We study the capture of galactic dark matter particles (DMP) in two-body and few-body systems with a symplectic map description. This approach allows modeling the scattering of $10^{16}$ DMPs after following the time evolution of the captured particle on about $10^9$ orbital periods of the binary system. We obtain the DMP density distribution inside such systems and determine the enhancement factor of their density in a center vicinity compared to its galactic value as a function of the mass ratio of the bodies and the ratio of the body velocity to the velocity of the galactic DMP wind. We find that the enhancement factor can be on the order of tens of thousands.
We study the capture of dark matter particles by neutron stars in close binary systems. By performing a direct numerical simulation, we find that there is a sizable amplification of the rate of dark matter capture by each of the companions. In case of the binary pulsar PSR J1906+0746 with the orbital period of 4 hours the amplification factor is 3.5. This amplification can be attributed to the energy loss by dark matter particles resulting from their gravitational scattering off moving companions.
We study the capture of galactic dark matter particles in the Solar System produced by rotation of Jupiter. It is shown that the capture cross section is much larger than the area of Jupiter orbit being inversely diverging at small particle energy. We show that the dynamics of captured particles is chaotic and is well described by a simple symplectic dark map. This dark map description allows to simulate the scattering and dynamics of $10^{14}$ dark matter particles during the life time of the Solar System and to determine dark matter density profile as a function of distance from the Sun. The mass of captured dark matter in the radius of Neptune orbit is estimated to be $2 cdot 10^{15} g$. The radial density of captured dark matter is found to be approximately constant behind Jupiter orbit being similar to the density profile found in galaxies.
We investigate the stability of prograde versus retrograde planets in circular binary systems using numerical simulations. We show that retrograde planets are stable up to distances closer to the perturber than prograde planets. We develop an analytical model to compute the prograde and retrograde mean motion resonances locations and separatrices. We show that instability is due to single resonance forcing, or caused by nearby resonances overlap. We validate our results regarding the role of single resonances and resonances overlap on orbit stability, by computing surfaces of section of the CR3BP. We conclude that the observed enhanced stability of retrograde planets with respect to prograde planets is due to essential differences between the phase-space topology of retrograde versus prograde resonances (at p/q mean motion ratio, prograde resonance is of order p - q while retrograde resonance is of order p + q).
We consider the long-range effect of the Higgs on the density of thermal-relic dark matter. While the electroweak gauge boson and gluon exchange have been previously studied, the Higgs is typically thought to mediate only contact interactions. We show that the Sommerfeld enhancement due to a 125 GeV Higgs can deplete TeV-scale dark matter significantly, and describe how the interplay between the Higgs and other mediators influences this effect. We discuss the importance of the Higgs enhancement in the Minimal Supersymmetric Standard Model, and its implications for experiments.
We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply the random matrix theory to the effective Hamiltonian formalism and derive analytically the probability distribution of the complexness parameter for two statistical ensembles describing the systems invariant under time reversal. For those with rigid spectra, we consider a Hamiltonian characterized by a picket-fence spectrum without spectral fluctuations. Then, in the more realistic case of a Hamiltonian described by the Gaussian Orthogonal Ensemble, we reveal and discuss the r^ole of spectral fluctuations.