# 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). Commented Aug 22, 2023 at 16:33
• @TomDonlon I’m using Gaia’s parallax data to calculate the distance to the object and absolute magnitude from there. Commented Aug 23, 2023 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. Commented Aug 26, 2023 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. Commented Aug 27, 2023 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. Commented Aug 27, 2023 at 10:18

• Thank you! That was really helpful. And no, I'm using something called phot_g_mean_mag as in the data. Commented Sep 2, 2023 at 9:54