Double White Dwarf Binaries in SDSS-V DR19 : A catalog of DA white dwarf binaries and constraints on the binary population

The fifth-generation Sloan Digital Sky Survey (SDSS-V) includes the first large-scale spectroscopic survey of white dwarfs (WDs) in the era of Gaia parallaxes. SDSS-V collects multiple exposures per target, making it ideal for binary detection. We present a search for hydrogen atmosphere (DA) double white dwarf (DWD) binaries in this rich dataset. We quantify radial velocity variations between sub-exposures to identify binary candidates, and also measure the orbital period for a subset of DWD binary candidates. We find 63 DWD binary candidates, of which 43 are new discoveries, and we provide tentative periods for 10 binary systems. Using these measurements, we place constraints on the binary fraction of the Galactic WD population with $< 0.4$ AU separations $f_{\mathrm{bin,0.4}} = 9\%$, and the power-law index of the initial separation distribution $\alpha = -0.62$. Using the simulated binary population, we estimate that $\leq 10$ super-Chandrasekhar binaries that merge within a Hubble time are expected in our sample. We predict that $\leq 5$ systems in our sample should be detectable via gravitational waves by LISA (Laser Interferometer Space Antenna), one of which has already been identified as a LISA verification source. We also estimate a total of about 10,000 - 20,000 LISA-detectable DWD binaries in the galaxy. Our catalog of WD+WD binary candidates in SDSS-V is now public, and promises to uncover a large number of exciting DWD systems.