Two varieties of the universal stellar initial mass function ( IMF ) viz. , the Kroupa and the Chabrier IMF , have emerged over the last decade to explain the observed distribution of stellar masses .
The possibility of the universal nature of the stellar IMF leads us to the interesting prospect of a universal mode of star-formation .
It is well-known that turbulent fragmentation of gas in the interstellar medium produces a lognormal distribution of density which is further reflected by the mass-function for clumps at low and intermediate masses .
Stars condense out of unstable clumps through a complex interplay between a number of dynamic processes which must be accounted for when tracing the origin of the stellar IMF .
In the present work , applying the theory of gravitational fragmentation we first derive the mass function ( MF ) for clumps .
Then a core mass function ( CMF ) is derived by allowing the clumps to fragment , having subjected each one to a random choice of gas temperature .
Finally , the stellar IMF is derived by applying a random core-to-star conversion efficiency , \epsilon , in the range of 5 % -15 % to each CMF .
We obtain a power-law IMF that has exponents within the error-bars on the Kropua IMF .
This derived IMF is preceded by a similar core mass function which suggests , gravoturbulent fragmentation plays a key role in assembling necessary conditions that relate the two mass-functions .
In this sense the star-formation process , at least at low redshifts where gas cooling is efficient , is likely to be universal .
We argue that the observed knee in the CMF and the stellar IMF may alternatively be interpreted in terms of the characteristic temperature at which gas in potential star-forming clouds is likely to be found .
Our results also show that turbulence in star-forming clouds is probably driven on large spatial scales with a power-spectrum steeper than Kolmogorov-type .