snorer.M_sigma

snorer.M_sigma(mBH)

Stellar dispersion relation under the influence of black hole. Also known as \(M-\sigma\) relation.

Parameters:

mBH : array_like
    Supermassive black hole mass, \(M_\odot\)

Returns:

out : scalar/ndarray
    Stellar velocity dispersion, km s−1. Out is scalar if the input is scalar too.

Notes

This function evaluates the stellar dispersion \(\sigma_s\) near supermassive black hole $$ \log_{10}\left(\frac{M_{\rm BH}}{M_\odot}\right) = 8.29 + 5.12\log_{10}\left(\frac{\sigma_s}{200\,{\rm km\,s^{-1}}}\right). $$

References

  1. N. McConnell et al., Nature 480, 215 (2011)