HAT-P-65b AND HAT-P-66b: TWO TRANSITING INFLATED HOT JUPITERS AND OBSERVATIONAL EVIDENCE FOR THE REINFLATION OF CLOSE-IN GIANT PLANETS^*

Both HAT-P-65 (R.A. = ${21}^{{\rm{h}}}{03}^{{\rm{m}}}37\buildrel{\rm{s}}\over{.} 44$, $\mathrm{decl}.\,=$ $+11^\circ 59^{\prime} 21\buildrel{\prime\prime}\over{.} 9$ [J2000], $V=13.145\pm 0.029$ mag, spectral type G2) and HAT-P-66 (${\rm{R}}.{\rm{A}}.\,=$ ${10}^{{\rm{h}}}{02}^{{\rm{m}}}17\buildrel{\rm{s}}\over{.} 52$, $\mathrm{decl}.\,=$ $+53^\circ 57^{\prime} 03\buildrel{\prime\prime}\over{.} 1$ [J2000], $V=12.993\pm 0.052$ mag, spectral type G0) were selected as candidate transiting planet systems based on Sloan r-band photometric time series observations carried out with the HATNet telescope network (Bakos et al. 2004).

HATNet consists of six 11 cm aperture telephoto lenses, each coupled to an APOGEE front-side-illuminated CCD camera, and each placed on a fully automated telescope mount. Four of the instruments are located at Fred Lawrence Whipple Observatory (FLWO) in Arizona, USA, while two are located on the roof of the Submillimeter Array hangar building at Mauna Kea Observatory (MKO) on the island of Hawaii, USA. Each instrument observes a $10\buildrel{\circ}\over{.} 6\times 10\buildrel{\circ}\over{.} 6$ field of view and continuously monitors one or two fields each night, where a field corresponds to one of 838 fixed pointings used to cover the full 4π celestial sphere. A typical field is observed for approximately 3 months using one or two instruments (e.g., field G342 containing HAT-P-65), while a handful of fields have been observed extensively using all six instruments in the network and with observations repeated in multiple seasons (e.g., field G101 containing HAT-P-66). The former observing strategy maximizes the sky coverage of the survey, while maintaining nearly complete sensitivity to transiting giant planets with orbital periods of a few days. The latter strategy substantially increases the sensitivity to Neptune- and super-Earth-size planets, as well as planets with periods greater than 10 days, but with the trade-off of covering a smaller area of the sky.

Table 1 summarizes the properties of the HATNet observations collected for each system, including which HAT instruments were used, the date ranges over which each target was observed, the median cadence of the observations, and the per-point photometric precision after trend filtering.

We reduce the HATNet observations to light curves, for all stars in a field with $r\lt 14.5$, following Bakos et al. (2004). We used aperture photometry routines based on the FITSH software package (Pál 2012) and filtered systematic trends from the light curves following Kovács et al. (2005) (i.e., TFA) and Bakos et al. (2010) (i.e., EPD). Transits were identified in the filtered light curves using the Box-fitting Least Squares method (BLS; Kovács et al. 2002). After identifying the transits, we then reapplied TFA while preserving the shape of the transit signal as described in Kovács et al. (2005). This procedure is referred to as signal-reconstruction TFA. The final trend-filtered and signal-reconstructed light curves are shown phase-folded in Figure 1, while the measurements are available in Table 2.

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Table 2.  Light-curve Data for HAT-P-65 and HAT-P-66

Objecta	BJDb	Magc	${\sigma }_{\mathrm{Mag}}$	Mag(orig)d	Filter	Instrument
	(2,400,000+)
HAT-P-65	55128.75175	−0.00921	0.01482	⋯	r	HATNet
HAT-P-65	55115.72468	−0.00946	0.01149	⋯	r	HATNet
HAT-P-65	55120.93574	−0.02459	0.01224	⋯	r	HATNet
HAT-P-65	55115.72489	−0.01377	0.01518	⋯	r	HATNet
HAT-P-65	55094.88211	−0.01227	0.01156	⋯	r	HATNet
HAT-P-65	55128.75370	−0.00283	0.01249	⋯	r	HATNet
HAT-P-65	55154.80831	−0.01096	0.01202	⋯	r	HATNet
HAT-P-65	55102.69977	−0.00937	0.01341	⋯	r	HATNet
HAT-P-65	55128.75445	−0.00558	0.01427	⋯	r	HATNet
HAT-P-65	55115.72734	0.00413	0.01208	⋯	r	HATNet

Notes.

^aEither HAT-P-65 or HAT-P-66. ^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 HATNet instruments (identified by "HATNet" in the "Instrument" column), these magnitudes have been corrected for trends using the EPD and TFA procedures applied in signal-reconstruction mode. For observations made with follow-up instruments (anything other than "HATNet" in the "Instrument" column), the magnitudes have been corrected for a quadratic trend in time, for variations correlated with three point-spread function (PSF) shape parameters, and with a linear basis of template light curves representing other systematic trends, which are fit simultaneously with the transit. ^dRaw magnitude values without correction for the quadratic trend in time, or for trends correlated with the shape of the PSF. 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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We searched the residual HATNet light curves of both objects for additional periodic signals using BLS. Neither target shows evidence for additional transits with BLS; however, this conclusion depends on the set of template light curves used in applying signal-reconstruction TFA to remove systematics. For HAT-P-65 we find that with an alternative set of templates the residuals display a marginally significant transit signal with a period of 2.573 days, which is only slightly different from the main transit period of $2.6054552\pm 0.0000031$ days. The transits detected at this period come from data points near orbital phase 0.25 when phased at the primary transit period. Since the detection of this additional signal depends on the template set used, and since any planet orbiting with a period so close to (but not equal to) that of the hot Jupiter HAT-P-65b would almost certainly be unstable, we suspect that the P = 2.573 day transit signal is not of physical origin.

We also searched the residual light curves for periodic signals using the Generalized Lomb–Scargle method (GLS; Zechmeister & Kürster 2009). For HAT-P-65 no statistically significant signal is detected in the GLS periodogram either. The highest peak in the periodogram is at a period of 0.035 days and has a semiamplitude of 1.2 mmag (using a Markov Chain Monte Carlo procedure to fit a sinusoid with a variable period yields a 95% confidence upper limit of 1.7 mmag on the semiamplitude). For HAT-P-66, for our default light curve (i.e., the one included in Table 2), we do see significant peaks in the periodogram at periods of P = 83.3029 and 0.98664 days (and its harmonics) and with formal false-alarm probabilities of 10⁻¹¹ and semiamplitudes of ∼0.02 mag. Given the effective sampling rate of the observations, the two signals are aliases of each other. Based on an inspection of the light curve, we conclude that this detected variability is likely due to additional systematic errors in the photometry that were not effectively removed by our filtering procedures, and that the signal is not astrophysical in nature. Indeed, if we use an alternative TFA template set in filtering the HAT-P-66 light curve, we detect no significant signal in the GLS spectrum, and we place an upper limit on the amplitude of any periodic signal of 1 mmag.

Spectroscopic observations of both HAT-P-65 and HAT-P-66 were carried out using TRES (Fűresz 2008) on the 1.5 m Tillinghast Reflector at FLWO, and HIRES (Vogt et al. 1994) on the Keck I 10 m at MKO. For HAT-P-65 we also obtained observations using the Fibre-fed Échelle Spectrograph (FIES) on the 2.5 m Nordic Optical Telescope (NOT; Djupvik & Andersen 2010) at the Observatorio del Roque de los Muchachos on the Spanish island of La Palma. For HAT-P-66 spectroscopic observations were also collected using the SOPHIE spectrograph on the 1.93 m telescope at the Observatoire de Haute-Provence (OHP; Bouchy et al. 2009) in France. The spectroscopic observations collected for each system are summarized in Table 3. Phase-folded high-precision radial velocity (RV) and spectral line bisector span (BS) measurements are plotted in Figure 2, together with our best-fit models for the RV orbital wobble of the host stars (Section 3.3). The individual RV and BS measurements are made available in Table 4 at the end of the paper.

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Table 3.  Summary of Spectroscopy Observations

Instrument	UT Date (s)	# Spec.	Res.	S/N Rangea	${\gamma }_{\mathrm{RV}}$ b	RV Precisionc
			(λ/${\rm{\Delta }}\lambda$)/1000		($\mathrm{km}\,{{\rm{s}}}^{-1}$)	(${\rm{m}}\,{{\rm{s}}}^{-1}$)
HAT-P-65
NOT 2.5 m/FIES	2010 Aug 21–22	2	46	24–28	−48.131	100
FLWO 1.5 m/TRES	2010 Oct 27	1	44	16.5	−47.768	100
NOT 2.5 m/FIES	2011 Oct 8	1	67	15	−47.799	1000
Keck I/HIRES	2010 Dec 14	1	55	80	⋯	⋯
Keck I/HIRES+I2	2010 Dec–2013 Aug	12	55	64–106	⋯	25
HAT-P-66
FLWO 1.5 m/TRES	2014 Nov–2015 Jun	10	44	17–22	7.973	43
OHP 1.93 m/SOPHIE	2015 Mar–2016 Jan	14	39	12–33	7.226	20
Keck I/HIRES+I2	2015 Dec–2016 Jan	5	55	78–119	⋯	12
Keck I/HIRES	2016 Feb 3	1	55	148	⋯	⋯

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 information for Keck I/HIRES, for which only relative velocities are 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 the I₂-free templates obtained with Keck I/HIRES.

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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 ${T}_{\mathrm{eff}\star }$, $\mathrm{log}{g}_{\star }$, 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 "reconnaissance" 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 (e.g., Latham et al. 2009). For HAT-P-65 we only obtained a single TRES observation, which, in combination with the FIES observations discussed below, rules out these false-positive scenarios. For HAT-P-66 the initial TRES RVs showed evidence of an orbital variation consistent with a planetary-mass companion producing the transits detected by HATNet, so we continued collecting higher signal-to-noise ratio (S/N) observations of this system with TRES. High-precision RVs and BSs were measured from these spectra via a multi-order analysis (e.g., Bieryla et al. 2014).

The FIES spectra of HAT-P-65 were reduced in a similar manner to the TRES data (Buchhave et al. 2010) and were used for reconnaissance. Two exposures were obtained using the medium-resolution fiber, while the third was obtained with the high-resolution fiber. One of the two medium-resolution observations had sufficiently high S/N to be used for characterizing the stellar atmospheric parameters (Section 3.1).

The HIRES observations of HAT-P-65 and HAT-P-66 were reduced to relative RVs in the solar system barycenter frame following the method of Butler et al. (1996), and to BSs following Torres et al. (2007). We also measured Ca ii HK chromospheric emission indices (the so-called S and $\,{\mathrm{log}}_{10}\,{R}_{\mathrm{HK}}^{\prime }$ indices) following Isaacson & Fischer (2010) and Noyes et al. (1984). The I₂-free template observations of each system were also used to determine the adopted stellar atmospheric parameters (Section 3.1).

The SOPHIE spectra of HAT-P-66 were collected as described in Boisse et al. (2013) and reduced following Santerne et al. (2014). One of the observations was obtained during a planetary transit and is excluded from the analysis.

In order to better determine the physical parameters of each TEP system and to aid in excluding blended stellar eclipsing binary false-positive scenarios, 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 Table 1, 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 after trend filtering. The images were reduced to light curves via aperture photometry based on the FITSH package (following Bakos et al. 2010) and filtered for trends, which were fit to the light curves simultaneously with the transit model (Section 3.3). The resulting trend-filtered light curves are plotted together with the best-fit transit model in Figure 3 for HAT-P-65 and in Figure 4 for HAT-P-66. The data are made available in Table 2.

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In order to detect possible neighboring stars that may be diluting the transit signals, we obtained J- and K_S-band snapshot images of both targets using the WIYN High-Resolution Infrared Camera (WHIRC) on the WIYN 3.5 m telescope at Kitt Peak National Observatory in Arizona. Observations were obtained on the nights of 2016 April 24, 27, and 28, with seeing varying between $\sim 0\buildrel{\prime\prime}\over{.} 5$ and $\sim 1^{\prime\prime}$. Images were collected at different nod positions. These were calibrated, background-subtracted, registered, and median-combined using the same tools that we used for reducing the KeplerCam images.

We find that HAT-P-65 has a neighbor located $3\buildrel{\prime\prime}\over{.} 6$ to the west with a magnitude difference of ${\rm{\Delta }}J=4.91\pm 0.01$ mag and ${\rm{\Delta }}K=4.95\pm 0.03$ mag relative to HAT-P-65 (Figure 5). The neighbor is too faint and distant to be responsible for the transits detected in either the HATNet or KeplerCam observations. The neighbor has a J − K color that is the same as HAT-P-65 to within the uncertainties, and is thus a background star with an effective temperature that is similar to that of HAT-P-65, and not a physical companion. No neighbor is detected within 10'' of HAT-P-66.

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Figure 6 shows the J- and K-band magnitude contrast curves for HAT-P-65 and HAT-P-66 based on these observations. These curves are calculated using the method and software described by Espinoza et al. (2016). The bands shown in these images represent the variation in the contrast limits depending on the position angle of the putative neighbor.

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High-precision atmospheric parameters, including the effective surface temperature ${T}_{\mathrm{eff}\star }$, the surface gravity $\mathrm{log}{g}_{\star }$, the metallicity $[\mathrm{Fe}/{\rm{H}}]$, and the projected rotational velocity $v\sin i$, were determined by applying the Stellar Parameter Classification (SPC; Buchhave et al. 2012) procedure to our high-resolution spectra. For HAT-P-65 this analysis was performed on the highest-S/N FIES spectrum and on our Keck I/HIRES I₂-free template spectrum (we adopt the weighted average of each parameter determined from the two spectra). For HAT-P-66 this analysis was performed on our Keck I/HIRES I₂-free template spectrum. We assume a minimum uncertainty of 50 K on ${T}_{\mathrm{eff}\star }$, 0.10 dex on $\mathrm{log}{g}_{\star }$, 0.08 dex on $[\mathrm{Fe}/{\rm{H}}]$, and 0.5 $\mathrm{km}\,{{\rm{s}}}^{-1}$ 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 Sozzetti et al. (2007), we combine the ${T}_{\mathrm{eff}\star }$ and $[\mathrm{Fe}/{\rm{H}}]$ values measured from the spectra with the stellar densities (${\rho }_{\star }$) determined from the light curves (based on the analysis in Section 3.3) to determine the physical parameters of the host stars (i.e., their masses, radii, surface gravities, ages, luminosities, and broadband absolute magnitudes) via interpolation within the Yonsei–Yale theoretical stellar isochrones (YY; Yi et al. 2001). Figure 7 compares the model isochrones to the measured ${T}_{\mathrm{eff}\star }$ and ${\rho }_{\star }$ values for each system.

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For HAT-P-65 the $\mathrm{log}{g}_{\star }$ value determined from this analysis differed by 0.19 dex ($\sim 1.9\sigma$) from the initial value determined through SPC. A difference of this magnitude is typical and reflects the difficulty of accurately measuring all four atmospheric parameters simultaneously via cross-correlation with synthetic templates (e.g., Torres et al. 2012). We therefore carried out a second SPC analysis of HAT-P-65 with $\mathrm{log}{g}_{\star }$ fixed based on this analysis, and then repeated the light-curve analysis and stellar parameter determination, finding no appreciable change in $\mathrm{log}{g}_{\star }$. For HAT-P-66 the $\mathrm{log}{g}_{\star }$ value determined from the YY isochrones differed by only 0.007 dex from the initial spectroscopically determined value, so we did not carry out a second SPC iteration in this case.

The adopted stellar parameters for HAT-P-65 and HAT-P-66 are listed in Table 5. We also collect in this table a variety of photometric and kinematic properties for each system from catalogs. Distances are determined using the listed photometry and assuming an ${R}_{V}=3.1$ Cardelli et al. (1989) extinction law.

Table 4.  Relative Radial Velocities and Bisector Spans for HAT-P-65 and HAT-P-66

Star	BJD	RVa	${\sigma }_{\mathrm{RV}}$ b	BS	${\sigma }_{\mathrm{BS}}$	Phase	Instrument
	(2,450,000+)	(${\rm{m}}\,{{\rm{s}}}^{-1}$)	(${\rm{m}}\,{{\rm{s}}}^{-1}$)	(${\rm{m}}\,{{\rm{s}}}^{-1}$)	(${\rm{m}}\,{{\rm{s}}}^{-1}$)
HAT-P-65
HAT-P-65	5544.74169	⋯	⋯	19.6	29.8	0.161	HIRES
HAT-P-65	5544.75713	−27.18	7.33	59.9	26.9	0.167	HIRES
HAT-P-65	5545.73503	65.09	6.31	20.1	10.9	0.542	HIRES
HAT-P-65	5814.97581	54.96	5.43	−23.6	7.4	0.880	HIRES
HAT-P-65	5850.91750	39.48	5.64	43.7	11.2	0.675	HIRES
HAT-P-65	5853.90364	67.84	5.18	−0.2	6.9	0.821	HIRES
HAT-P-65	5878.76104	−74.79	5.32	−1.6	4.4	0.361	HIRES
HAT-P-65	5879.78830	79.69	5.53	−1.7	5.2	0.756	HIRES
HAT-P-65	5880.82088	−70.82	5.50	0.2	6.5	0.152	HIRES
HAT-P-65	5881.83486	−15.35	6.61	−21.2	8.1	0.541	HIRES
HAT-P-65	5904.71775	−81.04	4.62	2.2	7.0	0.324	HIRES
HAT-P-65	6193.91043	−34.59	5.57	5.4	5.3	0.319	HIRES
HAT-P-65	6534.99676	−65.37	5.92	5.5	12.5	0.231	HIRES
HAT-P-66
HAT-P-66	6991.98631	−26.96	45.68	⋯	⋯	0.227	TRES
HAT-P-66	7061.78904	85.42	58.94	⋯	⋯	0.713	TRES
HAT-P-66	7064.81417	132.13	59.20	⋯	⋯	0.731	TRES
HAT-P-66	7079.67198	54.56	57.38	⋯	⋯	0.730	TRES
HAT-P-66	7110.88787	−60.24	49.59	⋯	⋯	0.233	TRES
HAT-P-66	7112.39413	74.38	17.40	4.6	31.3	0.740	Sophie
HAT-P-66	7136.46148	84.58	12.70	0.8	22.9	0.838	Sophie
HAT-P-66	7146.66832	−108.08	42.72	⋯	⋯	0.272	TRES
HAT-P-66	7166.67684c	170.19	73.39	⋯	⋯	0.004	TRES
HAT-P-66	7167.68267	−22.39	54.73	⋯	⋯	0.343	TRES
HAT-P-66	7168.70209	116.29	42.72	⋯	⋯	0.686	TRES
HAT-P-66	7180.66291	190.92	75.28	⋯	⋯	0.710	TRES
HAT-P-66	7191.40443	−132.24	20.50	−42.1	36.9	0.324	Sophie
HAT-P-66	7193.37858c	137.63	47.00	−204.0	84.6	0.989	Sophie
HAT-P-66	7195.40734	71.00	16.30	61.3	29.3	0.671	Sophie
HAT-P-66	7331.65788	−22.35	16.10	30.7	29.0	0.515	Sophie
HAT-P-66	7333.68313	−89.69	13.40	33.6	24.1	0.196	Sophie
HAT-P-66	7334.67374	9.77	10.60	17.4	19.1	0.529	Sophie
HAT-P-66	7335.68108	94.91	11.70	57.0	21.1	0.868	Sophie
HAT-P-66	7379.14314	−17.16	4.52	5.2	5.5	0.492	HIRES
HAT-P-66	7400.62823	92.74	13.00	48.4	23.4	0.721	Sophie
HAT-P-66	7402.71917	−53.77	17.00	−29.5	30.6	0.424	Sophie
HAT-P-66	7403.52312	91.28	18.30	−6.8	32.9	0.695	Sophie
HAT-P-66	7404.61059	−18.72	17.00	−3.1	30.6	0.061	Sophie
HAT-P-66	7405.56638	−60.84	14.00	25.1	25.2	0.382	Sophie
HAT-P-66	7412.16895	51.53	3.81	4.8	8.7	0.604	HIRES
HAT-P-66	7413.08806	61.91	3.34	−3.3	4.6	0.913	HIRES
HAT-P-66	7413.94835	−67.66	2.93	5.4	3.0	0.202	HIRES
HAT-P-66	7415.04674	37.83	3.20	−14.4	5.7	0.572	HIRES
HAT-P-66	7422.94521	⋯	⋯	2.3	2.2	0.230	HIRES

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. RVs are not measured for the I₂-free HIRES template spectra, but spectral line BSs are measured for these spectra. ^bInternal errors excluding the component of astrophysical jitter considered in Section 3.3. ^cThese observations were excluded from the analysis because they were obtained during transit and the RVs may be affected by the Rossiter–McLaughlin effect.

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The two stars are quite similar, with masses of $1.212\pm 0.050$ ${M}_{\odot }$ and ${1.255}_{-0.054}^{+0.107}$ ${M}_{\odot }$ for HAT-P-65 and HAT-P-66, respectively, and with respective radii of $1.860\pm 0.096$ ${R}_{\odot }$ and ${1.881}_{-0.095}^{+0.151}$ ${R}_{\odot }$. The stars are moderately evolved, with ages of $5.46\pm 0.61$ Gyr and ${4.66}_{-1.12}^{+0.52}$ Gyr (these are 84% ± 10% and ${83}_{-20}^{+9}$% of each star's full lifetime, respectively). As we point out in Section 4, there appears to be a general trend among the host stars of highly inflated planets in which the largest planets are preferentially found around moderately evolved stars. HAT-P-65 and HAT-P-66 are in line with this trend.

Table 5.  Stellar Parameters for HAT-P-65 and HAT-P-66^a

	HAT-P-65	HAT-P-66
Parameter	Value	Value	Source
Astrometric properties and cross-identifications
2MASS-ID	21033731+1159218	10021743+5357031	⋯
GSC-ID	GSC 1111-00383	GSC 3814-00307	⋯
R.A. (J2000)	${21}^{{\rm{h}}}{03}^{{\rm{m}}}37\buildrel{\rm{s}}\over{.} 44$	${10}^{{\rm{h}}}{02}^{{\rm{m}}}17\buildrel{\rm{s}}\over{.} 52$	2MASS
Decl. (J2000)	$+11^\circ 59^{\prime} 21\buildrel{\prime\prime}\over{.} 9$	$+53^\circ 57^{\prime} 03\buildrel{\prime\prime}\over{.} 1$	2MASS
${\mu }_{{\rm{R}}.{\rm{A}}.}$ ($\mathrm{mas}\,{\mathrm{yr}}^{-1}$)	$5.5\pm 1.9$	$-9.2\pm 1.8$	UCAC4
${\mu }_{\mathrm{Decl}.}$ ($\mathrm{mas}\,{\mathrm{yr}}^{-1}$)	$-4.0\pm 1.9$	$-11.4\pm 2.4$	UCAC4
Spectroscopic properties
${T}_{\mathrm{eff}\star }$ (K)	$5835\pm 51$	$6002\pm 50$	SPCb
$\mathrm{log}{g}_{\star }$ (cgs)	$4.18\pm 0.10$	$3.96\pm 0.10$	SPCc
$[\mathrm{Fe}/{\rm{H}}]$	$0.100\pm 0.080$	$0.035\pm 0.080$	SPC
$v\sin i$ ($\mathrm{km}\,{{\rm{s}}}^{-1}$)	$7.10\pm 0.50$	$7.57\pm 0.50$	SPC
${v}_{\mathrm{mac}}$ ($\mathrm{km}\,{{\rm{s}}}^{-1}$)	1.0	1.0	Assumed
${v}_{\mathrm{mic}}$ ($\mathrm{km}\,{{\rm{s}}}^{-1}$)	2.0	2.0	Assumed
${\gamma }_{\mathrm{RV}}$ (${\rm{m}}\,{{\rm{s}}}^{-1}$)	$-47.77\pm 0.10$	$7.97\pm 0.10$	TRESd
${S}_{\mathrm{HK}}$	$\cdots$	⋯	HIRES
$\mathrm{log}{R}_{\mathrm{HK}}^{\prime }$	$\cdots$	⋯	HIRES
Photometric properties
B (mag)	$13.818\pm 0.021$	$13.552\pm 0.027$	APASSe
V (mag)	$13.145\pm 0.029$	$12.993\pm 0.052$	APASSe
I (mag)	$12.46\pm 0.10$	$12.339\pm 0.084$	TASS Mark IVf
g (mag)	$13.445\pm 0.016$	$13.209\pm 0.021$	APASSe
r (mag)	$12.948\pm 0.033$	$12.859\pm 0.064$	APASSe
i (mag)	$12.784\pm 0.097$	$12.771\pm 0.064$	APASSe
J (mag)	$11.892\pm 0.026$	$12.001\pm 0.022$	2MASS
H (mag)	$11.604\pm 0.022$	$11.735\pm 0.022$	2MASS
Ks (mag)	$11.528\pm 0.025$	$11.675\pm 0.022$	2MASS
Derived properties
${M}_{\star }$ (${M}_{\odot }$)	$1.212\pm 0.050$	${1.255}_{-0.054}^{+0.107}$	YY+${\rho }_{\star }$+SPCg
${R}_{\star }$ (${R}_{\odot }$)	$1.860\pm 0.096$	${1.881}_{-0.095}^{+0.151}$	YY+${\rho }_{\star }$+SPC
$\mathrm{log}{g}_{\star }$ (cgs)	$3.983\pm 0.035$	$3.993\pm 0.045$	YY+${\rho }_{\star }$+SPC
${\rho }_{\star }$ (${\rm{g}}\,{\mathrm{cm}}^{-3}$)	$0.266\pm 0.035$	$0.269\pm 0.040$	Light curves
${L}_{\star }$ (${L}_{\odot }$)	$3.59\pm 0.40$	${4.12}_{-0.46}^{+0.71}$	YY+${\rho }_{\star }$+SPC
MV (mag)	$3.43\pm 0.13$	$3.26\pm 0.15$	YY+${\rho }_{\star }$+SPC
MK (mag,ESO)	$1.93\pm 0.12$	$1.86\pm 0.14$	YY+${\rho }_{\star }$+SPC
Age (Gyr)	$5.46\pm 0.61$	${4.66}_{-1.12}^{+0.52}$	YY+${\rho }_{\star }$+SPC
AV (mag)	$0.090\pm 0.052$	$0.0000\pm 0.0062$	YY+${\rho }_{\star }$+SPC
Distance (pc)	$841\pm 45$	${927}_{-49}^{+75}$	YY+${\rho }_{\star }$+SPC

Notes. For both 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.

^aWe adopt the IAU 2015 Resolution B3 nominal values for the solar and Jovian parameters (Prša et al. 2016) for all of our calculations, taking ${R}_{{\rm{J}}}$ to be the nominal equatorial radius of Jupiter. Where necessary we assume $G=6.6408\times {10}^{-11}$ m³ kg⁻¹ s⁻¹. Because Yi et al. (2001) do not specify the assumed value for G or ${M}_{\odot }$, we take the stellar masses from these isochrones at face value without conversion. Any discrepancy results in an error that is less than 1%, which is well below the observational uncertainty. We note that the standard values assumed in prior HAT planet discovery papers are very close to the nominal values adopted here. In all cases the conversion results in changes to measured parameters that are indetectable at the level of precision to which they are listed. ^bSPC—Stellar Parameter Classification procedure for the analysis of high-resolution spectra (Buchhave et al. 2012), applied to the TRES spectra of HAT-P-65 and the Keck/HIRES spectra of HAT-P-66. These parameters rely primarily on SPC but also have a small dependence on the iterative analysis incorporating the isochrone search and global modeling of the data. ^cThe spectroscopically determined value of $\mathrm{log}{g}_{\star }$ is from our initial SPC analysis, where ${T}_{\mathrm{eff}\star }$, $\mathrm{log}{g}_{\star }$, $[\mathrm{Fe}/{\rm{H}}]$, and $v\sin i$ were all varied. Systematic errors are common when all four parameters are varied. The adopted values for ${T}_{\mathrm{eff}\star }$, $[\mathrm{Fe}/{\rm{H}}]$, and $v\sin i$ stem from a second iteration of SPC, where $\mathrm{log}{g}_{\star }$ is fixed to the value determined through the light-curve modeling and isochrone comparison. This value is listed under the "Derived properties" section of the table. ^dIn addition to the uncertainty listed here, there is a ∼0.1 $\mathrm{km}\,{{\rm{s}}}^{-1}$ systematic uncertainty in transforming the velocities to the IAU standard system. ^eFrom APASS DR6 as listed in the UCAC4 catalog (Zacharias et al. 2013). ^fDroege et al. (2006). ^gYY+${\rho }_{\star }$+SPC = based on the YY isochrones (Yi et al. 2001), ${\rho }_{\star }$ as a luminosity indicator, and the SPC results.

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In order to exclude blend scenarios, we carried out an analysis following Hartman et al. (2012). 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 SPC. We also simulate composite cross-correlation functions (CCFs) 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 both HAT-P-65 and HAT-P-66. For HAT-P-65 we are able to exclude blend scenarios, based solely on the photometry, with greater than $3.7\sigma$ confidence, while for HAT-P-66 we are able to exclude them with greater than $3.9\sigma$ confidence. For both objects, the blend models that come closest to fitting the photometric data (those that could not be rejected with $5\sigma$ confidence) can additionally be rejected due to the predicted large-amplitude BS and RV variations, which we do not observe.

In order to determine the physical parameters of the TEP systems, we carried out a global modeling of the HATNet and KeplerCam photometry and the high-precision RV measurements following Pál et al. (2008), Bakos et al. (2010), and Hartman et al. (2012). We use the Mandel & Agol (2002) transit model to fit the light curves, with limb-darkening coefficients fixed to the values tabulated by Claret (2004) for the atmospheric parameters of the stars and the broadband filters used in the observations. For the KeplerCam follow-up light curves we account for instrumental variations by using a set of linear basis vectors in the fit. The vectors that we use include the time of observations, the time squared, three parameters describing the shape of the PSF, and light curves for the 20 brightest nonvariable stars in the field (TFA templates). For the TFA templates we use the same linear coefficient (which is varied in the fit) for all light curves collected for a given transiting planet system through a given filter, while for the other basis vectors we use a different coefficient for each light curve. For the HATNet light curves we use a Mandel & Agol (2002) model and apply the fit to the signal-reconstruction TFA data (see Section 2.1). The RV curves are modeled using a Keplerian orbit, where we allow the zero point for each instrument to vary independently in the fit, and we include an RV jitter term added in quadrature to the formal uncertainties. The jitter is treated as a free parameter, which we fit for, and is taken to be independent for each instrument.

All observations of an individual system are modeled simultaneously using a Differential Evolution Markov Chain Monte Carlo procedure (ter Braak 2006). We visually inspect the Markov Chains and also apply a Geweke (1992, pp. 169–93) test to verify convergence and determine the burn-in period. For both systems we consider two models: a fixed-circular-orbit model and an eccentric-orbit model. To determine which model to use, we estimate the Bayesian evidence ratio from the Markov Chains following Weinberg et al. (2013) and find that for both systems the fixed-circular model has a greater evidence, and therefore we adopt the parameters that come from this model. The resulting parameters for both planetary systems are listed in Table 6. We also list the 95% confidence upper limit on the eccentricity for each system.

Table 6.  Orbital and Planetary Parameters for HAT-P-65b and HAT-P-66b^a

	HAT-P-65b	HAT-P-66b
Parameter	Value	Value
Light-curve parameters
P (days)	$2.6054552\pm 0.0000031$	$2.9720860\pm 0.0000057$
Tc ($\mathrm{BJD}$)b	$2456409.33263\pm 0.00046$	$2457258.79907\pm 0.00072$
T14 (days)b	$0.1819\pm 0.0022$	$0.1958\pm 0.0028$
${T}_{12}={T}_{34}$ (days)b	$0.0215\pm 0.0023$	$0.0174\pm 0.0025$
$a/{R}_{\star }$	$4.57\pm 0.20$	${5.01}_{-0.32}^{+0.21}$
$\zeta /{R}_{\star }$ c	$12.438\pm 0.080$	$11.226\pm 0.096$
${R}_{p}$/${R}_{\star }$	$0.1045\pm 0.0024$	$0.0872\pm 0.0024$
b2	${0.215}_{-0.079}^{+0.070}$	${0.110}_{-0.081}^{+0.106}$
$b\equiv a\cos i/{R}_{\star }$	${0.464}_{-0.094}^{+0.070}$	${0.33}_{-0.16}^{+0.13}$
i (deg)	$84.2\pm 1.3$	$86.2\pm 1.8$
Limb-darkening coefficientsd
${c}_{1},r$	$0.3439$	$0.3077$
${c}_{2},r$	$0.3359$	$0.3559$
${c}_{1},i$	$0.2544$	$0.2249$
${c}_{2},i$	$0.3414$	$0.3551$
${c}_{1},z$	$0.1949$	$0.1703$
${c}_{2},z$	$0.3379$	$0.3491$
RV parameters
K (${\rm{m}}\,{{\rm{s}}}^{-1}$)	$68\pm 11$	$93.5\pm 5.7$
ee	$\lt 0.304$	$\lt 0.090$
RV jitter HIRES (${\rm{m}}\,{{\rm{s}}}^{-1}$)f	$26.0\pm 7.1$	$\lt 43.2$
RV jitter TRES (${\rm{m}}\,{{\rm{s}}}^{-1}$)	⋯	$\lt 22.1$
RV jitter SOPHIE (${\rm{m}}\,{{\rm{s}}}^{-1}$)	⋯	$\lt 16.3$
Planetary parameters
${M}_{p}$ (${M}_{{\rm{J}}}$)	$0.527\pm 0.083$	$0.783\pm 0.057$
${R}_{p}$ (${R}_{{\rm{J}}}$)	$1.89\pm 0.13$	${1.59}_{-0.10}^{+0.16}$
$C({M}_{p},{R}_{p})$ g	$0.10$	$0.29$
${\rho }_{p}$ (${\rm{g}}\,{\mathrm{cm}}^{-3}$)	$0.096\pm 0.025$	${0.242}_{-0.061}^{+0.045}$
$\mathrm{log}{g}_{p}$ (cgs)	$2.560\pm 0.090$	${2.884}_{-0.081}^{+0.051}$
a (au)	$0.03951\pm 0.00054$	${0.04363}_{-0.00064}^{+0.00121}$
${T}_{\mathrm{eq}}$ (K)	$1930\pm 45$	${1896}_{-42}^{+66}$
Θh	$0.0180\pm 0.0031$	$0.0336\pm 0.0034$
${\mathrm{log}}_{10}\langle F\rangle$ (cgs)i	$9.495\pm 0.041$	${9.465}_{-0.039}^{+0.060}$

Notes. For both 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.

^aWe adopt the IAU 2015 Resolution B3 nominal values for the solar and Jovian parameters (Prša et al. 2016) for all of our calculations, taking ${R}_{{\rm{J}}}$ to be the nominal equatorial radius of Jupiter. Where necessary we assume $G=6.6408\times {10}^{-11}$ m³ kg⁻¹s⁻¹. Because Yi et al. (2001) do not specify the assumed value for G or ${M}_{\odot }$, we take the stellar masses from these isochrones at face value without conversion. Any discrepancy results in an error that is less than 1%, which is well below the observational uncertainty. We note that the standard values assumed in prior HAT planet discovery papers are very close to the nominal values adopted here. In all cases the conversion results in changes to measured parameters that are indetectable at the level of precision to which they are listed. ^bTimes 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. ${T}_{14}$: 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. ^cReciprocal 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). ^dValues for a quadratic law, adopted from the tabulations by Claret (2004) according to the spectroscopic (SPC) 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 the 95% confidence upper limit. ^gCorrelation coefficient between the planetary mass ${M}_{p}$ and radius ${R}_{p}$ estimated from the posterior parameter distribution. ^hThe Safronov number is given by ${\rm{\Theta }}=\tfrac{1}{2}{({V}_{\mathrm{esc}}/{V}_{\mathrm{orb}})}^{2}=(a/{R}_{p})({M}_{p}/{M}_{\star })$ (see Hansen & Barman 2007). ⁱIncoming flux per unit surface area, averaged over the orbit.

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We find that HAT-P-65b has a mass of $0.527\pm 0.083$ ${M}_{{\rm{J}}}$, a radius of $1.89\pm 0.13$ ${R}_{{\rm{J}}}$, and an equilibrium temperature (assuming zero albedo and full redistribution of heat) of $1930\pm 45$ K and is consistent with a circular orbit, with a 95% confidence upper limit on the eccentricity of $e\lt 0.304$. HAT-P-66b has similar properties, with a mass of $0.783\pm 0.057$ ${M}_{{\rm{J}}}$, a radius of ${1.59}_{-0.10}^{+0.16}$ ${R}_{{\rm{J}}}$, an equilibrium temperature (same assumptions) of ${1896}_{-42}^{+66}$ K, and an eccentricity of $e\lt 0.090$ with 95% confidence.

With radii of $1.89\pm 0.13$ ${R}_{{\rm{J}}}$ and ${1.59}_{-0.10}^{+0.16}$ ${R}_{{\rm{J}}}$, HAT-P-65b and HAT-P-66b are among the largest hot Jupiters known. Both planets are found around moderately evolved stars approaching the end of their main-sequence lifetimes. With an estimated age of $5.46\pm 0.61$ Gyr, HAT-P-65 is 84% ± 10% of the way through its total life span, while HAT-P-66, with an age of ${4.66}_{-1.12}^{+0.52}$ Gyr, is ${83}_{-20}^{+9}$% of the way through its life span. Looking at the broader sample of TEPs that have been discovered to date, we find that the largest exoplanets are preferentially found around moderately evolved stars.

This effect may be a by-product of the more physically important correlation between planet radius and equilibrium temperature (e.g., Fortney et al. 2007; Enoch et al. 2012; and Spiegel & Burrows 2013), with the planet equilibrium temperature increasing in time as its host star evolves and becomes more luminous. We will address the question of how the correlation between planet radius and host star fractional age that we demonstrate here relates to the radius–equilibrium temperature correlation in Section 4.1.1. While the planet radius–equilibrium temperature correlation is well known, whether or not the radii of planets can actually increase in time as their equilibrium temperatures increase has not been previously established. As discussed in Sections 1 and 4.1.4, the answer to this question has important theoretical implications for understanding the physical mechanism behind the inflation of close-in giant planets. To address this question, we will first attempt to determine whether or not there is a statistically signification correlation between planetary radii and the evolutionary status of their host stars.

Figure 8 shows TEP host stars on a ${T}_{\mathrm{eff}\star }$–${\rho }_{\star }$ diagram. These two parameters are directly measured for TEP systems and, together with the $[\mathrm{Fe}/{\rm{H}}]$ of the star, are the primary parameters used to characterize the stellar hosts. Here we limit the sample to systems with planets having ${R}_{p}\gt 0.5$ ${R}_{{\rm{J}}}$ and $P\lt 10$ days. Because observational selection effects vary from survey to survey, we show separately the systems discovered by HAT (both HATNet and HATSouth), WASP, Kepler, TrES, and KELT, which are the surveys that have discovered well-characterized planets with ${R}_{p}\gt 1.5$ ${R}_{{\rm{J}}}$. The data for the HAT, WASP, TrES, and KELT systems are drawn from a database of TEPs that we privately maintain, and are listed, together with references, in Table 7 at the end of this paper. These are planets that have been announced on the arXiv pre-print server as of 2016 June 2, and are supplemented by some additional fully confirmed planets from HAT that had not been announced by that date. For Kepler we take the data from the NASA Exoplanet archive.¹⁷ In Figure 8 we distinguish between hosts with planets having ${R}_{p}\gt 1.5$ ${R}_{{\rm{J}}}$ and hosts with planets having ${R}_{p}\lt 1.5$ ${R}_{{\rm{J}}}$. The lower bound in each panel shows the solar-metallicity, 200 Myr ZAMS isochrone from the YY models, while the upper bound shows the locus of points for stars having an age that is the lesser of 13.7 Gyr or 90% of their total lifetime, again assuming solar metallicity and using the YY models. For all of the surveys considered, planets with $R\gt 1.5$ ${R}_{{\rm{J}}}$ tend to be found around host stars that are more evolved (closer to the 90% lifetime locus) than planets with $R\lt 1.5$ ${R}_{{\rm{J}}}$. Moreover, very few highly inflated planets have been discovered around stars close to the ZAMS. The largest planets also tend to be found around hot/massive stars and have the highest level of irradiation.

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For another view of the data, in Figure 9 we plot the mass–radius relation of close-in TEPs with the color scale of each point showing the fractional isochrone-based age of the system (taken to be equal to $\tau =(t-200\,\mathrm{Myr})/({t}_{\mathrm{tot}}-200\,\mathrm{Myr})$). Here ${t}_{\mathrm{tot}}$ for a system is the maximum age of a star with a given mass and metallicity according to the YY models (Figure 10). We show the fractional age, rather than the age in Gyr, as the stellar lifetime is a strong function of stellar mass, and the largest planets also tend to be found around more massive stars with shorter total lifetimes. Because the star formation rate in the Galaxy has been approximately constant over the past ∼8 Gyr (e.g., Snaith et al. 2015), for a star of a given mass we expect τ to be uniformly distributed between 0 and 1. In order to perform a consistent analysis, we recompute ages for all of the WASP, Kepler, TrES, and KELT systems using the YY models, together with the spectroscopically measured ${T}_{\mathrm{eff}\star }$ and $[\mathrm{Fe}/{\rm{H}}]$ and transit-inferred stellar densities listed in Table 7. In Figure 9 we focus on systems with $P\lt 10$ days and ${t}_{\mathrm{tot}}\lt 10\,\mathrm{Gyr}$. Again it is apparent that the largest-radius planets tend to be around stars that are relatively old. Note that due to the finite age of the Galaxy, there has been insufficient time for stars with ${t}_{\mathrm{tot}}\gt 10$ Gyr to reach their main-sequence lifetimes. The restriction on ${t}_{\mathrm{tot}}$, which is effectively a cut on host star mass, limits the sample to stars that could be discovered at any stage in their evolution. If we do not apply this cut, then the apparent correlation between fractional age and planet radius becomes even more significant, but this is likely due to observational bias.

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The planets shown in Figure 9 have a variety of orbital separations and host star masses. Because the evolution of a planet depends on its stellar environment, we expect there to be a variance in the planet radius at fixed planet mass. In order to better compare planets likely to have similar histories (but which have different ages and thus are at different stages in their history), in Figure 11 we replot the mass–radius relation, but this time binning by host star mass and orbital semimajor axis. Note that in comparing planets with the same semimajor axis we are assuming that orbital evolution can be neglected. Again we use the color scale of points to denote the fractional age of the system. We choose a 3 × 3 binning to allow a sufficient number of planets in at least some of the bins to be able to detect a statistical trend. Unfortunately, because we limited by the small sample of planets, we are forced to use relatively large bins, so there is likely to still be significant variation in the evolution of different planets within a bin. Bearing this caveat in mind, we note that the same trend of larger-radius planets, at a given planet mass, being found around more evolved stars is seen when comparing only planets with similar host star masses and at similar orbital separations. If anything, the gradient in fractional age with planet radius is more pronounced in Figure 11 than it is in Figure 9 (see especially the center row and bottom center panel of Figure 11). If enhanced irradiation acts to slow a planet's contraction but does not reinflate the planet, then we would expect to see the opposite trend in Figure 11. Namely, a planet of a given mass at a given orbital separation around a star of a given mass should decrease, or remain constant, in size over time, despite the increasing irradiation as its host star evolves. This is not what we see. In Section 4.1.1 we follow a more statistically rigorous method to show that planetary radii increase in time with increasing irradiation, rather than being set by the initial irradiation.

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To establish the statistical significance of the trends seen in Figures 8–11, in Figure 12 we plot the fractional isochrone-based age τ against planetary radius, restricted to systems with ${t}_{\mathrm{tot}}\lt 10\,\mathrm{Gyr}$. Both the HAT and WASP data have positive correlations between R_P and the fractional age. A Spearman nonparametric rank-order correlation test gives a correlation coefficient of $0.344$ between R_P and the fractional age for HAT, with a 1.4% false-alarm probability. For the WASP sample we find a correlation coefficient of $0.277$ and a false-alarm probability of 3.5%. The Kepler, TrES, and KELT data sets are too small to perform a robust test for correlation, but they each show a similar trend. When all of the data are combined, we find a correlation coefficient of $0.347$ and a false-alarm probability of only 0.0041%. While the correlation is relatively weak, explaining only a modest amount of the overall scatter in the data, it has a high statistical significance and is extremely unlikely to be due to random chance.

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Figure 13 is similar to Figure 12, except that here we restrict the analysis to planets with $0.4\,{M}_{{\rm{J}}}\lt {M}_{p}\lt 2.0\,{M}_{{\rm{J}}}$, which is roughly the range over which the most highly inflated planets have been discovered (e.g., Figure 9). In this case we still find a statistically significant difference between the fractional ages of stars hosting large-radius planets and those hosting small-radius planets, although, due to the smaller sample size, the overall significance is somewhat reduced compared to the sample when no restriction is placed on planet mass (the correlation coefficient itself is somewhat higher). Quantitatively we find that the HAT sample has a Spearman correlation coefficient of $0.428$ and a false-alarm probability of 0.84%, the WASP sample has a correlation coefficient of $0.273$ and a false-alarm probability of 7.7%, and the combined sample has a correlation coefficient of $0.398$ and a false-alarm probability of 0.0068%.

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In order to compare planets with similar evolutionary histories, and in analogy to Figure 11, in Figure 14 we plot the fractional age against planet radius gridded by host star mass and orbital semimajor axis. Here we combine all of the data but restrict the sample to only planets with $0.4\,{M}_{{\rm{J}}}\lt {M}_{P}\lt 2.0\,{M}_{{\rm{J}}}$ around stars with ${t}_{\mathrm{tot}}\lt 10\,\mathrm{Gyr}$. We see the correlation again in several grid cells, so long as there is a sufficiently large sample.

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Of course, these correlations are likely biased due to observational selection effects. We estimate the effect of observational selections on the measured correlation below in Section 4.1.2, where we conclude that the correlation is reduced, but still significant, after accounting for selections.

We conclude that there is a statistically significant positive correlation between ${R}_{p}$ and the fractional age of the system. This correlation is seen in samples of transiting planets found by multiple surveys, with strikingly similar results found for the largest two samples (from WASP and HAT). The largest-radius planets have generally been found around more evolved stars.

4.1.1. Relation to the Correlation between Radius and Equilibrium Temperature

It is important to note that the correlation between radius and equilibrium temperature (or flux) is much stronger than the apparent correlation between planet radius and the fractional age of the host star. In fact, the data are consistent with the latter correlation being entirely a by-product of the former correlation. However, the data also indicate that the radii of planets dynamically increase in time as their host stars become more luminous and the planetary equilibrium temperatures increase.

To demonstrate this, we perform a Bayesian linear regression model comparison using the BayesFactor package in R,¹⁸ which follows the approach of Liang et al. (2008) and Rouder & Morey (2012). We test models of the form

$$\begin{eqnarray}&&\mathrm{ln}{R}_{p}={c}_{0}+{c}_{1}\mathrm{ln}{T}_{\mathrm{eq},\mathrm{now}}+{c}_{2}\mathrm{ln}{T}_{\mathrm{eq},\mathrm{ZAMS}}+{c}_{3}\mathrm{ln}a+{c}_{4}\tau ,\end{eqnarray} \tag{ 1 }$$

where c₀–c₄ are varied linear parameters, and we compare all combinations of models where parameters other than c₀ are fixed to 0. This particular parameterization is motivated by Enoch et al. (2012), who found that the radii of close-in Jupiter-mass planets are best modeled by a function of the form given above with ${c}_{2}\equiv {c}_{4}\equiv 0$, and we now include the ${T}_{\mathrm{eq},\mathrm{ZAMS}}$ and τ parameters to test whether age is an important additional variable, and/or whether the data could be equally well described if we used the initial equilibrium temperature of the planet (which does not change in time) rather than the present-day equilibrium temperature (which increases in time due to the evolution of the host). Here we consider the full sample of well-characterized planets with $P\lt 10$ days, ${R}_{p}\gt 0.5$ ${R}_{{\rm{J}}}$, $0.4\,{M}_{{\rm{J}}}\lt {M}_{p}\lt 2.0\,{M}_{{\rm{J}}}$, and ${t}_{\mathrm{tot}}\lt 10\,\mathrm{Gyr}$. Table 8 lists the linear coefficient estimates and the Bayesian evidences, sorting from highest to lowest, for each of the 15 models under comparison.

Table 7.  Adopted Parameters for Transiting Planet Systems Discovered by HAT, KELT, TrES, and WASP

Planet	Period	${M}_{p}$	${R}_{p}$	${T}_{\mathrm{eq}}$	${T}_{\mathrm{eff}\star }$	${\rho }_{\star }$	$[\mathrm{Fe}/{\rm{H}}]$	${M}_{\star }$	Age	${t}_{\mathrm{tot}}$	References
	(days)	(${M}_{{\rm{J}}}$)	(${R}_{{\rm{J}}}$)	(K)	(K)	(${\rm{g}}\,{\mathrm{cm}}^{-3}$)		(${M}_{\odot }$)	(Gyr)	(Gyr)
HAT-P-10/	3.722	0.487 ± 0.018	${1.005}_{-0.027}^{+0.032}$	1020 ± 17	4980 ± 60	${2.374}_{-0.189}^{+0.208}$	0.13 ± 0.08	0.830 ± 0.030	7.90 ± 3.80	19.95	28
WASP-11b	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
HAT-P-11b	4.888	0.081 ± 0.009	0.422 ± 0.014	878 ± 15	4780 ± 50	${2.699}_{-0.222}^{+0.242}$	0.31 ± 0.05	${0.810}_{-0.030}^{+0.020}$	${6.50}_{-4.10}^{+5.90}$	19.95	45
HAT-P-12b	3.213	0.211 ± 0.012	${0.959}_{-0.021}^{+0.029}$	963 ± 16	4650 ± 60	${2.999}_{-0.214}^{+0.175}$	−0.29 ± 0.05	0.733 ± 0.018	2.50 ± 2.00	19.95	32
HAT-P-13b	2.916	0.850 ± 0.038	1.281 ± 0.079	${1656}_{-43}^{+46}$	5653 ± 90	${0.448}_{-0.071}^{+0.082}$	0.41 ± 0.08	${1.220}_{-0.100}^{+0.050}$	${5.00}_{-0.70}^{+2.50}$	6.80	34, 51
HAT-P-14b	4.628	2.232 ± 0.059	1.150 ± 0.052	1570 ± 34	6600 ± 90	${0.618}_{-0.066}^{+0.078}$	0.11 ± 0.08	1.386 ± 0.045	1.30 ± 0.40	4.20	50
HAT-P-15b	10.864	1.946 ± 0.066	1.072 ± 0.043	904 ± 20	5568 ± 90	${1.137}_{-0.122}^{+0.142}$	0.22 ± 0.08	1.013 ± 0.043	${6.80}_{-1.60}^{+2.50}$	13.10	55
HAT-P-16b	2.776	4.193 ± 0.094	1.289 ± 0.066	1626 ± 40	6158 ± 80	${0.908}_{-0.113}^{+0.134}$	0.17 ± 0.08	1.218 ± 0.039	2.00 ± 0.80	6.60	52
HAT-P-17b	10.339	0.530 ± 0.019	1.000 ± 0.030	787 ± 15	5246 ± 80	${2.123}_{-0.188}^{+0.207}$	0.00 ± 0.08	0.861 ± 0.039	6.90 ± 3.30	19.95	97
HAT-P-18b	5.508	0.197 ± 0.013	0.995 ± 0.052	852 ± 28	4803 ± 80	${2.589}_{-0.359}^{+0.432}$	0.10 ± 0.08	0.770 ± 0.031	${12.40}_{-6.40}^{+4.40}$	19.95	75
HAT-P-19b	4.009	0.292 ± 0.018	1.132 ± 0.072	1010 ± 42	4989 ± 126	${2.169}_{-0.353}^{+0.438}$	0.23 ± 0.08	0.842 ± 0.042	8.80 ± 5.20	19.95	75
HAT-P-1b	4.465	0.524 ± 0.031	1.225 ± 0.059	1306 ± 30	6076 ± 27	${1.150}_{-0.161}^{+0.188}$	0.21 ± 0.03	${1.133}_{-0.079}^{+0.075}$	${2.70}_{-2.00}^{+2.50}$	8.70	11, 13, 18
HAT-P-20b	2.875	7.246 ± 0.187	0.867 ± 0.033	970 ± 23	4595 ± 80	${3.196}_{-0.297}^{+0.336}$	0.35 ± 0.08	0.756 ± 0.028	${6.70}_{-3.80}^{+5.70}$	19.95	84
HAT-P-21b	4.124	4.063 ± 0.161	1.024 ± 0.092	1283 ± 50	5588 ± 80	${0.992}_{-0.200}^{+0.260}$	0.01 ± 0.08	0.947 ± 0.042	10.20 ± 2.50	15.00	84
HAT-P-22b	3.212	2.147 ± 0.061	1.080 ± 0.058	1283 ± 32	5302 ± 80	${1.154}_{-0.140}^{+0.164}$	0.24 ± 0.08	0.916 ± 0.035	12.40 ± 2.60	18.85	84
HAT-P-23b	1.213	2.090 ± 0.111	1.368 ± 0.090	2056 ± 66	5905 ± 80	${0.915}_{-0.152}^{+0.189}$	0.15 ± 0.04	1.130 ± 0.035	4.00 ± 1.00	8.55	84
HAT-P-24b	3.355	0.685 ± 0.033	1.242 ± 0.067	1637 ± 42	6373 ± 80	${0.737}_{-0.105}^{+0.129}$	−0.16 ± 0.08	1.191 ± 0.042	2.80 ± 0.60	5.95	56
HAT-P-25b	3.653	0.567 ± 0.022	${1.190}_{-0.056}^{+0.081}$	1202 ± 36	5500 ± 80	${1.616}_{-0.247}^{+0.213}$	0.31 ± 0.08	1.010 ± 0.032	3.20 ± 2.30	13.50	96
HAT-P-26b	4.235	0.059 ± 0.007	${0.565}_{-0.032}^{+0.072}$	${1001}_{-37}^{+66}$	5079 ± 88	${2.351}_{-0.714}^{+0.443}$	−0.04 ± 0.08	0.816 ± 0.033	${9.00}_{-4.90}^{+3.00}$	19.95	77
HAT-P-27b	3.040	0.660 ± 0.033	${1.038}_{-0.058}^{+0.077}$	1207 ± 41	5302 ± 88	${1.842}_{-0.306}^{+0.269}$	0.29 ± 0.10	0.945 ± 0.035	${4.40}_{-2.60}^{+3.80}$	17.10	80
HAT-P-28b	3.257	0.636 ± 0.037	${1.189}_{-0.075}^{+0.102}$	1371 ± 50	5681 ± 88	${1.143}_{-0.239}^{+0.233}$	0.12 ± 0.08	1.024 ± 0.046	5.80 ± 2.30	12.05	79
HAT-P-29b	5.723	${0.778}_{-0.040}^{+0.076}$	${1.107}_{-0.082}^{+0.136}$	${1260}_{-45}^{+64}$	6087 ± 88	${0.926}_{-0.251}^{+0.201}$	0.21 ± 0.08	1.207 ± 0.046	2.20 ± 1.00	6.90	79
HAT-P-2b	5.633	9.090 ± 0.240	${1.157}_{-0.062}^{+0.073}$	1540 ± 30	6290 ± 60	${0.435}_{-0.065}^{+0.073}$	0.14 ± 0.08	1.360 ± 0.040	2.60 ± 0.50	4.55	60
HAT-P-30b	2.811	0.711 ± 0.028	1.340 ± 0.065	1630 ± 42	6304 ± 88	${0.974}_{-0.113}^{+0.137}$	0.13 ± 0.08	1.242 ± 0.041	${1.00}_{-0.50}^{+0.80}$	6.05	81
HAT-P-31b	5.005	${2.171}_{-0.077}^{+0.105}$	${1.070}_{-0.320}^{+0.480}$	${1450}_{-110}^{+230}$	6065 ± 100	${0.690}_{-0.260}^{+0.340}$	0.15 ± 0.08	${1.218}_{-0.063}^{+0.089}$	${3.17}_{-1.11}^{+0.70}$	6.55	74
HAT-P-32b	2.150	0.860 ± 0.164	1.789 ± 0.025	1786 ± 26	6207 ± 88	${0.903}_{-0.047}^{+0.050}$	−0.04 ± 0.08	1.160 ± 0.041	2.70 ± 0.80	7.00	85
HAT-P-33b	3.474	0.762 ± 0.101	1.686 ± 0.045	1782 ± 28	6446 ± 88	${0.442}_{-0.030}^{+0.033}$	0.07 ± 0.08	1.375 ± 0.040	2.30 ± 0.30	4.25	85
HAT-P-34b	5.453	3.328 ± 0.211	${1.197}_{-0.092}^{+0.128}$	1520 ± 60	6442 ± 88	${0.542}_{-0.122}^{+0.129}$	0.22 ± 0.04	1.392 ± 0.047	${1.70}_{-0.50}^{+0.40}$	4.35	95
HAT-P-35b	3.647	1.054 ± 0.033	1.332 ± 0.098	1581 ± 45	6096 ± 88	${0.590}_{-0.098}^{+0.120}$	0.11 ± 0.08	1.236 ± 0.048	${3.50}_{-0.50}^{+0.80}$	6.10	95
HAT-P-36b	1.327	1.832 ± 0.099	1.264 ± 0.071	1823 ± 55	5560 ± 100	${1.099}_{-0.159}^{+0.194}$	0.26 ± 0.10	1.022 ± 0.049	${6.60}_{-1.80}^{+2.90}$	12.80	95
HAT-P-37b	2.797	1.169 ± 0.103	1.178 ± 0.077	1271 ± 47	5500 ± 100	${1.942}_{-0.351}^{+0.342}$	0.03 ± 0.10	0.929 ± 0.043	${3.60}_{-2.20}^{+4.10}$	16.25	95
HAT-P-38b	4.640	0.267 ± 0.020	${0.825}_{-0.063}^{+0.092}$	1082 ± 55	5330 ± 100	${1.588}_{-0.415}^{+0.413}$	0.06 ± 0.10	0.886 ± 0.044	10.10 ± 4.80	19.50	104
HAT-P-39b	3.544	0.599 ± 0.099	${1.571}_{-0.081}^{+0.108}$	1752 ± 43	6430 ± 100	${0.461}_{-0.063}^{+0.059}$	0.19 ± 0.10	1.404 ± 0.051	2.00 ± 0.40	4.20	94
HAT-P-3b	2.900	${0.596}_{-0.026}^{+0.024}$	${0.899}_{-0.049}^{+0.043}$	${1127}_{-39}^{+49}$	5185 ± 46	${2.254}_{-0.281}^{+0.423}$	0.27 ± 0.04	${0.928}_{-0.054}^{+0.044}$	${1.50}_{-1.40}^{+5.40}$	18.15	3, 11, 59
HAT-P-40b	4.457	0.615 ± 0.038	1.730 ± 0.062	1770 ± 33	6080 ± 100	${0.196}_{-0.020}^{+0.020}$	0.22 ± 0.10	${1.512}_{-0.109}^{+0.045}$	${2.70}_{-0.30}^{+0.90}$	3.35	94
HAT-P-41b	2.694	0.800 ± 0.102	${1.685}_{-0.051}^{+0.076}$	1941 ± 38	6390 ± 100	${0.418}_{-0.042}^{+0.033}$	0.21 ± 0.10	1.418 ± 0.047	2.20 ± 0.40	4.05	94
HAT-P-42b	4.642	0.975 ± 0.126	1.277 ± 0.149	1427 ± 58	5743 ± 50	${0.467}_{-0.111}^{+0.154}$	0.27 ± 0.08	1.179 ± 0.067	${5.10}_{-0.70}^{+1.80}$	7.65	112
HAT-P-43b	3.333	0.660 ± 0.083	${1.283}_{-0.034}^{+0.057}$	1361 ± 24	5645 ± 74	${1.091}_{-0.106}^{+0.083}$	0.23 ± 0.08	${1.048}_{-0.042}^{+0.031}$	${5.70}_{-1.10}^{+1.90}$	11.65	112
HAT-P-44b	4.301	0.392 ± 0.031	${1.280}_{-0.074}^{+0.145}$	${1126}_{-42}^{+67}$	5295 ± 100	${1.402}_{-0.388}^{+0.277}$	0.33 ± 0.10	0.939 ± 0.041	8.90 ± 3.90	17.50	123
HAT-P-45b	3.129	${0.892}_{-0.099}^{+0.137}$	${1.426}_{-0.087}^{+0.175}$	${1652}_{-52}^{+90}$	6330 ± 100	${0.776}_{-0.220}^{+0.149}$	0.07 ± 0.10	1.259 ± 0.058	2.00 ± 0.80	5.65	123
HAT-P-46b	4.463	${0.493}_{-0.052}^{+0.082}$	${1.284}_{-0.133}^{+0.271}$	${1458}_{-75}^{+140}$	6120 ± 100	${0.676}_{-0.291}^{+0.249}$	0.30 ± 0.10	${1.284}_{-0.060}^{+0.095}$	${2.50}_{-1.00}^{+0.70}$	5.75	123
HAT-P-47b	4.732	0.206 ± 0.039	1.313 ± 0.045	1605 ± 22	6703 ± 50	${0.564}_{-0.045}^{+0.049}$	0.00 ± 0.08	1.387 ± 0.038	1.50 ± 0.30	3.95	161
HAT-P-48b	4.409	0.168 ± 0.024	1.131 ± 0.054	1361 ± 25	5946 ± 50	${0.847}_{-0.093}^{+0.109}$	0.02 ± 0.08	1.099 ± 0.041	${4.70}_{-0.80}^{+1.30}$	8.80	161
HAT-P-49b	2.692	1.730 ± 0.205	${1.413}_{-0.077}^{+0.128}$	${2131}_{-42}^{+69}$	6820 ± 52	${0.353}_{-0.069}^{+0.049}$	0.07 ± 0.08	1.543 ± 0.051	1.50 ± 0.20	2.95	126
HAT-P-4b	3.057	0.556 ± 0.068	${1.367}_{-0.044}^{+0.052}$	${1686}_{-26}^{+30}$	5860 ± 80	${0.427}_{-0.058}^{+0.073}$	0.24 ± 0.08	${1.248}_{-0.120}^{+0.070}$	${4.60}_{-1.00}^{+2.20}$	6.20	5, 11, 71
HAT-P-50b	3.122	1.350 ± 0.073	1.288 ± 0.064	1862 ± 34	6280 ± 49	0.357 ± 0.037	−0.18 ± 0.08	${1.273}_{-0.115}^{+0.049}$	${3.37}_{-0.27}^{+1.44}$	4.75	135
HAT-P-51b	4.218	0.309 ± 0.018	1.293 ± 0.054	1192 ± 21	5449 ± 50	${1.223}_{-0.135}^{+0.100}$	0.27 ± 0.08	0.976 ± 0.028	8.20 ± 1.70	15.15	135
HAT-P-52b	2.754	0.818 ± 0.029	1.009 ± 0.072	1218 ± 37	5131 ± 50	1.750 ± 0.290	0.28 ± 0.08	0.887 ± 0.027	9.40 ± 4.10	19.95	135
HAT-P-53b	1.962	1.484 ± 0.056	1.318 ± 0.091	1778 ± 48	5956 ± 50	0.870 ± 0.130	0.00 ± 0.08	1.093 ± 0.043	${4.67}_{-0.83}^{+1.45}$	8.90	135
HAT-P-54b	3.800	0.760 ± 0.032	0.944 ± 0.028	818 ± 12	4390 ± 50	${3.876}_{-0.253}^{+0.283}$	−0.13 ± 0.08	0.645 ± 0.020	${3.90}_{-2.10}^{+4.30}$	19.95	132
HAT-P-55b	3.585	0.582 ± 0.056	1.182 ± 0.055	1313 ± 26	5808 ± 50	${1.380}_{-0.143}^{+0.167}$	−0.03 ± 0.08	1.013 ± 0.037	4.20 ± 1.70	11.50	151
HAT-P-56b	2.791	2.180 ± 0.250	1.466 ± 0.040	1840 ± 21	6566 ± 50	0.627 ± 0.033	−0.08 ± 0.08	1.296 ± 0.036	2.01 ± 0.35	4.75	140
HAT-P-57b	2.465	${0.000}_{-0.000}^{+1.850}$	1.413 ± 0.054	2200 ± 76	7500 ± 250	${0.615}_{-0.036}^{+0.022}$	−0.25 ± 0.25	1.470 ± 0.120	${1.00}_{-0.51}^{+0.67}$	2.85	137
HAT-P-58b	4.014	0.394 ± 0.034	${1.203}_{-0.063}^{+0.090}$	${1500}_{-29}^{+49}$	5931 ± 50	0.564 ± 0.066	0.01 ± 0.08	${1.110}_{-0.042}^{+0.080}$	${6.10}_{-1.66}^{+0.82}$	8.45	162
HAT-P-59b	4.142	1.624 ± 0.061	1.121 ± 0.066	1273 ± 27	5665 ± 50	1.070 ± 0.130	0.41 ± 0.08	1.089 ± 0.022	4.30 ± 1.00	10.20	162
HAT-P-5b	2.788	1.060 ± 0.110	${1.254}_{-0.056}^{+0.051}$	${1539}_{-32}^{+33}$	5960 ± 100	${1.019}_{-0.129}^{+0.162}$	0.24 ± 0.15	${1.157}_{-0.081}^{+0.043}$	${2.60}_{-1.40}^{+2.10}$	8.10	6,11
HAT-P-60b	4.795	0.492 ± 0.049	${1.116}_{-0.064}^{+0.150}$	${1662}_{-42}^{+73}$	6462 ± 50	${0.357}_{-0.082}^{+0.055}$	−0.24 ± 0.08	1.310 ± 0.070	2.88 ± 0.56	4.10	162
HAT-P-61b	1.902	${1.103}_{-0.071}^{+0.052}$	${0.968}_{-0.047}^{+0.061}$	1526 ± 36	5551 ± 50	1.510 ± 0.180	0.40 ± 0.08	1.043 ± 0.022	${2.70}_{-2.50}^{+1.80}$	11.95	162
HAT-P-62b	2.645	0.801 ± 0.088	${1.131}_{-0.053}^{+0.074}$	1523 ± 31	5601 ± 50	0.840 ± 0.087	0.45 ± 0.08	1.103 ± 0.028	5.40 ± 0.89	9.60	162
HAT-P-63b	3.378	0.638 ± 0.023	1.213 ± 0.094	1246 ± 32	5365 ± 50	1.320 ± 0.180	0.43 ± 0.08	0.976 ± 0.022	7.20 ± 2.00	14.95	162
HAT-P-64b	4.007	0.750 ± 0.160	1.790 ± 0.140	${1741}_{-35}^{+48}$	6302 ± 50	${0.332}_{-0.054}^{+0.040}$	−0.01 ± 0.08	1.369 ± 0.046	2.87 ± 0.30	4.10	162
HAT-P-65b	2.605	0.527 ± 0.083	1.890 ± 0.130	1930 ± 45	5835 ± 51	0.266 ± 0.036	0.10 ± 0.08	1.212 ± 0.050	5.46 ± 0.61	6.50	166
HAT-P-66b	2.972	0.783 ± 0.057	${1.590}_{-0.100}^{+0.160}$	${1897}_{-42}^{+66}$	6002 ± 50	0.269 ± 0.040	0.04 ± 0.08	${1.255}_{-0.054}^{+0.107}$	${4.66}_{-1.12}^{+0.52}$	5.60	166
HAT-P-6b	3.853	${1.059}_{-0.052}^{+0.053}$	${1.330}_{-0.058}^{+0.064}$	${1675}_{-31}^{+32}$	6570 ± 80	${0.581}_{-0.080}^{+0.088}$	−0.13 ± 0.08	${1.290}_{-0.066}^{+0.064}$	${2.30}_{-0.60}^{+0.50}$	4.65	10, 11, 58
HAT-P-7b	2.205	1.820 ± 0.030	1.500 ± 0.020	${2140}_{-60}^{+110}$	6350 ± 80	0.271 ± 0.003	0.26 ± 0.08	1.530 ± 0.040	2.14 ± 0.26	3.25	12, 46, 47, 48
HAT-P-8b	3.076	${1.520}_{-0.160}^{+0.180}$	${1.500}_{-0.060}^{+0.080}$	1700 ± 35	6200 ± 80	${0.458}_{-0.063}^{+0.058}$	0.01 ± 0.08	1.280 ± 0.040	3.40 ± 1.00	5.20	31
HAT-P-9b	3.923	0.780 ± 0.090	1.400 ± 0.060	1530 ± 40	6350 ± 150	${0.782}_{-0.135}^{+0.166}$	0.12 ± 0.20	1.280 ± 0.130	${1.60}_{-1.40}^{+1.80}$	5.50	23,103
HATS-10b	3.313	0.526 ± 0.081	${0.969}_{-0.045}^{+0.061}$	1407 ± 39	5880 ± 120	${1.150}_{-0.160}^{+0.120}$	0.15 ± 0.10	1.101 ± 0.054	3.30 ± 1.70	9.40	138
HATS-11b	3.619	0.850 ± 0.120	1.510 ± 0.078	1637 ± 48	6060 ± 150	${0.471}_{-0.052}^{+0.037}$	−0.39 ± 0.06	1.000 ± 0.060	${7.70}_{-1.60}^{+2.20}$	9.40	156
HATS-12b	3.143	2.380 ± 0.110	1.350 ± 0.170	2097 ± 89	6408 ± 75	${0.196}_{-0.044}^{+0.057}$	−0.10 ± 0.04	1.489 ± 0.071	2.36 ± 0.31	3.00	156
HATS-13b	3.044	0.543 ± 0.072	1.212 ± 0.035	1244 ± 20	5523 ± 69	1.930 ± 0.110	0.05 ± 0.06	0.962 ± 0.029	2.50 ± 1.70	14.55	131
HATS-14b	2.767	1.071 ± 0.070	${1.039}_{-0.022}^{+0.032}$	1276 ± 20	5408 ± 65	${1.682}_{-0.126}^{+0.071}$	0.28 ± 0.03	0.967 ± 0.024	4.90 ± 1.70	15.70	131, 145
HATS-15b	1.747	2.170 ± 0.150	1.105 ± 0.040	1505 ± 30	5311 ± 77	1.570 ± 0.120	0.00 ± 0.05	0.871 ± 0.023	${11.00}_{-2.00}^{+1.40}$	19.95	150
HATS-16b	2.687	3.270 ± 0.190	1.300 ± 0.150	${1592}_{-82}^{+61}$	5738 ± 79	${0.720}_{-0.130}^{+0.260}$	0.10 ± 0.05	0.970 ± 0.035	9.50 ± 1.80	14.50	150
HATS-17b	16.255	1.338 ± 0.065	0.777 ± 0.056	814 ± 25	5846 ± 78	1.380 ± 0.270	0.30 ± 0.03	1.131 ± 0.030	2.10 ± 1.30	8.95	154
HATS-18b	0.838	1.980 ± 0.077	${1.337}_{-0.049}^{+0.102}$	2060 ± 59	5600 ± 120	${1.380}_{-0.210}^{+0.130}$	0.28 ± 0.08	1.037 ± 0.047	4.20 ± 2.20	12.25	167
HATS-19b	4.570	0.427 ± 0.071	${1.660}_{-0.210}^{+0.270}$	1570 ± 110	5896 ± 77	${0.340}_{-0.110}^{+0.150}$	0.24 ± 0.05	1.303 ± 0.083	${3.94}_{-0.50}^{+0.96}$	5.40	164
HATS-1b	3.446	${1.855}_{-0.196}^{+0.262}$	${1.302}_{-0.098}^{+0.162}$	${1359}_{-59}^{+89}$	5870 ± 100	${1.241}_{-0.370}^{+0.317}$	−0.06 ± 0.12	0.986 ± 0.054	6.00 ± 2.80	12.50	114
HATS-20b	3.799	0.273 ± 0.035	0.776 ± 0.055	1147 ± 36	5406 ± 49	1.980 ± 0.480	0.03 ± 0.05	0.910 ± 0.026	6.40 ± 3.40	17.50	164
HATS-21b	3.554	${0.332}_{-0.030}^{+0.040}$	${1.123}_{-0.054}^{+0.147}$	${1284}_{-31}^{+55}$	5695 ± 67	1.550 ± 0.380	0.30 ± 0.04	1.080 ± 0.026	2.30 ± 1.70	10.60	164
HATS-22b	4.723	2.740 ± 0.110	${0.953}_{-0.029}^{+0.048}$	${858}_{-17}^{+24}$	4803 ± 55	3.260 ± 0.680	0.00 ± 0.04	0.759 ± 0.019	${4.60}_{-4.00}^{+5.80}$	19.95	163
HATS-23b	2.161	1.470 ± 0.072	${1.860}_{-0.400}^{+0.300}$	1654 ± 54	5780 ± 120	${0.920}_{-0.110}^{+0.200}$	0.28 ± 0.07	1.121 ± 0.046	4.20 ± 1.50	9.20	163
HATS-24b	1.348	2.440 ± 0.180	${1.487}_{-0.054}^{+0.078}$	2067 ± 39	6346 ± 81	${1.096}_{-0.085}^{+0.059}$	0.00 ± 0.05	1.212 ± 0.033	${0.88}_{-0.45}^{+0.67}$	6.15	163
HATS-25b	4.299	0.613 ± 0.042	1.260 ± 0.100	1277 ± 42	5715 ± 73	1.030 ± 0.200	0.02 ± 0.05	0.994 ± 0.035	7.50 ± 1.90	12.70	159
HATS-26b	3.302	0.650 ± 0.076	1.750 ± 0.210	1918 ± 61	6071 ± 81	0.219 ± 0.033	−0.02 ± 0.05	${1.299}_{-0.056}^{+0.113}$	${4.04}_{-0.94}^{+0.62}$	4.85	159
HATS-27b	4.637	0.540 ± 0.130	1.520 ± 0.140	1661 ± 50	6438 ± 64	0.370 ± 0.059	0.09 ± 0.04	1.415 ± 0.045	2.31 ± 0.21	3.90	159
HATS-28b	3.181	0.672 ± 0.087	1.194 ± 0.070	1253 ± 35	5498 ± 84	1.680 ± 0.270	0.01 ± 0.06	0.929 ± 0.036	6.20 ± 2.80	16.10	159
HATS-29b	4.606	0.653 ± 0.063	1.251 ± 0.061	1212 ± 30	5670 ± 110	1.170 ± 0.110	0.16 ± 0.08	1.032 ± 0.049	${5.50}_{-1.70}^{+2.60}$	11.95	159
HATS-2b	1.354	1.345 ± 0.150	1.168 ± 0.030	1577 ± 31	5227 ± 95	${1.718}_{-0.127}^{+0.133}$	0.15 ± 0.05	0.882 ± 0.037	9.70 ± 2.90	19.95	111
HATS-30b	3.174	0.706 ± 0.039	1.175 ± 0.052	1414 ± 32	5943 ± 70	1.340 ± 0.190	0.06 ± 0.05	1.093 ± 0.031	2.30 ± 1.20	9.20	159
HATS-31b	3.378	0.880 ± 0.120	1.640 ± 0.220	1823 ± 81	6050 ± 120	${0.275}_{-0.061}^{+0.082}$	0.00 ± 0.07	1.275 ± 0.096	4.30 ± 1.10	5.25	165
HATS-32b	2.813	0.920 ± 0.100	${1.249}_{-0.096}^{+0.144}$	1437 ± 58	5700 ± 110	1.190 ± 0.230	0.39 ± 0.05	1.099 ± 0.044	3.50 ± 1.80	9.90	165
HATS-33b	2.550	1.192 ± 0.053	${1.230}_{-0.081}^{+0.112}$	1429 ± 38	5659 ± 85	1.420 ± 0.170	0.29 ± 0.05	1.062 ± 0.032	3.00 ± 1.70	11.25	165
HATS-34b	2.106	0.941 ± 0.072	1.430 ± 0.190	1445 ± 42	5380 ± 73	1.440 ± 0.250	0.25 ± 0.07	0.955 ± 0.031	7.70 ± 2.70	16.30	165
HATS-35b	1.821	1.266 ± 0.077	${1.570}_{-0.130}^{+0.170}$	2100 ± 100	6300 ± 100	0.530 ± 0.180	0.21 ± 0.06	1.347 ± 0.060	2.29 ± 0.55	4.85	165
HATS-3b	3.548	1.071 ± 0.136	1.381 ± 0.035	1648 ± 24	6351 ± 76	${0.617}_{-0.041}^{+0.046}$	−0.16 ± 0.07	1.209 ± 0.036	${3.20}_{-0.40}^{+0.60}$	5.70	115
HATS-4b	2.517	1.323 ± 0.028	1.020 ± 0.037	1315 ± 21	5403 ± 50	${1.784}_{-0.122}^{+0.143}$	0.43 ± 0.08	1.001 ± 0.020	2.10 ± 1.60	13.65	127
HATS-5b	4.763	0.237 ± 0.012	0.912 ± 0.025	1025 ± 17	5304 ± 50	${2.001}_{-0.165}^{+0.180}$	0.19 ± 0.08	0.936 ± 0.028	${3.60}_{-1.90}^{+2.60}$	17.25	124
HATS-6b	3.325	0.319 ± 0.070	0.998 ± 0.019	712 ± 5	3770 ± 100	4.360 ± 0.150	0.20 ± 0.09	${0.574}_{-0.027}^{+0.020}$	0.00 ± 0.00	19.95	133
HATS-7b	3.185	0.120 ± 0.012	${0.563}_{-0.034}^{+0.046}$	1084 ± 32	4985 ± 50	${2.206}_{-0.356}^{+0.326}$	0.25 ± 0.08	0.849 ± 0.027	7.80 ± 5.00	19.95	143
HATS-8b	3.584	0.138 ± 0.019	${0.873}_{-0.075}^{+0.123}$	${1324}_{-38}^{+79}$	5679 ± 50	${1.159}_{-0.373}^{+0.220}$	0.21 ± 0.08	1.056 ± 0.037	5.10 ± 1.70	11.25	139
HATS-9b	1.915	0.837 ± 0.029	1.065 ± 0.098	${1823}_{-35}^{+52}$	5366 ± 70	${0.427}_{-0.070}^{+0.030}$	0.34 ± 0.05	1.030 ± 0.039	10.80 ± 1.50	12.55	138
KELT-10b	4.166	${0.679}_{-0.038}^{+0.039}$	${1.399}_{-0.049}^{+0.069}$	${1377}_{-23}^{+28}$	5948 ± 74	${0.889}_{-0.088}^{+0.062}$	${0.09}_{-0.10}^{+0.11}$	${1.112}_{-0.061}^{+0.055}$	${3.20}_{-0.51}^{+0.37}$	7.50	148
KELT-15b	3.329	${0.910}_{-0.220}^{+0.210}$	${1.443}_{-0.057}^{+0.110}$	${1642}_{-25}^{+45}$	${6003}_{-52}^{+56}$	${0.514}_{-0.076}^{+0.034}$	0.05 ± 0.03	${1.181}_{-0.050}^{+0.051}$	${3.89}_{-0.19}^{+0.18}$	5.95	149
KELT-1b	1.218	${27.230}_{-0.480}^{+0.500}$	${1.110}_{-0.022}^{+0.032}$	${2422}_{-26}^{+32}$	6518 ± 50	${0.597}_{-0.039}^{+0.026}$	0.01 ± 0.07	1.324 ± 0.026	${1.66}_{-0.17}^{+0.18}$	4.30	99
KELT-2Ab	4.114	1.486 ± 0.088	${1.306}_{-0.067}^{+0.081}$	${1716}_{-33}^{+39}$	${6148}_{-49}^{+48}$	${0.296}_{-0.041}^{+0.039}$	−0.01 ± 0.07	${1.310}_{-0.029}^{+0.032}$	${3.08}_{-0.12}^{+0.09}$	3.95	98
KELT-3b	2.703	${1.462}_{-0.066}^{+0.067}$	${1.358}_{-0.069}^{+0.068}$	${1821}_{-37}^{+35}$	6304 ± 49	${0.556}_{-0.054}^{+0.065}$	${0.05}_{-0.08}^{+0.08}$	${1.282}_{-0.060}^{+0.062}$	${2.50}_{-0.26}^{+0.14}$	4.90	116
KELT-4Ab	2.990	${0.902}_{-0.059}^{+0.060}$	${1.699}_{-0.045}^{+0.046}$	1823 ± 27	6206 ± 75	${0.411}_{-0.017}^{+0.018}$	$-{0.12}_{-0.07}^{+0.07}$	${1.201}_{-0.061}^{+0.067}$	${3.21}_{-0.17}^{+0.13}$	4.65	153
KELT-6b	7.846	${0.430}_{-0.046}^{+0.045}$	${1.193}_{-0.077}^{+0.130}$	${1313}_{-38}^{+59}$	6102 ± 43	${0.387}_{-0.088}^{+0.068}$	$-{0.28}_{-0.04}^{+0.04}$	${1.085}_{-0.040}^{+0.043}$	${5.65}_{-0.27}^{+0.22}$	7.00	125
KELT-7b	2.735	1.280 ± 0.180	${1.533}_{-0.047}^{+0.046}$	2048 ± 27	${6789}_{-49}^{+50}$	${0.419}_{-0.035}^{+0.027}$	${0.14}_{-0.08}^{+0.07}$	${1.535}_{-0.054}^{+0.066}$	${1.15}_{-0.10}^{+0.06}$	2.95	134
KELT-8b	3.244	${0.867}_{-0.061}^{+0.065}$	${1.860}_{-0.160}^{+0.180}$	${1675}_{-55}^{+61}$	${5754}_{-55}^{+54}$	${0.369}_{-0.067}^{+0.073}$	0.27 ± 0.04	${1.211}_{-0.066}^{+0.078}$	${4.24}_{-0.25}^{+0.29}$	5.55	141
TrES-1b	3.030	${0.752}_{-0.046}^{+0.047}$	${1.067}_{-0.021}^{+0.022}$	${1140}_{-12}^{+13}$	5230 ± 50	${2.400}_{-0.120}^{+0.014}$	0.02 ± 0.05	${0.878}_{-0.040}^{+0.038}$	${1.50}_{-0.74}^{+0.82}$	17.70	11, 22
TrES-2b	2.471	${1.200}_{-0.053}^{+0.051}$	1.224 ± 0.041	1498 ± 17	${5850}_{-38}^{+38}$	${1.372}_{-0.059}^{+0.061}$	$-{0.02}_{-0.06}^{+0.06}$	${0.983}_{-0.063}^{+0.059}$	${2.75}_{-0.50}^{+0.38}$	9.85	1, 2, 11, 18, 19
TrES-4b	3.554	${0.925}_{-0.082}^{+0.081}$	${1.783}_{-0.086}^{+0.093}$	1785 ± 29	6200 ± 75	${0.314}_{-0.032}^{+0.034}$	0.14 ± 0.09	${1.404}_{-0.134}^{+0.066}$	${2.58}_{-0.18}^{+0.16}$	3.80	4,25
TrES-5b	1.482	1.778 ± 0.063	1.209 ± 0.021	1484 ± 41	5171 ± 36	${1.938}_{-0.098}^{+0.104}$	0.20 ± 0.08	0.893 ± 0.024	${5.30}_{-0.78}^{+0.84}$	18.45	83
WASP-100b	2.849	2.030 ± 0.120	1.690 ± 0.290	2190 ± 140	6900 ± 120	${0.280}_{-0.070}^{+0.140}$	−0.03 ± 0.10	1.570 ± 0.100	${1.36}_{-0.13}^{+0.11}$	2.35	128
WASP-101b	3.586	0.500 ± 0.040	1.410 ± 0.050	1560 ± 35	6380 ± 120	0.884 ± 0.061	0.20 ± 0.12	1.340 ± 0.070	${0.20}_{-0.08}^{+0.26}$	4.80	128
WASP-103b	0.926	1.490 ± 0.088	${1.528}_{-0.047}^{+0.073}$	${2508}_{-70}^{+75}$	6110 ± 160	${0.584}_{-0.055}^{+0.030}$	0.06 ± 0.13	${1.220}_{-0.036}^{+0.039}$	${2.73}_{-0.56}^{+0.47}$	5.25	118
WASP-104b	1.755	1.272 ± 0.047	1.137 ± 0.037	1516 ± 39	5450 ± 130	1.704 ± 0.099	0.32 ± 0.09	1.076 ± 0.049	${1.28}_{-1.13}^{+0.74}$	12.10	121
WASP-106b	9.290	1.925 ± 0.076	${1.085}_{-0.028}^{+0.046}$	1140 ± 29	6000 ± 150	${0.628}_{-0.055}^{+0.014}$	−0.09 ± 0.09	1.192 ± 0.054	${3.80}_{-0.52}^{+0.61}$	6.30	121
WASP-10b	3.093	${3.150}_{-0.110}^{+0.130}$	1.080 ± 0.020	${1119}_{-28}^{+26}$	4675 ± 100	3.099 ± 0.088	0.03 ± 0.20	${0.750}_{-0.028}^{+0.040}$	${4.79}_{-3.04}^{+3.96}$	19.95	26, 36, 57
WASP-117b	10.022	0.276 ± 0.009	${1.021}_{-0.065}^{+0.076}$	${1024}_{-26}^{+30}$	6040 ± 90	0.990 ± 0.140	−0.11 ± 0.14	1.126 ± 0.029	${2.95}_{-0.71}^{+0.51}$	7.40	120
WASP-119b	2.500	1.230 ± 0.080	1.400 ± 0.200	1600 ± 80	5650 ± 100	0.760 ± 0.250	0.14 ± 0.10	1.020 ± 0.060	${5.60}_{-0.75}^{+1.55}$	8.90	155
WASP-120b	3.611	5.010 ± 0.260	1.515 ± 0.083	1890 ± 50	6450 ± 120	0.285 ± 0.031	−0.05 ± 0.07	1.450 ± 0.110	2.16 ± 0.18	3.20	147
WASP-121b	1.275	${1.183}_{-0.062}^{+0.064}$	1.865 ± 0.044	2358 ± 52	6459 ± 140	${0.617}_{-0.013}^{+0.011}$	0.13 ± 0.09	${1.353}_{-0.079}^{+0.080}$	${1.18}_{-0.36}^{+0.28}$	4.05	146
WASP-122b	1.710	1.284 ± 0.051	${1.731}_{-0.062}^{+0.063}$	1960 ± 50	${5774}_{-74}^{+75}$	${0.517}_{-0.025}^{+0.025}$	${0.32}_{-0.06}^{+0.06}$	${1.223}_{-0.043}^{+0.038}$	${4.00}_{-0.29}^{+0.31}$	6.35	147, 149
WASP-123b	2.978	0.920 ± 0.050	1.327 ± 0.074	1510 ± 40	5740 ± 130	0.782 ± 0.080	0.18 ± 0.08	1.207 ± 0.089	${4.46}_{-0.74}^{+0.58}$	8.20	147
WASP-124b	3.373	0.600 ± 0.070	1.240 ± 0.030	1400 ± 30	6050 ± 100	1.397 ± 0.071	−0.02 ± 0.11	1.070 ± 0.050	${0.18}_{-0.04}^{+0.47}$	7.45	155
WASP-126b	3.289	0.280 ± 0.040	${0.960}_{-0.050}^{+0.100}$	1480 ± 60	5800 ± 100	${0.790}_{-0.170}^{+0.080}$	0.17 ± 0.08	1.120 ± 0.060	${4.20}_{-0.63}^{+0.41}$	8.00	155
WASP-12b	1.091	1.410 ± 0.100	1.790 ± 0.090	2516 ± 36	${6300}_{-100}^{+200}$	0.494 ± 0.042	${0.30}_{-0.15}^{+0.05}$	1.350 ± 0.140	${1.61}_{-0.40}^{+0.31}$	4.05	27
WASP-130b	11.551	1.230 ± 0.040	0.890 ± 0.030	833 ± 18	5600 ± 100	1.670 ± 0.130	0.26 ± 0.10	1.040 ± 0.040	${0.18}_{-0.03}^{+0.02}$	10.60	158
WASP-131b	5.322	0.270 ± 0.020	1.220 ± 0.050	1460 ± 30	5950 ± 100	0.412 ± 0.037	−0.18 ± 0.08	1.060 ± 0.060	${5.80}_{-0.62}^{+0.47}$	7.20	158
WASP-132b	7.134	0.410 ± 0.030	0.870 ± 0.030	763 ± 16	4750 ± 100	${2.823}_{-0.200}^{+0.099}$	0.22 ± 0.13	0.800 ± 0.040	${3.17}_{-1.92}^{+1.57}$	19.95	158
WASP-133b	2.176	1.160 ± 0.090	1.210 ± 0.050	1790 ± 40	5700 ± 100	0.550 ± 0.040	0.29 ± 0.12	1.160 ± 0.080	${4.36}_{-0.54}^{+0.47}$	6.75	155
WASP-135b	1.401	1.900 ± 0.080	1.300 ± 0.090	${1717}_{-40}^{+46}$	5680 ± 60	1.580 ± 0.210	0.02 ± 0.13	1.010 ± 0.070	${2.16}_{-1.11}^{+0.91}$	10.70	160
WASP-13b	4.353	${0.460}_{-0.050}^{+0.060}$	${1.210}_{-0.120}^{+0.140}$	${1417}_{-58}^{+62}$	5826 ± 100	${0.610}_{-0.140}^{+0.170}$	0.00 ± 0.20	${1.030}_{-0.090}^{+0.110}$	${4.49}_{-0.70}^{+1.97}$	6.65	17, 100
WASP-140b	2.236	2.440 ± 0.070	${1.440}_{-0.180}^{+0.420}$	1320 ± 40	5300 ± 100	1.950 ± 0.250	0.12 ± 0.10	0.900 ± 0.040	${2.69}_{-1.22}^{+1.17}$	15.10	158
WASP-141b	3.311	2.690 ± 0.150	1.210 ± 0.080	1540 ± 50	6050 ± 120	0.692 ± 0.099	0.29 ± 0.09	1.250 ± 0.060	${2.15}_{-0.50}^{+0.36}$	5.65	158
WASP-142b	2.053	0.840 ± 0.090	1.530 ± 0.080	2000 ± 60	6060 ± 150	0.423 ± 0.056	0.26 ± 0.12	1.330 ± 0.080	${2.54}_{-0.43}^{+0.35}$	4.50	158
WASP-14b	2.244	${7.341}_{-0.496}^{+0.508}$	${1.281}_{-0.082}^{+0.075}$	${1866}_{-42}^{+37}$	6475 ± 100	${0.765}_{-0.085}^{+0.111}$	0.00 ± 0.20	${1.211}_{-0.122}^{+0.127}$	${0.79}_{-0.40}^{+0.37}$	4.30	35, 39
WASP-157b	3.952	0.574 ± 0.093	1.045 ± 0.044	1339 ± 93	5840 ± 140	1.300 ± 0.320	0.34 ± 0.09	1.260 ± 0.120	${0.18}_{-0.04}^{+0.67}$	7.65	157
WASP-15b	3.752	0.542 ± 0.050	1.428 ± 0.077	1652 ± 28	6300 ± 100	0.515 ± 0.052	−0.17 ± 0.11	1.180 ± 0.120	${2.93}_{-0.32}^{+0.25}$	4.80	21
WASP-16b	3.119	${0.855}_{-0.076}^{+0.043}$	${1.008}_{-0.060}^{+0.083}$	${1280}_{-21}^{+35}$	5700 ± 150	${1.710}_{-0.250}^{+0.180}$	0.01 ± 0.10	${1.022}_{-0.129}^{+0.074}$	${0.20}_{-0.04}^{+1.45}$	10.35	30
WASP-17b	3.735	0.486 ± 0.032	1.991 ± 0.081	1771 ± 35	6650 ± 80	0.474 ± 0.042	−0.19 ± 0.09	1.306 ± 0.026	${1.99}_{-0.19}^{+0.17}$	3.75	87
WASP-18b	0.941	10.430 ± 0.380	1.165 ± 0.057	${2384}_{-30}^{+58}$	6400 ± 100	0.972 ± 0.088	0.00 ± 0.09	1.281 ± 0.069	${0.45}_{-0.33}^{+0.20}$	5.15	33, 38
WASP-19b	0.789	1.168 ± 0.023	1.386 ± 0.032	2050 ± 40	5500 ± 100	${1.401}_{-0.059}^{+0.066}$	0.02 ± 0.09	0.970 ± 0.020	${6.25}_{-1.39}^{+1.34}$	13.65	44, 78
WASP-1b	2.520	${0.918}_{-0.090}^{+0.091}$	${1.514}_{-0.047}^{+0.052}$	${1811}_{-27}^{+34}$	6110 ± 45	${0.549}_{-0.059}^{+0.009}$	0.23 ± 0.08	${1.301}_{-0.047}^{+0.049}$	${2.69}_{-0.23}^{+0.16}$	5.30	8, 11, 82
WASP-20b	4.900	0.313 ± 0.018	1.458 ± 0.057	1379 ± 32	5950 ± 100	0.631 ± 0.047	−0.01 ± 0.06	1.202 ± 0.040	${4.15}_{-0.45}^{+0.55}$	6.75	130
WASP-21b	4.323	0.270 ± 0.010	${1.143}_{-0.030}^{+0.045}$	${1321}_{-26}^{+30}$	5800 ± 100	${0.920}_{-0.085}^{+0.058}$	−0.40 ± 0.10	0.860 ± 0.040	${9.91}_{-1.58}^{+1.38}$	13.00	41,88
WASP-22b	3.533	0.588 ± 0.017	${1.158}_{-0.038}^{+0.061}$	1466 ± 34	6000 ± 100	${0.864}_{-0.095}^{+0.066}$	−0.05 ± 0.08	1.109 ± 0.026	${3.58}_{-0.60}^{+0.42}$	7.45	43,69
WASP-23b	2.944	${0.884}_{-0.099}^{+0.088}$	${0.962}_{-0.056}^{+0.047}$	${1119}_{-21}^{+22}$	5150 ± 100	${2.601}_{-0.038}^{+0.035}$	−0.05 ± 0.13	${0.780}_{-0.120}^{+0.130}$	${1.30}_{-0.78}^{+1.36}$	18.85	65
WASP-24b	2.341	${1.032}_{-0.037}^{+0.038}$	${1.104}_{-0.057}^{+0.052}$	${1660}_{-42}^{+44}$	6075 ± 100	${1.054}_{-0.100}^{+0.140}$	0.07 ± 0.10	${1.129}_{-0.025}^{+0.027}$	${1.27}_{-0.46}^{+0.50}$	6.55	53
WASP-25b	3.765	0.580 ± 0.040	${1.220}_{-0.050}^{+0.060}$	1212 ± 35	5703 ± 100	1.820 ± 0.140	−0.07 ± 0.10	1.000 ± 0.030	${1.00}_{-0.85}^{+0.65}$	11.00	86
WASP-26b	2.757	1.028 ± 0.021	1.281 ± 0.075	1637 ± 45	5950 ± 100	0.709 ± 0.088	−0.02 ± 0.09	1.111 ± 0.028	${4.02}_{-0.42}^{+0.63}$	7.00	42,69
WASP-28b	3.409	0.907 ± 0.043	1.213 ± 0.042	1468 ± 37	6150 ± 140	1.107 ± 0.082	−0.29 ± 0.10	1.021 ± 0.050	${2.44}_{-0.81}^{+0.68}$	7.20	130
WASP-29b	3.923	0.244 ± 0.020	${0.792}_{-0.035}^{+0.056}$	980 ± 40	4800 ± 150	${2.200}_{-0.320}^{+0.280}$	0.11 ± 0.14	0.825 ± 0.033	${11.68}_{-4.10}^{+3.31}$	19.95	54
WASP-2b	2.152	${0.915}_{-0.093}^{+0.090}$	${1.071}_{-0.083}^{+0.080}$	1304 ± 54	5200 ± 200	${2.050}_{-0.150}^{+0.260}$	0.02 ± 0.05	0.890 ± 0.120	${4.68}_{-2.38}^{+2.22}$	17.65	7, 11, 82, 110
WASP-30b	4.157	60.960 ± 0.890	0.889 ± 0.021	1474 ± 25	6100 ± 100	0.758 ± 0.027	−0.08 ± 0.10	1.166 ± 0.026	${3.26}_{-0.51}^{+0.36}$	6.50	76
WASP-31b	3.406	0.478 ± 0.030	1.537 ± 0.060	1568 ± 33	6203 ± 98	0.858 ± 0.073	−0.19 ± 0.09	1.161 ± 0.026	${2.86}_{-0.53}^{+0.35}$	6.55	67
WASP-32b	2.719	3.600 ± 0.070	1.180 ± 0.070	1560 ± 50	6100 ± 100	1.130 ± 0.140	−0.13 ± 0.10	1.100 ± 0.030	${1.87}_{-0.69}^{+0.61}$	7.15	62
WASP-34b	4.318	0.590 ± 0.010	${1.220}_{-0.080}^{+0.110}$	1250 ± 30	5700 ± 100	${1.770}_{-0.563}^{+0.917}$	−0.02 ± 0.10	1.010 ± 0.070	${0.20}_{-0.05}^{+1.31}$	10.75	64
WASP-35b	3.162	0.720 ± 0.060	1.320 ± 0.030	1450 ± 20	6050 ± 100	1.171 ± 0.042	−0.15 ± 0.09	1.070 ± 0.020	${2.31}_{-0.72}^{+0.67}$	7.75	73
WASP-36b	1.537	2.270 ± 0.068	1.269 ± 0.030	${1700}_{-44}^{+42}$	5800 ± 150	${1.719}_{-0.068}^{+0.075}$	−0.31 ± 0.12	1.020 ± 0.032	${2.56}_{-1.30}^{+1.13}$	10.60	93
WASP-37b	3.577	${1.696}_{-0.128}^{+0.123}$	${1.136}_{-0.051}^{+0.060}$	${1325}_{-15}^{+25}$	5800 ± 150	${0.923}_{-0.097}^{+0.064}$	−0.40 ± 0.12	${0.849}_{-0.040}^{+0.067}$	${9.06}_{-2.09}^{+1.63}$	12.10	72
WASP-38b	6.872	2.712 ± 0.065	${1.079}_{-0.044}^{+0.053}$	${1261}_{-23}^{+24}$	6150 ± 80	0.673 ± 0.058	−0.12 ± 0.07	1.216 ± 0.041	${3.42}_{-0.30}^{+0.20}$	6.10	63
WASP-39b	4.055	0.280 ± 0.030	1.270 ± 0.040	${1116}_{-32}^{+33}$	5400 ± 150	${1.830}_{-0.100}^{+0.120}$	−0.12 ± 0.10	0.930 ± 0.030	${5.31}_{-2.17}^{+1.81}$	15.40	66
WASP-3b	1.847	${1.875}_{-0.036}^{+0.031}$	${1.290}_{-0.120}^{+0.050}$	${1960}_{-76}^{+33}$	6400 ± 100	${0.780}_{-0.070}^{+0.210}$	0.00 ± 0.20	${1.240}_{-0.110}^{+0.060}$	${0.98}_{-0.44}^{+0.46}$	4.60	9, 14, 49
WASP-41b	3.052	0.920 ± 0.070	1.210 ± 0.070	1235 ± 50	5450 ± 150	1.790 ± 0.200	−0.08 ± 0.09	0.940 ± 0.030	${4.36}_{-1.78}^{+1.64}$	14.30	90
WASP-42b	4.982	0.500 ± 0.035	1.080 ± 0.057	995 ± 34	5200 ± 150	1.930 ± 0.200	0.05 ± 0.13	${0.881}_{-0.081}^{+0.086}$	${4.96}_{-2.27}^{+2.09}$	16.90	91
WASP-43b	0.813	1.780 ± 0.100	${0.930}_{-0.090}^{+0.070}$	1370 ± 70	4400 ± 200	${3.810}_{-0.510}^{+0.860}$	−0.05 ± 0.17	0.580 ± 0.050	${6.71}_{-5.61}^{+6.35}$	19.95	70
WASP-44b	2.424	${0.893}_{-0.066}^{+0.071}$	${1.090}_{-0.140}^{+0.130}$	1343 ± 64	5400 ± 150	${1.877}_{-0.423}^{+0.762}$	0.06 ± 0.10	0.948 ± 0.034	${2.31}_{-2.11}^{+1.24}$	13.65	101
WASP-45b	3.126	1.005 ± 0.053	${1.170}_{-0.140}^{+0.280}$	1198 ± 69	5100 ± 200	1.496 ± 0.381	0.36 ± 0.12	${0.910}_{-60.000}^{+0.060}$	${8.29}_{-3.22}^{+2.15}$	18.05	101
WASP-46b	1.430	2.100 ± 0.073	1.327 ± 0.058	1654 ± 50	5600 ± 150	1.694 ± 0.169	−0.37 ± 0.13	0.957 ± 0.034	${6.97}_{-2.37}^{+1.90}$	14.45	101
WASP-47b	4.159	1.164 ± 0.091	1.134 ± 0.039	1220 ± 20	5400 ± 100	1.017 ± 0.013	0.18 ± 0.07	1.084 ± 0.037	${9.83}_{-2.04}^{+1.10}$	14.95	102, 142, 144
WASP-47d	9.031	${0.027}_{-0.011}^{+0.012}$	0.321 ± 0.012	${943}_{-17}^{+17}$	5400 ± 100	1.017 ± 0.013	0.18 ± 0.07	1.084 ± 0.037	${9.79}_{-2.01}^{+1.12}$	14.95	102, 142
WASP-47e	0.790	0.038 ± 0.012	0.162 ± 0.006	${2126}_{-39}^{+39}$	5400 ± 100	1.017 ± 0.013	0.18 ± 0.07	1.084 ± 0.037	${9.86}_{-1.86}^{+1.06}$	15.00	102, 142, 144
WASP-48b	2.144	0.980 ± 0.090	1.670 ± 0.080	2030 ± 70	6000 ± 150	0.310 ± 0.028	−0.12 ± 0.12	1.190 ± 0.040	${4.30}_{-1.18}^{+0.78}$	5.50	73
WASP-49b	2.782	0.378 ± 0.027	1.115 ± 0.047	1369 ± 39	5600 ± 150	1.425 ± 0.085	−0.23 ± 0.07	${0.938}_{-0.076}^{+0.080}$	${7.84}_{-1.97}^{+1.28}$	14.55	91
WASP-4b	1.338	1.237 ± 0.064	1.365 ± 0.021	1650 ± 30	5500 ± 100	${1.728}_{-0.047}^{+0.016}$	−0.03 ± 0.09	0.925 ± 0.040	${3.79}_{-1.28}^{+1.25}$	13.45	15, 20
WASP-50b	1.955	${1.468}_{-0.086}^{+0.091}$	1.153 ± 0.048	1393 ± 30	5400 ± 100	${2.090}_{-0.130}^{+0.140}$	−0.12 ± 0.08	${0.892}_{-0.074}^{+0.080}$	${3.36}_{-1.42}^{+1.28}$	15.55	68
WASP-52b	1.750	0.460 ± 0.020	1.270 ± 0.030	1315 ± 35	5000 ± 100	2.480 ± 0.110	0.03 ± 0.12	0.870 ± 0.030	${4.06}_{-2.23}^{+2.18}$	19.95	105
WASP-54b	3.694	0.626 ± 0.023	${1.650}_{-0.180}^{+0.090}$	${1742}_{-69}^{+49}$	6100 ± 100	${0.296}_{-0.028}^{+0.085}$	−0.27 ± 0.08	${1.201}_{-0.036}^{+0.034}$	${4.91}_{-0.44}^{+0.36}$	5.80	106
WASP-55b	4.466	0.570 ± 0.040	${1.300}_{-0.030}^{+0.050}$	1290 ± 25	5900 ± 100	${1.200}_{-0.099}^{+0.042}$	−0.20 ± 0.08	1.010 ± 0.040	${4.28}_{-1.03}^{+1.12}$	9.80	102
WASP-56b	4.617	${0.571}_{-0.035}^{+0.034}$	${1.092}_{-0.033}^{+0.035}$	${1216}_{-24}^{+25}$	5600 ± 100	1.040 ± 0.060	0.12 ± 0.06	1.017 ± 0.024	${6.01}_{-0.98}^{+1.09}$	11.30	106
WASP-57b	2.839	${0.672}_{-0.046}^{+0.049}$	${0.916}_{-0.014}^{+0.017}$	${1251}_{-22}^{+21}$	5600 ± 100	${2.319}_{-0.089}^{+0.062}$	−0.25 ± 0.10	0.954 ± 0.027	${0.69}_{-0.51}^{+0.64}$	13.60	106
WASP-58b	5.017	0.890 ± 0.070	1.370 ± 0.200	1270 ± 80	5800 ± 150	0.820 ± 0.270	−0.45 ± 0.09	0.940 ± 0.100	${10.21}_{-2.11}^{+1.94}$	12.75	105
WASP-59b	7.920	0.863 ± 0.045	0.775 ± 0.068	670 ± 35	4650 ± 150	4.390 ± 0.900	−0.15 ± 0.11	0.719 ± 0.035	${0.14}_{-0.03}^{+0.03}$	19.95	105
WASP-5b	1.628	1.637 ± 0.082	1.171 ± 0.057	${1706}_{-48}^{+52}$	5700 ± 100	1.130 ± 0.110	0.09 ± 0.09	1.021 ± 0.063	${4.45}_{-0.94}^{+0.75}$	10.20	15, 37, 89
WASP-60b	4.305	0.514 ± 0.034	0.860 ± 0.120	1320 ± 75	5900 ± 100	1.020 ± 0.280	−0.04 ± 0.09	1.078 ± 0.035	${3.72}_{-0.68}^{+0.68}$	8.50	105
WASP-61b	3.856	2.060 ± 0.170	1.240 ± 0.030	1565 ± 35	6250 ± 150	${0.687}_{-0.024}^{+0.011}$	−0.10 ± 0.12	1.220 ± 0.070	${2.51}_{-0.53}^{+0.38}$	5.35	102
WASP-62b	4.412	0.570 ± 0.040	1.390 ± 0.060	1440 ± 30	6230 ± 80	0.833 ± 0.085	0.04 ± 0.06	1.250 ± 0.050	${1.88}_{-0.36}^{+0.32}$	5.85	102
WASP-63b	4.378	0.380 ± 0.030	${1.430}_{-0.060}^{+0.100}$	1540 ± 40	5550 ± 100	${0.279}_{-0.035}^{+0.024}$	0.08 ± 0.07	1.320 ± 0.050	${7.19}_{-0.71}^{+0.53}$	8.00	102
WASP-64b	1.573	1.271 ± 0.068	1.271 ± 0.039	1689 ± 49	5550 ± 150	${1.198}_{-0.062}^{+0.075}$	−0.08 ± 0.11	1.004 ± 0.028	${7.70}_{-2.08}^{+1.63}$	13.30	109
WASP-65b	2.311	1.550 ± 0.160	1.112 ± 0.059	1480 ± 10	5600 ± 100	${1.280}_{-0.060}^{+0.040}$	−0.07 ± 0.07	0.930 ± 0.140	${7.25}_{-1.44}^{+0.94}$	13.65	113
WASP-66b	4.086	2.320 ± 0.130	1.390 ± 0.090	1790 ± 60	6600 ± 150	${0.342}_{-0.040}^{+0.051}$	−0.31 ± 0.10	1.300 ± 0.070	${2.29}_{-0.23}^{+0.20}$	3.35	102
WASP-67b	4.614	0.420 ± 0.040	${1.400}_{-0.200}^{+0.300}$	1040 ± 30	5200 ± 100	1.860 ± 0.210	−0.07 ± 0.09	0.870 ± 0.040	${9.66}_{-2.28}^{+1.77}$	19.95	102
WASP-68b	5.084	0.950 ± 0.030	${1.270}_{-0.060}^{+0.110}$	${1488}_{-32}^{+49}$	5910 ± 60	${0.367}_{-0.071}^{+0.042}$	0.22 ± 0.08	1.240 ± 0.030	${3.58}_{-0.23}^{+0.13}$	4.95	119
WASP-69b	3.868	0.260 ± 0.017	1.057 ± 0.047	963 ± 18	4700 ± 50	2.170 ± 0.180	0.15 ± 0.08	0.826 ± 0.029	${18.46}_{-2.04}^{+1.12}$	19.95	129
WASP-6b	3.361	${0.503}_{-0.038}^{+0.019}$	${1.224}_{-0.052}^{+0.051}$	${1194}_{-57}^{+58}$	5450 ± 100	${1.890}_{-0.140}^{+0.160}$	−0.20 ± 0.09	${0.880}_{-0.080}^{+0.050}$	${5.94}_{-1.83}^{+1.37}$	16.05	16
WASP-70Ab	3.713	0.590 ± 0.022	${1.164}_{-0.102}^{+0.073}$	1387 ± 40	5700 ± 80	${0.870}_{-0.110}^{+0.190}$	−0.01 ± 0.06	1.106 ± 0.042	${7.57}_{-1.10}^{+0.80}$	11.40	129
WASP-71b	2.904	2.258 ± 0.072	1.500 ± 0.110	2066 ± 67	6050 ± 100	0.179 ± 0.030	0.15 ± 0.07	1.572 ± 0.062	${2.50}_{-0.17}^{+0.18}$	3.00	108
WASP-72b	2.217	${1.410}_{-0.045}^{+0.050}$	${1.010}_{-0.080}^{+0.120}$	${2064}_{-62}^{+90}$	6250 ± 100	${0.374}_{-0.080}^{+0.062}$	−0.06 ± 0.09	${1.327}_{-0.035}^{+0.043}$	${2.87}_{-0.27}^{+0.18}$	4.15	109
WASP-73b	4.087	${1.880}_{-0.060}^{+0.070}$	${1.160}_{-0.080}^{+0.120}$	${1790}_{-51}^{+75}$	6030 ± 120	${0.212}_{-0.056}^{+0.028}$	0.14 ± 0.14	${1.340}_{-0.040}^{+0.050}$	${2.62}_{-0.29}^{+0.22}$	3.25	119
WASP-74b	2.138	0.950 ± 0.060	1.560 ± 0.060	1910 ± 40	5990 ± 110	0.477 ± 0.025	0.39 ± 0.13	1.480 ± 0.120	${2.45}_{-0.35}^{+0.30}$	4.90	136
WASP-75b	2.484	1.070 ± 0.050	1.270 ± 0.048	1710 ± 20	6100 ± 100	0.790 ± 0.060	0.07 ± 0.09	1.140 ± 0.070	${2.51}_{-0.53}^{+0.38}$	6.20	113
WASP-76b	1.810	0.920 ± 0.030	${1.830}_{-0.040}^{+0.060}$	2160 ± 40	6250 ± 100	${0.404}_{-0.025}^{+0.011}$	0.23 ± 0.10	1.460 ± 0.070	${2.15}_{-0.25}^{+0.24}$	3.95	152
WASP-77Ab	1.360	1.760 ± 0.060	1.210 ± 0.020	${1669}_{-24}^{+24}$	5500 ± 80	${1.633}_{-0.028}^{+0.023}$	0.00 ± 0.11	1.002 ± 0.045	${4.40}_{-1.20}^{+1.15}$	13.45	117
WASP-78b	2.175	0.890 ± 0.080	1.700 ± 0.110	2350 ± 80	6100 ± 150	0.176 ± 0.025	−0.35 ± 0.14	1.330 ± 0.090	${3.82}_{-0.38}^{+0.40}$	4.10	92
WASP-79b	3.662	0.900 ± 0.080	2.090 ± 0.140	1900 ± 50	6600 ± 100	0.310 ± 0.040	0.03 ± 0.10	1.520 ± 0.070	${1.69}_{-0.16}^{+0.17}$	2.90	92
WASP-7b	4.955	${0.960}_{-0.180}^{+0.120}$	${0.915}_{-0.040}^{+0.046}$	${1379}_{-23}^{+35}$	6400 ± 100	${0.929}_{-0.179}^{+0.152}$	0.00 ± 0.10	${1.280}_{-0.190}^{+0.090}$	${0.57}_{-0.37}^{+0.26}$	5.00	24
WASP-80b	3.068	${0.554}_{-0.039}^{+0.030}$	${0.952}_{-0.027}^{+0.026}$	${814}_{-19}^{+19}$	4145 ± 100	${4.400}_{-0.028}^{+0.030}$	−0.14 ± 0.16	0.570 ± 0.050	${15.95}_{-6.17}^{+3.43}$	19.95	107
WASP-82b	2.706	1.240 ± 0.040	${1.670}_{-0.050}^{+0.070}$	2190 ± 40	6500 ± 80	${0.223}_{-0.020}^{+0.008}$	0.12 ± 0.11	1.630 ± 0.080	${1.70}_{-0.14}^{+0.13}$	2.55	152
WASP-83b	4.971	0.300 ± 0.030	${1.040}_{-0.050}^{+0.080}$	1120 ± 30	5480 ± 110	${1.369}_{-0.180}^{+0.100}$	0.29 ± 0.12	1.110 ± 0.090	${3.95}_{-1.13}^{+0.84}$	12.20	136
WASP-88b	4.954	0.560 ± 0.080	${1.700}_{-0.070}^{+0.130}$	${1772}_{-45}^{+54}$	6430 ± 130	${0.226}_{-0.042}^{+0.028}$	−0.08 ± 0.12	1.450 ± 0.050	${2.07}_{-0.19}^{+0.17}$	2.80	119
WASP-89b	3.356	5.900 ± 0.400	1.040 ± 0.040	1120 ± 20	4955 ± 100	1.920 ± 0.099	0.15 ± 0.14	0.920 ± 0.080	${10.68}_{-2.64}^{+2.08}$	19.95	136
WASP-8b	8.159	${2.247}_{-0.074}^{+0.083}$	${1.048}_{-0.079}^{+0.042}$	${951}_{-28}^{+21}$	5600 ± 80	${1.680}_{-0.160}^{+0.310}$	0.17 ± 0.07	${1.033}_{-0.050}^{+0.058}$	${1.04}_{-0.88}^{+0.64}$	11.10	40
WASP-90b	3.916	0.630 ± 0.070	1.630 ± 0.090	1840 ± 50	6440 ± 130	0.282 ± 0.028	0.11 ± 0.14	1.550 ± 0.100	${1.79}_{-0.26}^{+0.20}$	2.90	152
WASP-94Ab	3.950	${0.452}_{-0.032}^{+0.035}$	${1.720}_{-0.050}^{+0.060}$	${1604}_{-22}^{+25}$	${6153}_{-76}^{+75}$	${0.486}_{-0.028}^{+0.016}$	0.26 ± 0.15	1.450 ± 0.090	${2.27}_{-0.39}^{+0.28}$	4.60	122
WASP-95b	2.185	${1.130}_{-0.040}^{+0.100}$	1.210 ± 0.060	1570 ± 50	5830 ± 140	${1.100}_{-0.180}^{+0.060}$	0.14 ± 0.16	1.110 ± 0.090	${2.35}_{-1.12}^{+0.80}$	7.90	128
WASP-96b	3.425	0.480 ± 0.030	1.200 ± 0.060	1285 ± 40	5500 ± 150	1.300 ± 0.100	0.14 ± 0.19	1.060 ± 0.090	${4.46}_{-1.51}^{+1.36}$	11.60	128
WASP-97b	2.073	1.320 ± 0.050	1.130 ± 0.060	1555 ± 40	5670 ± 110	1.310 ± 0.130	0.23 ± 0.11	1.120 ± 0.060	${2.40}_{-0.95}^{+0.77}$	9.75	128
WASP-98b	2.963	0.830 ± 0.070	1.100 ± 0.040	1180 ± 30	5550 ± 140	2.810 ± 0.100	−0.60 ± 0.19	0.690 ± 0.060	${2.19}_{-1.73}^{+2.37}$	16.00	128
WASP-99b	5.753	2.780 ± 0.130	${1.100}_{-0.050}^{+0.080}$	1480 ± 40	6150 ± 100	${0.381}_{-0.056}^{+0.028}$	0.21 ± 0.15	1.480 ± 0.100	${2.41}_{-0.33}^{+0.31}$	4.05	128

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Table 8.  Parameter Estimates and Bayesian Evidence for Models of the Form Equation (1)

$\mathrm{ln}{T}_{\mathrm{eq},\mathrm{now}}$	$\mathrm{ln}{T}_{\mathrm{eq},\mathrm{ZAMS}}$	$\mathrm{ln}a$	τ	Bayesian
c1	c2	c3	c4	Evidence
0.92 ± 0.12	0	0.273 ± 0.075	0	$2.66\times {10}^{9}$
0.81 ± 0.14	0	0.216 ± 0.086	0.107 ± 0.088	$9.99\times {10}^{8}$
0.96 ± 0.20	−0.07 ± 0.21	0.263 ± 0.079	0	$5.01\times {10}^{8}$
0.558 ± 0.099	0	0	0.223 ± 0.077	$2.53\times {10}^{8}$
0.77 ± 0.25	0.03 ± 0.23	0.216 ± 0.086	0.111 ± 0.096	$2.09\times {10}^{8}$
0.57 ± 0.25	−0.01 ± 0.24	0	0.217 ± 0.088	$4.75\times {10}^{7}$
0.658 ± 0.099	0	0	0	$2.93\times {10}^{7}$
0	0.492 ± 0.098	0	0.332 ± 0.077	$1.73\times {10}^{7}$
0.90 ± 0.22	−0.29 ± 0.21	0	0	$1.17\times {10}^{7}$
0	0.62 ± 0.14	0.123 ± 0.084	0.291 ± 0.080	$9.95\times {10}^{6}$
0	0.76 ± 0.14	0.224 ± 0.086	0	$7.84\times {10}^{4}$
0	0.53 ± 0.11	0	0	$1.44\times {10}^{4}$
0	0	−0.153 ± 0.067	0.392 ± 0.086	$2.37\times {10}^{3}$
0	0	0	0.364 ± 0.087	$9.04\times {10}^{2}$
0	0	−0.094 ± 0.074	0	$4.87\times {10}^{-1}$

Note. The models tested are sorted from highest to lowest evidence. The Bayesian evidence is reported relative to that for a model with only a freely varying mean for the $\mathrm{ln}{R}_{p}$ values. For each parameter we report the mean and standard deviation of its posterior probability distribution.

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We find that the model with the highest Bayesian evidence has the form

$$\begin{eqnarray}&&\mathrm{ln}{R}_{p}={c}_{0}+{c}_{1}\mathrm{ln}{T}_{\mathrm{eq},\mathrm{now}}+{c}_{3}\mathrm{ln}a\end{eqnarray} \tag{ 2 }$$

with an evidence that is $2.7\times {10}^{9}$ times higher than the evidence for a model where ${c}_{1}\equiv {c}_{2}\equiv {c}_{3}\equiv {c}_{4}\equiv 0$. This finding is consistent with that of Enoch et al. (2012). The next-highest-evidence model has the form

$$\begin{eqnarray}&&\mathrm{ln}{R}_{p}={c}_{0}+{c}_{1}\mathrm{ln}{T}_{\mathrm{eq},\mathrm{now}}+{c}_{3}\mathrm{ln}a+{c}_{4}\tau \end{eqnarray} \tag{ 3 }$$

with an evidence that is 0.37 times that of the highest-evidence model. So indeed including τ provides no additional explanatory power beyond what is already provided by ${T}_{\mathrm{eq},\mathrm{now}}$ and a.

At the same time, we also find that models with $\mathrm{ln}{T}_{\mathrm{eq},\mathrm{now}}$ have substantially higher evidence than models using $\mathrm{ln}{T}_{\mathrm{eq},\mathrm{ZAMS}}$ in place of $\mathrm{ln}{T}_{\mathrm{eq},\mathrm{now}}$, while the model using both $\mathrm{ln}{T}_{\mathrm{eq},\mathrm{ZAMS}}$ and τ has higher evidence than the model using $\mathrm{ln}{T}_{\mathrm{eq},\mathrm{ZAMS}}$ alone. Moreover, we find that the maximum posterior value for c₄ is greater than zero in all cases where it is allowed to vary. In other words, planet radii are more strongly correlated with the present-day equilibrium temperature than they are with the zero-age main-sequence (ZAMS) equilibrium temperature, and if the latter is used in place of the former, then a significant positive correlation between radius and host star fractional age remains.

Based on this, we conclude that the radii of close-in Jupiter-mass giant planets are determined by their present-day equilibrium temperature and semimajor axis, and that the radii of planets increase over time as their equilibrium temperatures increase.