Neutrinos are produced during stellar evolution by means of thermal and thermonuclear processes. We model the cumulative neutrino flux expected at Earth from all stars in the Milky Way: the Galactic stellar neutrino flux (GS$ν$F). We account for the star formation history of our Galaxy and reconstruct the spatial distribution of Galactic stars by means of a random sampling procedure based on Gaia Data Release 2. We use the stellar evolution code $\texttt{MESA}$ to compute the neutrino emission for a suite of stellar models with solar metallicity and zero-age-main-sequence mass between $0.08M_\odot$ and $100\ M_\odot$, from their pre-main sequence phase to their final fates. We then reconstruct the evolution of the neutrino spectral energy distribution for each stellar model in our suite. The GS$ν$F lies between $\mathcal{O}(1)$ keV and $\mathcal{O}(10)$ MeV, with thermal (thermonuclear) processes responsible for shaping neutrino emission at energies smaller (larger) than $0.1$ MeV. Stars with mass larger than $\mathcal{O}(1\ M_\odot)$, located in the thin disk of the Galaxy, provide the largest contribution to the GS$ν$F. Moreover, most of the GS$ν$F originates from stars distant from Earth about $5-10$ kpc, implying that a large fraction of stellar neutrinos can reach us from the Galactic Center. Solar neutrinos and the diffuse supernova neutrino background have energies comparable to those of the GS$ν$F, challenging the detection of the latter. However, directional information of solar neutrino and GS$ν$F events, together with the annual modulation of the solar neutrino flux, could facilitate the GS$ν$F detection; this will kick off a new era for low-energy neutrino astronomy, also providing a novel probe to discover New Physics.
