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We perform nonlocal thermodynamic equilibrium (NLTE) model atmosphereanalyses of the three hottest hypervelocity stars (space velocities between$\approx$ 1500-2800 km s$^{-1}$) known to date, which were recently discoveredspectroscopically and identified as runaways from Type Ia supernovae. Thehottest of the three (J0546$+$0836, effective temperature $T_\mathrm{eff}$ =95,000 $\pm$ 15,000 K, surface gravity log g = $5.5 \pm 0.5$) has anoxygen-dominated atmosphere with a significant amount of carbon (C = $0.10 \pm0.05$, O = $0.90 \pm 0.05$, mass fractions). Its mixed absorption+emission linespectrum exhibits photospheric absorption lines from O V and O VI as well as OIII and O IV emission lines that are formed in a radiation-driven wind with amass-loss rate of the order of $10^{-8}$ $M_\odot$ yr$^{-1}$.Spectroscopically, J0546$+$0836 is a [WC]-PG1159 transition-type pre-whitedwarf. The second object (J0927$-$6335) is a PG1159-type white dwarf with apure absorption-line spectrum dominated by C III/C IV and O III/O IV. We find$T_\mathrm{eff}$ = 60,000 $\pm$ 5000 K, log g = $7.0 \pm 0.5$, and a carbon-and oxygen-dominated atmosphere with C = $0.47 \pm 0.25$, O = $0.48 \pm 0.25$,and possibly a minute amount of helium (He = $0.05 \pm 0.05$). Comparison withpost-AGB evolutionary tracks suggests a mass of $M\approx0.5$ $M_\odot$ forboth objects, if such tracks can safely be applied to these stars. We find thethird object (J1332$-$3541) to be a relatively massive ($M=0.89 M_\odot$)hydrogen-rich (DAO) white dwarf with $T_\mathrm{eff}$ = 65,657 $\pm$ 2390 K,log g = $8.38 \pm 0.08$, and abundances H = $0.65 \pm 0.04$ and He = $0.35 \pm0.04$. We discuss our results in the context of the "dynamically drivendouble-degenerate double-detonation" (D$^6$) scenario proposed for the originof these stars.

The photospheres of the hottest fastest stars in the Galaxy