<p>If you had <span class="math-container">$N$</span> stars with age <span class="math-container">$t_i$</span>, mass <span class="math-container">$m_i$</span> and luminosity in a certain band <span class="math-container">$L_i$</span>, the mass weighted age would be</p>
<p><span class="math-container">$$\left&lt; t\right&gt;_m = \frac{\sum_1^N m_i t_i}{\sum_1^N m_i},$$</span></p>
<p>while the light weighted age would be</p>
<p><span class="math-container">$$\left&lt; t\right&gt;_L = \frac{\sum_1^N L_i t_i}{\sum_1^N L_i}.$$</span></p>

CC BY-SA 4.0
2022-08-16T20:18:05.473Z
2022-08-16T20:18:05.473Z
Prallax
<p>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 &quot;weighted&quot; just mean measured, e.g age estimated from mass measurements vs estimated from light measurements?</p>
<p>An example of the usage can be found here: <a href="https://ned.ipac.caltech.edu/level5/Sept14/Conroy/Conroy4.html" rel="nofollow noreferrer">ned.ipac.caltech.edu/level5/Sept14/Conroy/Conroy4.html</a></p>

CC BY-SA 4.0
2022-08-12T23:18:46.427Z
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 https://ned.ipac.caltech.edu/level5/Sept14/Conroy/Conroy4.html
James K
CC BY-SA 4.0
2022-08-12T23:38:16.993Z
Thank you @JamesK, and yes, that is a good example of a text which uses the term and which I don't fully understand.
CuriousCosmos
CC BY-SA 4.0
2022-08-17T08:41:46.783Z
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
planetmaker
<galaxy><mass><age><stellar-population>
What is mass-weighted age?
CuriousCosmos
# What is mass-weighted age?

(Asked by: username_0 on 2022-08-12)

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](https://ned.ipac.caltech.edu/level5/Sept14/Conroy/Conroy4.html)

**Tags:** galaxy, mass, age, stellar-population
> **Comments:**
> **username_1**: 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 https://ned.ipac.caltech.edu/level5/Sept14/Conroy/Conroy4.html  
> **username_0**: Thank you @JamesK, and yes, that is a good example of a text which uses the term and which I don't fully understand.  
> **username_2**: 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  

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## 1 answers

### Answer by username_3 on 2022-08-16. Score: 4

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

$$\left< t\right>\_m = \frac{\sum\_1^N m\_i t\_i}{\sum\_1^N m\_i},$$

while the light weighted age would be

$$\left< t\right>\_L = \frac{\sum\_1^N L\_i t\_i}{\sum\_1^N L\_i}.$$


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