Bondi–Hoyle–Lyttleton accretion flow revisited: Analytic solution

摘要

The time-steady equation for a 1D wind accretion flow, i.e. the Bondi–Hoyle–Lyttleton (BHL) equation, is investigated analytically. The BHL equation is well known to have infinitely many solutions. Traditionally, the accretion radius has been assumed to be $2 extit {GM}/v_{infty }^{2}$, but its mathematical foundation has not been clarified because of the non-uniqueness of the solution. Here, we assume that the solution curves possess physically nice characteristics, i.e. velocity and line mass-density increase monotonically with radial distance. This condition restricts the accretion radius to the range $left (0.71 - 1.0 ight ) imes 2 extit {GM}/v_{infty }^{2}$. Further assumptions, specifically, that the solution curves for velocity and line mass-density are convex upward, restrict the accretion radius to $(0.84 - 0.94) imes 2 extit {GM}/v_{infty }^{2}$, and $0.90 imes 2 extit {GM}/v_{infty }^{2}$, respectively. Therefore, we conclude that the accretion radius is almost uniquely determined to be $0.90 imes 2 extit {GM}/v_{infty }^{2}$.