This contribution describes the difficult task of inferring the IMF from local star-count data , by discussing the mass–luminosity relation , unresolved binary , triple and quadruple systems , abundance and age spreads and Galactic structure , all of which must be accounted for properly for the results to be meaningful .
A consensus emerges that the local IMF may be represented by a two-part power-law , with indices \alpha = 1 - 1.5 for stars with mass { { { { m \mbox { $ \mathrel { \mathchoice { { \mbox { \lower 2.15 pt \vbox { \halign { \cr } $% \displaystyle \hfil < $ \cr$ \displaystyle \hfil \sim$ } } } } } { { \mbox { \lower 2.15 pt \vbox% { \halign { \cr } $ \textstyle \hfil < $ \cr$ \textstyle \hfil \sim$ } } } } } { { \mbox { \lower 2.1 % 5 pt \vbox { \halign { \cr } $ \scriptstyle \hfil < $ \cr$ \scriptstyle \hfil \sim$ } } } } } { { % \mbox { \lower 2.15 pt \vbox { \halign { \cr } $ \scriptscriptstyle \hfil < $ \cr$% \scriptscriptstyle \hfil \sim$ } } } } } } $ } 0.5 M _ { \odot } , and the Salpeter value \alpha = 2.3 for more massive stars , but some uncertainties remain .
Notable is also that the sensitivity of the stellar luminosity function ( LF ) to the derivative of the mass–luminosity relation is very evident in the ( local ) Hipparcos and HST , open-cluster and globular-cluster LFs , thus allowing tests of stellar structure theory .
The upcoming astrometry space missions DIVA and GAIA will undoubtedly lead to significant advances in this field .