HAT-P-58b–HAT-P-64b: Seven Planets Transiting Bright Stars^*

Periodic transit events were first identified for all seven systems based on time-series photometric observations obtained with the HATNet wide-field photometric network (Bakos et al. 2004). The instruments and filters used, number of measurements collected and date range over which they were collected, observational cadence, and photometric precision achieved are all listed in Tables 1 and 2 for each of the seven systems. The raw HATNet images were reduced to light curves following Bakos et al. (2004), making use of aperture and image subtraction photometry routines based on the FITSH software package Pál (2012). Following Bakos et al. (2010) we filtered variations from the light curves that are correlated with a variety of auxiliary parameters, and we then applied the trend-filtering algorithm (TFA) of Kovács et al. (2005). The latter operates by fitting each light curve as a linear combination of "template" light curves (in our case these are light curves for a random sample of non-variable stars distributed across the image plane and in magnitude) and then subtracting the best-fit model from the light curve being filtered. In our initial pass we apply the filtering in signal recovery mode, where we assume the light curve contains no astrophysical variations. We then use the box least-squares (BLS; Kovács et al. 2002) method to search the filtered light curves for periodic transits. Once recovered, we then re-apply the trend filtering, this time in signal-reconstruction mode, where we simultaneously fit to the light curve the linear filter and a periodic box-shaped transit model. This produces a filtered light curve without distorting the transit signal. The final trend-filtered photometric data for each system are shown phase-folded in Figure 1, and in Figures 7–12 at the end of the paper, while the measurements are available in Table 4.

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We used the vartools package (Hartman & Bakos 2016) to search the residual HATNet light curves of each target for additional periodic transit signals using BLS, but do not find any significant signals attributable to additional transiting planets around these stars. For HAT-P-58 the highest peak in the BLS spectrum (in the residual light curve) is at P = 38.5 days with a signal-to-pink noise ratio (S/N_pink) of 5.5 (we require S/N_pink > 7.0 for detection) and a transit depth of 6.3 mmag. For HAT-P-59 we detect a signal at the sidereal frequency, which is presumably due to systematic errors in the photometry that are not fully removed through external parameter decorrelation (EPD) and TFA. The first harmonic of this same signal is also detected with the generalized Lomb–Scargle periodogram (GLS; Zechmeister & Kürster 2009), and when it is filtered from the light curve using a Fourier series fit, we find no other significant transit signals with BLS. Altogether, we find the following peaks, significances, and transit depths in the residual light curves:

• 1.  
  HAT-P-58, P = 38.5 days, S/N_pink = 5.5, 6.3 mmag;
• 2.  
  HAT-P-59, P = 1.59 days, S/N_pink = 6.0, 2.3 mmag;
• 3.  
  HAT-P-60, P = 2.48 days, S/N_pink = 6.1, 2.3 mmag;
• 4.  
  HAT-P-61, P = 61.8 days, S/N_pink = 5.2, 2.7 mmag;
• 5.  
  HAT-P-62, P = 0.146 days, S/N_pink = 6.1, 2.9 mmag;
• 6.  
  HAT-P-63, P = 0.194 days, S/N_pink = 6.0, 8.3 mmag;
• 7.  
  HAT-P-64, P = 0.438 days, S/N_pink = 6.7, 2.3 mmag.

We also used vartools to search the residual HATNet light curves for continuous periodic variability with the GLS periodogram. For HAT-P-58, HAT-P-60, and HAT-P-62–HAT-P-64 we do not detect any periodic signals, and place 95% confidence upper limits on the peak-to-peak amplitudes of such signals of 2.0 mmag for HAT-P-58, 0.96 mmag for HAT-P-60, 1.2 mmag for HAT-P-62, 3.9 mmag for HAT-P-63, and 2.0 mmag for HAT-P-64. For HAT-P-59 a strong signal with a period of P = 0.49976 ± 0.00086 days is detected with a peak-to-peak amplitude of 16.6 mmag. Given the close proximity of the period to twice the sidereal frequency, we suspect that this signal is most likely due to systematic errors in the photometry that are not fully corrected through EPD and the TFA. After subtracting a Fourier series model from the light curve, the GLS periodogram finds no additional signals present in the data, and we place a 95% confidence upper limit of 1.5 mmag on the peak-to-peak amplitude of any such signals. For HAT-P-61 we detect a possible signal with a period of 10.6 ± 0.5 days and with a formal false alarm probability of 0.16% and peak-to-peak amplitude of 2.6 mmag. The GLS periodogram is shown in Figure 3. This may correspond to the photometric rotation period of the star, in which case the equatorial rotation velocity of 4.7 km s⁻¹ is 2σ larger than the spectroscopically measured projected rotation velocity of $v\sin i=3.69\pm 0.50$ km s⁻¹.

Spectroscopic observations of the TEP systems were carried out using the Tillinghast Reflector Echelle Spectrograph (TRES; Fűrész 2008) on the 1.5 m Tillinghast Reflector at FLWO, the SOPHIE spectrograph (Bouchy et al. 2009) on the Observatoire de Haute Provence (OHP) 1.93 m telescope in France, HIRES (Vogt et al. 1994) on the Keck-I 10 m at MKO together with its I₂ absorption cell, the High Dispersion Spectrograph (HDS; Noguchi et al. 2002) and its I₂ cell (Kambe et al. 2002) on the Subaru 8 m at MKO, the Astrophysical Research Consortium Echelle Spectrometer (ARCES; Wang et al. 2003) on the ARC 3.5 m telescope at Apache Point Observatory (APO) in New Mexico, the fiber-fed Échelle Spectrograph (FIES) on the Nordic Optical Telescope (NOT) 2.5 m (Djupvik & Andersen 2010) in La Palma, Spain, and the Network of Robotic Echelle Spectrographs (NRES; Siverd et al. 2018) on the LCOGT 1 m network. Table 3 summarizes the spectroscopic observations collected for each TEP system. Phased high-precision RV and bisector span (BS) measurements are shown for each system in Figures 1 and 7–12. The data are listed in Table 12 at the end of the paper.

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The TRES observations were reduced to spectra and cross-correlated against synthetic stellar templates to measure the RVs and to estimate T_eff⋆, $\mathrm{log}g$, and $v\sin i$. Here we followed the procedure of Buchhave et al. (2010), initially making use of a single order containing the gravity and temperature-sensitive Mg b lines. Based on these observations we quickly ruled out common false positive scenarios, such as transiting M dwarf stars, or blends between giant stars and pairs of eclipsing dwarf stars. For HAT-P-59 through HAT-P-63 the initial TRES RVs exhibited low-amplitude variations consistent with planetary mass companions, so we continued to collect spectroscopic observations with TRES for these objects with the aim of confirming them as TEP systems, measuring the masses of the planets, and providing high-precision stellar atmospheric parameters, including the stellar metallicities. For this work high-precision RVs and spectral line BSs were determined based on a multi-order analysis of the spectra (e.g., Bieryla et al. 2014), while the atmospheric parameters were determined using the Stellar Parameter Classification (SPC; Buchhave et al. 2012) method. For HAT-P-58 and HAT-P-64 the TRES observations were used solely for reconnaissance and were not included in the analysis described in Section 3.3.

The SOPHIE observations of HAT-P-59, HAT-P-60, HAT-P-63, and HAT-P-64 were reduced to RVs and BSs following Boisse et al. (2013). In all cases the RVs show variations consistent with planetary mass companions, and with the variations seen using other spectrographs.

The HIRES observations of HAT-P-58, HAT-P-60, HAT-P-61, and HAT-P-64 were reduced to relative RVs following the method of Butler et al. (1996), and to BSs following Torres et al. (2007). We also measured Ca ii H and K chromospheric residual emission indices (the so-called S and ${\mathrm{log}}_{10}{R}_{\mathrm{HK}}^{{\prime} }$ indices) following Isaacson & Fischer (2010) and Noyes et al. (1984). For HAT-P-64 we measured stellar atmospheric parameters from the I₂-free template spectra using the SPC.

The HDS observations of HAT-P-63 were reduced to relative RVs following Sato et al. (2002, 2012) and to BSs following Torres et al. (2007). The RVs are seen to vary in phase with the photometric ephemeris of the TEP, and are consistent with the variations seen with the TRES and SOPHIE spectrographs for this system.

The ARCES spectrum of HAT-P-63 was reduced following Hartman et al. (2015) and Buchhave et al. (2012) and was used for reconnaissance. The RV and atmospheric parameters of HAT-P-63 determined from this spectrum are consistent with the results from TRES.

The FIES spectra of HAT-P-63 and HAT-P-64 were reduced following Buchhave et al. (2010). For HAT-P-63 the first spectrum was obtained using the medium-resolution fiber, while the other spectra were obtained with the high-resolution fiber. For HAT-P-64 all four spectra were obtained with the high-resolution fiber. While the spectra were intended to be used for measuring the masses of the planetary companions, the resulting RV precision was insufficient for this purpose, given the small number of observations obtained. We therefore do not include these measurements in our analyses of HAT-P-63 or HAT-P-64.

NRES spectra of HAT-P-60 were collected from the McDonalds Observatory and Wise Observatory LCOGT 1 m facilities. We obtained 22 useful spectra with an S/N between 32 and 65, measured at ∼5150 Å. The exposure time for all spectra was 1800 s. In order to obtain the wavelength-calibrated spectra and extract high-precision RVs, we adapted the CERES pipeline (Brahm et al. 2017). We limited the order extraction to the central 50 orders, covering the wavelength range from 4194 to 7445 Å.

In order to determine the physical parameters of each TEP system, we conducted follow-up photometric time-series observations of each object using KeplerCam on the 1.2 m telescope at FLWO. These observations are summarized in Tables 1 and 2, where we list the dates of the observed transit events, the number of images collected for each event, the cadence of the observations, the filters used, and the per-point photometric precision achieved. The images were reduced to light curves following Bakos et al. (2010), which are plotted in Figures 1 and 7–12. The data are provided in Table 4.

Five of the seven planetary systems presented here were observed by the NASA TESS mission (Ricker et al. 2015), as summarized in Tables 1 and 2. Of particular note is HAT-P-59 which is located in the northern TESS continuous viewing zone, and had data from Sectors 14, 15, 16, 17, 18, 20, and 21 that we included in the analysis. We were not able to extract useful photometry for this system from the Sector 19 observations. The two systems that did not have TESS observations were either too close to the ecliptic plane (HAT-P-63), or located only on the edge of a CCD in Sector 19, with no useful data collected (HAT-P-62).

We note that HAT-P-59b and HAT-P-60b have both been independently identified as candidate transiting planets based on the TESS observations. HAT-P-59b (a.k.a. TOI-1826.01) is listed as a community-identified candidate on ExoFOP-TESS, while HAT-P-60b (a.k.a. TOI-1580.01) is listed as a candidate identified by the MIT quick-look pipeline. All of the systems presented here were detected and confirmed as planets by the HATNet team prior to the launch of the TESS mission.

The five systems with TESS observations were all observed in long-cadence mode, and we extracted simple aperture photometry for them from the TESS Full-Frame Image (FFI) data using the Lightkurve tool (Lightkurve Collaboration et al. 2018). Here we made use of the TESSCut API (Brasseur et al. 2019) to download 10 × 10 pixel FFI cutouts around each source, and made use of the automated mask routine in Lightkurve to generate the apertures using a threshold of 3.0, and to generate the background regions using a threshold of 0.001. We then used VARTOOLS (Hartman & Bakos 2016) to apply a moving median filter to remove large systematic variations from the light curves. This was done by first manually removing regions from the light curves with excessive systematic behavior, then masking the transits and performing a median filter with a 0.5 day window. We then performed a monotonic spline interpolation over the masked regions of the light curves to estimate the systematic corrections to apply to the in-transit portions of the data. Note that the procedures above will likely erase the rotation induced and other long-term variation of the stars. The resulting light curves are shown, together with the best-fit models, in Figures 2 and 13–16. These data are also made available in Table 4.

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As for the HATNet observations, we used the vartools package to search the residual TESS light curves of each target for additional periodic transit signals using BLS, and for additional sinusoidal periodic signals using the GLS periodogram. Table 5 gives the ephemeris information and significance for the top peak in the BLS spectrum of the TESS residuals for each system. None of the systems shows strong evidence for additional periodic transit signals. In a few cases (HAT-P-58 and HAT-P-59) there is marginal evidence for signals with S/N_pink > 7 (see Hartman & Bakos 2016 for a definition of this measure as used in vartools), though these are likely false alarms, and future observations by TESS in its extended mission should confirm or refute these. None of the systems shows evidence for a continuous periodic variation detected by the GLS periodogram, though any such variations would likely be removed by the median-filtering procedure that we applied to the light curves.

In order to detect nearby stellar companions which may be diluting the transit signals, we obtained high spatial resolution speckle imaging observations of all seven systems. For HAT-P-58–HAT-P-62 and HAT-P-64 we used the Differential Speckle Survey Instrument (DSSI; Horch et al. 2009, 2011, 2012; Howell et al. 2011), while for HAT-P-63 we used the newer NN-explore Exoplanet Stellar Speckle Imager (NESSI; Scott et al. 2018). Both instruments were used with the WIYN 3.5 m telescope ²³ at Kitt Peak National Observatory in Arizona.

The DSSI observations were gathered between the nights of UT 2015 September 26 and UT 2015 October 3. A dichroic beamsplitter is used to obtain simultaneous imaging through 692 nm and 880 nm filters. Each observation consists of a sequence of 1000 40 ms exposures readout on 128 × 128 pixel (28 × 28) subframes, which are reduced to reconstructed images following Horch et al. (2011). These images are searched for companions, and when none are detected, 5σ lower limits on the differential magnitude between a putative companion and the primary star are determined as a function of angular separation as described in Horch et al. (2011).

The NESSI observation was gathered on the night of UT 2017 September 7, in this case using a dichroic beamsplitter to image at 562 and 832 nm. The observing mode and reduction method are similar to those used for DSSI, and have been detailed in Scott et al. (2018). In this case the 256 × 256 pixel subframe has a field of view of 46 × 46.

For HAT-P-60 we obtained a single observation, while for the other six objects we obtained five observations apiece. In all cases no companions are detected within 12, and we place limits on the differential magnitudes in the blue and red filters as shown in Figures 4 and 17–22. We find limiting magnitude differences at ∼02 of

• 1.  
  HAT-P-58—Δm₆₉₂ > 3.22 and Δm₈₈₀ > 2.65
• 2.  
  HAT-P-59—Δm₆₉₂ > 3.14 and Δm₈₈₀ > 2.74
• 3.  
  HAT-P-60—Δm₆₉₂ > 4.04 and Δm₈₈₀ > 3.41
• 4.  
  HAT-P-61—Δm₆₉₂ > 2.85 and Δm₈₈₀ > 2.62
• 5.  
  HAT-P-62—Δm₆₉₂ > 3.16 and Δm₈₈₀ > 2.81
• 6.  
  HAT-P-63—Δm₅₆₂ > 3.82 and Δm₈₃₂ > 3.55
• 7.  
  HAT-P-64—Δm₆₉₂ > 2.60 and Δm₈₈₀ > 2.80.

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In addition to the companion limits based on the WIYN 3.5 m/DSSI observations, we also queried the UCAC 4 catalog (Zacharias et al. 2013) for neighbors within 20'' and the Gaia DR2 catalog (Gaia Collaboration et al. 2018) for neighbors within 10'' that may dilute either the HATNet or KeplerCam photometry. We find that HAT-P-60, HAT-P-62, and HAT-P-64 have fainter neighbors in Gaia DR2, while only the neighbor for HAT-P-62 is also detected in UCAC 4. The neighbors have separations and G-band magnitude differences as follows:

• 1.  
  HAT-P-60—9088 southeast, ΔG = 10.79 mag
• 2.  
  HAT-P-62—5565 northwest, ΔG = 2.10 mag, ΔV = 2.18 mag
• 3.  
  HAT-P-64—2510 northwest, ΔG = 6.38 mag.

Based on the Gaia DR2 parallaxes the neighbors to HAT-P-60 and HAT-P-62 are background objects that are not physically associated with the planet hosts. No parallax, proper motion, or color information is available for the neighbor to HAT-P-64. This neighbor is at a projected separation of 1667 au from the planet host, if it is physically associated. The neighbors to HAT-P-60 and HAT-P-64 are too faint to significantly affect the photometry and the resulting planet and stellar parameters, and can be ruled out as the source of the detected transit signals. We do account for the neighbor to HAT-P-62 (ΔG = 2.10 mag) in the analysis of this system as described in Section 3.3.

High-precision atmospheric parameters, including the effective surface temperature T_eff⋆, the surface gravity $\mathrm{log}g$, the metallicity [Fe/H], and the projected rotational velocity $v\sin i$, were determined by applying the SPC to our high-resolution spectra. For HAT-P-58 through HAT-P-63 this analysis was performed on the TRES spectra, while for HAT-P-64 we made use of the Keck-I/HIRES I₂-free template spectra. The analysis was performed separately on each spectrum and we took the weighted average of the results over all spectra obtained for each target. Here we assumed minimum uncertainties of 50 K on T_eff⋆, 0.10 dex on $\mathrm{log}g$, 0.08 dex on [Fe/H], and 0.5 km s⁻¹ on $v\sin i$, which reflects the systematic uncertainty in the method, and is based on applying the SPC analysis to observations of spectroscopic standard stars. Following Torres et al. (2012), we then revised the atmospheric parameters of the stars in an iterative fashion. We carried out a joint analysis of the light curves and RV curves to determine the mean stellar density ρ_⋆ for each host. We then combined the T_eff⋆ and [Fe/H] from the spectra with ρ_⋆ to determine the surface gravities via interpolation within the Yonsei–Yale theoretical stellar isochrones (Yi et al. 2001). The surface gravities were then fixed to the values from this procedure in a second iteration of the SPC where only T_eff⋆, [Fe/H] and $v\sin i$ were allowed to vary. Note that this procedure for determining the fixed value of $\mathrm{log}{g}_{\star }$ was performed prior to the release of Gaia DR2, and we chose not to perform an additional iteration of the SPC making use of the Gaia DR2 parallax. The expected change in the atmospheric parameters were in all cases smaller than the systematic uncertainties.

The final spectroscopic parameters, together with catalog astrometry and photometry are listed for the host stars in Tables 6 and 7.

Table 6. Astrometric, Spectroscopic, and Photometric Parameters for HAT-P-58, HAT-P-59, HAT-P-60, and HAT-P-61

	HAT-P-58	HAT-P-59	HAT-P-60	HAT-P-61
Parameter	Value	Value	Value	Value	Source
Astrometric properties and cross-identifications
TIC-ID	9443323	229400092	354469661	259506033
TOI-ID	⋯	1826.01	1580.01	⋯
2MASS-ID	04352318 + 5652055	19295008 + 6231452	01530777 + 5203140	05015525 + 5007526
GSC-ID	GSC 3740-01482	GSC 4234-02195	GSC 3292-01330	GSC 3352-00595
Gaia DR2-ID	277493615044741376	2241743203599727744	359678187913760384	256580182331399296
R.A. (ICRS J2015.5)	04h35m23.1828s	19h29m50.0701s	01h53m07.7727s	05h01m55.2577s	Gaia DR2
Decl. (ICRS J2015.5)	$+56^\circ 52^{\prime} 05\buildrel{\prime\prime}\over{.} 5848$	$+62^\circ 31^{\prime} 45\buildrel{\prime\prime}\over{.} 1751$	$+52^\circ 03^{\prime} 14\buildrel{\prime\prime}\over{.} 01977$	$+50^\circ 07^{\prime} 52\buildrel{\prime\prime}\over{.} 5746$	Gaia DR2
μR.A. (mas yr−1)	−10.883 ± 0.072	20.957 ± 0.046	26.51 ± 0.11	−11.021 ± 0.067	Gaia DR2
μdecl. (mas yr−1)	11.862 ± 0.064	−6.056 ± 0.043	6.165 ± 0.075	−21.440 ± 0.063	Gaia DR2
Parallax (mas)	1.912 ± 0.047	3.738 ± 0.019	4.260 ± 0.049	2.923 ± 0.035	Gaia DR2
Spectroscopic properties
Teff⋆ (K)	5931 ± 50	5665 ± 50	6462 ± 50	5551 ± 50	SPC a
[Fe/H]	0.012 ± 0.080	0.409 ± 0.080	−0.237 ± 0.080	0.396 ± 0.080	SPC
$v\sin i$ (km s−1)	4.91 ± 0.50	3.04 ± 0.50	10.42 ± 0.50	3.69 ± 0.50	SPC
vmac (km s−1)	1.0	1.0	1.0	1.0	Assumed
vmic (km s−1)	2.0	2.0	2.0	2.0	Assumed
γRV (km s−1)	−35.97 ± 0.10	−20.477 ± 0.027	6.582 ± 0.027	4.810 ± 0.022	TRES b
SHK	0.150 ± 0.010	⋯	0.1236 ± 0.0022	0.240 ± 0.012	HIRES
$\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$	−5.057 ± 0.072	⋯	−5.309 ± 0.033	−4.719 ± 0.032	HIRES
Photometric properties
G (mag) c	12.72020 ± 0.00020	11.67870 ± 0.00030	9.56360 ± 0.00030	12.93860 ± 0.00040	Gaia DR2
BP (mag) c	13.1422 ± 0.0016	12.0587 ± 0.0011	9.8631 ± 0.0012	13.4067 ± 0.0018	Gaia DR2
RP (mag) c	12.13470 ± 0.00090	11.15850 ± 0.00050	9.1320 ± 0.0013	12.33560 ± 0.00080	Gaia DR2
B (mag)	13.690 ± 0.089	12.581 ± 0.094	10.230 ± 0.040	14.040 ± 0.056	APASS d
V (mag)	12.971 ± 0.073	11.883 ± 0.065	9.710 ± 0.050	13.188 ± 0.029	APASS d
I (mag)	⋯	11.073 ± 0.078	9.077 ± 0.042	12.05 ± 0.12	TASS Mark IV e
g (mag)	13.28 ± 0.12	12.16 ± 0.10	⋯	13.550 ± 0.045	APASS d
r (mag)	12.74 ± 0.12	11.650 ± 0.050	⋯	12.915 ± 0.033	APASS d
i (mag)	12.50 ± 0.12	11.478 ± 0.050	9.421 ± 0.040	12.675 ± 0.051	APASS a
J (mag)	11.429 ± 0.022	10.581 ± 0.020	8.677 ± 0.052	11.598 ± 0.021	2MASS f
H (mag)	11.075 ± 0.020	10.268 ± 0.018	8.396 ± 0.029	11.263 ± 0.029	2MASS f
Ks (mag)	10.978 ± 0.023	10.208 ± 0.022	8.368 ± 0.031	11.141 ± 0.020	2MASS f
W1 (mag)	10.856 ± 0.022	10.144 ± 0.023	8.308 ± 0.026	11.089 ± 0.022	WISE f
W2 (mag)	10.906 ± 0.021	10.211 ± 0.020	8.320 ± 0.026	11.176 ± 0.022	WISE f
W3 (mag)	10.359 ± 0.061	10.191 ± 0.037	8.260 ± 0.028	⋯	WISE f

Notes.

^a SPC = Stellar Parameter Classification procedure for the analysis of high-resolution spectra (Buchhave et al. 2012), applied to the TRES spectra of HAT-P-58–HAT-P-61. These parameters rely primarily on the SPC, but have a small dependence also on the iterative analysis incorporating the isochrone search and global modeling of the data. ^b In addition to the uncertainty listed here, there is a ∼0.1 km s⁻¹ systematic uncertainty in transforming the velocities to the IAU standard system. ^c 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. ^d From APASS DR6 for as listed in the UCAC 4 catalog (Zacharias et al. 2013). ^e From the Amateur Sky Survey (TASS) catalog release IV (Droege et al. 2006). ^f All 2MASS and WISE photometry listed have "A" photometric quality flags, except the K_s flag for HAT-P-62 which has an "E" flag. The W3 measurement was excluded from the analysis of systems for which this value is not listed. These were excluded due to high photometric uncertainties and/or poor-quality flags.

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Table 7. Astrometric, Spectroscopic, and Photometric Parameters for HAT-P-62, HAT-P-63, and HAT-P-64

	HAT-P-62	HAT-P-63	HAT-P-64
Parameter	Value	Value	Value	Source
Astrometric properties and cross-identifications
TIC-ID	453064665	1635721458	455036659
TOI-ID	⋯	⋯	⋯
2MASS-ID	04580102 + 4818038	17581730 + 0545409	04355384 + 0225526
GSC-ID	GSC 3348-01101	GSC 0429-01697	GSC 0086-00341
Gaia DR2-ID	255397142179844224	4474644332250439552	3279418602369232000
R.A. (ICRS J2015.5)	04h58m01.0287s	17h58m17.3121s	04h35m53.8469s	Gaia DR2
Decl. (ICRS J2015.5)	$+48^\circ 18^{\prime} 03\buildrel{\prime\prime}\over{.} 7570$	$+05^\circ 45^{\prime} 40\buildrel{\prime\prime}\over{.} 9400$	$+02^\circ 25^{\prime} 52\buildrel{\prime\prime}\over{.} 6434$	Gaia DR2
μR.A. (mas yr−1)	14.732 ± 0.080	− 14.871 ± 0.036	7.784 ± 0.079	Gaia DR2
μdecl. (mas yr−1)	− 43.776 ± 0.061	− 0.301 ± 0.039	− 3.863 ± 0.044	Gaia DR2
parallax (mas)	2.839 ± 0.040	2.450 ± 0.024	1.505 ± 0.035	Gaia DR2
Spectroscopic properties
Teff⋆ (K)	5601 ± 50	5365 ± 50	6302 ± 50	SPC a
[Fe/H]	0.449 ± 0.080	0.428 ± 0.080	− 0.010 ± 0.080	SPC
$v\sin i$ (km s−1)	3.55 ± 0.50	3.22 ± 0.50	12.70 ± 0.50	SPC
vmac (km s−1)	1.0	1.0	1.0	Assumed
vmic (km s−1)	2.0	2.0	2.0	Assumed
γRV (km s−1)	50.424 ± 0.025	− 68.994 ± 0.057	25.22 ± 0.10	FEROS or HARPS b
SHK	⋯	⋯	0.1453 ± 0.0068	HIRES
$\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$	⋯	⋯	− 5.062 ± 0.057	HIRES
Photometric properties
G (mag) c	12.43620 ± 0.00030	13.51060 ± 0.00030	12.62210 ± 0.00010	Gaia DR2
BP (mag) c	12.8932 ± 0.0013	14.0381 ± 0.0012	12.98580 ± 0.00080	Gaia DR2
RP (mag) c	11.84000 ± 0.00090	12.84760 ± 0.00080	12.09530 ± 0.00070	Gaia DR2
B (mag)	⋯	14.729 ± 0.066	13.446 ± 0.011	APASS d
V (mag)	⋯	13.753 ± 0.065	12.771 ± 0.010	APASS d
I (mag)	⋯	⋯	12.105 ± 0.070	TASS Mark IV e
g (mag)	⋯	14.258 ± 0.026	13.062 ± 0.013	APASS d
r (mag)	⋯	13.418 ± 0.093	12.553 ± 0.075	APASS d
i (mag)	⋯	13.136 ± 0.086	12.440 ± 0.037	APASS d
J (mag)	11.144 ± 0.029	12.021 ± 0.021	11.485 ± 0.026	2MASS
H (mag)	10.803 ± 0.041	11.630 ± 0.028	11.225 ± 0.025	2MASS
Ks (mag)	10.701 ± 0.026	11.512 ± 0.023	11.123 ± 0.021	2MASS
W1 (mag)	0 ± 0	11.453 ± 0.022	11.058 ± 0.021	WISE
W2 (mag)	0 ± 0	11.514 ± 0.022	11.055 ± 0.021	WISE
W3 (mag)	⋯	⋯	⋯	WISE

Notes.

^a SPC = Stellar Parameter Classification procedure for the analysis of high-resolution spectra (Buchhave et al. 2012), applied to the TRES spectra of HAT-P-62 and HAT-P-63, and to the HIRES I₂-free template spectra of HAT-P-64. These parameters rely primarily on the SPC, but have a small dependence also on the iterative analysis incorporating the isochrone search and global modeling of the data. ^b In addition to the uncertainty listed here, there is a ∼0.1 km s⁻¹ systematic uncertainty in transforming the velocities to the IAU standard system. ^c 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. ^d From APASS DR6 for as listed in the UCAC 4 catalog (Zacharias et al. 2013). ^e From the Amateur Sky Survey (TASS) catalog release IV (Droege et al. 2006). ^f All 2MASS and WISE photometry listed have "A" photometric quality flags, except the K_s flag for HAT-P-62 which has an "E" flag. The W3 measurement was excluded from the analysis of systems for which this value is not listed. These were excluded due to high photometric uncertainties and/or poor-quality flags.

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The final atmospheric parameters are then treated as observations which are simultaneously fitted, together with the light curves, RV curves, parallaxes, and catalog broadband photometry as described in Section 3.3. Here the fitting procedure makes use of the PARSEC stellar evolution models (Marigo et al. 2017) to constrain the physical properties of the stars. The final derived physical parameters of the stars, based on this method, including M_⋆, R_⋆, $\mathrm{log}{g}_{\star }$, ρ_⋆, L_⋆, T_eff⋆, [Fe/H], the age of the system, the V-band extinction A_V , and the distance to the system are listed in Tables 8 and 9. Note that the values of T_eff⋆ and [Fe/H] listed here are the optimized values that are varied in the joint analysis, and may differ from the values for those parameters determined from modeling the spectra listed in Tables 6 and 7. Figures 1 and 7–12 show the de-reddened Gaia DR2 BP − RP colors versus absolute G magnitudes for each star compared to the PARSEC stellar evolution models, and also show the broadband spectral energy distribution (plotted as magnitude versus filter) of each star compared to the PARSEC models. We find that the best-fit models are in reasonably good agreement with the observations for all host stars. For example, the resulting derived distance measurements are within 1σ of the values determined solely from the Gaia DR2 parallax measurements for all seven systems. While individual photometric or spectroscopic measurements may differ by as much as 3σ from the model for some systems (e.g., the derived [Fe/H] metallicity of − 0.224 ± 0.057 versus spectroscopically observed [Fe/H] metallicity of 0.012 ± 0.080 for HAT-P-58), discrepancies at this level are common when jointly fitting all of the stellar data using isochrones to constrain the stellar properties. These differences are most likely due to underestimated systematic errors in (some of) the measurements, and/or systematic errors in the isochrone models.

Table 8. Derived Stellar Parameters for HAT-P-58, HAT-P-59, HAT-P-60, and HAT-P-61

	HAT-P-58	HAT-P-59	HAT-P-60	HAT-P-61
Parameter	Value	Value	Value	Value
M⋆ (M☉)	1.031 ± 0.028	1.008 ± 0.022	1.435 ± 0.012	1.004 ± 0.033
R⋆ (R☉)	1.530 ± 0.034	1.1038 ± 0.0073	${2.197}_{-0.020}^{+0.027}$	0.938 ± 0.011
$\mathrm{log}{g}_{\star }$ (cgs)	4.082 ± 0.020	4.356 ± 0.013	3.9114 ± 0.0097	4.496 ± 0.021
ρ⋆ (g cm−3)	0.405 ± 0.026	1.059 ± 0.038	${0.1909}_{-0.0071}^{+0.0054}$	1.715 ± 0.094
L⋆ (L☉)	2.86 ± 0.15	1.132 ± 0.015	6.44 ± 0.17	0.767 ± 0.031
Teff⋆ (K)	6078 ± 48	5678 ± 16	6212 ± 26	5587 ± 45
[Fe/H]	− 0.224 ± 0.057	0.217 ± 0.049	0.037 ± 0.037	0.194 ± 0.060
Age (Gyr)	${7.11}_{-0.72}^{+0.27}$	7.3 ± 1.0	${2.765}_{-0.056}^{+0.042}$	2.6 ± 2.0
AV (mag)	0.737 ± 0.034	0.048 ± 0.011	0.120 ± 0.019	0.389 ± 0.043
Distance (pc)	519 ± 11	267.3 ± 1.3	235.4 ± 2.3	343.2 ± 3.9

Note. The listed parameters are those determined through the joint differential evolution Markov chain analysis described in Section 3.3. For all four systems the fixed-circular-orbit model has a higher Bayesian evidence than the eccentric-orbit model. We therefore assume a fixed-circular orbit in generating the parameters listed here.

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Table 9. Derived Stellar Parameters for HAT-P-62, HAT-P-63, and HAT-P-64

	HAT-P-62	HAT-P-63	HAT-P-64
Parameter	Value	Value	Value
M⋆ (M☉)	1.023 ± 0.020	0.925 ± 0.023	1.298 ± 0.021
R⋆ (R☉)	1.170 ± 0.016	${0.9661}_{-0.0082}^{+0.0110}$	${1.735}_{-0.028}^{+0.041}$
$\mathrm{log}{g}_{\star }$ (cgs)	4.312 ± 0.015	4.435 ± 0.015	4.072 ± 0.015
ρ⋆ (g cm−3)	0.901 ± 0.042	1.448 ± 0.061	0.350 ± 0.018
L⋆ (L☉)	1.232 ± 0.053	0.714 ± 0.028	${4.66}_{-0.17}^{+0.29}$
Teff⋆ (K)	5629 ± 48	${5400}_{-39}^{+55}$	6457 ± 29
[Fe/H]	0.414 ± 0.090	0.251 ± 0.061	$-{0.113}_{-0.056}^{+0.027}$
Age (Gyr)	8.1 ± 1.1	9.0 ± 1.7	2.88 ± 0.13
AV (mag)	0.339 ± 0.046	0.506 ± 0.046	${0.650}_{-0.021}^{+0.014}$
Distance (pc)	353.1 ± 4.4	408.0 ± 4.0	${655}_{-11}^{+17}$

Note. The listed parameters are those determined through the joint differential evolution Markov chain analysis described in Section 3.3. For all three systems the fixed-circular-orbit model has a higher Bayesian evidence than the eccentric-orbit model. We therefore assume a fixed-circular orbit in generating the parameters listed here.

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In order to exclude blend scenarios we carried out an analysis following Hartman et al. (2012), as updated in Hartman et al. (2019). Here we attempt to model the available photometric data (including light curves and catalog broadband photometric measurements) for each object as a blend between an eclipsing binary star system and a third star along the line of sight (either a physical association or a chance alignment). The physical properties of the stars are constrained using the Padova isochrones (Girardi et al. 2002), while we also require that the brightest of the three stars in the blend have atmospheric parameters consistent with those measured with the SPC. We also simulate composite cross-correlation functions and use them to predict RVs and BSs for each blend scenario considered.

Based on this analysis we rule out blended stellar eclipsing binary scenarios for all seven systems. The results for each object are as follows.

• 1.  
  HAT-P-58: All blend models tested yield higher χ² fits to the photometry than the model of a single star with a transiting planet, and can be rejected with ∼1σ confidence. Those models that cannot be rejected with at least 5σ confidence based solely on the photometry predict BS variations in excess of 1 km s⁻¹ (however, the measured BS rms scatter from HIRES is 21 m s⁻¹).
• 2.  
  HAT-P-59: All blend models tested yield higher χ² fits to the photometry than the model of a single star with a transiting planet, and can be rejected with 3σ confidence. Those models that cannot be rejected with at least 5σ confidence based solely on the photometry predict BS variations in excess of 100 m s⁻¹ (however, the measured BS rms scatter from TRES is 50 m s⁻¹) and RV variations that do not reproduce the observed sinusoidal variation.
• 3.  
  HAT-P-60: All blend models tested can be rejected with at least 5σ confidence based solely on the photometry.
• 4.  
  HAT-P-61: Similar to HAT-P-59, all blend models tested yield higher χ² fits to the photometry than the model of a single star with a transiting planet, and can be rejected with 2σ confidence based on the photometry alone. Those models that cannot be rejected with at least 5σ confidence based solely on the photometry predict HIRES BS variations in excess of 100 m s⁻¹ (the measured BS rms scatter from HIRES is 5 m s⁻¹), TRES BS variations in excess of 200 m s⁻¹ (the measured BS rms scatter from TRES is 50 m s⁻¹), and RV variations that do not reproduce the observed sinusoidal variation.
• 5.  
  HAT-P-62: All blend models tested have higher χ² fits to the photometry than the model of a single star with a transiting planet, and can be rejected with at least 1σ confidence. Those models that cannot be rejected with at least 5σ confidence can be rejected based on the BS observations. These blend models yield an rms scatter for the BSs in excess of 390 m s⁻¹, whereas the measured TRES BS rms scatter is 35 m s⁻¹.
• 6.  
  HAT-P-63: Similar to HAT-P-59, all blend models tested yield higher χ² fits to the photometry than the model of a single star with a transiting planet, and can be rejected with 1.5σ confidence based on the photometry alone. Those models that cannot be rejected with at least 5σ confidence based solely on the photometry predict HDS BS variations in excess of 60 m s⁻¹ (the measured BS rms scatter from HDS is 13 m s⁻¹), SOPHIE BS variations in excess of 400 m s⁻¹ (the measured BS rms scatter from SOPHIE is 26 m s⁻¹), and RV variations in excess of ∼200 m s⁻¹ that do not reproduce the observed sinusoidal variation.
• 7.  
  HAT-P-64: All blend models tested have higher χ² fits to the photometry than the model of a single star with a transiting planet, and can be rejected with at least 1σ confidence. Those models that cannot be rejected with at least 5σ confidence predict a BS rms scatter of at least 160 m s⁻¹, compared to the measured BS rms of 35 m s⁻¹ for the Keck/HIRES observations.

The analysis described above was carried out before the release of Gaia DR2 or TESS data. The consistency between the distance inferred for each source by this method, assuming it is a single star with a planet, and the Gaia DR2 distance only bolsters the basic conclusion that none of these systems is a blended stellar eclipsing binary. Moreover, the TESS light curves showed no features (such as secondary eclipses or large ellipsoidal variations) that would be indicative of a blended eclipsing binary that might motivate a re-analysis.

In order to determine the physical parameters of the TEP systems, we carried out a global modeling of the HATNet, KeplerCam, and TESS photometry, the high-precision RV measurements, the SPC T_eff⋆ and [Fe/H] measurements, the Gaia DR2 parallax, and the Gaia DR2, APASS, TASS Mark IV, 2MASS, and WISE broadband photometry (G, BP, RP, B, V, g, r, i, R, I_C , J, H, K_S , W₁, W₂, W₃, W₄; where available).

We fit Mandel & Agol (2002) transit models to the light curves assuming quadratic limb darkening. The limb-darkening coefficients are allowed to vary in the fit, but we use the tabulations from Claret et al. (2012, 2013) and Claret (2018) to place informative Gaussian prior constraints on their values, assuming a prior uncertainty of 0.2 for each coefficient.

We allow for a dilution of the HATNet transit depth in cases where there are neighbors blended with the targets in the low spatial resolution survey images (HAT-P-61–HAT-P-64). For TESS we allow for dilution for all five observed systems, and also binned the model to account for the 30 minute exposure time (Kipping 2010). For the KeplerCam light curves we include a quadratic trend in time, linear trends with up to three parameters describing the shape of the point-spread function (PSF), and a simultaneous application of the TFA (Kovács et al. 2005) in our model for each event to correct for systematic errors in the photometry. For HAT-P-62 we also include dilution factors in the KeplerCam model to account for the blending with the 521 neighbor. To do this we simulate KeplerCam images of the primary target and its neighbor using the observed PSF and drawing i-band magnitudes for each component from normal distributions with means and standard deviations based on the measured i magnitudes for each source from APASS. We also simulate images without the neighbor. We then carry out aperture photometry on the simulated images and compare the flux measured with and without the neighbor to determine the expected dilution. The median and standard deviation of the dilution are then calculated from all simulations for a given night to establish Gaussian priors which are placed on the dilution parameters which we vary in our modeling.

We fit Keplerian orbits to the RV curves allowing the zero-point for each instrument to vary independently in the fit, and allowing for RV jitter which we also vary as a free parameter for each instrument.

To model the additional stellar atmospheric, parallax, and photometry observations we introduce four new model parameters which are allowed to vary in the fit: the distance modulus (m − M)₀, the V-band extinction A_V , and the stellar atmospheric parameters T_eff⋆ and [Fe/H]. Each link in the Markov chain yields a combination of (T_eff⋆, ρ_⋆, [Fe/H]) which we use to determine the stellar mass, radius, $\mathrm{log}g$, luminosity, and absolute magnitude in various bandpasses by comparison with the PARSEC stellar evolution models (specifically PARSEC realease v1.2S + CLIBRI release PR16, as in Marigo et al. 2017) which we generated using the CMD 3.0 web interface by L. Girardi. ²⁴ Note that ρ_⋆ is not varied directly in the fit, but rather can be computed from the other transit and orbital parameters which are varied. These absolute magnitudes, together with the model distance modulus and polynomial relations for the extinction in each bandpass as a function of A_V and T_eff⋆, are used to compute model values for the broadband photometry measurements to be compared to the observations. The polynomial relations for the extinction were determined based on tabulating the PARSEC isochrones at A_V = 1 and at A_V = 0, where the extinction coefficients are computed by the CMD interface on a star-by-star basis assuming the Cardelli et al. (1989) and O'Donnell (1994) R_V = 3.1 extinction law. See Hartman et al. (2019) for details. Here we assume systematic errors of 0.002 mag, 0.005 mag, and 0.003 mag on the G, BP and RP photometry, respectively, following Evans et al. (2018). These systematic uncertainties are added in quadrature to the statistical uncertainties on the measurements listed in the Gaia DR2 catalog.

For A_V we make use of the MWDUST 3D Galactic extinction model (Bovy et al. 2016) to tabulate the extinction in 0.1 kpc steps in the direction of the source. For a given (m − M)₀ we then perform linear interpolation among these values to estimate the expected A_V at that distance. We treat this expected value as a Gaussian prior, with a 1σ uncertainty of 20% the maximum value.

We use a differential evolution Markov chain Monte Carlo procedure to explore the fitness landscape and to determine the posterior distribution of the parameters. When a proposed link in the Markov chain falls outside of the parameter values spanned by the stellar evolution models (e.g., if a star with a density greater than what is allowed by the stellar evolution models at a given temperature and metallicity is proposed) the link is rejected and the previous link is retained. In this manner the fitting procedure used here forces the solutions to match to the theoretical stellar evolution models. We tried fitting both fixed-circular-orbit and free-eccentricity models to the data, and for all seven systems found that the data are consistent with a circular orbit. We therefore adopt the parameters that come from the fixed-circular-orbit models for all of the systems. The resulting parameters for HAT-P-58b, HAT-P-59b, HAT-P-60b, and HAT-P-61b are listed in Table 10, while for HAT-P-62b, HAT-P-63b, and HAT-P-64b they are listed in Table 11.

Table 10. Orbital and Planetary Parameters for HAT-P-58b, HAT-P-59b, HAT-P-60b, and HAT-P-61b

	HAT-P-58b	HAT-P-59b	HAT-P-60b	HAT-P-61b
Parameter	Value	Value	Value	Value
Light-curve parameters
P (days)	4.0138379 ± 0.0000024	4.1419771 ± 0.0000012	4.7947813 ± 0.0000024	1.90231289 ± 0.00000077
Tc (BJDTDB − 2450000) a	7369.03094 ± 0.00056	8618.54088 ± 0.00021	8360.94029 ± 0.00056	7851.21119 ± 0.00047
T14 (days) a	0.1729 ± 0.0015	0.09747 ± 0.00097	0.2098 ± 0.0015	0.0691 ± 0.0012
T12 = T34 (days) a	0.0193 ± 0.0010	0.02624 ± 0.00099	0.02557 ± 0.00073	0.01372 ± 0.00085
a/R⋆	7.02 ± 0.15	9.87 ± 0.12	${6.146}_{-0.077}^{+0.057}$	6.90 ± 0.13
ζ/R⋆ b	13.00 ± 0.10	26.81 ± 0.41	10.81 ± 0.10	35.46 ± 0.88
Rp /R⋆	0.0895 ± 0.0017	0.10452 ± 0.00096	0.07622 ± 0.00055	0.0984 ± 0.0025
b2	${0.285}_{-0.032}^{+0.033}$	${0.689}_{-0.015}^{+0.013}$	${0.446}_{-0.018}^{+0.014}$	${0.589}_{-0.026}^{+0.024}$
$b\equiv a\cos i/{R}_{\star }$	${0.534}_{-0.031}^{+0.030}$	${0.8299}_{-0.0089}^{+0.0077}$	${0.668}_{-0.014}^{+0.011}$	${0.767}_{-0.017}^{+0.015}$
i (deg)	85.64 ± 0.34	85.180 ± 0.100	83.75 ± 0.17	83.62 ± 0.24
HATNet blend factors c
Blend factor 1	⋯	⋯	⋯	0.87 ± 0.10
Blend factor 2	⋯	⋯	⋯	0.915 ± 0.065
TESS blend factors c
Blend factor 1	0.940 ± 0.038	0.997 ± 0.012	0.9957 ± 0.0018	0.694 ± 0.040
Blend factor 2	⋯	0.9993 ± 0.0018	⋯	⋯
Blend factor 3	⋯	0.9982 ± 0.0047	⋯	⋯
Blend factor 4	⋯	0.9989 ± 0.0038	⋯	⋯
Blend factor 5	⋯	0.996 ± 0.023	⋯	⋯
Blend factor 6	⋯	0.996 ± 0.012	⋯	⋯
Blend factor 7	⋯	0.9993 ± 0.0018	⋯	⋯
Limb-darkening coefficients d
c1, R	⋯	⋯	⋯	0.38 ± 0.16
c2, R	⋯	⋯	⋯	0.36 ± 0.17
c1, r	0.23 ± 0.14	0.43 ± 0.16	0.47 ± 0.15	0.40 ± 0.16
c2, r	0.25 ± 0.17	0.36 ± 0.17	0.28 ± 0.15	0.39 ± 0.16
c1, i	0.18 ± 0.10	0.32 ± 0.14	0.18 ± 0.12	0.32 ± 0.16
c2, i	0.14 ± 0.15	0.21 ± 0.15	0.09 ± 0.14	0.30 ± 0.16
c1, z	⋯	⋯	${0.137}_{-0.096}^{+0.129}$	⋯
c2, z	⋯	⋯	0.12 ± 0.15	⋯
c1, T	0.26 ± 0.13	0.16 ± 0.11	0.19 ± 0.11	0.31 ± 0.14
c2, T	0.24 ± 0.16	0.29 ± 0.14	0.23 ± 0.15	0.29 ± 0.16
RV parameters
K (m s−1)	46.4 ± 3.6	192.6 ± 7.7	54.1 ± 3.5	173 ± 11
e e	<0.073	<0.030	<0.250	<0.113
RV jitter HIRES (m s−1) f	<12.6	⋯	12.3 ± 3.7	<61.3
RV jitter TRES (m s−1)	⋯	<38.4	<12.4	39 ± 11
RV jitter SOPHIE (m s−1)	⋯	<17.6	<15.0	⋯
RV jitter NRES/ELP (m s−1)	⋯	⋯	56 ± 13	⋯
RV jitter NRES/TLV (m s−1)	⋯	⋯	22 ± 19	⋯
Planetary parameters
Mp (MJ)	0.372 ± 0.030	1.540 ± 0.067	0.574 ± 0.038	1.057 ± 0.070
Rp (RJ)	1.332 ± 0.043	1.123 ± 0.013	1.631 ± 0.024	0.899 ± 0.027
C(Mp , Rp ) g	0.02	− 0.16	− 0.02	− 0.04
ρp (g cm−3)	0.194 ± 0.024	1.347 ± 0.081	0.164 ± 0.013	1.80 ± 0.20
$\mathrm{log}{g}_{p}$ (cgs)	2.714 ± 0.045	3.481 ± 0.023	2.730 ± 0.032	3.510 ± 0.040
a (au)	0.04994 ± 0.00044	0.05064 ± 0.00037	0.06277 ± 0.00017	0.03010 ± 0.00034
Teq (K)	1622 ± 18	1277.8 ± 6.5	1772 ± 12	1505 ± 16
Θ h	0.0269 ± 0.0023	0.1367 ± 0.0058	0.0306 ± 0.0020	0.0702 ± 0.0047
${\mathrm{log}}_{10}\langle F\rangle$ (cgs) i	9.193 ± 0.019	8.7787 ± 0.0088	9.347 ± 0.012	9.063 ± 0.018

Notes. For all four systems the fixed-circular-orbit model has a higher Bayesian evidence than the eccentric-orbit model. We therefore assume a fixed-circular orbit in generating the parameters listed here.

^a Times are in barycentric Julian date on the dynamical time system, including the correction for leap seconds. T_c : Reference epoch of mid-transit that minimizes the correlation with the orbital period. T₁₄: 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 Markov chain Monte Carlo 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 HATNet and TESS light curves. This factor accounts for dilution of the transit due to blending from neighboring stars and over-filtering of the light curve (in cases where we do not apply signal-reconstruction TFA). These factors are varied in the fit, and we allow independent factors for observations obtained for different HATNet fields and different TESS sectors. For HAT-P-58–HAT-P-60 we do not include these factors for HATNet because the stars are well isolated on the HATNet images, and we apply signal-reconstruction TFA to preserve the signal shape while filtering the light curves. ^d Values for a quadratic law. These are allowed to vary in the fit, using the tabulations from Claret et al. (2012, 2013) and Claret (2018) to place informative Gaussian prior constraints on their values. ^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. In cases where the jitter is consistent with zero we list the 95% confidence upper limit. ^g Correlation coefficient between the planetary mass M_p and radius R_p estimated from the posterior parameter distribution. ^h The Safronov number is given by ${\rm{\Theta }}=\tfrac{1}{2}{({V}_{\mathrm{esc}}/{V}_{\mathrm{orb}})}^{2}=(a/{R}_{p})({M}_{p}/{M}_{\star })$ (see Hansen & Barman 2007). ⁱ Incoming flux per unit surface area, averaged over the orbit.

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Table 11. Orbital and Planetary Parameters for HAT-P-62b, HAT-P-63b, and HAT-P-64b

	HAT-P-62b	HAT-P-63b	HAT-P-64b
Parameter	Value	Value	Value
Light-curve parameters
P (days)	2.6453235 ± 0.0000039	3.377728 ± 0.000013	4.0072320 ± 0.0000017
Tc (BJDTDB − 2450000)a	7118.38979 ± 0.00044	6382.94256 ± 0.00053	7751.46354 ± 0.00063
T14 (days)a	0.1293 ± 0.0012	0.1222 ± 0.0016	0.2052 ± 0.0020
T12 = T34 (days)a	0.01183 ± 0.00050	0.01392 ± 0.00058	0.0199 ± 0.0010
a/R⋆	6.93 ± 0.11	9.56 ± 0.14	6.67 ± 0.12
ζ/R⋆ b	17.02 ± 0.17	18.45 ± 0.27	10.79 ± 0.11
Rp /R⋆	0.0942 ± 0.0019	0.1191 ± 0.0032	0.1007 ± 0.0034
b2	${0.063}_{-0.035}^{+0.036}$	${0.069}_{-0.030}^{+0.040}$	${0.054}_{-0.030}^{+0.046}$
$b\equiv a\cos i/{R}_{\star }$	${0.250}_{-0.084}^{+0.064}$	${0.262}_{-0.066}^{+0.068}$	${0.232}_{-0.079}^{+0.085}$
i (deg)	87.93 ± 0.64	88.45 ± 0.44	88.01 ± 0.70
HATNet blend factorsc
Blend factor	0.839 ± 0.055	⋯	0.748 ± 0.072
TESS blend factorsc
Blend factor	⋯	⋯	0.871 ± 0.062
Limb-darkening coefficientsd
c1, r	0.36 ± 0.15	0.44 ± 0.15	0.26 ± 0.14
c2, r	0.31 ± 0.18	0.38 ± 0.16	0.26 ± 0.17
c1, i	0.33 ± 0.10	0.47 ± 0.13	0.26 ± 0.14
c2, i	0.22 ± 0.16	0.41 ± 0.14	0.27 ± 0.17
c1, T	⋯	⋯	0.29 ± 0.11
c2, T	⋯	⋯	0.37 ± 0.16
RV parameters
K (m s−1)	110 ± 13	87.3 ± 3.2	62 ± 18
ee	<0.101	<0.069	<0.101
RV jitter HIRES (m s−1)f	⋯	⋯	21 ± 10
RV jitter TRES (m s−1)	33 ± 11	<1.9	⋯
RV jitter SOPHIE (m s−1)	⋯	16 ± 10	<69.2
RV jitter HDS (m s−1)	⋯	<2.4	⋯
Planetary parameters
Mp (MJ)	0.761 ± 0.088	0.614 ± 0.024	${0.58}_{-0.13}^{+0.18}$
Rp (RJ)	1.073 ± 0.029	1.119 ± 0.033	1.703 ± 0.070
C(Mp , Rp )g	0.02	− 0.25	0.06
ρp (g cm−3)	0.77 ± 0.11	0.540 ± 0.055	${0.144}_{-0.035}^{+0.046}$
$\mathrm{log}{g}_{p}$ (cgs)	3.214 ± 0.056	3.082 ± 0.034	2.69 ± 0.12
a (au)	0.03772 ± 0.00024	0.04294 ± 0.00035	0.05387 ± 0.00030
Teq (K)	1512 ± 13	1237 ± 11	${1766}_{-16}^{+22}$
Θh	0.0522 ± 0.0061	0.0506 ± 0.0026	${0.0281}_{-0.0064}^{+0.0084}$
${\mathrm{log}}_{10}\langle F\rangle$ (cgs)i	9.072 ± 0.015	8.722 ± 0.015	${9.341}_{-0.016}^{+0.021}$

Note. For all three systems the fixed-circular-orbit model has a higher Bayesian evidence than the eccentric-orbit model. We therefore assume a fixed-circular orbit in generating the parameters listed here. For all further tablenotes refer to Table 10.

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