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Astron. Astrophys. 327, 57-60 (1997)

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3. Result

3.1. Several physical parameters of different regimes

From Eqs. (1)-(13), we get

[EQUATION]

Where [FORMULA] is the efficiency of mass-energy conversion divided by the canonical value 0.1 ( 1990II)

If we adopt the different opacities from different regimes as in the work by CSD(1990II), then from Eq. (14), we get

[EQUATION]

Here [FORMULA] has the same meaning as in CSD's (1990II), [FORMULA] is the luminosity in [FORMULA], [FORMULA] is the central density in [FORMULA], and X is a dimensionless quantity as in CSD's [FORMULA] (1990II), that is

[EQUATION]

where [FORMULA] is the Schwarzschild radius. According to CSD (1990II), we have

[EQUATION]

Results obtained from equ.14 to 18 are given in Table 1, and illustrated in Fig. 1-3, which display [FORMULA], [FORMULA], H and [FORMULA] as functions of the radius X for the different regimes. [FORMULA], [FORMULA], [FORMULA], [FORMULA] all being set equal to unity for simplicity, and we let [FORMULA], [FORMULA]. The scale height [FORMULA] is in [FORMULA], the central density [FORMULA] is in [FORMULA], and

[EQUATION]

The solid lines correspond to the case with [FORMULA], and dashed lines correspond to the case with [FORMULA].

[TABLE]

Table 1

In regimes A, C, and E, the physical parameters have the same functional dependence, and differ only by constant multiplication factors. In these regimes, [FORMULA] changes with radius as [FORMULA], and changes with self-gravitation as [FORMULA]. [FORMULA] changes with radius as [FORMULA], and with self-gravitation as [FORMULA]. In regimes D and F, [FORMULA] is the same as in CSD's(1990II), but [FORMULA] differs with CSD's (1990II) because of self-gravitation and magnetic field, [FORMULA] is related to self-gravation as [FORMULA]. In regimes A, C, D, E and F, [FORMULA] changes uniformly with X as [FORMULA], and changes with self-gravitation as [FORMULA]. Fig. 1 shows that [FORMULA] decreases with increasing self-gravitation. Fig. 2 expresses that the thickness [FORMULA] becomes flat with increasing self-gravitation. This result is very similar to the work by Schneider(1996). Fig. 3 shows that the central density [FORMULA] increases with increasing self-gravitation.

[FIGURE] Fig. 1. The solid line corresponds to a=0, and the dashed line a=10.

[FIGURE] Fig. 2. Both the solid line and the dashed line hold the same meaning as Fig. 1.

[FIGURE] Fig. 3. Both the solid line and the dashed line hold the same meaning as Fig. 1.

3.2. Several typical radii of different regions and two important radii

We consider that the temperatures of two adjacent regions are the same.

Region 1, corresponding to regime A, for [FORMULA] with

[EQUATION]

Region 2, corresponding to regime C, for [FORMULA] with

[EQUATION]

Region 3, corresponding to regime D, for [FORMULA] with

[EQUATION]

Region 4, corresponding to regime E, for [FORMULA]

One important quantity is the radius [FORMULA], where the effective temperture is equal to [FORMULA] K.

It is given by

[EQUATION]

If we let [FORMULA] [FORMULA] 1, then

[EQUATION]

This value is greater than CSD's result (1990II) about 2 times, when we adopt a smaller value of a.

Another important quantity is the radius [FORMULA] which corresponds to a column density of [FORMULA], that is given by

[EQUATION]

It is easy to see that [FORMULA] is independent with self-gravitation(this is the same as CSD's result, 1990II), but is greater than CSD's result (1990II) about 1.54 times because of the magnetic field.

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© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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