28 days, which could be caused by
moonlight in the photometry. There is also a significant peak between 40 and
50 days but this is not consistent with the upper limit from the ${v\,\sin
i_{*}}$ and the estimate of 24 days from the log$\,\rm{R^{\prime}_{HK}}$ so it
is unlikely to correspond with the rotation period. Finally, HATS-54 has
numerous significant peaks. There is a significant peak at roughly 27 days,
which is broadly consistent with the previous estimates. We conclude, like the
other stars presented in this paper, that HATS-54 is slowly rotating.

As a final check, we explored alternative methods, including autocorrelation
and GP regression in addition to LS periodogram (Gillen et al., 2020), via the
Rotation Toolkit (RoTo)333https://github.com/joshbriegal/roto, but do not
detect clear rotation patterns beyond the aforementioned suggestive signals.

####  3.1.4 Stellar Properties

Using the parameters obtained for the stellar radii, masses, effective
temperatures and luminosities, we can compare our host stars to the general
population of stars that host planets, where the planets have defined masses
and radii. This is a sample of approximately 950 stars, and a stellar mass-
radius diagram and a Hertzsprung-Russell diagram can be seen in Figures 3 and
4, respectively.

Figure 3: Stars that host exoplanets with defined radii and masses (grey
points) with errorbars suppressed for clarity. The stars presented in this
paper are plotted as coloured points with errorbars. It can be seen that three
of the stars presented in this paper lie in relatively sparse regions of
(stellar) mass-radius space while NGTS-25 lies in the general population. The
stellar sample was obtained from the NASA Exoplanet Archive
(https://exoplanetarchive.ipac.caltech.edu/).  Figure 4: A Hertzsprung-Russell
diagram for the same stellar sample described in Figure 3. The errorbars are
suppressed for clarity. The stars presented in this paper are plotted as
coloured points with errorbars. Of particular note is NGTS-24, which appears
to be beginning to transition off the main-sequence. HATS-54 also appears to
be towards the end of its main-sequence lifetime.

From these figures, it appears that NGTS-25 is on the main-sequence and lies
in the general population of stars. NGTS-23 and HATS-54 both occupy a sparse
region of mass-radius parameter space. Finally, NGTS-24 is in an even less
populated region of mass-radius space and appears to be transitioning off the
main-sequence if it has not already done so. This appears a reasonable
conclusion given its age and spectral type (see Table 4). Therefore, it is an
interesting target given the rarity of hot Jupiters around sub-giant stars
(Villaver & Livio, 2009; Hansen, 2010; Schlaufman & Winn, 2013). We also
conclude that HATS-54 and NGTS-23 are both towards the end of their lifetimes
on the main-sequence and will evolve off the main-sequence within a few Gyrs.
Again, this seems to be in good agreement with their ages and spectral type.
These conclusions are further supported from the findings in Section 4.1, in
which all three stars show significant evolution within relatively short
periods of time.

###  3.2 Global Modelling

We determined the physical parameters of the systems, including planet radius
and mass, via a simultaneous fit to the photometric and spectroscopic data
using the open-source astronomy software package allesfitter (Günther &
Daylan, 2019, 2021). allesfitter combines the packages ellc (light curve and
RV models; Maxted 2016), emcee (MCMC sampling; Foreman-Mackey et al. 2013),
dynesty (nested sampling; Speagle 2020), and celerite (Gaussian Process (GP)
models; Foreman-Mackey et al. 2017). This combination allows allesfitter to
model a variety of signals, including stellar variability and transit-timing
variations.

Given the length of time for the initial MCMC fits to converge, a nested
sampling approach was taken to produce the global fits. However, quick MCMC
fits (100 walkers and 5000 steps) to the NGTS data were used to refine priors
on parameters such as transit epoch and transit depth. Gaussian priors were
placed on the stellar mass, radius and temperature using the results from the
SED fitting (see Table 4). We adopted a quadratic limb darkening law for the
photometric data as parameterized in Kipping (2013). Gaussian processes with a
Matern 3/2 kernel were used to fit any out-of-transit variability and for this
reason we removed lightcurves from the final models that did not have a
sufficient out-of-transit baseline. Therefore, for NGTS-23b we did not include
the EulerCam data or the SAAO 1.0 m data in our final fits, while for HATS-54b
we did not use the EulerCam data taken on the 2019/03/25 or either night of
the photometry taken by the SAAO 1.0 m in our final fits. Transits that were
not included in the final models can be found in appendix 7 for completeness.
However, for HATS-54b we made use of both photometry and radial velocity
measurements from Espinoza et al. (2019) in our global models. Furthermore, as
multiple spectrographs were used to obtain radial velocity measurements for
each system, we fit for a constant instrumental velocity offset for each
spectrograph.

For each system, we ran multiple fits before performing our final fit. We
first tested removing RV points that were measured during transit as these
points could have been affected by the Rossiter-McLaughlin effect (Rossiter,
1924; McLaughlin, 1924). We found that removing these points did not
significantly alter the results and therefore these in-transit RV points were
included in the final fits.

Finally, we ran two additional fits for each planet – one where the planet was
fixed on a circular orbit (i.e. $e=0$), and another where the eccentricity was
allowed to vary freely. Each of the latter fits resulted in non-zero
eccentricity values. However, many small eccentricity values are spurious and
Lucy & Sweeney (1971) define a probabilistic test to determine whether a small
e is statistically significant from 0. By adopting a 5$\%$ level of
significance, they find that if the condition $e>2.45\,\sigma_{e}$ is
satisfied (where $\sigma_{e}$ is the observational uncertainty on $e$), then
one can be confident that the measured eccentricity is real. We find that all
of our measurements fail to meet this criteria, and we therefore fixed the
eccentricity to be zero in our final fits. This is in-line with both
theoretical predictions, and the observed population of hot Jupiters, where
orbital eccentricity is often consistent with zero (e.g. Anderson et al.,
2012).

We use allesfitter to fit our data for the key physical parameters of each
system, including the planet’s orbital period $P$, the radius ratio
$R_{P}$/$R_{*}$, and the radial velocity semi-amplitude $K$. A full list of
physical properties and their values for each planet can be found in Table 5.
Figure 1 shows the phase-folded lightcurves for each object. Similarly, the
phase-folded radial velocity data for each star is shown in Figure 2.

Table 5: Planetary parameters for the four systems presented in this paper. The final 2 columns display the updated planetary parameters for HATS-54b/NGTS-22b alongside those from the discovery paper (Espinoza et al., 2019). Property |  NGTS-23b |  NGTS-24b |  NGTS-25b | HATS-54b / NGTS-22b
---|---|---|---|---
|  |  |  |  Updated |  Discovery
|  |  |  |  |
$P$ (days) |  $4.0764326\pm 0.0000041$ |  $3.4678796\pm 0.0000070$ |  $2.8230930\pm 0.0000033$ |  2.5441765±0.0000024 |  2.5441828±0.0000043
$T_{C}$ (BJD) |  $2458431.77134\pm 0.00048$ |  $2458100.6229\pm 0.0011$ |  $2458204.26373\pm 0.00050$ |  2457780.01023±0.00061 |  2457780.01102±0.00089
$T_{14}$ (hours) |  $3.919\pm 0.031$ |  2.929${}^{+0.095}_{-0.083}$ |  $2.466\pm 0.025$ |  2.468${}^{+0.044}_{-0.041}$ |  2.5008±0.0456
$R_{\rm P}/R_{*}$ |  0.1048${}^{+0.0011}_{-0.0011}$ |  0.0768${}^{+0.0028}_{-0.0023}$ |  0.1231${}^{+0.0011}_{-0.0013}$ |  0.0848±0.0014 |  0.0832±0.0025
$a/R_{*}$ |  8.72${}^{+0.10}_{-0.13}$ |  6.37${}^{+0.29}_{-0.31}$ |  9.78${}^{+0.12}_{-0.16}$ |  6.48±0.14 |  6.15±0.16
$b$ |  0.134${}^{+0.094}_{-0.091}$ |  0.821±0.026 |  0.113${}^{+0.097}_{-0.072}$ |  0.715${}^{+0.024}_{-0.026}$ |  0.740${}^{+0.022}_{-0.023}$
$i$ $(\degree)$ |  89.12${}^{+0.53}_{-0.64}$ |  82.61${}^{+0.52}_{-0.61}$ |  89.34${}^{+0.42}_{-0.58}$ |  83.67±0.34 |  83.08±0.36
$e$ |  0 (fixed) |  0 (fixed) |  0 (fixed) |  0 (fixed) |  <0.126
$K$ $(\rm{km\,s^{-1}})$ |  $0.078\pm 0.011$ |  0.062${}^{+0.011}_{-0.010}$ |  $0.100\pm 0.006$ |  0.108±0.006 |  0.105±0.014
$R_{P}({R_{\rm J}})$ |  $1.267\pm 0.030$ |  1.214${}^{+0.058}_{-0.062}$ |  1.023${}^{+0.035}_{-0.052}$ |  1.015±0.024 |  1.067±0.052
$M_{P}({M_{\rm J}})$ |  0.613±0.097 |  0.520${}^{+0.120}_{-0.110}$ |  0.639${}^{+0.058}_{-0.052}$ |  0.753±0.057 |  0.76±0.10
$\rho_{P}$ $(\rm{g\,cm^{-3}})$ |  0.373${}^{+0.070}_{-0.064}$ |  0.359${}^{+0.120}_{-0.087}$ |  0.892${}^{+0.099}_{-0.089}$ |  0.940${}^{+0.120}_{-0.110}$ |  0.77±0.16
$a$ (au) |  0.0504±0.012 |  0.0479${}^{+0.0028}_{-0.0030}$ |  0.0388${}^{+0.0014}_{-0.0020}$ |  0.0370±0.0010 |  0.03763±0.00024
${T_{\rm{eq}}}$ (K) |  1327${}^{+17}_{-16}$ |  1499${}^{+41}_{-36}$ |  1101${}^{+15}_{-14}$ |  1429±24 |  1625±22
$\rm{Irradiation}\,(\rm{W\,m^{-2}})$ |  (1.03±0.07)$\times 10^{6}$ |  (1.66${}^{+0.24}_{-0.26}$)$\times 10^{6}$ |  (4.62${}^{+0.63}_{-0.57}$)$\times 10^{5}$ |  (1.29${}^{+0.08}_{-0.09}$)$\times 10^{6}$ |  (1.57${}^{+0.09}_{-0.08}$)$\times 10^{6}$

##  4 Results and discussion

All the planets presented in this work have radii between 1.02 - 1.27 ${R_{\rm
J}}$ and masses between 0.52 - 0.75 ${M_{\rm J}}$. This places them in the
general population of hot Jupiters (Figure 5), with planetary bulk densities
ranging from 0.359 $\rm{g\,cm^{-3}}$ to 0.940 $\rm{g\,cm^{-3}}$.

Figure 5: Exoplanets with defined masses and radii (grey points) with
errorbars suppressed for clarity. The planets presented in this paper are
plotted as coloured points with errorbars. All four planets presented are
found to lie within the general population of hot Jupiters. The exoplanet
sample was obtained using the NASA Exoplanet Archive
(https://exoplanetarchive.ipac.caltech.edu/)

Our stellar parameters for HATS-54 (NGTS-22) are generally in good agreement
with those from Espinoza et al. (2019). $T_{\mathrm{eff}}$, ${\log\,g}$,
$M_{*}$, $[Fe/H]$ and ${v_{\rm{mic}}}$ all agree within the error bars. The
radius values are within $2\sigma$ while the luminosity values are within
$3\sigma$. There are significant differences between the ${v\,{\sin i}_{*}}$
and ${v_{\rm{mac}}}$ values reported in the discovery paper and the values
determined in this work. However, as Espinoza et al. (2019) assumed a
${v_{\rm{mac}}}$ value that is lower than the value in this paper, this will
result in a larger ${v\,{\sin i}_{*}}$ due to the degeneracy between the two
properties. Given the age and spectral type of HATS-54, our slowly rotating
value seems more appropriate. There was also disagreement on the extinction
values but the value from Espinoza et al. (2019) is high given the limit from
both Schlegel et al. (1998) and Schlafly & Finkbeiner (2011).

The planetary parameters obtained for HATS-54b (NGTS-22b) are in good
agreement with those reported in the discovery paper. Most of the values agree
within error bars but $a/R_{*}$ and the impact parameter, $b$, differ by less
than $2\sigma$. However, the main difference is that Espinoza et al. (2019)
could only constrain $e<0.126$ whereas we fixed $e=0$ as non-zero eccentricity
is likely spurious given that our eccentric models returned an eccentricity
value of ${e}=0.023{\raisebox{2.15277pt}{\tiny${}^{+0.033}_{-0.017}$}}$.

###  4.1 Orbital Decay Time-scales

Given the late age of two of our systems (NGTS-24 and HATS-54), we thought it
useful to calculate the orbital decay time-scales for our planets. We use the
following equation to calculate the rate of orbital decay (Goldreich & Soter,
1966; Ogilvie, 2014; Patra et al., 2020):

$\frac{dP}{dt}=-\frac{27\pi}{2Q^{\prime}_{*}}\left(\frac{M_{p}}{M_{*}}\right)\left(\frac{R_{*}}{a}\right)^{5}$
(1)

where $Q^{\prime}_{*}=3Q_{*}/2k_{2}$. $Q_{*}$ and $Q^{\prime}_{*}$ are the
tidal quality factor and the reduced tidal quality factor, respectively, while
$k_{2}$ is the dimensionless quadrupolar Love number. We also only consider
the equilibrium tide within the convection zone in this analysis as none of
our systems satisfy the criterion for the dynamical tide to be considered.
This is because the inertial waves (that constitute the dynamical tide) are
only excited if the orbital period is twice the stellar rotation period (i.e.
${P_{\rm{orb}}}>P_{*}/2$). Therefore, for our analysis, we can use
$Q^{\prime}_{*}$ as defined in Strugarek et al. (2017).444This analysis
requires the depth of the convection zone. Therefore the radius and mass of
the core were determined using
http://www.astro.wisc.edu/~townsend/static.php?ref=ez-web

Using the orbital period and the rate of decay, we are able to make a
prediction for the length of time for the planetary orbit to decay completely
(i.e. where its orbital period is zero). This assumes a constant rate of decay
and thus will likely over-estimate the time taken for the orbit to decay. We
also have ignored the effects of stellar wind which would likely decrease the
inspiral time as well. Finally, as the star evolves off the main-sequence the
tidal quality factor can change by orders of magnitude, which dramatically
impacts the decay time. This could in-part explain the lack of hot Jupiters
observed around sub-giant stars (Villaver & Livio, 2009; Hansen, 2010;
Schlaufman & Winn, 2013).

A summary of all the estimated decay time-scales can be found in Table 6.
Although we have estimated the rate of decay for these systems, we are likely
unable to measure these due to their long decay time-scales. For example, the
observed orbital decay rate of WASP-12b is several orders of magnitude higher
than for any of the stars presented here (Maciejewski et al., 2016; Patra et
al., 2017; Yee et al., 2020). The long orbital decay time-scales, while an
estimation, suggest that all four planets are in a relatively stable
configuration while the respective host star remains on the main-sequence.

However, we see that when the star evolves, the orbital decay time-scale
rapidly decreases, which agrees with the observations that there is a lack of
hot Jupiters around sub-giant stars. Of particular interest is NGTS-24b as its
host star will soon evolve off the main-sequence if it is not already doing
so. There is some tentative evidence to suggest that NGTS-24b is already
beginning to evolve off the main-sequence (see Table 4 and Figure 4).
Therefore, we expect that the star will change significantly within 500
million years causing the inspiral time to reduce significantly. This leads to
the planet being engulfed within 600 million years. For comparison, HATS-54
will take 2 billion years before it evolves to a stage where it will have a
similar inspiral time.

Table 6: Summary of the decay time-scales for the four planets presented in this paper. In column 2, "Age", we list two values for each star. The first is the stellar age estimation from Table 4. For comparison, the second value indicates the age at which the star is estimated to begin evolving off of the main-sequence. For NGTS-25b, this later age was decided to be 10 Gyrs older than its determined age. ${M_{\rm{c}}}$ and ${R_{\rm c}}$ are the mass and radius of the core respectively. $Q^{\prime}_{*}$ is the reduced tidal quality factor, $\frac{dP}{dt}$ is the rate of orbital decay and $t_{a}$ is the associated time for the planetary orbit to decay. The stellar rotation period was assumed to be 30 days in each scenario. We note that the assumption of an incorrect stellar rotation period does not affect the results much unless the true period is $<<$1day. Star | Age (Gyrs) |  $M_{*}$ (${M_{\odot}}$) |  $R_{*}$ (${R_{\odot}}$) |  $L_{*}$ (${L_{\odot}}$) |  ${M_{\rm c}}$ (${M_{\odot}}$) |  ${R_{\rm c}}$ (${R_{\odot}}$) | $Q^{\prime}_{*}$ | $\frac{dP}{dt}$ |  $t_{a}$ (Gyrs)
---|---|---|---|---|---|---|---|---|---
NGTS-23 | 6.39 | 1.01 | 1.24 | 1.920 | 1.00 | 0.95 | 6.49$\times 10^{6}$ | -7.43$\times 10^{-14}$ | 150
8.89 | 1.01 | 2.32 | 3.371 | 0.63 | 0.94 | 3.15$\times 10^{5}$ | -3.51$\times 10^{-11}$ | 0.32
NGTS-24 | 4.77 | 1.26 | 1.64 | 2.792 | 1.23 | 1.18 | 2.43$\times 10^{6}$ | -7.02$\times 10^{-13}$ | 14
5.27 | 1.26 | 2.94 | 4.485 | 0.52 | 0.93 | 3.16$\times 10^{5}$ | -1.00$\times 10^{-10}$ | 0.09
NGTS-25 | 3.49 | 0.91 | 0.86 | 0.511 | 0.88 | 0.57 | 1.06$\times 10^{7}$ | -3.12$\times 10^{-14}$ | 248
13.49 | 0.91 | 1.06 | 0.912 | 0.87 | 0.70 | 4.60$\times 10^{6}$ | -2.05$\times 10^{-13}$ | 38
HATS-54 | 7.96 | 1.05 | 1.23 | 1.302 | 1.02 | 0.89 | 4.17$\times 10^{6}$ | -6.05$\times 10^{-13}$ | 12
(NGTS-22) | 9.96 | 1.05 | 2.11 | 2.360 | 0.66 | 0.88 | 4.98$\times 10^{5}$ | -7.54$\times 10^{-11}$ | 0.09

###  4.2 Inflation

Many hot Jupiters that are highly irradiated are observed to have low
densities (Laughlin et al., 2011; Weiss et al., 2013; Thorngren & Fortney,
2018). Previous studies have suggested that this is driven by inflation
mechanisms that become effective above an incident flux of approximately
$2\times 10^{5}\,\rm{W\,m^{-2}}$ (Demory & Seager, 2011; Miller & Fortney,
2011).

We calculated the irradiation received by each planet and found that all four
are irradiated above this threshold (see Table 5). Therefore, we would expect
that our planets might exhibit larger than expected radii due to inflation.

We follow the procedure laid out by Tilbrook et al. (2021) and Costes et al.
(2020), who utilise the work of Baraffe et al. (2008) (hereafter B08) and
Sestovic et al. (2018) (hereafter S18) to determine whether a planet is
inflated. Using the work from B08 we obtain estimated radii for non-inflated
planets that we can compare with expected inflated radii from S18.

B08 produced planetary evolution models that account for previous limitations,
such as quantifying the effect of metallicity. Notably, radius decreases with
increasing heavy element mass so by assuming a low metallicity of 0.02 - 0.1
for each planet, we are able to provide an upper limit for the non-inflated
radii. Differences between the predicted value and the observed radius could
indicate that inflation mechanisms have affected the radius.

S18 implement hierarchical Bayesian modelling and a forward model to infer
relationships between incident flux and radius. The increase in radius,
$\Delta R$, is also dependent on the mass of the planet. All four of the
planets presented in this paper fall into the same range (0.37 - 0.98 ${M_{\rm
J}}$), and we therefore use the corresponding equation to derive the expected
radius increase due to inflation for each:

$\centering\Delta R=0.70\times(\mathrm{log_{10}F}-5.5).\@add@centering$ (2)

The baseline radius in S18 is ${R_{\rm{base}}}=(0.98\pm 0.04)\>{R_{\rm J}}$
for this mass regime. Therefore, the inflated radius is calculated as:

${R_{\rm{inflated}}}=0.98+\Delta R.$ (3)

These inflated radii can then be compared with the derived radii from our
global models.

For NGTS-23b, the observed radius is consistent with the inflated radius as
predicted by S18 within error-bars. It is also larger than the estimated non-
inflated radius by more than $6\sigma$. It is therefore reasonable to conclude
that NGTS-23b is inflated. NGTS-24b has a radius greater than the estimated
non-inflated radius, but it is not as large as the expected inflated radius.
Although there is less than a $3\sigma$ difference between the observed radius
and the expected non-inflated radius, the model from S18 fails to predict the
behaviour. However, due to the high irradiation and the low planetary density
it is likely that this planet is inflated. Therefore, our results could be
indicative that density is a more suitable parameter than planetary radius to
determine whether a planet is inflated. HATS-54b has a radius that is
consistent with the non-inflated model and disagrees with the inflated
prediction by more than $6\sigma$. Therefore, it appears that HATS-54b is not
inflated. Finally, NGTS-25b is consistent with both inflated and non-inflated
predictions so we are not able to draw any firm conclusions for this planet.
However, this is not altogether surprising given that NGTS-25b has a lower
level of irradiation compared to the other planets presented in this paper. A
summary of the inflation results can be found in Table 7.

Table 7: Quantification of the inflation of the four planets. Note the masses in this table are not the true planetary masses but are the masses used to calculate the non-inflated radius. $\Delta$R is the expected change in radius caused by inflation mechanisms. Planet | Irradiation $(\rm{W\,m^{-2}})$ |  $M_{*}$ (${M_{\rm J}}$) |  $R_{\rm{non-inflated}}$ (${R_{\rm J}}$) |  $\Delta R$ (${R_{\rm J}}$) |  $R_{\rm{inflated}}$ (${R_{\rm J}}$) |  $R_{\rm{observed}}$ (${R_{\rm J}}$)
---|---|---|---|---|---|---
NGTS-23b | (1.03±0.07)$\times 10^{6}$ | 0.5 | 1.017-1.093 | 0.36${}^{+0.01}_{-0.02}$ | 1.34±0.04 | 1.27±0.03
NGTS-24b | (1.66${}^{+0.24}_{-0.26}$)$\times 10^{6}$ | 0.5 | 1.009-1.072 | 0.50±0.03 | 1.48±0.05 | 1.21±0.06
NGTS-25b | (4.62${}^{+0.63}_{-0.57}$)$\times 10^{5}$ | 0.5-1.0 | 1.009-1.186 | 0.12±0.03 | 1.10±0.05 | 1.02${}^{+0.04}_{-0.05}$
HATS-54b | (1.29${}^{+0.08}_{-0.09}$)$\times 10^{6}$ | 0.5-1.0 | 1.009-1.106 | 0.42±0.01 | 1.40±0.04 | 1.02±0.02
Figure 6: Exoplanets from the NASA Exoplanet Archive
(https://exoplanetarchive.ipac.caltech.edu/) with masses between 0.37 - 0.97
${M_{\rm J}}$. The purple dashed line shows the predicted ‘inflated’ radii
(Sestovic et al., 2018) with the associated standard deviation shown as dashed
brown lines. The hot Jupiters presented in this paper are plotted as coloured
points with errorbars.

Similar to the results from Tilbrook et al. (2021), our results are in tension
with the claim from S18 that there is not a population of non-inflated hot
Jupiters in the mass range 0.37-0.98 ${M_{\rm J}}$. Although all of the
incident fluxes are larger than the threshold for inflation ($2\times
10^{5}\,\rm{W\,m^{-2}}$ \- Demory & Seager, 2011; Miller & Fortney, 2011), it
appears that HATS-54b is not inflated. It is also unclear whether NGTS-24b and
NGTS-25b are inflated. Given that this is simply the minimum limit at which
planets begin to appear inflated and that the incident flux for NGTS-25b is
not much greater than this limit, it is not too surprising that NGTS-25b is
not inflated. However, as new evidence suggests that gaseous planets may
experience ‘reinflation’ as the star evolves off the main-sequence (Hartman et
al., 2016; Komacek et al., 2020; Thorngren et al., 2020, 2021), it is somewhat
surprising that NGTS-24b cannot be confirmed to be inflated as it experiences
relatively high levels of irradiation. Therefore, NGTS-24b may be an
interesting candidate to study to better understand the impact of additional
parameters on the mechanisms driving inflation.

In particular, metallicity might play an important role as, for the systems
reported in this paper, the only planet orbiting a metal-poor star was also
the only planet that agreed with the inflated radius predictions. This agrees
with the expectation that radii decrease as the fraction of heavy elements in
a planet increases (Thorngren et al., 2016). It is already known that hot
Jupiter radii vary with age (Baraffe et al., 2008; Miller et al., 2009;
Thorngren & Fortney, 2018), and additionally, differing system ages could
indicate a difference in planetary migration times, and therefore variations
in the level of stellar irradiation compared to what they currently
experience. The detailed effects of additional parameters, such as
metallicity, eccentricity and system age, are not yet fully understood.
However, they could potentially explain why planets may exhibit different
levels of radius inflation despite receiving similar levels of irradiation.

Furthermore, the number of known hot Jupiters has increased greatly since the
publication of S18, therefore it would be beneficial to have an updated model
with an aim of understanding the impact of various factors as this could
describe the inflation relationships more accurately. Understanding the
dependence on these parameters is crucial to determining the underlying
inflation mechanisms.

##  5 Conclusions

We report the discovery of three new hot Jupiters and the independent
detection of HATS-54b. Each planet was originally identified from photometry
from the Next Generation Transit Survey (NGTS), and was confirmed through
additional photometry with the Transiting Exoplanet Survey Satellite (TESS).
Other ground-based follow-up observations were carried out at the South
African Astronomical Observatory (SAAO) with the 1.0 m and 1.9 m telescopes,
as well as with EulerCam on the 1.2m Euler Telescope at La Silla Observatory.
Radial velocity measurements made with the HARPS, CORALIE and FEROS
spectrographs allowed for the masses of all four planets to be determined.

Spectral analysis via iSpec and SED fitting via ARIADNE revealed the
properties of the host stars in each system, which were found to be F, G or
K-type stars (see Table 4). We also attempted to constrain the rotation
periods of the stars and from this determined that the four stars were likely
to be slowly rotating. Global fits to the data were produced using the open-
source astronomy software package allesfitter. Our results for HATS-54b
(NGTS-22b) are consistent with the original discovery paper (Espinoza et al.,
2019). From the orbital decay time-scales of the 4 planets presented in this
paper, they all appear to be on stable orbits while the host star remains on
the main-sequence.

All four planets receive a level of irradiation above the minimum threshold
for the onset of planetary inflation mechanisms (Demory & Seager, 2011; Miller
& Fortney, 2011). Therefore, we sought to determine whether any of the planets
experienced inflation by comparing our derived radii with predictions from
evolutionary models (Baraffe et al., 2008). In addition, we examined the
predicted additional radius change due to inflation, $\Delta R$, through the
flux-mass-radius relations outlined in Sestovic et al. (2018). We found that
NGTS-23b is likely inflated while NGTS-24b is more likely to be inflated than
not inflated. NGTS-25b is consistent with both inflated and non-inflated
models so we are unable to determine whether it is inflated. HATS-54b is
unlikely to be inflated as it is consistent with the non-inflated models.

Finally, similar to Tilbrook et al. (2021), we note that there is a disparity
between some of our derived radii and those predicted by the inflationary
forward model of Sestovic et al. (2018). Through the inclusion of both new hot
Jupiter data and additional parameters, such as system age and heavy metal
fraction, the accuracy of inflationary parameterisation can be improved, which
would help improve our understanding of the physical processes behind the
inflation of hot Jupiters.

## Acknowledgements

Based on data collected under the NGTS project at the ESO La Silla Paranal
Observatory. The NGTS facility is operated by the consortium institutes with
support from the UK Science and Technology Facilities Council (STFC)
ST/M001962/1, ST/S002642/1 and ST/W003163/1. This study is based on
observations collected at the European Southern Observatory under ESO
programmes 0102.A-9011, 0103.A-9004, 0103.C-0719, 0104.A-9012, 0104.C-0588 and
105.20G9. We acknowledge the use of public TESS data from pipelines at the
TESS Science Office and at the TESS Science Processing Operations Centre. This
paper includes data collected with the TESS mission, obtained from the MAST
data archive at the Space Telescope Science Institute (STScI). Funding for the
TESS mission is provided by the NASA Explorer Program. STScI is operated by
the Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5–26555. This paper uses observations made at the South African
Astronomical Observatory (SAAO). JSJ greatfully acknowledges support by
FONDECYT grant 1201371 and from the ANID BASAL projects ACE210002 and
FB210003. JIV acknowledges support of CONICYT-PFCHA/Doctorado
Nacional-21191829. The contributions at the University of Warwick by PJW, RGW
and SG have been supported by STFC through consolidated grants ST/L000733/1
and ST/P000495/1. DJA acknowledges support from the STFC via an Ernest
Rutherford Fellowship (ST/R00384X/1). MNG acknowledges support from the
European Space Agency (ESA) as an ESA Research Fellow. JAGJ acknowledges
support from grants HST-GO-15955.004-A and HST-AR-16617.001-A from the Space
Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.
JAGJ acknowledges support from NASA under grant number 80NSSC22K0125 from the
TESS Cycle 4 Guest Investigator Program. The contributions of FB, ML, OT, and
SU have been carried out within the framework of the NCCR PlanetS supported by
the Swiss National Science Foundation under grants 51NF40_182901 and
51NF40_205606. ML also acknowledges support of the Swiss National Science
Foundation under grant number PCEFP2_194576. DGJ acknowledges the support of
the Department for Economy (DfE).

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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##  Appendix A Additional Photometry

(a) Additional Photometry for NGTS-23b.

(b) Additional Photometry for HATS-54b (NGTS-22b).

Figure 7: Phase-folded photometry for NGTS-23b and HATS-54b (NGTS-22b). These
transits were not used in the fitting procedure as there was not sufficient
baseline to characterise the out of transit behaviour.

##  Appendix B Sample NGTS photometry

Table 8: Sample NGTS photometry for each object. The full tables are available
in a machine-readable format from the online journal.

Time | Normalised Flux | Flux error
---|---|---
(BJD-2450000) |  |
7981.8851 | 1.016 | 0.022
7981.8852 | 1.002 | 0.022
7981.8854 | 0.978 | 0.022
7981.8855 | 0.999 | 0.022
7981.8857 | 1.022 | 0.022
… | … | …
8195.5415 | 1.020 | 0.020
8195.5416 | 1.007 | 0.020
8195.5417 | 1.056 | 0.020
8195.5419 | 1.012 | 0.020
8195.5420 | 0.956 | 0.020
(a) NGTS Photometry for NGTS-23.

Time | Normalised Flux | Flux error
---|---|---
(BJD-2450000) |  |
8097.8107 | 0.993 | 0.010
8097.8108 | 0.985 | 0.010
8097.8110 | 0.977 | 0.010
8097.8111 | 1.011 | 0.010
8097.8113 | 1.013 | 0.010
… | … | …
8295.5989 | 0.969 | 0.014
8295.5991 | 1.001 | 0.014
8295.5992 | 0.975 | 0.014
8295.5993 | 1.013 | 0.014
8295.5995 | 1.007 | 0.014
(b) NGTS Photometry for NGTS-24.

Time | Normalised Flux | Flux error
---|---|---
(BJD-2450000) |  |
8203.8697 | 1.009 | 0.022
8203.8698 | 0.984 | 0.022
8203.8700 | 1.051 | 0.022
8203.8701 | 0.983 | 0.022
8203.8702 | 0.959 | 0.022
… | … | …
8423.5825 | 1.001 | 0.022
8423.5826 | 1.020 | 0.022
8423.5828 | 0.968 | 0.022
8423.5829 | 0.954 | 0.022
8423.5831 | 0.984 | 0.022
(c) NGTS Photometry for NGTS-25.

Time | Normalised Flux | Flux error
---|---|---
(BJD-2450000) |  |
7374.8169 | 0.991 | 0.017
7374.8171 | 0.999 | 0.017
7375.8065 | 0.979 | 0.019
7375.8068 | 0.970 | 0.019
7375.8069 | 1.004 | 0.019
… | … | …
7632.4995 | 0.996 | 0.018
7632.4997 | 0.994 | 0.018
7632.4998 | 0.982 | 0.018
7632.5000 | 0.968 | 0.018
7632.5001 | 1.018 | 0.018
(d) NGTS Photometry for HATS-54 (NGTS-22).

##  Appendix C Radial Velocity Data

Table 9: Radial velocity data for the four systems. Target | BJD | RV | RV error | FWHM | contrast | BIS | instrument
---|---|---|---|---|---|---|---
| (-2450000) | ($\rm{km\,s^{-1}}$) | ($\rm{km\,s^{-1}}$) | ($\rm{km\,s^{-1}}$) |  | ($\rm{km\,s^{-1}}$) |
NGTS-23 | 8780.748 | 22.344 | 0.058 | 8.499 | 29.492 | 0.085 | HARPS
8781.748 | 22.325 | 0.033 | 8.376 | 29.162 | 0.016 | HARPS
8783.744 | 22.217 | 0.033 | 8.406 | 28.960 | 0.024 | HARPS
8784.756 | 22.315 | 0.040 | 8.445 | 29.733 | 0.162 | HARPS
8843.670 | 22.306 | 0.034 | 8.477 | 28.427 | 0.198 | HARPS
8844.657 | 22.180 | 0.023 | 8.376 | 28.400 | 0.104 | HARPS
8868.586 | 22.212 | 0.018 | 8.374 | 27.577 | 0.017 | HARPS
8418.650 | 22.415 | 0.080 | 8.946 | 31.387 | -0.019 | CORALIE
8424.713 | 22.254 | 0.076 | 8.926 | 31.042 | 0.703 | CORALIE
8428.803 | 22.292 | 0.075 | 9.093 | 31.454 | -0.112 | CORALIE
8736.888 | 22.281 | 0.028 | - | - | 0.082 | FEROS
8798.817 | 22.176 | 0.032 | - | - | -0.101 | FEROS
8800.690 | 22.245 | 0.025 | - | - | 0.025 | FEROS
8847.709 | 22.288 | 0.023 | - | - | 0.106 | FEROS
8848.621 | 22.216 | 0.023 | - | - | -0.009 | FEROS
8850.645 | 22.390 | 0.019 | - | - | -0.014 | FEROS
8851.688 | 22.291 | 0.022 | - | - | 0.050 | FEROS
8852.642 | 22.199 | 0.019 | - | - | 0.111 | FEROS
NGTS-24 | 8595.671 | -15.272 | 0.084 | 9.264 | 42.373 | -0.011 | CORALIE
8640.590 | -15.180 | 0.084 | 9.176 | 42.392 | -0.088 | CORALIE
8667.515 | -15.296 | 0.084 | 9.022 | 43.598 | 0.109 | CORALIE
8829.810 | -15.364 | 0.074 | 9.026 | 37.061 | -0.004 | CORALIE
8843.768 | -15.394 | 0.085 | 9.113 | 43.453 | 0.237 | CORALIE
8847.794 | -15.335 | 0.011 | - | - | 0.014 | FEROS
8848.802 | -15.247 | 0.012 | - | - | 0.026 | FEROS
8849.777 | -15.305 | 0.014 | - | - | -0.011 | FEROS
8850.770 | -15.347 | 0.011 | - | - | 0.027 | FEROS
8851.764 | -15.229 | 0.012 | - | - | 0.034 | FEROS
8852.769 | -15.270 | 0.011 | - | - | -0.007 | FEROS
NGTS-25 | 9377.789 | -22.926 | 0.009 | 6.801 | 41.105 | 0.057 | HARPS
9411.722 | -22.913 | 0.011 | 6.878 | 40.947 | 0.054 | HARPS
9412.775 | -23.060 | 0.014 | 6.819 | 41.233 | 0.073 | HARPS
9426.658 | -23.009 | 0.021 | 6.841 | 40.176 | 0.007 | HARPS
9428.610 | -22.931 | 0.015 | 6.897 | 40.651 | 0.011 | HARPS
9429.675 | -23.068 | 0.014 | 6.742 | 41.160 | -0.027 | HARPS
9430.706 | -23.112 | 0.056 | 6.927 | 37.081 | 0.117 | HARPS
9432.638 | -23.093 | 0.014 | 6.934 | 40.522 | 0.007 | HARPS
9433.636 | -23.032 | 0.016 | 6.829 | 40.429 | 0.068 | HARPS
9461.668 | -23.055 | 0.017 | 6.748 | 41.118 | 0.073 | HARPS
9462.671 | -22.923 | 0.017 | 6.761 | 40.849 | 0.044 | HARPS
9470.521 | -22.987 | 0.019 | 6.845 | 40.277 | 0.089 | HARPS
8704.642 | -23.285 | 0.165 | 8.407 | 92.508 | 0.168 | CORALIE
8717.567 | -22.566 | 0.227 | 8.508 | 193.087 | 0.105 | CORALIE
HATS-54 (NGTS-22) | 8613.692 | 46.189 | 0.011 | 7.858 | 50.059 | -0.064 | HARPS
8615.664 | 46.066 | 0.007 | 7.837 | 50.219 | -0.031 | HARPS
8616.656 | 46.191 | 0.008 | 7.837 | 49.736 | -0.003 | HARPS
8617.649 | 45.981 | 0.014 | 7.847 | 48.371 | -0.010 | HARPS
8642.655 | 46.064 | 0.009 | 7.798 | 50.454 | 0.033 | HARPS
8546.699 | 46.124 | 0.151 | 9.206 | 58.315 | -4.184 | CORALIE
8547.824 | 46.269 | 0.099 | 8.644 | 55.326 | -0.176 | CORALIE
8565.688 | 46.198 | 0.118 | 8.889 | 49.903 | 0.080 | CORALIE
8566.837 | 45.971 | 0.084 | 8.581 | 51.157 | -0.218 | CORALIE
8593.533 | 46.200 | 0.132 | 8.649 | 49.514 | 0.141 | CORALIE
8601.602 | 46.208 | 0.094 | 8.737 | 53.746 | -0.085 | CORALIE
8591.597 | 46.100 | 0.011 | - | - | -0.022 | FEROS
8592.680 | 46.135 | 0.029 | - | - | 0.004 | FEROS
8593.569 | 46.227 | 0.013 | - | - | 0.005 | FEROS
8594.619 | 45.938 | 0.013 | - | - | 0.006 | FEROS
8597.574 | 45.965 | 0.014 | - | - | -0.075 | FEROS
8599.601 | 46.040 | 0.013 | - | - | -0.037 | FEROS
8599.648 | 45.968 | 0.014 | - | - | 0.006 | FEROS
8599.798 | 46.007 | 0.015 | - | - | -0.066 | FEROS

##  Appendix D NGTS periodograms

(a) NGTS-23b

(b) NGTS-24b

(c) NGTS-25b

(d) HATS-54b (NGTS-22b)

Figure 8: GLS periodograms for the NGTS photometry.