Galactic Stellar Halo Luminosity Function
We measure the luminosity function (LF) of the Milky Way's stellar halo, using a magnitude complete, distance limited sample of stars from $Gaia$ DR3. Stars with high transverse velocities are selected, to isolate a high purity sample of the local halo. We adopt a cutoff transverse velocity of 250$\,$km$\,$s$^{-1}$, yielding 24,471 stars, and compute the halo LF, taking into account the effects of sample selection criteria. The LF displays similar features as are found in the well-probed LF of nearby, metal-rich disk stars, showing a strong peak at an absolute magnitude of around $M_G=10$, and a flattening near $M_G\sim7$ (Wielen dip). The $Gaia$ sample yields the first measurement of the LF continuously from the dimmest main sequence halo stars (subdwarfs) at an absolute $M_G$ magnitude near 13 mag to bright giants at $M_G\sim-3$. We obtain a local stellar halo number density of $1.7\times10^{-4}$ stars$\,$pc$^{-3}$ and disk-to-halo ratio by stellar number density of 480:1. We convert the $Gaia$ $G$ band measurements for our sample stars to Johnson-Kron-Cousins $V$ band, compute the $V$-band halo LF, and compare it to previous studies published over many decades that cover a wide range of techniques used. We discuss applications of the LF to the measurement of the luminosity and stellar mass of the Milky Way halo.