# Period-Luminosity Relation of Cepheids via Gaia Data

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:

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:

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. 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.

• 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). Aug 22 at 16:33
• @TomDonlon I’m using Gaia’s parallax data to calculate the distance to the object and absolute magnitude from there. Aug 23 at 15:52
• 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. Aug 26 at 19:32
• @ProfRob I indeed performed a simple inversion. What do you suggest I do? See 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. Aug 27 at 10:01
• 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. Aug 27 at 10:18

Here is a similar plot I adapted from Clementini et al. (2019). 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.

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) ?

• Thank you! That was really helpful. And no, I'm using something called phot_g_mean_mag as in the data. Sep 2 at 9:54