Using Gaia DR3 to Calibrate Cepheid Star Luminosity to Give Confidence to the Cosmic Distance Ladder
Abstract:
Bibliography/Citations:
Darling, David. “Cosmic Distance Ladder.” David Darling, https://www.daviddarling.info/encyclopedia/C/cosmic_distance_ladder.html. Accessed 12 Mar. 2023.
Gaia Archive, 13 June 2022, https://gea.esac.esa.int/archive/. Accessed 12 Mar. 2023.
Riess, Adam G., et al. “Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with ΛCDM.” The Astrophysical Journal Letters, vol. 908, no. 1, 2021, https://doi.org/10.3847/2041-8213/abdbaf.
Wielgórski, Piotr, et al. “An Absolute Calibration of the near-Infrared Period–Luminosity Relations of Type II Cepheids in the Milky Way and in the Large Magellanic Cloud.” The Astrophysical Journal, vol. 927, no. 1, 2022, p. 89., https://doi.org/10.3847/1538-4357/ac470c.
Additional Project Information
Research Plan:
Rationale:
In our universe exist variable stars that have a pulsating brightness. RR Lyrae and Cepheid stars are the two main types of pulsating variable stars. Thanks to Cepheid stars, astronomers could derive the Period-Luminosity Relation that helps compute the distance to stars, leading us to the creation of the Cosmic Distance Ladder. The Cosmic Distance Ladder is a series of different methods and objects astronomers employ to observe distant phenomena. Each rung of this ladder progressively allows us to see further. The techniques on the higher rungs depend on the stability of the lower rungs. Using Cepheid stars, we can see out to 300,000 lightyears away. The problem that plagued the astrophysics community is the lack of reliability in the stars’ distance. Prior to the Gaia Data Release 3, the most reliable estimate was 10s of stars. However, with the DR3, the number of stars goes into the hundreds. We will be able to use large samples of stars where we can independently verify their distance, and therefore their luminosity. Calibrating these stars will give more confidence to the entire distance ladder.
Research Question:
Using Gaia’s Data Release 3 identified Cepheid variable stars, can we improve the calibration of the period-luminosity relationship, and therefore give confidence to the Cosmic Distance Ladder?
Hypothesis:
If we use Gaia's Delta Cepheid file from Data Release 3, we can identify ways to improve the period-luminosity relation by examining Cepheid stars with a parallax and absolute magnitude with <0.1 uncertainty. With these improvements, the upper rungs of the Cosmic Distance Ladder will have significantly higher accuracy, providing us with greater confidence in the measured distances.
Materials:
- Computer
- Spreadsheet application
- Delta Cepheid file from Gaia Archives
Procedure:
- Obtain all relevant information for Cepheid variable stars from the Gaia Data Release 3 through Gaia Archive
- Go to Advanced (ADQL)
- Go to “Gaia Data Release 3” and click on “Variability”
- Download gaiadr3.vari_cepheid
- Upload CSV file to a spreadsheet application
Risk and Safety:
There were no risk and safety hazards in this study.
Data Analysis:
- Organize the complete data set so that you are only analyzing FUNDAMENTAL star classification and not FIRST_OVERTURN
- Filter out stars with poorly measured distance. Parallax should not be negative. Uncertainty should be less than 0.1
- Filter out stars with poorly measured absolute magnitudes. Uncertainty should be less than 0.1
- For the filtered stars:
- Find average absolute magnitude in the g-band (G)
- Find the measured average apparent magnitude (g)
- Find the distance (d) using the distance modulus G = g + 5 - 5 log (d)
- Make the standard plot of G vs. log(P)-1 where P is the pulsation period of the variable
- This should be a linear function with a negative slope and intercept
- The slope and intercept are the calibration constants of interest
- Make a residual plot for the distances measured
Questions and Answers
1. What was the major objective of your project and what was your plan to achieve it?
a. Was that goal the result of any specific situation, experience, or problem you encountered?
The most recent calibration of Cepheid stars was conducted utilizing 75 Milky Way Cepheid parallaxes extracted from the Gaia Early Data Release 3. My present calibration incorporates all Delta Cepheid stars from the final Gaia's Data Release 3, comprising 419 accurately measured stars from the Milky Way. There are other research groups who have done similar studies, but this calibration includes the most number of Cepheid stars yet. We will focus on the period-luminosity relation and where the stars place on the graph.
b. Were you trying to solve a problem, answer a question, or test a hypothesis?
Yes, I was trying to improve the accuracy of the lower rungs of the cosmic distance ladder. Through this, I believe that I can increase the overall accuracy of the cosmic distance ladder, which could in turn improve the accuracy of measurements made with the James Webb Space Telescope (JWST.) This could be an important contribution to the field of astronomy, as accurate distance measurements are essential for understanding the nature and evolution of the universe.
2. What were the major tasks you had to perform in order to complete your project?
a. For teams, describe what each member worked on.
- I had to retrieve the Delta Cepheid file from the Gaia DR3
- Organize data so that I only analyzed fundamental Cepheid stars with well measured parallax and magnitude (<0.1 uncertainty)
- Calculations:
- Measure distance (in parsecs)
- distance uncertainty
- absolute magnitude in the green band
- absolute magnitude in the green band uncertainty
- log (Period - 1)
- Plot absolute magnitude in the green band vs. log (P-1)
- Using the values of the absolute magnitude in the green band vs. log (P-1), calculate:
- Slope
- Intercept
- Slope uncertainty
- Intercept uncertainty
- Slope Uncertainty/Intercept Uncertainty
- Plot a residual plot with the distances calculated
3. What is new or novel about your project?
a. Is there some aspect of your project's objective, or how you achieved it that you haven't done before?
Based on my research background, I had not previously engaged directly with a telescope data archive. Furthermore, I have not worked directly with the period-luminosity relation before. This was an entirely novel process for me, but this research experience provided a wealth of knowledge and skills.
b. Is your project's objective, or the way you implemented it, different from anything you have seen?
This project’s objective is not new. Other groups have also calibrated Cepheid stars. However, the current endeavor distinguishes itself by implementing this method to a significantly larger number of stars, thereby yielding more precise and accurate calculations.
c. If you believe your work to be unique in some way, what research have you done to confirm that it is?
Here, I am solely looking at the green band magnitudes provided by the Gaia Data Release 3.
4. What was the most challenging part of completing your project?
a. What problems did you encounter, and how did you overcome them?
One of the initial hurdles that I encountered in the duration of my research involved accessing the Delta Cepheid file from the Gaia Data Release 3. The user interface of this archive is known to be quite cumbersome, and proved to be a non-intuitive experience for me, a researcher who lacked familiarity with its interface. However, through perseverance and dedication, I became proficient in navigating the system by learning Structured Query Language (SQL). By acquiring this skill set, I was able to effectively extract the requisite data from the archive and upload it to a CSV file for analysis.
b. What did you learn from overcoming these problems?
I am thankful for this project, as it provided me with the opportunity to expand my skill set. In order to access the Gaia Data Release 3, I acquired proficiency in utilizing SQL. Furthermore, to analyze the extracted data, I became skilled in using spreadsheet programs, specifically Google Sheets. This project enabled a significant enhancement in my data analysis abilities. The Delta Cepheid file encompassed information for slightly over 13,000 stars. This facilitated my acquisition of knowledge concerning the process of determining the precision of star measurements and other ways of knowing if data is useful for my project or not.
5. If you were going to do this project again, are there any things you would you do differently the next time?
If I were to undertake this project anew, I would incorporate the metallicity of stars into my analysis, given that it significantly influences their luminosity. I had excluded this factor in my previous analysis as Gaia had not measured the metallicity of the stars accurately. Its inclusion would enhance the precision of the Cepheid star rung in the cosmic distance ladder.
When measuring the magnitudes of stars, Gaia only measures them in the green-band (g-band) of the visible light spectrum. If I were to do this project again, then I would account for the entire visible light spectrum.
Interstellar extinction refers to the absorption of light and other forms of electromagnetic radiation by gas and dust that originates from other stars. In the event of Gaia detecting Cepheid stars, it is plausible that dust impeded the accurate measurement of a star's true magnitude. If I were to redo this research, I would account for interstellar extinction.
These three factors would greatly influence the slope uncertainty, bringing it much lower than 51%.
6. Did working on this project give you any ideas for other projects?
I want to see if my calibrations can help add the cosmic distance ladder to one of the methods of detecting old galaxies. The James Webb Space Telescope (JWST) employs the cosmic distance ladder in its measurements. The cosmic distance ladder is only accurate if the bottom rungs are extremely well measured. With my work with the lower rungs of the ladder, the JWST will have a much higher accuracy rate.
7. How did COVID-19 affect the completion of your project?
No, it did not.