betaPic_comet_modelling

[vasmax88]

Hello Dear Sebastian,

your work is very interesting for me.
I'm trying to figure out your code.
Where did you get the file ''betaPic_mag_res.dat"?
What is variable "ulimb" in function "disk_intensity" and why it is =0.79? It value taken from papire Brogi 2012?
What are the parameters specified in the variable "par" they have labels : "t_{mid}", "b", "c_e", "lambda","P", in part "Exocomet model"?
I don't understand where the variable 'theta" is defined for "lnlike()" functions. Can you tell where it comes from?

Thank you so much. I will be glad if you give an answer.

Maksym Vasykenko

[sebastian-zieba]

Hi Maksym,

I am happy to help you. To your questions:

• ''betaPic_mag_res.dat": I got this light curve by subtracting the first 50ish strongest pulsations from the TESS light curve. I did it back then with a tool called PERIOD04 (https://www.univie.ac.at/tops/Period04/) but there are also python scripts which you can use to subtract periodic signals from data (eg. SMURFS https://github.com/MarcoMuellner/SMURFS or Pyriod https://github.com/keatonb/Pyriod)
• ulimb is the linear limb darkening coefficient. Limb darkening arises because stars aren’t uniformly bright disk but get fainter at the edges. This effect has to be taken into account when you fit transits.
• We didn’t actually use ulimb=0.79 in the final paper. It’s just in the Jupyter Notebook to perform some initial estimates. But if you look at the exocomet_fit.ipynb Notebook, you’ll see that disk_intensity is used in modelexi which fixes the ulimb value to 0.275 later. There are different approaches to get limb darkening parameters for your star. The one we used in the paper is based on Claret 2000. But you can also use for example EXOCTK (https://exoctk.stsci.edu/limb_darkening). Just enter the parameters of your star and you'll have your limb darkening parameter(s).
• t_{mid}", "b", "c_e", "lambda","P":
  • t_mid is the transit time, it’s basically the time between the first dimming and when the star is back to full luminosity
  • b is the impact parameter. See here for a description: https://www.paulanthonywilson.com/exoplanets/exoplanet-detection-techniques/the-exoplanet-transit-method/ . We actually fixed it b=0 because our set of parameters was pretty degenerate.
  • c_e is a normalization parameter
  • lambda describes the exponential factor with which the star comes back to full brightness (see paper for more information and formulae)
• theta just describes the set of free parameters when you perform an MCMC. It’s just established to call it like that. Have for example a look at this tutorial for “emcee” (a python package you can use to do MCMCs) https://emcee.readthedocs.io/en/stable/tutorials/line/#maximum-likelihood-estimation

I hope I could answer your questions! :)

Best,
Sebastian