Abstract

We present photometry of four transits of the planetary system HAT-P-13, obtained using defocused telescopes. We analyse these, plus nine data sets from the literature, in order to determine the physical properties of the system. The mass and radius of the star are MA= 1.320 ± 0.048 ± 0.039 M and RA= 1.756 ± 0.043 ± 0.017 R (statistical and systematic error bars). We find the equivalent quantities for the transiting planet to be Mb= 0.906 ± 0.024 ± 0.018 MJup and Rb= 1.487 ± 0.038 ± 0.015 RJup, with an equilibrium temperature of forumla K. Compared to previous results, which were based on much sparser photometric data, we find the star to be more massive and evolved, and the planet to be larger, hotter and more rarefied. The properties of the planet are not matched by standard models of irradiated gas giants. Its large radius anomaly is in line with the observation that the hottest planets are the most inflated, but at odds with the suggestion of inverse proportionality to the [Fe/H] of the parent star. We assemble all available times of transit mid-point and determine a new linear ephemeris. Previous findings of transit timing variations in the HAT-P-13 system are shown to disagree with these measurements, and can be attributed to small-number statistics.

1 INTRODUCTION

The discovery of the HAT-P-13 by Bakos et al. (2009) elicited substantial interest. The transiting extrasolar planet (TEP) HAT-P-13 b and its host star HAT-P-13 A are rather typical examples of these objects, with two exceptions. First, the star is the second most metal-rich known to host a TEP after XO-2 A1 (Burke et al. 2007) (but see the discussion on host star [Fe/H] values in Enoch et al. 2011). Secondly, there is a third component in the system which is clearly detected in the radial velocity measurements of the host star (Bakos et al. 2009). HAT-P-13 c has an orbit with a period of 446.22 ± 0.27 d, an eccentricity of 0.6616 ± 0.0052 and a minimum mass of 14.28 ± 0.28 MJup (Winn et al. 2010b). This object is expected to induce transit timing variations (TTVs) within the HAT-P-13 A,b system, which potentially allow the structure of the planet to be probed (Mardling & Lin 2004; Batygin, Bodenheimer & Laughlin 2009). HAT-P-13 is unfortunately not the best system for such analyses, as its relatively long and shallow transits are not conducive to precise timing measurements.

An observation of the Rossiter–McLaughlin effect by Winn et al. (2010b) has shown that the projected angle between the orbital axis of HAT-P-13 b and the rotational axis of the parent star is consistent with zero. This is in line with the fact that misaligned axes are only found for TEP systems containing a star hotter than roughly 6250 K (Schlaufman 2010; Winn et al. 2010a; Albrecht et al. 2011). Winn et al. (2010b) also found a long-term drift in the radial velocity measurements of the star, which may be the signature of a fourth component to the system on an orbit of much longer period.

Szabó et al. (2010) attempted to detect a transit of the third body, at a time predicted by Winn et al. (2010b), but were not successful. Their observational campaign included scrutiny of two transits of HAT-P-13 b, whose times of occurrence agreed well with the predicted timings. Pál et al. (2011) subsequently presented photometry of three transits, all of whose mid-points fell earlier than expected according to an ephemeris built on the observations of Bakos et al. (2009) and Szabó et al. (2010). Pál et al. interpreted this as evidence of TTVs. Nascimbeni et al. (2011b) presented high-speed photometry of five transits in early 2011, taken as part of the TASTE project (Nascimbeni et al. 2011a). They confirmed that a linear ephemeris could not explain the available transit timings, and postulated that a sinusoidal TTV with an amplitude of 0.005 d was a good match to the available transit timings. Sinusoidal TTVs have previously been seen for WASP-3 (Pollacco et al. 2008; Maciejewski et al. 2010) and WASP-10 (Christian et al. 2009; Maciejewski et al. 2011) but have not yet been confirmed.2 The putative TTVs for HAT-P-13 have been challenged by Fulton et al. (2011), who presented observations of 10 transits over two observing seasons. They found that a linear ephemeris was an acceptable match to all transit timing measurements, with the exception of the first of the two obtained by Szabó et al. (2010).

The physical properties of the HAT-P-13 system have been derived by Bakos et al. (2009) and Winn et al. (2010b), who used the same light curves. Since these studies, a wealth of new photometric data has been gathered. This has been used to investigate putative TTVs, but has not been brought to bear on improving the physical properties of the system. In this work, we present new photometry covering four transits and use all available high-quality photometry to measure refined physical properties of HAT-P-13.

2 OBSERVATIONS AND DATA REDUCTION

Two full transits of HAT-P-13 were observed with the BFOSC imager mounted on the 1.52-m G. D. Cassini Telescope3 at Loiano Observatory, Italy. We used a Gunn i filter and autoguided throughout. We had to reject a small number of data points in both transits, as they were affected by pointing jumps which compromised the data quality. A summary of our observations is given in Table 1 and the full data can be found in Table 2.

Table 1

Log of the observations presented in this work. Nobs is the number of observations and ‘moon illum.’ is the fractional illumination of the moon at the mid-point of the transit. The aperture sizes are the radii of the software apertures for the object, inner sky and outer sky, respectively.

Transit Date Start time (utEnd time (utNobs Exposure time (s) Filter Airmass Moon illum. Aperture sizes (pixel) Scatter (mmag) 
Cassini 2011 02 06 19:21 00:37 127 120 Thuan–Gunn i 1.17 → 1.00 → 1.10 0.129 25, 35, 55 0.77 
Cassini 2011 04 17 18:58 23:50 147 90 Thuan–Gunn i 1.03 → 2.11 0.998 18, 30, 50 0.93 
Portalegre 2011 01 31 22:13 05:21 128 180 Cousins I 1.11 → 1.01 → 1.64 0.041 10, 35, 45 2.47 
Portalegre 2011 02 03 20:53 02:55 119 150 Cousins I 1.25 → 1.01 → 1.16 0.008 10, 35, 45 2.53 
Transit Date Start time (utEnd time (utNobs Exposure time (s) Filter Airmass Moon illum. Aperture sizes (pixel) Scatter (mmag) 
Cassini 2011 02 06 19:21 00:37 127 120 Thuan–Gunn i 1.17 → 1.00 → 1.10 0.129 25, 35, 55 0.77 
Cassini 2011 04 17 18:58 23:50 147 90 Thuan–Gunn i 1.03 → 2.11 0.998 18, 30, 50 0.93 
Portalegre 2011 01 31 22:13 05:21 128 180 Cousins I 1.11 → 1.01 → 1.64 0.041 10, 35, 45 2.47 
Portalegre 2011 02 03 20:53 02:55 119 150 Cousins I 1.25 → 1.01 → 1.16 0.008 10, 35, 45 2.53 
Table 2

Excerpts of the light curves of HAT-P-13. The full data set will be made available at the CDS.

Telescope BJD(TDB) Diff. mag. Uncertainty 
Cassini 245 5599.30664 0.000 61 0.000 90 
Cassini 245 5599.52535 −0.000 85 0.000 78 
Cassini 245 5669.29046 −0.000 14 0.001 08 
Cassini 245 5669.49355 0.000 66 0.001 17 
Portalegre 245 5596.37076 −0.5552 0.0018 
Portalegre 245 5596.62212 −0.5460 0.0017 
Portalegre 245 5593.42575 −2.0886 0.0022 
Portalegre 245 5593.72313 −2.0970 0.0024 
Telescope BJD(TDB) Diff. mag. Uncertainty 
Cassini 245 5599.30664 0.000 61 0.000 90 
Cassini 245 5599.52535 −0.000 85 0.000 78 
Cassini 245 5669.29046 −0.000 14 0.001 08 
Cassini 245 5669.49355 0.000 66 0.001 17 
Portalegre 245 5596.37076 −0.5552 0.0018 
Portalegre 245 5596.62212 −0.5460 0.0017 
Portalegre 245 5593.42575 −2.0886 0.0022 
Portalegre 245 5593.72313 −2.0970 0.0024 

The telescope was defocused so the point spread functions (PSFs) resembled annuli of widths 15–25 pixel, in order to reduce the light from the target and comparison stars to a maximum of roughly 35 000 count pixel−1. This approach reduces the susceptibility of the data to flat-fielding noise and increases the efficiency of the observations. A detailed description of the defocusing method can be found in Southworth et al. (2009a,b), and an instance of its use with the Cassini Telescope in Southworth et al. (2010). Several images were taken with the telescope properly focused, and used to verify that there were no faint stars within the defocused PSF of HAT-P-13.

Data reduction was undertaken using standard methods pertaining to aperture photometry. Software aperture positions were specified by hand but shifted to account for pointing variations, which were found by cross-correlating each image against the reference image used to place the apertures. We found that the results were insensitive to the choice of aperture sizes (within reason) and to whether flat-fields were used in the data reduction process. Differential-photometry light curves were obtained with respect to an optimal ensemble of four comparison stars constructed as outlined by Southworth et al. (2009a). The times of observation were converted to barycentric Julian date on the TDB time-scale, using the idl procedures of Eastman, Siverd & Gaudi (2010).

Two full transits were observed by JG from CROW-Portalegre, Portugal, using an f/5.6 30-cm Schmidt–Cassegrain Telescope, a KAF1603 CCD camera operating at a plate scale of 1.12forumla pixel−1, and a Cousins I filter. The data were reduced by standard methods, using median-combined bias, dark and flat-field calibration observations. Aperture photometry was performed with C-Munipack4 and differential-magnitude light curves obtained with respect to an ensemble of five comparison stars.

3 LIGHT-CURVE ANALYSIS

We have analysed the Cassini and literature photometric observations of HAT-P-13 by the methods of the Homogeneous Studies project (Southworth 2008, 2009, 2010, 2011), which are briefly summarized below. The light curves and their best-fitting models are shown in Fig. 1 for the data presented in this paper, and in Fig. 2 for previously published observations. The ensuing parameters of the fit are given in Table 3 and detailed results for each data set can be found in an online-only supplement (Appendix A, see Supporting Information). The Portalegre transits were analysed using the same methods, but only the transit times are used below due to the comparatively large scatter of these data.

Figure 1

New data presented in this work, compared to the best jktebop fits using the quadratic LD law. The dates of the light curves are labelled using the format month/day. The residuals of the fits are plotted in the lower half of the figure, offset from zero.

Figure 1

New data presented in this work, compared to the best jktebop fits using the quadratic LD law. The dates of the light curves are labelled using the format month/day. The residuals of the fits are plotted in the lower half of the figure, offset from zero.

Figure 2

Phased light curves of HAT-P-13 compared to the best jktebop fits using the quadratic LD law (left-hand panel). They are shown in the same order as in Table 3. The residuals of the fits are plotted in the right-hand panel, offset to bring them into the same relative position as the corresponding best fit in the left-hand panel.

Figure 2

Phased light curves of HAT-P-13 compared to the best jktebop fits using the quadratic LD law (left-hand panel). They are shown in the same order as in Table 3. The residuals of the fits are plotted in the right-hand panel, offset to bring them into the same relative position as the corresponding best fit in the left-hand panel.

Table 3

Parameters of the jktebop fits to the light curves of HAT-P-13. The final parameters correspond to the weighted mean of the results for the 10 light curves.

Source rA+rb k i (°) rA rb 
Cassini i band 0.211 ± 0.014 0.0932 ± 0.0015 81.6 ± 1.0 0.193 ± 0.013 0.0180 ± 0.0014 
Bakos FLWO i band 0.193 ± 0.011 0.085 92 ± 0.000 84 82.61 ± 0.87 0.178 ± 0.010 0.0153 ± 0.0010 
SzabóV band 0.192 ± 0.030 0.0836 ± 0.0046 83.8 ± 3.2 0.178 ± 0.028 0.0148 ± 0.0031 
SzabóR band 0.207 ± 0.024 0.0872 ± 0.0026 81.7 ± 1.8 0.190 ± 0.022 0.0165 ± 0.0019 
Pál R band 0.217 ± 0.034 0.0895 ± 0.0073 81.5 ± 2.6 0.200 ± 0.031 0.0178 ± 0.0036 
Pál I band 0.210 ± 0.019 0.0887 ± 0.0032 81.5 ± 1.3 0.193 ± 0.017 0.0171 ± 0.0018 
Nascimbeni R band 0.2103 ± 0.0048 0.086 68 ± 0.000 52 81.97 ± 0.36 0.1852 ± 0.0044 0.01606 ± 0.00042 
Fulton FTN Z band 0.231 ± 0.023 0.0882 ± 0.0041 80.2 ± 1.6 0.212 ± 0.021 0.0187 ± 0.0021 
Fulton FLWO i band 0.208 ± 0.016 0.0868 ± 0.0023 81.5 ± 1.2 0.191 ± 0.015 0.0166 ± 0.0017 
Fulton Sedgwick i band 0.199 ± 0.017 0.0873 ± 0.0029 82.4 ± 1.4 0.183 ± 0.016 0.0159 ± 0.0017 
Final results   81.93 ± 0.26 0.1863 ± 0.0034 0.01622 ± 0.00034 
Bakos et al. (2009) 0.1856 0.0844 ± 0.0013 83.4 ± 0.6 0.1712 ± 0.0076 0.01445 
Winn et al. (2010b) 0.1839 0.08389 ± 0.00081 83.40 ± 0.68 0.1697 ± 0.0072 0.01424 
Fulton et al. (2011) 0.1967 0.0855 ± 0.0011 82.45 ± 0.46 0.1812 ± 0.0056 0.01549 
Source rA+rb k i (°) rA rb 
Cassini i band 0.211 ± 0.014 0.0932 ± 0.0015 81.6 ± 1.0 0.193 ± 0.013 0.0180 ± 0.0014 
Bakos FLWO i band 0.193 ± 0.011 0.085 92 ± 0.000 84 82.61 ± 0.87 0.178 ± 0.010 0.0153 ± 0.0010 
SzabóV band 0.192 ± 0.030 0.0836 ± 0.0046 83.8 ± 3.2 0.178 ± 0.028 0.0148 ± 0.0031 
SzabóR band 0.207 ± 0.024 0.0872 ± 0.0026 81.7 ± 1.8 0.190 ± 0.022 0.0165 ± 0.0019 
Pál R band 0.217 ± 0.034 0.0895 ± 0.0073 81.5 ± 2.6 0.200 ± 0.031 0.0178 ± 0.0036 
Pál I band 0.210 ± 0.019 0.0887 ± 0.0032 81.5 ± 1.3 0.193 ± 0.017 0.0171 ± 0.0018 
Nascimbeni R band 0.2103 ± 0.0048 0.086 68 ± 0.000 52 81.97 ± 0.36 0.1852 ± 0.0044 0.01606 ± 0.00042 
Fulton FTN Z band 0.231 ± 0.023 0.0882 ± 0.0041 80.2 ± 1.6 0.212 ± 0.021 0.0187 ± 0.0021 
Fulton FLWO i band 0.208 ± 0.016 0.0868 ± 0.0023 81.5 ± 1.2 0.191 ± 0.015 0.0166 ± 0.0017 
Fulton Sedgwick i band 0.199 ± 0.017 0.0873 ± 0.0029 82.4 ± 1.4 0.183 ± 0.016 0.0159 ± 0.0017 
Final results   81.93 ± 0.26 0.1863 ± 0.0034 0.01622 ± 0.00034 
Bakos et al. (2009) 0.1856 0.0844 ± 0.0013 83.4 ± 0.6 0.1712 ± 0.0076 0.01445 
Winn et al. (2010b) 0.1839 0.08389 ± 0.00081 83.40 ± 0.68 0.1697 ± 0.0072 0.01424 
Fulton et al. (2011) 0.1967 0.0855 ± 0.0011 82.45 ± 0.46 0.1812 ± 0.0056 0.01549 

The light curves were modelled using the jktebop5 code. The primary fitted parameters were the sum and ratio of the fractional radii of the star and planet, rA+rb and k=rb/rA, and the orbital inclination, i. The fractional radii of the components are defined as rA=RA/a and rb=Rb/a, where a is the orbital semimajor axis, and RA and Rb are the true radii of the two objects. Additional parameters of the fit included the magnitude level outside transit and the mid-point of the transit.

We generated solutions with each of five limb-darkening (LD) laws (linear, quadratic, square-root, logarithmic and cubic), and with three different treatments of the LD coefficients. The first possibility is to fix both coefficients to values predicted using model atmospheres; this leads to a dependence on stellar theory as well as slightly worse fits due to the larger number of degrees of freedom. The second option is to fit for both coefficients, but this is possible only when the data are of extremely high quality. Unless otherwise stated, we go for a third alternative: fit for the linear LD coefficients and fix the non-linear one to theoretically predicted values [‘LD-fit/fix’ in the nomenclature of Southworth (2010)]. The two coefficients are highly correlated (e.g. Southworth, Bruntt & Buzasi 2007a) so the theoretical dependence inherent in this approach is negligible.

Uncertainties in each solution were calculated in two ways: from 1000 Monte Carlo (MC) simulations (Southworth, Maxted & Smalley 2004), and with a residual-permutation (RP) algorithm (Jenkins, Caldwell & Borucki 2002). The larger of the two possible error bars was retained for each fitted parameter. Orbital eccentricity (e) and periastron longitude (ω) were incorporated using the constraints e cos ω=−0.0099 ± 0.0036 and e sin ω=−0.0060 ± 0.0069 (Winn et al. 2010b). These constraints were treated as observational data and ecos ω and esin ω were included as fitted parameters.

3.1 Analysis of each data set

The two Cassini transits were modelled together, after scaling the observational errors for each transit to give a reduced χ2 of forumla. This step is necessary because the errors returned by the aperture photometry routine we use are usually too small. Due to the possibility of TTVs in the HAT-P-13 system, one has to be careful when combining data. In this case we fitted for the orbital period (Porb) and the mid-point of the first transit, which is equivalent to fitting for the two transit mid-points. The RP error bars were selected because they are larger than the MC ones. The LD-fit/fix results were adopted. A final value for each photometric parameter was obtained by taking the weighted mean of the four values from the fits for the non-linear LD laws. Its error bar was taken to be the largest of the four alternative values, with a contribution added in quadrature to account for any dependence of the parameter value on the choice of LD law.

Bakos et al. (2009) presented i-band data obtained with the 1.2-m telescope and KeplerCam at the F. L. Whipple Observatory (FLWO). The 3719 data points extend over seven transits within an interval of approximately 1 yr, but only two of these transits have full phase coverage. We therefore converted the timestamps into orbital phase (using the ephemeris calculated by Fulton et al. 2011), sorted them and combined each set of eight consecutive points, to obtain 466 phase-binned points. This will wash out any TTVs present over that time interval, but inspection of fig. 7 in Bakos et al. (2009) shows that no significant variations exist. A preliminary fit returned forumla so the error bars were scaled up by forumla. The LD-fit/fix results are adopted and combined as above. The RP errors were larger than the MC ones, which is unusual for phase-binned data (Southworth 2011) but accounted for in our analysis.

Szabó et al. (2010) obtained V- and R-band coverage of two transits; we did not consider the V-band data of the second transit as it suffers from systematic errors. The R-band observations were solved with Porb as a fitted parameter, so the solutions are not sensitive to the effects of putative TTVs. Given the limited quantity of the data we did not attempt LD-fitted solutions. In both cases, we found that correlated noise was unimportant and adopted the LD-fit/fix solutions. The T0 values from the two data sets (referenced to cycle −12) are in poor agreement with each other (see Tables A3 and A4), and roughly bracket the time of mid-point derived by Szabó et al. (2010). All three timings deviate from the ephemeris derived below by much more than the derived uncertainties.

Pál et al. (2011) presented photometry of three transits from two telescopes located at Konkoly Observatory. The first transit was obtained with the Schmidt Telescope and a CCD camera equipped with a Bessell I filter. The second and third came from the 1.0-m telescope with VersArray CCD camera and a Cousins R filter. The two data sets were modelled separately after scaling up their error bars to enforce forumla. For both bands we adopted the LD-fit/fix solutions. The MC error bars are larger than the RP ones, indicating that red noise is not important.

The data presented by Nascimbeni et al. (2011b) were obtained with the Asiago 1.82-m Telescope and AFOSC imager, through a Cousins R filter. They comprise 12 585 observations covering five closely adjacent transits with cadences ranging from 5.8 to 9.7 s. The data were taken over only 38 days, so can be combined without suffering smearing effects due to TTVs with periodicities above several months. We therefore phase-binned them by a factor of 25 into 504 bins, during which process a 4σ clip removed 11 of the observations. A preliminary fit returned forumla so the supplied observational errors were left unmodified. The results show a strong preference for weaker LD than theoretical expectations, and the values for rA and rb depend somewhat on the treatment of LD. The LD-fixed solutions can be rejected due to a lower quality of fit, and the LD-fitted equivalents return unphysical coefficients, so the LD-fit/fix alternatives were adopted. RP errors are smaller than MC ones, as we ordinarily find for phase-binned data.

Fulton et al. (2011) obtained photometry of 10 transits of HAT-P-13, of which only four were fully covered. These include two transits taken just over a year apart using the Faulkes Telescope North (FTN) and a Z filter, which were solved with a free Porb to allow for the possibility of TTVs. A third transit was obtained in the i band with the FLWO 1.2 m. Finally, one i-band transit from the Sedgwick 0.8 m is accompanied by a partial transit obtained only three nights earlier, allowing these data to be modelled with Porb fixed to any reasonable value. We found that the error bars of the Sedgwick and FTN data had to be multiplied by forumla and forumla, respectively, to obtain forumla. For the FTN and Sedgwick data, we were able to adopt the LD-fit/fix solutions, but for FLWO had to stick to LD-fixed as attempts to fit for LD coefficients returned unphysical values. For the FTN and FLWO data, the RP errors are moderately larger than those from the MC algorithm, implying that correlated noise is significant in these light curves.

3.2 Combined results

The photometric parameters resulting from the 10 light curves are collected in Table 3. We calculated the weighted means to obtain final values of these quantities. The forumla values of the averaging process are all below 0.5, with the exception of k. We deduce that the 10 light curves are in sufficient mutual agreement. The final values are dominated by the results from the Asiago light curve, which is easily the best of the available data sets.

For k the averaging process yields forumla, so the agreement between the light curve solutions is not so good. The Cassini data are the primary contributor to this situation, as they point to a larger k than the rest of the data sets. Individual solutions of the two Cassini light curves yield similar values of k. Moderate disagreements in k have been frequently seen in the Homogeneous Studies papers and can be attributed to starspot activity and/or systematic errors in the light curve. k is also determined to a high precision (by comparison to rA, rb and i) so systematic differences are comparatively obvious.

Our final photometric parameters (Table 3) are somewhat different to values based on the discovery photometry (Bakos et al. 2009; Winn et al. 2010b). In particular, we find a lower i and larger rA. The latter quantity is observationally strongly tied to rb, so our results point towards a larger star and planet than previously proposed. Our photometric parameters agree reasonably well with those proposed recently by Fulton et al. (2011), but have smaller uncertainties.

4 ON THE TRANSIT TIMINGS OF HAT-P-13 B

The third body in the HAT-P-13 system, known to have an eccentric orbit with ec= 0.6616 ± 0.0052 and Porb, c= 446.22 ± 0.27 d from radial velocity measurements, is expected to cause TTVs within the inner HAT-P-13 A,b system (Bakos et al. 2009; Payne & Ford 2011). Bakos et al. found ‘suggestive’ but not ‘significant’ evidence for TTVs in their data obtained in their 2007–08 and 2008–09 observing seasons. Szabó et al. (2010) obtained an improved orbital ephemeris and placed an upper limit of 0.001 d on size of the phenomenon, with the inclusion of their two transit times from the 2009–10 season.

However, the times of three transits acquired by Pál et al. (2011) during the 2010–11 season were about 22 min early with respect to the previous orbital ephemerides, leading Pál et al. to claim a significant detection of TTVs. The timings found by Pál et al. were supported by Nascimbeni et al. (2011b) on the basis of five new transits obtained during the same observing season. Nascimbeni et al. demonstrated that a sinusoidal TTV function provided a good fit to all existing timing measurements.

Fulton et al. (2011) have subsequently presented 10 transit timings which cast doubt on the possibility of TTVs: five from the 2010–11 season which agree well with those from Pál et al. (2011) and Nascimbeni et al. (2011b), and five from the previous season which conflict with the timings found by Szabó et al. (2010). Fulton et al. reanalysed all published follow-up observations of HAT-P-13 and concluded that they were consistent with a linear ephemeris with the exception of the first transit data set from Szabó et al. (2010).

In order to firmly establish the character of the situation, we have collected all available transit mid-point times for the HAT-P-13 A,b system. We have used the timings as quoted by the original sources, rather than adopting those from the reanalysis by Fulton et al. (2011). We included 10 timings obtained by amateur astronomers and placed on the AXA6 and TRESCA7 websites. We rejected amateur timings which are based on data that are either very scattered or do not cover a full transit.

Transit timings were obtained from our own observations by fitting jktebop models to each transit following the LD-fit/fix prescription. The flux normalization was allowed to vary linearly with time. Errors were estimated from RP and from 1000 MC simulations, and were multiplied by 2 in order to guard against any undetected systematic noise in the data. At the request of the referee we also assessed correlated noise using the ‘β’ approach (e.g. Winn et al. 2007). We evaluated values for individual transits and for groups of between 2 and 10 data points, finding a maximum β of 1.26. The corresponding increases in the uncertainties in the T0 values are smaller than the factor of 2 we used above.

All timings were placed on the BJD(TDB) time system. We fitted a straight line to obtain a new orbital ephemeris, finding forumla with one obvious outlier. After the rejection of the offending point, which is the first timing from Szabó et al. (2010), we obtained  

formula
with forumla. The bracketed quantities represent the uncertainties in the ephemeris, and have been increased to account for the excess forumla. The full list of transit timings and their references is given in Table 4. It should be noted that many of the timings are measured from data covering only part of a transit, which is known to reduce their reliability (e.g. Gibson et al. 2009).

Table 4

Times of minimum light of HAT-P-13 and their residuals versus the ephemeris derived in this work.

Time of minimum BJD(TDB) − 2400000 Cycle no. Residual (JD) Reference 
54581.62443 ± 0.00122 −204.0 −0.00183 Bakos et al. (2009) 
54777.01324 ± 0.00100 −137.0 −0.00099 Bakos et al. (2009) 
54779.92990 ± 0.00063 −136.0 −0.00057 Bakos et al. (2009) 
54782.84394 ± 0.00155 −135.0 −0.00277 Bakos et al. (2009) 
54849.92099 ± 0.00075 −112.0 0.00080 Bakos et al. (2009) 
54882.00078 ± 0.00150 −101.0 0.00197 Bakos et al. (2009) 
54960.74005 ± 0.00178 −74.0 0.00281 Bakos et al. (2009) 
55167.79647 ± 0.00280 −3.0 0.00631 Gary(AXA) 
55194.03566 ± 0.00229 6.0 −0.00065 Fulton et al. (2011) 
55196.95450 ± 0.00127 7.0 0.00195 Fulton et al. (2011) 
55199.86837 ± 0.00123 8.0 −0.00041 Tieman(TRESCA) 
55199.86867 ± 0.00131 8.0 −0.00011 Fulton et al. (2011) 
55231.94542 ± 0.00091 19.0 −0.00199 Fulton et al. (2011) 
55249.45117 ± 0.00200 25.0 0.00634 Szabó et al. (2010) 
55269.86567 ± 0.00180 32.0 0.00717 Gary(AXA) 
55272.77577 ± 0.00120 33.0 0.00103 Gary(AXA) 
55272.77627 ± 0.00250 33.0 0.00153 Foote(AXA) 
55275.69207 ± 0.00180 34.0 0.00109 Gary(AXA) 
55275.69312 ± 0.00266 34.0 0.00214 Fulton et al. (2011) 
55307.77077 ± 0.00370 45.0 0.00117 Gary(AXA) 
55310.69197 ± 0.00250 46.0 0.00613 Gary(AXA) 
55511.90854 ± 0.00141 115.0 0.00226 Fulton et al. (2011) 
55558.56302 ± 0.00098 131.0 −0.00307 Pál et al. (2011) 
55561.48416 ± 0.00400 132.0 0.00183 Pál et al. (2011) 
55564.39876 ± 0.00180 133.0 0.00019 Nascimbeni et al. (2011b) 
55584.81455 ± 0.00153 140.0 0.00231 Dvorak(TRESCA) 
55590.64523 ± 0.00179 142.0 0.00052 Pál et al. (2011) 
55593.55879 ± 0.00185 143.0 −0.00216 This work (Portalegre) 
55593.56147 ± 0.00115 143.0 0.00052 Nascimbeni et al. (2011b) 
55596.47291 ± 0.00140 144.0 −0.00428 Naves(TRESCA) 
55596.47327 ± 0.00202 144.0 −0.00392 This work (Portalegre) 
55596.47662 ± 0.00305 144.0 −0.00057 Nascimbeni et al. (2011b) 
55599.39267 ± 0.00075 145.0 −0.00076 Nascimbeni et al. (2011b) 
55599.39446 ± 0.00100 145.0 0.00103 This work (Cassini) 
55602.31068 ± 0.00167 146.0 0.00101 Nascimbeni et al. (2011b) 
55613.97390 ± 0.00225 150.0 −0.00072 Fulton et al. (2011) 
55616.89290 ± 0.00152 151.0 0.00204 Fulton et al. (2011) 
55619.80786 ± 0.00134 152.0 0.00076 Fulton et al. (2011) 
55622.72351 ± 0.00166 153.0 0.00018 Fulton et al. (2011) 
55669.38140 ± 0.00126 169.0 −0.00175 This work (Cassini) 
Time of minimum BJD(TDB) − 2400000 Cycle no. Residual (JD) Reference 
54581.62443 ± 0.00122 −204.0 −0.00183 Bakos et al. (2009) 
54777.01324 ± 0.00100 −137.0 −0.00099 Bakos et al. (2009) 
54779.92990 ± 0.00063 −136.0 −0.00057 Bakos et al. (2009) 
54782.84394 ± 0.00155 −135.0 −0.00277 Bakos et al. (2009) 
54849.92099 ± 0.00075 −112.0 0.00080 Bakos et al. (2009) 
54882.00078 ± 0.00150 −101.0 0.00197 Bakos et al. (2009) 
54960.74005 ± 0.00178 −74.0 0.00281 Bakos et al. (2009) 
55167.79647 ± 0.00280 −3.0 0.00631 Gary(AXA) 
55194.03566 ± 0.00229 6.0 −0.00065 Fulton et al. (2011) 
55196.95450 ± 0.00127 7.0 0.00195 Fulton et al. (2011) 
55199.86837 ± 0.00123 8.0 −0.00041 Tieman(TRESCA) 
55199.86867 ± 0.00131 8.0 −0.00011 Fulton et al. (2011) 
55231.94542 ± 0.00091 19.0 −0.00199 Fulton et al. (2011) 
55249.45117 ± 0.00200 25.0 0.00634 Szabó et al. (2010) 
55269.86567 ± 0.00180 32.0 0.00717 Gary(AXA) 
55272.77577 ± 0.00120 33.0 0.00103 Gary(AXA) 
55272.77627 ± 0.00250 33.0 0.00153 Foote(AXA) 
55275.69207 ± 0.00180 34.0 0.00109 Gary(AXA) 
55275.69312 ± 0.00266 34.0 0.00214 Fulton et al. (2011) 
55307.77077 ± 0.00370 45.0 0.00117 Gary(AXA) 
55310.69197 ± 0.00250 46.0 0.00613 Gary(AXA) 
55511.90854 ± 0.00141 115.0 0.00226 Fulton et al. (2011) 
55558.56302 ± 0.00098 131.0 −0.00307 Pál et al. (2011) 
55561.48416 ± 0.00400 132.0 0.00183 Pál et al. (2011) 
55564.39876 ± 0.00180 133.0 0.00019 Nascimbeni et al. (2011b) 
55584.81455 ± 0.00153 140.0 0.00231 Dvorak(TRESCA) 
55590.64523 ± 0.00179 142.0 0.00052 Pál et al. (2011) 
55593.55879 ± 0.00185 143.0 −0.00216 This work (Portalegre) 
55593.56147 ± 0.00115 143.0 0.00052 Nascimbeni et al. (2011b) 
55596.47291 ± 0.00140 144.0 −0.00428 Naves(TRESCA) 
55596.47327 ± 0.00202 144.0 −0.00392 This work (Portalegre) 
55596.47662 ± 0.00305 144.0 −0.00057 Nascimbeni et al. (2011b) 
55599.39267 ± 0.00075 145.0 −0.00076 Nascimbeni et al. (2011b) 
55599.39446 ± 0.00100 145.0 0.00103 This work (Cassini) 
55602.31068 ± 0.00167 146.0 0.00101 Nascimbeni et al. (2011b) 
55613.97390 ± 0.00225 150.0 −0.00072 Fulton et al. (2011) 
55616.89290 ± 0.00152 151.0 0.00204 Fulton et al. (2011) 
55619.80786 ± 0.00134 152.0 0.00076 Fulton et al. (2011) 
55622.72351 ± 0.00166 153.0 0.00018 Fulton et al. (2011) 
55669.38140 ± 0.00126 169.0 −0.00175 This work (Cassini) 

The two timings from Szabó et al. (2010) both deviate from the orbital ephemeris above, being later by 8.6σ and 3.2σ. Our own analyses of these data return timings which are similarly distant from expectations. A detailed reanalysis of the corresponding data performed by Fulton et al. (2011) resulted in a timing for the second of these transits which conflicts less with a linear ephemeris (1.6σ). The discrepancy of the first transit remains unexplained. A few of the amateur timings are late by a similar amount to this one, but with larger error bars.

We conclude that the available data do not provide a clear indication of the existence of TTVs, primarily on the basis that we cannot conceive of a reasonable TTV function which is a significant improvement over a linear ephemeris. The transits which occur later than predicted by our ephemeris are not grouped together, but are interleaved with ones which happen at the expected times. An explanation involving TTVs therefore would require a highly contrived functional form.

So where did the previous suggestions of TTVs come from? Pál et al. (2011) used an earlier ephemeris, tuned on the Bakos et al. (2009) and Szabó et al. (2010) observations, to show that their transit timings were earlier than expected. The dotted line in Fig. 3 represents this ephemeris and shows that it fails to match the more recent transit timings. Nascimbeni et al. (2011b) suggested that a sinusoidal TTV of amplitude 0.005 d and period 1150 d was in good correspondence with the observations, as demonstrated by their fig. 2. We have endeavoured to place this periodic variation, whose parameters were not fully specified, on to Fig. 3, with a little manual fine-tuning. The 2009–10 transit timings obtained by Fulton et al. (2011) clearly dismiss the sinusoidal TTV proposed by Nascimbeni et al. (2011b), leaving a linear ephemeris as the only reasonable option.

Figure 3

Plot of the residuals of the timings of mid-transit of HAT-P-13 versus a linear ephemeris. The timings in black are from this work, in grey are from Bakos et al. (2009), blue from Szabó et al. (2010), lilac from Pál et al. (2011), green from Nascimbeni et al. (2011b), red from Fulton et al. (2011) and open circles for the amateur timings. The solid line shows the ephemeris from the current work and the dotted line that from Bakos et al. (2009). The dashed curve is an approximate representation of the possible periodicity proposed by Nascimbeni et al. (2011b).

Figure 3

Plot of the residuals of the timings of mid-transit of HAT-P-13 versus a linear ephemeris. The timings in black are from this work, in grey are from Bakos et al. (2009), blue from Szabó et al. (2010), lilac from Pál et al. (2011), green from Nascimbeni et al. (2011b), red from Fulton et al. (2011) and open circles for the amateur timings. The solid line shows the ephemeris from the current work and the dotted line that from Bakos et al. (2009). The dashed curve is an approximate representation of the possible periodicity proposed by Nascimbeni et al. (2011b).

5 PHYSICAL PROPERTIES OF THE HAT-P-13 SYSTEM

Several sets of information exist from which the properties of the HAT-P-13 A,b system can be derived. Analysis of the available light curves has given values for Porb, i, rA and rb. The high-precision radial velocities procured by Bakos et al. (2009) and Winn et al. (2010b) supply measurements of the velocity amplitude of the star (KA= 106.04 ± 0.73 m s−1) and the orbital eccentricity (e= 0.0133 ± 0.0041). Analysis of the spectra by Bakos et al. (2009) furthermore leads to estimates of the stellar effective temperature (Teff= 5653 ± 90 K) and metallicity ([Fe/H] =+0.41 ± 0.08). Finally, constraints on the properties of the star can be obtained by interpolation within tabulated predictions from stellar evolutionary models.

Our solution process (Southworth 2009) consists of finding the best agreement between the observed and model-predicted Teff values, and the measured rA and calculated RA/a. This is done using the velocity amplitude of the planet, Kb, as a solution control parameter and calculating the full system properties using standard formulae (e.g. Hilditch 2001). The system properties comprise the mass, radius, surface gravity and mean density for the star (MA, RA, log gA and ρA) and planet (Mb, Rb, gb and ρb), the orbital semimajor axis (a), the planetary equilibrium temperature and Safronov (1972) number (forumla, Θ) and an estimate of the evolutionary age of the star.

The statistical errors on the resulting values are calculated using a perturbation analysis (Southworth, Maxted & Smalley 2005) which yields a full error budget for each output quantity. The use of theoretical models incurs a dependence on stellar theory which is assessed by running separate solutions with each of five different sets of model tabulations (see Southworth 2010, for details). Finally, an alternative empirical estimate of the physical properties is obtained using a calibration (Southworth 2011) based on eclipsing binary star systems, inspired by Enoch et al. (2010) and Torres, Andersen & Giménez (2010). The control parameter Kb represents the constraints obtained from stellar theory. Note that the values gb, ρA and forumla are not reliant on constraints from stellar theory (Seager & Mallén-Ornelas 2003; Southworth, Wheatley & Sams 2007b; Southworth 2011).

The sets of physical properties arising from each of the five stellar model tabulations and from the empirical calibration are given in Table A11. For the final results in Table 5 we adopted the unweighted mean of each parameter from the solutions for the five stellar models. The statistical error is the largest of the individual error bars, and the systematic error is the standard deviation of the five values. Compared to previous studies, we find a larger and more evolved star and a correspondingly slightly more massive but significantly bigger and hotter planet. The extensive photometric data set considered in this work leads to more precise measurements of the physical properties, but the uncertainties in rA and rb continue to dominate the error budget. The uncertainty in MA stems mainly from that in [Fe/H], suggesting that a new spectral synthesis study would also be useful in improving our understanding of the HAT-P-13 system.

Table 5

Final physical properties of the HAT-P-13 system, compared with results from the literature. Where two error bars are given, the first refers to the statistical uncertainties and the second to the systematic errors.

  This work (final)  Bakos et al. (2009)  Winn et al. (2010b) 
M A (M 1.320 ± 0.048 ± 0.039  forumla   forumla  
R A (R 1.756 ± 0.043 ± 0.017  1.559 ± 0.082  1.559 ± 0.080 
log gA (cgs)  4.070 ± 0.020 ± 0.004  4.13 ± 0.04   
ρA 0.244 ± 0.013     
M b (MJup 0.906 ± 0.024 ± 0.018  forumla   0.851 ± 0.038 
R b (RJup 1.487 ± 0.038 ± 0.015  1.281 ± 0.079  1.272 ± 0.065 
g b (m s−1 10.15 ± 0.43  12.9 ± 1.5   
ρb ( ρJup 0.257 ± 0.017 ± 0.003  forumla    
forumla (K)  1725 ± 31  1653 ± 45   
Θ  0.0404 ± 0.0023 ± 0.0004  0.046 ± 0.003   
a (au)  0.04383 ± 0.00053 ± 0.00043  forumla    
Age (Gyr)  forumla   forumla    
  This work (final)  Bakos et al. (2009)  Winn et al. (2010b) 
M A (M 1.320 ± 0.048 ± 0.039  forumla   forumla  
R A (R 1.756 ± 0.043 ± 0.017  1.559 ± 0.082  1.559 ± 0.080 
log gA (cgs)  4.070 ± 0.020 ± 0.004  4.13 ± 0.04   
ρA 0.244 ± 0.013     
M b (MJup 0.906 ± 0.024 ± 0.018  forumla   0.851 ± 0.038 
R b (RJup 1.487 ± 0.038 ± 0.015  1.281 ± 0.079  1.272 ± 0.065 
g b (m s−1 10.15 ± 0.43  12.9 ± 1.5   
ρb ( ρJup 0.257 ± 0.017 ± 0.003  forumla    
forumla (K)  1725 ± 31  1653 ± 45   
Θ  0.0404 ± 0.0023 ± 0.0004  0.046 ± 0.003   
a (au)  0.04383 ± 0.00053 ± 0.00043  forumla    
Age (Gyr)  forumla   forumla    

6 SUMMARY

The HAT-P-13 system is unusual, in that a transiting hot Jupiter and its host star are accompanied by a clearly detected third component on a wider orbit. Such a configuration should result in HAT-P-13 c inducing TTVs within the HAT-P-13 A,b system, which may be detectable within a comparatively short time period. This possibility has generated substantial interest, resulting in a large body of photometric observations covering many transits of the star by the inner planet. We have assembled the available transit timing measurements and shown that they are most easily explained by a linear ephemeris, albeit with a small number of values which occur later than expected. The discrepant measurements are not clumped together, so could only be explained via highly complex functional forms. Previous claims of TTVs can be attributed to small-number statistics, although continued photometric monitoring has a good chance of turning up something interesting in the future.

We have presented new observations of four transits, obtained using telescope defocusing techniques. Including previously published data, we have 10 good sets of transit light curves. These were each analysed within the context of our Homogeneous Studies project (Southworth 2008, 2009, 2010, 2011), and a good agreement between the results was found. We combined them with the measured spectroscopic properties of the host star and several sets of theoretical stellar model predictions to find the physical properties of the system. HAT-P-13 is now well characterized, although additional photometric and spectroscopic measurements would allow further improvement. We have included it in the TEPCat catalogue8 of the physical properties of transiting planetary systems.

We find a significantly different set of physical properties compared to previous studies, which had access to only two of the 10 photometric data sets used here. The star is more massive, larger and more evolved. The planet, whose properties are measured relative to its host star, is similarly heavier and bigger. Its lower density and higher equilibrium temperature place it firmly in the ‘pM’ class advocated by Fortney et al. (2008). Its radius is too large to match the values predicted by the models of Fortney, Marley & Barnes (2007) or Baraffe et al. (2008).

Laughlin, Crismani & Adams (2011) found that the radius anomaly (the measured radius of a TEP versus that predicted by theoretical models) is correlated with equilibrium temperature, and possibly inversely correlated with host star [Fe/H]. The large radius anomaly and high equilibrium temperature of HAT-P-13 b corroborate the former observation, but the highly metal-rich nature of the parent star ([Fe/H] = 0.41 ± 0.08) is contrary to the latter suggestion.

Footnotes

2
A sinusoidal TTV was claimed for OGLE-TR-111 by Díaz et al. (2008), but has been refuted by Adams et al. (2010).
3
Information on the 1.52-m Cassini Telescope and BFOSC can be found at http://www.bo.astro.it/loiano/.
5
jktebop is written in fortran77 and the source code is available at http://www.astro.keele.ac.uk/~jkt/.
6
Amateur Exoplanet Archive, http://brucegary.net/AXA/x.htm.
7
The TRansiting ExoplanetS and CAndidates (TRESCA) website can be found at http://var2.astro.cz/EN/tresca/index.php.
8
The Transiting Extrasolar Planets Catalogue can be found online at http://www.astro.keele.ac.uk/~jkt/tepcat/

The reduced light curves presented in this work will be made available at the CDS (http://cdsweb.u-strasbg.fr/) and at http://www.astro.keele.ac.uk/~jkt/. This observational campaign has been possible thanks to the generous allocation of telescope time by the TAC of the Bologna Observatory and to the invaluable help of the technical staff. JS acknowledges financial support from STFC in the form of an Advanced Fellowship. We thank Andras Pál for supplying photometric data and the anonymous referee for insightful comments. The following internet-based resources were used in research for this paper: the ESO Digitized Sky Survey; the NASA Astrophysics Data System; the SIMBAD data base operated at CDS, Strasbourg, France; and the arXiv scientific paper preprint service operated by Cornell University.

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