# Wind-fed Accretion and White Dwarf stars

Can a White Dwarf star in a binary system accrete matter via the Wind-fed accretion process?

• There are various stages of a white dwarf star - and most of them are binary systems. It depends if the second star transfers mass to white dwarf - if it does it will most likely create a super nova. It depends upon the meaning of "wind-fed" accretion. – Cinaed Simson Apr 15 '19 at 22:13

Wind fed accretion would work for a white dwarfs as it would for any other star or compact object of similar mass.

As a rough figure, you could argue that a white dwarf will accrete the material from within a Bondi-Hoyle radius $$R_a \simeq \frac{2GM_{\rm WD}}{v_r^2}\ ,$$ where $$v_r$$ is the velocity of the wind material with respect to the white dwarf (either the wind speed or the orbital speed, whichever is larger).

The rate of mass gained by the white dwarf is then $$\dot{M}_{\rm WD} \simeq \pi R_a^2 v_r\ ,$$ where $$\rho$$ is the density of wind material near the white dwarf, which in turn depends on the mass loss rate of the other star and the separation of the two stars.

You will see that the radius of the white dwarf does not come into these expressions at all. That is, a typical 0.6 solar mass white dwarf will accrete just as much mass as any other 0.6 solar mass star.

However, compact objects involving neutron stars or black holes are far more likely to be observed as wind-fed accretion sources because: (I) They are more like 1.4 solar masses or more and have larger Bondi-Hoyle radii. (II) Their smaller radii means material picks up more kinetic energy as it falls into their potential wells. This means the gas gets very much hotter and becomes a source of X-rays, making them easier to spot. They are also commonly found as companions to youthful, high mass stars with very high mass loss rates. This option isn't open to white dwarfs, since any companion must necessarily be quite old, to accommodate the white dwarf's evolutionary timescale.

There can be examples of wind-fed white dwarf accretion found among the symbiotic binary systems, where the wind from a companion, low-mass red giant is slow, dense and easy to accrete.