Clustering Financial Time Series using their Correlations and their Distributions
Correlations of Mass Distributions between Dark Matter and Visible Matter
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Transcript of Correlations of Mass Distributions between Dark Matter and Visible Matter
Correlations of Mass DistributionsCorrelations of Mass Distributionsbetween between
Dark Matter and Visible MatterDark Matter and Visible Matter
Yuriy Mishchenko and Chueng-Ryong JiYuriy Mishchenko and Chueng-Ryong JiNC State University NC State University
Raleigh, NCRaleigh, NC
KIAS-APCTP-DMRC Workshop on “The Dark Side of the Universe” May 24, 2005
MotivationMotivation • 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)
OutlineOutline
• 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
Gravitational Lensing EffectGravitational Lensing Effect
• gravitational lensing is phenomenon of light deflection in gravitational field
• allows to restore 2D projected mass distribution
Einstein Cross Q2237+0305 Einstein Cross Q2237+0305
CL0024+1654CL0024+1654
Dark vs. Visible in Galaxy ClustersDark vs. Visible in Galaxy Clusters
from J. Tyson, G. Kochanski, I. Dell’Antonio, astro-ph/9801193
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Power Law ModelPower Law Model
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J. Tyson, G. Kochanski, I. Dell’Antonio, astro-ph/9801193
Dark vs. Visible in Galaxy ClustersDark 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:J. Tyson, G. Kochanski, I. Dell’Antonio, 1998:
Correlation between Dark Matter and Visible Matter
• 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
Thermodynamic PrincipleThermodynamic Principle
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Log-Log Linear Correlation
4.41.2 4.41.2
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Dark Matter in Spiral GalaxiesDark Matter in Spiral Galaxies
Rotation Curve represents gas/stars circular orbit velocity as function of distance from the galaxy’s center
spiral galaxy NGC2403
Dark vs. Visible in Spiral GalaxiesDark vs. Visible in Spiral Galaxies
• 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.
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M. Persic, P. Salucci, F. Stel, 1996:M. Persic, P. Salucci, F. Stel, 1996:
Universal Rotation Curve of Spiral Galaxy
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Universal Rotation Curves in Spiral GalaxiesUniversal 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
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Luminosity Dependence of URCs Luminosity Dependence of URCs
Correlation of Mass DensityCorrelation 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)log( v )log( d
)/exp()( optd rrar
Exponential Thin Disk )/2.3exp( optv rr
It corresponds to T~105 K consistent with the temperatureof the interstellar gas.
Dark vs. Visible in Spiral GalaxiesDark vs. Visible in Spiral Galaxies
Dark vs. Visible in Spiral GalaxiesDark vs. Visible in Spiral Galaxies
M visible: 3.2 dark: a
-18.5 2.52-2.55 3.2 1.28 2.50
-21.5 1.85-2.03 3.2 0.97 3.31
-23.5 1.56-1.76 3.2 0.78 4.11
best fit values of a for different luminosities M
)/2.3exp()( optv rrr
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)/exp()( optd rrar
4.41.2 …remember obtained for CL0024+1654,
Log-Log-Linear Correlation in Spiral GalaxiesLog-Log-Linear Correlation in Spiral Galaxies
Dark vs. Visible MatterDark 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?How do we interprete?
Interpretation of ResultsInterpretation 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.
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Massive neutrinos and/or axions < 25MeVWIMP ~ 10GeV-1TeVSUSY lightest particles(e.g. neutralino)>30GeV
Discussions and ConclusionsDiscussions 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?
Things to do: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…
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C.Ji, Gungwon Kang and Jungjai Lee, work in progress…