HAT-P-18b AND HAT-P-19b: TWO LOW-DENSITY SATURN-MASS PLANETS TRANSITING METAL-RICH K STARS^*

Table 1 summarizes the HATNet discovery observations of each new planetary system. The calibration of the HATNet frames was carried out using standard photometric procedures. The calibrated images were then subjected to star detection and astrometric determination, as described in 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 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.

• 1.  
  HAT-P-18–GSC 2594−00646 (also known as 2MASS 17052315+3300450; α = 17^h05^m23.28s, δ = +33°00'450; J2000; V = 12.759; Droege et al. 2006). A signal was detected for this star with an apparent depth of ∼18.5 mmag, and a period of P = 5.5080 days (see Figure 1). The drop in brightness had a first-to-last-contact duration, relative to the total period, of q = 0.0205 ±  0.0002, corresponding to a total duration of Pq = 2.716 ±  0.021 hr.
• 2.  
  HAT-P-19–GSC 2283−00589 (also known as 2MASS 00380401+3442416; α = 00^h38^m04.02s, δ = +34°42'417; J2000; V = 12.901; Droege et al. 2006). A signal was detected for this star with an apparent depth of ∼22.0 mmag, and a period of P = 4.0088 days (see Figure 2). The drop in brightness had a first-to-last-contact duration, relative to the total period, of q = 0.0295 ±  0.0004, corresponding to a total duration of Pq = 2.837 ±  0.034 hr.

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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 such false positives are associated with large RV variations in the star (tens of km s⁻¹) that are easily recognized. We made use of three different facilities to conduct these observations, including the Harvard–Smithsonian Center for Astrophysics (CfA) Digital Speedometer (DS; Latham 1992), and the Tillinghast Reflector Echelle Spectrograph (TRES; Füresz 2008), both on the 1.5 m Tillinghast Reflector at the Whipple Observatory on Mount Hopkins, Arizona, and the FIbre-fed Échelle Spectrograph (FIES; Frandsen & Lindberg 1999) on the 2.5 m Nordic Optical Telescope (NOT; Djupvik & Andersen 2010) at La Palma, Spain. We used these facilities to obtain high-resolution spectra, 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. We also use these spectra to estimate the effective temperatures, surface gravities, and projected rotational velocities of the stars. With these observations, 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. The observations and results for both stars are summarized in Table 2. Below we provide a brief description of each of the instruments used, the data reduction, and the analysis procedure.

We used the DS to conduct observations of both HAT-P-18 and HAT-P-19. This instrument delivers high-resolution spectra (λ/Δλ ≈ 35, 000) over a single order centered on the Mg i b triplet (∼5187 Å). We measure the RV and stellar atmospheric parameters from the spectra following the method described by Torres et al. (2002).

We used FIES to conduct observations of HAT-P-19. We used the medium and the high-resolution fibers with resolving powers of λ/Δλ ≈ 46, 000 and 67, 000 respectively, giving a wavelength coverage of ∼3600–7400 Å. The spectra were extracted and analyzed to measure the RV and stellar atmospheric parameters following the procedures described by Buchhave et al. (2010). The velocities were corrected to the same system as the DS observations (heliocentric velocities with the gravitational redshift of the Sun subtracted) using 10 observations of the velocity standard HD 182488 obtained on the same nights as observations of HAT-P-19.

A single observation of HAT-P-19 was obtained with TRES. We used the medium-resolution fiber to obtain a spectrum with a resolution of λ/Δλ ≈ 44, 000 and a wavelength coverage of ∼3900–8900 Å. The spectrum was extracted and analyzed in a similar manner to the FIES observations. The velocity was corrected to the same system as the DS observations using a single TRES measurement of HD 182488 obtained on the same night. The velocity uncertainty reported in this case is our estimate of the systematic error based on the rms of multiple observations of HD 182488 obtained on other nights close in time.

Based on the reconnaissance spectroscopy observations we find that both systems have 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 either target star has a stellar companion. Additionally, both stars have surface gravity measurements which indicate that they are dwarfs. We note that for HAT-P-19 all three instruments yielded similar results for the RV and stellar parameters. There is a ∼1 km s⁻¹ difference between the DS and the TRES/FIES observations of HAT-P-19. The last DS observation was obtained only four nights before the first FIES observation, and the DS and FIES data sets each span significantly more than four nights, but do not show internal variations at the ∼1 km s⁻¹ level. We conclude that the velocity difference between the instruments does not indicate a physical variation in the velocity of HAT-P-19. The DS observations are all weak, with only a few counts per pixel, and the sky velocity is slightly more negative than the system velocity in all cases. This velocity difference may be due to a systematic error in the DS velocities due to sky contamination.

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 3. The RV measurements and uncertainties for HAT-P-18 are given in Table 4, and for HAT-P-19 in Table 5. The period-folded data, along with our best fit described below in Section 3, are displayed in Figure 3 for HAT-P-18, and in Figure 4 for HAT-P-19. For HAT-P-18, we exclude five RV measurements that are significant outliers from the best-fit model. These points are all strongly affected by contamination from scattered moonlight (see Section 3.2.1). Below we briefly describe the instruments used, the data reduction, and the analysis procedure.

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Observations were made of HAT-P-18 and HAT-P-19 with the High Resolution Echelle Spectrometer (HIRES) instrument (Vogt et al. 1994) on the Keck I telescope located on Mauna Kea, Hawaii. 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. Exposures were obtained 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). For each target, two additional exposures were taken without the iodine cell; in both cases we used the second, higher S/N, observation as the 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.

We also made use of the High-Dispersion Spectrograph (HDS; Noguchi et al. 2002) on the Subaru telescope on Mauna Kea, Hawaii to obtain high-S/N spectroscopic observations of HAT-P-19 from which we derived high-precision RV measurements. Observations were made over three consecutive nights using a slit width of 06, yielding a resolving power of λ/Δλ ≈ 60, 000. We used the I2b setup which provides a wavelength coverage of ∼3500–6200 Å. To reduce the effect of changes in the barycentric velocity correction during an exposure, we limited exposure times to 15 minutes. As for Keck/HIRES, we made use of an iodine gas absorption cell to establish an accurate wavelength fiducial for each exposure. We also obtained six spectra without the iodine cell, which were combined to form the template observation. The spectra were extracted and reduced to relative RVs in the solar system barycentric frame following the methods described by Sato et al. (2002, 2005).

In each figure, we also show 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.

In order to permit a more accurate modeling of the light curves, we conducted additional photometric observations with the KeplerCam CCD camera on the FLWO 1.2 m telescope. The observations for each target are summarized in Table 1.

The reduction of these images, including basic calibration, astrometry, and aperture photometry, was performed as described by Bakos et al. (2010). We performed EPD and TFA to remove trends simultaneously with the light curve modeling (for more details, see Section 3, and Bakos et al. 2010). The final time series, together with our best-fit transit light curve model, are shown in the top portion of Figures 5 and 6 for HAT-P-18 and HAT-P-19, respectively; the individual measurements are reported in Tables 6 and 7.

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Fundamental parameters for each of the host stars, including 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 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 each star, SME yielded the following initial values and uncertainties (which we have conservatively increased by a factor of two to include our estimates of the systematic errors).

• 1.  
  HAT-P-18–effective temperature T_eff⋆ = 4850 ±  75 K, stellar surface gravity log g_⋆ = 4.7 ±  0.1 (cgs), metallicity [Fe/H] = +0.12 ±  0.05 dex, and projected rotational velocity vsin i = 1.2 ±  0.5 km s⁻¹.
• 2.  
  HAT-P-19–effective temperature T_eff⋆ = 5037 ±  44 K, stellar surface gravity log g_⋆ = 4.7 ±  0.1 (cgs), metallicity [Fe/H] = +0.24 ±  0.03 dex, and projected rotational velocity vsin i = 2.4 ±  0.5 km s⁻¹.

As discussed in Section 3.2.1, contamination from scattered moonlight affects the bisector spans (BS) and RVs measured for HAT-P-18 and the BS measured for HAT-P-19. For HAT-P-18, the moon was below the horizon when the template used for the SME analysis was obtained, so it is not affected by contamination. For HAT-P-19, we estimate that scattered moonlight may have contributed ∼0.1% of the total flux to the template spectrum used for SME analysis. The error in the parameters that results from this contamination is likely dwarfed by other systematic errors in the parameter determination.

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 in practice. For planetary transits, a stronger constraint is often provided by the a/R_⋆ 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 3.3). 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_⋆, which removes degeneracies. We take this approach here, as described below. The validity of our assumption, namely that the best physical model describing our data is a planetary transit (as opposed to a blend), is shown later in Section 3.2.1.

For each system, 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 Section 3.3, 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 Yonsei-Yale (YY; Yi et al. 2001) for both stars. The comparison against the model isochrones was carried out for each of 10,000 Monte Carlo trial sets for HAT-P-18, and 20,000 Monte Carlo trial sets for HAT-P-19 (see Section 3.3). Parameter combinations corresponding to unphysical locations in the H-R diagram (41% of the trials for HAT-P-18 and 31% of the trials for HAT-P-19) were ignored, and replaced with another randomly drawn parameter set. For each system, we carried out a second SME iteration in which we adopted the value of log g_⋆ so determined 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

• 1.  
  HAT-P-18–T_eff⋆ = 4803 ±  80 K, log g_⋆ = 4.56 ±  0.06, [Fe/H] = +0.10 ±  0.08, and vsin i = 0.5 ±  0.5 km s⁻¹.
• 2.  
  HAT-P-19–T_eff⋆ = 4990 ±  130 K, log g_⋆ = 4.53 ±  0.06 (fixed), [Fe/H] = +0.23 ±  0.08, and vsin i = 0.7 ±  0.5 km s⁻¹.

In each case, the conservative uncertainties for T_eff⋆ and [Fe/H] have been increased by a factor of two over their formal values, as before. For each system, a further iteration did not change log g_⋆ significantly, so we adopted the values stated above, together with the new log g_⋆ values resulting from the global modeling, as the final atmospheric properties of the stars. They are collected in Table 8 for both stars.

With the adopted spectroscopic parameters, the model isochrones yield the stellar mass and radius, and other properties. These are listed for each of the systems in Table 8. According to these models HAT-P-18 is a dwarf star with an estimated age of 12.4^+4.4_−6.4 Gyr, and HAT-P-19 is a dwarf star with an estimated age of 8.8 ±  5.2 Gyr. 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 7. 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 with triangles.

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The stellar evolution modeling provides color indices that may be compared against the measured values as a sanity check. For each star, the best available measurements are the near-infrared magnitudes from the 2MASS Catalogue (Skrutskie et al. 2006), which are given in Table 8. These are converted to the photometric system of the models (ESO system) using the transformations by Carpenter (2001). The resulting color index is J − K = 0.623 ±  0.036 and J − K = 0.583 ±  0.031 for HAT-P-18 and HAT-P-19, respectively. These are both within 1σ of the predicted values from the isochrones of J − K = 0.61 ±  0.02 and J − K = 0.57 ±  0.03. The distance to each object may be computed from the absolute K magnitude from the models and the 2MASS K_s magnitudes, which has the advantage of being less affected by extinction than optical magnitudes. The results are given in Table 8, where in each case the uncertainty excludes possible systematics in the model isochrones that are difficult to quantify.

Our initial spectroscopic analyses discussed in Sections 2.2 and 2.3 rule out the most obvious astrophysical false positive scenarios. However, more subtle phenomena such as blends (contamination by an unresolved eclipsing binary, whether in the background or associated with the target) can still mimic both the photometric and spectroscopic signatures we see. In the following sections, we consider and rule out the possibility that such scenarios may have caused the observed photometric and spectroscopic features.

3.2.1. Spectral Line-bisector Analysis

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 for each system based on the Keck spectra (and the Subaru spectra for HAT-P-19) was done as described in Section 5 of Bakos et al. (2007).

Each system shows excess scatter in the BS, above what is expected from the measurement errors (see Figure 3, third panel; and Figure 4, fourth panel). For HAT-P-18, there may be a slight correlation between the RV and BS, while for HAT-P-19 no correlation is apparent. Such a correlation could indicate that the photometric and spectroscopic signatures are due to a blend scenario rather than a single planet transiting a single star. We note that for HAT-P-19, the Keck spectra show excess BS variation, while the Subaru spectra do not.

Following our earlier work (Kovács et al. 2010; Hartman et al. 2009), we investigated the effect of contamination from moonlight on the measured BS values. As in Kovács et al. (2010), we estimate the expected BS value for each spectrum by modeling the spectrum cross-correlation function (CCF) as the sum of two Lorentzian functions, shifted by the known velocity difference between the star and the moon, and scaled by their expected flux ratio (estimated following Equation (3) of Hartman et al. 2009). We refer to the simulated BS value as the sky contamination factor (SCF). We find a strong correlation between the SCF and BS for both systems (see Figure 8). After correcting for this correlation, we find that the BS show no significant variations, and the correlation between the RV and BS variations is insignificant for both systems. Therefore, we conclude that the velocity variations are real for both stars, and that both stars are orbited by close-in giant planets. An independent method for arriving at this same conclusion is also presented in the following section.

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We have also investigated the effect of sky contamination on the measured RVs. The expected RV due to sky contamination for a given spectrum is estimated by finding the peak of the simulated CCF. Note that the real RV measurements are obtained by directly modeling the spectra and not by performing cross-correlation. We therefore only expect a crude agreement between the estimated RVs due to sky contamination, and the real RVs. Figure 9 compares the expected RVs to the measured RV residuals from the best-fit model for HAT-P-18 and HAT-P-19. For HAT-P-18, we find a rough correlation between the estimated and measured RV residuals. Five of the RV measurements which are significant outliers from the best-fit model are rejected. These spectra are also among the most strongly affected by sky contamination. For HAT-P-19, the values do not appear to be correlated.

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3.2.2. Blend Modeling of the Photometry

This section describes the procedure we followed for each system to model the HATNet photometry, the follow-up photometry, and the RVs simultaneously. Our model for the follow-up light curves used analytic formulae based on 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 and Sloan g-band were interpolated from the tables by Claret (2004) for the spectroscopic parameters of each star as determined from the SME analysis (Section 3.1). The transit shape was parameterized 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 these show negligible correlations (see Bakos et al. 2010). The relation between ζ/R_⋆ and the quantity a/R_⋆, used in Section 3.1, 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 a simplified version of the Mandel & Agol (2002) analytic functions (an expansion in terms of Legendre polynomials), for the reasons described in Bakos et al. (2010). Following the formalism presented by Pál (2009a), the RVs were fitted with an eccentric Keplerian model parameterized 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. For each system, we assigned the transit number N_tr = 0 to the first complete follow-up light curve. For HAT-P-18b, this was the light curve obtained on 2008 April 25, and for HAT-P-19b this was the light curve obtained on 2009 December 1. The adjustable parameters in the fit that determine the ephemeris were chosen to be the time of the first transit center observed with HATNet (T_c,−71, and T_c,−204 for HAT-P-18b, and HAT-P-19b respectively) and that of the last transit center observed with the FLWO 1.2 m telescope (T_c,+69, and T_c,0 for HAT-P-18b, and HAT-P-19b, respectively). We used these as opposed to 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. For HAT-P-18b, the eight main parameters describing the physical model were thus the times of first and last transit center, R_p/R_⋆, b², ζ/R_⋆, K, k ≡ ecos ω, and h ≡ esin ω. For HAT-P-19b, we included as a ninth parameter a velocity acceleration term to account for an apparent linear drift in the velocity residuals after fitting for a Keplerian orbit. Three additional parameters were included for HAT-P-18b that have to do with the instrumental configuration. For HAT-P-19b, six additional parameters were included. These include the HATNet blend factors B_inst (one for each HATNet field for HAT-P-19b), which accounts for possible dilution of the transit in the HATNet light curve from background stars due to the broad PSF (20'' FWHM), the HATNet out-of-transit magnitude M_0,HATNet (also one for each HATNet field for HAT-P-19b), and the relative zero point γ_rel of the Keck RVs (and the Subaru RVs for HAT-P-19b).

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 has 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 FWHM, elongation, and position angle of the image). The functional forms of the above parameters contained six coefficients, including the auxiliary out-of-transit magnitude of the individual events. For each system the EPD parameters were independent for all nights, implying 12, and 24 additional coefficients in the global fit for HAT-P-18b and HAT-P-19b, respectively. For the global TFA analysis we chose 20 template stars for each system that had good quality measurements for all nights and on all frames, implying an additional 20 parameters in the fit for each system. In both cases, the total number of fitted parameters (43 and 49 for HAT-P-18b and HAT-P-19b, respectively) was much smaller than the number of data points (422, and 438, counting only RV measurements and follow-up photometry measurements).

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 linear 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 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).

Following this procedure, we obtained the a posteriori distributions for all fitted variables, and other quantities of interest such as a/R_⋆. As described in Section 3.1, a/R_⋆ was used together with stellar evolution models to infer a theoretical value for log g_⋆ that is significantly more accurate than the spectroscopic value. The improved estimate was in turn applied to a second iteration of the SME analysis, as explained previously, in order to obtain better estimates of T_eff⋆ and [Fe/H]. The global modeling was then repeated with updated limb-darkening coefficients based on those new spectroscopic determinations. The resulting geometric parameters pertaining to the light curves and velocity curves for each system are listed in Table 9.

Table 9. Orbital and Planetary Parameters for HAT-P-18b and HAT-P-19b^a

Parameter	HAT-P-18b	HAT-P-19b
Light curve parameters
P (days) ...	5.508023 ± 0.000006	4.008778 ± 0.000006
Tc (BJD)b ...	2454715.02174 ± 0.00020	2455091.53417 ± 0.00034
T14 (days)b ...	0.1131 ± 0.0009	0.1182 ± 0.0014
T12 = T34 (days)b ...	0.0150 ± 0.0008	0.0172 ± 0.0014
a/R⋆ ...	16.04 ± 0.75	12.24 ± 0.67
ζ/R⋆ ...	20.36 ± 0.08	19.76 ± 0.12
Rp/R⋆ ...	0.1365 ± 0.0015	0.1418 ± 0.0020
b2 ...	0.105+0.040−0.040	0.163+0.055−0.057
b ≡ acos i/R⋆ ...	0.324+0.055−0.078	0.404+0.061−0.088
i (deg) ...	88.8 ± 0.3	88.2 ± 0.4
Limb-darkening coefficientsc
a, i (linear term, i filter) ...	0.4372	0.4135
b, i (quadratic term) ...	0.2276	0.2459
a, g ...	0.8477	0.8016
b, g ...	−0.0060	0.0368
RV parameters
K (m s−1) ...	27.1 ± 1.6	42.0 ± 2.1
$\dot{\gamma }$ (m s−1 day−1) ...	...	0.439 ± 0.048
kRVd ...	−0.035 ± 0.038	−0.009 ± 0.029
hRVd ...	0.063 ± 0.062	−0.058 ± 0.054
e ...	0.084 ± 0.048	0.067 ± 0.042
ω (deg) ...	120 ± 56	256 ± 77
RV jitter (m s−1) ...	5.0	6.7
Secondary eclipse parameters
Ts (BJD) ...	2454717.65 ± 0.13	2455093.515 ± 0.074
Ts,14 ...	0.127 ± 0.014	0.107 ± 0.010
Ts,12 ...	0.0173 ± 0.0029	0.0149 ± 0.0020
Planetary parameters
Mp (MJ) ...	0.197 ± 0.013	0.292 ± 0.018
Rp (RJ) ...	0.995 ± 0.052	1.132 ± 0.072
C(Mp, Rp)e ...	0.19	0.35
ρp (g cm−3) ...	0.25 ± 0.04	0.25 ± 0.04
log gp (cgs) ...	2.69 ± 0.05	2.75 ± 0.05
a (AU) ...	0.0559 ± 0.0007	0.0466 ± 0.0008
Teq (K) ...	852 ± 28	1010 ± 42
Θf ...	0.029 ± 0.002	0.028 ± 0.002
〈F〉 (108 erg s−1 cm−2)g ...	1.19 ± 0.16	2.35 ± 0.41

Notes. ^aWe list the median value of each parameter from its MCMC a posteriori distribution. We also provide the upper and lower 1σ error bars about the median for each parameter. ^bT_c: reference epoch of mid-transit that minimizes the correlation with the orbital period. It corresponds to N_tr = 24. T₁₄: total transit duration, time between first to last contacts; T₁₂ = T₃₄: ingress/egress time, time between first and second, or third and fourth contacts. BJD is calculated from UTC. ^cValues for a quadratic law, adopted from the tabulations by Claret (2004) according to the spectroscopic (SME) parameters listed in Table 8. ^dThe Lagrangian orbital parameters derived from the global modeling, and primarily determined by the RV data. ^eCorrelation coefficient between the planetary mass M_p and radius R_p. ^fThe Safronov number is given by $\Theta = \frac{1}{2}(V_{\rm esc}/V_{\rm orb})^2 = (a/R_{p})(M_{p}/ M_\star)$ (see Hansen & Barman 2007). ^gIncoming flux per unit surface area, averaged over the orbit.

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Included in each table is the RV "jitter." This is a component of noise that we added in quadrature to the internal errors for the RVs in order to achieve χ²/dof = 1 from the RV data for the global fit. It is unclear to what extent this excess noise is intrinsic to the star, and to what extent it is due to instrumental effects which have not been accounted for in the internal error estimates.

The planetary parameters and their uncertainties can be derived by combining the a posteriori distributions for the stellar, light curve, and RV parameters. In this way we find masses and radii for each planet. These and other planetary parameters are listed at the bottom of Table 9. We find:

• 1.  
  HAT-P-18b–the planet has mass M_p = 0.197 ±  0.013 M_J, radius R_p = 0.995 ±  0.052 R_J, and mean density ρ_p = 0.25 ±  0.04 g cm⁻³.
• 2.  
  HAT-P-19b–the planet has mass M_p = 0.292 ±  0.018 M_J, radius R_p = 1.132 ±  0.072 R_J, and mean density ρ_p = 0.25 ±  0.04 g cm⁻³.

Both planets have an eccentricity consistent with zero (e = 0.084 ±  0.048 for HAT-P-18b, and e = 0.067 ±  0.042 for HAT-P-19b). As mentioned above, for HAT-P-19, the RV residuals from a single-Keplerian orbital fit exhibit a linear trend in time. We therefore included an acceleration term to account for this trend. We find $\dot{\gamma }=$ 0.439 ±  0.048 m s⁻¹ day⁻¹. In Section 4, we consider the implication of additional bodies (stellar or planetary) in the HAT-P-19 system.

From the Fortney et al. (2007) planetary models, the expected radius for a coreless 0.20 ±  0.01 M_J planet orbiting a 4.5 Gyr star with a Solar-equivalent semimajor axis of 0.1073 ±  0.0071 AU is ∼1.02 R_J, which is consistent with the measured radius for HAT-P-18b of 1.00 ±  0.05 R_J. The preferred age for HAT-P-18 from the YY isochrones (12.4^+4.4_−6.4 Gyr) is somewhat older than 4.5 Gyr, in which case the expected planetary radius would be even smaller. If a slight core of 10 M_⊕ is assumed, the expected radius of 0.91 R_J is below the measured radius. We conclude therefore that HAT-P-18b is a predominately hydrogen–helium gas giant planet, and does not possess a significant heavy element core.

HAT-P-18b is perhaps most similar in properties to the slightly higher density planet HAT-P-12b (M = 0.211 ± 0.012 M_J, R = 0.959^+0.029_−0.021 R_J; Hartman et al. 2009). Both planets orbit K dwarfs (HAT-P-18 has mass M_⋆ = 0.77 ± 0.03 M_☉, and HAT-P-12 has mass M_⋆ = 0.73 ± 0.02 M_☉). However, HAT-P-18 appears to be older than HAT-P-12, having an isochrone age of 12.4^+4.4_−6.4 Gyr compared with 2.5 ± 2.0 Gyr for HAT-P-12. HAT-P-18 is also more metal rich ([Fe/H] = +0.10 ± 0.08) than HAT-P-12 ([Fe/H] = −0.36 ± 0.04).

Like HAT-P-18b, HAT-P-19b also does not appear to possess a significant heavy element core. From the Fortney et al. (2007) planetary models, the expected radius for a coreless 0.29 ±  0.02 M_J planet orbiting a 4.5 Gyr star with a Solar-equivalent semi-major axis of 0.0763 ±  0.0065 AU is ∼1.02 R_J, which is lower than the measured radius for HAT-P-19b of 1.13 ±  0.07 R_J. If an age of 1.0 Gyr is assumed, the expected planet radius increases to 1.06 R_J, but is still slightly lower than, though consistent with, the measured radius.

Like HAT-P-18b, HAT-P-19b is also very similar in mass/radius to another TEP, in this case WASP-21b (M = 0.30 ±  0.01 M_J, R = 1.07 ±  0.05 R_J; Bouchy et al. 2010). WASP-21b orbits a somewhat hotter star than HAT-P-19b (WASP-21 has M = 1.01^+0.024_−0.025 M_☉, while HAT-P-19 has M = 0.84 ±  0.04 M_☉). HAT-P-19 is also more metal rich than WASP-21 ([Fe/H] = +0.23 ±  0.08 for HAT-P-19, while [Fe/H] = −0.4 ±  0.1 for WASP-21).

As noted in Section 3.3, the RV residuals of HAT-P-19 show a linear trend in time, which is evidence for a third body in the system. The evidence for this trend comes entirely from the Keck/HIRES observations which span 144 days. Although the Subaru/HDS observations predate the Keck/HIRES observations, the uncertain RV zero-point difference between these two data sets prevents us from comparing the Subaru/HDS observations with the Keck/HIRES observations to extend the baseline for measuring the linear variation in the RV residuals. The Subaru/HDS observations span only three days, so the trend is not evident in this data set. Following Winn et al. (2010), we set $\dot{\gamma } \sim G M_{c} \sin i_{c} / a_{c}^2$ to give an order-of-magnitude constraint on the third body, assuming the orbit is circular. This gives

$$\begin{equation} \left(\frac{M_{c}\sin i_{c}}{M_{\rm J}} \right) \left(\frac{a_{c}}{1\, \rm AU} \right)^{-2} \sim 0.9. \end{equation} \tag{ 2 }$$

The time span of the RV measurements, and the lack of evidence for jerk ($\ddot{\gamma }$) in the RV residuals, lets us put a rough limit on the third body's orbital period of P_c ≳ 2 × 144 = 288 days, or a_c ≳ 0.8 AU. This gives a rough lower limit on the mass of the third body of M_c ≳ 0.6 M_J, though this depends on the eccentricity, argument of periastron, and time of conjunction. The object could also be a low-mass star with M > 90 M_J if it has a_c ≳ 10 AU.

As noted in the introduction, the previously known Saturn-mass planets exhibited a suggestive correlation between core mass (or density) and host star metallicity. The two low density planets HAT-P-12b and WASP-21b are consistent with having no core, and orbit sub-solar metallicity stars. While the higher density planets Kepler-9b, Kepler-9c, CoRoT-8b, WASP-29b, and HD 149026b are consistent with having substantial cores, and orbit super-solar metallicity stars. The apparent correlation between planet core mass and host star metallicity was previously noted by Guillot et al. (2006) and Burrows et al. (2007) for all TEPs known at the time (nine and fourteen respectively). Many of the planets with M ≳ 0.4 M_J have radii that are larger than can be accommodated by theoretical models, so it is unclear whether the inferred core masses are physically meaningful for these planets. Nonetheless, for planets in the mass range 0.4–0.7 M_J Enoch et al. (2010) find that planet radius is inversely proportional to host star metallicity, which is what would be expected if the heavy element content of these planets (or core mass) is proportional to host star metallicity. Figure 11 shows the relation between core mass inferred from the Fortney et al. (2007) models and stellar metallicity for planets with 0.15 M_J < M < 0.4 M_J, and 0.4 M_J < M < 0.6 M_J. HAT-P-18b and HAT-P-19b do not follow the correlation that was previously seen for the other Saturn-mass planets. However, since the sample size of known Saturn-mass TEPs is still quite small, further discoveries are needed to illuminate the properties of planets in this mass range.

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