Transit observations of the exoplanet WASP-13b

High precision transit observations of the exoplanet WASP-13b with the RISE instrument


WASP-13b is a sub-Jupiter mass exoplanet orbiting a G1V type star with a period of days. The current uncertainty in its impact parameter () resulted in poorly defined stellar and planetary radii. To better constrain the impact parameter we have obtained high precision transit observations with the RISE instrument mounted on m Liverpool Telescope. We present four new transits which are fitted with an MCMC routine to derive accurate system parameters. We found an orbital inclination of degrees resulting in stellar and planetary radii of  and , respectively. This suggests that the host star has evolved off the main-sequence and is in the shell hydrogen-burning phase. We also discuss how the limb darkening affects the derived system parameters. With a density of , WASP-13b joins the group of low density planets whose radii are too large to be explained by standard irradiation models. We derive a new ephemeris for the system, (HJD) and days. The planet equilibrium temperature (K) and the bright host star (mag) make it a good candidate for follow-up atmospheric studies.

methods: data analysis – methods: observational – stars: planetary systems – stars: individual (WASP-13) –techniques: photometric

1 Introduction

The discovery of the first short-period transiting planet HD 209458b (Charbonneau et al., 2000; Henry et al., 2000) opened a new field of exoplanetary research. Their advantageous geometry allow us to estimate accurate planetary mass and radii. The bulk density of the planet provides information on its composition (Guillot, 2005; Fortney et al., 2007) and places constraints on planetary structure and formation models.

Interestingly, many of the short-period planets are bloated relative to baseline models ( e.g. Bodenheimer et al. 2003; Fortney et al. 2007), which assume a hydrogen/helium planet contracting under strong stellar irradiation. We define the radius anomaly of exoplanets as the difference between the measured radius and theoretical radius. Negative radius anomalies, i.e. denser planets, can be explained by different planet composition or/and the presence of a core (Guillot et al., 2006; Burrows et al., 2007). However, the majority of the hot giant planets have low density (i.e. radius anomalies larger than zero) that are harder to reconcile. Several theories have been presented to explain the positive radius anomalies of hot exoplanets: these include tidal heating (Bodenheimer et al., 2001), kinetic heating due to winds (Guillot & Showman, 2002), enhanced atmospheric opacities (Burrows et al., 2007) and ohmic dissipation (Batygin et al., 2011). Although these theories can explain individual systems, only the recent ohmic dissipation theory (Batygin et al., 2011), can successfully explain all of the known exoplanets radius anomalies (Laughlin et al., 2011). The lowest density hot Jupiters, such as WASP-13b, are particularly important to shed light on the physical mechanisms that lead to inflated planets.

For bright transiting systems, further insight into their physical properties can be obtained through followup observations. Transmission spectroscopy, which consists of measuring the stellar light filtered through the planet’s atmosphere during transit, provides information into exoplanet atmospheres (Charbonneau et al., 2002; Vidal-Madjar et al., 2003). Observation of secondary eclipses (i.e. occultations) offers the potential for directly measuring planetary emission spectra (e.g. Deming et al. 2005; Grillmair et al. 2008; Charbonneau et al. 2008). Finally, the ability to measure the sky-projected angle between the stellar rotation axis and planetary orbit, through the Rossiter-McLaughlin effect (Rossiter, 1924; McLaughlin, 1924), can yield clues about the formation and migration processes (Fabrycky & Winn, 2009; Triaud et al., 2010; Winn et al., 2010).

Followup opportunities benefit from accurate planetary and stellar parameters. However, obtaining high signal-to-noise transit observations from the ground is difficult. Consequently even some of the planets with bright host stars are lacking good quality light curves, and hence have poorly determined planetary parameters. This is the case for WASP-13b (Skillen et al., 2009) where it was not possible to accurately constrain the impact parameter () due to the lack of a high precision transit light curve.

WASP-13b is a low-mass planet with   in a 4.3 day circular orbit (Skillen et al., 2009). Its host star is G1V type with  , K, and solar metallicity. WASP-13b was discovered in 2006-2007 by the SuperWASP-north survey (Pollacco et al., 2006). As mentioned above, the impact parameter is not well constrained and two possible sets of system parameters are presented in the discovery paper for two possible impact parameters; and . This results in large uncertainties in both stellar (), and planetary radii (). The adopted solution suggests that the host star has evolved off the main-sequence to the shell hydrogen burning phase. Therefore, this system is interesting in the context of exoplanet evolution, and with a bright host star (V=10.4 mag) is a good candidate for followup studies.

In this paper, we present four high precision transit observations of WASP-13b which are described in Section 2. Our data allow us to determine the inclination of the system and directly derive the mean stellar density and hence, better constraint the stellar and planetary radii. We discuss our transit model in Section 3 and present the updated parameters of the system in Section 4. In Section 5 we discuss the discrepancy between theoretical and empirical limb darkening coefficients. Finally, we discuss our results in Section 6.

2 Observations

WASP-13b was observed with RISE (Steele et al., 2008; Gibson et al., 2008; Barros et al., 2011) mounted on the 2.0m Liverpool Telescope on La Palma, Canary Islands. RISE is a frame transfer e2v CCD with a pixel scale of 0.54 arcsec/pixel that results in a 9.4 9.4 arcmin field-of-view. It has a wideband filter covering nm which corresponds approximately to V+R. For exposures longer than 1 second, RISE has a deadtime of only 35 ms. To reduce the deadtime to the minimum (Barros et al., 2011) we used an exposure time of 1 second which required a defocussing of -1.0 mm to avoid saturation of the bright comparison star (mag). Defocussing is also important to decrease systematic noise due to poor guiding (Barros et al., 2011).

The data were reduced using the ultracam pipeline (Dhillon et al., 2007) which is optimized for time-series photometry. Each frame was bias subtracted and flat field corrected. We performed differential photometry relative to an ensemble of comparison stars in the field, confirmed to be non-variable. For each observation we sampled different aperture radii and chose the aperture radius that minimised the noise. The photometric errors include shot noise, readout and background noise.

On 2009-01-29 we obtained an ingress of WASP-13b and an egress on 2009-05-05. We obtained full transits of WASP-13b on 2010-02-03 and 2011-01-13. Unfortunately, both observations were degraded by some clouds. Observations with transparency lower than 94% were clipped. On 2010-02-03 the transit observation was interrupted after ingress due to the derotator reaching its limiting position and the two parts of this transit are treated as separate observations. This observation shows systematics near the rotator interruption and is affected by clouds before the egress. We experimented removing it from the final analysis and concluded that its inclusion does not bias the results. On the last 20 minutes of the 2011-01-13 observation the position of the star in the CCD varied by 10 pixels in the x and 15 pixels in y which caused an additional trend in the light curve. Due to its effect on the normalisation of the light curve, the last 20 minutes of the 2011-01-13 observation were clipped. The number of exposures taken, estimated FWHM and aperture radius used for each observation are given in Table 1. We also included in our analysis, the previously published transit of WASP-13 taken with m James Gregory Telescope (JGT) at St Andrews University on 2008-02-16 (Skillen et al., 2009).

Date number exposures FWHM aperture radius
pixel pixel
2009-01-29 4400 17 23
2009-05-05 10780 21 24
2010-02-03 17000 17 22
2011-01-13 16000 24 27
Table 1: WASP-13 observation log.

The final high precision transit light curves for WASP-13b are shown in Figure 1 along with the best-fit model described in Section 3.2. We overplot the model residuals and the estimated uncertainties, which are discussed in Section 3.1. To illustrate the quality of our results we also show the phase folded weighted combination of all the light curves in Figure 2. Around -0.01 in phase the only high precision data is from the 2011-01-13 light curve that shows extra scatter. is below the transit model. The remaining transit phases are better sampled and hence have smaller errors.

Figure 1: Transit observations of WASP-13b. From top to bottom in chronological order; JGT 2008 February 16, RISE 2009 January 01, RISE 2009 May 05, RISE 2010 February 03 and RISE 2011 January 13. We superimpose the best-fit transit model and also show the residuals for each light curve at the bottom of the figure. The RISE data are binned into 30 second periods, and bins displaced vertically for clarity. The individual RISE light curves plotted here are available in electronic form at CDS.
Figure 2: Phase-folded combined transit light curve of WASP-13b. The data was optimally binned in 150 phase bins for clarity. We superimpose the best-fit transit model. Note that here we do not account for the different limb darkening of the RISE and the JGT light curves.

3 Data analysis

3.1 Photometric errors

As mentioned above the initial photometric errors include only shot noise, readout and background noises, which underestimates the true errors. To obtain a more reliable estimate of the errors we begin by scaling the errors of each light curve so that the reduced of the best fitting model is 1.0. This resulted in the multiplication of the errors by , , , , and , for the 2008, Jan 2009, May 2009, ingress 2010, egress 2010 and 2011 light curves, respectively. For the RISE observations, this indicates that the photometric errors are higher than expected from photon noise, probably due to the non-photometric conditions of these observations.

Exoplanet transit observations are also affected by time correlated noise which can lead to underestimated parameter uncertainties (Pont et al., 2006; Carter & Winn, 2009). The residuals displayed in Figure 1 show that the photometric noise is dominated by white noise. Nevertheless, we included time-correlated noise following the procedure from Gillon et al. (2009). Using the residuals of the best fit model, we estimated the amplitude of the red noise, , to be ppm (Jan 2009), ppm (May 2009), ppm (ingress 2010), ppm (egress 2010), and ppm (2011). For the 2008 light curve, the red noise was found to be negligible. These errors were added in quadrature to the rescaled photometric errors and were used in the final Markov Chain Monte Carlo (MCMC) chains.

3.2 Determination of system parameters

To determine the planetary and orbital parameters, we fitted the four RISE light curves and the original JGT light curve of WASP-13b simultaneously. We used the same procedure as for WASP-21b (Barros et al., 2011) which is based on the Mandel & Agol (2002) transit model parametrised by the normalised separation of the planet, , ratio of planet radius to star radius, , orbital inclination, , and the transit epoch, , of each light curve. We account for a linear trend with time for each light curve parametrised by the out of transit flux and flux gradient. Due to the short orbital period and age of the system we expect the orbit has circularised (see below), hence a circular orbit was assumed. The transit model is coupled with an MCMC procedure to obtain accurate parameters and uncertainties as outlined in Barros et al. (2011). We included the quadratic limb darkening coefficients (LDC) from the models of Howarth (2011a) for K, and which were the closest tabulations to the parameters from Skillen et al. (2009); for the RISE filter V+R, and and for the R filter of JGT, and . We initially kept the limb darkening parameters fixed during the fit. We treated the two parts of the 2010-02-03 observations as separate transits to correctly account for the normalisation but restricted them to have the same . Including the two linear normalisation parameters for each light curve, a total of 20 parameters were fitted. Besides the linear normalization, no extra trends were removed from the light curves.

We computed seven MCMC chains, each of points and different initial parameters. The initial 20% of each chain that corresponded to the burn in phase were discarded and the remaining parts merged into a master chain. We define the best fit parameter as the mode of its probability distribution and the 1 limits as the value at which the integral of the distribution equals 34.1% from each side of the mode. The Gelman & Rubin (1992) statistic was calculated for each fitted parameter and we concluded that chain convergence was good.

To test how the limb darkening coefficients affect the derived system parameters we experimented with fitting the limb darkening coefficients of the RISE light curves which have higher precision. Our tests indicate that the quality of the RISE light curves is not enough to fit for both limb darkening coefficients (see also Gibson et al. 2008), and hence, we choose to fit the linear LDC which dominates. The quadratic LDC of the RISE light curves and both LDCs of the JGT light curve were kept fixed. Therefore, in this second MCMC procedure 21 parameters were fitted.

4 Results

In Table 2, we present the system parameters of WASP-13 and the 1 uncertainties derived from the MCMC analysis for both the fixed and fitted LDCs. The first set of parameters can be directly derived from the light curve analysis. The parameters were derived using the equations of Seager & Mallén-Ornelas (2003); Southworth et al. (2007); Kipping (2010). Specifically, the refers to the total transit duration and is defined by equation 15 of Kipping (2010).

The derived linear limb darkening coefficient, , is statistically significantly different from the theoretical value . The chain convergence was good and the linear LDC parameter is well constrained by our observations. We adopt the fitted LDC solution because according to the F-test it is significantly () better than the fixed LDC one. In section 5 we present a more in depth discussion about the discrepancy between the fitted and theoretical LDCs.

All the parameters of both solutions are within . We found that the inclination of the orbit is degrees and the derived stellar density is . This is significantly lower than previously assumed ( Skillen et al. 2009), implying an evolved star. To obtain the stellar and planetary radii we need to determine the stellar mass, as explained in the next section.

Parameter LDC fixed LDC fitted
Linear LDC for RISE
Normalised separation
Planet/star radius ratio
Transit duration [hours]
Transit duration [hours]
Orbital inclination [degrees]
Impact parameter []
Stellar density []
Orbital semimajor axis [AU]
Stellar mass []
Stellar radius []
Planet mass []
Planet radius []
Planet density []
Table 2: WASP-13 system parameters.

4.1 Stellar mass and age

Our high quality transit light curves allow an accurate estimate of the stellar density. This, combined with stellar models, can be used to constrain the stellar mass and age. We interpolate the Yonsei-Yale evolution tracks (Demarque et al., 2004) for (Skillen et al., 2009) which are plotted in Figure 3. Also shown are the position of WASP-13 with the effective temperature from Skillen et al. (2009) and our value of . We derive a stellar mass of and a stellar age of Gyr. Both agree with the estimate in the original discovery paper. Using the stellar reflex velocity from Skillen et al. (2009), m/s, we estimate a planetary mass of .

In Figure 4 we show the evolutionary tracks for a stellar mass of 1.0, 1.09 and 1.2  adapted from Demarque et al. (2004) and we overplot the position of WASP-13. These models suggest that WASP-13 has evolved to the hydrogen-shell burning phase and is close to entering the sub-giant branch. However, the uncertainty in the WASP-13 metallicity ( ) affects the determination of the evolutionary status of WASP-13. According to the Demarque et al. (2004) models, if WASP-13 has a metallicity of +0.2 then it could have a mass of 1.2 which is above the critical mass for the stellar cores to become convective and where details on the treatment of convective overshooting became important. In this case, the evolutionary status would be more uncertain but probably WASP-13 would be in the contraction phase before the hydrogen-shell burning phase starts.

Figure 3: Isochrone models (solid lines) from Demarque et al. (2004) for WASP-13 using [Fe/H] =0 from Skillen et al. (2009) and assuming solar composition Z=0.0181. The age in Gyr is marked in the left of the respective model. We also show the mass tracks (dashed lines) for and . We overplot the (Skillen et al., 2009) and our fitted for WASP-13.
Figure 4: Evolutionary mass tracks from Demarque et al. (2004) for the same stellar parameters as Fig. 3 for stellar masses of 1.2, 1.09 and 1.0  from left to right. For the 1.09  evolutionary mass track we also show the 5, 6,7 and 8 Gyr points.

We obtain a larger stellar and planetary radius ( and ) than previously reported in Skillen et al. (2009). Our derived parameters are consistent with the “b=0.46” adopted solution presented in the discovery paper, although our precision is almost times better.

4.2 Transit times

The estimated transit times were used to update the linear ephemeris,


We found days and T, which was set to the mid-transit time of the 2011 light curve. The updated period was used in the final MCMC procedures.

Time residuals from the linear ephemeris are given in Table 3. The partial transits show a larger deviation from the linear ephemeris which was also noted for the case of TrES-3b (Gibson et al., 2009). These authors concluded that the uncertainties in the transit times of partial transits are underestimated, probably due to the lack of out-of-transit data needed for normalisation. Therefore, although the time residual of the May2009 transit is significant at 4 sigma, this could be due to normalisation errors rather than an intrinsic transit timing variation. For example, removing the out-of-transit data of the May2009 light curve results in a difference in the estimated mid-transit time of s . This suggests the presence of additional red noise in the light curve that affects the transit times which should be regarded with caution. Hence, we conclude that the time residuals of WASP-13b are probably consistent with a linear ephemeris, but encourage further transit timing observations.

Date Epoch Time residuals (sec) Uncertainty (sec)
2008-02-16 -244 235 82
2009-01-29 -164 83 42
2009-05-05 -142 -211 51
2010-02-03 -79 -92 39
2011-01-13 0 114 44
Table 3: Time residuals from the linear ephemeris.

5 Limb darkening

Our measured linear limb darkening parameter () is statistically different from the one predicted from stellar models (). We choose the theoretical LDCs from stellar models of Howarth (2011a) because they include the ’V+R’ RISE filter.

Disagreement between the empirical and theoretical LDCs has been reported for other systems (e.g. Southworth 2008; Barros et al. 2011) including for higher quality light curves from HST (Claret, 2009), CoRoT (Sing 2010, Csizmadia, Sz. et al in prep) and Kepler (Kipping & Bakos, 2011). This suggests that the discrepancy is not due to insufficient quality of our light curves. Moreover, Claret (2009) concluded that uncertainties in the stellar temperature and metallicity cannot explain the difference between the theoretical and empirical LDCs. Therefore, the causes of this discrepancy are not clear.

Recently, Howarth (2011b) showed that LDCs derived from transit observations depend on the impact parameter and cannot be directly compared with the theoretical values. This is because for a higher impact parameter the transit shape is less sensitive to the global LD law. This can lead to up to a 60% difference in the estimated LDCs (Howarth, 2011b). Fortunately, this insensitivity also means that the effect on the transit parameters is relatively small. Using a synthetic photometry/atmosphere-model, Howarth (2011b) predicts that this geometric effect leads to an underestimation of the linear LDC of the quadratic law which qualitatively explains our estimated linear LDC. If this was the only cause of the discrepancy we should adopt the theoretical LDC solution for the system parameters because it would remove the correlation between the LDCs and the impact parameter providing more accurate results.

Using HST and Kepler data, Howarth (2011b) concluded that accounting for this geometrical dependency leads to better agreement between the measured and predicted LDCs. However, this cannot reproduce all of the empirical data suggesting that there could be other causes of the discrepancy. Tentative explanations include the missing physics in the atmospheric models like, for example, the effects of faculae and granulation (Csizmadia, Sz. et al in prep.) and the plane-parallel approximation in stellar models (Neilson & Lester, 2011). In this case, it would be advisable to adopt the fitted LDC solution for the system parameters because it is less dependent on the stellar models.

Further investigation of very high precision transit light curves such as from the Kepler mission is needed to better understand the difference between the measured and theoretical LDCs. This will help to decide if we should fit for the LDCs in lower quality light curves.

6 Discussion and Conclusion

We have presented four new transit light curves of WASP-13b including two full transits. To derive the parameters of the system, we used the same MCMC procedure as Barros et al. (2011) by fitting these new light curves together with a previous JGT transit of WASP-13b (Skillen et al., 2009). We estimated the uncertainties accounting for formal errors and systematic noise.

Our derived value of the linear LDC is statistically significantly different from the theoretical value predicted for stellar atmospheres models. Although this does not significantly affect the derived system parameters it can be important for stellar atmosphere models. We adopt the fitted LDC solution because it is a statistical significantly better fit to the data.

The impact parameter of WASP-13b was poorly constrained in the discovery paper () though the higher value was adopted. We obtain , which is close to the previous adopted value although slightly higher. This implies a larger stellar radius of which combined with the evolution models of Demarque et al. (2004) points to an age of Gyrs for the host star. It also suggests that WASP-13 has evolved off the main-sequence and is now in the shell hydrogen burning phase which would imply that in less than Gyr the star will engulf the planet’s current orbit. The evolutionary status of WASP-13 favours a slightly higher mass for the host star of which also implies a slightly higher planetary mass of .

We derived a larger planetary radius for WASP-13b, (), than previously reported and hence a lower density, (). Therefore, WASP-13b is the fifth lowest density exoplanet known after Kepler-7b (Latham et al., 2010), WASP-17b (Anderson et al., 2010), TrES-4b (Mandushev et al., 2007) and CoRoT-5b (Rauer et al., 2009) and its properties are important for irradiation models. We estimate an equilibrium temperature for WASP-13b of K. The hydrogen/helium coreless models of Fortney et al. (2007) predict a radius of for WASP-13b. This is in agreement with the radius derived from the polynomial fit of Laughlin et al. (2011) to the baseline models of Bodenheimer et al. (2003), R. We derive a radius anomaly for WASP-13b of (Laughlin et al., 2011). Therefore, WASP-13b is inflated relative to the theoretical thermal irradiation models for gas giant planets.

The circularization timescale for WASP-13b is 0.011-0.11 Gyr for . Therefore, we expect a circular orbit and it is unlikely that the inflated radius of WASP-13 could be explained by tidal dissipation. Enhanced atmospheric opacities of solar, plus the correction due to the transit radius effect (Burrows et al., 2007), can explain a radius anomaly of for a 7.4 Gyr planet and hence might be able to explain the radius anomaly of WASP-13b. The models of Bodenheimer et al. (2003) which include kinetic heating (Guillot & Showman, 2002) can also explain the radius of WASP-13b. Finally, the ohmic dissipation model of Batygin et al. (2011) explains all known exoplanet radii.

According to the classification of Fortney et al. (2008), WASP-13b belongs to the highly irradiated “pM” class planets. These have considerable opacities due to molecular hazes of TiO and VO and are expected to have temperature inversions in their atmosphere. This can be tested by secondary eclipse observations. The large scale height of WASP-13b, Km, and its bright host star, , makes it also a good target for transmission spectroscopy. Probing the atmospheric composition of this planet can shed light on its inflated radius.

7 Acknowledgements

The RISE instrument mounted at the Liverpool Telescope was designed and built with resources made available from Queen’s University Belfast, Liverpool John Moores University and the University of Manchester. The Liverpool Telescope is operated on the island of La Palma by Liverpool John Moores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial support from the UK Science and Technology Facilities Council. We thank Tom Marsh for the use of the ultracam pipeline. We thank the anonymous referee for interesting suggestions.


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