HAT-P-14b: A 2.2 M_J EXOPLANET TRANSITING A BRIGHT F STAR^*

The transits of HAT-P-14b were detected with the HAT-10 telescope located in Arizona. Observations in a field containing the star GSC 3086-00152 were made on a nightly basis between 2005 May and July, as permitted by weather conditions. We gathered 1246 exposures of 150 s with a cadence of 3.2 minutes, 206 exposures of 180 s at 3.7 minute cadence, and 1991 exposures of 300 s at a 5.7 minute cadence. The reason for the somewhat inhomogeneous data set is that the observations were acquired during the commissioning phase of HAT-10. The first exposures with 150 s cadence were taken with an Apogee ALTA E42 back-illuminated CCD through a Cousins I-band filter. Exposure times were increased to 180 s after some initial testing. Finally, the CCD was replaced with an Apogee E10 front-illuminated model, and exposure times were further increased to 300 s. Each image contained approximately 22,000 stars down to a brightness limit of I ∼ 14.0. For the brightest stars in the field we achieved a photometric precision of 3.5 mmag per image in the combined light curve.

The calibration of the HATNet frames was carried out using standard photometric procedures. The calibrated images were then subjected to star detection and an astrometric solution, as described in more detail by Pál & Bakos (2006). Aperture photometry was performed on each image at the stellar centroids derived from the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) catalog and the individual astrometric solutions. The resulting light curves were decorrelated (cleaned of trends) using the External Parameter Decorrelation (EPD; see Bakos et al. 2010) technique in "constant" mode and the Trend Filtering Algorithm (TFA; see Kovács et al. 2005). The light curves were then searched for periodic box-shaped signals using the Box Least-Squares (BLS; Kovács et al. 2002) method. We detected a significant signal in the light curve of GSC 3086-00152 (also known as 2MASS 17202788+3814317; α = 17^h20^m2796, δ = +38°14'318; J2000; V = 9.98; Droege et al. 2006), with an apparent depth of 4.5 mmag, and a period of P = 4.6277 days (see Figure 1). The drop in brightness had a first-to-last-contact duration q, relative the total period P, of q = 0.0197 ± 0.0004, corresponding to a total duration of Pq = 2.189 ± 0.040 hr.

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HAT-P-14 falls in an overlapping area between two HATNet fields internally labeled G194 and G195. While the discovery was made on the basis of the G194 light curve, the signal was later recovered in the 3189 I-band observations from field G195. These latter data were taken during the commissioning phase of the HAT-5 telescope at FLWO, in early 2003, making this one of the TEPs with the longest photometric coverage. Curiously, the signal is present in the early HAT-5 (G195) data with higher significance than in field G194. The discovery of HAT-P-14 in 2003 was probably missed due to a combination of factors, including our different criteria for scheduling follow-up observations at the time, and the lack of the TFA, which was only implemented and brought into regular use in 2005.

As is routine in the HATNet project, all candidates are subjected to careful scrutiny before investing valuable time on large telescopes. This includes spectroscopic observations at relatively modest facilities to establish whether the transit-like feature in the light curve of a candidate might be due to astrophysical phenomena other than a planet transiting a star. Many of these false positives are associated with large RV variations in the star (tens of km s⁻¹) that are easily recognized. For this we have made use here of the Harvard-Smithsonian Center for Astrophysics (CfA) Digital Speedometer (DS; Latham 1992), an echelle spectrograph mounted on the FLWO 1.5 m telescope. This instrument delivers high-resolution spectra (λ/Δλ ≈ 35,000) over a single order centered on the Mg i b triplet (∼5187 Å), with typically low signal-to-noise ratios (S/Ns) that are nevertheless sufficient to derive RVs with moderate precisions of 0.5–1.0 km s⁻¹ for slowly rotating stars. The same spectra can be used to estimate the effective temperature, surface gravity, and projected rotational velocity of the host star, as described by Torres et al. (2002). With this facility we are able to reject many types of false positives, such as F dwarfs orbited by M dwarfs, grazing eclipsing binaries, or triple or quadruple star systems. Additional tests are performed with other spectroscopic material described in the next section.

For HAT-P-14 we obtained four observations with the DS between April and May of 2008. The velocity measurements showed an rms residual of 0.28 km s⁻¹, consistent with no detectable RV variation within the precision of the measurements. All spectra were single-lined, i.e., there is no evidence for additional stars in the system. The atmospheric parameters we infer from these observations are the following: effective temperature T_eff⋆ = 6500 ± 100 K, surface gravity log g_⋆ = 3.5 ± 0.25 (log cgs), and projected rotational velocity vsin i = 11.7 ± 1.0 km s⁻¹. The effective temperature corresponds to a mid-F dwarf. The mean heliocentric RV of HAT-P-14 is γ_RV = −20.81 ± 0.28 km s⁻¹.

Given the statistically significant transit detection by HATNet, and the encouraging DS results that rule out obvious false positives, we proceeded with the follow-up of this candidate by obtaining high-resolution, high-S/N spectra in order to characterize the RV variations with higher precision, and to refine the determination of the stellar parameters. For this we used the HIRES instrument (Vogt et al. 1994) on the Keck I telescope located on Mauna Kea, Hawaii, between 2008 May 15 and 2009 October 1. The width of the spectrometer slit was 086, resulting in a resolving power of λ/Δλ ≈ 55,000, with a wavelength coverage of ∼3800–8000 Å.

We obtained a total of 14 exposures through an iodine gas absorption cell, which was used to superimpose a dense forest of I₂ lines on the stellar spectrum and establish an accurate wavelength fiducial (see Marcy & Butler 1992). An additional exposure was taken without the iodine cell, for use as a template in the reductions. Relative RVs in the solar system barycentric frame were derived as described by Butler et al. (1996), incorporating full modeling of the spatial and temporal variations of the instrumental profile. The RV measurements and their uncertainties are listed in Table 1. The period-folded data, along with our best fit described below in Section 4, are displayed in Figure 2.

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In the same figure we show also the relative 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 the prescription given by Vaughan et al. (1978), after matching each spectrum to a reference spectrum using a transformation that includes a wavelength shift and a flux scaling that is a polynomial as a function of wavelength. The transformation was determined on regions of the spectra that are not used in computing this indicator. Note that our relative S index has not been calibrated to the scale of Vaughan et al. (1978). We do not detect any significant variation of the index correlated with orbital phase; such a correlation might have indicated that the RV variations could be due to stellar activity, casting doubt on the planetary nature of the candidate. There is no sign of emission in the cores of the Ca ii H and K lines in any of our spectra, from which we conclude that the chromospheric activity level in HAT-P-14 is very low.

In order to permit a more accurate modeling of the light curve, we conducted additional photometric observations with the KeplerCam CCD camera on the FLWO 1.2 m telescope. We observed five transit events of HAT-P-14 on the nights of 2008 October 19, 2009 February 2, 2009 March 25, 2009 April 8, and 2009 May 15 (Figure 3). A Sloan i-band filter was used for all observations. The number of images we acquired on each of these events is 326, 239, 470, 359, and 304, respectively. The exposure times were 10, 13, 20, 15, and 15 s, resulting in a cadence of 22, 25, 32, 27, and 27 s. The reduction of these images, including basic calibration, astrometry, aperture photometry, and trend removal, was performed as described by Bakos et al. (2010). The final time series are shown in the top portion of Figure 3, along with our best-fit transit light curve model described below; the individual measurements are reported in Table 2.

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Fundamental parameters of the host star HAT-P-14 such as the mass (M_⋆) and radius (R_⋆), which are needed to infer the planetary properties, depend strongly on other stellar quantities that can be derived spectroscopically. For this we have relied on our template spectrum 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). This analysis yielded the following initial values: effective temperature T_eff⋆ = 6310 ± 80 K, surface gravity log g_⋆ = 3.80 ± 0.10 (cgs), metallicity [Fe/H] = −0.02 ± 0.05 dex, and projected rotational velocity vsin i = 8.8 ± 0.5 km s⁻¹. The temperature and metallicity uncertainties have been conservatively increased by a factor of 2 over their nominal values, based on previous experience, to account for possible systematic errors.

In principle, the effective temperature and metallicity, along with the surface gravity taken as a luminosity indicator, could be used as constraints to infer the stellar mass and radius by comparison with stellar evolution models. However, the effect of log g_⋆ on the spectral line shapes is rather subtle, and as a result it is typically difficult to determine accurately, so that it is a rather poor luminosity indicator for this particular application. A trigonometric parallax is unfortunately unavailable for HAT-P-14 since the star was not included among the targets of the Hipparcos mission (Perryman et al. 1997), despite being bright enough. In any case, for planetary transits a stronger constraint on the luminosity is often provided by a/R_⋆, the normalized semimajor axis, which is closely related to ρ_⋆, the mean stellar density. The quantity a/R_⋆ can be derived directly from the transit light curves (see Sozzetti et al. 2007, and also Section 4.2). This, in turn, allows us to improve on the determination of the spectroscopic parameters by supplying an indirect constraint on the weakly determined spectroscopic value of log g_⋆ that removes degeneracies. We take this approach here, as described below.

Our initial values of T_eff⋆, log g_⋆, and [Fe/H] were used to determine auxiliary quantities needed in the global modeling of the follow-up photometry and RVs (specifically, the limb-darkening coefficients). This modeling, the details of which are described in the next section, uses a Monte Carlo approach to deliver the numerical probability distribution of a/R_⋆ and other fitted variables. For further details we refer the reader to Pál (2009b). When combining a/R_⋆ (used as a proxy for luminosity) with assumed Gaussian distributions for T_eff⋆ and [Fe/H] based on the SME determinations, a comparison with stellar evolution models allows the probability distributions of other stellar properties to be inferred, including log g_⋆. Here we use the stellar evolution calculations from the Yonsei-Yale (YY) series by Yi et al. (2001). The comparison against the model isochrones was carried out for each of 10,000 Monte Carlo trial sets (see Section 4.2). Parameter combinations corresponding to unphysical locations in the H-R diagram (1% of the trials) were ignored, and replaced with another randomly drawn parameter set. The result for the surface gravity, log g_⋆ = 4.25 ± 0.03, is significantly different from our initial SME analysis, which is not surprising in view of the strong correlations among T_eff⋆, [Fe/H], and log g_⋆ that are often present in spectroscopic determinations. Therefore, we carried out a second iteration in which we adopted this value of log g_⋆ and held it fixed in a new SME analysis (coupled with a new global modeling of the RV and light curves), adjusting only T_eff⋆, [Fe/H], and vsin i. This gave T_eff⋆ = 6600 ± 90 K, [Fe/H] = +0.11 ± 0.08, and vsin i = 8.4 ± 0.5 km s⁻¹, in which the conservative uncertainties for the first two have been increased by a factor of 2 over their formal values, as before. A further iteration did not change log g_⋆ significantly, so we adopted the values stated above as the final atmospheric properties of the star. They are collected in Table 3, together with the adopted values for the macroturbulent and microturbulent velocities.

We note that the effective temperature also changed rather significantly from the first SME iteration, by about 300 K. An external check on the accuracy of T_eff⋆ may be obtained from color indices derived from existing brightness measurements for HAT-P-14. Photometric measurements on a standard system are available from the Tycho-2, 2MASS, and TASS catalogs (Høg et al. 2000; Skrutskie et al. 2006; Droege et al. 2006), and are summarized in the second block of Table 3. We constructed seven different color indices, and applied color/temperature calibrations by Ramírez & Meléndez (2005; available for six of the color indices), Casagrande et al. (2006; four color indices), and González Hernández & Bonifacio (2009; five color indices). These relations include terms that depend on metallicity. Because such photometric temperatures are very sensitive to reddening, we examined the dust maps by Schlegel et al. (1998) in the direction to HAT-P-14 and obtained E(B − V) = 0.030, after a small correction for distance using the value of 205 ± 11 pc reported below. Two other reddening estimates of 0.022 and 0.033 were obtained similarly from Burstein & Heiles (1982) and Hakkila et al. (1997), respectively. We adopt the straight average of the three measures, E(B − V) = 0.028 ± 0.015, with a conservative uncertainty.

We corrected each of the color indices for reddening, and computed weighted temperature averages for each set of calibrations, with weights determined from the individual temperature uncertainties. The latter include all photometric errors, the uncertainty in both the reddening and the metallicity, and the scatter of the calibrations themselves. The seven color indices are not completely independent, but nevertheless give a useful sense of the scatter. The agreement between the 15 separate estimates from all three calibrations is quite satisfactory, the dispersion being 112 K. The mean of the three calibration averages is T_eff = 6598 ± 100 K, which is in excellent accord with the final spectroscopic value from SME and supports its accuracy.

With the adopted spectroscopic parameters the model isochrones yield the stellar mass and radius M_⋆ = 1.386 ± 0.045 M_☉ and R_⋆ = 1.468 ± 0.054 R_☉, along with other properties listed at the bottom of Table 3. HAT-P-14 is a slightly evolved F star with an estimated age of 1.3 ± 0.4 Gyr, according to these models. The inferred location of the star in a diagram of a/R_⋆ versus T_eff⋆, analogous to the classical H-R diagram, is shown in Figure 5. The stellar properties and their 1σ and 2σ confidence ellipsoids are displayed against the backdrop of Yi et al. (2001) isochrones for the measured metallicity of [Fe/H] = +0.11, and a range of ages. For comparison, the location implied by the initial SME results is also shown (triangle), and corresponds to a somewhat more evolved state.

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The distance to the star may be obtained by comparing the absolute magnitudes inferred from the stellar evolution models against the apparent brightness measurements mentioned earlier. For this we use the V, I_C, J, H, and K_s magnitudes, corrected for extinction using A(V) = 3.1 × E(B − V) appropriately scaled to each passband following Cardelli et al. (1989). The near-infrared magnitudes from 2MASS were transformed to the ESO system of the isochrones using the relations by Carpenter (2001). The five distance estimates agree with each other to within a few pc. The average is 205 ± 11 pc, where the uncertainty includes all sources of error (photometric and spectroscopic), but excludes possible systematics from the evolution models themselves, which are difficult to quantify.

This section describes the procedure we followed to model the HATNet photometry, the follow-up photometry, and the RVs simultaneously. Our model for the follow-up light curves used analytic formulae from Mandel & Agol (2002) for the eclipse of a star by a planet, with limb darkening being prescribed by a quadratic law. The limb darkening coefficients for the Sloan i band were interpolated from the tables by Claret (2004) for the spectroscopic parameters of the star as determined from the SME analysis (Section 4.1). The transit shape was parametrized by the normalized planetary radius p ≡ R_p/R_⋆, the square of the impact parameter b², and the reciprocal of the half-duration of the transit ζ/R_⋆. We chose these parameters because of their simple geometric meanings and the fact that they show negligible correlations (see Bakos et al. 2010). The relation between ζ/R_⋆ and the quantity a/R_⋆, used in Section 4.1, is given by

$$\begin{equation} a/R_\star = P/2\pi (\zeta /R_\star) \sqrt{1-b^2} \sqrt{1-e^2}/(1+e \sin \omega) \end{equation} \tag{ 1 }$$

(see, e.g., Tingley & Sackett 2005). Our model for the HATNet data was the simplified "P1P3" version of the Mandel & Agol (2002) analytic functions (an expansion in terms Legendre polynomials), for the reasons described by Bakos et al. (2010). Following the formalism presented by Pál (2009a), the RVs were fitted with an eccentric Keplerian model parametrized by the semiamplitude K and Lagrangian elements k ≡ ecos ω and h ≡ esin ω, in which ω is the longitude of periastron.

We assumed that there is a strict periodicity in the individual transit times. We assigned the transit number N_tr = 0 to the first complete follow-up light curve gathered on 2009 March 25. The adjustable parameters in the fit that determine the ephemeris were chosen to be the time of the first transit center in HATNet field G195, T_c,−473, and that of the last transit center observed with the FLWO 1.2 m telescope, T_c,+11. We used these as opposed to the period and reference epoch in order to minimize correlations between parameters (see Pál et al. 2008). Times of mid-transit for intermediate events were interpolated using these two epochs and the corresponding transit number of each event, N_tr. The eight main parameters describing the physical model were thus T_c,−473, T_c,+11, R_p/R_⋆, b², ζ/R_⋆, K, k ≡ ecos ω, and h ≡ esin ω. Five additional ones were included that have to do with the instrumental configuration. These are the HATNet blend factors B_inst (one for each HATNet field, G194 and G195), which account for possible dilution of the transit in the HATNet light curves from background stars due to the broad PSF (20'' FWHM), the HATNet out-of-transit magnitudes M_0,HATNet (one for each field), and the relative zero point γ_rel of the Keck RVs.

We extended our physical model with an instrumental model that describes brightness variations caused by systematic errors in the measurements. This was done in a similar fashion to the analysis presented by Bakos et al. (2010). The HATNet photometry had already been EPD- and TFA-corrected before the global modeling, so we only considered corrections for systematics in the follow-up light curves. We chose the "ELTG" method, i.e., EPD was performed in "local" mode with EPD coefficients defined for each night, and TFA was performed in "global" mode using the same set of stars and TFA coefficients for all nights. The five EPD parameters were the hour angle (representing a monotonic trend that changes linearly over time), the square of the hour angle (reflecting elevation), and the stellar profile parameters (equivalent to the FWHM, elongation, and position angle of the image). The functional forms of the above effects contained six coefficients, including the auxiliary out-of-transit magnitude of the individual events. The EPD parameters were independent for all five nights, implying 30 additional coefficients in the global fit. For the global TFA analysis we chose 20 template stars that had good quality measurements for all nights and on all frames, implying an additional 20 parameters in the fit. Thus, the total number of fitted parameters was 13 (physical model with 5 configuration-related parameters) + 30 (local EPD) + 20 (global TFA) = 63, i.e., much smaller than the total number of data points (1711).

The joint fit was performed as described in Bakos et al. (2010). We minimized χ² in the space of parameters by using a hybrid algorithm, combining the downhill simplex method (AMOEBA; see Press et al. 1992) with a classical least-squares algorithm. Uncertainties for the parameters were derived applying the Markov Chain Monte Carlo method (MCMC; see Ford 2006) using "Hyperplane-CLLS" chains (Bakos et al. 2010). This provided the full a posteriori probability distributions of all adjusted variables. The length of the chains was 10,000 points. The a priori distributions of the parameters for these chains were chosen to be Gaussian, with eigenvalues and eigenvectors derived from the Fisher covariance matrix for the best-fit solution. The Fisher covariance matrix was calculated analytically using the partial derivatives given by Pál (2009a).