The Fourier formalism for relativistic axion-photon conversion, with astrophysical applications

We study the weak mixing of photons and relativistic axion-like particles (axions) in plasmas with background magnetic fields, ${bf B}$. We show that, to leading order in the axion-photon coupling, the conversion probability, $P_{gamma to a}$, is given by the one-dimensional power spectrum of the magnetic field components perpendicular to the particle trajectory. Equivalently, we express $P_{gamma to a}$ as the Fourier transform of the magnetic field autocorrelation function, and establish a dictionary between properties of the real-space magnetic field and the energy-dependent conversion probability. For axions more massive than the plasma frequency, ($m_a>omega_{rm pl}$), we use this formalism to analytically solve the problem of perturbative axion-photon mixing in a general magnetic field. In the general case where $m_a/omega_{rm pl}$ varies arbitrarily along the trajectory, we show that a naive application of the standard formalism for resonant conversion can give highly inaccurate results, and that a careful calculation generically gives non-resonant contributions at least as large as the resonant contribution. Furthermore, we demonstrate how techniques based on the Fast Fourier Transform provide a new, highly efficient numerical method for calculating axion-photon mixing. We briefly discuss magnetic field modelling in galaxy clusters in the light of our results and argue, in particular, that a recently proposed regular model used for studying axion-photon mixing (specifically applied to the Perseus cluster) is inconsistent with observations. Our formalism suggest new methods to search for imprints of axions, and will be important for spectrographs with percent level sensitivity, which includes existing X-ray observations by Chandra as well as the upcoming Athena mission.

Constraining ultra light fermionic dark matter with Milky Way observations

The equation of state for a degenerate gas of fermions at zero temperature in the non relativistic case is a polytrope, i.e. $p=gamma rho^{5/3}/m_F^{8/3}$. If dark matter is modelled by such non interacting fermion, this dependence in the mass of the fermion $m_F$ explains why if dark matter is very heavy the effective pressure of dark matter is negligible. Nevertheless, if the mass of the dark matter is very small, the effective pressure can be very large, and thus, a system of self-gravitating fermions can be formed. In this work we model the dark matter halo of the Milky-Way by solving the Tolman-Oppenheimer-Volkoff equations, with the equation of state for a partially degenerate ultralight non interacting fermion. It is found that in order to fit its rotational velocity curve of the Milky Way, the mass of the fermion should be in the range $29 ~mbox{eV} < m_F < 33~$eV. Moreover, the central density is constrained to be in the range of $46 < rho_0<61$ GeV/cm$^3$. The fermionic dark matter halo has a very different profile as compared with the standard Navarro-Frenk-White profile, thus, the possible indirect signals for annihilating dark matter may change by orders of magnitude. We found bounds for the annihilation cross section in this case by using the Saggitarius A* spectral energy distribution. Those limits are very strong confirming the idea that the lighter the dark matter particle is, the darkest it becomes.

String compactification, QCD axion and axion-photon-photon coupling

It is pointed out that there exist a few problems to be overcome toward an observable sub-eV QCD axion in superstring compactification. We give a general expression for the axion decay constant. For a large domain wall number $N_{DW}$, the axion decay constant can be substantially lowered from a generic value of a scalar singlet VEV. The Yukawa coupling structure in the recent $Z_{12-I}$ model is studied completely, including the needed nonrenormalizable terms toward realistic quark and lepton masses. In this model we find an approximate global symmetry and vacuum so that a QCD axion results but its decay constant is at the GUT scale. The axion-photon-photon coupling is calculated for a realistic vacuum satisfying the quark and lepton mass matrix conditions. It is the first time calculation of $c_{agammagamma}$ in realistic string compactifications: $c_{agammagamma}={5/3}-1.93simeq -0.26$.

Axion-photon conversion in strongly magnetised plasmas

Axion dark matter can resonantly convert to photons in the magnetosphere of neutron stars, possibly giving rise to radio signals observable on Earth. This method for the indirect detection of axion dark matter has recently received significant attention in the literature. The calculation of the radio signal is complicated by a number of effects; most importantly, the gravitational infall of the axions onto the neutron star accelerates them to semi-relativistic speed, and the neutron star magnetosphere is highly anisotropic. Both of these factors complicate the calculation of the conversion of axions to photons. In this work, we present the first fully three-dimensional calculation of the axion-photon conversion in highly magnetised anisotropic media. Depending on the axion trajectory, this calculation leads to orders-of-magnitude differences in the conversion compared to the simplified one-dimensional calculation used so far in the literature, altering the directionality of the produced photons. Our results will have important implications for the radio signal one would observe in a telescope.