Powerlaw approximation

The luminosity evolution of a single age stellar population can be well approximated by a powerlaw of the form

L ∝ (t-t*)-κ,
with t* the time of formation of the stellar population. The powerlaw approximation holds to a few percent for all common passbands and ages >1 Gyr; its accuracy is demonstrated below for the V and K bands. The coefficient of the powerlaw depends on the passband, the IMF, and the metallicity.

The coefficients used in the calculator were derived from the Bruzual & Charlot (2003) models, using a Salpeter IMF, Solar metallicity, and the Padova (1994) tracks. Different filters, metallicities, or IMF's can be accomodated as follows:
1) determine the powerlaw coefficient by plotting log(M/L) versus log(age)
2) enter the coefficient directly in the box next to the Help link.

Advantages of the powerlaw approximation are that it explicitly eliminates any dependence on H0; that different models can be easily added (through determination of their values for κ); and that it offers computational simplicity. The disadvantage is that the approximation is not valid for very young ages. Note that such ages never enter the computation if the time interval for morphological transformation to early-type is set at ~ 0.1 x the age of the Universe, or larger.

The black curves are Bruzual & Charlot (2003) models for a Salpeter IMF, Solar metallicity, and the Padova (1994) tracks. Red lines are best-fit powerlaws to the evolution at ages > 1.4 Gyr. The coefficient of the best fit powerlaw is listed in the top left.