EVOLUTION OF A PRIMORDIAL BLACK-HOLE INSIDE A ROTATING SOLAR-TYPE STAR

We study the accretion-driven evolution of a primordial black hole at the centre of the Sun or any solar-type star. We show that, if the sta r's rotation is small enough for the accretion to be radial, then the black hole grows at the fast 'Bondi' rate [so the remaining life of th e star is 50(M(.)/M)s when the hole's mass is M], and the flow produce s luminosity at the rather low 'Flammang' level [L(F1) = 2.5 x 10(34)( M/M(.)) erg s(-1)]. As a result, the growing hole has no influence on the star's external appearance until tens of minutes before it complet ely destroys the star. We also examine the effects of a solar-like rot ation. If the inflowing fluid elements retain their angular momentum, the accretion will centrifugally hang up and form an 'accretion torus' near the growing hole, until the hole's mass, M, reaches M(+) = 10(-3 )M(.); thereafter, the inflow will be radial. We show that, when M < M (v) = 10(-11)M(.), molecular viscosity removes angular momentum fast e nough to prevent such an accretion torus forming. Similarly, magnetic torques preclude the formation of a torus when M < M(B) + 6 x 10(-8)B( 0)(3/4)M(.), where B-0 is the magnetic field strength at the star's ce ntre. For M above these regimes but below M(+), an accretion torus pro bably does form, and may increase the luminosity L above L(F1) and slo w the flow M below Bondi. However, until at most 3 d before the star i s destroyed, L cannot increase by more than about an order of magnitud e, because a higher L would produce strong convection outside the accr etion torus and the resulting turbulent viscosity would remove so much angular momentum from the flow as to prevent the torus from forming i n the first place. As a corollary, the 'solar neutrino problem' cannot be solved by postulating a small black hole at the Sun's centre.