We present the results of an investigation of the local escape velocity ( V _ { \mathrm { esc } } ) - line strength index relationship for 48 early type galaxies from the SAURON sample , the first such study based on a large sample of galaxies with both detailed integral field observations and extensive dynamical modelling .
Values of V _ { \mathrm { esc } } are computed using Multi Gaussian Expansion ( MGE ) photometric fitting and axisymmetric , anisotropic Jeans ’ dynamical modelling simultaneously on HST and ground-based images .
We determine line strengths and escape velocities at multiple radii within each galaxy , allowing an investigation of the correlation within individual galaxies as well as amongst galaxies .
We find a tight correlation between V _ { \mathrm { esc } } and the line-strength indices .
For Mgb we find that this correlation exists not only between different galaxies but also inside individual galaxies - it is both a local and global correlation .
The Mgb-V _ { \mathrm { esc } } relation has the form : \log ( \mathrm { Mgb } / 4 \mathrm { \AA } ) = ( 0.32 \pm 0.03 ) \log ( \mathrm { V } _ { \mathrm { esc } } / % 500 \mathrm { km / s } ) - ( 0.031 \pm 0.007 ) with an rms scatter \sigma = 0.033 .
The relation within individual galaxies has the same slope and offset as the global relation to a good level of agreement , though there is significant intrinsic scatter in the local gradients .
We transform our line strength index measurements to the single stellar population ( SSP ) equivalent ages ( t ) , metallicity ( [ Z/H ] ) and enhancement ( [ \alpha /Fe ] ) and carry out a principal component analysis of our SSP and V _ { \mathrm { esc } } data .
We find that in this four-dimensional parameter space the galaxies in our sample are to a good approximation confined to a plane , given by \log \mathrm { ( } { V } _ { \mathrm { esc } } / 500 \mathrm { km / s } ) = 0.85 \mathrm { [ Z / H ] } +0.43 \log% ( \mathrm { t } / \mathrm { Gyrs } ) - 0.20 .
It is surprising that a combination of age and metallicity is conserved ; this may indicate a ‘ conspiracy ’ between age and metallicity or a weakness in the SSP models .
How the connection between stellar populations and the gravitational potential , both locally and globally , is preserved as galaxies assemble hierarchically may provide an important constraint on modelling .