https://drive.google.com/open?id=0By4_OxQdf-GpbzlOM2cxbjFvZlk
Second, we were to create a program that fits the transit data for HD 209458b. I used a brute force method to fit the transit data. After looking up values for the host star's radius, the semi-major axis of the planets orbit, and the inclination of the orbital plane, my python code cyclically tries values for the period, radius of the planet, and time of periastron while calculating a chi-squared statistic for each combination of parameters. It records the values for period, planet radius, and time of periastron that minimize the chi-squared statistic and writes them to a file called HD209458b_parameters.txt.
I had problems with my limb-darkening implementation with my fitting program so in an effort to get reasonable results, limb-darkening was not taken into account during the fitting procedure.
The following is a link to the code (fitting_transit.py), the input data (100binned.txt), a holistic plot of the fit (HD209458b_fit.png), a zoomed in plot of the fit of one transit (HD209458b_close_fit.png), and a file with the final best-fit parameters for the chi-squared value, the time of periastron, the planet radius, and the period of the orbit (HD209458b_parameters.txt).
https://drive.google.com/open?id=0By4_OxQdf-GpZ2VRT3pJcTBDOHM
The resultant fit for one transit is shown below.
The values that my fitting program calculate are listed below, as well as the literature values provided on the Extrasolar Planet Encyclopedia (http://exoplanet.eu/catalog/hd_209458_b/).
My values
Time_periastron = 2459490.74074 BJD
I had problems with my limb-darkening implementation with my fitting program so in an effort to get reasonable results, limb-darkening was not taken into account during the fitting procedure.
The following is a link to the code (fitting_transit.py), the input data (100binned.txt), a holistic plot of the fit (HD209458b_fit.png), a zoomed in plot of the fit of one transit (HD209458b_close_fit.png), and a file with the final best-fit parameters for the chi-squared value, the time of periastron, the planet radius, and the period of the orbit (HD209458b_parameters.txt).
https://drive.google.com/open?id=0By4_OxQdf-GpZ2VRT3pJcTBDOHM
The resultant fit for one transit is shown below.
The values that my fitting program calculate are listed below, as well as the literature values provided on the Extrasolar Planet Encyclopedia (http://exoplanet.eu/catalog/hd_209458_b/).
My values
Time_periastron = 2459490.74074 BJD
Period = 3.51863425926 days
Radius of planet = 1.34985507246 Jupiter radii
Literature values
Time_periastron = 2452968.399 JD
Period = 3.52472 days
Radius of planet = 1.38 Jupiter radii
Comparing these, we see that the period is comparable within %1 and the radius is comparable within %3. However, the time of periastron is much less reliable where our value is incorrect by over ~6,500 days. If this difference were some integer multiple of the period then the discrepancy could be explained, however, it is not. To obtain more reliable results for our parameters, we would need to develop a better method for determining a "best fit" as well as correctly incorporating limb-darkening (ie: MCMC, etc.).
Radius of planet = 1.34985507246 Jupiter radii
Literature values
Time_periastron = 2452968.399 JD
Period = 3.52472 days
Radius of planet = 1.38 Jupiter radii
Comparing these, we see that the period is comparable within %1 and the radius is comparable within %3. However, the time of periastron is much less reliable where our value is incorrect by over ~6,500 days. If this difference were some integer multiple of the period then the discrepancy could be explained, however, it is not. To obtain more reliable results for our parameters, we would need to develop a better method for determining a "best fit" as well as correctly incorporating limb-darkening (ie: MCMC, etc.).
