HAT-P-39b–HAT-P-41b: THREE HIGHLY INFLATED TRANSITING HOT JUPITERS^*

Table 1 summarizes the photometric observations of each new planetary system, including the discovery observations made with the HATNet system. The HATNet images were processed and reduced to trend-filtered light curves following the procedure described by Bakos et al. (2010). 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 below (see Figure 1).

• 1.  
  HAT-P-39–GSC 1364-01424 (also known as Two Micron All Sky Survey (2MASS) 07350197+1749482; $\alpha = 07^{\mathrm h}35^{\mathrm m}01\mbox{$.\!\!^{\mathrm s}$}97$, δ = +17°49'483; J2000; V = 12.422; Droege et al. 2006). A signal was detected for this star with an apparent depth of ∼10.9 mmag and a period of P = 3.5439 days.
• 2.  
  HAT-P-40–GSC 3607-01028 (also known as 2MASS 22220308+4527265; $\alpha = 22^{\mathrm h}22^{\mathrm m}03\mbox{$.\!\!^{\mathrm s}$}00$, δ = +45°27'266; J2000; V = 11.699; Droege et al. 2006). A signal was detected for this star with an apparent depth of ∼4.4 mmag and a period of P = 4.4572 days.
• 3.  
  HAT-P-41–GSC 0488-02442 (also known as 2MASS 19491743+0440207; $\alpha = 19^{\mathrm h}49^{\mathrm m}17\mbox{$.\!\!^{\mathrm s}$}40$, δ = +04°40'207; J2000; V = 11.087; Droege et al. 2006). A signal was detected for this star with an apparent depth of ∼8.4 mmag and a period of P = 2.6940 days.

Zoom In Zoom Out Reset image size

High-resolution, low-signal-to-noise (S/N) "reconnaissance" spectra were obtained for HAT-P-39, HAT-P-40, and HAT-P-41 using the Harvard-Smithsonian Center for Astrophysics Digital Speedometer (DS; Latham 1992) until it was retired in 2009, and thereafter the Tillinghast Reflector Echelle Spectrograph (TRES; Fűrész 2008), both on the 1.5 m Tillinghast Reflector at the Fred Lawrence Whipple Observatory (FLWO) in AZ. The reconnaissance spectroscopic observations and results for each system are summarized in Table 2. The DS observations were reduced and analyzed following the procedure described by Torres et al. (2002), while the TRES observations were reduced and analyzed following the procedure described by Quinn et al. (2012) and Buchhave et al. (2010).

Based on the observations summarized in Table 2, we find that all three systems have RV root mean square (rms) residuals consistent with no detectable RV variation within the precision of the measurements. All spectra were single-lined, i.e., there is no evidence that any of these targets consist of more than one star. Note that while there is a close companion to HAT-P-41 (Section 2.5), it was resolved by the TRES guider and the light from the companion did not go down the fiber. The gravities for all of the stars indicate that none of the stars are giants, though HAT-P-40 may be slightly evolved.

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. The observations were made with HIRES (Vogt et al. 1994) on the Keck-I telescope in HI and with FIES on the Nordic Optical Telescope on the island of La Palma, Spain (Djupvik & Andersen 2010). We used the high-resolution fiber (providing spectra with a resolution of R = 67, 000) for four of the FIES observations, and the medium-resolution fiber (R = 46, 000) for five of the FIES observations. The HIRES observations were reduced to RVs in the barycentric frame following the procedure described by Butler et al. (1996), while the FIES observations were reduced following Buchhave et al. (2010). The RV measurements and uncertainties are given in Tables 3–5 for HAT-P-39 through HAT-P-41, respectively. The period-folded data along with our best fit, described below in Section 3, are displayed in Figures 2–4.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In each figure, we also show the spectral-line bisector spans (BSs) computed from the Keck/HIRES spectra following Torres et al. (2007), the FWHM of the Keck/HIRES spectral lines (computed from the cross-correlation function (CCF), in a similar manner to the BSs), and the S activity index calculated following Isaacson & Fischer (2010).

We conducted additional photometric observations of the three stars with the KeplerCam CCD camera on the FLWO 1.2 m telescope, the Spectral CCD on the 2.0 m Faulkes Telescope North (FTN) at Haleakala Observatory in HI, and the CCD imager on the Byrne Observatory at Sedgwick (BOS) 0.8 m telescope, at Sedgwick Reserve in the Santa Ynez Valley, CA. Both FTN and BOS are operated by the Las Cumbres Observatory Global Telescope (LCOGT¹⁶; T. M. Brown et al. 2012, in preparation). The observations for each target are summarized in Table 1.

The reduction of the KeplerCam images to light curves was performed as described by Bakos et al. (2010). The FTN and BOS images were reduced in a similar manner. We performed an external parameter decorrelation (EPD) and a trend filtering algorithm (TFA) to remove trends simultaneously with the light-curve modeling (for more details, see Bakos et al. 2010). The final time series, together with our best-fit transit light curvelight-curve model, are shown in the top portion of Figures 5–7, while the individual measurements are reported in Tables 6–8.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We obtained high-resolution imaging of HAT-P-41 on the night of 2011 June 21 using the Clio2 near-IR imager on the MMT 6.5 m telescope in AZ. Observations were obtained with the adaptive optics (AO) system in H band and in L' band. Figure 8 shows the resulting H-band image of HAT-P-41, which easily resolves the 356 ± 002 neighbor.

Zoom In Zoom Out Reset image size

Based on these observations, we measure the H- and L'-band magnitudes of the neighbor relative to HAT-P-41 to be ΔH = 2.46 ± 0.06 mag and ΔL' = 2.6 ± 2.0 mag. Assuming that the star is a physical companion to HAT-P-41, these magnitude differences are consistent with the neighbor being a ∼0.7 M_☉ K dwarf, or roughly ∼3.5 mag fainter than HAT-P-41 in the i band.

The KeplerCam observations of HAT-P-41 described in Section 2.4 show HAT-P-41 to have an elongation in the wing of its point-spread function (PSF) due to the companion, but the seeing is not good enough to resolve the stars given the magnitude difference. We use the daophot and allstar programs (Stetson 1987, 1992) to obtain PSF-fitting photometry for the two stars and find that the neighbor is fainter in the i band by Δi ≈ 3.3 mag, with an uncertainty of at least 0.1 mag. We conclude that the broadband photometry is consistent with HAT-P-41 having a K dwarf binary companion. At the distance of HAT-P-41, the 35 angular separation corresponds to a projected physical separation of ∼1000 AU between the two stars.

We measured the stellar atmospheric parameters for each star using the Keck/HIRES iodine-free template spectra, together with the Spectroscopy Made Easy (SME; Valenti & Piskunov 1996) package, and the Valenti & Fischer (2005) atomic line database. For each star, we obtained the following initial values and uncertainties.

• 1.  
  HAT-P-39. Effective temperature T_eff⋆ = 6325 ± 100 K, metallicity [Fe/H] = 0.14 ± 0.1 dex, stellar surface gravity log g_⋆ = 4.04 ± 0.1 (cgs), and projected rotational velocity vsin i = 12.7 ± 0.5 km s⁻¹.
• 2.  
  HAT-P-40. Effective temperature T_eff⋆ = 6140 ± 100 K, metallicity [Fe/H] = 0.25 ± 0.1 dex, stellar surface gravity log g_⋆ = 4.04 ± 0.1 (cgs), and projected rotational velocity vsin i = 6.7 ± 0.5 km s⁻¹.
• 3.  
  HAT-P-41. Effective temperature T_eff⋆ = 6007 ± 100 K, metallicity [Fe/H] = 0.06 ± 0.1 dex, stellar surface gravity log g_⋆ = 3.68 ± 0.06 (cgs), and projected rotational velocity vsin i = 20.6 ± 0.5 km s⁻¹.

As described in our previous papers (e.g., Bakos et al. 2010), these initial values were used to determine the quadratic limb-darkening coefficients for each star from the Claret (2004) tables. We then used the mean stellar density, determined from the normalized semimajor axis a/R_⋆, together with the effective temperature and metallicity to determine an initial estimate of the mass and radius of each star from the Yonsei–Yale (YY) isochrones (Yi et al. 2001). This provided a refined estimate of the stellar surface gravity, which we fixed in a second iteration of SME for each star. For each system, a third iteration did not change log g_⋆ appreciably, so we adopted the values from the second iteration as the final spectroscopic parameters for each star. These parameters are listed in Table 9. In this same table, we also list the available broadband photometric magnitudes from the literature and the physical parameters, such as the stellar masses and radii, which are determined from the spectroscopic parameters together with the model isochrones. As discussed in Section 3.3, we adopt the parameters assuming a circular orbit for each planet. Some of the parameters, especially the derived stellar masses and radii, depend on the eccentricity; Table 10 lists the values for these parameters when the eccentricity is allowed to vary.

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 9. In each case, the stellar properties and their 1σ and 2σ confidence ellipsoids 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 results are also shown (in each case with a triangle). Note the significant change in the estimated temperature, particularly for HAT-P-41, between the first and second SME iterations. As shown recently by Torres et al. (2012), when SME is applied in the iterative fashion described in this paper to TEP host stars, the temperature after the second iteration tends to be systematically higher than after the first iteration for stars with T_eff ≳ 6200 K. This is presumably due to hot stars having fewer and broader lines than cool stars, making it difficult to simultaneously infer the surface gravity, temperature, and metallicity from their spectra. When a star hosts a transiting planet, the strong constraint on the stellar density, which comes from the transit, makes it possible to reduce the number of free parameters in modeling the spectrum, yielding a more accurate determination of those parameters.

Zoom In Zoom Out Reset image size

We determine the distance to and extinction of each star by comparing the J, H, and K_S magnitudes from the Two Micron All Sky Survey (2MASS) catalog (Skrutskie et al. 2006), and the V and I_C magnitudes from the TASS Mark IV catalog (Droege et al. 2006), to the expected magnitudes from the stellar models. We use the transformations by Carpenter (2001) to convert the 2MASS magnitudes to the photometric system of the models (ESO), and use the Cardelli et al. (1989) extinction law, assuming a total-to-selective extinction ratio of R_V = 3.1, to relate the extinction in each bandpass to the V-band extinction A_V. The resulting A_V and distance measurements are given in Table 9. We find total V-band extinctions of A_V = 0.171 ± 0.135, 0.353 ± 0.127, and 0.248 ± 0.134 mag for HAT-P-39 through HAT-P-41, respectively. For comparison, the total line-of-sight extinctions in each direction, estimated from the Schlegel et al. (1998) dust maps, are 0.146 mag, 0.724 mag, and 0.513 mag. Following Bonifacio et al. (2000), we estimate the expected distance-corrected extinction to each source to be 0.113 mag, 0.306 mag, and 0.157 mag, respectively. For HAT-P-39 and HAT-P-40, the measured and expected values are consistent. For HAT-P-41, the broadband photometry appears to point to a slightly redder star than expected based on the spectroscopic temperature and expected extinction. As noted in Section 2.5, HAT-P-41 has a close companion that is unresolved in the 2MASS or TASS catalogs. This companion is the probable cause of the discrepancy between the expected and observed magnitudes of HAT-P-41.

As discussed in Section 3.3, both HAT-P-39 and HAT-P-41 show high RV jitter, with values of 43.0 m s⁻¹ and 33.4 m s⁻¹, respectively. While these values are higher than for most exoplanet host stars, they are typical of F dwarfs with projected rotation velocities greater than 10 km s⁻¹. Using the empirical relation between vsin i and jitter found by Saar et al. (2003), the expected jitter for an F dwarf with vsin i = 10 km s⁻¹ is ∼30 m s⁻¹. As discussed in Hartman et al. (2011) in the context of HAT-P-32 and HAT-P-33, two rapidly rotating F dwarfs with jitter values in excess of those seen for HAT-P-39 and HAT-P-41, the physical origin of this jitter is not clear, though Saar et al. (1998) argue that for F dwarfs it is probably due to convective inhomogeneities on the stellar surfaces that vary in time.

The analyses of our reconnaissance spectroscopic observations, discussed in Section 2.2, rule out the most obvious astrophysical false positive scenarios for HAT-P-39 through HAT-P-41. Additionally, the spectral-line BS analyses that we conducted (Figures 2–4) provide constraints on more subtle blend scenarios similar to that presented in Torres et al. (2004). However, because HAT-P-39 and HAT-P-41 have high RV jitter, and consequently, high BS scatter (∼80 m s⁻¹ and ∼30 m s⁻¹, respectively), relative to their RV semiamplitudes (63.6 ± 10.4 m s⁻¹ and 92.5 ± 11.6 m s⁻¹, respectively), the BS test provides a less stringent constraint on possible blend scenarios than it does in a case such as HAT-P-40 (BS scatter of ∼10 m s⁻¹ and RV semiamplitude of 58.1 ± 2.9 m s⁻¹). To provide additional support for the planetary interpretation of the observations of each system, we conduct detailed blend analyses of the light curves (including both the HATNet discovery light curves and all available follow-up light curves) and absolute photometry following Hartman et al. (2011).

In Figure 10 we show, for each system, the histogram of Δχ² values between the best-fit transiting planet model and the best-fit blend model for simulated data sets having the same noise properties as the observed residuals from the best-fit blend model (see Hartman et al. 2011 for a more detailed discussion). In this same figure, we also show the Δχ² difference between the best-fit models applied to the observations. We find that for HAT-P-39 and HAT-P-41, we can reject blend scenarios involving combinations of three stars with greater than 3σ and 5σ confidence, respectively, based solely on the photometry. For HAT-P-39, the detailed shape of the transit, as determined from the follow-up light curves, contributes most of the χ² difference between the models, while for HAT-P-41 it is the lack of out-of-transit variations, as determined from the HATNet light curve, that contributes most of the χ² difference. For HAT-P-40, we are unable to rule out blend scenarios based solely on the photometry however; in this case, the lack of BS or FWHM variations rules out such blends. To quantify this, we simulate the CCF of blended systems, which could plausibly fit the photometric data (configurations which cannot be rejected with greater than 5σ confidence) and find that in all cases either the RV or FWHM of the blended configuration varies by several km s⁻¹, or the BS varies by greater than ∼100 m s⁻¹, greatly exceeding the observational limits on any such variations. Similarly for HAT-P-39, we find that stellar blend configurations which cannot be rejected with greater than 5σ confidence predict greater than 500 m s⁻¹ variations in the RV or BS of the Keck spectra, which are well above the observational constraints.

Zoom In Zoom Out Reset image size

As discussed in Section 2.5, HAT-P-41 has a close neighbor that we estimate to be ∼3.5 mag fainter in the i band. While such a neighbor could, in principle, be eclipsed by an object that would produce a ∼1% dip in the blended light curve, as we have shown here, the detailed shape of the light curve cannot be produced using physically possible combinations of stars (i.e., stars with parameters determined from stellar evolution models). We note that the KeplerCam observations show no evidence for variations in the flux centroid that correlate with the photometry, providing further evidence that the observed variation is not due to a deep eclipse in the poorly resolved neighbor.

While we can rule out, for each of the systems, blend scenarios involving only stellar-mass components, we cannot rule out scenarios involving binary star systems with one component hosting a transiting planet. Indeed, for HAT-P-41 we find that including a ∼0.7 M_☉ star in the system provides a slightly better fit to the photometric observations. In this case, we actually know that there is a faint companion (though it is either unresolved in our light curves or in the available absolute broadband photometry measurements), so it is reassuring to find that the blend analysis of the photometric data also points to the existence of this companion. For HAT-P-39, we can rule out binary companion stars with M < 1.24 M_☉, while for HAT-P-40 and HAT-P-41, we cannot rule out binary companions of any mass up to that of the mass inferred for the brighter star in the system. While massive binary companions in general should be easier to detect in the spectrum, if the two stars have very similar average velocities, the resulting variations in BS, FWHM, and RV measurements can be less than the constraints set by the observations.

We conclude that each system presented here contains a transiting planet; however, we cannot definitively claim that these are all single stars. High-resolution imaging, or further high-precision RVs would be needed to rule out, or discover, binary star companions. There is no evidence that either HAT-P-39 or HAT-P-40 is a binary system, so we treat each of these as single stars in the analysis that follows. For HAT-P-41, there is a resolved neighbor that we account for in our analysis of the system.

We modeled the HATNet photometry, the follow-up photometry, and the high-precision RV measurements using the procedure described by Bakos et al. (2010). Following the discussion by Eastman et al. (2012), we made two important changes to our analysis procedure compared to what was done in Bakos et al. (2010). As noted in Section 3.5.3 of Eastman et al. (2012), there is a common mistake in the implementation of the Metropolis–Hastings (M-H) algorithm for conducting a Markov Chain Monte Carlo (MCMC) analysis whereby the Markov Chain is not increased when a proposed transition is rejected. We discovered that the implementation we have been using for the analysis of HATNet planets has made this mistake and we have corrected it for the analysis of the planets presented in this paper. We found that this bug tends to inflate the error bars on the determined parameters by a factor of a few parts in a hundred. Errors given in previous discovery papers may thus be slightly overestimated. The second significant change that we have made is to use $\sqrt{e} \cos \omega$ and $\sqrt{e} \sin \omega$ as jump parameters, rather than ecos ω and esin ω. Previously, we had been assuming uniform priors on the latter jump parameters, which amounts to assuming a linear prior on the eccentricity e, creating a bias toward measuring nonzero eccentricities. As other authors have noted, using $\sqrt{e} \cos \omega$ and $\sqrt{e} \sin \omega$ leads to a uniform prior on e. We found that this change had a much more significant impact on our determined parameters than did correcting the bug in our implementation of M-H. For example, for HAT-P-39b, the eccentricity that we find is 0.094 ± 0.086 compared with 0.161 ± 0.094 when using our old jump parameters.

We also made a few minor changes to the analysis for the particular planets presented in this paper. For the analysis of HAT-P-41, we allowed independent RV zero points for the Keck/HIRES RVs, the high-resolution NOT/FIES RVs, and the medium-resolution NOT/FIES RVs. To account for the contribution from the neighbor to the photometry, we also fixed the third light in the i band to 4%, based on our PSF-fitting analysis of the KeplerCam observations of this system.

For each of the planets, we added in quadrature a component of stellar jitter to the formal Keck/HIRES RV errors such that χ² per degree of freedom is unity. For HAT-P-41, we did not add a jitter term to the FIES/NOT RV errors because the formal errors for these observations exceeded the scatter in the RV residuals. We find that both HAT-P-39 and HAT-P-41 require relatively high jitter values (43.0 m s⁻¹ and 33.4 m s⁻¹, respectively), while HAT-P-40 requires significantly less jitter (6.2 m s⁻¹). To see whether the excess RV scatter for HAT-P-39 or HAT-P-41 could be due to additional planets in these systems, we examined the Lomb–Scargle frequency spectra (Lomb 1976; Scargle 1982; Press & Rybicki 1989) of the RV residuals of both stars and found no significant peaks. As discussed in Section 3.1, these values are consistent with the jitter seen in other stars with comparable spectral types and projected rotation velocities. Note that despite the significant RV scatter, the orbital variation is detected at high confidence for all three planets. Quantitatively, for HAT-P-39 the orbital variation is detected with ∼6σ confidence, for HAT-P-40 it is detected with ∼20σ confidence, and for HAT-P-41 it is detected with ∼8σ confidence.

For each planet, we performed the fit both allowing eccentricity to vary and fixing it to zero. The resulting parameters for each system are listed in Table 11, assuming circular orbits, and in Table 12 allowing eccentric orbits. We use a Lucy & Sweeney (1971) test to determine the significance of the measured eccentricities of each system. We find that the observations of all three systems are consistent with the planets being on circular orbits (the circular orbit hypothesis is rejected with 45% confidence, 86% confidence, and 91% confidence, for HAT-P-39b, HAT-P-40b, and HAT-P-41b, respectively; for reference the confidence level would need to be greater than 99.7% for the detection of a nonzero eccentricity to be significant at the 3σ level, which is generally taken as a minimum level of significance). In the past, we have generally presented parameters for systems allowing the eccentricity to vary, even in cases where the observations are consistent with a circular orbit, on the grounds that this provides a more conservative estimate of the errors. However, as discussed recently by Anderson et al. (2012), the best-fit parameters that result from allowing the eccentricity to vary are often biased relative to the circular orbit values, and in most cases further follow-up observations, such as occultation observations, reveal the planets to be on circular orbits after all. We therefore suggest adopting the circular orbit parameters as the most probable values for each planet. These are given in Table 11. For reference, Table 12 lists the resulting parameters when the eccentricities are varied.

Table 12. Orbital and Planetary Parameters for HAT-P-39b–HAT-P-41b Allowing Eccentric Orbits^a

Parameter	HAT-P-39b	HAT-P-40b	HAT-P-41b
	Value	Value	Value
Light-curve parameters
a/R⋆	6.74 ± 0.77	5.39 ± 0.28	5.97 ± 0.52
ζ/R⋆	12.76 ± 0.08	8.49 ± 0.04	12.99 ± 0.06
i (deg)	87.1+1.1− 1.5	88.0+0.9− 1.2	87.9 ± 0.9
RV parameters
K (m s−1)	63.8 ± 10.6	55.4 ± 2.5	95.6 ± 10.4
$\sqrt{e} \cos \omega$	0.094 ± 0.189	0.041 ± 0.064	−0.189 ± 0.100
$\sqrt{e} \sin \omega$	−0.008 ± 0.263	0.300+0.074− 0.137	−0.293+0.244− 0.120
ecos ω	0.022 ± 0.074	0.012 ± 0.018	−0.068 ± 0.039
esin ω	−0.001 ± 0.114	0.092 ± 0.051	−0.105 ± 0.086
e	0.094 ± 0.086	0.095 ± 0.048	0.139 ± 0.063
ω (deg)	188 ± 115	83 ± 42	237 ± 38
RV jitter (m s−1)	42.7	4.1	27.5
Secondary eclipse parameters
Ts (BJD)	2455189.310 ± 0.168	2455819.895 ± 0.052	2454985.092 ± 0.068
Ts, 14	0.1741 ± 0.0378	0.3048 ± 0.0300	0.1397 ± 0.0241
Ts, 12	0.0176 ± 0.0084	0.0239 ± 0.0029	0.0135 ± 0.0027
Planetary parameters
Mp (MJ)	0.596 ± 0.099	0.584 ± 0.035	0.812 ± 0.094
Rp (RJ)	1.565+0.292− 0.169	1.900 ± 0.127	1.529+0.185− 0.136
C(Mp, Rp)	0.08	0.03	0.32
ρp (g cm−3)	0.19+0.10− 0.06	0.11 ± 0.02	0.28+0.09− 0.07
log gp (cgs)	2.77 ± 0.14	2.60 ± 0.06	2.93 ± 0.09
a (AU)	0.0509+0.0012− 0.0009	0.0607 ± 0.0014	0.0424 ± 0.0007
Teq (K)	1751+137− 87	1843 ± 60	1879 ± 88
Θ	0.027 ± 0.006	0.025 ± 0.002	0.032 ± 0.004
〈F〉 (109 erg s−1 cm−2)	2.12+0.85− 0.38	2.60 ± 0.34	2.82+0.65− 0.44

Note. ^aQuantities and definitions are as in Table 11, which gives our adopted values, determined assuming circular orbits. Here, we do not list parameters that are effectively independent of the eccentricity.

Download table as:  ASCIITypeset image