HATS-74Ab, HATS-75b, HATS-76b, and HATS-77b: Four Transiting Giant Planets Around K and M Dwarfs^*

All four of the systems presented here were discovered as transiting planet candidates by the HATSouth ground-based transiting planet survey (Bakos et al. 2013) as we discuss in Section 2.1.1. Following the detection of transits for these four systems by HATSouth, we proposed for short-cadence NASA TESS observations for all of these systems through the NASA TESS Guest Investigator program (G011214). All four objects showed clear transits in the TESS data (Section 2.1.2) and were independently selected as transit candidates, based on these observations, by the TESS team.

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2.1.1. HATSouth

HATSouth uses a network of 24 telescopes, each 0.18 m in aperture, and 4K × 4K front-side-illuminated CCD cameras. These are attached to a total of six fully automated mounts, each with an associated enclosure, which are in turn located at three sites around the Southern Hemisphere. The three sites are Las Campanas Observatory (LCO) in Chile, the site of the H.E.S.S. gamma-ray observatory in Namibia, and Siding Spring Observatory (SSO) in Australia. The operations and observing procedures of the network were described by Bakos et al. (2013), while the method for reducing the images to trend-filtered light curves and searching for candidate transiting planets was described by Penev et al. (2013). We note that trend filtering makes use of the Trend-Filtering Algorithm (TFA) of Kovács et al. (2005), while transit signals are detected using the Box-fitting Least Squares (BLS) method of Kovács et al. (2002). The HATSouth observations of each system are summarized in Table 1, and displayed in Figures 1, 2, 3, and 4, while the light-curve data are made available in Table 2.

Table 1. Summary of Photometric Observations

Instrument/Field a	Date(s)	# Images b	Cadence c	Filter	Precision d
			(s)		(mmag)
HATS-74A
HS-1/G563	2010 Jan–2010 Aug	3875	277	r	44.4
HS-3/G563	2010 Jan–2010 Aug	5197	281	r	46.0
HS-5/G563	2010 Jan–2010 Aug	636	271	r	41.9
TESS/Sector9	2019 Mar 1–25	15918	120	T	24.8
CTIO0.9 m	2014 Feb 12	74	240	R	7.5
LCO 1 m/Sinistro	2019 Jun 13	50	206	i	4.6
TCS 1.5 m/MuSCAT2	2020 Jan 29	371	30	g	59.0
TCS 1.5 m/MuSCAT2	2020 Jan 29	189	60	r	16.6
TCS 1.5 m/MuSCAT2	2020 Jan 29	189	60	i	16.5
TCS 1.5 m/MuSCAT2	2020 Jan 29	189	60	zS	10.7
TSC 1.5 m/MuSCAT2	2020 Mar 2	384	30	g	33.8
TCS 1.5 m/MuSCAT2	2020 Mar 2	196	60	r	9.7
TCS 1.5 m/MuSCAT2	2020 Mar 2	195	60	i	7.0
TCS 1.5 m/MuSCAT2	2020 Mar 2	195	60	zS	5.5
HATS-75
HS-1/G548.focus	2014 Sep–2015 Apr	1677	1071	r	53.2
HS-2/G548.focus	2014 Jun–2015 Mar	2011	1209	r	52.6
HS-3/G548.focus	2014 Sep–2015 Mar	1486	1217	r	52.4
HS-4/G548.focus	2014 Jun–2015 Mar	1702	1222	r	51.0
HS-5/G548.focus	2014 Sep–2015 Mar	1381	1232	r	52.1
HS-6/G548.focus	2014 Jul–2015 Mar	1672	1200	r	51.5
HS-1/G548	2014 Sep–2015 Apr	6547	287	r	28.5
HS-2/G548	2014 Jun–2015 Apr	7590	348	r	28.2
HS-3/G548	2014 Sep–2015 Mar	5284	352	r	27.4
HS-4/G548	2014 Jun–2015 Mar	5976	352	r	26.9
HS-5/G548	2014 Sep–2015 Mar	4945	359	r	31.6
HS-6/G548	2014 Jul–2015 Mar	5956	351	r	30.0
TESS/Sector4	2018 Oct–Nov	14368	120	T	13.9
TESS/Sector5	2018 Nov–Dec	16376	120	T	13.1
LCO 1 m/Sinistro	2019 Sep 23	44	276	${g}^{{\prime} }$	2.8
LCO 0.4 m	2020 Jan 2	38	314	zS	11.6
LCO 1 m/Sinistro	2020 Sep 17	83	181	zS	2.6
HATS-76
HS-1/G597	2014 Jan–2014 Mar	1228	286	r	38.6
HS-3/G597	2013 Sep–2014 Feb	4540	285	r	44.4
HS-5/G597	2013 Sep–2014 Mar	4915	278	r	44.7
TESS/Sector5	2018 Nov–Dec	16362	120	T	36.1
LCO1 m/Sinistro	2019 Sep 20	44	327	${g}^{{\prime} }$	4.9
TRAPPIST-South	2020 Oct 20	48	130	I+z	9.1
TRAPPIST-South	2020 Oct 29	138	130	I+z	10.2
HATS-77
HS-1/G607	2011 Jan–2012 Jun	6703	289	r	43.3
HS-3/G607	2011 Jan–2012 Jun	3179	294	r	48.4
HS-5/G607	2011 Jan–2012 Jun	2544	288	r	44.6
TESS/Sector 9	2019 Mar 1–25	15726	120	T	39.4
LCO 1 m/Sinistro	2019 Jun 14	55	147	${i}^{{\prime} }$	5.9
Mt. Stuart0.3 m	2020 May 31	66	191	${g}^{{\prime} }$	32.8
LCO 2 m/MuSCAT3	2021 Jan 5	44	404	g	2.2
LCO 2 m/MuSCAT3	2021 Jan 5	73	244	r	1.1
LCO 2 m/MuSCAT3	2021 Jan 5	92	194	i	1.2
LCO 2 m/MuSCAT3	2021 Jan 5	44	404	zS	1.5

Notes.

^a For HATSouth data we list the HATSouth unit, CCD, and field name from which the observations are taken. HS-1 and -2 are located at Las Campanas Observatory in Chile, HS-3 and -4 are located at the H.E.S.S. site in Namibia, and HS-5 and -6 are located at Siding Spring Observatory in Australia. Each unit has 4 CCDs. Each field corresponds to one of 838 fixed pointings used to cover the full 4π celestial sphere. All data from a given HATSouth field and CCD number are reduced together, while detrending through External Parameter Decorrelation (EPD) is done independently for each unique unit+CCD+field combination. Observations with ".focus" included in the name are from light curves derived from focusing frames, which are shorter 30 s exposures that are taken every 20–30 minutes to refine the focus of the cameras. ^b Excluding any outliers or other data not included in the modeling. ^c The median time between consecutive images rounded to the nearest second. Due to factors such as weather, the day–night cycle, guiding, and focus corrections, the cadence is only approximately uniform over short timescales. ^d The rms of the residuals from the best-fit model. Note that in the case of HATSouth and TESS observations the transit may appear artificially shallower due to overfiltering and/or blending from unresolved neighbors. As a result the signal-to-noise ratio (S/N) of the transit may be less than what would be calculated from Rp/R_⋆ and the rms estimates given here.

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Table 2. Light-Curve Data for HATS-74A, HATS-75, HATS-76, and HATS-77

Object a	BJD b	Mag c	σMag	Mag(orig) d	Filter	Instrument
HATS-74	2455254.76774	−0.08602	0.05337	⋯	r	HS
HATS-74	2455322.31035	0.04862	0.03805	⋯	r	HS
HATS-74	2455280.74579	−0.01962	0.02762	⋯	r	HS
HATS-74	2455379.46209	0.05838	0.04105	⋯	r	HS
HATS-74	2455263.42771	0.01115	0.03608	⋯	r	HS
HATS-74	2455294.60127	0.03434	0.03152	⋯	r	HS
HATS-74	2455247.84123	−0.02098	0.02971	⋯	r	HS
HATS-74	2455289.40588	−0.00697	0.08795	⋯	r	HS
HATS-74	2455374.26713	0.06199	0.04867	⋯	r	HS
HATS-74	2455327.50711	0.01042	0.06350	⋯	r	HS

Notes.

^a Either HATS-74A, HATS-75, HATS-76, or HATS-77. ^b Barycentric Julian Dates in this paper are reported on the Barycentric Dynamical Time (TDB) system. ^c The out-of-transit level has been subtracted. For observations made with the HATSouth instruments (identified by "HS" in the "Instrument" column) these magnitudes have been corrected for trends using the EPD and TFA procedures applied prior to fitting the transit model. This procedure may lead to an artificial dilution in the transit depths. For several of these systems neighboring stars are blended into the TESS observations as well. The blend factors for the HATSouth and TESS light curves are listed in Table 7. For observations made with follow-up instruments (anything other than "HS", or "TESS" in the "Instrument" column), the magnitudes have been corrected for a quadratic trend in time, and for variations correlated with up to three PSF shape parameters, fit simultaneously with the transit. ^d Raw magnitude values without correction for the quadratic trend in time, or for trends correlated with the seeing. These are only reported for the follow-up observations. A portion is shown here for guidance regarding its form and content.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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2.1.2. TESS

2.1.3. Photometric Rotation Periods

We also searched the HATSouth and TESS light curves for other periodic signals using the Generalized Lomb-Scargle method (GLS; Zechmeister & Kürster 2009), and for additional transit signals by applying a second iteration of BLS. Both of these searches were performed on the residual light curves after subtracting the best-fit transit models. We analyzed the HATSouth and TESS light curves separately for each object.

We detect no evidence for additional variability in the HATSouth light curve of HATS-74A. The highest peak in the GLS periodogram of the HATSouth residual light curve of HATS-74A has a 95% confidence upper limit on the semiamplitude of 4.9 mmag, and the highest peak in the BLS periodogram has a transit depth of 16.7 mmag. The TESS light curve, however, does show evidence for a periodic signal, with a period of 4.745422 ± 0.000040 days and a semiamplitude of 1.86 ± 0.41 mmag (Figure 9, left) that we interpret as the photometric rotation period of the star. The GLS false alarm probability, calibrated using a bootstrap procedure, is 10⁻⁴. No significant additional transit signals are revealed by BLS, with the highest peak in the BLS spectrum having a transit depth of 4.3 mmag.

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The GLS analysis of the HATSouth light curve of HATS-75 reveals a significant periodic signal, with a period of 35.0435 ± 0.0017 days, semiamplitude of 1.71 ± 0.21 mmag, and false alarm probability of 10⁻¹¹ (Figure 9, right). The BLS analysis identifies this same signal in the HATSouth light curve, but the morphology of the phase-folded light curve clearly indicates that this is rotational variability due to starspots, rather than a transit signal. No other transit signals are seen in the HATSouth light curve. We do not detect any variability in the residual TESS light curve of HATS-75. Note that the rotation period identified by HATSouth is too long to be detectable in the TESS data given the 27 day window for each sector, and the detrending procedures that remove low-frequency variability from the TESS light curves.

We detect a P = 15.16063 ± 0.00048 day periodic signal in the HATSouth light curve of HATS-76 using GLS (Figure 10). The signal has a semiamplitude of 7.46 ± 0.66 mmag and a false alarm probability of 10⁻³². BLS also identifies this same signal, but it is clearly starspot-induced rotational variability. No other signals are identified by BLS. As for HATS-75, we do not detect the rotational variability in the TESS light curve of HATS-76 due to the long period relative to the 27 day observing window. No additional signals are detected by BLS in the TESS light curve either.

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For HATS-77, no signals are identified in either the HATSouth or TESS light curves. The highest peak in the GLS periodogram of the HATSouth light curve has a 95% confidence upper limit on its semiamplitude of 4.1 mmag. The corresponding upper limit for the TESS light curve is 3.1 mmag. The highest peak in the BLS spectrum of the HATSouth residuals has a depth of 13 mmag, while for the TESS residuals it is 6.0 mmag.

The spectroscopic observations carried out to confirm and characterize the four transiting planet systems presented here are summarized in Section 3. The facilities used include: Échelle spectrograph on the du Pont 2.54 m, ³¹ WiFeS on the ANU 2.3 m (Dopita et al. 2007), ARCES on the ARC 3.5 m (Wang et al. 2003), FEROS on the MPG 2.2 m (Kaufer & Pasquini 1998), ARCoIRIS on the Blanco 4 m (Abbott et al. 2016), and ESPRESSO on the VLT 8.2 m (Pepe et al. 2021). The du Pont, WiFeS, ARCES, and FEROS observations were obtained only for HATS-74A, while all four systems were observed with ARCoIRIS and ESPRESSO.

A 1200 s exposure of HATS-74A was obtained with the Échelle spectrograph on the du Pont 2.54 m telescope at Las Campanas Observatory in Chile on 2011 May 18. The spectrum had a resolution of R ≡ λ/Δλ = 40,000, and covered the wavelength range of 3700–7000 Å. Th–Ar lamp spectra were obtained before and after the observation to calibrate the wavelength scale of the science spectrum. The spectrum was extracted from the observation and analyzed following the procedure used by Jordán et al. (2014) to reduce observations from the Coralie and FEROS spectrographs. The spectrum had S/N = 7, and thus only a low precision RV measurement was possible, and estimates of the stellar spectroscopic parameters based on this observation are unreliable.

HATS-74A was subsequently observed with the Wide Field Spectrograph (WiFeS; Dopita et al. 2007) on the ANU2.3 m telescope at SSO. The WiFeS data were reduced and analyzed following Bayliss et al. (2013). We obtained two spectra at a resolution of R = 3000 to determine the effective temperature, surface gravity, and metallicity of the star, while four spectra were obtained at R = 7000 to search for large-amplitude RV variations that would indicate the presence of a stellar mass companion. The RV measurements extracted from the R = 7000 spectra had very large uncertainties (median value of 30 km s⁻¹) and were not useful for ruling out large-amplitude RV variations.

Three optical spectra of HATS-74A were obtained with the Astrophysics Research Consortium Échelle Spectrograph (ARCES; Wang et al. 2003) on the Astrophysics Research Consortium (ARC) 3.5 m telescope at Apache Point Observatory in New Mexico. The observations were performed and reduced to wavelength-calibrated spectra in the manner discussed by Brahm et al. (2015). The observations were then analyzed using the Spectral Parameter Classification program (SPC; Buchhave et al. 2012). We found that two of the spectra had S/N that were too low to yield useful measurements, while a third spectrum obtained with S/N ∼ 9 yielded an RV measurement of 17.9 ± 0.6 km s⁻¹. The atmospheric parameters estimated from the spectra hinted at a cool surface temperature of T_eff⋆ ∼ 4000 K, but due to the low S/N, reliable surface gravity, metallicity and $v\sin i$ measurements could not be derived from these observations.

A single FEROS observation of HATS-74A was obtained and reduced to a wavelength-calibrated spectrum, and RV and BS measurements using the CERES software package (Brahm et al. 2017a). The CERES package produced a high effective temperature of 7000 K and low metallicity of [Fe/H] = −2.0 dex, which we find to often be the case for M dwarfs with temperatures below the T_eff⋆ = 4000 K lower limit of the model spectra used for cross-correlation by the package. The measurements RV of 15.87 ± 0.11 km s⁻¹ is consistent with the higher-precision RV measurements of the system obtained with ESPRESSO.

Because all four objects have surface temperatures that are too low to apply the ZASPE package of Brahm et al. (2017b), we obtained near-infrared spectra of all four systems using the "Astronomy Research using the Cornell InfraRed Imaging Spectrograph" (ARCoIRIS) instrument on the Blanco 4 m at CTIO (Abbott et al. 2016). ARCoIRIS is a fixed slit spectrograph. It reaches a resolution of R ∼ 3500 over a large wavelength range from 0.80 to 2.47 microns by cross-dispersing the reflected grating light. For each science frame, we used the Fowler readout mode and took subsequent CuHeAr lamp spectra. We interleaved telluric standard star observations in the course of the night, matching the spectral type A0V and close in air mass. All stars were observed in an ABBA pattern. We analyzed the raw ARCoIRIS frames using SpexTool (Vacca et al. 2003; Cushing et al. 2004), obtaining wavelength-calibrated and telluric-corrected spectra. Given the mixed cloud conditions, we did not attempt to flux calibrate the spectra. Stellar atmospheric parameters were obtained by downgrading our spectra to match the IRTF/SpeX resolution and applying the procedure described in Newton et al. (2014, 2015). These are the atmospheric parameters that we adopt for the joint analysis discussion in Section 3.1. We also obtained ARCoIRIS spectra of two known M dwarfs (namely GJ176 and GJ205) for which we applied the same procedure. The ARCoIRIS spectra for our targets, along with IRTF/SpeX and ARCoIRIS spectra for standards, are shown in Figure 11.

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In order to detect the radial velocity variation of each star due to the transiting companions, and thereby determine the mass of each transiting companion, and confirm these as transiting planet systems, we obtained VLT 8.2 m/ESPRESSO observations of all four objects. A large telescope was needed to perform these observations due to the faintness, in optical bandpasses, of the host stars. The observations were carried out through the queue service mode between 2019 September and 2019 December. We used an exposure time of 1800 s for all observations, and obtained five exposures each for HATS-74A, HATS-75, and HATS-77, and four exposures for HATS-76. The observing and reduction procedures were the same as those discussed in (Bakos et al. 2020), making use of version 2.0.0 of the ESPRESSO pipeline in the ESO Reflex environment (Freudling et al. 2013) to produce high-precision RVs and bisector span measurements via cross-correlation with an M2 spectra mask. During the observations, the target was placed on fiber A, while fiber B pointed to the sky for simultaneous monitoring. For all four objects, the resulting RVs showed clear variations in phase with the transit ephemerides and consistent with Keplerian orbital variations due to transiting planets. The phase-folded observations are shown in Figures 1, 2, 3, and 4, while the radial velocity and bisector span data are made available in Table 5.

We obtained additional follow-up time-series photometry for each system using larger 0.3–2 m ground-based telescopes to obtain higher photometric precision light curves from higher-spatial-resolution images than those available from HATSouth or TESS. As summarized in Table 1, the facilities that we made use of for this purpose include: the imager on the CTIO 0.9 m (Subasavage et al. 2010), the imagers on the Las Cumbres Observatory (Brown et al. 2013) 0.4 m network (LCO 0.4 m), the Sinistro imagers on the Las Cumbres Observatory 1 m network (LCO 1 m), the MuSCAT2 imager (Narita et al. 2019) on the 1.5 m Telescopio Carlos Sanchez (TCS) at Teide Observatory, the MuSCAT3 imager (Narita et al. 2020) at LCO's 2 m telescope at Haleakala Observatory, and the imager on the Mt. Stuart 0.3 m telescope near Dunedin, New Zealand. The CTIO 0.9 m observations were carried out by the HATSouth team, while the other observations were carried out by members of the TESS Follow-up Observing Program (TFOP; Collins et al. 2018), and were made available to the community through the ExoFOP-TESS portal. ³² For the TFOP observations, we used the TESS Transit Finder, which is a customized version of the Tapir software package (Jensen 2013), to schedule the observations, and the photometric data were extracted using AstroImageJ (Collins et al. 2017).

High-spatial-resolution images were obtained for all four objects by members of TFOP and made available on ExoFOP-TESS as part of the standard process for vetting transit candidates and properly accounting for transit dilution that may be caused by the presence of stellar companions (Ciardi et al. 2015; Schlieder et al. 2021). Optical speckle imaging was carried out at 562 and 832 nm with the twin Zorro and `Alopeke imagers ³³ (Scott et al. 2021, in press) mounted on the Gemini 8 m South and North telescopes, respectively. Near-infrared (NIR) adaptive optics (AO) imaging in Brγ and the J band was performed with the NIRC 2 instrument on the Keck 2 m for HATS-74A, and in the K_s band with the NaCo instrument on the VLT 8 m for HATS-75. Finally, J- and K_s -band imaging of HATS-77 was obtained with WHIRC on the ARC 3.5 m. The observations with this latter instrument were gathered by the HATSouth team before the TESS mission. The optical and near-infrared techniques complement each other in terms of resolution and sensitivity to yield a more complete picture of the presence of nearby and (possibly) bound companions, with the optical speckle typically having a better resolution and the NIR AO having better sensitivity. The various observations are described below.

HATS-76 and HATS-77 were observed with Zorro, and HATS-74A and HATS-75 were observed with `Alopeke. The two instruments provide simultaneous speckle imaging in two bands (562 and 832 nm) with output data products including a reconstructed image with robust contrast limits on companion detections (e.g., Howell et al. 2016). Images were collected and subjected to Fourier analysis in our standard reduction pipeline (see Howell et al. 2011). We find that all four targets are single stars within the contrast achieved by the observations (4–5 mag) from the diffraction limit (20 mas) out to 12. At the distances of these HATS stars (d = 195 to 414 pc) these angular limits correspond to spatial limits of 4–8 au out to 230–500 au. We note that AO imaging reveals a companion to HATS-74A at 0844 that was not immediately apparent in the `Alopeke data.

The NaCo (Lenzen et al. 2003; Rousset et al. 2003) data were collected in a nine-point grid dither pattern, with the star position moved 2'' for each exposure. We ensured the star was within the upper left quadrant of the detector for all images since other quadrants of the detector suffer from light and dark column striping in the images. We collected 9 individual frames, each with exposure time 75 s, using the Ks filter. The dither pattern allows for a sky background frame to be constructed from a median combination of the science frames themselves. We reduced the raw data using a custom code that performs bad pixel and flatfield correction, subtracts the sky background, aligns the stellar position between images, and finally coadds the nine individual frames. We visually inspected images to search for companions and did not find companions anywhere in the field of view, which extends to at least 49 from the star in all directions. To quantify the sensitivity of the final image, we injected fake companions into the data cube at a range of separations and position angles. We retrieved these fake companions and measured the S/N of each fake companion. We then scaled the flux of the fake companions, such that they could be retrieved at 5σ. Finally, the sensitivity was averaged over position angle. We are sensitive to companions 3.7 mag fainter than the host beyond 400 mas, and to companions 5 mag fainter than the host in the background-limited regime beyond 700 mas. Our NaCo detection limits as a function of radius for HATS-75 are shown in Figure 13.

HATS-74A was observed with the NIRC2 instrument on Keck II behind the natural guide star AO system (Wizinowich et al. 2000). The observations were made on 2019 June 10 UT 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'' and was repeated twice, with each dither offset from the previous dither by 05. The camera was in the narrow-angle mode with a full field of view of ∼10'' and a pixel scale of approximately 00099442 per pixel. The observations were made in the narrowband Brγ filter (λ_o = 2.1686; Δλ = 0.0326 μ m) and the narrowband J_cont filter (λ_o = 1.2132; Δλ = 0.0198 μm), each with an integration time of 60 s with one coadd per frame for a total of 540 s on target per filter.

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, and the flats were normalized such that the median value of the flats is unity. Sky frames were generated from the median average of the nine 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 an intrapixel 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 FWHM of the point-spread function; 0064 and 0121 for Brγ and J_cont observations, respectively. The sensitivities of the final combined AO image were determined by injecting simulated sources azimuthally around the primary target every 20° at separations of integer multiples of the central source's FWHM (Furlan et al. 2017). The brightness of each injected source was scaled until standard aperture photometry detected it with 5σ significance. The resulting brightness of the injected sources relative to the target set the contrast limits at that injection location. The final 5σ 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.

Additional imaging results are available for all four objects from Gaia DR2 (Gaia Collaboration et al. 2018), which is sensitive to neighbors with G ≤ 20 mag down to a limiting resolution of ∼1'' (e.g., Ziegler et al. 2018).

Based on the NIRC2 observations we find that HATS-74A has a 0844 ± 00014 neighbor at a position angle of 46° east of north. The neighbor has magnitudes, relative to HATS-74A, of ΔBrγ =2.615 ± 0.013 mag and ΔJ = 2.642 ± 0.030 mag (Figure 12). The neighbor is not obviously apparent in the `Alopeke images, however (Figure 12). Finally, the neighbor is also listed in the Gaia DR2 catalog with a projected separation of 084 and a relative magnitude of ΔG = 3.1830 ± 0.0049 mag. The neighbor has a parallax of 3.80 ± 0.63 mas and a proper motion of μ_R.A. = −41.4 ± 1.4mas yr⁻¹, and μ_decl. = 42.6 ± 1.5 mas yr⁻¹, which are consistent with the values listed for HATS-74A (π = 3.425 ± 0.042 mas, μ_R.A. = −38.86 ± 0.12 mas yr⁻¹, and μ_decl. = 39.679 ± 0.077 mas yr⁻¹), indicating that the neighbor is very likely a bound companion to HATS-74A, and we henceforth refer to it has HATS-74B. Given the distance to HATS-74A (Table 6), the measured angular separation between HATS-74A and HATS-74B corresponds to a projected physical separation of 238.4 ± 3.9 au. Assuming HATS-74B is a main-sequence companion to HATS-74A with the same age, metallicity, distance, and extinction, then from the blend analysis that we discuss in Section 3.2 we find that HATS-74B has a stellar mass of 0.2284 ± 0.0078 M_⊙.

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No neighbors are detected for the other three systems, HATS-75, HATS-76, or HATS-77. Figures 13–15 show contrast limits on any resolved neighbors that are derived based on the high-resolution imaging that we have reported for these three objects.

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We perform a global fit to the light curves, radial velocities, spectroscopically measured stellar atmospheric parameters, broadband photometry, and parallax from Gaia DR2 using the methods described in Hartman et al. (2019), with modifications as summarized most recently by Bakos et al. (2020). The fit is carried out using a modified version of the lfit program, which is included in the fitsh software package (Pál 2012). The light curves are modeled using the Mandel & Agol (2002) transit model with quadratic limb darkening. The limb-darkening coefficients are allowed to vary in the fit. We place Gaussian prior constraints on the limb-darkening coefficients using the tables of Claret et al. (2012, 2013) and Claret (2018) and assume a prior uncertainty of 0.2 for each coefficient.

We include in the model several parameters for the physical and observed properties of the host star, including the effective temperature, the metallicity, the distance modulus, and the V-band extinction A_V . These parameters are, in turn, constrained by the observed spectroscopic stellar atmospheric parameters (as measured in Section 2.2), the photometry, and the parallax. Together with the parameters used to describe the transit and radial velocity observations, these parameters are sufficient to determine the bulk physical properties of the stars and their transiting planets. We fit the data using two different methods to relate the stellar mass to the stellar radius, metallicity, and luminosity: (1) an empirical method that uses the stellar mean density measured from the transit and radial velocity observations to determine the stellar mass from the stellar radius, which is itself inferred from the effective temperature and luminosity (this method is similar to that of, e.g., Stassun et al. 2017); and (2) using version 1.2 of the MIST stellar evolution models (Paxton et al. 2011, 2013, 2015; Choi et al. 2016; Dotter 2016) to impose an additional constraint on the stellar relations that is typically tighter than the observed constraint on the stellar mean density. Note that here we take a different approach from prior HATSouth discovery papers that generally made use of the PARSEC stellar evolution models (Marigo et al. 2017) instead. In each case, we assume both the orbital eccentricity is zero and allow the eccentricity to be a free parameter.

A Differential Evolution Markov Chain Monte Carlo (DEMCMC) procedure is used to sample the posterior parameter distribution. See Hartman et al. (2019) for a full list of the parameters that we vary, and their assumed priors. The fit includes the optical broadband photometry from Gaia DR2 and APASS, NIR photometry from 2MASS, and IR photometry from WISE. For WISE we exclude the W4 band for all systems as none of the objects were detected in that bandpass, while for HATS-74A, HATS-76, and HATS-77 we also exclude the W3 bands. These observations, together with the stellar atmospheric parameters, the parallax, and the reddening, constrain the luminosity of the star. To model the reddening, we assume a R_V = 3.1 Cardelli et al. (1989) dust law parameterized by A_V , and use the mwdust 3D Galactic extinction model (Bovy et al. 2016) to place a prior constraint on its value.

For HATS-74A we excluded the Gaia DR2 BP and RP measurements as we expect these to be contaminated in a nontrivial way from blending with the 08 neighbor HATS-74B (Section 2.4). For the J, H, K_S , W1, and W2 bandpasses HATS-74A and HATS-74B are completely blended. In these cases we estimated Δmag values in each bandpass from the MIST isochrones assuming a 0.23 M_⊙ stellar mass for the companion, and that its age, metallicity, distance, and reddening are the same as those for HATS-74A, determined in an initial iteration of the analysis. These Δmag values, which are given in the footnotes to Table 4, were then used to subtract the flux from HATS-74B from each bandpass measurement. The corrected magnitudes are then included in the fit, and are what we list for HATS-74A in Table 4.

Table 4. Astrometric, Spectroscopic, and Photometric Parameters for HATS-74A, HATS-75, HATS-76, and HATS-77

	HATS-74A	HATS-75	HATS-76	HATS-77
Parameter	Value	Value	Value	Value	Source
Astrometric properties and cross-identifications
2MASS-ID	11240360–1933257	04034783–2524320	04412154–3219128	09591770–2723339
TIC-ID	219189765	44737596	170849515	11561667
TOI-ID	737.01	552.01	555.01	730.01
GAIADR2-ID	3545653561942122368	5082914338199586560	4877426575724467456	5466556141521710592
R.A. (J2000)	11h24m03.5929s	04h03m47.8440s	04h41m21.5520s	09h59m17.6640s	GAIA DR2
Decl. (J2000)	$-19^\circ 33^{\prime} 25.6653^{\prime\prime}$	$-25^\circ 24^{\prime} 32.1170^{\prime\prime}$	$-32^\circ 19^{\prime} 13.5029^{\prime\prime}$	$-27^\circ 23^{\prime} 34.1427^{\prime\prime}$	GAIA DR2
μR.A.(mas yr−1)	-38.86 ± 0.12	12.872 ± 0.038	-5.429 ± 0.057	-24.64 ± 0.10	GAIA DR2
μDecl.(mas yr−1)	39.679 ± 0.077	− 1.753 ± 0.048	-38.609 ± 0.090	− 8.286 ± 0.098	GAIA DR2
parallax (mas)	3.425 ± 0.042	5.100 ± 0.029	2.564 ± 0.038	2.265 ± 0.056	GAIA DR2
Spectroscopic properties
Teff⋆ (K)	3775 ± 54	3812 ± 79	3990 ± 120	4082 ± 69	ARCoIRIS a
[Fe/H]	0.294 ± 0.088	0.28 ± 0.12	0.29 ± 0.13	−0.12 ± 0.10	ARCoIRIS
γRV (m s−1)	15850 ± 12	39997.7 ± 5.4	8597 ± 11	− 7758 ± 43	ESPRESSO b
Photometric properties c
Prot (d) d	4.745422 ± 0.000040	35.0435 ± 0.0017	15.16063 ± 0.00048	⋯	HATSouth
G (mag) e	15.9706 ± 0.0029	14.90330 ± 0.00040	15.79420 ± 0.00060	15.7364 ± 0.0011	GAIA DR2
BP (mag) e	⋯	16.0189 ± 0.0026	16.6962 ± 0.0057	16.5518 ± 0.0054	GAIA DR2
RP (mag) e	⋯	13.8535 ± 0.0013	14.8610 ± 0.0020	14.8547 ± 0.0038	GAIA DR2
B (mag)	⋯	17.120 ± 0.019	⋯	17.716 ± 0.010	APASS g
V (mag)	⋯	15.759 ± 0.036	⋯	16.354 ± 0.010	APASS g
g (mag)	⋯	16.503 ± 0.070	⋯	17.10 ± 0.25	APASS g
r (mag)	⋯	15.156 ± 0.090	⋯	15.746 ± 0.060	APASS g
i (mag)	⋯	14.230 ± 0.070	⋯	15.212 ± 0.010	APASS g
J (mag) f	13.341 ± 0.023	12.481 ± 0.023	13.690 ± 0.029	13.779 ± 0.029	2MASS
H (mag) f	12.687 ± 0.029	11.756 ± 0.026	12.984 ± 0.024	13.047 ± 0.029	2MASS
Ks (mag) f	12.452 ± 0.031	11.584 ± 0.021	12.812 ± 0.033	12.934 ± 0.032	2MASS
W1 (mag) f	12.342 ± 0.023	11.486 ± 0.024	12.758 ± 0.024	12.847 ± 0.024	WISE
W2 (mag) f	12.326 ± 0.023	11.502 ± 0.022	12.784 ± 0.026	12.870 ± 0.027	WISE
W3 (mag)	⋯	11.61 ± 0.19	⋯	⋯	WISE

Notes.

^a The parameters are estimated from the ARCoIRIS NIR spectra. ^b The error on γ_RV is determined from the orbital fit to the RV measurements, and does not include the systematic uncertainty in transforming the velocities to the IAU standard system. The velocities have not been corrected for gravitational redshifts. ^c We only include in the table catalog magnitudes that were included in our analysis of each system. In some cases, magnitudes we list as ⋯ the bandpass magnitude for a source when this magnitude is available in the indicated source catalog. These magnitudes are excluded from the analysis for reasons discussed in Section 3.1. ^d Photometric rotation period. ^e The listed uncertainties for the Gaia DR2 photometry are taken from the catalog. For the analysis we assume additional systematic uncertainties of 0.002 mag, 0.005 mag, and 0.003 mag for the G, BP, and RP bands, respectively. ^f The listed J, H, K_S , W1, and W2 magnitudes for HATS-74A have been corrected for blending with HATS-74B, assuming this latter object is a 0.23 M_⊙ main-sequence star with the same age and metallicity as HATS-74A (Table 6). Following these assumptions, we adopt ΔJ = 2.6418, ΔH = 2.7294, ΔK_S = 2.6473, ΔW1 = 2.5259, and ΔW2 = 2.3352 between HATS-74B and HATS-74A in removing the contribution of HATS-74B from the catalog photometry. ^g From APASS DR6 as listed in the UCAC 4 catalog (Zacharias et al. 2013).

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We find that for all four transiting planet systems the orbits are consistent with being circular when the eccentricities are varied and that the stellar parameters are more robustly constrained when imposing the stellar evolution model constraints. We therefore choose to adopt the parameters that stem from fixing the orbit to be circular and imposing the stellar evolution models as a constraint on the stellar physical parameters.

The best-fit models are compared to the various observational data for the four transiting planet systems in Figures 1–8. The adopted stellar parameters derived from the analysis are listed in Table 6, while the adopted planetary parameters are listed in Table 7. We also list in Table 7 the 95% confidence upper limit on the eccentricity that comes from allowing the eccentricity to vary in the fit.

Table 6. Adopted Derived Stellar Parameters for HATS-74A, HATS-75, HATS-76, and HATS-77

	HATS-74A	HATS-75	HATS-76	HATS-77
Parameter	Value	Value	Value	Value
M⋆ (M⊙)	0.6010 ± 0.0080	${0.6017}_{-0.0055}^{+0.0074}$	${0.662}_{-0.021}^{+0.016}$	0.655 ± 0.014
R⋆ (R⊙)	0.5758 ± 0.0055	0.5848 ± 0.0026	0.6259 ± 0.0079	0.6428 ± 0.0066
$\mathrm{log}g\star$ (cgs)	4.696 ± 0.011	4.6831 ± 0.0069	4.665 ± 0.016	4.638 ± 0.014
ρ⋆ (g cm − 3)	${4.43}_{-0.14}^{+0.18}$	${4.239}_{-0.065}^{+0.091}$	3.80 ± 0.17	${3.48}_{-0.12}^{+0.17}$
L⋆ (L⊙)	0.0608 ± 0.0015	0.06359 ± 0.00069	0.0916 ± 0.0029	0.1019 ± 0.0028
Teff⋆ (K)	3776.9 ± 9.5	3790.4 ± 5.7	4016 ± 17	4071 ± 13
[Fe/H]	${0.514}_{-0.021}^{+0.033}$	${0.522}_{-0.028}^{+0.051}$	${0.322}_{-0.049}^{+0.065}$	0.253 ± 0.039
Age (Gyr)	11.0 ± 5.1	14.9 + 3.3 − 4.3	4.6 + 8.7 − 4.0	12.1 ± 5.0
AV (mag)	${0.1960}_{-0.0150}^{+0.0100}$	0.0560 ± 0.0095	0.062 ± 0.012	${0.111}_{-0.019}^{+0.013}$
Distance (pc)	286.6 ± 3.0	195.3 ± 1.0	389.9 ± 5.6	413.9 ± 5.9
MB (M⊙) a	0.2284 ± 0.0078	<0.38	<0.24	<0.53

Notes. The listed parameters are those determined through the joint differential evolution Markov Chain analysis described in Section 3.1. For all four systems the RV observations are consistent with a circular orbit, and we assume a fixed circular orbit in generating the parameters listed here. Systematic errors in the bolometric correction tables or stellar evolution models are not included and may dominate the error budget for some of these parameters.

^a For HATS-75, HATS-76, and HATS-77 we list the 95% confidence upper limit on the mass of any unresolved stellar companion based on modeling the system as a blend between a transiting planet system and an unresolved wide stellar binary companion (Section 3.2). For HATS-74A we list the estimated mass for the 0844 neighbor in Gaia DR2, which we determined to be a common proper-motion and parallax companion to HATS-74A (Section 2.4).

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Table 7. Adopted Orbital and Planetary Parameters for HATS-74Ab, HATS-75b, HATS-76b, and HATS-77b

	HATS-74Ab	HATS-75b	HATS-76b	HATS-77b
Parameter	Value	Value	Value	Value
Light-curve parameters
P (days)	1.73185606 ± 0.00000055	2.7886556 ± 0.0000011	1.9416423 ± 0.0000014	3.0876262 ± 0.0000016
Tc (BJD_TDB) a	2458392.02654 ± 0.00024	2458611.05487 ± 0.00027	2458424.55556 ± 0.00053	2459136.69378 ± 0.00020
T14 (days) a	0.06889 ± 0.00064	0.07969 ± 0.00065	0.0774 ± 0.0011	0.09282 ± 0.00070
T12 = T34 (days) a	0.01256 ± 0.00049	0.01256 ± 0.00036	0.01254 ± 0.00067	0.01610 ± 0.00061
a/R⋆	8.90 ± 0.10	${12.037}_{-0.062}^{+0.086}$	9.12 ± 0.14	${12.06}_{-0.14}^{+0.19}$
ζ/R⋆ b	${35.31}_{-0.42}^{+0.56}$	29.71 ± 0.38	30.76 ± 0.67	26.02 ± 0.28
Rp/R⋆	0.1844 ± 0.0030	0.1555 ± 0.0021	0.1772 ± 0.0045	0.1865 ± 0.0024
b2	${0.165}_{-0.033}^{+0.029}$	${0.165}_{-0.029}^{+0.024}$	${0.079}_{-0.048}^{+0.051}$	${0.107}_{-0.033}^{+0.028}$
$b\equiv a\cos i/{R}_{\star }$	${0.406}_{-0.043}^{+0.034}$	${0.406}_{-0.038}^{+0.029}$	${0.281}_{-0.105}^{+0.080}$	${0.328}_{-0.054}^{+0.041}$
i (deg)	87.39 ± 0.29	88.07 ± 0.15	88.24 ± 0.59	88.44 ± 0.27
Dilution factors c
HATSouth 1	0.954 ± 0.046	0.756 ± 0.061	0.892 ± 0.056	0.906 ± 0.054
HATSouth 2	⋯	0.956 ± 0.030	⋯	⋯
TESS 1	0.963 ± 0.033	0.937 ± 0.032	0.966 ± 0.033	0.9927 ± 0.0095
TESS 2	⋯	0.949 ± 0.028	⋯	⋯
Limb-darkening coefficients d
c1, g	0.39 ± 0.17	0.36 ± 0.13	0.47 ± 0.14	0.47 ± 0.12
c2, g	0.29 ± 0.20	0.34 ± 0.17	0.34 ± 0.15	0.38 ± 0.14
c1, r	0.40 ± 0.15	0.29 ± 0.12	0.34 ± 0.16	${0.365}_{-0.087}^{+0.117}$
c2, r	0.23 ± 0.18	0.21 ± 0.17	0.31 ± 0.17	0.34 ± 0.15
c1, R	0.30 ± 0.14	⋯	⋯	⋯
c2, R	0.29 ± 0.17	⋯	⋯	⋯
c1, i	0.45 ± 0.14	⋯	⋯	0.34 ± 0.10
c2, i	0.27 ± 0.18	⋯	⋯	${0.21}_{-0.14}^{+0.18}$
c1, zs	0.32 ± 0.12	${0.170}_{-0.090}^{+0.120}$	⋯	⋯
c2, zs	0.17 ± 0.16	0.10 ± 0.16	⋯	⋯
c1, T	${0.19}_{-0.10}^{+0.14}$	0.28 ± 0.12	0.34 ± 0.14	0.55 ± 0.15
c2, T	0.17 ± 0.17	0.34 ± 0.16	0.36 ± 0.17	0.35 ± 0.15
RV parameters
K (m s−1)	346 ± 34	99.2 ± 7.9	562 ± 15	253 ± 63
e e	<0.044	<0.064	<0.062	<0.045
RV jitter ESPRESSO (m s−1)	<32.1	<2.8	<19.0	<87.3
Planetary parameters
Mp (MJ)	1.46 ± 0.14	0.491 ± 0.039	2.629 ± 0.089	${1.374}_{-0.074}^{+0.100}$
Rp (RJ)	1.032 ± 0.021	0.884 ± 0.013	1.079 ± 0.031	1.165 ± 0.021
C(Mp, Rp) g	− 0.01	− 0.11	0.01	− 0.01
ρ p (g cm − 3)	1.64 ± 0.19	0.878 ± 0.084	2.58 ± 0.23	${1.077}_{-0.081}^{+0.112}$
$\mathrm{log}{g}_{p}$ (cgs)	3.529 ± 0.063	3.192 ± 0.038	3.747 ± 0.029	${3.398}_{-0.028}^{+0.038}$
a (au)	0.02384 ± 0.00011	${0.032742}_{-0.000099}^{+0.000134}$	${0.02658}_{-0.00029}^{+0.00021}$	0.03607 ± 0.00025
Teq (K)	895.1 ± 5.7	772.3 ± 2.3	939.8 ± 6.7	828.3 ± 5.9
Θ h	0.112 ± 0.011	0.0602 ± 0.0049	0.1947 ± 0.0075	0.129 ± 0.032
${\mathrm{log}}_{10}\langle F\rangle$ (cgs) i	8.163 ± 0.011	7.9066 ± 0.0051	8.247 ± 0.012	8.028 ± 0.012

Notes. For all systems we adopt a model in which the orbit is assumed to be circular. See the discussion in Section 3.1.

^a Times are in Barycentric Julian Date calculated on the Barycentric Dynamical Time (TDB) system. T_c : Reference epoch of midtransit that minimizes the correlation with the orbital period. T₁₂: total transit duration, time between first to last contact; T₁₂ = T₃₄: ingress/egress time, time between first and second, or third and fourth contact. ^b Reciprocal of the half duration of the transit used as a jump parameter in our MCMC analysis in place of a/R_⋆. It is related to a/R_⋆ by the expression $\zeta /{R}_{\star }=a/{R}_{\star }(2\pi (1+e\sin \omega ))/(P\sqrt{1-{b}^{2}}\sqrt{1-{e}^{2}})$ (Bakos et al. 2010). ^c Scaling factor applied to the model transit that is fit to the HATSouth and TESS light curves. This factor accounts for dilution of the transit due to blending from neighboring stars and/or overfiltering of the light curve. These factors are varied in the fit, with independent values adopted for each light curve. For HATS-75 we list separately the independent dilution factors determined for the focus frame, and science frame HATSouth images, and for the TESS Sectors four and five light curves. ^d Values for a quadratic law. The limb-darkening parameters were directly varied in the fit, using the tabulations from Claret et al. (2012, 2013), Claret (2018) to place Gaussian prior constraints on their values, assuming a prior uncertainty of 0.2 for each coefficient. ^e The 95% confidence upper limit on the eccentricity determined when $\sqrt{e}\cos \omega$ and $\sqrt{e}\sin \omega$ are allowed to vary in the fit. ^f Term added in quadrature to the formal RV uncertainties for each instrument. This is treated as a free parameter in the fitting routine. ^g Correlation coefficient between the planetary mass Mp and radius Rp estimated from the posterior parameter distribution. ^h The Safronov number is given by ${\rm{\Theta }}=\tfrac{1}{2}{({V}_{\mathrm{esc}}/{V}_{\mathrm{orb}})}^{2}=(a/{Rp})({Mp}/{M}_{\star })$ (see Hansen & Barman 2007). ⁱ Incoming flux per unit surface area, averaged over the orbit.

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We performed a blend modeling of each system following the procedure described in Hartman et al. (2019). In summary, our blend modeling attempts to fit all of the observations excepting the radial velocity data using various combinations of stars with parameters constrained by the MIST models. We find that for HATS-76 a model consisting of a single star with a transiting planet provides a better fit (a greater likelihood or equivalently lower χ²) to the light curves, spectroscopic stellar atmospheric parameters, broadband catalog photometry, and astrometric parallax measurements than the best-fit blended stellar eclipsing binary models. The blended stellar eclipsing binary models involve more free parameters than the transiting planet model, and thus can be rejected on the grounds that they are both poorer-fitting and higher complexity models. However, for HATS-75, and HATS-77, we find that blends between a foreground star and a background eclipsing binary provide somewhat better fits to these data than do models consisting of a single star with a transiting planet. In these cases, comparably good fits to the data can be found for models consisting of a star with both a transiting planet and an unresolved stellar companion. For all three systems, the improvement in χ² for the blends can be attributed to the increased number of free parameters that are included in these more complicated models. For these two systems we simulated radial velocities for the model blend scenarios by simulating composite cross-correlation functions. We find that for HATS-75 the blend scenarios that we considered would produce radial velocity variations in excess of 600 m s⁻¹ that do not vary sinusoidally in phase with the transit ephemeris. This is in contrast to the observed radial velocity variation that has K = 99.2 ± 7.9 m s⁻¹ and that is in phase with the transit ephemeris. Similarly, for HATS-77 we find that the simulated blended eclipsing binary radial velocities do not vary sinusoidally in phase with the ephemeris, and that the scatter is in excess of 1 km s⁻¹ compared to the observed radial velocity variation with K = 562 ± 15 m s⁻¹ in phase with the transits. We conclude therefore that the blended eclipsing binary scenarios that might reproduce the photometric data for HATS-75 and HATS-77 can be ruled out on the grounds that they do not reproduce the radial velocity observations. We therefore consider HATS-75 and HATS-77, like HATS-76, to be confirmed transiting planet systems.

For HATS-74A, with its known resolved neighbor (Section 2.4), we considered four scenarios: (1) a transiting planet around the brighter source, with the fainter source being a bound companion; (2) a transiting planet around the fainter source, with the brighter source being a bound stellar companion; (3) the brighter source being a blend between a bright foreground star and a background stellar eclipsing binary, and the fainter source being unrelated to either the foreground star or the eclipsing binary; (4) the brighter source being a foreground star, and the fainter source being a background stellar eclipsing binary. In all cases we assume the 2MASS J, H, K_S , and the W1 and W2 photometry is blended between the two known sources, while ΔJ from the NIRC2 observations, and G and the parallax values from Gaia DR2 are unblended. The mass of both resolved stars is varied in the fits. They are assumed either to have the same age, distance, metallicity, and extinction, or independent values for these, depending on the scenario considered.

We find that scenarios (2) and (4) for HATS-74A do not fit the data included in the modeling, and can be therefore easily ruled out. Scenario (3) provides a somewhat better fit to the data than scenario (1), however, it uses seven extra parameters and the improvement in χ² can be fully attributed to the additional model complexity. As an additional check on scenario (3) we simulated radial velocity observations for 1000 blend scenarios drawn randomly from the posterior chain. For each draw from the chain we simulated the radial velocity observations in two ways: (a) assuming the resolved star is also resolved in the ESPRESSO observations, and (b) assuming it is not resolved in the ESPRESSO observations. We find that in all cases the simulated radial velocities show much larger variations (well in excess of 1 km s⁻¹) compared to the observed ones (K = 346 ± 34 m s⁻¹), and, moreover, they do not exhibit a clean, in-phase Keplerian orbital variation. We conclude therefore that scenario (3) is not consistent with all of the observations, and confirm that HATS-74A is a transiting planet system, with a resolved binary star companion. The modeling carried out for scenario (1) yields a mass for the binary star companion of 0.2284 ± 0.0078 M_⊙, which we adopt in Table 6.

For HATS-75, HATS-76, and HATS-77 we place limits on the presence of any unresolved binary star companions based on this modeling, which we also list in Table 6. Additionally, we note that any such companion would need to satisfy the contrast limits based on the null detection of companions in the high-resolution imaging discussed in Section 2.4. Finally, we note that there is no evidence of correlation of the bisector span measurements with the orbital phase for any of the systems.