How Does Age, Mass, and Magnitude Mathematically Relate in Star Clusters?

[randa177]

I've been searching inliterature/trying to solve on my own this dilemma:

What is the mathematical relation that describes the age, mass and apparent magnitude (V) of a star cluster?

I know the mass luminosity relation L=M³
I also know that m = - 2.5 log L
And we can get the age from the HR diagram... but how does it mathematically relate to the magnitude (V) and mass... any idea?

(The reason I am asking this is that the modern stellar synthesis models can create the plot of V vs log age for different masses, but what is the relation governing these factors? )

 

[randa177]

Does my question make sense?

 

[harcel]

Yes, it does. At least most of it. The first relation you quote (L~M^3) is wrong, it holds for stars, not for star clusters. For a star cluster (of sufficiently high mass, higher than about 1000 Msun) the mass and luminosity are linearly proportional to each other (makes sense right? N times more stars, N times more light).

We can get the age from the HR diagram? I presume you mean you can estimate the age from the HR diagram main-sequence turn-off point. That is true. But if you have all stars in an HR diagram too, you might also have its V magnitude (unless it's in bolometric luminosities).

To get the plot you are referring you need to convolve all spectra of all stars (or the composite spectrum of all stars) with the V-band filter profile and compare that to a reference spectrum that belongs to the magnitude system (flat for AB magnitudes, Vega's spectrum for vegamags and so on).

Let me know if you need more info!

 

[randa177]

Yes, it does. At least most of it. The first relation you quote (L~M^3) is wrong, it holds for stars, not for star clusters. For a star cluster (of sufficiently high mass, higher than about 1000 Msun) the mass and luminosity are linearly proportional to each other (makes sense right? N times more stars, N times more light).

We can get the age from the HR diagram? I presume you mean you can estimate the age from the HR diagram main-sequence turn-off point. That is true. But if you have all stars in an HR diagram too, you might also have its V magnitude (unless it's in bolometric luminosities).

To get the plot you are referring you need to convolve all spectra of all stars (or the composite spectrum of all stars) with the V-band filter profile and compare that to a reference spectrum that belongs to the magnitude system (flat for AB magnitudes, Vega's spectrum for vegamags and so on).

Let me know if you need more info!

It took me a while to reply back, but I am still struggling with this question. The problem si that I don't have the spectra of all stars (I actuall don't have any spectrum of any star in the cluster). Is there another way to do it?