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Photometry

The density of stars near a MDO will rise very sharply in the region where the MDO dominates the mass. This basically comes from Jeans' equations expressing hydrostatic equilibrium, in the form

$\displaystyle {G\,M_{\rm DO}\over r^2}=-{\nabla \rho\sigma^2\over\rho}\,.$ (11.1)

If the velocity dispersion does not rise very rapidly, $ \sigma^2\approx$ constant, then the density must rise very rapidly, $ d\ln(\rho)/dr\propto -1/r^2$ hence $ \rho\propto \exp(1/r)$. So a rapid increase in density of light toward the centre could signify the presence of a SMBH.

However, the region where the MDO dominates may be very small, of order $ r_{\rm MDO}\approx {GM_{\rm DO}/ \sigma^2}$. As viewed from Earth for a QSO at distance $ D$, the angular extent will be $ \approx 1{\hbox{\rm arcsec}}
(M_{\rm DO}/2\times 10^8\hbox{$M_\odot$})\,(\sigma/200{\hbox{\rm km s$^{-1}$}})^{-2}\,(D/5{\hbox{\rm Mpc}})$. Such a small extent is hard to see from the ground (due to atmospheric seeing), and Hubble Space Telescope (HST) will be needed.

Now some galaxies do indeed show a dramatic increase in brightness - a cusp - toward the centre, even at HST resolution. Unfortunately, it is also known that the velocity dispersion $ \sigma^2$ is not constant. So we cannot claim this proves the presence of a MDO - it's a good indication though.


next up previous contents
Next: Stellar kinematics Up: Evidence for a SMBH Previous: Evidence for a SMBH
Tom Theuns
平成19年2月7日