HAT-P-9b: A LOW-DENSITY PLANET TRANSITING A MODERATELY FAINT F STAR^*

Transiting extra-solar planets are important astrophysical objects as they allow us to test planetary structure and evolution theory (e.g., Fortney 2008; Burrows et al. 2008; Baraffe et al. 2008), especially because they yield a measurement of the planetary mass and radius. Over the last few years, the sample of known transiting planets has grown substantially, leading to an improved theoretical understanding of their physical nature (e.g., Guillot et al. 2006; Burrows et al. 2007; Fortney et al. 2008; Chabrier & Baraffe 2007). In addition, the increasing sample of transiting planets enabled the discovery of some interesting correlations, such as the mass–period relation (Mazeh et al. 2005; Gaudi et al. 2005). The astrophysics behind these correlations is not fully understood, and a clear way toward progress is the discovery of many more transiting planets.

We report here the discovery of another transiting planet detected by the HATNet project¹⁰ (Bakos et al. 2002, 2004), labeled HAT-P-9b, and our determination of its parameters, including mass, radius, density, and surface gravity. In Section 2, we describe our photometric and spectroscopic observations, and in Section 3 we derive the stellar parameters. The orbital solution is performed in Section 4, and a discussion of possible blend scenarios is brought in Section 5. The determination of the light curve parameters and the planet's physical parameters is described in Section 6, and we bring a discussion in Section 7.

2.1. Detection of the Transit in the HATNet Data

HAT-P-9 is positioned in HATNet's internally labeled field G176, centered at α = 07^h28^m, δ = 37°30'. This field was observed in network mode by the HAT-6 telescope, located at the Fred Lawrence Whipple Observatory (FLWO) of the Smithsonian Astrophysical Observatory (SAO), and the HAT-9 telescope at the Submillimeter Array (SMA) site atop Mauna Kea, HI. In total, 6884 exposures were obtained at a 5.5 min cadence between 2004 November 26 and 2005 October 21 (UT).

Preliminary reduction included standard bias, dark and flat-field corrections, followed by an astrometric solution using the code of Pál & Bakos (2006). Photometry was applied using fine-tuned aperture photometry while the raw light curves were processed by our external parameter decorrelation technique. Next, the trend filtering algorithm (TFA; Kovács et al. 2005) was applied to get the final light curves. To search for the signature of a transiting planet in the light curves we used the box least squares (BLS; Kovács et al. 2002) algorithm.

A transit-like signal was identified in the light curve of HAT-P-9 (GSC 02463 − 00281, 2MASS J07204044+3708263), which is a V = 12.3 mag star, fainter than most transiting planet host stars detected with small-aperture, wide-field, ground-based campaigns. The HATNet light curve is presented in the top panel of Figure 1, folded on the ephemeris obtained from analyzing the follow-up light curves (P = 3.92289 days and T_c = 2454417.9077, see Section 2.4), showing a flux decrement of ∼1% at phase zero. The figure shows a small shift between phase zero and transit center, suggesting a possible slight difference in the ephemeris for the HATNet data and the photometric follow-up data, obtained ∼1000 days apart (see Section 7 for further discussion). This transiting planet candidate, along with others from the same field, was selected for follow-up observations to investigate its nature.

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2.2. Early Spectroscopy Follow-Up

2.3. High-Precision Spectroscopy Follow-Up

2.4. Photometry Follow-Up

The mass (M_p) and radius (R_p) of a transiting planet, determined from transit photometry and RV data, are dependent also on those of the parent star. In order to determine the stellar properties needed to place M_p and R_p on an absolute scale, we made use of stellar evolution models along with the observational constraints from spectroscopy and photometry, as described in Torres et al. (2008). Because of its relative faintness, the host star does not have a parallax measurement from Hipparcos, and thus a direct estimate of the absolute magnitude is not available for use as a constraint. An alternative approach is to use the surface gravity of the star, which is a measure of the evolutionary state of the star and therefore has a very strong influence on the radius. However, log g is a difficult quantity to measure spectroscopically and is often strongly correlated with other spectroscopic parameters (see Section 2.2). It has been pointed out by Sozzetti et al. (2007) that the normalized separation of the planet, a/R_⋆, can provide a much better constraint for stellar parameter determination than the spectroscopic log g. The a/R_⋆ quantity can be determined directly from the photometric observations with no additional assumptions (other than the values of the parameters describing limb-darkening, which is a second-order effect), and it is related to the mean density of the host star. As discussed later in Section 6, an analytic fit to the light curve yields a/R_⋆ = 8.6 ± 0.2. This value, along with T_eff from Section 2.2, and assuming [Fe/H] = 0.0 ± 0.2, was compared with the Yonsei–Yale stellar evolution models of Yi et al. (2001). This resulted in values for the stellar mass and radius of M_⋆ = 1.16^+0.12_−0.15 M_☉ and R_⋆ = 1.28 ± 0.08 R_☉, and an estimated age of 3.6^+3.3_−2.2 Gyr. The result for log g was 4.29^+0.03_−0.04, consistent with the value derived from the DS spectra.

Nevertheless, in order to verify the overall consistency of our results and refine the stellar parameters, we carried out a new iteration. We imposed this latter value of log g (coming from stellar evolution modeling), and analyzed the DS spectra by allowing the metallicity, vsin i, and T_eff to vary. The new results were [Fe/H] = 0.12 ± 0.20, vsin i = 11.9 ± 1.0 km s^-1, and T_eff = 6350 ± 150 K. Repeating the stellar evolution modeling resulted in M_⋆ = 1.28 ± 0.13 M_☉, R_⋆ = 1.32 ± 0.07 R_☉, and an age of 1.6^+1.8_−1.4 Gyr. The stellar properties are summarized in Table 3 and they correspond to a late F star.

Table 3. Summary of Stellar Parameters for HAT-P-9

Parameter	Value	Source
R.A.	07h 20m 4044	2MASS
Decl.	+37° 08' 263	2MASS
mV (mag)	12.297 ± 0.063	TASS
Teff (K)	6350 ± 150	DS + Yonsei–Yale
vsin i (km s-1)	11.9 ± 1.0	DS + Yonsei–Yale
log g	4.29+0.03−0.04	DS + Yonsei–Yale + light curve shape
[Fe/H] (dex)	0.12 ± 0.20	DS + Yonsei–Yale
Mass (M☉)	1.28 ± 0.13	Yonsei–Yale + light curve shape
Radius (R☉)	1.32 ± 0.07	Yonsei–Yale + light curve shape
log(L⋆/L☉)	0.41+0.08−0.09	Yonsei–Yale
MV (mag)	3.7+0.3−0.2	Yonsei–Yale
Age (Gyr)	1.6+1.8−1.4	Yonsei–Yale + light curve shape
B − V (mag)	0.50+0.06−0.05	Yonsei–Yale
Distance (pc)a	480 ± 60	Yonsei–Yale

Note. ^aAssuming extinction of A(V) = 0.15 mag (see Section 3).

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We also used our SOPHIE high-resolution spectra to estimate vsin i and [Fe/H]. Based on our result for B − V from the stellar evolution models, of B − V = 0.50^+0.06_−0.05 mag, we got vsin i = 10.1 ± 1.0 km s^-1, and [Fe/H] = +0.18 ± 0.10 dex. Those values are close to the results from the DS spectra and the stellar evolution model. However, the SOPHIE spectra were taken in high-efficiency mode, where there is a known problem with removing the echelle blaze function. Hence, these estimates are used only for comparison, and are not included in our final result.

To check our spectroscopically determined T_eff we used several publicly available color indices for this star, and the calibrations of Ramírez & Meléndez (2005) and Casagrande et al. (2006) to derive independent temperature estimates, using the [Fe/H] value found above in these calibrations. We adjusted the reddening until the photometric temperature matched the spectroscopic temperature, yielding E(B − V) = 0.053 (Ramírez & Meléndez 2005) and E(B − V) = 0.043 (Casagrande et al. 2006). We adopted the mean value of 0.048 as reddening, implying an extinction of A(V) = 0.15 mag. Note that the Burstein & Heiles (1982) reddening maps for this celestial position (l, b = 181.1, 21.4) give E(B − V) = 0.072 and the Schlegel et al. (1998) maps yield E(B − V) = 0.065, broadly consistent with our findings, especially if we take into account that these latter methods measure the total reddening along the line of sight.

Using the V magnitude from the TASS survey (Droege et al. 2006), V = 12.297 ± 0.063 mag, the absolute V magnitude from the stellar evolution model, and the A(V) = 0.15 mag value determined above, the distance to HAT-P-9 is 480 ± 60 pc.

Our 15 RV measurements from SOPHIE were fitted with a Keplerian orbit model solving for the velocity semi-amplitude K and the center-of-mass velocity γ, holding the period and transit epoch fixed at the well-determined values from photometry (see Table 4). The eccentricity was set to zero. The fit yields K = 84.7 ± 7.9 m s^-1 and γ = 22.665 ± 0.006 km s^-1. The observations and fitted RV curve are displayed in the top panel of Figure 2. The residuals are presented in the bottom panel of the same figure. RMS residuals are 22.1 m s^-1, consistent with the RV uncertainties. The value of χ² is 12.4 for 13 degrees of freedom.

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Table 4. Orbital Fit and Planetary Parameters for the HAT-P-9b System

Parameter	Value
Ephemeris
Period (day)a	3.92289 ± 0.00004
Tc (HJD)a	2454417.9077 ± 0.0003
Transit duration (day)	0.143 ± 0.004
Ingress duration (day)	0.019 ± 0.003
Orbital parameters
γ (km s-1)	22.665 ± 0.006
K (m s-1)	84.7 ± 7.9
e a	0
$\rm Light curve$ parameters
a/R⋆	8.6 ± 0.2
Rp/R⋆	0.1083 ± 0.0005
b	0.52 ± 0.03
Planetary parameters
i (deg)	86.5 ± 0.2
a (AU)	0.053 ± 0.002
Mp (MJ)	0.78 ± 0.09
Rp (RJ)	1.40 ± 0.06
ρp (g cm-3)	0.35 ± 0.06
gp (m s-2)b	9.8 ± 1.0
Teq (K)c	1530 ± 40
Θ d	0.046 ± 0.007
fp (109 erg cm−2 s−1)e	1.3+0.3−0.3

Notes. ^aFixed in the orbital fit. ^bBased on only directly observable quantities; see Southworth et al. (2007, Equation (4)). ^cPlanetary thermal-equilibrium surface temperature. ^dSafronov number; see Hansen & Barman (2007, Equation (2)). ^eStellar flux at the planet.

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We tested the reality of the velocity variations by examining the spectral line bisector spans (BSs) of the star using our SOPHIE data. If the measured velocity changes are due only to distortions in the line profiles arising from contamination of the spectrum by the presence of a binary with a period of 3.92 days, we would expect the BSs (which measure line asymmetry) to vary with this period, resulting in a correlation between BS and RV (see, e.g., Queloz et al. 2001; Torres et al. 2005). As shown in Figure 4, the BSs show no significant variations, except one or two outliers. The correlation coefficient between BS and RV for all 15 measurements is −0.38. Ignoring the extreme point reduces the correlation to −0.18.

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In order to estimate the statistical significance of a correlation between BS and RV we define the following statistics:

$$\begin{equation} r_{\sigma } = \frac{\sigma _{\rm BS, fit}}{\sigma _{\rm BS}}, \end{equation} \tag{ 1 }$$

where σ_BS is the standard deviation of the BS values and σ_BS,fit the standard deviation of the residuals of a BS fit to the RVs. Both standard deviations are the unbiased estimators. For pure noise r_σ will equal 1.0. When fitting the BSs to the RVs of all 15 measurements, using polynomials of degrees 1–3 we got r_σ in the range 0.984–1.043, consistent with no significant correlation.

Another sign of a binary would be a dependence between the RV amplitude and the template used. This may happen when the components of the blended binary are of a different spectral type than the primary target. We re-calculated the RVs using F0 and K5 templates, and got an amplitude consistent with our original value, within 1σ (not shown).

These analyses indicate that the orbiting body is a planet with high significance.

To determine the light curve parameters of HAT-P-9b we fitted the four available transit light curves simultaneously, as described in Shporer et al. (2008). A circular orbit was assumed. We adopted a quadratic limb-darkening law for the star, and determined the appropriate coefficients, u₁ and u₂, by interpolating on the Claret (2000, 2004) grids for the atmospheric model described above. For the Wise 0.46 m light curve, observed with no filter, we adopted the Cousins R-band limb-darkening coefficients as the CCD response resembles a "wide-R" filter (Brosch et al. 2008). The values of the limb-darkening coefficients used for each light curve are listed in Table 2.

The drop in flux in the light curves was modeled with the formalism of Mandel & Agol (2002). The five adjusted parameters in the fit were (1) the period P, (2) the mid-transit time of the N_tr = 0 transit event, T_c,0, denoted simply as T_c, (3) the relative planetary radius, r ≡ R_p/R_⋆, (4) the orbital semi-major axis scaled by the stellar radius, a/R_⋆, and (5) the impact parameter, b ≡ acos(i)/R_⋆, where i is the orbital inclination angle.

Accounting for correlated noise in the photometric data (Pont et al. 2006) was done similarly to the "time-averaging" method of Winn et al. (2008; see also Shporer et al. 2008). After a preliminary analysis we binned the residual light curves using bin sizes close to the duration of ingress and egress, which is 27 min. The presence of correlated noise in the data was quantified as the ratio between the standard deviation of the binned residual light curve and the expected standard deviation assuming pure white noise. This ratio is calculated separately for each bin size and we defined β to be the largest ratio among the bin sizes we used. For each light curve we multiplied the relative flux errors by β and repeated the analysis. The β value of each light curve is listed in Table 2.

We used the Markov Chain Monte Carlo algorithm (MCMC; see, e.g., Holman et al. 2007) to derive the best-fit parameters and their uncertainties. The MCMC algorithm results in a distribution of each of the fitted parameters. We took the distribution median to be the best-fit value and the values at 84.13 and 15.87 percentiles to be the +1σ and −1σ confidence limits, respectively.

Our four follow-up light curves are presented in Figure 3, where the fitted model is overplotted and the residuals are also shown. The result for the radius ratio is R_p/R_⋆ = 0.1083 ± 0.0005, and the normalized separation is a/R_⋆ = 8.6 ± 0.2. From the mass of the star (Table 3), the orbital parameters (Section 4), and the light curve parameters, the physical planetary parameters (such as mass and radius) are calculated in a straightforward way, and are summarized in Table 4. We note that a/R_⋆, as derived from the light curve fit, is an important constraint for the stellar parameter determination (Section 3), which in turn defines the limb-darkening coefficients that are used in the light curve analytic fit. Thus, after the initial analytic fit to the light curves and the stellar parameter determination, we performed another iteration of the light curve fit. We found that the change in parameters was imperceptible.

We present here the discovery of a new transiting extra-solar planet, HAT − P − 9b, with a mass of 0.78 ± 0.09 M_Jup, radius of 1.40 ± 0.06 R_Jup, and orbital period of 3.92289 ± 0.00004 days. The V = 12.3 mag host star is among the faintest planet host stars identified with small-aperture, wide-field, ground-based campaigns. In fact, together with WASP-5 (Anderson et al. 2008), they are currently the faintest planet host stars discovered with such campaigns, where the transit depth is below 2%.

To show the main characteristics of the new planet relative to the currently known transiting planets, we plot in Figure 5 the position of the latter on the radius–mass diagram on the top panel, and the mass–period diagram on the bottom panel. In both panels HAT-P-9b position is marked by an open circle.

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The radius–mass diagram, presented here in log–log scale, visually shows that the new planet has a low density, of ρ_p = 0.35 ± 0.06 g cm^-3, similar to that of HD 209458b (e.g., Knutson et al. 2007; Mazeh et al. 2000), WASP-1b (Cameron et al. 2007; Shporer et al. 2007; Charbonneau et al. 2007), HAT-P-1b (Bakos et al. 2007; Winn et al. 2007b), and CoRoT-Exo-1b (Barge et al. 2008).

Comparing the measured radius to the modeled radius of Burrows et al. (2007), for the same stellar luminosity, semi-major axis, and (core-less) planet mass as the HAT-P-9 system, shows that the measured value is larger than the modeled one by 1–2σ. In this comparison we assumed solar opacity for the planetary atmosphere. As shown by Burrows et al. (2007), the transit radius effect together with enhanced planetary atmospheric opacities, relative to solar opacity, can be responsible for inflating the planetary radius. Since atmospheric opacities are related to the host star metallicity, and HAT-P-9 metallicity seems to be super-solar, it is likely that these two effects account for the radius difference, as is the case for WASP-1b (Burrows et al. 2007; see their Figure 7). Other mechanisms that may explain the increased radius involve downward transport and dissipation of kinetic energy (Showman & Guillot 2002), and layered convection (Chabrier & Baraffe 2007).

According to its T_eq and Safronov number, listed in Table 4, HAT-P-9b is likely a Class II planet, as defined by Hansen & Barman (2007). This classification is in accordance with its low density, since members of this class usually have smaller masses and larger radii than those of Class I.

The stellar incident flux at the planet is f_p = 1.3^+0.3_−0.310⁹ erg cm⁻² s⁻¹, which is at the lower end of the f_p range for pM planets, according to the pL/pM planet classification of Fortney et al. (2008). Since it is positioned near the transition region in f_p between these two classes of planets it may be used to further characterize them.

In the mass–period diagram the new planet is positioned near XO-1b (McCullough et al. 2006; Holman et al. 2006), OGLE-TR-182b (Pont et al. 2008), OGLE-TR-111b (Pont et al. 2004; Winn et al. 2007a), and HAT-P-6b (Noyes et al. 2008). The position of HAT-P-9b  along with that of neighboring planets suggests that the mass–period relation (Mazeh et al. 2005; Gaudi et al. 2005), i.e., the decrease of planetary mass with increasing orbital period, levels off at periods ≳3 days.

The ephemeris obtained here is based on the four follow-up light curves. We compared it to the mid-transit time of the HATNet light curve, obtained some 1000 days earlier, by propagating the error on the period. The result shows a difference of about 1.5σ between the mid-transit times of the follow-up light curves and that of the HATNet light curve. Future follow-up light curves will be able to study more thoroughly this possible discrepancy.

Finally, we note that due to the line-of-sight stellar rotation velocity of 11.9 ± 1.0 km s^-1 and the non-zero impact parameter 0.52 ± 0.03, this planet is a good candidate for the measurement of the Rossiter–Mclaughlin effect (e.g., Winn et al. 2005). Equation (6) of Gaudi & Winn (2007) gives an expected amplitude for the effect of more than 100 m s^-1, which is larger than the orbital amplitude. However, since this is a relatively faint star, with V = 12.3 mag, such a measurement will be challenging.

Operation of the HATNet project is funded by NASA grants NNG04GN74G and NNX08AF23G. These observations have been partially funded by the Optical Infrared Coordination network (OPTICON), a major international collaboration supported by the Research Infrastructures Programme of the European Commissions Sixth Framework Programme. T.M. acknowledges support from the Ministry of Science, Culture & Sport through a grant to encourage French–Israeli scientific collaboration. G.B. is a National Science Foundation Fellow, under grant AST-0702843. We acknowledge partial support from the Kepler Mission under NASA Cooperative Agreement NCC2-1390 (DWL, PI). G.K. thanks the Hungarian Scientific Research Fund (OTKA) support through grant K-60750. G.T. acknowledges partial support for this work from NASA Origins grant NNG04LG89b.