The Scaling Relations of Galaxy Clusters and Their Dark Matter Halos (original) (raw)
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Cosmology and cluster halo scaling relations
Monthly Notices of the Royal Astronomical Society, 2009
We explore the effects of dark matter and dark energy on the dynamical scaling properties of galaxy clusters. We investigate the cluster Faber-Jackson (FJ), Kormendy and Fundamental Plane (FP) relations between the mass, radius and velocity dispersion of cluster-sized haloes in cosmological N-body simulations. The simulations span a wide range of cosmological parameters, representing open, flat and closed Universes. Independently of the cosmology, we find that the simulated clusters are close to a perfect virial state and do indeed define an FP. The fitted parameters of the FJ, Kormendy and FP relationships do not show any significant dependence on m and/or. One outstanding effect is the influence of m on the thickness of the FP. Following the time evolution of our models, we find slight changes of FJ and Kormendy parameters in highm universe, along with a slight decrease of FP fitting parameters. We also see an initial increase of the FP thickness followed by a convergence to a nearly constant value. The epoch of convergence is later for higher values of m , while the thickness remains constant in the lowm models. We also find a continuous increase of the FP thickness in the standard cold dark matter cosmology. There is no evidence that these differences are due to the different power spectrum slopes at cluster scales. From the point of view of the FP, there is little difference between clusters that quietly accreted their mass and those that underwent massive mergers. The principal effect of strong mergers is to significantly change the ratio of the half-mass radius r half to the harmonic mean radius r h .
Monthly Notices of the Royal Astronomical Society, 2014
Early-type galaxies (ETGs) are observed to be more compact, on average, at z ≳ 2 than at z ≃ 0, at fixed stellar mass. Recent observational works suggest that such size evolution could reflect the similar evolution of the host dark matter halo density as a function of the time of galaxy quenching. We explore this hypothesis by studying the distribution of halo central velocity dispersion (σ 0) and half-mass radius (r h) as functions of halo mass M and redshift z, in a cosmological Λ-CDM N-body simulation. In the range 0 ≲ z ≲ 2.5, we find σ 0 ∝ M 0.31−0.37 and r h ∝ M 0.28−0.32 , close to the values expected for homologous virialized systems. At fixed M in the range 10 11 M ⊙ ≲ M ≲ 5.5 × 10 14 M ⊙ we find σ 0 ∝ (1 + z) 0.35 and r h ∝ (1 + z) −0.7. We show that such evolution of the halo scaling laws is driven by individual haloes growing in mass following the evolutionary tracks σ 0 ∝ M 0.2 and r h ∝ M 0.6 , consistent with simple dissipationless merging models in which the encounter orbital energy is accounted for. We compare the N-body data with ETGs observed at 0 ≲ z ≲ 3 by populating the haloes with a stellar component under simple but justified assumptions: the resulting galaxies evolve consistently with the observed ETGs up to z ≃ 2, but the model has difficulty reproducing the fast evolution observed at z ≳ 2. We conclude that a substantial fraction of the size evolution of ETGs can be ascribed to a systematic dependence on redshift of the dark matter haloes structural properties.
Scaling Laws for Dark Matter Halos in Late-Type and Dwarf Spheroidal Galaxies
The Astrophysical Journal, 2016
Published mass models fitted to galaxy rotation curves are used to study the systematic properties of dark matter (DM) halos in late-type and dwarf spheroidal (dSph) galaxies. Halo parameters are derived by fitting non-singular isothermals to (V 2 −V 2 vis) 1/2 , where V (r) is the observed rotation curve and V vis is the rotation curve of the visible matter. The latter is calculated from the surface brightness assuming that the mass-to-light ratio M/L is constant with radius. "Maximum disk" values of M/L are adjusted to fit as much of the inner rotation curve as possible without making the halo have a hollow core. Rotation curve decomposition becomes impossible fainter than absolute magnitude M B ≃ −14, where V becomes comparable to the velocity dispersion of the gas. To increase the luminosity range further, we include dSph galaxies, which are physically related to spiral and irregular galaxies. Combining the data, we find that DM halos satisfy well defined scaling laws analogous to the "fundamental plane" relations for elliptical galaxies. Halos in less luminous galaxies have smaller core radii r c , higher central densities ρ 0 , and smaller central velocity dispersions σ. Scaling laws provide new and detailed constraints on the nature of DM and on galaxy formation and evolution. Some simple implications include: 1-A single, continuous physical sequence of increasing mass extends from dSph galaxies with M B ≃ −7.6 to Sc I galaxies with M B ≃ −22.4. 2-The high DM densities in dSph galaxies are normal for such tiny galaxies. Since virialized density depends on collapse redshift z coll , ρ 0 ∝ (1 + z coll) 3 , the smallest dwarfs formed at least ∆z coll ≃ 7 earlier than the biggest spirals. 3-The high DM densities of dSphs implies that they are real galaxies formed from primordial density fluctuations. They are not tidal fragments. Tidal dwarfs cannot retain even the low DM densities of their giant-galaxy progenitors. In contrast, dSphs have higher DM densities than do giant-galaxy progenitors. 4-The fact that, as luminosity decreases, dwarf galaxies become much more numerous and also more nearly dominated by DM raises the possibility that there exists a large population of objects that are completely dark. Such objects are a canonical prediction of cold DM theory. If they exist, "empty halos" are likely to be small and dense-that is, darker versions of Draco and UMi. 5-The slopes of the DM parameter correlations provide a measure on galactic mass scales of the slope n of the power spectrum |δ k | 2 ∝ k n of primordial density fluctuations. Our preliminary results not yet corrected for baryonic compression of DM give n ≃ −1.9 ± 0.2. This is consistent with cold DM theory.
Dark Halo and Disk Galaxy Scaling Laws in Hierarchical Universes
The Astrophysical Journal, 2000
We use cosmological N-body/gasdynamical simulations that include star formation and feedback to examine the proposal that scaling laws between the total luminosity, rotation speed, and angular momentum of disk galaxies reflect analogous correlations between the structural parameters of their surrounding dark matter halos. The numerical experiments follow the formation of galaxy-sized halos in two Cold Dark Matter dominated universes: the standard Ω = 1 CDM scenario and the currently popular ΛCDM model. We find that the slope and scatter of the I-band Tully-Fisher relation are well reproduced in the simulations, although not, as proposed in recent work, as a result of the cosmological equivalence between halo mass and circular velocity: large systematic variations in the fraction of baryons that collapse to form galaxies and in the ratio between halo and disk circular velocities are observed in our numerical experiments. The Tully-Fisher slope and scatter are recovered in this model as a direct result of the dynamical response of the halo to the assembly of the luminous component of the galaxy. We conclude that models that neglect the self-gravity of the disk and its influence on the detailed structure of the halo cannot be used to derive meaningful estimates of the scatter or slope of the Tully-Fisher relation. Our models fail, however, to match the zero-point of the Tully-Fisher relation, as well as that of the relation linking disk rotation speed and angular momentum. These failures can be traced, respectively, to the excessive central concentration of dark halos formed in the Cold Dark Matter cosmogonies we explore and to the formation of galaxy disks as the final outcome of a sequence of merger events. Disappointingly, our feedback formulation, calibrated to reproduce the empirical correlations linking star formation rate and gas surface density established by Kennicutt, has little influence on these conclusions. Agreement between model and observations appears to demand substantial revision to the Cold Dark Matter scenario or to the manner in which baryons are thought to assemble and evolve into galaxies in hierarchical universes.
Secular evolution of galaxies and galaxy clusters in decaying dark matter cosmology
Physical Review D, 2009
If the dark matter sector in the Universe is composed by metastable particles, galaxies and galaxy clusters are expected to undergo significant secular evolution from high to low redshift. We show that the decay of dark matter, with a lifetime compatible with cosmological constraints, can be at the origin of the observed evolution of the Tully-Fisher relation of disk galaxies and alleviate the problem of the size evolution of elliptical galaxies, while being consistent with the current observational constraints on the gas fraction of clusters of galaxies.
The Cosmological Origin of Disk Galaxy Scaling Laws
We discuss possible origins of scaling laws relating structural properties of disk galaxies within the context of hierarchically clustering theories of galaxy formation. Using gasdynamical simulations that incorporate the effects of star formation we illustrate these global trends and highlight the difficulties faced by models that envision disk galaxies as the final outcome of a hierarchical sequence of merger events. In particular, we focus on the cosmological origin of the Tully-Fisher relation, and argue that this correlation between the total luminosity and rotation speed of disk galaxies is a natural result of the approximately scale free formation process of the massive halos they inhabit. Although the slope and scatter of the Tully-Fisher relation can be readily reproduced in hierarchical formation scenarios, the observed zero-point of the relation is inconsistent with simulations of galaxy formation in Cold Dark Matter universes, a difficulty that can be traced to the high central mass concentration of dark halos formed in this cosmogony. This result indicates that substantial revision to the new "standard" model of structure formation (ΛCDM) may be needed in order to accommodate observations on the scale of individual disk galaxies.
Monthly Notices of The Royal Astronomical Society, 2010
We examine correlations between masses, sizes and star formation histories for a large sample of low-redshift early-type galaxies, using a simple suite of dynamical and stellar population models. We confirm an anticorrelation between the size and stellar age and go on to survey for trends with the central content of dark matter (DM). An average relation between the central DM density and galaxy size of <ρDM> ~ R-2eff provides the first clear indication of cuspy DM haloes in these galaxies - akin to standard Λ cold dark matter haloes that have undergone adiabatic contraction. The DM density scales with galaxy mass as expected, deviating from suggestions of a universal halo profile for dwarf and late-type galaxies. We introduce a new fundamental constraint on galaxy formation by finding that the central DM fraction decreases with stellar age. This result is only partially explained by the size-age dependencies, and the residual trend is in the opposite direction to basic DM halo expectations. Therefore, we suggest that there may be a connection between age and halo contraction and that galaxies forming earlier had stronger baryonic feedback, which expanded their haloes, or lumpier baryonic accretion, which avoided halo contraction. An alternative explanation is a lighter initial mass function for older stellar populations.
Galaxy mass and luminosity scaling laws determined by weak gravitational lensing
Arxiv preprint astro-ph/ …, 2001
We present new measurements of scaling laws relating the luminosity of galaxies to the amplitude and shape of their dark matter halos. Early imaging and spectroscopic data from the Sloan Digital Sky Survey are used to make weak lensing measurements of the surface mass density contrast ∆Σ + around classes of lens objects. This surface mass density contrast as a function of radius is a measure of the galaxy-mass correlation function (GMCF). Because spectroscopic redshifts are available for all lens objects, the mass and distance scales are well constrained. The GMCF measured around ∼31,000 lenses is well fit by a power law of the form ∆Σ + = (2.5 +0.7 −0.6 )(R/1Mpc) −0.8±0.2 hM ⊙ pc −2 . We compare this GMCF to galaxy luminosity, type, and environment, and find that it varies strongly with all three. We quantify these variations by comparing the normalization of a fit to the inner 260 h −1 kpc (M 260 ) to the galaxy luminosity. While M 260 is not strongly related to luminosity in bluest band (u ′ ), there is a simple, linear relation between M 260 and luminosity in redder bands (g ′ , r ′ , i ′ , and z ′ ). We test the universality of these mass-to-light scalings by independently measuring them for spiral and elliptical galaxies, and for galaxies in a variety of environments. We find remarkable consistency in these determinations in the red bands, especially i ′ and z ′ . This consistency across a wide range of systems suggests that the measured scaling represents an excellent cosmic average, and that the integrated star formation history of galaxies is strongly related to the dark matter environments in which they form. Future studies of galaxy mass and its relation to luminosity should concentrate on luminosities measured in red bands.
Halo-driven size and velocity dispersion evolution of early-type galaxies
Early-type galaxies (ETGs) are observed to be more compact, on average, at z 2 than at z ≃ 0, at fixed stellar mass. Recent observational works suggest that such size evolution could reflect the similar evolution of the host dark matter halo density as a function of the time of galaxy quenching. We explore this hypothesis by studying the distribution of halo central velocity dispersion (σ 0) and half-mass radius (r h) as functions of halo mass M and redshift z, in a cosmological Λ-CDM N-body simulation. In the range 0 z 2.5, we find σ 0 ∝ M 0.31−0.37 and r h ∝ M 0.28−0.32 , close to the values expected for homologous virialized systems. At fixed M in the range 10 11 M ⊙ M 5.5 × 10 14 M ⊙ we find σ 0 ∝ (1 + z) 0.35 and r h ∝ (1 + z) −0.7. We show that such evolution of the halo scaling laws is driven by individual haloes growing in mass following the evolutionary tracks σ 0 ∝ M 0.2 and r h ∝ M 0.6 , consistent with simple dissipationless merging models in which the encounter orbital energy is accounted for. We compare the N-body data with ETGs observed at 0 z 3 by populating the haloes with a stellar component under simple but justified assumptions: the resulting galaxies evolve consistently with the observed ETGs up to z ≃ 2, but the model has difficulty reproducing the fast evolution observed at z 2. We conclude that a substantial fraction of the size evolution of ETGs can be ascribed to a systematic dependence on redshift of the dark matter haloes structural properties.
Monthly Notices of The Royal Astronomical Society, 2010
We examine correlations between masses, sizes and star formation histories for a large sample of low-redshift early-type galaxies, using a simple suite of dynamical and stellar population models. We confirm an anticorrelation between the size and stellar age and go on to survey for trends with the central content of dark matter (DM). An average relation between the central DM density and galaxy size of 〈ρDM〉∝R−2eff provides the first clear indication of cuspy DM haloes in these galaxies – akin to standard Λ cold dark matter haloes that have undergone adiabatic contraction. The DM density scales with galaxy mass as expected, deviating from suggestions of a universal halo profile for dwarf and late-type galaxies.We introduce a new fundamental constraint on galaxy formation by finding that the central DM fraction decreases with stellar age. This result is only partially explained by the size–age dependencies, and the residual trend is in the opposite direction to basic DM halo expectations. Therefore, we suggest that there may be a connection between age and halo contraction and that galaxies forming earlier had stronger baryonic feedback, which expanded their haloes, or lumpier baryonic accretion, which avoided halo contraction. An alternative explanation is a lighter initial mass function for older stellar populations.