A New Flaring Black Widow Candidate and Demographics of Black Widow Millisecond Pulsars in the Galactic Field

We present the discovery of a new optical/X-ray source likely associated with the Fermi $\gamma$-ray source 4FGL J1408.6-2917. Its high-amplitude periodic optical variability, large spectroscopic radial velocity semi-amplitude, evidence for optical emission lines and flaring, and X-ray properties together imply the source is probably a new black widow millisecond pulsar binary. We compile the properties of the 41 confirmed and suspected field black widows, finding a median secondary mass of $0.027\pm0.003\,M_{\odot}$. Considered jointly with the more massive redback millisecond pulsar binaries, we find that the "spider" companion mass distribution remains strongly bimodal, with essentially zero systems having companion masses between $\sim0.07-0.1\,M_{\odot}$. X-ray emission from black widows is typically softer and less luminous than in redbacks, consistent with less efficient particle acceleration in the intrabinary shock in black widows, excepting a few systems that appear to have more efficient "redback-like" shocks. Together black widows and redbacks dominate the census of the fastest-spinning field millisecond pulsars in binaries with known companion types, making up $\gtrsim$80% of systems with $P_{\rm{spin}}<2\,\rm{ms}$. Similar to redbacks, the neutron star masses in black widows appear on average significantly larger than the canonical $1.4\,M_{\odot}$, and many of the highest-mass neutron stars claimed to date are black widows with $M_{\rm{NS}}\gtrsim2.1\,M_{\odot}$. Both of these observations are consistent with an evolutionary picture where spider millisecond pulsars emerge from short orbital period progenitors that had a lengthy period of mass transfer initiated while the companion was on the main sequence, leading to fast spins and high masses.