HAT-P-34b–HAT-P-37b: FOUR TRANSITING PLANETS MORE MASSIVE THAN JUPITER ORBITING MODERATELY BRIGHT STARS^*

Table 1 summarizes the HATNet discovery observations of each new planetary system. The HATNet images were processed and reduced to trend-filtered light curves following the procedure described by Bakos et al. (2010) and Pál (2009b). The light curves were searched for periodic box-shaped signals using the Box Least-Squares (BLS; see Kovács et al. 2002) method. We detected significant signals in the light curves of the stars summarized in Table 2; see also Figure 1.

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Table 2. Summary of Discovery Data

Host Planet	GSC	2MASS	R.A.	Decl.	Va	Depthb	Period
			(HH:MM:SS)	(DD:MM:SS)	(mag)	(mmag)	(days)
HAT-P-34	1622-01261	20124688+1806175	$20^{\mathrm h}12^{\mathrm m}46\mbox{$.\!\!^{\mathrm s}$}80$	+18°06'175	10.162 ± 0.073	7.9	5.4527
HAT-P-35	0203-01079	08130018+0447132	$08^{\mathrm h}13^{\mathrm m}00\mbox{$.\!\!^{\mathrm s}$}19$	+04°47'133	12.46 ± 0.11	9.0	3.6467
HAT-P-36	3020-02221	12330390+4454552	$12^{\mathrm h}33^{\mathrm m}03\mbox{$.\!\!^{\mathrm s}$}96$	+44°54'553	12.262 ± 0.068	14.7	1.3273
HAT-P-37	3553-00723	18571105+5116088	$18^{\mathrm h}57^{\mathrm m}11\mbox{$.\!\!^{\mathrm s}$}16$	+51°16'089	13.23 ± 0.32c	18.1	2.7974

Notes. ^aFrom Droege et al. 2006. ^bNote that the apparent depth of the HATNet transit for all four targets is shallower than the true transit depth due to blending with unresolved neighbors in the low spatial resolution HATNet images (the median FWHM of the point-spread function at the center of a HATNet image is ∼25''). Also, we applied the trend-filtering procedure in non-signal-reconstructive mode, which reduces the transit depth while increasing the signal-to-noise ratio of the detection. For each system, the ratio of the planet and stellar radii, which is related to the true transit depth, is determined in Section 3.2 using the higher spatial resolution photometric follow-up observations described in Section 2.4. ^cFrom Lasker et al. 2008.

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High-resolution, low-S/N "reconnaissance" spectra were obtained for HAT-P-34 and HAT-P-35 using the Tillinghast Reflector Echelle Spectrograph (TRES; Fűrész 2008) on the 1.5 m Tillinghast Reflector at FLWO. These observations were reduced and analyzed following the procedure described by Quinn et al. (2012) and Buchhave et al. (2010); the results are listed in Table 3. For both objects the spectra were single-lined, and showed RV variations on the order of ∼100 m s⁻¹. Proper phasing of the RV with the photometric ephemeris gives confidence in acquiring further, high signal-to-noise spectroscopic observations to refine the orbit (see Section 2.3). While for HAT-P-34 the variations initially did not appear to phase with the photometric ephemeris, we entertained the possibility of a very significant non-zero eccentricity, and pursued follow-up of the target. For HAT-P-35 the variations were in phase with the photometric ephemeris indicating a ∼2.7 M_J companion. For both HAT-P-36 and HAT-P-37 we obtained two TRES spectra near each of the predicted quadrature phases. For both objects the spectra were single-lined. For HAT-P-36 the resulting RV measurements showed ∼400 m s⁻¹ variation in phase with the photometric ephemeris, while for HAT-P-37 the RV measurements showed ∼260 m s⁻¹ variation in phase with the ephemeris. We opted to continue observing both of these objects using TRES with the aim of confirming the planets. The TRES observations of HAT-P-36 and HAT-P-37 are discussed further in the following subsection.

We proceeded with the follow-up of each candidate by obtaining high-resolution, high-S/N spectra to characterize the RV variations, and to refine the determination of the stellar parameters. These observations are summarized in Table 4. The RV measurements and uncertainties for HAT-P-34 through HAT-P-37 are given in the Appendix. The period-folded data, along with our best fit described below in Section 3, are displayed in Figures 2–5.

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Four facilities were used in the confirmation of these planets (including three separate facilities used for HAT-P-34). These facilities are HIRES (Vogt et al. 1994) on the 10 m Keck I telescope in Hawaii, the High-Dispersion Spectrograph (HDS; Noguchi et al. 2002) on the 8.3 m Subaru telescope in Hawaii, the FIbre-fed Échelle Spectrograph (FIES) on the 2.5 m Nordic Optical Telescope (NOT) at La Palma, Spain (Djupvik & Andersen 2010), and TRES on the FLWO 1.5 m telescope.

The HIRES and HDS observations made use of the iodine-cell method (Marcy & Butler 1992; Butler et al. 1996) for precise wavelength calibration and relative RV determination, while the FIES and TRES observations made use of Th-Ar lamp spectra obtained before and after the science exposures. The HIRES observations were reduced to relative RVs in the barycentric frame following Butler et al. (1996), Johnson et al. (2009), and Howard et al. (2010); the HDS observations were reduced following Sato et al. (2002, 2005); and the FIES and TRES observations were reduced following Buchhave et al. (2010).

We found that for all four systems the RV residuals from the best-fit models, described below in Section 3.2, exhibit excess scatter over what is expected based on the formal measurement uncertainties. Such excess scatter, or "jitter" has been well known for stars, and can stem from multiple sources. The excess is in the residuals of the observations with respect to a physical (and possibly instrumental) model. If this model is not adequate, the residuals can be larger than expected. For example, in the case of HAT-P-34b, ignoring the linear trend in the RVs would lead to a much increased "jitter." Additional planets may cause jitter, as the limited number of RV observations is not enough to uniquely identify and model such systems. The typical source of the jitter, however, is the star itself, namely inhomogeneities (spots, flares, plages, etc.) on the stellar surface (e.g., Makarov et al. 2009; Martínez-Arnáiz et al. 2010) causing jitters up to 100 ms. Granulation and stellar oscillations contribute on a smaller scale, but are present for non-active stars that are outside the instability strip. A recent publication by Cegla et al. (2012) discusses the stellar jitter due to variable gravitational redshift of the star, as the stellar radius changes due to oscillations (ΔR of 10⁻⁴ causing ∼0.1 m s⁻¹). And, of course, systematics in the instrument further inflate the jitter. A review of RV jitter of stars observed by the Keck telescope is given in Wright (2005).

In order to ensure realistic estimates of the system parameter uncertainties we add in quadrature an RV jitter to the formal RV measurement uncertainties such that χ² per degree of freedom is unity for the best-fit model for each planet. We adopt an independent jitter for the observations made by each instrument of each planet. The RV uncertainties given in the tables presented in the Appendix do not include this jitter; we do include the jitter in Figures 2–5.

For HAT-P-34 and HAT-P-35 we also show the S index, which is a measure of the chromospheric activity of the star derived from the flux in the cores of the Ca ii H and K lines. This index was computed following Isaacson & Fischer (2010) and has been calibrated to the scale of Vaughan et al. (1978). A procedure for obtaining calibrated S index values from the TRES spectra has not yet been developed, so we do not provide these measurements for HAT-P-36 or HAT-P-37. We convert the S index values to log R'_HK following Noyes et al. (1984) and find median values of log R'_HK = −4.859 and log R'_HK = −5.242 for HAT-P-34 and HAT-P-35, respectively. These values imply that neither star has a particularly high level of chromospheric activity.

Following Queloz et al. (2001) and Torres et al. (2007), we checked whether the measured radial velocities are not real, but are instead caused by distortions in the spectral line profiles due to contamination from a nearby unresolved eclipsing binary. A bisector (BS) analysis for each system based on the Keck and TRES spectra was done as described in Section 5 of Bakos et al. (2007a). For HAT-P-35, which is relatively faint, we found that the measured BSs were significantly affected by scattered moonlight and applied an empirical correction for this effect following Hartman et al. (2009; see also Kovács et al. 2010). For HAT-P-34 the BS scatter is fairly high (∼25 m s⁻¹), but this is in line with the high RV jitter (∼60 m s⁻¹), which is typical of an F star with vsin i = 24.0 ± 0.5 km s⁻¹ (Saar et al. 2003; Hartman et al. 2011b).

None of the systems show significant bisector span variations (relative to the semi-amplitude of the RV variations) that phase with the photometric ephemeris. Such variations are generally expected if the transit and RV signals were due to blends rather than planets. While the lack of bisector span variations does not exclude all blend scenarios, it does significantly limit the possible blend scenarios that can reproduce our current data within the measurement errors, i.e., configurations that are compatible with the photometric and spectroscopic observations, proper motions, color indices, and moderately high resolution imaging. We have found in the past that invoking detailed blend modeling to exclude all possible blend configurations and confirm the planet hypothesis (e.g., Hartman et al. 2011a, Sections 3.2.2 and 3.2.3) is rarely of any incremental value when the ingress and egress durations are short relative to the total transit duration, the RV variations exhibit a Keplerian orbit in phase with the photometric ephemeris, and bisector spans show no correlation with the orbit. We conclude that the velocity variations detected for all four stars are real, and that each star is orbited by a close-in giant planet.

In order to permit a more accurate modeling of the light curves, we conducted additional photometric observations using the KeplerCam CCD camera on the FLWO 1.2 m telescope, and the Spectral Instrument CCD on the 2.0 m Faulkes Telescope North (FTN) at Haleakala Observatory in Hawaii, which is operated by the Las Cumbres Observatory Global Telescope (LCOGT). The observations for each target are summarized in Table 1.

The reduction of these images was performed as described by Bakos et al. (2010). We applied External Parameter Decorrelation (EPD; Bakos et al. 2010) and the Trend Filtering Algorithm (TFA; Kovács et al. 2005) to remove trends simultaneously with light-curve modeling. The final time series, together with our best-fit transit light-curve models, are shown in the top portion of Figures 6–9 for HAT-P-34 through HAT-P-37, respectively. The individual measurements, permitting independent analysis by other researchers, are reported in the Appendix.

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Stellar atmospheric parameters for HAT-P-34 and HAT-P-35 were measured using our template spectra obtained with the Keck/HIRES instrument, and the analysis package known as Spectroscopy Made Easy (SME; Valenti & Piskunov 1996), along with the atomic line database of Valenti & Fischer (2005). For HAT-P-36 and HAT-P-37 the stellar atmospheric parameters were determined by cross-correlating the TRES observations against a finely sampled grid of synthetic spectra based on Kurucz (2005) model atmospheres. This procedure, known as Stellar Parameter Classification (SPC), will be described in detail in a forthcoming paper (L. A. Buchhave et al., in preparation). We note that SPC has been performed in the past on numerous HATNet transiting planet candidates (Buchhave, personal communication), and the results were consistent with those of SME.

For each star, we obtained the following initial spectroscopic parameters and uncertainties:

• 1.  
  HAT-P-34—effective temperature T_eff⋆ = 6400 ± 100 K, metallicity [Fe/H] = +0.21 ± 0.1 dex, stellar surface gravity log g_⋆ = 3.98 ± 0.1 (cgs), and projected rotational velocity vsin i = 24.5 ± 1.0 km s⁻¹.
• 2.  
  HAT-P-35—effective temperature T_eff⋆ = 5940 ± 88 K, metallicity [Fe/H] = +0.01 ± 0.08 dex, stellar surface gravity log g_⋆ = 3.98 ± 0.1 (cgs), and projected rotational velocity vsin i = 0.5 ± 0.5 km s⁻¹.
• 3.  
  HAT-P-36—effective temperature T_eff⋆ = 5850 ± 100 K, metallicity [Fe/H] = +0.38 ± 0.1 dex, stellar surface gravity log g_⋆ = 4.73 ± 0.17 (cgs), and projected rotational velocity vsin i = 2.86 ± 0.5 km s⁻¹.
• 4.  
  HAT-P-37—effective temperature T_eff⋆ = 5570 ± 100 K, metallicity [Fe/H] = +0.09 ± 0.1 dex, stellar surface gravity log g_⋆ = 4.67 ± 0.1 (cgs), and projected rotational velocity vsin i = 2.95 ± 0.5 km s⁻¹.

Following Bakos et al. (2010), these initial values of T_eff⋆, log g_⋆, and [Fe/H] were used to determine the quadratic limb-darkening coefficients needed in the global modeling of the follow-up photometry (summarized in Section 3.2). This analysis yields ρ_⋆, the mean stellar density, which is closely related to a/R_⋆, the normalized semimajor axis, and provides a tighter constraint on the stellar parameters than does the spectroscopically determined log g_⋆ (e.g., Sozzetti et al. 2007). We combined ρ_⋆, T_eff⋆, and [Fe/H] with stellar evolution models from the Yonsei–Yale (YY) series by Yi et al. (2001) to determine probability distributions of other stellar properties, including log g_⋆. For each system we carried out a second SME or SPC iteration in which we adopted the new value of log g_⋆ so determined and held it fixed in a new SME or SPC analysis, adjusting only T_eff⋆, [Fe/H], and vsin i, followed by a second global modeling of the RV and light curves, together with improved limb darkening parameters. The final atmospheric parameters that we adopt, together with stellar parameters inferred from the YY models (such as the mass, radius and age) are listed in Table 5 for all four stars.

The inferred location of each star in a diagram of a/R_⋆ versus T_eff⋆, analogous to the classical H-R diagram, is shown in Figure 10. In each case the stellar properties and their 1σ and 2σ confidence ellipses are displayed against the backdrop of model isochrones for a range of ages, and the appropriate stellar metallicity. For comparison, the locations implied by the initial SME and SPC results are also shown (in each case with a triangle).

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The stellar evolution modeling provides color indices that we compared against the measured values as a sanity check. For each star we used the near-infrared magnitudes from the Two Micron All Sky Survey (2MASS) Catalogue (Skrutskie et al. 2006), which are given in Table 5. These were converted to the photometric system of the models (ESO) using the transformations by Carpenter (2001). The resulting 2MASS-based color indices were all consistent (within 1σ) with the stellar model based color indices.

The distance for each star given in Table 5 was computed from the absolute K magnitude from the models and the 2MASS K_s magnitudes, ignoring extinction.

Table 6. Orbital and Planetary Parameters for HAT-P-34b through HAT-P-37b

Parameter	HAT-P-34b	HAT-P-35b	HAT-P-36b	HAT-P-37b
	Value	Value	Value	Value
Light-curve parameters
P (days) ...	5.452654 ± 0.000016	3.646706 ± 0.000021	1.327347 ± 0.000003	2.797436 ± 0.000007
Tc (BJD)a ...	2455431.59629 ± 0.00055	2455578.66081 ± 0.00050	2455565.18144 ± 0.00020	2455642.14318 ± 0.00029
T14 (days)a ...	0.1455 ± 0.0016	0.1640 ± 0.0018	0.0923 ± 0.0007	0.0971 ± 0.0015
T12 = T34 (days)a ...	0.0121 ± 0.0013	0.0162 ± 0.0017	0.0107 ± 0.0007	0.0153 ± 0.0013
a/R⋆ ...	9.48 ± 0.64	7.45 ± 0.37	4.66 ± 0.22	9.32+0.42− 0.57
ζ/R⋆ ...	14.99 ± 0.09	13.52 ± 0.09	24.51 ± 0.14	24.33 ± 0.18
Rp/R⋆ ...	0.0801 ± 0.0026	0.0954 ± 0.0027	0.1186 ± 0.0012	0.1378 ± 0.0030
b2 ...	0.113+0.080− 0.062	0.128+0.078− 0.066	0.097+0.057− 0.048	0.255+0.044− 0.056
b ≡ acos i/R⋆ ...	0.336+0.099− 0.128	0.357+0.092− 0.127	0.312+0.078− 0.105	0.505+0.041− 0.062
i (deg) ...	87.1 ± 1.2	87.3 ± 1.0	86.0 ± 1.3	86.9+0.4− 0.5
Quadratic limb-darkening coefficientsb
c1, i (linear term) ...	0.1785	0.2198	0.3142	0.3156
c2, i (quadratic term) ...	0.3825	0.3587	0.3113	0.3032
c1, z ...	0.1269	...	...	0.2477
c2, z ...	0.3728	...	...	0.3082
RV parameters
K (m s−1) ...	343.1 ± 21.3	120.7 ± 2.2	334.7 ± 14.5	177.7 ± 14.8
ecos ωc ...	0.410 ± 0.031	−0.004 ± 0.013	−0.002 ± 0.032	−0.017 ± 0.039
esin ωc ...	0.156 ± 0.052	−0.017 ± 0.026	0.051 ± 0.040	0.007 ± 0.060
e ...	0.441 ± 0.032	0.025 ± 0.018	0.063 ± 0.032	0.058 ± 0.038
ω (deg) ...	20 ± 14	248 ± 93	95 ± 63	164 ± 84
$\dot{\gamma }$ (m s−1 d−1) ...	0.8683 ± 0.4719	...	...	...
RV jitter
Keck/HIRES (m s−1) ...	56.0	3.7	...	...
Subaru/HDS (m s−1) ...	32.0	...	...	...
NOT/FIES (m s−1) ...	0.0	...	...	...
FLWO 1.5/TRES (m s−1) ...	...	...	33.6	25.8
Secondary eclipse parameters
Ts (BJD) ...	2455435.721 ± 0.099	2455580.476 ± 0.030	2455565.844 ± 0.027	2455643.512 ± 0.070
Ts, 14 ...	0.1871 ± 0.0170	0.1596 ± 0.0076	0.1013 ± 0.0071	0.0981 ± 0.0083
Ts, 12 ...	0.0176 ± 0.0052	0.0156 ± 0.0019	0.0120 ± 0.0015	0.0153 ± 0.0029
Planetary parameters
Mp (MJ) ...	3.328 ± 0.211	1.054 ± 0.033	1.832 ± 0.099	1.169 ± 0.103
Rp (RJ) ...	1.197+0.128− 0.092	1.332 ± 0.098	1.264 ± 0.071	1.178 ± 0.077
C(Mp, Rp)d ...	0.23	0.49	0.11	0.02
ρp (g cm−3) ...	2.40 ± 0.63	0.55 ± 0.11	1.12 ± 0.19	0.89 ± 0.19
log gp (cgs) ...	3.76 ± 0.08	3.17 ± 0.06	3.45 ± 0.05	3.32 ± 0.07
a (AU) ...	0.0677 ± 0.0008	0.0498 ± 0.0006	0.0238 ± 0.0004	0.0379 ± 0.0006
Teq (K) ...	1520 ± 60	1581 ± 45	1823 ± 55	1271 ± 47
Θe...	0.269 ± 0.029	0.064 ± 0.005	0.067 ± 0.005	0.081 ± 0.009
〈F〉 (109 erg s−1 cm−2)f ...	1.21+0.23− 0.16	1.41+0.19− 0.14	2.49 ± 0.30	0.589+0.102− 0.075

Notes. ^aT_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. Barycentric Julian dates (BJD) throughout the paper are calculated from Coordinated Universal Time (UTC). ^bValues for a quadratic law, adopted from the tabulations by Claret (2004) according to the spectroscopic (SME) parameters listed in Table 5. ^cLagrangian orbital parameters derived from the global modeling, and primarily determined by the RV data. ^dCorrelation coefficient between the planetary mass M_p and radius R_p. ^eThe Safronov number is given by Θ = (1/2)(V_esc/V_orb)² = (a/R_p)(M_p/M_⋆) (see Hansen & Barman 2007). ^fIncoming flux per unit surface area, averaged over the orbit.

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We simultaneously modeled the HATNet photometry, the follow-up photometry, and the high-precision RV measurements using the procedures described by Bakos et al. (2010). Namely, the best fit was determined by a downhill simplex minimization, and was followed by a Monte Carlo Markov Chain run to scan the parameter space around the minimum, and establish the errors (Pál 2009b). For each system we used a Mandel & Agol (2002) transit model, together with the EPD and TFA trend-filters, to describe the follow-up light curves, a Mandel & Agol (2002) transit model for the HATNet light curve(s), and a Keplerian orbit using the formalism of Pál (2009a) for the RV curve(s). For HAT-P-34 we included a linear trend in the RV model, but find that it is only significant at the ∼2σ level; the planet and stellar parameters are changed by less than 1σ when the trend is not included in the fit. The parameters that we adopt for each system are listed in Table 6. In all cases we allow the eccentricity to vary so that the uncertainty on this parameter is propagated into the uncertainties on the other physical parameters, such as the stellar and planetary masses and radii; the observations of HAT-P-35b, HAT-P-36b, and HAT-P-37b are consistent with these planets being on circular orbits.

HAT-P-34b is a relatively massive M_p = 3.328 ± 0.211 M_J planet on a relatively long-period (P = 5.452654 ± 0.000016 days), eccentric (e = 0.441 ± 0.032) orbit. There are only five known transiting planets with higher eccentricities (HAT-P-2b, e = 0.5171 ± 0.0033, Pál et al. 2010; Bakos et al. 2007a; CoRoT-10b, e = 0.53 ± 0.04, Bonomo et al. 2010; CoRoT-20b, e = 0.562 ± 0.013, Deleuil et al. 2012; HD 17156b, e = 0.669 ± 0.008, Madhusudhan & Winn 2009; and HD 80606b, e = 0.9330 ± 0.0005, Hébrard et al. 2010), all of which have longer orbital periods than HAT-P-34b. Of these planets, HAT-P-2b is most similar in orbital period to HAT-P-34b, but it has a mass that is more than two times larger than that of HAT-P-34b. Two planets with masses, radii, and equilibrium temperatures within 10% of the values of HAT-P-34b (assuming zero albedo and full heat redistribution) are CoRoT-18b (Hébrard et al. 2011) and WASP-32b (Maxted et al. 2010); however, neither of these planets has a significant eccentricity.

HAT-P-34b is a promising target for measuring the RM effect (Rossiter 1924; McLaughlin 1924), since the host star is bright (V = 10.16), has a significant spin (vsin i= 24.0 ± 0.5 km s⁻¹), and the transit is moderately long (T₁₄ = 0.1455 ± 0.0016 days). Also, the transit is far from equatorial (b = 0.336^+0.099_{− 0.128}), a configuration that is important for resolving the degeneracy between vsin i and λ, which is the sky-plane projected angle between the planetary orbital normal and the stellar spin axis. Winn et al. (2010) pointed out that hot Jupiters around stars with T_eff⋆ ≳ 6250 K have a higher chance of being misaligned. Based on the effective temperature of the host star 6442 ± 88 K, we thus expect that HAT-P-34b has a higher chance of misalignment (note that this may not necessarily yield a non-zero λ, if HAT-P-34b's orbit is tilted along the line of sight). Alternatively, Schlaufman (2010) used a stellar rotation model and observed vsin i values to statistically identify TEP systems that may be misaligned along the line of sight, and concluded these preferentially occur at M_⋆ > 1.2 M_☉. Based on the stellar mass alone (1.39 M_☉) we conclude that the chances for misalignment are increased.

HAT-P-35b is a very typical M_p = 1.054 ± 0.033 M_J, R_p = 1.332 ± 0.098 R_J planet on a P = 3.646706 ± 0.000021 day orbit and with an equilibrium temperature of T_eq = 1581 ± 45 K (again, assuming zero albedo and full heat redistribution). There are four other planets with masses, radii, and equilibrium temperatures that are all within 10% of the values for HAT-P-35b. These are HAT-P-5b (Bakos et al. 2007b), HAT-P-6b (Noyes et al. 2008), OGLE-TR-211b (Udalski et al. 2008), and WASP-26b (Smalley et al. 2010). The stellar effective temperature (6096 ± 88 K) is close to the assumed border-line between well-aligned and misaligned systems, making it an interesting system for testing the RM effect (with the caveat that vsin i, and thus the expected amplitude of the anomaly is low).

HAT-P-36b is a very short-period (P = 1.327347 ± 0.000003 days) planet with a mass of M_p = 1.832 ± 0.099 M_J, a radius of R_p = 1.264 ± 0.071 R_J, and an equilibrium temperature of T_eq = 1823 ± 55 K. There are two other planets with masses, radii, and equilibrium temperatures within 10% of the values for HAT-P-36b: TrES-3b (O'Donovan et al. 2007) and WASP-3b (Pollacco et al. 2008).

Like the preceding planets, HAT-P-37b also has very typical physical properties, with M_p = 1.169 ± 0.103 M_J, R_p = 1.178 ± 0.077 R_J, P = 2.797436 ± 0.000007 days, and T_eq = 1271 ± 47 K. Three planets with masses, radii, and equilibrium temperatures within 10% of the values for HAT-P-37b are HD 189733b (Bouchy et al. 2005), OGLE-TR-113b (Bouchy et al. 2004), and XO-5b (Burke et al. 2008). HAT-P-37 lies just outside of the field of view of the Kepler space mission and is listed in the Kepler Input Catalog (KIC)¹⁴ as KIC 12396036.

According to Adams & Laughlin (2006), the eccentricity of a hot Jupiter's orbit decays due to both the tides on the star and the tides on the planet, with the tides on the planet dominating the circularization as long as the tidal quality factor of the planet (Q_P) is not much larger than the star's (Q_⋆). Both of these factors are highly uncertain with various theoretical and observational constraints ranging over several orders of magnitude. In particular, tidal circularization of main-sequence stars (Claret & Cunha 1997; Meibom & Mathieu 2005; Zahn & Bouchet 1989; Zahn 1989) seems to indicate 10⁵ ≲ Q_⋆ ≲ 10⁶. On the other hand, the discovery of extremely short-period massive planets, the two most dramatic being WASP-18b (Hellier et al. 2009) and WASP-19b (Hellier et al. 2011), seems to be inconsistent with such efficient dissipation (Penev et al. 2012), requiring much larger values of Q_⋆ ≳ 10⁸, which coincide well with the theoretical values derived by Penev & Sasselov (2011), who argue that binary stars and star–planet systems are subject to different modes of dissipation in the star. The tidal dissipation parameter in the planet has also been the subject of many studies attempting to constrain it either from theory (Bodenheimer et al. 2003; Ogilvie & Lin 2004) or from the observed configuration of Jupiter's satellites (Goldreich & Soter 1966) giving 10⁵ ≲ Q_P ≲ 10⁷.

With this in mind we conclude that the circularization of HAT-P-34b's orbit is likely dominated by the tidal dissipation in the planet and using Q_P = 10⁶ and the expression for the tidal circularization timescale from Adams & Laughlin (2006), we estimate the eccentricity of HAT-P-34b should decay on the scale of 2 Gyr, i.e., it is not in conflict with theoretical expectations. The possible outer companion indicated by the RV trend may also be responsible for pumping the eccentricity of the inner planet HAT-P-34b (see Correia et al. 2012 for a discussion).

Figure 11 shows HAT-P-34b on the orbital-period–eccentricity plane of TEPs with well determined parameters (using our own compilation that attempts to keep up with various refinements to these parameters). It is apparent that eccentricity is correlated with orbital period and with planet mass, as expected from tidal theory. HAT-P-34b lies in a sparse position in these diagrams; for example, it has a high eccentricity for its period, the only similar planet being HAT-P-2b.

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Figure 12 is a "tidal" plot (see Figure 3 of Pont et al. 2011), showing TEPs with well measured properties in the a/R_p–M_p/M_⋆ plane, using more data points (including the present discoveries) than Pont et al. (2011). Since $\tau _c = (4/63)Q_P\sqrt{(a^3/GM_{\star }}(a/R_P)^5M_{p}/M_\star$, we expect planets with small relative semimajor axis (a/R_P) or planets with small relative mass (M_p/M_⋆) to be circularized. This is indeed the case, as shown by the intensity (color) scale representing eccentricity. For hot Jupiters that migrate in by circularization of an initially very eccentric orbit, the expected "parking distance" is ∼2a_H (Ford & Rasio 2006), where a_H is the semimajor axis at which the radius of the planet equals its Hill radius. The thick solid line in Figure 12 shows this relation. A fairly good match for the dividing line between the circularized (denoted by black points) and eccentric (gray or color) points is at a ≈ 4a_H (marked with a thin solid line). This relation now includes very small mass Kepler discoveries. HAT-P-34b belongs to the sparse group of high relative semimajor axis (a/R_p) and massive extrasolar planets.

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The following tables present the spectroscopic data (radial velocities, bisector spans, and activity index measurements) and high-precision photometric data for the four planets presented in this paper. Measurements derived from the high-precision spectroscopic observations of HAT-P-34 through HAT-P-37 are given in Tables 7–10, respectively. Tables 11–14 give the follow-up photometric observations for each of these systems.