We presented refined planetary, stellar and orbital parameters for the HAT-P-2(b) transiting extrasolar planetary system. Our improved analysis was based on numerous radial velocity data points, including both new measurements and data taken from the literature. We have also carried out high precision follow-up photometry. The refined parameters have uncertainties that are smaller by a factor of∼2 in the planetary parameters and a factor of
∼3−4 in the orbital parameters than the previously reported values of Bakos et al. (2007b).
We note that the density of the planet turned out to be significantly smaller that the value by Bakos et al. (2007b), namelyρp = 7.6±1.1 g cm−3, moreover, the uncertainty reported by Bakos et al. (2007b) was significantly larger. In our analysis we did not rely on the distance of the system, i.e. we did not use the absolute magnitude as a luminosity indicator. Instead, our stellar evolution modelling was based on the density of the star, an other luminosity indicator related to precise light curve and RV parameters. We have compared the estimated distance of the system (which was derived from the absolute magnitudes, known from the stellar modelling) with the Hipparcos distances. We found that our newly estimated distance falls between the two values available from the different reductions of Hipparcos raw data.
The improved orbital eccentricity and argument of pericenter allow us to estimate the time of the possible secondary transits. We found that secondary transits occur at the orbital phase of φsec = 0.1886±0.0020, i.e. 1 day 1 hour and 30 minutes (± 16 minutes) after primary transit events.
The zero insolation planetary isochrones of Baraffe et al. (2003) give an expected ra-dius of Rp,Baraffe03 = 1.02± 0.02RJup, that is slightly smaller than the measured radius of 1.12+0.07−0.05RJup. The work of Fortney et al. (2007) takes into account not only the evo-lutionary age and the total mass of the planet but the incident stellar flux and the mass of the planet’s core. By scaling the semimajor axis of HAT-P-2b to one that yields the same incident flux from a solar-type star on a circular orbit, taking into account both the luminosity of the star and the correction for the orbital eccentricity given by equa-tion (4.44), we obtained a′ = 0.033 ± 0.003 AU. Using this scaled semimajor axis, the interpolation based on the tables provided by Fortney et al. (2007) yields radii between
4.5. DISCUSSION
Rp,Fortney,0 = 1.142 ±0.003RJup (core-less planets) and Rp,Fortney,100 = 1.111±0.003RJup (core-dominated planets, with a core of Mp,core = 100M⊕). Although these values agree nicely with our value ofRp = 1.123+0.071−0.054RJup, the relatively large uncertainty ofRp excludes any further conclusion for the size of the planet’s core. Recent models of Baraffe, Chabrier &
Barman (2008) also give the radius of the planet as the function of evolutionary age, metal en-richment and an optional insolation for equivalent to scaled semimajor axis ofa′ = 0.045 AU.
Using this latter insolation, their models yield Rp,Baraffe08,0.02 = 1.055 ± 0.006RJup (for metal poor, Z = 0.02 planets) and Rp,Baraffe08,0.10 = 1.008± 0.006RJup (for more metal rich, Z = 0.10 planets). These values are slightly smaller than the actual radius of HAT-P-2b, however, the actual insolation of HAT-P-2b is roughly two times larger than the insolation implied by a′ = 0.045 AU. Since the respective planetary radii of Baraffe, Chabrier & Barman (2008) for zero insolation give R(0)p,Baraffe08,0.02 = 1.009±0.006RJup and R(0)p,Baraffe08,0.10 = 0.975±0.006RJup for the respective cases of Z = 0.02 and Z = 0.10 metal enrichment, an extrapolation for a two times larger insolation would put the expected plan-etary radius in the range of ∼ 1.10RJup. This is consistent with the models of Fortney et al. (2007) as well as with the measurements. However, as discussed earlier in the case of Fortney et al. (2007) models, the uncertainty in Rp does not let us properly constrain the metal enrichment.
HAT-P-2b will remain an interesting target, as a member of an emerging heavy-mass population. Further photometric measurements will refine the light curve parameters and therefore more precise stellar parameters can also be obtained. This will yield smaller un-certainties in the physical planetary radius, thus some parameters of the planetary evolution models, such as the metal enrichment can be obtained more explicitly. Moreover, observa-tions of secondary eclipses will reveal the planetary atmosphere temperature which now is poorly constrained. Since the secondary eclipse occurs shortly after periastron passage, the temperature and therefore the contrast might be high enough to detect the occultation with a good signal-to-noise ratio.
Chapter 5 Summary
Transiting extrasolar planets are the only group among the extrasolar planets whose basic physical parameters, such as mass and radius can be determined without any ambiguity.
Therefore, these planets provide a great opportunity to determine other properties, such as the characteristics of the planetary interior or their atmosphere. Recently, wide-field photo-metric surveys became the most prominent observation techniques for detecting transiting planets and these surveys yielded several dozens of discoveries. Since such wide-field surveys yield massive amount of data which cannot be efficiently and consistently processed by the available existing software solutions, I started developing a new package in order to overcome the related problems. The development of this package has been related to the Hungarian-made Automated Telescope Network (HATNet) project, one of the most successful initiatives searching for transiting extrasolar planets.
The aims of my work were both implementing the algorithms related to the photometric reduction in a form of a standalone software package, as well as applying these programs in the analysis of the HATNet data. Additionally, the photometric reduction is intended to work on data obtained by other facilities, typically 1m-class telescopes (such as the 48”
telescope at Fred Lawrence Whipple Observatory or the Schmidt telescope at the Piszk´estet˝o Mountain Station).
Of course, both the confirmation of planetary candidates and the characterization of known objects require other types of technologies such as spectroscopy, radial velocity mea-surements and stellar evolution modelling. In order to perform a consistent determination of the planetary, orbital and stellar parameters of transiting exoplanetary systems, my work also focused on to include these additional types of measurements and methods in the data analysis.
In this PhD thesis I presented a new software package intended to perform photometric data reduction on massive amount of astronomical images. Existing software solutions do not provide a consistent framework for the reduction of images acquired by wide-field and
undersampled instrumentation. During the development of the related algorithms and the implementation, I focused on the issues related to these problems in order to have a ho-mogeneous reduction environment, ranging from the calibration of frames to the final light curve generation and analysis. This new package has been successfully applied in processing the images of the HATNet and led to the discovery and confirmation of almost a dozen of transiting extrasolar planets.
Acknowledgments
First of all, I would like to thank my parents and family for their immutable support during the years of my studies and in my whole life.
I would like to thank G´asp´ar Bakos for inviting to the project and for the possibility to be a member of people working in the field of transiting extrasolar planets. I also thank my supervisor, B´alint ´Erdi for the opportunity to be a PhD student at the E¨otv¨os University and for his help in the proofreading. I am grateful to the hospitality of the Harvard-Smithsonian Center for Astrophysics, where this work has been partially carried out. I would like to thank G´asp´ar, his wife Krisztina Meiszel and and other friends, Istv´an Cziegler, G´abor F˝ur´esz, Bence Kocsis, M´aria Pet˝o and D´avid V´egh for their continuous and great help related to the life in Cambridge and around Boston.
I thank Brigitta Sip˝ocz for her comments, ideas for improvements and bug reports related to the data analysis programs. I also thank collaborators at the Harvard-Smithsonian CfA and the Konkoly Observatory, Joel Hartman, G´abor Kov´acs, G´eza Kov´acs, Robert Noyes and Guillermo Torres for their help.
I would like to say thanks to my friends Bal´azs Dianiska, ´Agnes K´osp´al, Andr´as L´aszl´o and Judit Szul´agyi for their encouragement and for their valuable comments on this dissertation.
Like so, I thank Eric Agol, Daniel Fabrycky, Bence Kocsis and Joshua Winn for their help during the preparation of various articles related to this field of science. I also thank Edward Miller, one of my former roommates for his help on the earlier versions of the draft.
Last but not least, I would like to thank P´eter ´Abrah´am, Ferenc Horvai and Csaba Kiss for their present support and the opportunity to continue the related research in the Konkoly Observatory.
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