Effects of Stellar Feedback on Stellar and Gas Kinematics of
  Star-Forming Galaxies at 0.6<z<1.0
  Recent zoom-in cosmological simulations have shown that stellar feedback can
flatten the inner density profile of the dark matter halo in low-mass galaxies.
A correlation between the stellar/gas velocity dispersion ($\sigma_{star}$,
$\sigma_{gas}$) and the specific star formation rate (sSFR) is predicted as an
observational test of the role of stellar feedback in re-shaping the dark
matter density profile. In this work we test the validity of this prediction by
studying a sample of star-forming galaxies at $0.6<z<1.0$ from the LEGA-C
survey, which provides high signal-to-noise measurements of stellar and gas
kinematics. We find that a weak but significant correlation between
$\sigma_{star}$ (and $\sigma_{gas}$) and sSFR indeed exists for galaxies in the
lowest mass bin (M$_\ast\sim10^{10}\,$M$_\odot$). This correlation, albeit with
a $\sim$35% scatter, holds for different tracers of star formation, and becomes
stronger with redshift. This result generally agrees with the picture that at
higher redshifts star formation rate was generally higher, and galaxies at
M$_\ast\lesssim10^{10}\,$M$_\odot$ have not yet settled into a disk. As a
consequence, they have shallower gravitational potentials more easily perturbed
by stellar feedback. The observed correlation between $\sigma_{star}$ (and
$\sigma_{gas}$) and sSFR supports the scenario predicted by cosmological
simulations, in which feedback-driven outflows cause fluctuations in the
gravitation potential that flatten the density profiles of low-mass galaxies.
