Returns a stellar radius estimate based on the scaling relations.
The two global observable seismic parameters, numax and deltanu, along with
temperature, scale with fundamental stellar properties (Brown et al. 1991;
Kjeldsen & Bedding 1995). These scaling relations can be rearranged to
calculate a stellar radius as
R = Rsol * (numax/numax_sol)(deltanu/deltanusol)^-2(Teff/Teffsol)^0.5
where R is the radius and Teff is the effective temperature, and the suffix
‘sol’ indicates a solar value. In this method we use the solar values for
numax and deltanu as given in Huber et al. (2011) and for Teff as given in
Prsa et al. (2016).
This code structure borrows from work done in Bellinger et al. (2019), which
also functions as an accessible explanation of seismic scaling relations.
If no value of effective temperature is given, this function will check the
meta data of the Periodogram object used to create the Seismology object.
These data will often contain an effective tempearture from the Kepler Input
Catalogue (KIC, https://ui.adsabs.harvard.edu/abs/2011AJ….142..112B/abstract),
or from the EPIC or TIC for K2 and TESS respectively. The temperature values in these
catalogues are estimated using photometry, and so have large associated uncertainties
(roughly 200 K, see KIC). For more better results, spectroscopic measurements of
temperature are often more precise.
NOTE: These scaling relations are scaled to the Sun, and therefore do not
always produce an entirely accurate result for more evolved stars.
The frequency of maximum power of the seismic mode envelope. If not
given an astropy unit, assumed to be in units of microhertz.
The frequency spacing between two consecutive overtones of equal radial
degree. If not given an astropy unit, assumed to be in units of
The effective temperature of the star. In units of Kelvin.
Error on numax. Assumed to be same units as numax
Error on deltanu. Assumed to be same units as deltanu
Error on Teff. Assumed to be same units as Teff.
Stellar radius estimate.