# Spherical Accretion (Bondi Model)

I have a question. I studied Bondi's model for spherical accretion. I know the assumptions made in the model are big and that they are rarely representative of what happens in astrophysics. What I wanted to ask is: is there a situation that suits this model even approximately, or it is a total idealization? Is there always an accretion disk, or may there be a situation where the accretion is spherical?

## 1 Answer

One example is that of the core of a Thorne–Żytkow object, or TŻO. It consists of a high-metallicity M class red giant or supergiant with a neutron star at its core. Generally, TŻOs form when a neutron star collides with a suitable red giant/supergiant. The neutron star settles into the center of the other star.

Eventually, the main source of energy for the TŻO comes from gravitational contraction of the envelope as gas from inside the star falls toward the surface of the neutron star. In this case, the change in mass $\dot{M}$ of the neutron star is (see Thorne & Żytkow (1977)): $$\dot{M}=4\pi r^2\rho v_{\text{in}}\mathscr{R}\tag{1}$$ The difference between $(1)$ and the underlying equation behind Bondi's formula is the factor of $\mathscr{R}$, a correction factor for relativistic redshift, which is given by $$\mathscr{R}=\sqrt{1-\frac{2GM_{tc}}{c^2r}}\tag{2}$$ where $M_{tc}$ is the total core mass. This formula may look familiar; it comes from the Schwarzschild metric. You need $\mathscr{R}$ to properly describe accretion onto any compact object. This is something needed not just in the case of TŻOs. However, Bondi's formula can be used nonetheless, if you multiply by $\mathscr{R}$.

That said, Bondi accretion can be used without relativistic compensations in a number of ways:

• Mass transfer in certain binary systems, where an envelope moves matter from one star to another.
• Protostellar clusters, where many young protostars move about, accreting gas.
• Galaxy clusters, where galaxies move through the intergalactic medium (IGM).