The relation between stellar mass and weak lensing signal around galaxies: implications for modified Newtonian dynamics

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-fitting slope  α= 0.74 ± 0.08  . This result is inconsistent with modified Newtonian dynamics (MOND), which predicts  α= 0.5  (we find  α > 0.5  with 99.7 per cent 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 ≳ 10¹¹ L_⊙). 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.     

Constraints on decaying dark matter from XMM–Newton observations of M31

We derive constraints on the parameters of the radiatively decaying dark matter (DM) particle, using the XMM–Newton EPIC spectra of the Andromeda galaxy (M31). Using the observations of the outer (5–13 arcmin) parts of M31, we improve the existing constraints. For the case of sterile neutrino DM, combining our constraints with the latest computation of abundances of sterile neutrinos in the Dodelson–Widrow (DW) scenario, we obtain the lower mass limit   m _s < 4 keV  , which is stronger than the previous one   m _s < 6 keV  , obtained recently by Asaka, Laine & Shaposhnikov. Comparing this limit with the most recent results on Lyman α forest analysis of Viel et al.  ( m _s > 5.6 keV  ), we argue that the scenario in which all the DM is produced via the DW mechanism is ruled out. We discuss, however, other production mechanisms and note that the sterile neutrino remains a viable candidate for DM, either warm or cold.     

Is an 11 eV sterile neutrino consistent with clusters, the cosmic microwave background and modified Newtonian dynamics?

In this paper, we show that if a single sterile neutrino exists such that     , it can serendipitously solve all outstanding issues of the Modified Newtonian Dynamics. We focus on fitting the angular power spectrum of the cosmic microwave background (CMB) in detail which is possible using a flat Universe with     and the usual baryonic and dark energy components. One cannot match the CMB if there is more than one massive sterile neutrino, nor with three active neutrinos of 2 eV. This model has the same expansion history as the Λ cold dark matter  (ΛCDM)  model and only differs at the galactic scale, where the modified dynamics outperform  ΛCDM  comprehensively. We discuss how an 11 eV sterile neutrino can explain the dark matter of galaxy clusters without influencing individual galaxies and potentially match the matter power spectrum.     

Clusters of galaxies with modified Newtonian dynamics

I consider X-ray emitting clusters of galaxies in the context of modified Newtonian dynamics (MOND). Self-gravitating isothermal gas spheres are not good representations of rich clusters; the X-ray luminosity at a given temperature is typically an order of magnitude larger than observed, and the predicted X-ray surface brightness distribution is not well-matched by the standard 'β-model' fits to the observations. Pure gas spheres with a density distribution described by a β-model also fail because, with MOND, these objects are far from isothermal and again overluminous. These problems may be resolved by adding an additional dark mass component in the central regions, here modelled by a constant density sphere contained within two core radii and having a mass typically of one to two times the total cluster mass in the gas. With this additional component, the observed luminosity–temperature relation for clusters of galaxies is reproduced, and the typical mass discrepancy in actual clusters is three to four times smaller than implied by Newtonian dynamics. Thus, while MOND significantly reduces the mass of the dark component in clusters it does not remove it completely. I speculate on the nature of the dark component and argue that neutrinos, with mass near the experimental upper limit are a possible candidate.     

Neutrinos as cluster dark matter

The dynamical mass of clusters of galaxies, calculated in terms of MOdified Newtonian Dynamics (MOND), is a factor of 2 or 3 times smaller than the Newtonian dynamical mass but remains significantly larger than the observed baryonic mass in the form of hot gas and stars in galaxies. Here I consider further the suggestion that the undetected matter might be in the form of cosmological neutrinos with mass of the order of 2 eV. If the neutrinos and baryons have comparable velocity dispersions and if the two components maintain their cosmological density ratio, then the electron density in the cores of clusters should be proportional to T ^3/2, as appears to be true in non-cooling flow clusters. This is equivalent to the 'entropy floor' proposed to explain the steepness of the observed luminosity–temperature relation, but here preheating of the medium is not required. Two-fluid (neutrino–baryon) hydrostatic models of clusters, in the context of MOND, reproduce the observed luminosity–temperature relation of clusters. If the β law is imposed on the gas density distribution, then the self-consistent models predict the general form of the observed temperature profile in both cooling and non-cooling flow clusters.     

Marriage à-la-MOND: Baryonic dark matter in galaxy clusters and the cooling flow puzzle

I start with a brief introduction to MOND phenomenology and its possible roots in cosmology—a notion that may turn out to be the most far reaching aspect of MOND. Next I discuss the implications of MOND for the dark matter (DM) doctrine: MOND’s successes imply that baryons determine everything. For DM this would mean that the puny tail of leftover baryons in galaxies wags the hefty DM dog. This has to occur in many intricate ways, and despite the haphazard construction history of galaxies—a very tall order. I then concentrate on galaxy clusters in light of MOND, which still requires some yet undetected cluster dark matter, presumably in some baryonic form (CBDM). This CBDM might contribute to the heating of the X-ray emitting gas and thus alleviate the cooling flow puzzle. MOND, qua theory of dynamics, does not directly enter the microphysics of the gas; however, it does force a new outlook on the role of DM in shaping the cluster gas dynamics: MOND tells us that the cluster DM is not cold dark matter, is not so abundant, and is not expected in galaxies; it is thus not subject to constraints on baryonic DM in galaxies. The mass in CBDM required in a whole cluster is, typically, similar to that in hot gas, but is rather more centrally concentrated, totally dominating the core. The CBDM contribution to the baryon budget in the universe is thus small. Its properties, deduced for isolated clusters, are consistent with the observations of the “bullet cluster”. Its kinetic energy reservoir is much larger than that of the hot gas in the core, and would suffice to keep the gas hot for many cooling times. Heating can be effected in various ways depending on the exact nature of the CBDM, from very massive black holes to cool, compact gas clouds.     

On the galaxy stellar mass function, the mass–metallicity relation and the implied baryonic mass function

A comparison between published field galaxy stellar mass functions (GSMFs) shows that the cosmic stellar mass density is in the range 4–8 per cent of the baryon density (assuming  Ω_b= 0.045  ). There remain significant sources of uncertainty for the dust correction and underlying stellar mass-to-light ratio even assuming a reasonable universal stellar initial mass function. We determine the   z < 0.05  GSMF using the New York University Value-Added Galaxy Catalog sample of 49 968 galaxies derived from the Sloan Digital Sky Survey and various estimates of stellar mass. The GSMF shows clear evidence for a low-mass upturn and is fitted with a double Schechter function that has  α₂≃−1.6  . At masses below  ∼10^8.5 M_⊙  , the GSMF may be significantly incomplete because of missing low-surface-brightness galaxies. One interpretation of the stellar mass–metallicity relation is that it is primarily caused by a lower fraction of available baryons converted to stars in low-mass galaxies. Using this principle, we determine a simple relationship between baryonic mass and stellar mass and present an 'implied baryonic mass function'. This function has a faint-end slope,  α₂≃−1.9  . Thus, we find evidence that the slope of the low-mass end of the galaxy mass function could plausibly be as steep as the halo mass function. We illustrate the relationship between halo baryonic mass function → galaxy baryonic mass function → GSMF. This demonstrates the requirement for peak galaxy formation efficiency at baryonic masses  ∼10¹¹ M_⊙  corresponding to a minimum in feedback effects. The baryonic-infall efficiency may have levelled off at lower masses.     

MOND plus classical neutrinos are not enough for cluster lensing

Clusters of galaxies offer a robust test bed for probing the nature of dark matter that is insensitive to the assumption of the gravity theories. Both Modified Newtonian Dynamics (MOND) and General Relativity (GR) would require similar amounts of non-baryonic matter in clusters as MOND boosts the gravity only mildly on cluster scales. Gravitational lensing allows us to estimate the enclosed mass in clusters on small (∼20–50 kpc) and large (∼several 100 kpc) scales independent of the assumptions of equilibrium. Here, we show for the first time that a combination of strong and weak gravitational lensing effects can set interesting limits on the phase-space density of dark matter in the centres of clusters. The phase-space densities derived from lensing observations are inconsistent with neutrino masses ranging from 2–7 eV, and hence do not support the 2 eV-range particles required by MOND. To survive, the most plausible modification for MOND may be an additional degree of dynamical freedom in a covariant incarnation.     

Velocity dispersions of dwarf spheroidal galaxies: dark matter versus MOND

We present predictions for the line-of-sight velocity dispersion profiles of dwarf spheroidal galaxies and compare them to observations in the case of the Fornax dwarf. The predictions are made in the framework of standard dynamical theory of spherical systems with different velocity distributions. The stars are assumed to be distributed according to Sérsic laws with parameters fitted to observations. We compare predictions obtained assuming the presence of dark matter haloes (with density profiles adopted from N -body simulations) with those resulting from Modified Newtonian Dynamics (MOND). If the anisotropy of velocity distribution is treated as a free parameter, observational data for Fornax are reproduced equally well by models with dark matter and with MOND. If stellar mass-to-light ratio of 1 M_⊙/L_⊙ is assumed, the required mass of the dark halo is     , two orders of magnitude larger than the mass in stars. The derived MOND acceleration scale is     . In both cases a certain amount of tangential anisotropy in the velocity distribution is needed to reproduce the shape of the velocity dispersion profile in Fornax.     

Galaxy cluster masses without non-baryonic dark matter

We apply the modified acceleration law obtained from Einstein gravity coupled to a massive skew symmetric field,   F _μνλ  , to the problem of explaining X-ray galaxy cluster masses without exotic dark matter. Utilizing X-ray observations to fit the gas mass profile and temperature profile of the hot intracluster medium (ICM) with King 'β-models', we show that the dynamical masses of the galaxy clusters resulting from our modified acceleration law fit the cluster gas masses for our sample of 106 clusters without the need of introducing a non-baryonic dark matter component. We are further able to show for our sample of 106 clusters that the distribution of gas in the ICM as a function of radial distance is well fitted by the dynamical mass distribution arising from our modified acceleration law without any additional dark matter component. In a previous work, we applied this theory to galaxy rotation curves and demonstrated good fits to our sample of 101 low surface brightness, high surface brightness and dwarf galaxies including 58 galaxies that were fitted photometrically with the single-parameter mass-to-light ratio ( M / L )_stars. The results obtained there were qualitatively similar to those obtained using Milgrom's phenomenological Modified Newtonian Dynamics (MOND) model, although the determined galaxy masses were quantitatively different, and MOND does not show a return to Keplerian behaviour at extragalactic distances. The results obtained here are compared to those obtained using Milgrom's phenomenological MOND model which does not fit the X-ray galaxy cluster masses unless an auxiliary dark matter component is included.     

Cosmological constraints from the X-ray gas mass fraction in relaxed lensing clusters observed with Chandra

We present precise measurements of the X-ray gas mass fraction for a sample of luminous, relatively relaxed clusters of galaxies observed with the Chandra observatory, for which independent confirmation of the mass results is available from gravitational lensing studies. Parametrizing the total (luminous plus dark matter) mass profiles using the model of Navarro, Frenk & White, we show that the X-ray gas mass fractions in the clusters asymptote towards an approximately constant value at a radius r ₂₅₀₀, where the mean interior density is 2500 times the critical density of the Universe at the redshifts of the clusters. Combining the Chandra results on the X-ray gas mass fraction and its apparent redshift dependence with recent measurements of the mean baryonic matter density in the Universe and the Hubble constant determined from the Hubble Key Project, we obtain a tight constraint on the mean total matter density of the Universe,     , and measure a positive cosmological constant,     . Our results are in good agreement with recent, independent findings based on analyses of anisotropies in the cosmic microwave background radiation, the properties of distant supernovae, and the large-scale distribution of galaxies.     

Searching for neutrinos from WIMP annihilations in the Galactic stellar disc

Weakly interacting massive particles (WIMPs) are a viable candidate for the relic abundance of dark matter (DM) produced in the early universe. So far, WIMPs have eluded direct detection through interactions with baryonic matter. Neutrino emission from accumulated WIMP annihilations in the solar core has been proposed as a signature of DM, but has not yet been detected. These null results may be due to small-scale DM density fluctuations in the halo with the density of our local region being lower than the average  (∼0.3 GeV cm⁻³)  . However, the accumulated neutrino signal from WIMP annihilations in the Galactic stellar disc would be insensitive to local density variations. Inside the disc, DM can be captured by stars causing an enhanced annihilation rate and therefore a potentially higher neutrino flux than what would be observed from elsewhere in the halo. We estimate a neutrino flux from the WIMP annihilations in the stellar disc to be enhanced by more than an order of magnitude compared to the neutrino fluxes from the halo. We offer a conservative estimate for this enhanced flux, based on the WIMP–nucleon cross-sections obtained from direct-detection experiments by assuming a density of  ∼0.3 GeV cm⁻³  for the local DM. We also compare the detectability of these fluxes with a signal of diffuse high-energy neutrinos produced in the Milky Way by the interaction of cosmic rays with the interstellar medium. These comparative signals should be observable by large neutrino detectors.     

The X-ray spectrum of NGC 7213 and the Seyfert–LINER connection

We present an XMM–Newton observation of the Seyfert–LINER (low-ionization nuclear emission-line region) galaxy NGC 7213. The RGS soft X-ray spectrum is well fitted with a power law plus soft X-ray collisionally ionized thermal plasma  ( kT = 0.18^+0.03_−0.01 keV)  . We confirm the presence of Fe  i , Fe  xxv and Fe  xxvi Kα emission in the EPIC spectrum and set tighter constraints on their equivalent widths of  82⁺¹⁰₋₁₃, 24⁺⁹₋₁₁  and 24⁺¹⁰₋₁₃ eV, respectively. We compare the observed properties together with the inferred mass accretion rate of NGC 7213 with those of other Seyfert and LINER galaxies. We find that NGC 7213 has intermediate X-ray spectral properties lying between those of the weak active galactic nucleus found in the LINER M81 and higher-luminosity Seyfert galaxies. There appears to be a continuous sequence of X-ray properties from the Galactic Centre through LINER galaxies to Seyferts, probably determined by the amount of material available for accretion in the central regions.     

The C/CO ratio in B335 and the decaying dark matter neutrino hypothesis

C¹⁸O J  = 2–1, C¹⁷O J  = 2–1 and [C  I ] ³P₁–³P₀ emission from the dense cold cloud B335 has been observed and modelled in order to determine the C/CO ratio. The observed ratio is compared with a prediction by Tarafdar who assumes a mechanism in which the CO dissociation is caused by photons of energy ∼ 13.8 eV. These were postulated by Sciama to result from the decay of dark matter neutrinos. Our value for the C/CO ratio sets an upper limit to the strength of the neutrino decay dissociation process, thus providing a significant datum for interstellar chemistry theory.     

Baryonic conversion tree: the global assembly of stars and dark matter in galaxies from the Sloan Digital Sky Survey

Using the spectroscopic sample of the Sloan Digital Sky Survey Data Release 1 (SDSS DR1), we measure how gas was transformed into stars as a function of time and stellar mass: the baryonic conversion tree (BCT). There is a clear correlation between early star formation activity and present-day stellar mass: the more massive galaxies have formed approximately 80 per cent of their stars at   z > 1  , while for the less massive ones the value is only approximately 20 per cent. By comparing the BCT with the dark matter merger tree, we find indications that star formation efficiency at   z > 1  had to be approximately a factor of two higher than today (∼10 per cent) in galaxies with present-day stellar mass larger than  2 × 10¹¹ M_⊙  , if this early star formation occurred in the main progenitor. Therefore, the λ cold dark matter (LCDM) paradigm can accommodate a large number of red objects. On the other hand, in galaxies with present-day stellar mass less than  10¹¹ M_⊙  , efficient star formation seems to have been triggered at   z ∼ 0.2  . We show that there is a characteristic mass  ( M _*∼ 10¹⁰ M_⊙)  for feedback efficiency (or lack of star formation). For galaxies with masses lower than this, feedback (or star formation suppression) is very efficient while for higher masses it is not. The BCT, determined here for the first time, should be an important observable with which to confront theoretical models of galaxy formation.     

Revisiting the baryon fractions of galaxy clusters: a comparison with WMAP 3-yr results

The universal baryonic mass fraction  (Ω_b/Ω_m)  can be sensitively constrained using X-ray observations of galaxy clusters. In this paper, we compare the baryonic mass fraction inferred from measurements of the cosmic microwave background with the gas mass fractions ( f _gas) of a large sample of clusters taken from the recent literature. In systems cooler than 4 keV, f _gas declines as the system temperature decreases. However, in higher temperature systems, f _gas( r ₅₀₀) converges to  ≈(0.12 ± 0.02)( h /0.72)^−1.5  , where the uncertainty reflects the systematic variations between clusters at r ₅₀₀. This is significantly lower than the maximum-likelihood value of the baryon fraction from the recently released Wilkinson Microwave Anisotropy Probe ( WMAP ) 3-yr results. We investigate possible reasons for this discrepancy, including the effects of radiative cooling and non-gravitational heating, and conclude that the most likely solution is that Ω_m is higher than the best-fitting WMAP value (we find  Ω_m= 0.36^+0.11_−0.08  ), but consistent at the 2σ level. Degeneracies within the WMAP data require that σ₈ must also be greater than the maximum likelihood value for consistency between the data sets.     

Observational constraints of sterile neutrinos in galaxies

We study a model in which degenerate sterile neutrinos account for galactic dark matter. We fit the rotation curves of 5 dwarf galaxies with the degenerate sterile neutrinos in hydrostatic equilibrium. Also we estimate the range of sterile neutrino mass by calculating the upper and lower bounds of the mass densities of sterile neutrino halos in the outermost regions of 21 normal galaxies. The observed rotation curves of 5 dwarf galaxies and 21 normal galaxies are consistent with having sterile neutrinos with mass (26–30) eV, and the similarity of the rotation curves of different galaxies emerges naturally in our model.     

Dark haloes of spiral galaxies: ISO photometry

We exclude hydrogen-burning stars, of any mass above the hydrogen-burning limit and any metallicity, as significant contributors to the massive haloes deduced from rotation curves to dominate the outer parts of spiral galaxies. We present and analyse images of four nearly edge-on bulgeless spiral galaxies (UGC 711, NGC 2915, UGC 12426, UGC 1459) obtained with ISOCAM (The CAMera instrument on board the Infrared Space Observatory ) at 14.5 and 6.75 μm. Our sensitivity limit for detection of any diffuse infrared emission associated with the dark haloes in these galaxies is a few tens of μJy per 6 × 6 arcsec² pixel, with this limit currently set by remaining difficulties in modelling the non-linear behaviour of the detectors. All four galaxies show zero detected signal from extended non-disc emission, consistent with zero halo-like luminosity density distribution. The 95 per cent upper limit on any emission, for NGC 2915 in particular, allows us to exclude very low mass main-sequence stars ( M  > 0.08 M⊙) and young brown dwarfs (≲1 Gyr) as significant contributors to dark matter in galactic haloes. Combining our results with those of the Galactic microlensing surveys, which exclude objects with M  < 0.01 M⊙, excludes almost the entire possible mass range of compact baryonic objects from contributing to Galactic dark matter.     

Wide triplets of galaxies: collapse on spatial scales of ∼1 Mpc

We study triple systems of galaxies with mean projected harmonic separation ≃0.6  h ⁻¹ Mpc     We call the systems 'wide triplets', in contrast to compact triplets with mean projected harmonic separation ≃0.04  h ⁻¹ Mpc, studied by Karachentsev et al. Data are taken for 108 wide triplets from a list compiled by Trofimov & Chernin; at least one-third of them are considered to be probably isolated physical systems. With typical crossing times of about the Hubble time, the wide triplets seem to be in a state of ongoing collapse. This is confirmed by a set of computer models which simulate well the observational characteristics of the ensemble of wide triplets. The simulations also give a statistical estimate of the total mass of a typical wide triplet: it proves to be ≃10¹³ M_⊙. This figure indicates that the dark matter mass is 15–30 times the mass of baryonic matter in the systems. The dynamics of wide triplets, as well as their dark matter content, provide new direct cosmological constraints by establishing that hierarchical evolution is occurring on a mass scale of ∼10¹³ M_⊙ and a spatial scale of ∼1 Mpc.     

Testing fundamental physics with distant star clusters: theoretical models for pressure-supported stellar systems

We investigate the mean velocity dispersion and the velocity dispersion profile of stellar systems in modified Newtonian dynamics (MOND), using the N -body code n-mody , which is a particle-mesh-based code with a numerical MOND potential solver developed by Ciotti, Londrillo & Nipoti. We have calculated mean velocity dispersions for stellar systems following Plummer density distributions with masses in the range of 10⁴ to  10⁹ M_⊙  and which are either isolated or immersed in an external field. Our integrations reproduce previous analytic estimates for stellar velocities in systems in the deep MOND regime  ( a _i, a _e≪ a ₀)  , where the motion of stars is either dominated by internal accelerations  ( a _i≫ a _e)  or constant external accelerations  ( a _e≫ a _i)  . In addition, we derive for the first time analytic formulae for the line-of-sight velocity dispersion in the intermediate regime  ( a _i∼ a _e∼ a ₀)  . This allows for a much-improved comparison of MOND with observed velocity dispersions of stellar systems. We finally derive the velocity dispersion of the globular cluster Pal 14 as one of the outer Milky Way halo globular clusters that have recently been proposed as a differentiator between Newtonian and MONDian dynamics.