New observations and transit solutions of the inflated exoplanets HAT-P-40b and HAT-P-51b

HAT-P-40b was identified as a candidate TEP based on observations made with the HATNet wide-field photometric instruments during 2004–2005 (Hartman et al. 2012). It transits the F9V (V = 11.7 mag) star GSC 3607–01028 with an orbital period of ∼4.572 d. The follow-up photometric observations in Sloan i filter were obtained with the FLWO, FTN and BOS telescopes in 2010–2011. The spectroscopic observations revealed a radial velocity curve (RVC) with semi-amplitude of 58.1 m s⁻¹.

Hartman et al. (2012) fitted the transit curves and RVC to derive period and initial epoch, orbital inclination, and relative stellar and relative planet radii (in units of planet orbital axis). The authors apply a Mandel & Agol (2002) model with fixed quadratic limb-darkening coefficients. The physical parameters of the star HAT-P-40, mass, radius, luminosity and distance, have been determined from a theoretical stellar model on the basis of its effective temperature and metallicity. Then the mass ratio and in turn the planet orbital axis are determined from the mass function. After that, the planet mass and radius are calculated.

Table 1 (column 2) reveals the obtained parameters by Hartman et al. (2012): period P (d); epoch T₀ of transit center (HJD 2450000+); orbital semi-major axis a (AU); orbital inclination i (deg); stellar temperature T_st (K); stellar mass M_st (M_⊙); stellar radius R_st (R_⊙); distance d (pc); limb-darkening law (LDL); limb-darkening coefficients (LDC); planet mass M_p (M_J ); planet radius R_p (R_J ); planet density ρ_p (g cm⁻³); planet temperature T_p (K); and Safronov number Θ.

Hartman et al. (2012) concluded that HAT-P-40b falls in the population of large radius (R > 1.5 R_J ), sub-Jupiter-mass planets, which are referred to as highly inflated planets.

HAT-P-51b was identified as a candidate TEP based on HATNet observations during 2008–2011. It transits the G0V (V = 13.4 mag) star GSC 2296–00637 with an orbital period of ∼4.218 d. The follow-up photometric observations in Sloan i filter were obtained with the FLWO telescope in 2012. The spectroscopic observations revealed RVC with semi-amplitude of 40 m s⁻¹.

Following the same procedure as for HAT-P-40, Hartman et al. (2015) obtained the parameter values given in Table 2 (second column). As a result, they classified HAT-P-51b as a hot Saturn-like planet that falls near the upper envelope of the distribution of points in the mass-radius diagram for transiting planets with 0.1 M_J < M < 10 M_J .

We think our transit solution of HAT-P-40b is more accurate than that of Hartman et al. (2012) because it is based on more precise data as well as it is a result of reproducing a complete transit curve as opposed to the partial transits fitted by the discoverers. The new observations led to improving the orbital period of HAT-P-40 (Table 1).

The derived stellar radius from the transit solution is bigger by 2% than that determined by Hartman et al. (2012) from stellar models (Table 1).

The obtained planet radius of 1.676 R_J is bigger than the value of 1.62 R_J calculated by the empirical relation of Enoch et al. (2012) for a Jupiter-mass planet. Thus, the solution of the newly-observed transit confirms the conclusion of Hartman et al. (2012) that HAT-P-40b belongs to the family of highly inflated Jupiters with 0.4 M_J < M < 1.5 M_J and R > 1.5 R_J .

The varying of T_p in the range 1000–2600 K led to changing of χ² by only 0.0007%. This means that the quality of our data does not allow determination of the planet temperature within this range.

The χ² values of the obtained best solutions for several LDLs differed by around 2%. The absolute minimum of χ² corresponded to the quadratic LDL (Table 1).

We found essential sensibility of the solution quality in terms of the LDC. It confirms the conclusion of Espinoza & Jordán (2015) that the fitting of the LDC in the transit-solution procedure leads to better results than fixing them to theoretical values. In the case of HAT-P-40, the fitted LDC for quadratic LDL u₁ = 0.310 and u₂ = 0.363 (Table 1) turned out close to the theoretical values u₁ = 0.329 and u₂ = 0.294 for filter R (Claret et al. 1995).

The precise astrometric Gaia distance of HAT-P-40 of 464.5 pc (Bailer-Jones et al. 2018) is smaller by around 7% than the calculated value by Hartman et al. (2012) based on the star luminosity obtained from the stellar models (Table 1). This means that probably the luminosity of HAT-P-40 estimated by the stellar models is bigger than the true value by the corresponding amount.

Our transit solution should be more accurate than that of Hartman et al. (2015) because it is based on more precise photometric data. The new observations led to improving the orbital period of HAT-P-51 (Table 1).

The stellar radius derived from our transit solution is bigger by 5% than that determined by Hartman et al. (2015) from stellar models (Table 2).

The planet radius of 1.414 R_J obtained from our transit solution is considerably bigger than the value of 0.923 R_J calculated by the empirical relation of Enoch et al. (2012) for a Saturn-mass planet.

The varying of the planet temperature T_p in the range 200–1600 K led to changing of χ² by only 0.01%. This means that the quality of our data does not allow precise determination of the planet temperature within this range.

The χ² values of the obtained best solutions for different LDLs differed by around 2%. The absolute minimum of χ² corresponded to the quadratic LDL of HAT-P-51. The fitted LDC for a quadratic LDL u₁ = 0.24 and u₂ = 0.28 (Table 2) turned out a little different from the theoretical values u₁ = 0.423 and u₂ = 0.242 for filter R (Claret et al. 1995).

The Gaia distance of HAT-P-51 of 440 pc (Bailer-Jones et al. 2018) is smaller by around 6% than the calculated value by Hartman et al. (2015) based on the star luminosity obtained from the stellar models (Table 2). This means that the luminosity of HAT-P-51 estimated by the stellar models is bigger than the true value.