Dark matter in elliptical galaxies

Elliptical galaxies with rapidly decreasing velocity dispersion profiles: NMAGIC models and dark halo parameter estimates for NGC 4494

<div style="text-align: justify;">Range of valid models for NGC 4697 (yellow), NGC 3379 (green) and NGC 4494 (magenta). From top to bottom as a function of radius: circular velocity, dark matter fraction, and anisotropy parameter.</div>
Range of valid models for NGC 4697 (yellow), NGC 3379 (green) and NGC 4494 (magenta). From top to bottom as a function of radius: circular velocity, dark matter fraction, and anisotropy parameter.
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Lucia Morganti, Ortwin Gerhard, Lodovico Coccato, Inma Martinez-Valpuesta & Magda Arnaboldi, 2013, MNRAS, 431, 3570

We present here dynamical models for NGC 4494, one of the intermediate-luminosity elliptical galaxies inferred to have an unusually diffuse dark matter halo. These axisymmetric models were obtained with the NMAGIC made-to-measure method, fitting photometric and kinematic data for different inclinations and gravitational potentials. The extended kinematic data include light spectra in multiple slitlets out to 3.5Re, and hundreds of planetary nebula velocities out to ≃7Re, thus allowing us to probe the dark matter content and orbital structure in the halo.

We carried out an extended study on how well the characteristic parameters of dark matter halos can be recovered via NMAGIC modelling of these data, using Monte-Carlo simulations on NGC 4494-like mock galaxies to estimate the appropriate confidence boundaries.

Our best-fitting models have a dark-matter fraction of 0.6 (+-0.1) at 5 Re with a 70% confidence level, and an approximately flat circular velocity curve (CVC) outside 0.5 Re. Comparing with two other quasi-Keplerian ellipticals, NGC 3379 and NGC 4697, whose velocity dispersion profiles also decrease rapidly from the centre outwards, the outer CVCs and dark matter haloes are quite similar. NGC 4494 shows a particularly high dark matter fraction inside 3Re, and a strong concentration of baryons in the centre.

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Regularizing made-to-measure particle models of galaxies

<div style="text-align: justify;">Typical particle weight distribution after a classical entropy regularization fit (black) and after Moving Priors entropy Regularization (red). MPR method avoid trails of extremely increased or decreased weights.</div>
Typical particle weight distribution after a classical entropy regularization fit (black) and after Moving Priors entropy Regularization (red). MPR method avoid trails of extremely increased or decreased weights.
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Lucia Morganti & Ortwin Gerhard, 2012, MNRAS, 422, 1571

Made-to-measure methods such as the parallel code NMAGIC have to solve underdetermined problems, where the number of constraints (photometric of kinematic observables) are usually much lower than the number of particle weights to define. A regularization method is therefore needed to make the method converge. Here we introduce a Moving Prior entropy Regularization method (MPR). The basic idea is to update the prior distribution needed by standard entropy regularization in parallel of the weight adaptation. The prior distribution is determined from the distribution of particles in phase-space. This allows one to construct smooth models from noisy data without erasing global phase-space gradients.

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Dynamical models of  NGC 4697 and NGC 3379


Flavio de Lorenzi et al. 2008, MNRAS, 385, 1729 (to the paper)

Flavio de Lorenzi et al. 2009, MNRAS, 395, 76 (to the paper)

De Lorenzi et al. (2008, 2009) combine long-slit kinematic data, SAURON data in the central region and PNe velocities and velocity dispersions in the halo to create dynamical models of the intermediate-luminosity galaxies NGC 4697 and NGC 3379 using the N-body particle code, NMAGIC. They find a range of potentials and anisotropy profiles that are consistent with the photometric and kinematic data. Therefore the inavailabilty of higher-order moments of the LOSVD in the haloes of these galaxies means the models suffer at the hands of the degeneracy existing between mass and anisotropy (and to a lesser extent, shape). As presently the discrete data provided by PNe and GCs are not of a high enough signal-to-noise ratio to derive higher order moments of the LOSVD, we need a different way to distinguish between the range of potentials and anisotropy profiles that are consistent with the data.

<div style="text-align: justify;">Typical set of observables as used to construct NMAGIC dynamical models of NGC 3379. The kinematic observations consist of integral field SAURON kinematic data (Shapiro et al. 2006) extending to &sim; 1/2-1 Re, slit kinematic data (Statler &amp; Smecker-Hane 1999) out to &sim; 1 1/2 Re and planetary nebulae (PNe) data (Douglas et al. 2007) out to &sim;7 Re, which allow to probe the outer halo. The luminosity distribution of the dynamical model is constrained from surface brightness photometric data (Capaccioli et al. 1990, Gebhardt et al. 2000). Often the surface brightness (SB) data are deprojected under some symmetry assumptions to obtain a luminosity density. For deprojecting the SB profile, we use Magorrian's (1999) deprojection method to obtain an axisymmetric intrinsic luminosity distribution.</div> Zoom Image
Typical set of observables as used to construct NMAGIC dynamical models of NGC 3379. The kinematic observations consist of integral field SAURON kinematic data (Shapiro et al. 2006) extending to ∼ 1/2-1 Re, slit kinematic data (Statler & Smecker-Hane 1999) out to ∼ 1 1/2 Re and planetary nebulae (PNe) data (Douglas et al. 2007) out to ∼7 Re, which allow to probe the outer halo. The luminosity distribution of the dynamical model is constrained from surface brightness photometric data (Capaccioli et al. 1990, Gebhardt et al. 2000). Often the surface brightness (SB) data are deprojected under some symmetry assumptions to obtain a luminosity density. For deprojecting the SB profile, we use Magorrian's (1999) deprojection method to obtain an axisymmetric intrinsic luminosity distribution.
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Gravitational potentials of nearby, massive elliptical galaxies

Churazov, E., Forman, W., Vikhlinin, A., Tremaine, S., Gerhard, O., Jones, C. 2008, MNRAS, 388, 1062

Massive ellipticals harbour a hot (T ~ 1 keV) interstellar medium (ISM) in the form of a low density (n < 0.1 cm-3) plasma trapped in the galaxy's gravitational potential. In massive ellipticals, the observed X-ray spectrum is dominated by emission from the ISM primarily via thermal bremsstrahlung and X-ray lines of heavy elements (Forman et al., 1985). In quiescent galaxies, where the gas is not significantly distorted by interactions with companion galaxies, one can assume hydrostatic equilibrium and use the temperature and density profiles derived from X-ray spectra to obtain a mass profile (e.g., Fukazawa et al., 2006). Churazov et al. (2008) obtain the potential of NGC 1399 and M87 and compare their profiles with that found in stellar dynamical models.

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