DARKexp

Statistical Mechanics Approach to Collisionless Relaxation and Dark Matter

Papers:


Statistical Mechanics of Collisionless Orbits. I. Origin of Central Cusps in Dark-matter Halos
Hjorth, J., Williams, L.L.R. 2010, ApJ, 722, 851

Statistical Mechanics of Collisionless Orbits. II. Structure of Halos
Williams, L.L.R., Hjorth, J. 2010, ApJ, 722, 856

Statistical Mechanics of Collisionless Orbits. III. Comparison with N-body Simulations
Williams, L.L.R., Hjorth, J., Wojtak, R. 2010, ApJ, 725, 282

Statistical Mechanics of Collisionless Orbits. IV. Distribution of Angular Momentum
Williams, L.L.R., Hjorth, J., Wojtak, R. 2014, ApJ, 783, 13

Non-universality of Dark-matter Halos: Cusps, Cores, and the Central Potential
Hjorth, Jens, Williams, Liliya L. R., Wojtak, Radosław, McLaughlin, Michael. 2015, ApJ, 811, 2

Testing DARKexp against energy and density distributions of Millennium-II halos
Nolting, Chris, Williams, Liliya L. R., Boylan-Kolchin, Michael, Hjorth, Jens. 2016, JCAP, 09, 042

Statistical Mechanics of Collisionless Orbits. V. The Approach to Equilibrium for Idealized Self-gravitating Systems
Williams, Liliya L. R., Hjorth, Jens. 2022, ApJ, 937, 67

Addressing the core-cusp and diversity problem of dwarf and disk galaxies using cold collisionless DARKexp theory
Liliya L.R. Williams, Jens Hjorth, Evan D. Skillman. 2025, submitted to JCAP

Entropy Evolution Towards DARKexp of IllustrisTNG Dark Matter Halos
Ashley Francis, Liliya L.R. Williams, Jens Hjorth. 2025, submitted to JCAP

DARKexp vs other models:


Collisionless dynamics in globular clusters
Williams, Liliya L. R., Barnes, Eric I., Hjorth, Jens. 2012, MNRAS, 423, 3589-3600. Testing phenomenological and theoretical models of dark matter density profiles with galaxy clusters
L. J. Beraldo e Silva, M. Lima, L. Sodré. 2013, MNRAS, 436, 2616

Kinematics of a globular cluster with an extended profile: NGC 5694
Bellazzini, M., Mucciarelli, A., Sollima, A., Catelan, M., Dalessandro, E., Correnti, M., D'Orazi, V., Cortés, C., Amigo, P. 2015, MNRAS, 446, 3130

CLASH: Joint Analysis of Strong-Lensing, Weak-Lensing Shear and Magnification Data for 20 Galaxy Clusters
Umetsu, K., Zitrin, A., Gruen, D., Merten, J., Donahue, M., Postman, M. arXiv:1507.04385


Rotation curves of 96 disk galaxies from the SPARC catalog fit with DARKexp:


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Download density profiles:


DARKexp model has 1 shape parameter, phi0, which is the dimensionless depth of the halo potential.

The distribution of scaled particle energy, e, of DARKexp models has a simple form, N(e)~exp(phi0-e)-1, which was derived in Paper I, but the corresponding density profiles for isotropic systems do not have an analytical form, so below we provide computed density profiles; see Paper II for how these were obtained from N(e).

Files are labeled by the DARKexp phi0, the scaled potential depth, the model's only shape parameter.
Note that the potential at the center, phi[r-->0], is phi0.
The radius r is scaled such that in 3D the "isothermal" slope, gamma=2, corresponds to log[r]=0.
The normalization of 3D and 2D density profiles are such that rho_3D,2D[r]=1 at r=1.

...And more finely spaced phi0 values: