arXiv subjects

R. H. Sanders

Publications and source records attributed to R. H. Sanders.

36 records · Page 2Linked to original sources

arXiv2006

The collapse of gas discs in non-axisymmetric galaxy cores

Below a threshold energy, gas in the constant density core of a triaxial galaxy can find no simple non-intersecting periodic orbit to act as an attractor for its trajectory (El-Zant et al. 2003). If a disc of gas arriving from further out in the galaxy dissipates sufficient energy to fall below this threshold, it will thereafter collapse into the very centre. Such a mechanism may be relevant to the early growth of super-massive black holes at the Eddington limit and the appearance of the quasar phenomenon at high redshift. This process is self-limiting in the sense that, when the black hole mass has grown to a significant fraction of the core mass, simple angular momentum conserving orbits are restored and accretion reverts to the slow viscous mode. The mechanism depends upon the pre-existence of constant density cores in triaxial spheroidal galaxies.

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arXiv2006

Solar system constraints on multi-field theories of modified dynamics

Any viable theory of modified Newtonian dynamcs (MOND) as modified gravity is likely to require fields in addition to the usual tensor field of General Relativity. For such theories the MOND phenomenology emerges from an effective fifth force probably associated with a scalar field. Here I consider the constraints imposed upon such theories by solar system phenomenology, primarily by the absence of significant deviations from inverse square attraction in the inner solar system as well as detectable local preferred frame effects. The current examples of multi-field theories can be constructed to satisfy these constraints and such theories lead inevitably to an anomalous non inverse-square force in the outer solar system.

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arXiv2006

Modified gravity without dark matter

On an empirical level, the most successful alternative to dark matter in bound gravitational systems is the modified Newtonian dynamics, or MOND, proposed by Milgrom. Here I discuss the attempts to formulate MOND as a modification of General Relativity. I begin with a summary of the phenomenological successes of MOND and then discuss the various covariant theories that have been proposed as a basis for the idea. I show why these proposals have led inevitably to a multi-field theory. I describe in some detail TeVeS, the tensor-vector-scalar theory proposed by Bekenstein, and discuss its successes and shortcomings. This lecture is primarily pedagogical and directed to those with some, but not a deep, background in General Relativity

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arXiv2005

MOND and Cosmology

I review various ideas on MOND cosmology and structure formation beginning with non-relativistic models in analogy with Newtonian cosmology. I discuss relativistic MOND cosmology in the context of Bekenstein's theory and propose an alternative biscalar effective theory of MOND in which the acceleration parameter is identified with the cosmic time derivative of a matter coupling scalar field. Cosmic CDM appears in this theory as scalar field oscillations of the auxiliary "coupling strength" field.

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arXiv2005

A tensor-vector-scalar framework for modified dynamics and cosmic dark matter

I describe a tensor-vector-scalar theory that reconciles the galaxy scale success of modified Newtonian dynamics (MOND) with the cosmological scale evidence for CDM. The theory provides a cosmological basis for MOND in the sense that the predicted phenomenology only arises in a cosmological background. The theory contains an evolving effective potential, and scalar field oscillations in this potential comprise the cold dark matter; the de Broglie wavelength of these soft bosons, however, is sufficiently large that they cannot accumulate in galaxies. The theory predicts, inevitably, a constant anomalous acceleration in the outer solar system which, depending upon the choice of parameters, can be consistent with that detected by the Pioneer spacecrafts.

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arXiv2004

Observational Cosmology

I discuss the classical cosmological tests-- angular size-redshift, flux-redshift, and galaxy number counts-- in the light of the cosmology prescribed by the intepretation of CMB anisotropies. The discussion is somewhat of a primer for physicists, with emphasis upon the possible systematic uncertainties in the observations and their interpretation. Given the curious composition of the Universe inherent in the emerging cosmological model, I stress the value of searching for inconsistencies rather than concordance, and suggest that the prevailing mood of triumphalism in cosmology is premature.

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arXiv2002

Clusters of galaxies with modified Newtonian dynamics (MOND)

X-ray emitting clusters of galaxies are considered in the context of modified Newtonian dynamics (MOND). I show that self-gravitating isothermal gas spheres are not good representations of rich clusters with respect to the radial gas density distribution as indicated by the X-ray surface brightness. Pure gas spheres with a density distribution described by a ``beta'' model, as observed, also fail because, with MOND, these objects are far from isothermal. These problems may be resolved by adding an additional dark mass component in the central regions; a constant density sphere contained within two core radii and having a total mass of one to two times that in the gas. With this additional component, the observed luminosity-temperature relation for clusters of galaxies is reproduced. When the observed X-ray surface brightness distribution in actual clusters is modeled by such a two-component structure, the typical mass discrepancy is three to four times smaller than with 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 this is not a fundamental problem for MOND.

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arXiv2001

Modified Newtonian dynamics and its implications

Milgrom has proposed that the appearance of discrepancies between the Newtonian dynamical mass and the directly observable mass in astronomical systems could be due to a breakdown of Newtonian dynamics in the limit of low accelerations rather than the presence of unseen matter. Milgrom's hypothesis, modified Newtonian dynamics or MOND, has been remarkably successful in explaining systematic properties of spiral and elliptical galaxies and predicting in detail the observed rotation curves of spiral galaxies with only one additional parameter-- a critical acceleration which is on the order of the cosmologically interesting value of $cH_o$. Here I review the empirical successes of this idea and discuss its possible extention to cosmology and structure formation.

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arXiv2001

The formation of cosmic structure with modified Newtonian dynamics

I consider the growth of inhomogeneities in a low-density baryonic, vacuum energy-dominated universe in the context of modified Newtonian dynamics (MOND). I first write down a two-field Langrangian-based theory of MOND (non-relativistic), which embodies several assumptions such as constancy of the MOND acceleration parameter, association of a MOND force with peculiar accelerations only, and the deceleration of the Hubble flow as a background field which influences the dynamics of a finite size region. In the context of this theory, the equation for the evolution of spherically symmetric over-densities is non-linear and implies very rapid growth even in a low-density background, particularly at the epoch when the putative cosmological constant begins to dominate the Hubble expansion. Small comoving scales enter the MOND regime earlier than larger scales and therefore evolve to large over-densities sooner. Taking the initial COBE-normalized power spectrum provided by CMBFAST (Seljak & Zeldarriaga 1996), I find that the final power-spectrum resembles that of the standard LCDM universe and thus retains the empirical successes of that model.

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arXiv2000

Comment on "The Bright Side of Dark Matter" by A. Edery

In a significant recent paper A. Edery undertakes a new study of light deflection in generalizations of general relativity (GR). He claims to prove that any metric-based gravitational theory that proposes to explain the flat rotation curves of disk galaxies without postulating dark matter halos must conflict with observations of gravitational lensing by galaxies and clusters of galaxies because any such theory inevitably make a negative contribution to light deflection. Here we show that some of the basic steps of Edery's argument are invalid, and no such general result obtains.

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arXiv1999

The fundamental plane of elliptical galaxies with modified Newtonian dynamics

The modified Newtonian dynamics (MOND), suggested by Milgrom as an alternative to dark matter, implies that isothermal spheres with a fixed anisotropy parameter should exhibit a near perfect relation between the mass and the fourth power of the velocity dispersion. This is consistent with the observed Faber-Jackson relation for elliptical galaxies-- a luminosity-velocity dispersion relation with large scatter. However, the observable global properties of elliptical galaxies comprise a three parameter family; they lie on a ``fundamental plane'' in a logarithmic space consisting of central velocity dispersion, effective radius, and luminosity. The scatter perpendicular to this plane is significantly less than that about the Faber-Jackson relation. I show here that, in order to match the observed global properties of elliptical galaxies with MOND, models must deviate from being strictly isothermal and isotropic; such objects can be approximated by high-order polytropic spheres with a radial orbit anisotropy in the outer regions. MOND imposes boundary conditions on the inner Newtonian regions which restrict these models to a dynamical fundamental plane which may differ from that implied by the traditional virial theorem. Scatter about this plane is relatively insensitive to the necessary deviations from homology.

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arXiv1998

The circumnuclear disk and ionized gas filaments as remnants of tidally disrupted clouds

Sticky particle calculations indicate that a coherent structure, a dispersion ring, forms when a cloud on a low angular momentum orbit passes close to the dynamical center of an isothermal sphere containing a central point mass. The cloud is tidally stretched and differentially wrapped, and dissipation in shocks organizes the gas into a precessing off-set elliptical ring which can persist for many rotation periods. The morphology and kinematics of the circumnuclear disk (CND) between 2 and 5 pc and the Northern arm in the inner 1 pc are well-represented by such structures. In the case of the Northern Arm, strong shocks which arise during the formation of the dispersion ring can lead to star formation even in the near tidal field of a massive black hole.

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arXiv1998

Resolving the virial discrepancy in clusters of galaxies with modified Newtonian dynamics

A sample of 197 X-ray emitting clusters of galaxies is considered in the context of Milgrom's modified Newtonian dynamics (MOND). It is shown that the gas mass, extrapolated via an assumed $β$ model to a fixed radius of 3 Mpc, is correlated with the gas temperature as predicted by MOND ($M_g \propto T^2$). The observed temperatures are generally consistent with the inferred mass of hot gas; no substantial quantity of additional unseen matter is required in the context of MOND. However, modified dynamics cannot resolve the strong lensing discrepancy in those clusters where this phenomenon occurs. The prediction is that additional baryonic matter may be detected in the central regions of rich clusters.

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arXiv1998

Rotation curves of UMa galaxies in the context of modified Newtonian dynamics

This is the third in a series of papers in which spiral galaxy rotation curves are considered in the context of Milgrom's modified dynamics (MOND). The present sample of 30 objects is drawn from a complete sample of galaxies in the Ursa Major cluster with photometric data by Tully et al. (1996) and 21 cm line data by Verheijen (1997). The galaxies are roughly all at the same distance (15 to 16 Mpc). The radio observations are made with the Westerbork Synthesis Array which means that the linear resolution of all rotation curves is comparable. The greatest advantage of this sample is the existance of K'-band surface photometry for all galaxies; the near-infrared emission, being relatively free of the effects of dust absorption and less sensitive to recent star formation, is a more precise tracer of the mean radial distribution of the dominant stellar population. The predicted rotation curves are calculated from the K'-band surface photometry and the observed distribution of neutral hydrogen using the simple MOND prescription where the one adjustable parameter is the mass of the stellar disk or the implied mass-to-light ratio. The predicted rotation curves generally agree with the observed curves and the mean M/L in the near-infrared is about 0.9 with a small dispersion. The fitted M/L in the B-band is correlated with B-V color in the sense predicted by population synthesis models. Including earlier work, about 80 galaxy rotation curves are now well-reproduced from the observed distribution of detectable matter using the MOND formula to calculate the gravitational acceleration; this lends considerable observational support to Milgrom's unconventional hypothesis.

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arXiv1997

Cosmology with Modified Newtonian Dynamics (MOND)

It is well-known that the application of Newtonian dynamics to an expanding spherical region leads to the correct relativistic expression (the Friedmann equation) for the evolution of the cosmic scale factor. Here, the cosmological implications of Milgrom's modified Newtonian dynamics (MOND) are considered by means of a similar procedure. Earlier work by Felten demonstrated that in a region dominated by modified dynamics, the expansion cannot be uniform (separations cannot be expressed in terms of a scale factor) and that any such region will eventually re-collapse regardless of the initial expansion velocity and mean density. Here I show that, because of the acceleration threshold for the MOND phenomenology, a region dominated by MOND will have a finite size which, in the early Universe ($z > 3$), is smaller than the horizon scale. Therefore, uniform expansion and homogeneity on horizon scale are consistent with MOND-dominated non-uniform expansion and the development of inhomogeneities on smaller scale. In the radiation-dominated era, the amplitude of MOND-induced inhomogeneities is much smaller than that implied by observations of the cosmic background radiation, and the thermal and dynamical history of the Universe is identical to that of the standard Big Bang. When matter first dominates the energy density of the Universe, the cosmology diverges from that of the standard model. Objects of galaxy mass are the first virialized objects to form (by z=10) and larger structure develops rapidly. At the present epoch, the Universe would be inhomogeneous out to a substantial fraction of the Hubble radius.

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arXiv1997

The Circumnuclear Material in the Galactic Centre: A Clue to the Accretion Process

On the basis of ``sticky particle'' calculations, it is argued that the gas features observed within 10 pc of the Galactic Centre-- the circumnuclear disk (CND) and the ionized gas filaments-- as well as the newly formed stars in the inner one parsec can be understood in terms of tidal capture and disruption of gas clouds on low angular momentum orbits in a potential containing a point mass. The calculations demonstrate that a dissipative component forms a ``dispersion ring'', an asymmetric elliptical torus precessing counter to the direction of rotation, and that this shape can be maintained for many orbital periods. For a range of plausible initial conditions, such a sturcture can explain the morphology and kinematics of the CND and of the most conspicuous ionized filament. While forming the dispersion ring, a small cloud with low specific angular momentum is drawn into a long filament which repeatedly collides with itself at high velocity. The compression in strong shocks is likely to lead to star formation even in the near tidal field of the point mass. This process may have general relevance to accretion onto massive black holes in normal and active galactic nuclei.

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arXiv1996

A stratified framework for scalar-tensor theories of Modified Dynamics

Although the modified dynamics (MOND) proposed by Milgrom successfully accounts for the systematics of galaxy rotation curves and cluster dynamics without invoking dark matter, the idea remains a largely ad hoc modification of Newtonian dynamics with no basis in deeper theory. Non-standard scalar-tensor theories have been suggested as a theoretical basis for MOND; however, any such theory with the usual conformal relation between the Einstein and physical metrics fails to predict the degree of light deflection observed in distant clusters of galaxies. In the present paper, I demonstrate that one can write down a framework for scalar-tensor theories which predict the MOND phenomenology for the low velocity (v<<c) dynamics of galaxies and clusters of galaxies and which are consistent with observations of extragalactic gravitational lenses provided that one drops the requirement of the Lorentz Invariance of gravitational dynamics. This leads to ``preferred frame'' theories characterized by a non-conformal relation between the two metrics. I describe a toy theory in which the local environment (the solar system, binary pulsars) is protected from detectable preferred frame effects by the very same non-standard (aquadratic) scalar Lagrangian which gives rise to the MOND phenomenology. Although this particular theory is also contrived, it represents a limiting case for two-field theories of MOND, and is consistent with a wide range of gravitational phenomena.

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arXiv1996

The published extended rotation curves of spiral galaxies: Confrontation with Modified Dynamics

A sample of 22 spiral galaxy rotation curves, measured in the 21 cm line of neutral hydrogen, is considered in the context of Milgrom's modified dynamics (MOND). Combined with the previous highly selected sample of Begeman et al. (1990), this comprises the current total sample of galaxies with published (or available) extended rotation curves and photometric observations of the light distribution. This is the observational basis of present quantitative understanding of the discrepancy between the visible mass and classical dynamical mass in galaxies. It is found that the gravitational force calculated from the observed distribution of luminous material and gas using the simple MOND formula can account for the overall shape and amplitude of these 22 rotation curves, and in some cases, the predicted curve agrees with the observed rotation curve in detail. The fitted rotation curves have, in 13 cases, only one free parameter which is the mass-to-light ratio of the luminous disk; in nine cases, there is an additional free parameter which is M/L of a central bulge or light concentration. The values of the global M/L (bulge plus disk) are reasonable and, when the gas mass is also included, show a scatter which is consistent with that in the Tully-Fisher relation. The success of the MOND prescription in predicting the rotation curves in this larger, less stringently selected sample, lends further support to the idea that dynamics or gravity is non-Newtonian in the limit of low accelerations and that it is unnecessary to invoke the presence of large quantities of unseen matter.

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