1. Galaxy Cluster Mass from Spectroscopic Magnification Measurements
Matt Mitchell
Dr. Eduardo Rozo, University of Arizona
NASA Space Grant Consortium Symposium
April 18, 2017

2. What Are Galaxy Clusters and Why Do We Care About their Masses?
Galaxy clusters are well…clusters of galaxies
Collections of galaxies
Dark Energy
Accelerated expansion discovered in 1998
We call the cause of this acceleration Dark Energy
“Dark” = Not observable
Total mass in the universe is important infer properties of Dark Energy

3. Gravitational Lensing
Einstein's theory of General Relativity
“Fabric” of Space-Time
Gravity is not a force, but a “stretch”
“Straight” paths are curved
Light, despite being massless, still curves
Massive objects behave similar to lenses
Old, well studied equations
Source: Hubble Telescope

4. Method for Mass Calibration
Luminosity effects and magnification
Lensing effects observed luminosity
Luminosity: brightness
Magnification: the ratio of observed to emitted luminosity
Magnification profile depends on mass profile
Usually, magnification increases towards the center
Observed Redshift depth
Redshift: distance
We can see further towards the center

5. Method (con’t) The average redshift signal Previous Results
Average redshift of background galaxies at a given radius subtracting the survey average
Zero at large distances, increases toward center
Previous Results
This analysis has been carried out before
Jean Coupon et Al.: 4.8 significance
Significance: Best fit mass divided by predicted error

6. Project Objectives Increase significance measurement of the method
Use more data
~800,000 background galaxies
~8,000 foreground clusters
Explore further statistical methods
Higher moments than average (i.e )

7. Data and Results Background Galaxies Foreground Clusters
Sloan Digital Sky Survey
Foreground Clusters
RedMaPPer Catalog
Developed new method for modeling relationship between measured signal and cluster mass
Relied more on the qualities of the sample
Minimum Radius 40kpc
Significance (σ)
6.6

8. Data and Results (Con’t)
40 kpc is too small
Stability of result
Brought minimum radius up to 200 kpc
Significance dropped
Could not be recovered using higher moments
Minimum Radius 200 kpc
Moment
Significance (σ)
First (average)
2.4
Second
3.1
Third
3.2

9. Analysis and Further Study
Lower significance than previous results
Due to untrustworthy data
Higher moments did not boost significance
Due to larger error in signal for higher moments
Dark Energy Spectroscopic Instrument (DESI)
Larger sample size could reduce signal error

10. Thank You!

11. The Physics of Magnification