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We analyze age-velocity dispersion relations (AVRs) from kinematics ofindividual stars in eight Local Group galaxies ranging in mass from Carina($M_{*} \sim 10^{6}$) to M31 ($M_{*} \sim 10^{11}$). Observationally the$\sigma$ vs. stellar age trends can be interpreted as dynamical heating of thestars by GMCs, bars/spiral arms, or merging subhalos; alternatively the starscould have simply been born out of a more turbulent ISM at high redshift andretain that larger velocity dispersion till present day - consistent withrecent IFU studies. To ascertain the dominant mechanism and better understandthe impact of instabilities and feedback, we develop models based on observedSFHs of these Local Group galaxies in order to create an evolutionary formalismwhich describes the ISM velocity dispersion due to a galaxy's evolving gasfraction. These empirical models relax the common assumption that the stars areborn from gas which has constant velocity dispersion at all redshifts. Usingonly the observed SFHs as input, the ISM velocity dispersion and a mid-planescattering model fits the observed AVRs of low mass galaxies without finetuning. Higher mass galaxies above $M_{vir} > 10^{11}$ need a largercontribution from latent dynamical heating processes (for example minormergers), in excess of the ISM model. Using the SFHs we also find thatsupernovae feedback does not appear to be a dominant driver of the gas velocitydispersion compared to gravitational instabilities - at least for dispersions$\sigma \gtrsim 25$ km/s. Together our results point to stars being born with avelocity dispersion close to that of the gas at the time of their formation,with latent dynamical heating operating with a galaxy mass-dependentefficiency. These semi-empirical relations may help constrain the efficiency offeedback and its impact on the physics of disk settling in galaxy formationsimulations.

A unified model for age-velocity dispersion relations in Local Group galaxies: Disentangling ISM turbulence and latent dynamical heating