1.4 Stellar Multiplicity
Gravity is a long range force. So concept of isolated star or binary systems or multiple systems are somewhat complicated. In many cases the closest neighbour of a star is situated at a distance much closer than the average separation between stars in a typical neighbourhood. Life time of such combination of stars is comparatively very long. Perhaps there may be seen the existence of some clusters containing even thousands to million stars or a small number of stars. They also live long but less than a binary system. Hence multiple systems are actually the midway between these clusters and binarysystems 11.
Stellar multiplicity comes to be an unquestionable feature of star formation process. The total frequency of binary and multiple systems, distribution of mass ratio and orbital periods are the most important factors of stellar evolutionin binary systems 12.
In the case of spectroscopic binaries, orbital period of a binary system may be easily calculated.The period distribution may be parametrized using a power law as f (P) ? P?, where P represents the orbital period and in most cases ? is taken as -1. A log- normal representation with P and a width for the distribution ?logPis also used by many authors.
The mass ratio q=M_sec/M_prim ?1 can be obtained from the flux ratio. The mass ratio distribution is flat for most of the range of primary masses and has an even weaker dependence on binary separation. The lowest mass ratio can be seen on the cores, in which most of the angular momentum is thrown away. As we go further into the lowest mass systems, steepness of the mass ratio distribution appears to be increasing. It acts as a restriction to the formation of the lowest mass systems 13.
Since most configurations of three body systems have inherent instabilities, there is greater probability for their break up into a binary and a third body. The theory which describes the three body break up process states that the probability of a final state is proportional to the volume of the phase space that allows this particular final state. This results in the expression, f (e) = 2e, where e is the eccentricity and f(e) is the distribution of eccentricity of the remnant binaries 12. Hence eccentricity is another important parameter in stellar evolution.
Multiplicity frequency of main sequence stars is a steep, monotonic function of stellar mass.Multiplicity frequency is seen to be increasing with increase in primary mass implying that high mass cores produce more fragments on average, because initially they carry more jeans masses, where multiplicity arises due to breakup 13.
The statement that “most stellar systems formed in the Galaxy are likely single and not binary” (Lada 2006) is not yet confirmed. But due to the greater number of low mass stars, most field stars are treated as single stars. Hence these fall in a region of less dense low mass star distribution 14.
In going from brown dwarfs to solar type stars multiplicity seems to be a smooth function of primary mass. By avoiding the case of short period spectroscopic binaries the above sentence is applicable to intermediate and high mass starstoo 13.

1.5 Initial Mass Function
The most important parameter describing the structure and evolution of a star is its mass. Distribution of stellar masses during birth is known as the Initial Mass Function (IMF) 15. IMF can be defined as the distribution of stellar mass formed during a star formation process in a given volume of space. Since masses of stars differs from each other, it is important to calculate the number of stars in a particular mass range to study the variation of IMF. Unfortunately mass of a star is very difficult to calculate 16. So it is calculated through an indirect way. Using mass – luminosity relation, conversion is possible from a single star luminosity function to a mass function. The number of stars formed in a certain range of mass and amount of mass accumulated in a star can be inferred from the conversion. The distribution of stellar systems and the importance of binary stars in star formation events can be gained from the comparison of single star luminosity function with system luminosity function 17.
IMF can be defined as the number of stars per unit volume per unit logarithmic mass,
From simple power law,

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EdwinSalpeter was the one who put forward the concept of IMF in 1955.
In terms of logarithmic mass,
?(logm)dlogm ~ m^(-?)
According to Salpeter,
Where ?=?-1
m: mass of a star
N: number of stars in the logarithmic mass range log (m) and log (m) + d (log (m))
Salpeter derived the mass function of Galactic field stars of masses 0.4M?


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