<p>You can, in fact, differentiate between the crossings of the instability strip in certain types of variable stars. There have been quite a few evolutionary models devoted to this, and many, as well as scores of observations, show that the pulsational period $P$ of a Cepheid variable changes during each crossing. Look at, for instance, the period changes of 60 galactic Cepheids, shown in Figure 2 of <a href="http://cds.cern.ch/record/611292/files/0304053.pdf" rel="nofollow noreferrer">Pietrukowicz</a>:</p>

<p><a href="https://i.sstatic.net/NcIOI.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NcIOI.png" alt="enter image description here"></a></p>

<p>The first and third crossings occur when the star is evolving redwards (towards the right of the HR diagram), and show positive $\dot{P}$. The second crossing occurs when the stars are evolving bluewards (towards the left of the HR diagram), and show negative $\dot{P}$.</p>

<p>Models and observations by <a href="http://arxiv.org/pdf/1407.8098.pdf" rel="nofollow noreferrer">Neilson et al. (2014)</a> show the same thing (see Figure 1):</p>

<p><a href="https://i.sstatic.net/gD6Jt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/gD6Jt.png" alt="enter image description here"></a></p>

<p>The initial large period change indicates the first crossing, the smaller negative period change indicates the second, and the third less drastic increase indicates the third.</p>

<p>Similar indicators should be present in further crossings (fourth and fifth crossings in the later stages of core and shell helium burnings), and while the amplitude of $\dot{P}/P^2$ would likely be different, the same general positive/negative trends should be present. For more information, see <a href="http://adsabs.harvard.edu/abs/2004A&amp;A...423..335T" rel="nofollow noreferrer">Turner &amp; Berdnikov (2004)</a>.</p>

<p>There doesn't seem to be as much information on period changes in non-Cepheid variable stars, although <a href="https://arxiv.org/abs/1310.0533" rel="nofollow noreferrer">Smith (2013)</a> states that most Mira variables show only minute period changes, if any, and RR Lyrae variables may show period increases as they evolve redwards across the instability strip toward the end of their lives, as is the case with Cepheids. This, by the way, does not fully agree with evolutionary theory.</p>

CC BY-SA 3.0
2016-08-25T16:25:48.613Z
2016-08-27T17:02:43.513Z
2016-08-27T17:02:43.513Z
HDE 226868
<p>I was thinking about the possibility of determining what phase of evolution a variable star is in when it is located in the instability strip (say, a Cepheid object). Can you differentiate whether it is evolving toward the blue (in HR diagram) or back toward the giant branch?</p>

<p>I was looking at a figure recently in Carroll and Ostlie's Intro to Astrophysics text, which brought this to mind. It shows on the HR diagram where Cepheids lie, which is right in this strip.</p>

<stellar-evolution><hr-diagram>
Variables in the Instability Strip
Tilt-Shifted
# Variables in the Instability Strip

(Asked by: username_0 on 2015-03-29)

I was thinking about the possibility of determining what phase of evolution a variable star is in when it is located in the instability strip (say, a Cepheid object). Can you differentiate whether it is evolving toward the blue (in HR diagram) or back toward the giant branch?

I was looking at a figure recently in Carroll and Ostlie's Intro to Astrophysics text, which brought this to mind. It shows on the HR diagram where Cepheids lie, which is right in this strip.

**Tags:** stellar-evolution, hr-diagram

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## 1 answers

### Answer by username_1 on 2016-08-25. Score: 2 | Accepted answer

You can, in fact, differentiate between the crossings of the instability strip in certain types of variable stars. There have been quite a few evolutionary models devoted to this, and many, as well as scores of observations, show that the pulsational period $P$ of a Cepheid variable changes during each crossing. Look at, for instance, the period changes of 60 galactic Cepheids, shown in Figure 2 of [Pietrukowicz](http://cds.cern.ch/record/611292/files/0304053.pdf):

[![enter image description here](https://i.sstatic.net/NcIOI.png)](https://i.sstatic.net/NcIOI.png)

The first and third crossings occur when the star is evolving redwards (towards the right of the HR diagram), and show positive $\dot{P}$. The second crossing occurs when the stars are evolving bluewards (towards the left of the HR diagram), and show negative $\dot{P}$.

Models and observations by [Neilson et al. (2014)](http://arxiv.org/pdf/1407.8098.pdf) show the same thing (see Figure 1):

[![enter image description here](https://i.sstatic.net/gD6Jt.png)](https://i.sstatic.net/gD6Jt.png)

The initial large period change indicates the first crossing, the smaller negative period change indicates the second, and the third less drastic increase indicates the third.

Similar indicators should be present in further crossings (fourth and fifth crossings in the later stages of core and shell helium burnings), and while the amplitude of $\dot{P}/P^2$ would likely be different, the same general positive/negative trends should be present. For more information, see [Turner & Berdnikov (2004)](http://adsabs.harvard.edu/abs/2004A&A...423..335T).

There doesn't seem to be as much information on period changes in non-Cepheid variable stars, although [Smith (2013)](https://arxiv.org/abs/1310.0533) states that most Mira variables show only minute period changes, if any, and RR Lyrae variables may show period increases as they evolve redwards across the instability strip toward the end of their lives, as is the case with Cepheids. This, by the way, does not fully agree with evolutionary theory.


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