18,854 research outputs found
Collisional interaction limits between dark matters and baryons in `cooling flow' clusters
Presuming weak collisional interactions to exchange the kinetic energy
between dark matter and baryonic matter in a galaxy cluster, we re-examine the
effectiveness of this process in several `cooling flow' galaxy clusters using
available X-ray observations and infer an upper limit on the heavy dark matter
particle (DMP)proton cross section . With a relative
collisional velocity dependent power-law form of where , our inferred upper
limit is \sigma_0/m_{\rm x}\lsim 2\times10^{-25} {\rm cm}^2 {\rm GeV}^{-1}
with being the DMP mass. Based on a simple stability analysis of
the thermal energy balance equation, we argue that the mechanism of
DMPbaryon collisional interactions is unlikely to be a stable
nongravitational heating source of intracluster medium (ICM) in inner core
regions of `cooling flow' galaxy clusters.Comment: 8 pages, 2 figures, MNRAS accepte
Feynman-Kac formula for heat equation driven by fractional white noise
We establish a version of the Feynman-Kac formula for the multidimensional
stochastic heat equation with a multiplicative fractional Brownian sheet. We
use the techniques of Malliavin calculus to prove that the process defined by
the Feynman-Kac formula is a weak solution of the stochastic heat equation.
From the Feynman-Kac formula, we establish the smoothness of the density of the
solution and the H\"{o}lder regularity in the space and time variables. We also
derive a Feynman-Kac formula for the stochastic heat equation in the Skorokhod
sense and we obtain the Wiener chaos expansion of the solution.Comment: Published in at http://dx.doi.org/10.1214/10-AOP547 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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