CLUMPY  Version_2015.06_corr2
Introduction

     I. What is CLUMPY?
     II. Fluxes from dark matter annihilation or decay
     III. Jeans analysis

________________________________________

I. What is CLUMPY?
CLUMPY is dedicated to the calculation of:

  1. the astrophysical J-factor from spherical or triaxial DM distribution (smooth + mean or drawn sub-haloes, inside or outside the Galaxy)
  2. $\gamma$-ray and $\nu$ fluxes (combining the astrophysical factor and the particle physics factor)
  3. Jeans analysis framework to reconstruct DM profiles from kinematic data (and possible interface with an MCMC engine)

We hope you will enjoy using CLUMPY whether you are

  • an experimentalist looking for realistic $\gamma$-ray skymaps to calculate your new instrument sensitivity, or simply to use them in model/template analyses;
  • an astrophysicist, e.g. working on the DM content of dSphs, whishing to calculate the J factor from kinematic data;
  • a theoretician wanting to plug his/her preferred particle physics model and see what is the corresponding $\gamma$-ray flux in various objects (Galaxy, dSph, etc.).
________________________________________

II. Fluxes from dark matter annihilation or decay
The $\gamma$-ray or $\nu$ flux $d\Phi_{\gamma,\nu}/dE$ from dark matter annihilating/decaying particles is expressed as the product of a particle physics term by an astrophysical contribution $J$. At energy $E$ and in the direction $(\psi,\theta)$, the flux integrated over the solid angle $\Delta \Omega=2\pi\,(1-\cos\,\alpha_{\rm int})$ is given by

\[ \frac{d\Phi_{\gamma,\nu}}{dE}(E,\psi,\theta,\Delta \Omega)=\frac{d\Phi^{PP}_{\gamma,\nu}}{dE}(E)\times J(\psi,\theta,\Delta \Omega) \,, \]

in which $d\Omega=d\beta \sin\alpha d\alpha$ is the elementary solid angle around the line of sight (l.o.s.) direction $\psi,\theta$ (longitude and latitude in Galactic coordinates, see framework here)

  • Particle physics term (see spectra.h)
    It depends on whether the DM candidate annihilates or decays. In this version (as in the previous one), we only consider the continuum emission (e.g., Cirelli et al., 2011)

    \begin{eqnarray*} \displaystyle \left[\frac{d\Phi_{\gamma,\nu}}{dE}(E)\right]^{\rm annihilation} &=& \frac{1}{4\pi}\,\sum_{f}\frac{dN^{f}_{\gamma,\nu}}{dE}\, B_{f} \times \frac{\langle \sigma_{\rm ann}v \rangle}{m_{\rm DM}^{2}\delta}\\ \displaystyle \left[\frac{d\Phi_{\gamma,\nu}}{dE}(E)\right]^{\rm decay} &=& \frac{1}{4\pi}\,\sum_{f}\frac{dN^{f}_{\gamma,\nu}}{dE}\, B_{f} \times \frac{1}{\tau_{\rm DM}{m_{\rm DM}} \end{eqnarray*}

    with $m_{\rm DM}$ the mass of the DM candidate, $B_f$ the branching ratio into the final state $f$ and its yield per reaction $dN^{f}_{\gamma,\nu}/dE$, and
    • $\sigma_{\rm ann}$ is the annihilation cross section, and $\langle\sigma_{\rm ann}v\rangle$ the annihilation rate averaged over the DM velocity distribution, $\delta$ equals 2 (resp. 4) for a Majorana (resp. Dirac) fermion;
    • $\tau_{\rm DM}$ is the decay lifetime ( $>10^{27}$~s).

  • Astrophysical $J$ (annihilation) or $D$ (decay) factor
    The astrophysical factor relies on the integration over the solid angle $\Delta \Omega$ of some power of the DM density $\rho(\psi,\theta, l,\alpha,\beta)$ at coordinate ( $l,\alpha,\beta)$ in the l.o.s. direction $(\psi, \theta)$:

    \begin{eqnarray*} J(\psi,\theta, \Delta \Omega) &=& \int_{0}^{\Delta \Omega}\int_{\rm{l.o.s}} dl \, d\Omega \times \,\rho^2 {\rm (annihilation)}\\ D(\psi,\theta, \Delta \Omega) &=& \int_{0}^{\Delta \Omega}\int_{\rm{l.o.s}} dl \, d\Omega \times \,\rho {\rm (decay)}\;. \end{eqnarray*}

Note that in depending on the community $J$- and $D$-factors are either expressed in astrophysics units ( $M_\odot^{2}\;{\rm kpc}^{-5}$ and $M_\odot\;{\rm kpc}^{-2}$ respectively) or particle physics units ( ${\rm GeV}^{2}~{\rm cm}^{-5}$ and ${\rm GeV~cm}^{-2}$ respectively). All calculations in CLUMPY are performed in astrophysics units, but a new keyword introduced in this version (gSIMU_IS_ASTRO_OR_PP_UNITS) allows the user to select the preferred units for the outputs (plots, ASCII and FITS files).

________________________________________

III. Jeans analysis
The Jeans equation is obtained after integrating the collisionless Boltzmann equation in spherical symmetry, assuming steady-state and negligible rotational support (Binney and Tremaine, Galactic Dynamics). It relates the dynamics of a collisionless tracer population (e.g. stars in a dwarf spheroidal galaxy or galaxies in a galaxy cluster) to the underlying gravitational potential. The equations and implementation in CLUMPY are fully decribed in jeans_analysis.h.