  SZ Lyn is an astrometric binary consisting of a $\delta$ Scuti star and an
unseen component. The two stars around each other in an almost circular orbit
(e=0.186) with a period of about 3.32 years. We aim to explore the physical
properties of the two components using the radial velocity method and
asteroseismology. Our results show that the $\delta$ Scuti variable is a
post-main sequence star with a helium core ($M_{\rm He}$=
0.1671$^{+0.0028}_{-0.0045}$ M$_{\odot}$ and $R_{\rm He}$=
0.1414$^{+0.0035}_{-0.0020}$ R$_{\odot}$) surrounded by a burning hydrogen
shell; its fundamental parameters is accurately calculated to be
$M$=1.82$^{+0.04}_{-0.02}$ M$_{\odot}$, $R$=2.91$^{+0.02}_{-0.02}$ R$_{\odot}$,
$L$=17.07$^{+1.28}_{-2.61}$ L$_{\odot}$, and $X_c$=0.078$^{+0.021}_{-0.004}$;
the mass of the invisible object is thus estimated to be $M_{\rm co}$=1.68
$^{+0.62}_{-0.60}$ M$_{\odot}$. Combined with the low-resolution LAMOST
spectrum, we suggest that the unseen object is an neutron star candidate. Our
work demonstrates the methodology of using the radial velocity method and
asteroseismology to detect the compact object in such an astrometric binary.
