ELSEVIER Chinese Astronomy and Astrophysics 38 (2014) 307–316

CHINESEASTRONOMYAND ASTROPHYSICS

Photometric Observation and Study of theTransiting Exoplanetary System HAT-P-8† �

TAN Hong-bo1,2� WANG Xiao-bin1 GU Sheng-hong1

Andrew Collier Cameron3

1Yunnan Astronomical Observatory, Chinese Academy of Sciences, Kunming 6500112University of Chinese Academy of Sciences, Beijing 100049

3School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews,Fife KY16 9SS UK

Abstract Three transit events of HAT-P-8 were observed by using the 1 mtelescope of Yunnan Observatory and the 2.4 m telescope of Lijiang AstronomicalStation in 2009 and 2012, respectively. The observational data are reduced withthe coarse de-correlation and SysRem algorithms in order to improve the signalto noise ratio of the transit signals. The MCMC (Markov Chain Monte Carlo)technique is applied to analyzing the three transit light curves simultaneously,then the new parameters of the HAT-P-8 system are derived. The new value ofthe radius of HAT-P-8b is smaller than that given by Latham et al., while it isconsistent with the value derived recently by Mancini et al.. By linear fittingon the 23 high-precision mid-transit times, the orbital period of HAT-P-8b isrefined as P=3.0763461±0.0000021 d, and from the (O−C) analysis no obviousTTV (Transit Timing Variation) signal has been detected.

Key words: planets and satellites: individual, methods: observational, meth-ods: data analysis

† Supported by Project of Important Directions in Knowledge Innovation Program of Chinese Academyof Sciences (KJCX2-YW-T24) and National Natural Science Foundation (10873031)

Received 2013–03–11; revised version 2013–04–10� A translation of Acta Astron. Sin. Vol. 54, No. 6, pp. 527–536, 2013� thb@ynao.ac.cn

0275-1062/01/$-see front matter c© 2014 Elsevier Science B. V. All rights reserved.PII:

0275-1062/14/$-see front matter © 2014 Elsevier B.V. All rights reserved.doi:10.1016/j.chinastron.2014.07.007

308 Tan Hong-bo et al. / Chinese Astronomy and Astrophysics 38 (2014) 307–316

1. INTRODUCTION

The study of extrasolar planets has obtained a further development thank of the discoveryof the Transit of ExoPlanet (TEP). Through an analysis of the photometric data of atransiting system, the principal parameters, such as the planet radius, the inclination ofits revolution orbit around the primary star, may be directly solved. If the radial velocitydata are combined with the analysis, the mass of the planet will also be obtained. Themeasurement of these parameters not only makes us be able to analyze the material structureand composition of the planet, but also plays a very important role for understanding theformation and evolution of the planet[1]. In addition, if the photometric observations of atransit event are made simultaneously at multiple wavebands, it will help to know about theatmospheric material composition of the planet[2−3]. And if the spectroscopic observationof a transit event is conducted, its Rossiter-Mclaughlin effect may be studied, and the anglebetween the orientation of revolution orbit and that of the rotation axis of the planet canbe measured[4]. At present, although more and more transiting exoplanetary systems havebeen successively discovered, however, they are lacking in follow-up long-term observationand investigation. The long-term observation and investigation of a known planetary systemcan optimize the parameters of the system and help us with a better understanding of thephysical properties of the planet on the one hand, and by monitoring the TTV and TDV(Transit Duration Variation) signals, we can confirm whether there exist other undiscoveredplanets in the system on the other side[5−8].

HAT-P-8b discovered by HATnet (Hungarian Automatic Telescope Net) is an expand-ing “hot Jupiter” with the mass Mp = 1.52+0.18

−0.16 MJ and the radius Rp = 1.50+0.08−0.06 RJ

(the upper and lower labels of the numerical values show their errors corresponding to 1σ),its orbital period around the primary star is (3.0763378 ± 0.000004) d[9], and the orbitaleccentricity is e = 0[10]. The primary star GSC02757-01152 of the system is one which hasthe metal abundance analogous to the sun, the spectral type of F8 and the visual magnitudeof V = 10.17 mag. Recently, in the observational study on the HAT-P-8 system, Manciniet al. discovered that HAT-P-8 has in fact a smaller radius of Rp = 1.321± 0.037 R

[11]J . In

this article, three new sets of photometric data of HAT-P-8 will be analyzed. In the secondsection of this article, the photometric observation and the method of data processing arepresented. In the third section, the parameters of the system are solved with the MCMCtechnique. In the fourth section, a discussion on the new parameters of the system and theconclusion on this work are made.

2. OBSERVATION AND DATA PROCESSING

2.1 The 1m Telescope of Yunnan ObservatoryTwo transit events of HAT-P-8 were observed with the Andor CCD camera installed

on the 1m telescope of Yunnan Observatory on November 6 and December 13 of 2009. Thepixels of this CCD were 2k×2k, corresponding to a viewing field of 7.3

′×7.3′. A R-band filter

was used in the two observations, and the CCD pixels were not read in parallel-packed mode.On November 6, the weather was always fine during the whole observation with a rathergood seeing, but the elevation angle of the target source was a little low (below 30◦) near the

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end of the observation; on December 13, it was fine during the whole observation, but theseeing was relatively inferior, and the elevation angle of the target source was comparativelylow (below 25◦). Because of the imperfect tracking of the telescope, a rather long exposuretime was adopted to get a sufficiently large CCD count under the rather low elevation ofthe source. The detailed observation information is listed in Table 1, in which Nobs meansthe number of image frames, Texp, exposure time, YO1m, the 1m telescope of YunnanObservatory, LJ2.4m, the 2.4m telescope of Lijiang Astronomical Station.

2.2 The 2.4m Telescope of Lijiang Astronomical StationA transit event of HAT-P-8 was observed with the YFOSC CCD camera installed on

the 2.4m telescope of Lijiang Astronomical Station on December 3 of 2012. The effectivepixels of this CCD were 2k×2k, corresponding to a viewing field of 10

′ × 10′. It was fine

in that night. A R-band filter was used in the whole observation, and the CCD pixels werenot read in parallel-packed mode. In order to improve the quality of data, an automaticguiding system was put on and the approach of defocused observation was adopted. Theexcellent automatic guiding system of the 2.4 m telescope ensured that the displacementof the star image on the whole CCD image would not exceed 2 pixel during the wholeobservation, and the defocused observation ensured to obtain not only more photons in thecase of unsaturated CCD count, but also a bigger point spread function to make the errorcaused by the inhomogeneity of flat field reduce to the least, thus to raise the accuracyof observational data[12−13]. It is a pity that when the transit happened, the sky was notdark utterly, the relatively bright skylight background resulted in rather large errors in thedata of first contact that we finally obtained. In the successive calculations of parameters,in order to raise the computing accuracy, those data with greater errors were neglected, aslisted in detail by Table 1.

Table 1 The observation log of HAT-P-8

Date Telescope Nobs Texp/s Airmass Filter Precision/mag2009-11-06 YO1m 411 25∼60 1.01∼2.28 R 0.00282009-12-13 YO1m 197 50∼100 1.02∼2.58 R 0.00252012-12-03 LJ2.4m 267 30∼40 1.01∼1.55 R 0.0010

2.3 Image ProcessingAll the CCD images we obtained are handled with the IRAF (Image Reduction and

Analysis Facility) software package. According to the standard process of image processing,at first the images are trimmed on the basis of the response of the CCD, then the combinationof high-quality images, which are selected from all the background images and evening flat-field images, are used to produce the background and flat-field images for image processing,then they are applied to conducting the background subtraction and flat-field correctionfor all the images, at last some cosmic ray events are rejected after all images are groupedaccording to the exposure time. Now, we have got finally the images which can be appliedto photometry. The aperture photometry on the processed images is performed with theAPPHOT software package of IRAF, and the instrumental magnitudes of the target sourceand the reference stars are obtained. So far as the choice of photometric aperture, we havetried several apertures, the aperture that gives the minimum dispersion of the light curve ofthe target source is chosen as the optimal one. On the basis of above-mentioned principles,

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20 pixel, 25 pixel and 70 pixel are chosen as the optimal apertures of the images obtained onNovember 6, December 13 of 2009 and on December 3 of 2012, respectively, and accordingto the distribution of reference stars in the viewing field and their brightness, the numbersof reference stars finally measured are 14, 9 and 12, respectively.

2.4 Correction for Systematic ErrorsBecause of the weakness of transit signals, systematic errors are bound to cause a

significant influence on the results of analysis. The systematic errors mixed in the measuredinstrumental magnitudes are corrected with the coarse de-correlation[14] and SysRem[15]

methods, thus the overall accuracy of the data are raised. In practice, an iterative analysisis carried out first for all the reference stars by using the coarse de-correlation method,thus the optimal mean magnitude of each star and the optimal zero-point of each imageare obtained and the correction for the every image is made, meanwhile, the stable high-precision comparison stars are picked up in this procedure. Then, with the SysRem methodthe comparison stars picked up in the above procedure are analyzed, and a further correctionfor the systematic errors of the data is calculated. In our observational viewing field, thetarget source is generally over two magnitudes brighter than the reference stars. For thesake of the best correction, when the systematic errors are corrected with the above method,the comparison stars as bright as possible should be selected. It is necessary to note thatbecause the systematic errors in the data are analyzed only by using the reference stars,but its own systematic tendency of the target source has not been considered, this tendencywill appear clearly on the obtained light curve of the target source[16]. So this systematictendency can be removed by fitting the infra-transit data of the event with a polynomial[17].Finally, in order to compare with the previous work of other astronomers, the data newlyobtained are transformed consistently into the time system of BJDTDB (Barycentric JulianDate). After these procedures, the final light curves of the transit events of HAT-P-8 areobtained as shown in Figure 1 (in which the ordinate ΔM(R)/mag indicates the relativemagnitude of the target source in the R band).

3. ANALYSIS

Three light curves obtained from the observations are analyzed with the MCMC techniqueto get the new physical parameters of the HAT-P-8 system. In our analysis, it is assumedthat the revolution orbit of the planet is circular, and the system is described with sixparameters (T0, P , �F , tT , b, M∗), in which T0 is the mid-transit time, P , the orbitalperiod of the planet, �F , transit depth, tT , transit duration, b, collision factor (to describethe path of the planet across the star disc), M∗, stellar mass [18]. For describing the lightcurve of a transit event, the Mandel and Agol’s small-scale planet model is adopted [19] withthe Claret’s 4-coefficient limb darkening law taken into consideration[20], in which the 4 limbdarkening coefficients of the star in the R band are obtained by interpolating the data tablegiven by Claret in 2000 according to the effective temperature (Teff), surface gravitationalacceleration (logg), metal abundance ([Fe/H]) and microscopic turbulent velocity (ξ) of thestar. The following values given by Latham et al. [9] and Valenti et al. [21] are adopted in ourcalculation: Teff=6200 K, logg=4.15, [Fe/H]=0.01, ξ=0.85 km/s. The posterior probabilitydistribution of each parameter of the system is obtained from a simultaneous analysis of the

Tan Hong-bo et al. / Chinese Astronomy and Astrophysics 38 (2014) 307–316 311

3 sets of photometric data with the Metropolis-Hastings algorithm, and then the optimalvalue and its uncertainty of each parameter are obtained from the posterior probabilitydistribution.

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Fig. 1 The light curves of HAT-P-8’s transit events. The horizontal axis represents the observing time

BJDTDB(2450000+), and the vertical axis represents the relative magnitude in the R band.

312 Tan Hong-bo et al. / Chinese Astronomy and Astrophysics 38 (2014) 307–316

3.1 Preliminary AnalysisAt first, a preliminary analysis of the 3 sets of photometric data is performed with the

MCMC technique to acquire the optimal solution which can epitomize these data. In ourcalculation, the initial values of the different parameters originate from published articles,and the step lengthes are first fixed according to the uncertainties of parameters given inthe literature, then they are adjusted on the basis of the acceptability in the calculation.Considered that the stellar mass can be calculated well enough from the concerned calibra-tion relation, so in actual calculations, the stellar mass is not a free parameter, and thevalue given by Mancini et al.[11] is adopted in this paper. To test the convergence, thecalculations are performed with diverse initial values and the different chain lengthes in therange of 104 ∼ 5 × 104, the obtained values of the different parameters basically have thesame posterior probability distribution, this implies the convergence of our calculation [22].Such a calculation gives an optimal solution which may describe simultaneously the 3 setsof data, in which the orbital period of the planet is P = 3.0763340 d. Then, with the orbitalperiod fixed as a new value, each set of data is separately analyzed, and the mid-transittime of the every transit event is obtained.

3.2 Study of Orbital PeriodIn order to have a precise orbital period of HAT-P-8b and to monitor the potential TTV

signal, a new accurate orbital period is obtained by means of least square fitting on the high-precision mid-transit times collected as far as we can. It is a pity that the observational dataused in this paper are either incomplete or not precise enough, this results in a considerableerror in the mid-transit times we have derived. In order to determine accurately the orbitalperiod, instead of our own mid-transit times, those carefully selected from articles and theExoplanet Transit Database (ETD)1 are used in our calculation. The selection criterionsare as follows: (1) the light curve of the transit event is complete and symmetrical; (2)the dispersion of transit data is relatively small; (3) the sampling points of transit data aresufficient. Accordingly, 23 mid-transit times are obtained as summarized in Table 2. A newlinear expression of epochs is finally derived as follows:

BJDTDB = 2454437.67413(14)+ 3.0763461(21)× E ,

in which E is the number of elapsed periods relative to the initial transit time (taking themid-transit time given by Latham et al.[9] in 2009 as a reference), the digits in parenthesesmean the error of the last two figures of the value before them. On the basis of above epochexpression, a (O−C) diagram is obtained as shown in Figure 2, from which we can find thatthe linear epoch expression can describe very well the mid-transit times, with the exceptionof the event (2455148.31400). After a careful examination of the light curve of this transitevent, it is found that the asymmetry of the curve is the cause leading to a comparativelygreat value of (O − C) on that point.

1 http://var2.astro.cz/ETD/index.php

Tan Hong-bo et al. / Chinese Astronomy and Astrophysics 38 (2014) 307–316 313

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Fig. 2 The (O − C) diagram for the orbital period study of HAT-P-8b

Table 2 The epochs of mid-transit of HAT-P-8

T0(BJDTDB − 2450000)/d Cycle (O − C)/d Source4437.67461 0 0.00047 Ref.[9]5046.79040 198 -0.00025 ETD5071.40170 206 0.00028 ETD5074.47520 207 -0.00256 ETD5126.77446 224 -0.00119 Ref.[11]5148.31400 231 0.00392 Ref.[11]5409.79920 316 -0.00028 Ref.[10]5434.41080 324 0.00054 Ref.[23]5437.48610 325 -0.00050 Ref.[11]5437.48434 325 -0.00226 ETD5440.56460 326 0.00165 ETD5452.86716 330 -0.00117 ETD5812.80021 447 -0.00061 ETD5837.41364 455 0.00205 ETD5840.48811 456 0.00017 Ref.[11]5840.48845 456 0.00051 Ref.[11]6166.58178 562 0.00116 Ref.[11]6166.58162 562 0.00100 Ref.[11]6166.57924 562 -0.00137 Ref.[11]6166.57760 562 -0.00302 Ref.[11]6175.81123 565 0.00095 ETD6203.49662 574 -0.00015 Ref.[11]6203.49682 574 -0.00004 Ref.[11]

3.3 Final SolutionThrough the period study mentioned above, a precise orbital period of HAT-P-8b is

obtained. Now, with the orbital period fixed at this value, the 3 sets of data obtained in theobservations are analyzed and solved again with the MCMC technique to obtain the finalparameters of the system. Several groups of chains with a length of 3× 104 are used in the

314 Tan Hong-bo et al. / Chinese Astronomy and Astrophysics 38 (2014) 307–316

calculation, and finally the identical posterior probability distributions of the parametersare obtained, according to which the optimal values of all parameters, as well as their 1σ

errors are derived as listed in Table 3, and the corresponding best-fit models are shownin Figure 3 (for the convenience of illustration, two sets of data and their correspondingtheoretical curves are moved up and down). The posterior probability distributions of apart of parameters are illustrated in Figure 4.

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Fig. 3 The observed light curves of transit events and the best fit models. The open circles represent the

individual observations, the solid line represents the theoretical model.

Table 3 The best fit parameters and their uncertainties derived from the MCMC

analysis

Parameter Symbol Value Unit

Transit epoch T0 BJDTDB2455935.86076+0.00052−0.00055 d

Orbital period P 3.0763461 ± 0.0000021 d

Planet/star area ratio (Rp/R∗)2 0.01019+0.00020−0.00034

Transit duration tT 0.1454+0.0013−0.0010 d

Impact parameter b 0.34+0.08−0.23 R∗

Orbital semi-major axis a 0.04388+0.00011−0.00014 au

Orbital inclination i 86.9+2.2−0.9 degree

Planet radius Rp 1.28+0.05−0.08 RJ

Stellar radius R∗ 1.49+0.05−0.08 R�

Stellar mass M∗ 1.19 M�

Tan Hong-bo et al. / Chinese Astronomy and Astrophysics 38 (2014) 307–316 315

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Fig. 4 The posterior probability distributions of the planet radius and stellar radius of the HAT-P-8

system

4. DISCUSSIONS AND CONCLUSIONS

Three sets of transit photometric data of HAT-P-8 are acquired in the observations withthe 1 m telescope of Yunnan Observatory and the 2.4m telescope of Lijiang AstronomicalStation, and a part of physical parameters of the HAT-P-8 system are optimized throughthe data analysis with the MCMC technique. In comparison with the results published byLatham et al. [9] in 2009, it is noticed that among the newly obtained parameters of thesystem, the planet radius Rp = 1.28+0.05

−0.08 RJ is nearly 15% smaller than Rp = 1.50+0.08−0.06 RJ,

the result given by Latham et al. [9], while it is consistent well with Rp = 1.321± 0.037 RJ,the result derived recently by Mancini et al. [11].

Based on the result of the analysis of radial velocity made by Latham et al. [9] and ournewly obtained parameters of the planetary system, the mass of HAT-P-8b is calculated tobe Mp = 1.23 ± 0.08 MJ. According to the theoretical model of Fortney et al. [24], for acoreless planet with the orbital semi-major axis of 0.024 au, the mass of 1.23 MJ and the ageof 3.4 Gyr, its radius is derived to be about 1.19 RJ. It can be seen that the radius value weobtained is obviously greater than the theoretical one. At present, following theories havebeen put forward to explain why the radius of a hot Jupiter becomes greater: (1) the tidalheating of stellar gravitation [25]; (2) the dynamical heating of stellar wind[26]; (3) the ohmicdissipation effect [27]. Although all these theories may explain the abnormality of planetradius, only is the ohmic dissipation effect applicable to all the exoplanets with an abnormalradius [28]. Using the mid-transit times collected by us, the epoch expression of the systemis calculated again, a new value of orbital period of the planet P = 3.0763461± 0.0000021 dis obtained, this result is consistent with those given in previous articles, and has a higheraccuracy. This is owing to the analysis of the high-precision mid-transit times that wecarefully selected. From the (O − C) diagram of the period analysis, it is found that alinear fitting may epitomize perfectly all data points, and therefore, there exist no TTVphenomena in this system at present.

316 Tan Hong-bo et al. / Chinese Astronomy and Astrophysics 38 (2014) 307–316

ACKNOWLEDGEMENT Thanks to the observation assistants of the 1m telescope ofYunnan Observatory and of the 2.4m telescope of Lijiang Astronomical Station for enthusi-astic help and thanks to every one of our team for great support.

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