Mass-Luminosity Relationship for Main Sequence Stars

Based on years of painstaking observations of binary star systems to deduce the masses of stars and distance determinations to find the luminosities of stars, a Mass-Luminosity Relationship for Main Sequence stars has been found:

    Roughly speaking,

      L/LSun ~ [M/MSun]β.

    According to the figure,

    Mass Range (Msun)

    Exponent, β

    100

    1.6

    10

    3.1

    1

    4.7

    0.1

    2.7

Using the Mass-Luminosity relation, we infer that the least massive stars are at the lower right hand part of the Main Sequence and that the most massive stars are at the upper left hand part of the Main Sequence. The Sun, a G2V star sits around the middle of the Main Sequence.

The fact that the luminosity depends so strongly on the mass of a star has great implications for how long stars live on the Main Sequence. We define,

τ = (Mc2)/L ∝ M1-β.

Massive stars have very short lifetimes compared to the Sun (which has a lifetime on the order of 9.84 billion years or so), as we will see later. For example, a star 12 times as massive as the Sun has a lifetime of 16.0 million years. A star 10 % the mass of the Sun has a lifetime of 10 trillion years, a lifetime greater than the current age of the Universe!