# What is mass-weighted age?

This seems to be a common term used in the field of stellar populations and galaxy evolution, but I can't find a good definition besides the fact that it is different from light-weighted age (a term I also don't understand). Does "weighted" just mean measured, e.g age estimated from mass measurements vs estimated from light measurements?

An example of the usage can be found here: ned.ipac.caltech.edu/level5/Sept14/Conroy/Conroy4.html

• Its always good to link to some examples of the use of this term, so answerers can see it in the context in which you are reading it. For example you could link to ned.ipac.caltech.edu/level5/Sept14/Conroy/Conroy4.html Aug 12, 2022 at 23:18
• Thank you @JamesK, and yes, that is a good example of a text which uses the term and which I don't fully understand. Aug 12, 2022 at 23:38
• generally 'weighted' implies some kind of scaling or adjustment by or for that property. I can imagine that in these context, stellar age is projected onto a range, say 0...1 for all stars. That means I kinda get their age relative to their respective life expectancy (which depends strongly on their mass). But I haven't read or seen these paper... so needs checking what they actually do Aug 17, 2022 at 8:41

If you had $$N$$ stars with age $$t_i$$, mass $$m_i$$ and luminosity in a certain band $$L_i$$, the mass weighted age would be
$$\left< t\right>_m = \frac{\sum_1^N m_i t_i}{\sum_1^N m_i},$$
$$\left< t\right>_L = \frac{\sum_1^N L_i t_i}{\sum_1^N L_i}.$$