HAT-P-10b: A LIGHT AND MODERATELY HOT JUPITER TRANSITING A K DWARF^*

All HATNet candidates are subjected to thorough investigation before using more precious time on large telescopes, such as Keck I, to observe them. One of the important tools for establishing whether the transit feature in the light curve of a candidate is due to astrophysical phenomena other than a planet transiting a star is the CfA Digital Speedometer (DS; Latham 1992), mounted on the FLWO 1.5 m telescope.

High-resolution spectra with low signal-to-noise ratio (S/N) from this facility have been used routinely in the past to derive RVs with moderate precision (roughly 1 km s⁻¹) and to determine the effective temperature and surface gravity of the host star, to weed out false alarms, such as F dwarfs orbited by M dwarfs, grazing eclipsing binaries, triple and quadruple star systems, or giant stars where the transit signal is either false, or comes from a nearby, blended eclipsing binary.

The RV measurements of HAT-P-10 showed an rms residual of 0.43 km s⁻¹, consistent with no detectable RV variation. Atmospheric parameters for the star, including the effective temperature T_eff = 5000 K, surface gravity log g = 4.5, and projected rotational velocity vsin i = 1.5 km s⁻¹, were derived as described by Torres et al. (2002). The effective temperature and surface gravity correspond to an early K dwarf.

Given the significant detection by HATNet, and the positive DS results that exclude the usual suspects, we proceeded with the follow-up of this candidate by obtaining high-resolution and high S/N spectra to characterize the RV variations and to determine the stellar parameters with higher precision. We obtained eight exposures with an iodine cell, plus one iodine-free template, using the HIRES instrument (Vogt et al. 1994) on the Keck I telescope located on Mauna Kea, Hawaii. The observations were made on the nights of 2008 March 21–22, July 27, and on three nights between September 12 and 17. The small RV variations based on the March 2007 run made this target a firm planet candidate, but more observations were required to derive an orbit and to check spectral bisector variations (see Section 4.2).

The width of the spectrometer slit used on HIRES was 086, resulting in a resolving power of λ/Δλ ≈ 55, 000, with a wavelength coverage of ∼3800–8000 Å. The iodine gas absorption cell was used to superimpose a dense forest of I₂ lines on the stellar spectrum and establish an accurate wavelength fiducial (see Marcy & Butler 1992). 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 final RV data and their errors are listed in Table 1. The folded data, with our best fit (see Section 4) superimposed, are plotted in Figure 2.

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We observed two complete transit events of HAT-P-10 on the night of 2008 September 19/20 MST and October 30/31 MST with the KeplerCam CCD on the FLWO 1.2 m telescope. On September 19,278 frames were acquired with a cadence of 74 s (60 s of exposure time) in Sloan z band, while on October 30, we gathered 405 frames with a cadence of nearly 60 s (40 s of exposure time) in Sloan i band. The reduction of the images was performed as follows. After bias and flat calibration, we derived an initial second-order astrometrical transformation between the ∼110 brightest stars and the 2MASS catalog, as described in Pál & Bakos (2006), yielding a residual of ∼0.3–0.4 pixels. In order to avoid systematic errors resulting from the proper motion of the stars, we generated a new catalog. This catalog was based on the detected stellar centroids, the coordinates of which were transformed to the same reference system using the initial astrometrical solutions, and then averaged using 3σ rejection. Using this new catalog as reference, the final astrometrical solution was derived for each frame, yielding a residual of ∼0.02–0.04 pixels. The primary reason for precise astrometry is to minimize the photometric errors that would originate from the centroiding errors for the individual stars on each frame. Instead, aperture photometry was performed on the above fixed positions, using a series of apertures with radii of 6.0, 7.5, 9.0, and 10.5 pixels. The instrumental magnitude transformation was also done in two steps: first, all magnitude values were transformed to the photometric reference frame (selected to be the sharpest image), using the individual Poisson noise error estimations as weights. In the second step, the magnitude fit was repeated using the mean individual light-curve magnitudes as reference and the rms of these light curves as weights. In both of the magnitude transformations, we excluded from the fit the target star itself and the 3σ outliers. We performed EPD against trends simultaneously with the light-curve modeling (for more details, see Section 4). From the series of apertures we chose the one with a radius of 7.5 pixels; this aperture yielded the smallest fit rms for both of the transit observations. This aperture falls in the middle of the aperture series, confirming the plausible selection for the apertures. The final light curves are shown in the upper plot of Figure 3, superimposed with our best-fit transit light-curve models (see also Section 4). Table 2 lists the individual magnitudes plotted in Figure 3.

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First, using the template spectrum obtained by the Keck/HIRES instrument, we derived the stellar atmospheric parameters. We used the Spectroscopy Made Easy (SME) package of Valenti & Piskunov (1996), which yielded the following values and uncertainties (which we have conservatively increased, based on past experience): T_eff = 4980 ± 60 K, log g_⋆ = 4.5 ± 0.1 (cgs), [Fe/H] = 0.13 ± 0.08, and vsin i = 0.5 ± 0.2 km s^-1.

In modeling both the HATNet and the follow-up transit light curves, we used the quadratic limb darkening formalism of Mandel & Agol (2002). The limb darkening coefficients corresponding to the above stellar atmospheric parameters were interpolated using the tables provided by Claret (2004). The coefficients we derived for I, z, and i photometric passbands were γ_1(I) = 0.3806, γ_2(I) = 0.2535, γ_1(z) = 0.3214, γ_2(z) = 0.2693, γ_1(i) = 0.4104, and γ_2(i) = 0.2457.

Following this, a joint fit was done using all of the available data, including the HATNet light curve, the follow-up light-curve, and the RV measurements. Throughout the analysis, we refer to the transit event observed on 2008 September 19–20 as N_tr = 0.

We adjusted the following parameters: T_c,−290, the time of first transit center in the HATNet campaign; T_c,+11, the time of the transit center on October 30/31; K, the RV semiamplitude; k = ecos ω and h = esin ω, the Lagrangian orbital elements related to the eccentricity and argument of periastron; p ≡ R_p/R_⋆, the fractional planetary radius; b², the square of the impact parameter; the quantity ζ/R_⋆, which is related to the transit duration T_dur as (ζ/R_⋆)⁻¹ = T_dur/2; and M₀ and M₁, the out-of-transit instrumental magnitudes of the HATNet and FLWO/KeplerCam light curves. As noted by Bakos et al. (2007b), the quantity ζ/R_⋆ shows only a small correlation with the other light-curve parameters (R_p/R_⋆, b²), which makes it a good parameter to use. For eccentric orbits, ζ/R_⋆ is related to the normalized semimajor axis a/R_⋆ as $\zeta /R_\star =(2\pi /P)(a/R_\star)\sqrt{1-e^2}(1-b^2)^{-1/2}(1+h)^{-1}$. To find the best-fit values and the uncertainties, we utilized the method of Markov chain Monte Carlo (MCMC; Ford 2006) which provides the a posteriori distribution of the adjusted parameters.

The values and uncertainties of the k and h orbital elements were found to be consistent with zero within nearly 1σ, namely, k = −0.09 ± 0.11 and h = −0.07 ± 0.06. Therefore, we conclude that the observations are consistent with a circular planetary orbit, and we repeated the fit by fixing the eccentricity to zero.

The key results for the simultaneous fit are reported in Table 4. In addition, the fit yielded T_c,−290 = 2453650.38936 ± 0.00190 (BJD), T_c,11 = 2454770.85425 ± 0.00016 (BJD). These were used to derive the epoch and the period as shown in Pál et al. (2008b). The jitter in the RVs that was needed to reconcile the reduced χ² of the fit with unity was 4.2 m s⁻¹. The error bars in Figure 2 (top and middle panels) have been inflated accordingly.

The results of the joint fit together with the initial results from spectroscopy enable us to refine the parameters of the star. As described by Sozzetti et al. (2007) and Torres et al. (2008), a/R_⋆ is a better luminosity indicator than the spectroscopic value of log g_⋆ since stellar surface gravity has only a subtle effect on the line profiles. Therefore, we used the values of T_eff and [Fe/H] from the initial SME analysis, together with the distribution of a/R_⋆ to estimate the stellar properties from comparison with the Yonsei–Yale (Y²) stellar evolution models by Yi et al. (2001) and Demarque et al. (2004). Using the relation between a/R_⋆ and ζ/R_⋆, we derive the a posteriori distribution for the former one, and used the derived stellar density as an input for the stellar evolution models in order to have an a posteriori distribution for the stellar parameters (see Pál et al. 2008a, 2008b, for more details). Since the mass and radius (and their respective distributions) of the star are known, it is straightforward to obtain the surface gravity and its uncertainty together. The derived surface gravity is log g_⋆ = 4.56 ± 0.02. Since the surface gravity from the initial SME analysis agrees well with the one derived above, we accept the latter as final value (listed together with other parameters in Table 3).

The stellar evolution modeling also yields the absolute magnitudes and colors in various photometric passbands. The derived V − I color of the star is (V − I)_YY = 0.92 ±  0.02, slightly smaller than the color from the The Amateur Sky Survey (TASS) catalog (Droege et al. 2006), namely (V − I)_TASS = 1.09 ±  0.11. Since this excess could be due to interstellar reddening, we used the 2MASS J magnitude to estimate the distance. The observed J-band magnitude of HAT-P-10, after conversion to the same system used by the (Yi et al. 2001) isochrones, is J = 10.020 ± 0.021 while the stellar modeling gives M_J = 4.530 ± 0.087, which lead to a distance modulus for the star of J − M_J = 5.489 ± 0.089, corresponding to a distance of d = 121.7 ± 4.2 pc.

The planetary parameters and their uncertainties can be derived by direct combination of the a posteriori distributions of the light-curve, RV, and stellar parameters. We find that the mass of the planet is M_p = 0.487 ± 0.018 M_J, the radius is R_p = 1.005^+0.032_−0.027 R_J, and its density is ρ_p = 0.594 ± 0.052 g cm⁻³. The planetary parameters are summarized at the bottom of Table 4.

Following Torres et al. (2007), we explored the possibility that the measured RVs 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 analysis based on the Keck spectra was done as described in Section 5 of Bakos et al. (2007a).

The first spectrum in Table 1 was taken through clouds, at high-air mass, and near full moon, and is visibly contaminated by another set of lines at the expected velocity separation of about −25 km s⁻¹ due to the moonlight. The line bisector is highly sensitive to any distortions in the line profiles, and is thus seriously affected in this case. The measured velocity, on the other hand, is affected only at a much lower level that we consider tolerable (although it still shows the largest negative residual). We have thus chosen not to use the bisector span from this spectrum, but to keep the velocity. Among the remaining bisector spans, we detect no variation in excess of the measurement errors (see Figure 2, bottom panel). The correlation between the RV and the bisector variations is insignificant. Therefore, we conclude that the velocity variations are real, and that the star is orbited by a close-in giant planet.