<p>Here is a similar plot I adapted from <a href="https://arxiv.org/abs/1805.02079" rel="nofollow noreferrer">Clementini et al. (2019)</a>. It shows mean absolute <em>Gaia</em> <em>G</em>-magnitude (derived from <em>Gaia</em>-DR2 parallaxes) versus period for 998 <em>known</em> Cepheid variables. I guess that corresponds reasonably well with what you have done.</p>
<p>The dashed line was added by Clementini et al. They believe stars below this line are either not Cepheids or there is a problem with the <em>Gaia</em> parallaxes or the published periods. Interestingly, you have few of this population in your plot? So either that's an improvement with the <em>Gaia</em> DR3 data (I assume this is what you are using) or a cleaner parent catalogue of Cepheids.</p>
<p><a href="https://i.sstatic.net/y9QNW.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/y9QNW.png" alt="P-L relationship" /></a></p>
<p><strong>I have added the red line</strong> (by hand) - this appears to be the red line plotted in your diagrams. Clearly this is not a good fit, although I would say your gradient look approximately the same. The reason why this gradient does not agree with the literature you quote is that the plot here uses absolute G-magnitude (which is not the same as the V-band) and there has been no attempt to remove extinction from the sample, which will certainly increase scatter and decrease the intercept value by the average extinction of an object in the sample. It will also bias the gradient since the more luminous Cepheids tend to be further away and perhaps have more extinction - this will artificially flatten (reduce) the gradient. This effect is clearly seen in Fig.6 of Clementini et al. where they compare the P-L relationship of galactic Cepheids over the whole sky, that are affected by varying levels of extinction, with a P-L relation for Cepheids in the Large Magellanic Cloud that have a close-to-uniform level of extinction. The P-L relation for the latter is clearly steeper.</p>
<p>It is a mystery however as to why there seems to be an offset between the data you show and the data plotted in Clementini et al. (2019). Are you using the intensity-weighted mean <em>G</em> magnitude (known as int_average_g in the <em>Gaia</em> Cepheid tables) ?</p>

CC BY-SA 4.0
2023-09-02T09:54:48.073Z
Thank you! That was really helpful. And no, I'm using something called `phot_g_mean_mag` as in the data.
Ambica Govind
CC BY-SA 4.0
2023-08-28T13:05:37.787Z
2023-08-28T13:05:37.787Z
ProfRob
<p>I was trying to verify Leavitt's Law of Period Luminosity Relationships of Cepheid Variables using Gaia data. To do this I calculated the period using the Lomb Scargle Periodogram for 1450 stars and obtained this:
<a href="https://i.sstatic.net/4Zddb.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/4Zddb.png" alt="enter image description here" /></a></p>
<p>On the X-axis is the logarithmic period and on Y is the Gaia G Band magnitude.
My optimum parameters for the slope and intercept were [-1.67799139,  0.33594401]. <br>
I verified my work with the period given in Gaia data which appeared to be in good agreement with the above result:
<a href="https://i.sstatic.net/QWfgX.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/QWfgX.png" alt="enter image description here" /></a></p>
<p>The optimum parameters were [-1.70140261,  0.36610869].<br>
My concern here is that the values I have obtained are a far cry from published results, [-2.67,-1.58] as in <a href="https://arxiv.org/abs/1911.13102" rel="nofollow noreferrer">this paper</a>. I have no idea why. I suppose this has to do with issues in epoch photometry in Gaia, but I can't pinpoint anything for sure. Additionally I'd like to know how to improve my analysis to agree with the actual Period-Luminosity relationship.</p>

CC BY-SA 4.0
2023-08-22T16:33:54.913Z
How are you computing absolute magnitude for these objects? Also, typically the Y axis is inverted from what you have shown here (so more negative magnitudes are higher on the plot).
Tom Donlon
CC BY-SA 4.0
2023-08-23T15:52:41.580Z
@TomDonlon I’m using Gaia’s parallax data to calculate the distance to the object and absolute magnitude from there.
Ambica Govind
CC BY-SA 4.0
2023-08-26T19:32:48.613Z
How are you using parallax to get distance? A simple inversion will bias your result to an incorrect value. What absolute magnitude are you plotting? Please give the source of the published results and what variables they relate.
ProfRob
CC BY-SA 4.0
2023-08-27T10:01:48.377Z
@ProfRob I indeed performed a simple inversion. What do you suggest I do?  See https://arxiv.org/abs/1911.13102. This employed a different way to calculate the distance. However, I don't understand why inverting the parallax should not work.
Ambica Govind
CC BY-SA 4.0
2023-08-27T10:18:26.710Z
The numbers in the abstract of that paper (-2.67, -1.58) or in the Tables are not those in your question. Please quote the source of your numbers and the exact relationship in your question.
ProfRob
CC BY-SA 4.0
2023-08-27T10:22:21.153Z
Note also that $M_G \neq M_V$. Please clarify *in your question* what is on the y-axis. Finally, if the parallax has a significant uncertainty, a simple inversion gives a biased result for the distance, since the uncertainty is symmetric in parallax, not in distance. Not an issue so long as the error in parallax is below 10%.
ProfRob
CC BY-SA 4.0
2023-08-28T11:33:07.313Z
@ProfRob Sorry but I can't find the paper where I found the earlier values. I have edited the question to include the results of this paper though. On the Y axis indeed is the G Band magnitude, and I understand that they aren't equal, but is the difference significant enough to cause such a huge change.
Ambica Govind
CC BY-SA 4.0
2023-08-28T11:38:09.497Z
I retried the analysis applying a cut of parallax_over_error>10 as you suggested. The values are [-1.8494995 ,  0.04656565]: better than before, yet quite different.
Ambica Govind
<luminosity><gaia><variable-star><cepheids><period>
Period-Luminosity Relation of Cepheids via Gaia Data
Ambica Govind
# Period-Luminosity Relation of Cepheids via Gaia Data

(Asked by: username_0 on 2023-08-21)

I was trying to verify Leavitt's Law of Period Luminosity Relationships of Cepheid Variables using Gaia data. To do this I calculated the period using the Lomb Scargle Periodogram for 1450 stars and obtained this:
[![enter image description here](https://i.sstatic.net/4Zddb.png)](https://i.sstatic.net/4Zddb.png)

On the X-axis is the logarithmic period and on Y is the Gaia G Band magnitude.
My optimum parameters for the slope and intercept were [-1.67799139, 0.33594401].   
I verified my work with the period given in Gaia data which appeared to be in good agreement with the above result:
[![enter image description here](https://i.sstatic.net/QWfgX.png)](https://i.sstatic.net/QWfgX.png)

The optimum parameters were [-1.70140261, 0.36610869].  
My concern here is that the values I have obtained are a far cry from published results, [-2.67,-1.58] as in [this paper](https://arxiv.org/abs/1911.13102). I have no idea why. I suppose this has to do with issues in epoch photometry in Gaia, but I can't pinpoint anything for sure. Additionally I'd like to know how to improve my analysis to agree with the actual Period-Luminosity relationship.

**Tags:** luminosity, gaia, variable-star, cepheids, period

> **Comments:**
> **username_1**: How are you computing absolute magnitude for these objects? Also, typically the Y axis is inverted from what you have shown here (so more negative magnitudes are higher on the plot).  
> **username_0**: @username_1 I’m using Gaia’s parallax data to calculate the distance to the object and absolute magnitude from there.  
> **username_2**: How are you using parallax to get distance? A simple inversion will bias your result to an incorrect value. What absolute magnitude are you plotting? Please give the source of the published results and what variables they relate.  
> **username_0**: @username_2 I indeed performed a simple inversion. What do you suggest I do?  See https://arxiv.org/abs/1911.13102. This employed a different way to calculate the distance. However, I don't understand why inverting the parallax should not work.  
> **username_2**: The numbers in the abstract of that paper (-2.67, -1.58) or in the Tables are not those in your question. Please quote the source of your numbers and the exact relationship in your question.  
> **username_2**: Note also that $M_G \neq M_V$. Please clarify *in your question* what is on the y-axis. Finally, if the parallax has a significant uncertainty, a simple inversion gives a biased result for the distance, since the uncertainty is symmetric in parallax, not in distance. Not an issue so long as the error in parallax is below 10%.  
> **username_0**: @username_2 Sorry but I can't find the paper where I found the earlier values. I have edited the question to include the results of this paper though. On the Y axis indeed is the G Band magnitude, and I understand that they aren't equal, but is the difference significant enough to cause such a huge change.  
> **username_0**: I retried the analysis applying a cut of parallax_over_error>10 as you suggested. The values are [-1.8494995 ,  0.04656565]: better than before, yet quite different.  

---

## 1 answers

### Answer by username_2 on 2023-08-28. Score: 4

Here is a similar plot I adapted from [Clementini et al. (2019)](https://arxiv.org/abs/1805.02079). It shows mean absolute *Gaia* *G*-magnitude (derived from *Gaia*-DR2 parallaxes) versus period for 998 *known* Cepheid variables. I guess that corresponds reasonably well with what you have done.

The dashed line was added by Clementini et al. They believe stars below this line are either not Cepheids or there is a problem with the *Gaia* parallaxes or the published periods. Interestingly, you have few of this population in your plot? So either that's an improvement with the *Gaia* DR3 data (I assume this is what you are using) or a cleaner parent catalogue of Cepheids.

[![P-L relationship](https://i.sstatic.net/y9QNW.png)](https://i.sstatic.net/y9QNW.png)

**I have added the red line** (by hand) - this appears to be the red line plotted in your diagrams. Clearly this is not a good fit, although I would say your gradient look approximately the same. The reason why this gradient does not agree with the literature you quote is that the plot here uses absolute G-magnitude (which is not the same as the V-band) and there has been no attempt to remove extinction from the sample, which will certainly increase scatter and decrease the intercept value by the average extinction of an object in the sample. It will also bias the gradient since the more luminous Cepheids tend to be further away and perhaps have more extinction - this will artificially flatten (reduce) the gradient. This effect is clearly seen in Fig.6 of Clementini et al. where they compare the P-L relationship of galactic Cepheids over the whole sky, that are affected by varying levels of extinction, with a P-L relation for Cepheids in the Large Magellanic Cloud that have a close-to-uniform level of extinction. The P-L relation for the latter is clearly steeper.

It is a mystery however as to why there seems to be an offset between the data you show and the data plotted in Clementini et al. (2019). Are you using the intensity-weighted mean *G* magnitude (known as int\_average\_g in the *Gaia* Cepheid tables) ?

> **Comments:**
> **username_0**: Thank you! That was really helpful. And no, I'm using something called `phot_g_mean_mag` as in the data.  

---

