Mathematical Principles of Theoretical Physics

1.10 Supernovae Explosion and AGN Jets.

1.10 Supernovae Explosion and AGN Jets

Supernovae explosion and the active galactic nucleus (AGN)jets are among the most impor-
tant astronomical phenomena, which are lack of reasonable explanation.
Relativistic, magnetic and thermal effects are main ingredients in astrophysical fluid dy-
namics, and are responsible for many astronomical phenomena. The thermal effect is de-
scribed by the Rayleigh number Re:

(1.10.1) Re=

mGr 0 r 1 β

κ ν

T 0 −T 1

r 1 −r 0

,

whereT 0 andT 1 are the temperatures at the bottom and top of an annular shellregionr 0 <
r<r 1 ; see e.g. (7.1.74) for other notations used here.
Based on our theory of black holes, including in particular the incompressibility and
closedness of black holes, the relativistic effect is described by theδ-factor:

(1.10.2) δ=
2 mG
c^2 r 0

.

wheremis the mass of the core 0<r<r 0.
Consider e.g. an active galactic nucleus (AGN), which occupies a spherical annular shell
regionRs<r<R 1 , whereRsis the Schwarzschild radius of the black hole core of the galaxy.
Thenr 0 =Rsand theδ-factor isδ=1. The relativistic effect is then reflected in the radial
force

Fr=

ν

2 α

∂

∂r

(

1

α

dα

dr

Pr

)

, α=

(

1 −

Rs

r

)− 1

,

which gives rise to a huge explosive force nearr=Rs:

(1.10.3)

ν

1 −Rs/r

R^2 s

r^4

Pr.

The relativistic effect is also reflected in the electromagnetic energy:

ν 0

2 α

∂

∂r

(

1

α

dα

dr

Hr

)

,

which consists of a huge explosive electromagnetic energy nearr=Rs:

(1.10.4)

ν 0

1 −Rs/r

R^2 s

r^4

Hr.

The basic mechanism of the formation of AGN jets is that the radial temperature gradient
causes vertical B ́enard convection cells. Each B ́enard convection cell has a vertical exit,
where the circulating gas is pushed by the radial force, and then erupts leading to a jet.
Each B ́enard convection cell is also an entrance, where the external gas is attracted into the
nucleus, is cycloaccelerated by the radial force as well, goes down to the interior boundary
r=Rs, and then is pushed toward to the exit. Thus the circulation cells form jets in their exits
and accretions in their entrances.