We present a Chandra study of the hot ISM in the giant elliptical galaxy NGC 4649 .
In common with other group-centred ellipticals , its temperature profile rises with radius in the outer parts of the galaxy , from \sim 0.7 keV at 2 kpc to \sim 0.9 keV by 20 kpc .
However , within the central \sim 2 kpc the trend reverses and the temperature peaks at \sim 1.1 keV within the innermost 200 pc .
Under the assumption of hydrostatic equilibrium , we demonstrate that the central temperature spike arises due to the gravitational influence of a quiescent central super-massive black hole .
We constrain the black hole mass ( { M _ { BH } } ) to ( 3.35 ^ { +0.67 } _ { -0.95 } ) \times 10 ^ { 9 } { M _ { \odot } } ( 90 % confidence ) , in good agreement with stellar kinematics measurements .
This is the first direct measurement of { M _ { BH } } based on studies of hydrostatic X-ray emitting gas , which are sensitive to the most massive black holes , and is a crucial validation of both mass-determination techniques .
This agreement clearly demonstrates the gas must be close to hydrostatic , even in the very centre of the galaxy , which is consistent with the lack of morphological disturbances in the X-ray image .
NGC 4649 is now one of only a handful of galaxies for which { M _ { BH } } has been measured by more than one method .
At larger radii , we were able to decompose the gravitating mass profile into stellar and dark matter ( DM ) components .
Unless one accounts for the DM , a standard Virial analysis of the stars dramatically over-estimates the stellar mass of the galaxy .
We find the measured J-band stellar mass-to-light ratio , 1.37 \pm 0.10 M _ { \odot } L _ { \odot } ^ { -1 } , is in good agreement with simple stellar population model calculations for this object .