Joint modelling of transit and stellar temperature using an MCMC ...

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CHAPTER 6. JOINT MODELLING OF TRANSIT AND STELLAR TEMPERATURE USING AN MCMC APPROACH 178 Figure 6.6: 2D MCMC chains, run with a prior of T eff =5516±33 K, and their posterior distributions. Same legend as Figure 6.3. Figure 6.7: The posterior distributions of T eff , a/R and i derived from the posterior distributions of k and b of Figure 6.6. The posterior distribution of M and R , derived from k, are also shown as used to derive a/R . Same legend as Figure 6.4.
CHAPTER 6. JOINT MODELLING OF TRANSIT AND STELLAR TEMPERATURE USING AN MCMC APPROACH 179 6.2.3 Discussion The MCMC best-fit models of CoRoT-2b’s IRF-filtered transit light curve are presented in Figure 6.8, and the parameters are summarised in Table 6.3. These models and values are compared to the parameters from Alonso et al. (2008) and the parameters derived with the Levenberg-Marquardt algorithm (fitting method used in Chapter 3). Table 6.3: Comparison table of the parameters of CoRoT-2b presented in the discovery paper, derived using the Levenberg-Marquardt algorithm (LMA), and derived using the Markov Chain Monte Carlo (MCMC) without and with a prior on the T eff . Alonso et al. (2008) LMA MCMC no T eff T eff=5516±33K P [d] T 0-2454237 [d] 0.53562 ± 0.00014 0.53534 ± 0.00002 0.53518 +0.00006 −0.00006 0.53518 +0.00006 −0.00007 R p/R 0.1667 ± 0.0006 0.1621 ± 0.0003 0.1618 +0.0005 −0.0010 0.1618 +0.0006 −0.0011 b 0.26 ± 0.01 0.25 ± 0.02 0.25 +0.04 −0.13 0.24 +0.05 −0.14 a/R 6.70 ± 0.03 6.56 ± 0.04 6.56 +0.16 −0.08 6.57 +0.17 −0.09 i [ ◦ ] 87.8 ± 0.1 87.8 ± 0.2 87.9 +1.1 −0.4 87.9 +1.2 −0.4 u a 0.41 ± 0.03 u b 0.06 ± 0.03 e Figure 6.8: Top panel: the binned phase-folded transit of CoRoT-2b, zoomed over the first half of the IRF-filtered transit. Over-plotted are the best transit models derived with the LMA and with the different MCMC runs. Bottom panel: the residual to the data of the LMA and MCMC transit models. Table 6.3 and Figure 6.8 show that both the LMA and the MCMC derive consistent planet parameters and transit model to the data. However, the uncertainties on the parameters derived from the MCMC are more conservative and better representative of the shape of the parameter space around the best model. The comparison show that the LMA has also found the global best minimum for this light curve. It also shows that adding a constraint on the T eff does not change the planet parameters derived
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