Correlations of Mass Distributions between Dark Matter and Visible Matter

1. Correlations of Mass Distributionsbetween Dark Matter and Visible Matter KIAS-APCTP-DMRC Workshop on “The Dark Side of the Universe” May 24, 2005 Yuriy Mishchenko and Chueng-Ryong Ji NC State University Raleigh, NC

2. Motivation • Universal Rotation Curves in Spiral Galaxies and Strong Gravitational Lensing in Galaxy Clusters provide convincing evidences of Dark Matter. • High Resolution Mass Map of CL0024+1654 is now available from the deep imaging with the Hubble Space Telescope. • Two dramatically different systems seem to exhibit a consistency in correlations of mass distributions between Dark Matter and Visible Matter. Y.Mishchenko and C.Ji, PRD68, 063503 (2003)

3. Outline • Gravitational Lensing -Galaxy Clusters CL0024+1654 -Mass Map by Tyson et al. -Simple but general theromodynamic analysis • Universal Rotation Curves -Spiral Galaxies with different luminosities -Consistency with the thermodynamic analysis • Discussions and Conclusions

4. Gravitational Lensing Effect • gravitational lensing is phenomenon of light deflection in gravitational field • allows to restore 2D projected mass distribution  Einstein Cross Q2237+0305

5. CL0024+1654

6. Dark vs. Visible in Galaxy Clusters from J. Tyson, G. Kochanski, I. Dell’Antonio, astro-ph/9801193

7. Power Law Model

8. J. Tyson, G. Kochanski, I. Dell’Antonio, astro-ph/9801193

9. Dark vs. Visible in Galaxy Clusters J. Tyson, G. Kochanski, I. Dell’Antonio, 1998: • presented analysis of Hubble telescope images of strong gravitational lensing in galaxy cluster CL0024+1654 • presented detailed mass map and radial “averaged” profiles for total and visible matter • primary conclusion was about inconsistency with Cold Dark Matter simulations (soft core)

10. Correlation between Dark Matter and Visible Matter

11. Flat Region around 100 kpc • projected density radial profiles presented on log-log scale for the total and visible matter distribution • if profiles were re-plotted on log-linear scale, one would observe exponential decay anomalous flat region at about 100kpc in the visible mass profile

13. Thermodynamic Principle Log-Log Linear Correlation

15. Dark Matter in Spiral Galaxies Rotation Curve represents gas/stars circular orbit velocity as function of distance from the galaxy’s center spiral galaxy NGC2403

16. Dark vs. Visible in Spiral Galaxies M. Persic, P. Salucci, F. Stel, 1996: • presented analysis of a sample of spiral galaxies’ Rotation Curves classified by galaxy luminosities and normalized to vopt and ropt . • found that majority of normalized RC in given luminosity group follow universal profiles (Universal Rotation Curves). • described URC in terms of simple mass model: dark spherical halo + exponential thin stellar disk.

17. Universal Rotation Curve of Spiral Galaxy

18. Universal Rotation Curves in Spiral Galaxies • In Persic, Salucci, Stel visible mass contribution is known but approximated with an analytical fit, • Dark halo contribution is parameterized, • Final Rotation Curve is described with

19. Luminosity Dependence of URCs

20. Correlation of Mass Density • URC can be fit in the region 0 r/ropt 2 with exponential dark hallo for all luminosities • For larger r and are linearly correlated Exponential Thin Disk It corresponds to T~105 K consistent with the temperature of the interstellar gas.

21. Dark vs. Visible in Spiral Galaxies

22. Dark vs. Visible in Spiral Galaxies Log-Log-Linear Correlation in Spiral Galaxies best fit values of a for different luminositiesM …remember  obtained for CL0024+1654,

23. Dark vs. Visible Matter We observed Log-Log-Linear correlation with essentially the same correlation coefficient in different spiral galaxies and a galaxy cluster. This is a remarkable coincidence… How do we interprete?

24. Interpretation of Results • Local Thermodynamic Equilibrium since it is unlikely that the molar mass ratio varies in a precise correlation with the temperature ratio to make kappa constant both for the galaxy clusters and the spiral galaxies. • Visible matter primarily consists of H, H2 and He. Massive neutrinos and/or axions < 25MeV WIMP ~ 10GeV-1TeV SUSY lightest particles(e.g. neutralino)>30GeV

25. Discussions and Conclusions • Correlations of mass distributions between dark matter and visible matter in two dramatically different systems, galaxy cluster and spiral galaxies, are remarkably consistent with each other. • Based on an almost isothermal Boltzmann distribution, we find K = 2.1~4.4 which indicate the typical mass scale of dark matter particles around the order of 100 MeV. • Since this is right around the QCD mass scale, any relation between the dark matter and QCD vacuum condensates?

26. Things to do: • Experimental – improve “statistics” • large survey of dark vs. visible matter in galaxy clusters… • Theoretical – investigate different possibilities • role of gravity in thermalization processes… • better understanding of galaxy cluster dynamics… • better understanding of spiral galaxy dynamics…

27. C.Ji, Gungwon Kang and Jungjai Lee, work in progress…