We analyze age-velocity dispersion relations ( AVRs ) from kinematics of individual stars in eight Local Group galaxies ranging in mass from Carina ( M _ { * } \sim 10 ^ { 6 } M _ { \odot } ) to M31 ( M _ { * } \sim 10 ^ { 11 } M _ { \odot } ) .
Observationally the \sigma vs. stellar age trends can be interpreted as dynamical heating of the stars by GMCs , bars/spiral arms , or merging subhalos ; alternatively the stars could have simply been born out of a more turbulent ISM at high redshift and retain that larger velocity dispersion till present day - consistent with recent IFU kinematic studies .
To ascertain the dominant mechanism and better understand the impact of instabilities and feedback , we develop models based on observed SFHs of these Local Group galaxies in order to create an evolutionary formalism which describes the ISM velocity dispersion due to a galaxy ’ s evolving gas fraction .
These empirical models relax the common assumption that the stars are born from gas which has constant velocity dispersion at all redshifts .
Using only the observed SFHs as input , the ISM velocity dispersion and a mid-plane scattering model fits the observed AVRs of low mass galaxies without fine tuning .
Higher mass galaxies above M _ { vir } \gtrsim 10 ^ { 11 } M _ { \odot } need a larger contribution from latent dynamical heating processes ( for example minor mergers ) , in excess of the ISM model .
Using the SFHs we also find that supernovae feedback does not appear to be a dominant driver of the gas velocity dispersion compared to gravitational instabilities - at least for dispersions \sigma \gtrsim 25 km s ^ { -1 } .
Together our results point to stars being born with a velocity dispersion close to that of the gas at the time of their formation , with latent dynamical heating operating with a galaxy mass-dependent efficiency .
These semi-empirical relations may help constrain the efficiency of feedback and its impact on the physics of disk settling in galaxy formation simulations .