In some circumstances, you might want to attempt to directly determine the absolute brightness temperature of the planet, instead of just the brightness relative to the star. Some physical models may require you to do this, for example the Zhang and Showman (2017) model.
To do this you need the absolute brightness of the star - don’t worry, spiderman has you covered! There are three options for stellar models that can be specified when the model parameters are initialized:
where options for the stellar model include “blackbody” (the default), “PHOENIX”, and “path_to_model” (a user-specified spectrum).
At the most basic level, you can assume that the spectrum of the star is simply blackbody with the effective temperature of the star. Users specify the effective temperature as a model parameter, and the bandpass of the observations must also be specified like so:
spider_params.T_s = 4520 # The stellar effective temperature in K spider_params.l1 = 1.1e-6 # The starting wavelength in meters spider_params.l2 = 1.7e-6 # The ending wavelength in meters
Blackbody stellar models are the default mode for spiderman. Over very wide bandpasses this will be good enough, but for narrower spectral ranges this could introduce significant errors, particularly for cooler stars with deep molecular absorption bands.
A more physically realistic option is to use model stellar spectra to determine the stellar flux - spiderman can do this as well, but it requires downloading an external library of spectra. The path to the library is specified using the .spidermanrc file, as follows:
Currently, the only supported model spectra are the R=10000 PHOENIX models from this page: ftp://phoenix.astro.physik.uni-goettingen.de/MedResFITS/R10000FITS/PHOENIX-ACES-AGSS-COND-2011_R10000FITS_Z-0.0.zip
Download and unpack the model spectra, then make a “.spidermanrc” file in your home directory with a line that points to this model spectra with the keyword PHOENIX_DIR, like this:
PHOENIX_DIR : /path/to/PHOENIX/
As for the blackbody, users specify the wavelength limits for the bandpass and the effective temperature of the star.
spider_params = spiderman.ModelParams(brightness_model = 'zhang', stellar_model = 'PHOENIX') spider_params.l1 = 1.1e-6 # The starting wavelength in meters spider_params.l2 = 1.7e-6 # The ending wavelength in meters spider_params.T_s = 4520 # The stellar effective temperature in K .. warning:: spiderman currently only interpolates the stellar flux in 1D (Temperature) and assumes by default that the star is a dwarf with logg 4.5 - 2d interpolation with logg will be included in a future update
Custom stellar spectrum¶
It is also possible to use your own stellar spectrum. To do this, simply specify the path to the spectrum when you initialize the ModelParams class:
web_p = spiderman.ModelParams(brightness_model = 'zhang', stellar_model = 'path_to_model')
where the spectrum is saved in a file called ‘path_to_model’. This file must be formatted in two columns, where column (1) has the wavelength in meters and column (2) has the stellar flux in units of W/m^3/sr.
Precalculating grids of models¶
In order to speed up computation, spiderman can automatically generate a grid of the summed stellar flux in the defined bandpass as a function of stellar effective temperature, when calculating the flux of the star given its effective temperature spiderman will then use this grid to interpolate on to find the appropriate temperature, to a high level of precision.
If you a running an MCMC, or another numerical method that requires you to call spiderman many thousands of times, especially if you are including the stellar temperature as a model parameter, you should precalculate this grid before begining the model fit and pass it to spiderman to increase the efficiency. This can be done very easily with the stellar_grid module:
stellar_grid = spiderman.stellar_grid.gen_grid(l1,l2,logg=4.5, stellar_model = stellar_model)
Where l1 and l2 are the begining and end of the spectral window in meters, logg is the cgs surface gravity of the star, and stellar_model is the model stellar spectrum (“blackbody”, “PHOENIX”, or “path_to_model”). The stellar_grid object is then passed to spiderman for every light curve generation instance, e.g.
lc = spider_params.lightcurve(t,stellar_grid=stellar_grid)
If a stellar grid is not provided, spiderman will calculate it internally every time lightcurve is called - this will be significantly less efficient for long runs.