<p>There is no clearly-defined "turn-off" magnitude. Stars move from the zero age main sequence (roughly speaking, where core hydrogen burning begins to dominate the luminosity) to the terminal age main sequence (where the core hydrogen runs out) relatively slowly, increasing in luminosity as they do so. Their evolution then accelerates redward in the colour magnitude diagram. The turn-off is roughly the most luminous star for which this acceleration in evolution is yet to occur, but this is confused/blurred by observational uncertainties, binarity, differential reddening and spreads in age and rotation rate.</p>

<p>In practice what you do if you really want to do a proper job of estimating the age, with uncertainties, is you do a population synthesis (including binaries and observational uncertainties) for clusters of stars with a variety of ages. You then compare these with the observations using maximum likelihood or Bayesian techniques (e.g. <a href="https://arxiv.org/abs/astro-ph/0609764" rel="nofollow noreferrer">Naylor &amp; Jeffries 2006</a>).</p>

CC BY-SA 3.0
2017-08-23T20:14:39.280Z
Thank you, I got pretty decent results just by estimating the magnitude at the turn off point, but was wondering if I could improve it somehow. This would certainly do the job, but it's too advance for what I'm doing!
Pikabu
CC BY-SA 3.0
2017-08-23T20:42:08.973Z
@Pikabu Yes, once you realise there could be binaries, then estimating by eye is ok to get an answer, however rigorous methods are needed to estimate uncertainties.
ProfRob
CC BY-SA 3.0
2017-08-23T19:33:36.523Z
2017-08-23T19:33:36.523Z
ProfRob
<p>So I have a CMD diagram and on the left, I have apparent magnitude and at the bottom, I have the color index. I would just estimate the magnitude of stars leaving the main sequence and continue from there, however, I was wondering if there's a way to do it more accurately?</p>

<p>I would take stars between certain magnitudes and calculate the average magnitude, but again, I'm estimating from where to where the MSTO point is... </p>

<astrophysics>
How do you determine the apparent magnitude of the stars leaving main sequence with CMD diagrams?
Pikabu
# How do you determine the apparent magnitude of the stars leaving main sequence with CMD diagrams?

(Asked by: username_0 on 2017-08-23)

So I have a CMD diagram and on the left, I have apparent magnitude and at the bottom, I have the color index. I would just estimate the magnitude of stars leaving the main sequence and continue from there, however, I was wondering if there's a way to do it more accurately?

I would take stars between certain magnitudes and calculate the average magnitude, but again, I'm estimating from where to where the MSTO point is...

**Tags:** astrophysics

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## 1 answers

### Answer by username_1 on 2017-08-23. Score: 1

There is no clearly-defined "turn-off" magnitude. Stars move from the zero age main sequence (roughly speaking, where core hydrogen burning begins to dominate the luminosity) to the terminal age main sequence (where the core hydrogen runs out) relatively slowly, increasing in luminosity as they do so. Their evolution then accelerates redward in the colour magnitude diagram. The turn-off is roughly the most luminous star for which this acceleration in evolution is yet to occur, but this is confused/blurred by observational uncertainties, binarity, differential reddening and spreads in age and rotation rate.

In practice what you do if you really want to do a proper job of estimating the age, with uncertainties, is you do a population synthesis (including binaries and observational uncertainties) for clusters of stars with a variety of ages. You then compare these with the observations using maximum likelihood or Bayesian techniques (e.g. [Naylor & Jeffries 2006](https://arxiv.org/abs/astro-ph/0609764)).

> **Comments:**
> **username_0**: Thank you, I got pretty decent results just by estimating the magnitude at the turn off point, but was wondering if I could improve it somehow. This would certainly do the job, but it's too advance for what I'm doing!  
> **username_1**: @Pikabu Yes, once you realise there could be binaries, then estimating by eye is ok to get an answer, however rigorous methods are needed to estimate uncertainties.  

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