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.     

An explanation for long flares from extragalactic globular cluster X-ray sources

We compare orbits in a thin axisymmetric disc potential in Modified Newtonian Dynamics (MOND) with those in a thin disc plus near-spherical dark matter halo predicted by a ΛCDM cosmology. Remarkably, the amount of orbital precession in MOND is nearly identical to that which occurs in a mildly oblate CDM Galactic halo (potential flattening   q = 0.9  ), consistent with recent constraints from the Sagittarius stream. Since very flattened mass distributions in MOND produce rounder potentials than in standard Newtonian mechanics, we show that it will be very difficult to use the tidal debris from streams to distinguish between a MOND galaxy and a standard CDM galaxy with a mildly oblate halo.
If a galaxy can be found with either a prolate halo or one that is more oblate than   q ∼ 0.9  this would rule out MOND as a viable theory. Improved data from the leading arm of the Sagittarius dwarf – which samples the Galactic potential at large radii – could rule out MOND if the orbital pole precession can be determined to an accuracy of the order of  ±1°  .     

Intrinsic correlation of galaxy shapes: implications for weak lensing measurements

Weak gravitational lensing is now established as a powerful method to measure mass fluctuations in the universe. It relies on the measurement of small coherent distortions of the images of background galaxies. Even low-level correlations in the intrinsic shapes of galaxies could however produce a significant spurious lensing signal. These correlations are also interesting in their own right, since their detection would constrain models of galaxy formation. Using     haloes found in N -body simulations, we compute the correlation functions of the intrinsic ellipticity of spiral galaxies assuming that the disc is perpendicular to the angular momentum of the dark matter halo. We also consider a simple model for elliptical galaxies, in which the shape of the dark matter halo is assumed to be the same as that of the light. For deep lensing surveys with median redshifts ∼1, we find that intrinsic correlations of ∼10⁻⁴ on angular scales     are generally below the expected lensing signal, and contribute only a small fraction of the excess signals reported on these scales. On larger scales we find limits to the intrinsic correlation function at a level ∼10⁻⁵, which gives a (model-dependent) range of separations for which the intrinsic signal is about an order of magnitude below the ellipticity correlation function expected from weak lensing. Intrinsic correlations are thus negligible on these scales for dedicated weak lensing surveys. For wider but shallower surveys such as SuperCOSMOS, APM and SDSS, we cannot exclude the possibility that intrinsic correlations could dominate the lensing signal. We discuss how such surveys could be used to calibrate the importance of this effect, as well as study spin–spin correlations of spiral galaxies.     

X-ray group and cluster mass profiles in MOND: unexplained mass on the group scale

Although very successful in explaining the observed conspiracy between the baryonic distribution and the gravitational field in spiral galaxies without resorting to dark matter (DM), the modified Newtonian dynamics (MOND) paradigm still requires DM in X-ray bright systems. Here, to get a handle on the distribution and importance of this DM, and thus on its possible form, we deconstruct the mass profiles of 26 X-ray emitting systems in MOND, with temperatures ranging from 0.5 to 9 keV. Initially, we compute the MOND dynamical mass as a function of radius, then subtract the known gas mass along with a component of galaxies which include the cD galaxy with   M / L _K = 1  . Next, we test the compatibility of the required DM with ordinary massive neutrinos at the experimental limit of detection  ( m _ν= 2 eV)  , with density given by the Tremaine–Gunn limit. Even by considering that the neutrino density stays constant and maximal within the central 100 or 150 kpc (which is the absolute upper limit of a possible neutrino contribution there), we show that these neutrinos can never account for the required DM within this region. The natural corollary of this finding is that, whereas clusters  ( T ≳ 3 keV)  might have most of their mass accounted for if ordinary neutrinos have a 2 eV mass, groups  ( T ≲ 2 keV)  cannot be explained by a 2 eV neutrino contribution. This means that, for instance, cluster baryonic dark matter (CBDM, Milgrom) or even sterile neutrinos would present a more satisfactory solution to the problem of missing mass in MOND X-ray emitting systems.     

Testing Bekenstein's relativistic Modified Newtonian Dynamics with lensing data

We propose to use multiple-imaged gravitational lenses to set limits on gravity theories without dark matter, specifically tensor–vector–scalar (TeVeS) theory, a theory which is consistent with fundamental relativistic principles and the phenomenology of Modified Newtonian Dynamics (MOND) theory. After setting the framework for lensing and cosmology, we analytically derive the deflection angle for the point lens and the Hernquist galaxy profile, and study their patterns in convergence, shear and amplification. Applying our analytical lensing models, we fit galaxy-quasar lenses in the CfA-Arizona Space Telescope Lens Survey (CASTLES) sample. We do this with three methods, fitting the observed Einstein ring sizes, the image positions, or the flux ratios. In all the cases, we consistently find that stars in galaxies in MOND/TeVeS provide adequate lensing. Bekenstein's toy μ function provides more efficient lensing than the standard MOND μ function. But for a handful of lenses, a good fit would require a lens mass orders of magnitude larger/smaller than the stellar mass derived from luminosity unless the modification function μ and modification scale a ₀ for the universal gravity were allowed to be very different from what spiral galaxy rotation curves normally imply. We discuss the limitation of present data and summarize constraints on the MOND μ function. We also show that the simplest TeVeS 'minimal-matter' cosmology, a baryonic universe with a cosmological constant, can fit the distance–redshift relation from the supernova data, but underpredicts the sound horizon size at the last scattering. We conclude that lensing is a promising approach to differentiate laws of gravity.     

Does the Fornax dwarf spheroidal have a central cusp or core?

The dark matter dominated Fornax dwarf spheroidal has five globular clusters orbiting at ∼1 kpc from its centre. In a cuspy cold dark matter halo the globulars would sink to the centre from their current positions within a few Gyr, presenting a puzzle as to why they survive undigested at the present epoch. We show that a solution to this timing problem is to adopt a cored dark matter halo. We use numerical simulations and analytic calculations to show that, under these conditions, the sinking time becomes many Hubble times; the globulars effectively stall at the dark matter core radius. We conclude that the Fornax dwarf spheroidal has a shallow inner density profile with a core radius constrained by the observed positions of its globular clusters. If the phase space density of the core is primordial then it implies a warm dark matter particle and gives an upper limit to its mass of ∼0.5 keV, consistent with that required to significantly alleviate the substructure problem.     

Chandra measurements of the distribution of mass in the luminous lensing cluster Abell 2390

We present spatially resolved X-ray spectroscopy of the luminous lensing cluster Abell 2390, using observations made with the Chandra observatory. The temperature of the X-ray gas rises with increasing radius within the central ∼ 200 kpc of the cluster, and then remains approximately isothermal, with kT =11.5_−1.6^+1.5 keV , out to the limits of the observations at r ∼1.0 Mpc . The total mass profile determined from the Chandra data has a form in good agreement with the predictions from numerical simulations. Using the parametrization of Navarro, Frenk and White, we measure a scale radius r _s∼0.8 Mpc and a concentration parameter c ∼3 . The best-fitting X-ray mass model is in good agreement with independent gravitational lensing results and optical measurements of the galaxy velocity dispersion in the cluster. The X-ray gas to total mass ratio rises with increasing radius with f _gas∼21 per cent at r =0.9 Mpc . The azimuthally averaged 0.3–7.0 keV surface brightness profile exhibits a small core radius and a clear 'break' at r ∼500 kpc , where the slope changes from S _X ∼^∝  r ^−1.5 to S _X ∼^∝  r ^−3.6 . The data for the central region of the cluster indicate the presence of a cooling flow with a mass deposition rate of 200–300 M_⊙ yr⁻¹ and an effective age of 2–3 Gyr .     

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.     

Seed magnetic Fields Generated by Primordial Supernova Explosions

The origin of the magnetic field in galaxies is an open question in astrophysics. Several mechanisms have been proposed related, in general, to the generation of small seed fields amplified by a dynamo mechanism. In general, these mechanisms have difficulty in satisfying both the requirements of a sufficiently high strength for the magnetic field and the necessary large coherent scales. We show that the formation of dense and turbulent shells of matter, in the multiple explosion scenario of Miranda &38; Opher for the formation of the large-scale structures of the Universe, can naturally act as a seed for the generation of a magnetic field. During the collapse and explosion of Population III objects, a temperature gradient not parallel to a density gradient can naturally be established, producing a seed magnetic field through the Biermann battery mechanism. We show that seed magnetic fields ∼ 10⁻¹²–10⁻¹⁴ G can be produced in this multiple explosion scenario on scales of the order of clusters of galaxies (with coherence length L  ∼ 1.8 Mpc) and up to ∼ 4.5 × 10⁻¹⁰ G on scales of galaxies ( L  ∼ 100 kpc).     

Empirical constraints on alternative gravity theories from gravitational lensing

If it is hypothesized that there is no dark matter, then some alternative gravitational theory must take the place of general relativity (GR) on the largest scales. Dynamical measurements can be used to investigate the nature of such a theory, but only where there is visible matter. Gravitational lensing is potentially a more powerful probe as it can be used to measure deflections far from the lens and, for sufficiently large separations, allow it to be treated as a point-mass. Microlensing within the local group does not yet provide any interesting constraints, as only images formed close to the deflectors are appreciably magnified, but stacking of multiple light-curves and observations of microlensing on cosmological scales may be able to discriminate between GR and non-dark matter theories. Galaxy–galaxy lensing is likely to be a more powerful probe of gravity, with the Sloan Digital Sky Survey (SDSS) commissioning data used here to constrain the deflection law of galaxies to be     for impact parameters in the range     . Together with observations of flat rotation curves, these results imply that, in any gravitational theory, photons must experience (close to) twice the deflection of massive particles moving at the speed of light (at least on these physical scales). The full SDSS data set will also be sensitive to asymmetry in the lensing signal and to variation of the deflection law with galaxy type. A detection of either of these effects would represent an independent confirmation that galaxies are dark matter-dominated; conversely, azimuthal symmetry of the shear signal would rule out the typically ellipsoidal haloes predicted by most simulations of structure formation.     

A comparison of different cluster mass estimates: consistency or discrepancy?

Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and its dynamical evolution. Using the hitherto largest sample of lensing clusters drawn from the literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is excellent agreement between the weak lensing, X-ray and isothermal sphere model-determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2–4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters, as well as from assuming an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.     

The orbit and mass of the Sagittarius dwarf galaxy

Possible orbital histories of the Sgr dwarf galaxy are explored. A special-purpose N -body code is used to construct the first models of the Milky Way–Sgr dwarf system in which both the Milky Way and the Sgr dwarf are represented by full N -body systems and followed for a Hubble time. These models are used to calibrate a semi-analytic model of the Sgr dwarf's orbit that enables us to explore a wider parameter space than is accessible to the N -body models. We conclude that the extant data on the Sgr dwarf are compatible with a wide range of orbital histories. At one extreme the Sgr dwarf initially possesses ∼10¹¹ M_⊙ and starts from a Galactocentric distance R _D(0)≳200 kpc. At the other extreme the Sgr dwarf starts with ∼10⁹ M_⊙ and R _D(0)∼60 kpc, similar to its present apocentric distance. In all cases the Sgr dwarf is initially dark matter dominated and the current velocity dispersion of the Sgr dwarf's dark matter is tightly constrained to be 21±2 km s⁻¹. This number is probably compatible with the smaller measured dispersion of the Sgr dwarf's stars because of (i) the dynamical difference between dark and luminous matter, and (ii) velocity anisotropy.     

High-redshift voids in the excursion set formalism

Voids are a dominant feature of the low-redshift galaxy distribution. Several recent surveys have found evidence for the existence of large-scale structure at high redshifts as well. We present analytic estimates of galaxy void sizes at redshifts   z ∼ 5–10  using the excursion set formalism. We find that recent narrow-band surveys at   z ∼ 5–6.5  should find voids with characteristic scales of roughly 20 comoving Mpc and maximum diameters approaching 40 Mpc. This is consistent with existing surveys, but a precise comparison is difficult because of the relatively small volumes probed so far. At   z ∼ 7–10  , we expect characteristic void scales of ∼14–20 comoving Mpc assuming that all galaxies within dark matter haloes more massive than  10¹⁰ M_⊙  are observable. We find that these characteristic scales are similar to the sizes of empty regions resulting from purely random fluctuations in the galaxy counts. As a result, true large-scale structure will be difficult to observe at   z ∼ 7–10  , unless galaxies in haloes with masses  ≲10⁹ M_⊙  are visible. Galaxy surveys must be deep and only the largest voids will provide meaningful information. Our model provides a convenient picture for estimating the 'worst-case' effects of cosmic variance on high-redshift galaxy surveys with limited volumes.     

Gravitational lensing of anisotropic sources

In strong gravitational lensing, the multiple images we see correspond to light rays that leave the source in slightly different directions. If the source emission is anisotropic, the images may differ from conventional lensing predictions (which assume isotropy). To identify scales on which source anisotropy may be important, we study the angle δ between the light rays emerging from the source, for different lensing configurations. If the lens has a power-law profile   M ∝ R ^γ  , the angle δ initially increases with lens redshift and then either diverges (for a steep profile  γ < 1  ), remains constant (for an isothermal profile  γ= 1  ), or vanishes (for a shallow profile  γ > 1  ) as   z _l→ z _s  . The scaling with lens mass is roughly  δ∝ M ^1/(2−γ)  . The results for an Navarro–Frenk–White (NFW) profile are qualitatively similar to those for a shallow power law, with δ peaking at about half the redshift of the source (not half the distance). In practice, beaming could modify the statistics of beamed sources lensed by massive clusters: for an opening angle  θ_jet  , there is a probability as high as   P ∼ 0.02–0.07(θ_jet/0.5°)⁻¹  that one of the lensed images may be missed (for  2 ≲ z _s≲ 6  ). Differential absorption within active galactic nuclei (AGNs) could modify the flux ratios of AGNs lensed by clusters; a sample of AGNs lensed by clusters could provide further constraints on the sizes of absorbing regions. Source anisotropy is not likely to be a significant effect in galaxy-scale strong lensing.     

The dark matter environment of the Abell 901/902 supercluster: a weak lensing analysis of the HST STAGES survey

We present a high-resolution dark matter reconstruction of the   z = 0.165  Abell 901/902 supercluster from a weak lensing analysis of the Hubble Space Telescope STAGES survey. We detect the four main structures of the supercluster at high significance, resolving substructure within and between the clusters. We find that the distribution of dark matter is well traced by the cluster galaxies, with the brightest cluster galaxies marking out the strongest peaks in the dark matter distribution. We also find a significant extension of the dark matter distribution of Abell 901a in the direction of an infalling X-ray group Abell 901α. We present mass, mass-to-light and mass-to-stellar mass ratio measurements of the structures and substructures that we detect. We find no evidence for variation of the mass-to-light and mass-to-stellar mass ratio between the different clusters. We compare our space-based lensing analysis with an earlier ground-based lensing analysis of the supercluster to demonstrate the importance of space-based imaging for future weak lensing dark matter 'observations'.     

Gaseous drag on a gravitational perturber in Modified Newtonian Dynamics and the structure of the wake

We calculate the structure of a wake generated by, and the dynamical friction force on, a gravitational perturber travelling through a gaseous medium of uniform density and constant background acceleration   g _ext  , in the context of Modified Newtonian Dynamics (MOND). The wake is described as a linear superposition of two terms. The dominant part displays the same structure as the wake generated in the Newtonian gravity scaled up by a factor  μ⁻¹( g _ext/ a ₀)  , where a ₀ is the constant MOND acceleration and μ the interpolating function. The structure of the second term depends greatly on the angle between   g _ext  and the velocity of the perturber. We evaluate the dynamical drag force numerically and compare our MOND results with the Newtonian case. We mention the relevance of our calculations to orbit evolution of globular clusters and satellites in a gaseous protogalaxy. Potential differences in the X-ray emission of gravitational galactic wakes in MOND and in Newtonian gravity with a dark halo are highlighted.     

Rotation in gravitational lenses

Gravitational lensing deflects light. A single lens deflector can only shear images, but cannot induce rotations. Multiple lens planes can induce rotations. Such rotations can be observed in quadruply imaged sources, and can be used to distinguish between two proposed solutions of the flux anomaly problem: substructures in lensing galaxies versus large-scale structure. We predict the expected amount of rotation due to large-scale structure in strong lensing systems, and show how this effect can be measured using ∼mas very long baseline interferometry astrometry of quadruple lenses with extended source structures. The magnitude of rotation is around 1°. The biggest theoretical uncertainty is the power spectrum of dark matter on very small scales. This procedure can potentially be turned around to measure the dark matter power spectrum on very small scales. We list the predicted rms rotation angles for several quadruple lenses with known lens and source redshifts.     

Vertical dynamics of disc galaxies in modified Newtonian dynamics

We investigate the possibility of discriminating between modified Newtonian dynamics (MOND) and Newtonian gravity with dark matter, by studying the vertical dynamics of disc galaxies. We consider models with the same circular velocity in the equatorial plane (purely baryonic discs in MOND and the same discs 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 find that the vertical velocity dispersion of deep MOND discs can be much larger than in the equivalent spherical Newtonian models. However, in the more realistic case of high surface density discs, this effect is significantly reduced, casting doubt on the possibility of discriminating between MOND and Newtonian gravity with dark matter by using current observations.