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

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