  A novel analysis is performed, incorporating time-of-flight (TOF) information
to study the interactions of dark matter (DM) with standard model particles.
After supernova (SN) explosions, DM with mass $m_\chi\lesssim\mathcal{O}({\rm
MeV})$ in the halo can be boosted by SN neutrinos (SN$\nu$) to relativistic
speed. The SN$\nu$ boosted DM (BDM) arrives on Earth with TOF which depends
only on $m_\chi$ and is independent of the cross section. These BDMs can
interact with detector targets in low-background experiments and manifest as
afterglow events after the arrival of SN$\nu$. The characteristic TOF spectra
of the BDM events can lead to large background suppression and unique
determination of $m_\chi$. New cross section constraints on $\sqrt{\sigma_{\chi
e} \sigma_{\chi\nu}}$ are derived from SN1987a in the Large Magellanic Cloud
with data from the Kamiokande and Super-Kamiokande experiments. Potential
sensitivities for the next galactic SN with Hyper-Kamiokande are projected.
This analysis extends the existing bounds on $\sqrt{\sigma_{\chi e}\sigma_{\chi
\nu}}$ over a broad range of $r_\chi=\sigma_{\chi \nu}/\sigma_{\chi e}$. In
particular, the improvement is by 1-3 orders of magnitude for
$m_\chi<\mathcal{O}(100\,{\rm keV})$ for $\sigma_{\chi e}\sim\sigma_{\chi
\nu}$. Prospects of exploiting TOF information in other astrophysical systems
to probe exotic physics with other DM candidates are discussed.
