  A light CP-even Standard Model (SM) gauge-singlet scalar $S$ can be produced
abundantly in the supernova core, via the nucleon bremsstrahlung process $N N
\to N N S$, due to its mixing with the SM Higgs boson. Including the effective
$S$ coupling to both nucleons and the pion mediators, we evaluate the
production amplitude for the $S$ particle and point out a key difference with
the well-known light CP-odd scalar (axion) and vector boson (dark photon)
cases. Taking the subsequent decay and re-absorption of $S$ into account, we
present a complete calculation of the energy loss rate for the $S$ particle. We
then use the SN1987A luminosity constraints to derive updated supernova limits
on the mixing of the scalar $S$ with the SM Higgs boson. We find that the
mixing angle $\sin\theta$ with the SM Higgs is excluded only in the narrow
range of $3.9 \times 10^{-7}$ to $7.0 \times 10^{-6}$, depending on the scalar
mass up to about 147 MeV, beyond which the supernova limit disappears.
