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

2. Motivation 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 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 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) J. Tyson, G. Kochanski, I. Dell’Antonio, 1998:

10. Correlation between Dark Matter and Visible Matter

11. 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 Flat Region around 100 kpc

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 presented analysis of a sample of spiral galaxies’ Rotation Curves classified by galaxy luminosities and normalized to v opt and r opt. 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. M. Persic, P. Salucci, F. Stel, 1996:

17. Universal Rotation Curve of Spiral Galaxy

18. Universal Rotation Curves in Spiral Galaxies 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/r opt  2 with exponential dark hallo for all luminosities For larger r and are linearly correlated Exponential Thin Disk It corresponds to T~10 5 K consistent with the temperature of the interstellar gas.

21. Dark vs. Visible in Spiral Galaxies

22. M  visible: 3.2dark: a  -18.52.52-2.553.21.282.50 -21.51.85-2.033.20.973.31 -23.51.56-1.763.20.784.11 best fit values of a for different luminosities M …remember  obtained for CL0024+1654, Log-Log-Linear Correlation in Spiral Galaxies

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, H 2 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…