SELF

58

O.N. Karavashkina and S.B. Karavashkin

Fig. 2.7. The diagram explaining Rayleigh - Taylor instability [1, p. 54, Fig. 19].

Researches show the interstellar space not so even and neutral medium as it could seem from far distance. "There are, first, the regions of neutral hydrogen H I and regions of ionised hydrogen H II whose kinetic temperature differs by two orders. There are relatively dense clouds with the concentration of gas particles exceeding few thousands per cubic centimetre, and quite rarefied medium between the clouds, where the concentration does not exceed 0,1 particle per 1 cm³ " [1, p. 53]. This all makes the interstellar medium quite heterogeneous. We have also account that there in space exist heterogeneities of magnetic fields - so-called potential wells, or Rayleigh - Taylor heterogeneities (see Fig. 2.7). It is believed that atoms of interstellar gas flowing to the region of smaller pressure or temperature polarise and can move in space only along magnetic force lines. Encountering in their way such field well, atoms accumulate in it to compensate the heterogeneity. Just so the denser clouds - gas-dust complexes - originate. Having reached definite densification, they condense into a star or an assemblage of stars; it is supposed that we are observing such phenomenon in Serpens (see Fig. 2.5). This picture can also be an example that not always the Rayleigh - Taylor potential wells can cause the densification. Besides the frontal densification, in that picture we see, how the region of densification divides along the front.

Well, but which forces can make this extremely rarefied medium to condensate into a star or even a star assemblage? The strength of galaxy magnetic field per se is not so high, so however extensive would be the heterogeneity, it would be insufficient, the more if the cloud compensates it.

After Shklovsky, the nebula can densify into a protostellar cloud even without any external cause, only under affection of gravitational attraction of the sum of all particles of gas and dust composing it. Shklovsky provides this supposition with the following computation.

"Suppose, we have some cloud of the radius R whose density and radius R are constant. The condition at which the cloud will compress under affection of its own gravitation is the negative sign of the total energy of cloud. This last consists of the negative gravitational energy W_g of interaction of all particles forming the cloud and of the positive thermal energy of these particles W. The negative sign of total energy means, the gravity forces tending to compress the cloud exceed the forces of gas pressure tending to scatter this cloud in all the surrounding space. Then we have

where A = 8,83*10⁷erg/mol*K , is the molecular mass, and is the average density of cloud. At the same time the gravity energy is

We see that W. at the constant density of cloud and temperature T grows with R as R³, whilst W_g R⁵   , i.e. it grows with R much faster. Consequently, at the given and T there exists such R₁ that at R > R₁ the cloud will inevitably compress under affection of its own gravity. When the mass M has been given, we can determine R₁ as

In this case (i.e., if the mass and temperature of the cloud have been given), if the size of cloud R < R₁, it will compress.

It is easy to make sure that "usual" clouds of interstellar gas with M M and R 1 parsec will not compress by their own gravity, but gas-dust complexes with M 10³ - 10⁴ M , T 50^o  and radius about tens parsecs will … Consider the case when the cloud mass is equal to the mass of Sun, and its temperature is 10 K. Then it follows from (2.1) that such cloud will compress, if its radius is less than 0,02 parsec. Hence, the density of such cloud will be 2*10 ^{- 18} g/cm³, and the gas concentration in it 10⁶ cm ^{- 3}- quite considerable value. But if the cloud mass is 10 Solar masses, we can check that the average concentration of the gas particles at which the cloud starts compression will be well less, 10⁴ cm ^{- 3} … we do meet the clouds with such concentration of gas" [1, p. 56- 57].

Shklovsky gives the examples of gas-dust complexes in which we now observe the star formation: "The mass of giant gas-dust complex Sagittarius B achieves 3*10 ⁶  solar masses, and its size is up to 50 pc. The concentration of molecular hydrogen in such clouds achieves few thousands per cubic centimetre. In the most dense clouds (e.g., in Orion nebula) the concentration of molecular hydrogen achieves 10⁷ cm ^{- 3}. We can notice that such high concentration puts such clouds as if between usual clouds of interstellar medium and extensive atmospheres of red giant stars" [1, p. 64].

Since the energy balance substantiated by Shklovsky seems to be inevitably rough but enough convincing, this leads us to choice the condensation beginning for our (some distinguishing from the conventional) model of star formation. This does not mean that we deny all other possibilities. But the star to form however otherwise, there first have to turn on the conditions of energy balance as Shklovsky described. We should not forget, in case of explosive beginning the star that originates a new star has already to exist, but it has to origin in some way, too. Shklovsky's calculation just answers this question, doing not denying the rest possibilities. And this calculation is important for us also because it allows us to follow the process from the very beginning.