HATS-50b through HATS-53b: Four Transiting Hot Jupiters Orbiting G-type Stars Discovered by the HATSouth Survey^*

The four new exoplanets reported in this work have been detected thanks to the HATSouth survey²⁰ (Bakos et al. 2013). This is a network of robotic wide-field telescopes, composed of six identical units located in three stations. The stations are distributed over three continents in the southern hemisphere, i.e., Las Campanas Observatory (LCO) in Chile, the H.E.S.S. site in Namibia, and Siding Spring Observatory (SSO) in Australia. Each unit consists of a single mount with four 18 cm Takahashi astrographs with a focal length of 500 mm, and four Apogee U16M Alta CCD cameras, which have 4k × 4k pixels of size 9.0 μm. With a plate scale of 3.7 arcsec pixel⁻¹, the total mosaic field-of-view on the sky is $8^\circ \times 8^\circ$. The survey operates in the visual, through Sloan-r filters, and the scientific images are obtained using an exposure time of 4 minutes. They are then automatically calibrated with bias, dark and flat images and are stored in the HATSouth archive at Princeton University. Each stellar field is monitored for roughly 2–3 months from each station, in order to get a 24 hr coverage, thus exploiting the great advantage coming from their large separation in longitude. Once a long time-series sequence ($\gt 7000$ images) for a single field is collected, then aperture photometry is performed to get light curves for each star with $9\lesssim r\lesssim 16$ mag in the field. The resulting light curves are treated with decorrelation and detrending algorithms²¹ and, finally, we look for possible transiting-planet periodic signals by running the Box-fitting Least Squares (BLS; Kovács et al. 2002) code for each of them. Planet candidates detected from the survey undergo spectroscopic characterization and, finally, their planetary nature is confirmed or excluded by precise radial-velocity measurements and photometric follow-up observations (Penev et al. 2013).

Since first light in 2009, the HATSouth survey has so far produced 6.25 million light curves for 5.07 million stars from observations covering 2609 square degrees. This is due to the overlap between the pointing of the cameras on a single mount and between the different pointing positions we use to tile the sky into target fields. As a matter of fact, some stars have multiple light curves from different cameras and pointing positions (e.g., HATS-4: Jordán et al. 2014). Based on these observations, we have so far identified 1883 candidate transiting planets of which 1120 have undergone follow-up observations. This leads so far to the determination that 636 of the candidates are false alarms or false positives, while we confirmed and published 44 planets.

Notable cases are: the two super-Neptunes HATS-7b (Bakos et al. 2015) and HATS-8b (Bayliss et al. 2015); HATS-6b, a warm Saturn-mass exoplanet orbiting an M star (Hartman et al. 2015); HATS-17b, the longest period transiting exoplanet discovered so far by a wide-field ground-based photometric survey (Brahm et al. 2016); HATS-18b, an extremely short-period planet spinning-up its host star (Penev et al. 2016); the detection of several very low-mass stars ($0.1\mbox{--}0.2\,{M}_{\odot }$) in eclipsing binary systems (Zhou et al. 2014, 2015).

Currently, dozens of other exoplanets have been confirmed by the HATSouth team and are undergoing analysis and preparation for publication.

This study presents the discovery of four new transiting planetary systems, which were detected following the procedure described above, and confirmed based on follow-up observations as described in the next sections; the new systems are HATS-50, HATS-51, HATS-52, and HATS-53. Each of them are composed of a moderately bright G-type star and a hot-Jupiter-type planet. The orbital periods are $3.8297$ days, $3.3489$ days, $1.3667$ days, and $3.8538$ days for HATS-50b, HATS-51b, HATS-52b, and HATS-53b, respectively, implying that we are dealing with new close-in hot Jupiters. Stellar coordinates, magnitudes, and cross-identifications are shown in Table 5. In particular, the magnitudes of the fours stars in the optical bands were taken from APASS (Henden et al. 2009), as listed in the UCAC 4 catalog (Zacharias et al. 2012), while those in the NIR bands are from the 2MASS catalog.

A summary of the HATSouth photometric observations for these objects is reported in Table 1. In particular, the four stars were observed thousands of times by the HATSouth telescopes between 2010 March and 2013 July; the corresponding phase-folded light curves are plotted in Figure 1, clearly showing typical transiting-planet signals with transit depths around 1%–2%. The data concerning all photometric observations are available in electronic format in Table 4.

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After having detected the planetary signals, we further analyze each of the four data sets to search for potential stellar variability/activity and additional periodic signals due to other transiting planets. This analysis was carried out by running BLS on the residuals of each HATSouth light curve and studying the Generalized Lomb–Scargle periodogram (GLS; Zechmeister & Kürster 2009). The results of these additional checks are as follows:

• 1.  
  By running BLS, we did not detected any significant periodic transit signal in the residuals of the HATS-51, HATS-52, and HATS-53 light curves. For the case of HATS-50, we noticed a marginal transit signal with a period of 0.76624822 days, ${T}_{{\rm{C}}}=2455274.38586$, depth of 3.2 mmag, and duration of 46 minutes (bottom panel of Figure 2). The candidate transit signal has a signal-to-noise ratio (S/N) of 7.5 in the phase-folded light curve and a BLS Signal-detection-efficiency (SDE) value of 7.38. Even though this signal is below our threshold for selecting candidates to follow up (top panel of Figure 2), it is worth noting given the presence of the confirmed hot Jupiter and the possibility of close companions to hot Jupiters (Becker et al. 2015). Therefore, HATS-50 could be an interesting target for a further short-cadence, time-series photometric monitoring with a more precise instrument, like TESS (Ricker & TESS Science Team 2017). However, given the density of the host star HATS-50 inferred from modeling the transits of HATS-50b (see Table 5), and the duration of the transits for the candidate signal, the candidate planet would have an orbital inclination that differs by more than 10° from that of the hot Jupiter. We finally note that a Mandel & Agol (2002) model fit indicates an implied radius in the super-Neptune regime. So, if this signal was really caused by an additional transiting planet, it would be firmly in the Neptune desert.
• 2.  
  By running GLS, we did not detect any significant periodic signal in the GLS spectrum of the light curve obtained for HATS-50, HATS-51, and HATS-53. For these three systems, we placed a 95% confidence upper limit of 0.95 mmag on the amplitude of any periodic signal between 0.01 days and 100 days. For HATS-52, we detected a sinusoidal signal with a periodicity of $P=15.63703\pm 0.00066$ days and an amplitude of 1.23 ± 0.25 mmag. The peak has an S/N of 20.3 in the spectrum, a periodogram value of ${\rm{\Delta }}{\chi }^{2}/{\chi }_{0}^{2}=0.0054$, and a false alarm probability (FAP), assuming Gaussian white noise, of $2\times {10}^{-5}$. We also assessed the FAP of GLS by performing a bootstrap analysis and obtaining a distribution of peak signals. From this, we estimated a more accurate FAP of $9\times {10}^{-5}$.This sinusoidal periodic signal can be related to the stellar activity and, therefore, presumably indicates its rotation period. However, considering that HATS-52 has a radius of ${R}_{\star }=1.046\pm 0.058\,{R}_{\odot }$ (see Table 5), this value of P implies that ${v}_{\mathrm{eq}}=3.60\pm 0.59\,\mathrm{km}\,{{\rm{s}}}^{-1}$ for HATS-52, which is $1.5\sigma$ below the spectroscopically determined value of $v\sin i=4.59\pm 0.64\,\mathrm{km}\,{{\rm{s}}}^{-1}$. So, there is a slight tension between these measurements if we identify the photometric periodicity of P = 15.6 days with the rotation period of the star.

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The first step that was undertaken in confirming the planetary nature of the four planetary candidates was to obtain a spectral reconnaissance of their host stars. This allows us to rule out the usual false positive cases (giant stars, binary systems, and blending with faint eclipsing binary systems). For this purpose, we used the Wide Field Spectrograph (WiFeS; Dopita et al. 2007), mounted on the ANU 2.3 m telescope at SSO. The spectroscopic parameters were estimated by taking low-resolution spectra (R = 3000). All four targets were identified as dwarf stars. We also took medium-resolution spectra (R = 7000), with the aim to search for possible RV variations at the ∼2 km s⁻¹ level, which are useful to rule out possible stellar companions. Details about the data reduction and the processing of the WiFeS spectra are summarized in Bayliss et al. (2013).

Precise RV measurements of the targets were then acquired by using several medium- and large-class telescopes, equipped with high-resolution spectrographs and working on wide ranges of optical wavelengths. They are summarized in Table 2, together with their main characteristics. With these instruments, it was possible to measure periodic RV variation of the stars, which is compatible with the presence of planet-type objects orbiting around them. In particular, we mainly used the FEROS spectrograph (Kaufer & Pasquini 1998), which is mounted on the MPG 2.2 m telescope at the ESO Observatory in La Silla, for monitoring the four targets. Other spectra were collected thanks to CORALIE (Queloz et al. 2001) on the Euler 1.2 m telescope, HARPS (Mayor et al. 2003) on the ESO 3.6 m telescope, which are also located at the La Silla observatory, and CYCLOPS mounted on the 3.9 m Anglo-Australian Telescope at SSO. For the case of HATS-50, which is the faintest star of the four ($V=14.0$ mag), we needed higher S/N measurements. These were obtained by taking seven spectra with the HIRES spectrograph (Vogt et al. 1994) on the Keck I 10 m telescope at Mauna Kea Observatory in Hawaii.

Table 2.  Summary of Spectroscopy Observations

Instrument	UT Date(s)	# Spec.	Res.	S/N Rangea	${\gamma }_{\mathrm{RV}}$ b	RV Precisionc
			${\rm{\Delta }}\lambda$/λ/1000		($\mathrm{km}\,{{\rm{s}}}^{-1}$)	(${\rm{m}}\,{{\rm{s}}}^{-1}$)
HATS-50
ANU 2.3 m/WiFeS	2014 Jun 3–5	3	7	21–90	−23.4	4000
ANU 2.3 m/WiFeS	2014 Jun 4	1	3	76	⋯	⋯
Euler 1.2 m/CORALIE	2014 Jun–Sep	4d	60	7–13	−20.176	73
MPG 2.2 m/FEROS	2014 Jul–2016 Sep	32d	48	14–55	−20.250	72
Keck I 10 m/HIRES+I2	2014 Sep–2015 Jul	7	48	110–155	⋯	29
Keck I 10 m/HIRES	2015 Jul 5	1	48	70	⋯	⋯
HATS-51
ANU 2.3 m/WiFeS	2014 Oct 7	1	3	46	⋯	⋯
ANU 2.3 m/WiFeS	2014 Oct 8–12	4	7	33–67	2.0	4000
Euler 1.2 m/CORALIE	2014 Oct–2016 Nov	24d	60	8–30	3.086	55
MPG 2.2 m/FEROS	2014 Dec–2015 Feb	14	48	60–97	3.087	55
AAT 3.9 m/CYCLOPS	2015 Feb–May	13	70	⋯	3.087	30
HATS-52
ANU 2.3 m/WiFeS	2014 Jul 3	1	3	58	⋯	⋯
ANU 2.3 m/WiFeS	2014 Jul–2015 Jan	4	7	14–50	13.8	4000
Euler 1.2 m/CORALIE	2015 Mar 28	1	60	11	13.30	⋯
ESO 3.6 m/HARPS	2015 Apr 6–8	3	115	10–13	13.384	15
MPG 2.2 m/FEROS	2015 Jun–2016 Feb	11	48	25–48	13.456	127
HATS-53
ANU 2.3 m/WiFeS	2015 Mar 30	1	3	30	⋯	⋯
ANU 2.3 m/WiFeS	2015 Mar–Apr	2	7	6–33	68.5	4000
ESO 3.6 m/HARPS	2015 Apr 7–8	2	115	7–12	71.945	23
MPG 2.2 m/FEROS	2015 Jun 6–20	11	48	21–40	71.950	28

Notes.

^aS/N per resolution element near 5180 Å. ^bFor high-precision RV observations included in the orbit determination, this is the zero-point RV from the best-fit orbit. For other instruments, it is the mean value. We do not provide this quantity for the lower resolution WiFeS observations, which were only used to measure stellar atmospheric parameters, or for the Keck I/HIRES spectra of HATS-50 from which only relative velocities have been measured. ^cFor high-precision RV observations included in the orbit determination, this is the scatter in the RV residuals from the best-fit orbit (which may include astrophysical jitter), for other instruments, this is either an estimate of the precision (not including jitter), or the measured standard deviation. We do not provide this quantity for low-resolution observations from the ANU 2.3 m/WiFeS. ^dWe list here the total number of spectra collected for each instrument, including observations that were excluded from the analysis due to very low S/N or substantial sky contamination. For HATS-50, we excluded one CORALIE spectrum and 5 FEROS spectra from the analysis. For HATS-51, we excluded 3 CORALIE spectra.

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More details about the instruments, the data reduction, and the computation of the corresponding RVs can be found in the previous works of the HATSouth team, e.g., Penev et al. (2013), Mohler-Fischer et al. (2003), and Bayliss et al. (2013). In particular, HARPS, FEROS, and CORALIE spectra were analyzed with the method described in Jordán et al. (2014) and Brahm et al. (2017a), while those coming from CYCLOPS in Addison et al. (2013). Finally, we refer the reader to Bakos et al. (2015) and Howard et al. (2010) for the analysis of the Keck/HIRES spectra.

The values of the RV measurements are reported in Table 3, while the phased RVs and bisector spans (BS) are plotted for each system in Figure 3. We also used the FEROS high-resolution spectra for an accurate determination of the stellar spectroscopic parameters (effective temperature, metal abundance, and projected rotational velocity) by applying the Zonal Atmospherical Stellar Parameter Estimator (ZASPE) routine (Brahm et al. 2017b). This analysis is discussed in Section 3.1.

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Table 3.  Relative Radial Velocities and Bisector Spans for HATS-50–HATS-53

BJD	RVa	${\sigma }_{\mathrm{RV}}$ b	BS	${\sigma }_{\mathrm{BS}}$	Phase	Instrument
(2450,000+)	(m s−1)	(m s−1)	(m s−1)	(m s−1)
HATS-50
6828.86592	−17.38	24.00	75.0	37.0	0.168	Coralie
6829.74512	24.62	26.00	118.0	43.0	0.398	Coralie
6857.78434	68.26	12.00	9.0	15.0	0.719	FEROS
6858.73766	14.26	11.00	11.0	14.0	0.968	FEROS
6859.76731	−56.74	12.00	4.0	16.0	0.237	FEROS
6862.68928d	144.26	33.00	50.0	41.0	0.000	FEROS
6907.82693	58.01	4.95	⋯	⋯	0.786	HIRES
6908.75386	31.96	5.67	⋯	⋯	0.028	HIRES
6909.74379	−4.97	11.27	⋯	⋯	0.287	HIRES
6911.50060	−62.38	41.00	−301.0	63.0	0.746	Coralie
6911.76564	49.40	4.49	⋯	⋯	0.815	HIRES
6912.49456d	−62.38	30.00	−178.0	51.0	0.005	Coralie
6912.79856	−36.69	4.79	⋯	⋯	0.084	HIRES
6913.78648	−68.78	5.12	⋯	⋯	0.342	HIRES
6932.53890	−176.74	13.00	−75.0	17.0	0.239	FEROS
6942.60598	0.26	13.00	−29.0	16.0	0.868	FEROS
6983.54362	67.26	11.00	23.0	15.0	0.557	FEROS
7166.81632	−64.74	15.00	−30.0	19.0	0.413	FEROS
7181.70212	−3.74	14.00	8.0	18.0	0.300	FEROS
7186.89313	112.26	18.00	75.0	24.0	0.655	FEROS
7188.70636	−22.74	13.00	15.0	18.0	0.129	FEROS
7209.04868	1.46	6.60	⋯	⋯	0.440	HIRES
7211.80755	−45.74	12.00	21.0	16.0	0.161	FEROS
7219.64476	−47.74	12.00	−19.0	17.0	0.207	FEROS
7223.64984	6.26	15.00	36.0	20.0	0.253	FEROS
7225.55693	62.26	11.00	−11.0	15.0	0.751	FEROS
7227.54760	−73.74	13.00	−41.0	17.0	0.271	FEROS
7235.52005	−191.74	34.00	99.0	20.0	0.352	FEROS
7236.84001	−114.74	17.00	129.0	19.0	0.697	FEROS
7297.66592	−52.74	18.00	−177.0	24.0	0.580	FEROS
7299.64213	−83.74	16.00	−16.0	22.0	0.096	FEROS
7557.80118	62.26	12.00	−28.0	17.0	0.505	FEROS
7558.81095	80.26	12.00	33.0	17.0	0.769	FEROS
7569.65730	106.26	15.00	93.0	22.0	0.601	FEROS
7576.64710	41.26	16.00	39.0	21.0	0.426	FEROS
7590.72922	−25.94	10.50	22.0	14.0	0.103	FEROS
7593.67838	4.86	12.90	54.0	17.0	0.874	FEROS
7612.71943	113.86	12.30	6.0	17.0	0.845	FEROS
7614.57198	79.66	12.60	127.0	16.0	0.329	FEROS
HATS-51
6939.83172	−15.58	17.00	−11.0	27.0	0.491	Coralie
6940.81069	104.42	63.00	5.0	68.0	0.783	Coralie
6941.86563	−73.58	19.00	−60.0	29.0	0.098	Coralie
6967.78670	132.42	19.00	116.0	29.0	0.838	Coralie
6969.79828	30.42	18.00	23.0	27.0	0.439	Coralie
6972.69347	−50.58	16.00	65.0	25.0	0.303	Coralie
6997.69160	178.26	10.00	87.0	12.0	0.768	FEROS
6997.73191	201.26	10.00	74.0	13.0	0.780	FEROS
6999.63851	−9.74	10.00	38.0	11.0	0.349	FEROS
7030.81040	36.26	10.00	2.0	10.0	0.657	FEROS
7033.73624	3.26	10.00	9.0	10.0	0.531	FEROS
7035.75138	−68.74	10.00	−4.0	11.0	0.133	FEROS
7036.67747	−49.74	10.00	6.0	10.0	0.409	FEROS
7037.79634	59.26	10.00	12.0	10.0	0.744	FEROS
7049.60146	−96.74	10.00	−22.0	10.0	0.269	FEROS
7050.67770	34.26	10.00	12.0	10.0	0.590	FEROS
7053.74327	−17.74	10.00	−18.0	10.0	0.505	FEROS
7054.60465	61.26	10.00	−5.0	10.0	0.763	FEROS
7055.64520	−94.74	10.00	−65.0	10.0	0.073	FEROS
7057.74745	8.26	10.00	−85.0	11.0	0.701	FEROS
7075.63657	−61.58	18.00	6.0	29.0	0.043	Coralie
7076.65198	−86.58	18.00	−2.0	29.0	0.346	Coralie
7078.63334	−0.58	18.00	−46.0	29.0	0.938	Coralie
7080.99763	18.92	9.40	⋯	⋯	0.644	CYCLOPS
7081.01370	42.82	6.40	⋯	⋯	0.649	CYCLOPS
7081.07820	59.12	8.60	⋯	⋯	0.668	CYCLOPS
7082.97896	−58.38	9.00	⋯	⋯	0.235	CYCLOPS
7082.99492	−49.68	7.60	⋯	⋯	0.240	CYCLOPS
7083.01087	−34.78	11.70	⋯	⋯	0.245	CYCLOPS
7149.86599	−104.58	13.50	⋯	⋯	0.208	CYCLOPS
7149.89323	−100.98	13.00	⋯	⋯	0.217	CYCLOPS
7149.90918	−123.48	20.90	⋯	⋯	0.221	CYCLOPS
7152.85935	−57.48	12.10	⋯	⋯	0.102	CYCLOPS
7152.86772	−72.48	20.40	⋯	⋯	0.105	CYCLOPS
7154.86321	77.12	5.30	⋯	⋯	0.701	CYCLOPS
7154.87917	113.72	6.70	⋯	⋯	0.705	CYCLOPS
7313.71457	−4.58	18.00	147.0	49.0	0.135	Coralie
7317.75708	−228.58	19.00	−74.0	38.0	0.342	Coralie
7318.73072	53.42	18.00	−27.0	38.0	0.633	Coralie
7408.69120	−28.58	12.00	16.0	20.0	0.496	Coralie
7409.69015	14.42	12.00	10.0	20.0	0.794	Coralie
7410.58904	82.42	14.00	−92.0	23.0	0.063	Coralie
7411.54533	−88.58	19.00	−141.0	32.0	0.348	Coralie
7464.64412	−70.58	17.00	−54.0	32.0	0.204	Coralie
7466.52399	82.42	17.00	25.0	29.0	0.765	Coralie
7640.86434	63.42	16.00	23.0	29.0	0.825	Coralie
7643.82622	61.42	13.00	−23.0	26.0	0.709	Coralie
7645.89470	−50.58	12.00	4.0	22.0	0.327	Coralie
HATS-52
7109.65449	−323.80	34.00	⋯	⋯	0.165	Coralie
7118.61984	378.20	24.00	−15.0	31.0	0.725	HARPS
7119.61676	−82.80	31.00	95.0	37.0	0.455	HARPS
7120.59836	−341.80	28.00	−8.0	37.0	0.173	HARPS
7181.53193	324.38	24.00	−136.0	24.0	0.759	FEROS
7185.51437	228.38	25.00	−24.0	24.0	0.673	FEROS
7186.48111	−235.62	22.00	125.0	21.0	0.380	FEROS
7187.48351	−333.62	25.00	−36.0	24.0	0.114	FEROS
7190.47681	−355.62	24.00	53.0	24.0	0.304	FEROS
7324.83438	566.38	19.00	146.0	18.0	0.615	FEROS
7325.84444	−219.62	15.00	86.0	15.0	0.354	FEROS
7327.85022	386.38	18.00	137.0	18.0	0.822	FEROS
7403.83591	−196.62	15.00	16.0	15.0	0.422	FEROS
7405.78818	330.38	17.00	33.0	17.0	0.850	FEROS
7447.77082	−15.62	18.00	−107.0	18.0	0.570	FEROS
HATS-53
7119.69799	57.38	45.00	−77.0	53.0	0.625	HARPS
7120.69688	86.38	19.00	−83.0	29.0	0.884	HARPS
7181.59141	72.23	16.00	54.0	21.0	0.686	FEROS
7182.52590	28.23	14.00	−17.0	18.0	0.928	FEROS
7183.59764	−86.77	14.00	13.0	18.0	0.206	FEROS
7184.48225	−9.77	15.00	15.0	19.0	0.436	FEROS
7185.62553	103.23	21.00	−43.0	28.0	0.732	FEROS
7186.57088	62.23	18.00	−63.0	24.0	0.978	FEROS
7187.63960	−48.77	18.00	−63.0	24.0	0.255	FEROS
7190.53242	−32.77	15.00	−65.0	19.0	0.006	FEROS
7192.50171	−36.77	21.00	−98.0	28.0	0.517	FEROS
7193.61040	82.23	15.00	6.0	19.0	0.804	FEROS
7194.49223	−27.77	14.00	16.0	17.0	0.033	FEROS

Notes.

^aThe zero-point of these velocities is arbitrary. An overall offset ${\gamma }_{\mathrm{rel}}$ fitted independently to the velocities from each instrument has been subtracted. ^bInternal errors excluding the component of astrophysical jitter are considered in Section 3.3.

A machine-readable version of the table is available.

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Table 4.  Light Curve Data for HATS-50, HATS-51, HATS-52, and HATS-53

Objecta	BJDb	Magc	${\sigma }_{\mathrm{Mag}}$	Mag(orig)d	Filter	Instrument
	(2400,000+)
HATS-50	55451.44267	0.00058	0.00718	⋯	r	HS/G580.4
HATS-50	55765.47934	0.00588	0.00716	⋯	r	HS/G580.4
HATS-50	55788.45820	0.00832	0.00928	⋯	r	HS/G580.4
HATS-50	55516.54955	−0.00368	0.01095	⋯	r	HS/G580.4
HATS-50	55478.25269	−0.01940	0.00810	⋯	r	HS/G580.4
HATS-50	55451.44609	−0.01299	0.00728	⋯	r	HS/G580.4
HATS-50	55738.67412	−0.00224	0.00857	⋯	r	HS/G580.4
HATS-50	55470.59492	−0.00388	0.00781	⋯	r	HS/G580.4
HATS-50	55765.48280	−0.00187	0.00699	⋯	r	HS/G580.4
HATS-50	55516.55298	0.01526	0.01119	⋯	r	HS/G580.4

Notes.

^aEither HATS-50, HATS-51, HATS-52, or HATS-53. ^bBarycentric Julian Date is computed directly from the UTC time without correction for leap seconds. ^cThe 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. The blend factors for the HATSouth light curves are listed in Table 6. For observations made with follow-up instruments (anything other than "HS" 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. ^dRaw 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.

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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Another important step for confirming and characterizing a transiting exoplanetary system consists of performing photometric follow-up observations of transit events. We can thus derive more precise measurements, with respect to the survey data, of the transit depth, duration, mid-transit time, and contact points of the corresponding light curves. An accurate knowledge of these photometric parameters are vital for robustly constraining the orbital parameters of the system and the physical parameters of both the star and the planet.

One complete transit event was observed with the PEST 0.3 m telescope²² for HATS-50b, HATS-52b, and HATS-53b through an R-band filter. Details of this telescope and the method used for reducing the data are described in Zhou et al. (2014). The other 11 transit light curves of the four targets were recorded using the 1 m telescopes (CTIO, SAAO, SSO) in the Las Cumbres Observatory Global Telescope network (LCOGT; Brown et al. 2013) and Sloan-${i}^{{\prime} }$ filters. The LCOGT telescopes and the corresponding data reduction are described in Hartman et al. (2015). An excerpt of these observations is reported in Table 1. The light curves are plotted in Figures 4–7, for HATS-50, HATS-51, HATS-52, and HATS-53, respectively, and are compared to our best-fit models.

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Lucky imaging observations were obtained through a ${z}^{{\prime} }$ filter for the HATS-51 and HATS-52 systems using the Astralux Sur camera (Hippler et al. 2009) on the New Technology Telescope (NTT) at La Silla Observatory in Chile, on the nights of 2015 December 22 and 23. Observations with this facility were carried out and reduced following Espinoza et al. (2016), but a plate scale of 15.20 mas pixel⁻¹ (derived in the work of Janson et al. 2017) was used. Figure 8 shows the reduced final images for each system, while Figure 9 shows the contrast curves based on these images produced using the technique and software described in Espinoza et al. (2016).

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For HATS-52, a neighboring source is clearly detected at a distance of 2.74 ± 0.03 arcsec to the east and 0.79 ± 0.03 arcsec to the south from the target (i.e., at a distance of 2.85 ± 0.03 arcsec from the target), with ${\rm{\Delta }}{z}^{{\prime} }=2.457\pm 0.013$ mag, relative to the target. Based on the photometric follow-up observations of this system that were carried out with the LCOGT 1 m telescope network (Section 2.5), we were able to determine that the transits occur around the star HATS-52 and not the neighbor. The final combined image has an effective FWHM of $0\buildrel{\prime\prime}\over{.} 0722\pm 0\buildrel{\prime\prime}\over{.} 0050$. The same source was detected by the GAIA space observatory (GAIA Data Release 1; Lindegren et al. 2016) at $\approx 2\buildrel{\prime\prime}\over{.} 8$ separation to the East from HATS-52, with ${\rm{\Delta }}{G}_{\mathrm{GAIA}}=2.26$. Closer sources were not detected.

For HATS-51, no neighbors were detected with the Astralux Sur camera (effective FWHM of $0\buildrel{\prime\prime}\over{.} 0431\pm 0\buildrel{\prime\prime}\over{.} 0053$) and neither with GAIA within ${10}^{{\prime\prime} }$. Instead, based on GAIA data, we report that HATS-50 has a neighbor at $2\buildrel{\prime\prime}\over{.} 1$ to the east (${\rm{\Delta }}G=2.97$), while HATS-53 has no neighbors within $8\buildrel{\prime\prime}\over{.} 0$.

As anticipated before, we used high-resolution FEROS spectra for determining the atmospheric properties (metallicity, effective temperature, and surface gravity) of the four stars. The spectra were analyzed with the ZASPE routine, which is comprehensively described in Brahm et al. (2017b).

Then, we followed the methodology of Sozzetti et al. (2007) for determining other stellar parameters (mass, radius, luminosity, age, etc.) together with their uncertainties. In brief, we performed a Markov chain Monte Carlo (MCMC) global analysis of our photometric and spectroscopic data, based on (i) the stellar effective temperature, ${T}_{\mathrm{eff}\star }$, and stellar metal abundance, [Fe/H], which were both determined with ZASPE, (ii) the stellar mean density, ${\rho }_{\star }$, estimated by modeling the photometric transit light curves, and (iii) using the Yonsei-Yale (YY; Yi et al. 2001) evolutionary tracks.

We determined the YY isochrones for each of the four systems over a wide range of ages. The values of the stellar parameters were obtained from the best agreement between the resulting values of ${\rho }_{\star }$ and ${T}_{\mathrm{eff}\star }$ and those estimated from the data. Figure 10 shows the locations of each star on an ${T}_{\mathrm{eff}\star }$–${\rho }_{\star }$ diagram. From this analysis, we kept the values of the stellar logarithmic surface gravities, $\mathrm{log}{g}_{\star }$, and used them as fixed parameters for a second iteration with ZASPE, which returned the final values of the parameters of the four stars. They are reported in Table 5, and all of our objects are G-type stars.

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Table 5.  Stellar Parameters for HATS-50–HATS-53

	HATS-50	HATS-51	HATS-52	HATS-53
Parameter	Value	Value	Value	Value	Source
Astrometric Properties and Cross-identifications
2MASS-ID	20014273-2604392	06512340-2903309	09202105-3116095	11463084-3351361
GSC-ID	GSC 6896-01012	GSC 6534-00607	GSC 7153-01785	GSC 7225-00413
R.A. (J2000)	20h01m4260	06h51m2340	09h20m2105	11h46m3072	2MASS
Decl. (J2000)	−26°04'393	−29°03'310	−31°16'096	−33°51'362	2MASS
μR.A. (mas yr−1)	3.2 ± 1.6	15.5 ± 1.2	27.7 ± 3.7	35.0 ± 2.0	UCAC4
μDecl. (mas yr−1)	1.6 ± 1.6	6.9 ± 1.1	16.0 ± 3.7	5.0 ± 2.1	UCAC4
Spectroscopic Properties
${T}_{\mathrm{eff}* }$ (K)	5990 ± 110	5758 ± 58	6010 ± 150	5644 ± 94	ZASPEa
[Fe = H]	0.300 ± 0.056	0.300 ± 0.030	0.22 ± 0.10	0.010 ± 0.066	ZASPE
$v$ sin $i$ (km s−1)	3.76 ± 0.54	3.98 ± 0.26	4.59 ± 0.64	2.50 ± 0.76	ZASPE
${v}_{\mathrm{mac}}$ (km s−1)	4.32 ± 0.17	3.962 ± 0.088	4.35 ± 0.23	3.79 ± 0.14	Assumed
$v\mathrm{mic}$ (km s−1)	1.225 ± 0.085	1.070 ± 0.034	1.24 ± 0.12	1.006 ± 0.049	Assumed
${\gamma }_{\mathrm{RV}}$ (m s−1)	−20250 ± 13	3093 ± 15	13456 ± 43	71949.5 ± 7.1	FEROSb
Photometric Properties
$G$ (mag)	13.8	12.24	13.54	13.57	GAIA DR1c
$B$ (mag)	14.718 ± 0.010	13.190 ± 0.030	14.316 ± 0.030	14.548 ± 0.040	APASSd
$V$ (mag)	14.033 ± 0.050	12.471 ± 0.030	13.669 ± 0.040	13.790 ± 0.030	APASSd
$g$ (mag)	⋯	12.766 ± 0.030	13.962 ± 0.020	14.137 ± 0.020	APASSd
$r$ (mag)	⋯	12.269 ± 0.040	13.490 ± 0.060	13.579 ± 0.030	APASSd
$i$ (mag)	13.535 ± 0.010	12.115 ± 0.040	13.409 ± 0.070	13.30 ± 0.28	APASSd
$J$ (mag)	12.643 ± 0.025	11.241 ± 0.023	12.523 ± 0.034	12.458 ± 0.025	2MASS
$H$ (mag)	12.373 ± 0.034	10.955 ± 0.024	12.218 ± 0.035	12.088 ± 0.027	2MASS
${K}_{s}$ (mag)	12.289 ± 0.027	10.867 ± 0.021	12.114 ± 0.030	12.046 ± 0.027	2MASS
Derived Properties
${M}_{* }$ (${M}_{* }$)	1.168 ± 0.042	1.187 ± 0.060	1.111 ± 0.054	0.964 ± 0.040	YY+ρ*+ZASPEe
${R}_{* }$ (${R}_{* }$)	1.117 ± 0.060	1.44 ± 0.18	1.046 ± 0.058	${1.101}_{-0.024}^{+0.031}$	YY+ρ*+ZASPE
$\mathrm{log}{g}_{* }$ (cgs)	4.411 ± 0.038	4.198 ± 0.088	4.445 ± 0.034	4.340 ± 0.019	YY+ρ*+ZASPE
${\rho }_{* }$ (g cm−3)f	${1.38}_{-0.23}^{+0.16}$	${0.56}_{-0.16}^{+0.21}$	${1.70}_{-0.24}^{+0.17}$	${1.026}_{-0.071}^{+0.048}$	Light curves
${\rho }_{* }$ (g cm−3)f	1.19 ± 0.16	${0.56}_{-0.16}^{+0.22}$	1.37 ± 0.18	${1.027}_{-0.071}^{+0.050}$	YY+Light Curves+ZASPE
${L}_{* }({L}_{\odot })$	1.39 ± 0.23	2.04 ± 0.54	1.17 ± 0.22	1.11 ± 0.11	YY+ρ*+ZASPE
${M}_{V}$ (mag)	4.44 ± 0.19	4.05 ± 0.27	4.64 ± 0.22	4.74 ± 0.12	YY+ρ*+ZASPE
${M}_{K}$ (mag,ESO)	3.01 ± 0.13	2.51 ± 0.26	3.17 ± 0.15	3.121 ± 0.066	YY+ρ*+ZASPE
Age (Gyr)	1.2 ± 1.1	${4.74}_{-0.51}^{+0.70}$	${1.2}_{-1.1}^{+1.5}$	9.0 ± 1.9	YY+ρ*+ZASPE
${A}_{V}$ (mag)	0.305 ± 0.098	${0.024}_{-0.024}^{+0.059}$	${0.025}_{-0.025}^{+0.108}$	0.112 ± 0.078	YY+ρ*+ZASPE
Distance (pc)	717 ± 43	478 ± 59	631 ± 44	613 ± 19	YY+ρ*+ZASPE

Notes. For all four systems, we adopt a model in which the orbit is assumed to be circular. See the discussion in Section 3.3.

^aZASPE = Zonal Atmospherical Stellar Parameter Estimator routine for the analysis of high-resolution spectra (Brahm et al. 2017b), applied to the FEROS spectra of each system. These parameters rely primarily on ZASPE but have a small dependence also on the iterative analysis incorporating the isochrone search and global modeling of the data. ^bThe error on ${\gamma }_{\mathrm{RV}}$ 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. ^cFrom GAIA Data Release 1 (Lindegren et al. 2016). HATS-50 has a neighbor at $2\buildrel{\prime\prime}\over{.} 1$ to the east (${\rm{\Delta }}\,G=2.97$); HATS-51 has no neighbor within ${10}^{{\prime\prime} };$ HATS-52 has a neighbor at $2\buildrel{\prime\prime}\over{.} 8$ to east (${\rm{\Delta }}\,G=2.26$). HATS-53 has no neighbor within ${8}^{{\prime\prime} }$. ^dFrom APASS DR6 for as listed in the UCAC 4 catalog (Zacharias et al. 2012). ^eYY+ρ_*+ZASPE = Based on the YY isochrones (Yi et al. 2001), ${\rho }_{* }$ as a luminosity indicator, and the ZASPE results. ^fIn the case of ${\rho }_{\star }$, we list two values. The first value is determined from the global fit to the light curves and RV data, without imposing a constraint that the parameters match the stellar evolution models. The second value results from restricting the posterior distribution to combinations of ${\rho }_{\star }$+${T}_{\mathrm{eff}\star }$+$[\mathrm{Fe}/{\rm{H}}]$ that match to a YY stellar model.

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The most likely values for ${T}_{\mathrm{eff}\star }$ and ${\rho }_{\star }$ for HATS-52 fall at a higher density than the lowest age isochrone tabulated in the models (see bottom left panel in Figure 10). The models and observations are consistent within $2\sigma$. For determining the physical parameters of this star, we exclude any ${T}_{\mathrm{eff}\star }$–${\rho }_{\star }$–$[\mathrm{Fe}/{\rm{H}}]$ point in the Markov chain that does not match to a stellar model. In Table 5, we list for each star the median stellar density based both on the full Mark chain (i.e., without enforcing a match to the stellar models) and on the chain after excluding points that do not match to a model.

We note that, while HATS-53 has physical characteristics similar to the Sun (${T}_{\mathrm{eff}\star }=5644\pm 94$, $[\mathrm{Fe}/{\rm{H}}]=0.010\,\pm 0.066$, ${M}_{\star }=0.964\pm 0.040\,{M}_{\odot }$, ${R}_{\star }={1.101}_{-0.024}^{+0.031}\,{R}_{\odot }$), HATS-50, HATS-51, and HATS-52 are more massive, larger, and metal richer ($[\mathrm{Fe}/{\rm{H}}]=0.300\pm 0.056$, $[\mathrm{Fe}/{\rm{H}}]\,=0.300\pm 0.030$ and $[\mathrm{Fe}/{\rm{H}}]=0.22\pm 0.10$ for HATS-50, HATS-51, and HATS-52, respectively). We note that HATS-51 is much less dense (${\rho }_{\star }={0.56}_{-0.16}^{+0.22}\,$ g cm⁻³) than the other three stars due to its large radius (${R}_{\star }=1.44\pm 0.18\,{R}_{\odot }$). Moreover, our analysis indicates that HATS-50 and HATS-52 are quite young, i.e., $1.2\pm 1.1$ Gyr and ${1.2}_{-1.1}^{+1.5}$ Gyr, respectively; these estimates are both consistent with their Zero Age Main Sequence implying a 95% confidence upper limit on the age of $t\lt 3.9\,\mathrm{Gyr}$ and $t\lt 3.8\,\mathrm{Gyr}$, for HATS-50 and HATS-52, respectively. HATS-51 has an intermediate age (${4.74}_{-0.51}^{+0.70}$ Gyr), whereas HATS-53 is quite old ($9.0\pm 1.9$ Gyr).

We also estimated the distance of the four stars by comparing their broad-multi-band photometry taken from public astronomical archives (see Table 5) with the predicted magnitudes in each filter from the isochrones. The extinction was determined assuming an ${R}_{V}=3.1$ law from Cardelli et al. (1989). For a consistency check, we used the NED online extinction calculator, based on Galactic extinction maps, for estimating the expected total line of site extinction for each source. Three of them (HATS-51, HATS-52, and HATS-53) passed this check, as we found values greater than the inferred A_V. In the case of HATS-50, our estimated A_V is very close to the value determined from the dust maps.

In order to exclude blend scenarios, we carried out an analysis following Hartman et al. (2012). We attempt to model the available photometric data (including light curves and catalog broad-band photometric measurements) for each object as a blend between an eclipsing binary star system and a third star along the line of sight. The physical properties of the stars are constrained using the Padova isochrones (Girardi et al. 2000), while we also require that the brightest of the three stars in the blend has atmospheric parameters consistent with those measured with ZASPE. We also simulate composite cross-correlation functions and use them to predict RVs and BSs for each blend scenario considered. The results for each system are as follows:

• 1.  
  HATS-50—all blend models tested for this system can be rejected in favor of a model of a single star with a planet with greater than $3\sigma$ confidence based solely on the photometry. Moreover, the blend models that come closest to fitting the photometric data (those rejected with less than $5\sigma$ confidence) would yield large BS variations in excess of $1\,\mathrm{km}\,{{\rm{s}}}^{-1}$, whereas the measured scatter in the BS values is only $62\,{\rm{m}}\,{{\rm{s}}}^{-1}$ based on FEROS. Based on this, we conclude that HATS-50 is not a blended stellar eclipsing binary system.
• 2.  
  HATS-51—we find that the best-fit blend models are indistinguishable from the best-fit planet model based on the photometry. However, all blend models tested that fit the photometry (i.e., those that cannot be rejected in favor of the best-fit single-star plus planet model with at least $5\sigma$ confidence) would have been easily identified as composite systems based on the spectroscopy, with BS and/or RV variations in excess of $1\,\mathrm{km}\,{{\rm{s}}}^{-1}$. For comparison, the measured FEROS BSs have a scatter of $46\,{\rm{m}}\,{{\rm{s}}}^{-1}$. Based on this, we rule out stellar eclipsing binary blend scenarios.
• 3.  
  HATS-52—similar to HATS-50, all blend models tested for this system can be rejected in favor of a model of a single star with a planet with greater than $3\sigma$ confidence based solely on the photometry, while blend models that come closest to fitting the photometric data (those rejected with less than $5\sigma$ confidence) would yield large BS variations in excess of $1\,\mathrm{km}\,{{\rm{s}}}^{-1}$. In this case, measured scatter in the BS values is $96\,{\rm{m}}\,{{\rm{s}}}^{-1}$ based on FEROS. Based on this, we conclude that HATS-52 is not a blended stellar eclipsing binary system.
• 4.  
  HATS-53—similar to HATS-50, all blend models tested for this system can be rejected in favor of a model of a single star with a planet with greater than $4\sigma$ confidence based solely on the photometry, while blend models that come closest to fitting the photometric data (those rejected with less than $5\sigma$ confidence) would yield large BS variations in excess of $1\,\mathrm{km}\,{{\rm{s}}}^{-1}$. In this case, measured scatter in the BS values is $47\,{\rm{m}}\,{{\rm{s}}}^{-1}$ based on FEROS. Based on this, we conclude that HATS-53 is not a blended stellar eclipsing binary system.

The physical parameters of the four planetary systems were estimated by modeling the HATSouth photometry, the follow-up photometry, and the high-precision RV measurements. For this task, we followed the robust procedures developed by the HAT team, which are exhaustively described in several of their exoplanet-discovery papers (e.g., Pál et al. 2008; Bakos et al. 2010; Hartman et al. 2012, 2015). Here, we give a brief summary.

The transit light curves taken by the HATSouth telescopes (Figure 1) were fitted by using Mandel & Agol (2002) models and considering possible dilution of the transit depth; this was done for taking care of possible (i) blending from neighboring stars, or (ii) over-correction made when the light curves were detrended during the reduction phase.

Concerning the photometric follow-up observations (Figures 4–7), the systematic noise of each data set was corrected during the modeling of the corresponding light curve, by including a quadratic trend in time. We also included linear trends with three parameters describing the measured shape of the PSF. These were included to account for possible variations in the photometry resulting from PSF-shape changes that can happen during the transit observation due to poor guiding or non-photometric conditions.

The RV curves, which we presented in Section 2.4, are composed of points that were measured with different spectrographs, which can present different zero-points and can be affected by RV jitter as well. Therefore, we modeled the RV curves (Figure 3) with Keplerian orbits considering the zero-point and the RV jitter for each instrument as free parameters.

Finally, the values of the physical parameters of the exoplanetary systems were obtained by exploring their parameter spaces by means of a Differential Evolution MCMC procedure. This allowed us to identify the most likely values for the parameters together with their $1\sigma$ confidence interval.

We also investigated the possibility that the orbits of the four planets are eccentric. This was done by performing the joint fit of each of the four data sets with both fixed circular orbits and free-eccentricity models. Then, we estimated the Bayesian evidence for each scenario following the method of Weinberg et al. (2013). This method involves using the Markov Chains produced in modeling the observations to identify a region of high posterior probability which dominates the Bayesian evidence, and then carrying out a Monte Carlo integration over this small domain to estimate the evidence. We find that in all cases, a model with a fixed circular orbit has a higher Bayesian evidence than a model where the eccentricity is allowed to vary, and we adopt the fixed circular orbit model for each system.

The resulting parameters for each system are reported in Table 6 and indicate that three of the planets are puffy, low-density, hot giants (HATS-50b, HATS-51b, and HATS-53b) with 3 days $\lt \,{P}_{\mathrm{orb}}\,\lt 4$ days, while the fourth (HATS-52b) is a high-density, massive (${M}_{{\rm{p}}}\approx 2.2\,{M}_{{\rm{J}}}$), close-in (${P}_{\mathrm{orb}}=1.37$ days; $a\approx 0.025\,\mathrm{au};$ ${T}_{\mathrm{eq}}\approx 1830$ K) hot Jupiter. The fours planets have a radius larger than Jupiter, and the least massive of the four is HATS-50b with a mass of $\approx 0.4\,{M}_{{\rm{J}}}$.

Table 6.  Orbital and Planetary Parameters for HATS50b–HATS53b

	HATS-50b	HATS-51b	HATS-52b	HATS-53b
Parameter	Value	Value	Value	Value
Light Curve Parameters
P (days)	$3.8297015\pm 0.0000046$	$3.3488702\pm 0.0000039$	$1.36665436\pm 0.00000094$	$3.8537768\pm 0.0000038$
Tc ($\mathrm{BJD}$)a	$2456870.34792\pm 0.00068$	$2457042.00405\pm 0.00058$	$2456929.03039\pm 0.00033$	$2457236.75653\pm 0.00049$
T14 (days)a	$0.1283\pm 0.0021$	$0.1384\pm 0.0020$	$0.0871\pm 0.0013$	$0.1461\pm 0.0016$
${T}_{12}={T}_{34}$ (days)a	$0.0144\pm 0.0015$	$0.0138\pm 0.0017$	$0.0131\pm 0.0013$	$0.01679\pm 0.00095$
$a/{R}_{\star }$	$9.72\pm 0.44$	$6.94\pm 0.74$	$5.14\pm 0.22$	${9.30}_{-0.22}^{+0.15}$
$\zeta /{R}_{\star }$ b	$17.55\pm 0.24$	$16.08\pm 0.16$	$26.90\pm 0.27$	$15.47\pm 0.11$
${R}_{{\rm{p}}}$/${R}_{\star }$	$0.1038\pm 0.0025$	$0.1010\pm 0.0038$	$0.1352\pm 0.0028$	$0.1250\pm 0.0028$
b2	${0.177}_{-0.073}^{+0.073}$	${0.093}_{-0.066}^{+0.095}$	${0.231}_{-0.074}^{+0.073}$	${0.039}_{-0.029}^{+0.039}$
$b\equiv a\cos i/{R}_{\star }$	${0.421}_{-0.099}^{+0.079}$	${0.30}_{-0.14}^{+0.13}$	${0.481}_{-0.084}^{+0.071}$	${0.198}_{-0.096}^{+0.082}$
i (deg)	$87.54\pm 0.66$	$87.1\pm 1.6$	$84.7\pm 1.1$	$88.78\pm 0.55$
HATSouth Dilution Factorsc
Dilution Factor 1	$0.816\pm 0.063$	$0.827\pm 0.063$	$0.916\pm 0.048$	$0.919\pm 0.044$
Dilution Factor 2	$0.880\pm 0.062$	⋯	⋯	⋯
Limb-darkening Coefficientsd
${c}_{1},r$	$0.3362$	$0.3801$	$0.3262$	$0.3816$
${c}_{2},r$	$0.3446$	$0.3173$	$0.3487$	$0.3101$
$0.3559$	$0.3120$	⋯	⋯	$0.3132$
${c}_{2},R$	$0.3470$	⋯	⋯	⋯
${c}_{1},i$	$0.2495$	$0.2833$	$0.2419$	$0.2888$
${c}_{2},i$	$0.3488$	$0.3306$	$0.3502$	$0.3179$
RV Parameters
K (${\rm{m}}\,{{\rm{s}}}^{-1}$)	$45\pm 12$	$94.9\pm 5.1$	$380\pm 23$	$79\pm 12$
ee	<0.516	<0.330	<0.246	<0.330
RV Jitter FEROS (${\rm{m}}\,{{\rm{s}}}^{-1}$)f	$69\pm 11$	$49\pm 11$	$124\pm 39$	$18\pm 12$
RV Jitter HARPS (${\rm{m}}\,{{\rm{s}}}^{-1}$)	⋯	⋯	$\lt 114.5$	$\lt 31.0$
RV Jitter CYCLOPS (${\rm{m}}\,{{\rm{s}}}^{-1}$)	⋯	$25.2\pm 7.8$	⋯	⋯
RV Jitter CORALIE (${\rm{m}}\,{{\rm{s}}}^{-1}$)	$\lt 286.0$	$58\pm 12$	⋯	⋯
RV Jitter HIRES (${\rm{m}}\,{{\rm{s}}}^{-1}$)	$28\pm 10$	⋯	⋯	⋯
Planetary Parameters
${M}_{{\rm{p}}}$ (${M}_{{\rm{J}}}$)	$0.39\pm 0.10$	$0.768\pm 0.045$	$2.24\pm 0.15$	$0.595\pm 0.089$
${R}_{{\rm{p}}}$ (${R}_{{\rm{J}}}$)	$1.130\pm 0.075$	$1.41\pm 0.19$	$1.382\pm 0.086$	$1.340\pm 0.056$
$C({M}_{{\rm{p}}},{R}_{{\rm{p}}})$ g	$0.09$	$0.25$	$0.35$	$0.11$
${\rho }_{{\rm{p}}}$ (${\rm{g}}\,{\mathrm{cm}}^{-3}$)	$0.33\pm 0.11$	${0.34}_{-0.11}^{+0.16}$	$1.06\pm 0.19$	$0.303\pm 0.055$
$\mathrm{log}{g}_{{\rm{p}}}$ (cgs)	${2.87}_{-0.14}^{+0.11}$	$2.98\pm 0.11$	$3.468\pm 0.052$	${2.912}_{-0.087}^{+0.060}$
a (au)	$0.05046\pm 0.00060$	$0.04639\pm 0.00077$	$0.02498\pm 0.00040$	$0.04753\pm 0.00066$
${T}_{\mathrm{eq}}$ (K)	$1348\pm 47$	$1553\pm 92$	$1834\pm 73$	$1312\pm 25$
Θh	$0.0296\pm 0.0080$	$0.0421\pm 0.0064$	$0.0725\pm 0.0064$	${0.0436}_{-0.0073}^{+0.0051}$
${\mathrm{log}}_{10}\langle F\rangle$ (cgs)i	$8.872\pm 0.060$	$9.12\pm 0.10$	$9.407\pm 0.069$	$8.825\pm 0.033$

Notes. For all four systems, we adopt a model in which the orbit is assumed to be circular. See the discussion in Section 3.3.

^aTimes are in Barycentric Julian Date calculated directly from UTC without correction for leap seconds. ${T}_{c}$: Reference epoch of mid transit that minimizes the correlation with the orbital period. ${T}_{12}$: total transit duration, time between first to last contact; ${T}_{12}={T}_{34}$: ingress/egress time, time between first and second, or third and fourth contact. ^bReciprocal of the half duration of the transit used as a jump parameter in our MCMC analysis in place of $a/{R}_{\star }$. It is related to $a/{R}_{\star }$ 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). ^cScaling factor applied to the model transit that is fit to the HATSouth light curves. This factor accounts for dilution of the transit due to blending from neighboring stars and over-filtering of the light curve. These factors are varied in the fit, with independent values adopted for each HATSouth light curve. The factors listed for HATS-50 are for the G580.4 and G625.3 light curves, respectively. For HATS-51, we list the factor for 601.2. For HATS-52, the listed factor is for G606.1. For HATS-53, the listed factor is for G610.4. ^dValues for a quadratic law, adopted from the tabulations by Claret (2004) according to the spectroscopic (ZASPE) parameters listed in Table 5. ^eThe 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. ^fTerm added in quadrature to the formal RV uncertainties for each instrument. This is treated as a free parameter in the fitting routine. In cases where the jitter is consistent with zero, we list its 95% confidence upper limit. ^gCorrelation coefficient between the planetary mass ${M}_{{\rm{p}}}$ and radius ${R}_{{\rm{p}}}$ estimated from the posterior parameter distribution. ^hThe Safronov number is given by ${\rm{\Theta }}=\tfrac{1}{2}{({V}_{\mathrm{esc}}/{V}_{\mathrm{orb}})}^{2}=(a/{R}_{{\rm{p}}})({M}_{{\rm{p}}}/{M}_{\star })$ (see Hansen & Barman 2007). ⁱIncoming flux per unit surface area, averaged over the orbit.

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In Section 2.3, we have discussed the possibility that HATS-50 may host another planet (HATS-50c) with a shorter orbital period (0.77 days). This putative planet could be the cause of the substantial residuals of the RV measurements of HATS-50, which are showed in Figure 3 (top left panel) after removing the model for planet b. We have therefore deeply investigated this possibility. Figure 11 shows the RVs for HATS-50, after subtracting the orbital variation due to the confirmed transiting hot Jupiter and phase folded at the period of the candidate inner transiting planet. The line shows the best-fit circular orbit at this period, while the shaded region shows the 1σ uncertainty bounds on this model. We find that the RVs are consistent with no variation at this period, with a best-fit RV semi-amplitude of $K=8.4\pm 11.8\,{\rm{m}}\,{{\rm{s}}}^{-1}$. The 95% confidence upper limit on the mass of the candidate inner transiting planet is thus ${M}_{\mathrm{pl},{\rm{c}}}\lt 0.16$ ${M}_{{\rm{J}}}$.

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