The evolution of globular clusters due to 2-body relaxation results in an outward flow of energy and at some stage all clusters need a central energy source to sustain their evolution. Henon provided the insight that we do not need to know the detail
s of the energy production in order to understand the relaxation-driven evolution of the cluster, at least outside the core. He provided two self-similar solutions for the evolution of clusters based on the view that the cluster as a whole determines the amount of energy that is produced in the core: steady expansion for isolated clusters, and homologous contraction for clusters evaporating in a tidal field. We combine these models: the half-mass radius increases during the first half of the evolution, and decreases in the second half; while the escape rate approaches a constant value set by the tidal field. We refer to these phases as `expansion dominated and `evaporation dominated. These simple analytical solutions immediately allow us to construct evolutionary tracks and isochrones in terms of cluster half-mass density, cluster mass and galacto-centric radius. From a comparison to the Milky Way globular clusters we find that roughly 1/3 of them are in the second, evaporation-dominated phase and for these clusters the density inside the half-mass radius varies with the galactocentric distance R as rho_h ~ 1/R^2. The remaining 2/3 are still in the first, expansion-dominated phase and their isochrones follow the environment-independent scaling rho_h ~ M^2; that is, a constant relaxation time-scale. We find substantial agreement between Milky Way globular cluster parameters and the isochrones, which suggests that there is, as Henon suggested, a balance between the flow of energy and the central energy production for almost all globular clusters.
We study the amplitude of the weak gravitational lensing signal as a function of stellar mass around a sample of relatively isolated galaxies. This selection of lenses simplifies the interpretation of the observations, which consist of data from the
Red- sequence Cluster Survey and the Sloan Digital Sky Survey. We find that the amplitude of the lensing signal as a function of stellar mass is well described by a power law with a best fit slope alpha= 0.74 pm 0.08. This result is inconsistent with Modified Newtonian Dynamics, which predicts alpha = 0.5 (we find alpha > 0.5 with 99.7% confidence). As a related test, we determine the MOND mass-to-light ratio as a function of luminosity. Our results require dark matter for the most luminous galaxies (L >=10^11 L_sun). We rule out an extended halo of gas or active neutrinos as a way of reconciling our findings with MOND. Although we focus on a single alternative gravity model, we note that our results provide an important test for any alternative theory of gravity.
The tight correlation between galaxy bulges and their central black hole masses likely emerges in a phase of rapid collapse and starburst at high redshift, due to the balance of gravity on gas with the feedback force from starbursts and the wind from
the black hole; the average gravity on per unit mass of gas is ~ 2 x 10^-10 m/sec^2 during the star burst phase. This level of gravity could come from the real r^{-1} cusps of Cold Dark Matter (CDM) halos, but the predicted gravity would have a large scatter due to dependence on cosmological parameters and formation histories. Better agreement is found with the gravity from the scalar field in some co-varia
Several rare coincidences of scales in standard particle physics are needed to explain (i) why neutrinos have mass, (ii) why the negative pressure of the cosmological dark energy (DE) coincides with the positive pressure of random motion of dark matt
er (DM) in bright galaxies, (iii) why Dark Matter in galaxies seems to have a finite phase-space density, and to follow the Tully-Fisher-Milgrom relation of galaxy rotation curves. The old idea of self-interacting DM is given a new spin: we propose that the neutrino spin-gravity coupling could lead to a cosmic neutrino dark fluid with a an internal energy density varying as function of the local acceleration of the neutrino fluid with respect the CMB background. We link the Tully-Fisher-Milgrom relation of spiral galaxies (or MOND) with the relativistic pressure of the neutrino dark fluid without modifying Einsteinian gravity.
Empirical theories of Dark Matter like MOND gravity and of Dark Energy like f(R) gravity were motivated by astronomical data. But could these theories be branches rooted from a more general hence natural framework? Here we propose the natural Lagrang
ian of such a framework based on simple dimensional analysis and co-variant symmetry requirements, and explore various outcomes in a top-down fashion. Our framework preserves the co-variant formulation of GR, but allows the expanding physical metric be bent by a single new species of Dark Fluid flowing in space-time. Its non-uniform stress tensor and current vector are simply functions of a vector field of variable norm, resembling the 4-vector electromagnetic potential description for the photon fluid, but is dark (e.g., by very early decoupling from the baryon-radiation fluid). The Dark Fluid framework naturally branches into a continuous spectrum of theories with Dark Energy and Dark Matter effects, including the $f(R)$ gravity, TeVeS-like theories, Einstein-Aether and $ uLambda$ theories as limiting cases. When the vector field degenerates into a pure Higgs-like scalar field, we obtain the physics for inflaton and quintessence. In this broad setting we emphasize the non-constant dynamical field behind the cosmological constant effect, and highlight plausible corrections beyond the classical MOND predictions. Choices of parameters can be made to pass BBN, PPN, and causality constraints. The Dark Fluid is inspired to unify/simplify the astronomically successful ingredients of previous constructions: the desired effects of inflaton plus quintessence plus Cold DM particle fields or MOND-like scalar field(s) are shown largely achievable by one vector field only.
We propose a unified single-field description of the galactic Dark Matter and various uniform scalar fields for the inflation and cosmological constant. The two types of effects could originate from a fluid of both spatially and temporally varying Va
cuum Energy if the vacuum has an uneven pressure caused by a photon-like vector field (of perhaps an unstable massive boson). We propose a most general Lagrangian with a {bf N}on-{bf u}niform Cosmological Constant for this vacuum fluid (dubbed as a Nu-Lambda fluid), working within the framework of Einsteinian gravity. This theory includes a continuous spectrum of plausible dark energy theories and gravity theories, e.g., inflation, quintessence, k-essence, f(R), Generalized Einstein-Aether f(K), MOND, TeVeS, BSTV etc. theories. It also suggests new models such as a certain f(K+R) model, which suggests intriguing corrections to MOND depending of redshift and density. Some specific constructions of the Nu-Lambda fluid (e.g., Zhaos V-$Lambda$ model) closely resemble the $Lambda$CDM cosmology on large scale, but fit galaxy rotation curves as good as MOND. Perturbed Einstein Equations in a simple $f(K_4)$ model are solvable and show effects of a DM coupled to DE. Incorporating the perturbation equations here into standard simulations for cosmological structure growth offers a chance to falsify examples of the Nu-Lambda theories.
Gravity is nearly a universal constant in the cusp of an NFW galaxy halo. Inside this external field an isothermal gas sphere will collapse and trigger a starburst if above a critical central pressure. Thus formed spheroidal stellar systems have Sers
ic-profile and satisfy the Faber-Jackson relation. The process is consistent with observed starbursts. We also recover the M_BH vs. velocity dispersion relation, if the gas collapse is regulated or resisted by the feedback from radiation from the central BH.
We investigate the possibility of discriminating between Modified Newtonian Dynamics (MOND) and Newtonian gravity with dark matter, by studying the vertical dynamics of disk galaxies. We consider models with the same circular velocity in the equatori
al plane (purely baryonic disks in MOND and the same disks in Newtonian gravity embedded in spherical dark matter haloes), and we construct their intrinsic and projected kinematical fields by solving the Jeans equations under the assumption of a two-integral distribution function. We found that the vertical velocity dispersion of deep-MOND disks can be much larger than in the equivalent spherical Newtonian models. However, in the more realistic case of high-surface density disks this effect is significantly reduced, casting doubts on the possibility of discriminating between MOND and Newtonian gravity with dark matter by using current observations.
We present semi-analytical constraint on the amount of dark matter in the merging bullet galaxy cluster using the classical Local Group timing arguments. We consider particle orbits in potential models which fit the lensing data. {it Marginally consi
stent} CDM models in Newtonian gravity are found with a total mass M_{CDM} = 1 x 10^{15}Msun of Cold DM: the bullet subhalo can move with V_{DM}=3000km/s, and the bullet X-ray gas can move with V_{gas}=4200km/s. These are nearly the {it maximum speeds} that are accelerable by the gravity of two truncated CDM halos in a Hubble time even without the ram pressure. Consistency breaks down if one adopts higher end of the error bars for the bullet gas speed (5000-5400km/s), and the bullet gas would not be bound by the sub-cluster halo for the Hubble time. Models with V_{DM}~ 4500km/s ~ V_{gas} would invoke unrealistic large amount M_{CDM}=7x 10^{15}Msun of CDM for a cluster containing only ~ 10^{14}Msun of gas. Our results are generalisable beyond General Relativity, e.g., a speed of $4500kms$ is easily obtained in the relativistic MONDian lensing model of Angus et al. (2007). However, MONDian model with little hot dark matter $M_{HDM} le 0.6times 10^{15}msun$ and CDM model with a small halo mass $le 1times 10^{15}msun$ are barely consistent with lensing and velocity data.
We explore the use of tidal streams from Galactic satellites to recover the potential of the Milky Way. Our study is motivated both by the discovery of the first lengthy stellar stream in the halo (cite{it98}) and by the prospect of measuring proper
motions of stars brighter than 20th magnitude in such a stream with an accuracy of $sim 4mu as/$yr, as will be possible with the Space Interferometry Mission (SIM). We assume that the heliocentric radial velocities of these stars can be determined from supporting ground-based spectroscopic surveys, and that the mass and phase-space coordinates of the Galactic satellite with which they are associated will also be known to SIM accuracy. Using results from numerical simulations as trial data sets, we find that, if we assume the correct form for the Galactic potential, we can predict the distances to the stars as a consequence of the narrow distribution of energy expected along the streams. We develop an algorithm to evaluate the accuracy of any adopted potential by requiring that the satellite and stars recombine within a Galactic lifetime when their current phase-space coordinates are integrated backwards. When applied to a four-dimensional grid of triaxial logarithmic potentials, with varying circular velocities, axis ratios and orientation of the major-axis in the disk plane, the algorithm can recover the parameters used for the Milky Way in a simulated data set to within a few percent using only 100 stars in a tidal stream.
