= Solution
A massive main-sequence donor loses material in a <stellar wind>. Gravitational capture by the <neutron star> can produce a nearly radial, supersonic infall when the captured material has little specific <angular momentum>. A <magnetic field> may channel the final infall toward polar <accretion columns>, where a standing <shock> decelerates the flow. Large <angular momentum> instead favours an <accretion disk>; strictly radial accretion is an idealization.
For <mean particle mass> $\mu$, the <ideal gas law> is $p_{\mathrm d}=\rho_{\mathrm d}k_{\mathrm B}T_{\mathrm d}/\mu$. Combining it with <1/b> gives
$$
\boxed{k_{\mathrm B}T_{\mathrm d}=\frac{\mu p_{\mathrm d}}{\rho_{\mathrm d}}
=\frac3{16}\mu v_{\mathrm u}^2.}
$$
For Newtonian <free fall> from a distance large compared with the stellar radius $R_*$, $v_{\mathrm u}^2\simeq2GM_*/R_*$. Therefore
$$
\boxed{T_{\mathrm d}\simeq\frac{3\mu GM_*}{8k_{\mathrm B}R_*},\qquad
k_{\mathrm B}T_{\mathrm d}\simeq\frac{3\mu GM_*}{8R_*}.}
$$
\b[TODO: a unique numerical <temperature> and characteristic photon band require source data not supplied here.] The held question gives $M_*=1.4M_\odot$ but gives neither $R_*$ nor a composition fixing $\mu$. The mass alone does not fix the free-fall speed or the <temperature>. For example, doubling $R_*$ at the same mass and composition halves both quantities in the last box.
A normalization, rather than an additional claimed datum, makes the scale explicit:
$$
T_{\mathrm d}=8.44\times10^{11}\,\mathrm K
\left(\frac{\mu}{m_p}\right)
\left(\frac{M_*}{1.4M_\odot}\right)
\left(\frac{10\,\mathrm{km}}{R_*}\right),
$$
$$
\boxed{k_{\mathrm B}T_{\mathrm d}=7.27\times10^7\,\mathrm{eV}
\left(\frac{\mu}{m_p}\right)
\left(\frac{M_*}{1.4M_\odot}\right)
\left(\frac{10\,\mathrm{km}}{R_*}\right).}
$$
Here $k_{\mathrm B}T$ is the characteristic particle <energy>; the mean translational <energy> of a nonrelativistic thermal particle is $3k_{\mathrm B}T/2$. If one additionally chose $R_*=10\,\mathrm{km}$ and $\mu=m_p$, this ideal one-temperature estimate would correspond to gamma-ray-scale thermal photon energies. Those are conditional choices, not information recovered from the source. Real accreting <neutron stars> commonly emit <X-rays>: electron-ion disequilibrium, <radiative cooling>, <radiation pressure>, reprocessing and relativistic infall invalidate a direct identification of this ideal ion-heating estimate with the escaping photon spectrum.
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