The Hernquist model revisited: 
Completely analytical anisotropic dynamical models

Baes, M.; Dejonghe, Herwig

doi:10.1051/0004-6361:20021064

Cited by 60 publications

(85 citation statements)

References 30 publications

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“…The Hernquist model is well studied (e.g. Baes & Dejonghe 2002) and it has been shown to provide a good fit to the mass profile of galaxy clusters (Rines et al 2000(Rines et al , 2001(Rines et al , 2003Rines & Diaferio 2006). This is also true of the Burkert model Biviano & Salucci 2006), but not of the SIS model (Rines et al 2003;Katgert et al 2004).…”

Section: The Mamposst Methodsmentioning

confidence: 98%

CLASH-VLT: The mass, velocity-anisotropy, and pseudo-phase-space density profiles of thez= 0.44 galaxy cluster MACS J1206.2-0847

Biviano

Rosati

Balestra

et al. 2013

A&A

160

174

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Aims. We constrain the mass, velocity-anisotropy, and pseudo-phase-space density profiles of the z = 0.44 CLASH cluster MACS J1206.2-0847, using the projected phase-space distribution of cluster galaxies in combination with gravitational lensing. Methods. We use an unprecedented data-set of 600 redshifts for cluster members, obtained as part of a VLT/VIMOS large program, to constrain the cluster mass profile over the radial range ∼0-5 Mpc (0-2.5 virial radii) using the MAMPOSSt and Caustic methods. We then add external constraints from our previous gravitational lensing analysis. We invert the Jeans equation to obtain the velocity-anisotropy profiles of cluster members. With the mass-density and velocity-anisotropy profiles we then obtain the first determination of a cluster pseudo-phase-space density profile. Results. The kinematics and lensing determinations of the cluster mass profile are in excellent agreement. This is very well fitted by a NFW model with mass M 200 = (1.4 ± 0.2) × 10 15 M and concentration c 200 = 6 ± 1, only slightly higher than theoretical expectations. Other mass profile models also provide acceptable fits to our data, of (slightly) lower (Burkert, Hernquist, and Softened Isothermal Sphere) or comparable (Einasto) quality than NFW. The velocity anisotropy profiles of the passive and star-forming cluster members are similar, close to isotropic near the center and increasingly radial outside. Passive cluster members follow extremely well the theoretical expectations for the pseudo-phase-space density profile and the relation between the slope of the mass-density profile and the velocity anisotropy. Star-forming cluster members show marginal deviations from theoretical expectations. Conclusions. This is the most accurate determination of a cluster mass profile out to a radius of 5 Mpc, and the only determination of the velocityanisotropy and pseudo-phase-space density profiles of both passive and star-forming galaxies for an individual cluster. These profiles provide constraints on the dynamical history of the cluster and its galaxies. Prospects for extending this analysis to a larger cluster sample are discussed.

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Section: The Mamposst Methodsmentioning

confidence: 98%

CLASH-VLT: The mass, velocity-anisotropy, and pseudo-phase-space density profiles of thez= 0.44 galaxy cluster MACS J1206.2-0847

Biviano

Rosati

Balestra

et al. 2013

A&A

160

174

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“…Various limits are already well-known. For example, when (p, c) = (1, 0) or (2, 1), this is the Hernquist (1990) potential generated by the distribution function first found by Baes & Dejonghe (2002). When (p, c) = (2, 0) or (4, 1), this is the isotropic Plummer (1911) model.…”

Section: The Simple Halo Modelsmentioning

confidence: 99%

Simple models for the distribution of dark matter

Evans

2005

A&A

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We introduce a simple family of models for representing the dark matter in galaxies. The potential and phase space distribution function are all elementary, while the density is cusped. The models are all hypervirial, that is, the virial theorem holds locally, as well as globally. As an application to dark matter studies, we compute some of the properties of γ-ray sources caused by neutralino self-annihilation in dark matter clumps.

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“…The early-days models mainly represented systems with a constant density core, such as the Plummer model or the isochrone sphere (Plummer 1911;Hénon 1960). It now appears that many dynamical systems such as galaxies and dark matter haloes contain a central density cusp; also for such models a number of representative potential-density pairs have been constructed and distribution function have been derived (Jaffe 1983;Hernquist 1990;Dehnen 1993;Tremaine et al 1994;Hiotelis 1994;Zhao 1996;Baes & Dejonghe 2002Buyle et al 2007).…”

Section: Introductionmentioning

confidence: 99%

Dynamical models with a general anisotropy profile

Baes¹,

Hese²

2007

A&A

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Aims. Both numerical simulations and observational evidence indicate that the outer regions of galaxies and dark matter haloes are typically mildly to significantly radially anisotropic. The inner regions can be significantly non-isotropic, depending on the dynamical formation and evolution processes. In an attempt to break the lack of simple dynamical models that can reproduce this behaviour, we explore a technique to construct dynamical models with an arbitrary density and an arbitrary anisotropy profile. Methods. We outline a general construction method and propose a more practical approach based on a parameterized anisotropy profile. This approach consists of fitting the density of the model with a set of dynamical components, each of which have the same anisotropy profile. Using this approach we avoid the delicate fine-tuning difficulties other fitting techniques typically encounter when constructing radially anisotropic models.Results. We present a model anisotropy profile that generalizes the Osipkov-Merritt profile, and that can represent any smooth monotonic anisotropy profile. Based on this model anisotropy profile, we construct a very general seven-parameter set of dynamical components for which the most important dynamical properties can be calculated analytically. We use the results to look for simple one-component dynamical models that generate simple potential-density pairs while still supporting a flexible anisotropy profile. We present families of Plummer and Hernquist models in which the anisotropy at small and large radii can be chosen as free parameters. We also generalize these two families to a three-parameter family that self-consistently generates the set of Veltmann potential-density pairs. These new analytical models are an important step forward compared to isotropic or Osipkov-Merritt models and can be used to generate the initial conditions for realistic simulations of galaxies or dark matter haloes.

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The Hernquist model revisited: Completely analytical anisotropic dynamical models

Cited by 60 publications

References 30 publications

CLASH-VLT: The mass, velocity-anisotropy, and pseudo-phase-space density profiles of thez= 0.44 galaxy cluster MACS J1206.2-0847

CLASH-VLT: The mass, velocity-anisotropy, and pseudo-phase-space density profiles of thez= 0.44 galaxy cluster MACS J1206.2-0847

Simple models for the distribution of dark matter

Dynamical models with a general anisotropy profile

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