arXiv subjects

Mordehai Milgrom

Publications and source records attributed to Mordehai Milgrom.

At least 91 records · Page 5Linked to original sources

arXiv2001

Does MOND follow from the CDM paradigm?

In a recent paper, Kaplinghat and Turner (2001) (KT) advertise that MOND can be derived naturally in the CDM paradigm. They actually proceed to produce a more limited result: Every galaxy should have a transition radius, $r_t$, below which baryons dominate, and above which dark matter (DM) takes over; the acceleration at $r_t$ is nearly the same for all galaxies; and due to a coincidences this is of order $a_0\sim cH_0$. This follows from their tacit, intermediate result, whereby CDM halos of galaxies have a very nearly universal acceleration profile $a(r)\approx v^2(r)/r\approx A\hat a(r/\ell)$, where A is universal, and only the scale $\ell$ varies from halo to halo. (This remains so when baryons are added because they assume a universal baryon-collapse factor.) The KT scenario is phenomenologically wrong--observed galaxies are simply not like that. For example, it precludes altogether the existence of LSB galaxies, in which the acceleration is everywhere smaller than $a_0$. The phenomenologically sound outcome--i.e., the role of $a_0$ as a transition acceleration in high-surface-brightness galaxies--pertains to only a small part of the statement of MOND. There are several other, independent roles that $a_0\sim cH_0$ plays in MOND phenomenology, and other predictions of MOND, not related to the value of $a_0$, that are not explainable in the KT scenario. The results of KT also disagree with those of CDM simulations, which, as they now stand, do not reproduce any aspect of MOND phenomenology.

astro-ph↗

arXiv2001

The shape of "dark matter" halos in disc galaxies according to the modified dynamics

Analyses of halo shapes for disc galaxies are said to give incongruous results. I point out that the modified dynamics (MOND) predicts for disc galaxies a distribution of fictitious dark matter that comprises two components: a pure disc and a rounder halo. The former dominates the true disc in regions of small accelerations, where it controls the z-dynamics in the disc (disc flaring etc.); it has a finite total mass. It also dominates the round component near the centre where the geometry is nearly planar. The second component controls motions far from the plane, has a total enclosed mass that diverges linearly with radius, and determines the rotation curve at large radii. Its ellipticity may be appreciable at small radii but vanishes asymptotically. This prediction of MOND differs from what one expects from galaxy-formation scenarios with dark matter. Analyses to date, which, as they do, assume one component--usually with a constant ellipticity, perforce give conflicting results for the best-value ellipticity, depending on whether they probe the disc or the sphere, small radii or large ones.

astro-ph↗

arXiv2000

Dwarf satellite galaxies in the modified dynamics

In the modified dynamics (MOND) the inner workings of dwarf satellites can be greatly affected by their mother galaxy-over and beyond its tidal effects. Because of MOND's nonlinearity a system's internal dynamics can be altered by an external field in which it is immersed (even when this field, by itself, is constant in space). As a result, the size and velocity dispersion of the satellite vary as the external field varies along its orbit. A notable outcome of this is a substantial increase in the dwarf's vulnerability to eventual tidal disruption-rather higher than Newtonian dynamics (with a dark-matter halo) would lead us to expect for a satellite with given observed parameters.

astro-ph↗

arXiv2000

Induction of supernova-like explosions by gamma-ray bursts in close binary systems

We propose that a gamma-ray burst in one member of a binary may induce a supernova-like explosion of a close, white-dwarf companion. Such an explosion might be brought about in rather light companions, which cannot undergo the standard accretion-induced explosion. This would give some GRB-associated supernova an appearance rather unlike that of the typical Type I. GRB 980425, if indeed associated with SN 1998bw, is too weak to have produced it through our proposed mechanism.

astro-ph↗

arXiv2000

The modified dynamics is conducive to galactic warp formation

There is an effect in the modified dynamics (MOND) that is conducive to formation of warps. Because of the nonlinearity of the theory the internal dynamics of a galaxy is affected by a perturber over and above possible tidal effects. For example, a relatively distant and light companion or the mean influence of a parent cluster, with negligible tidal effects, could still produce a significant warp in the outer part of a galactic disk. We present results of numerical calculations for simplified models that show, for instance, that a satellite with the (baryonic) mass and distance of the Magellanic clouds can distort the axisymmetric field of the Milky Way enough to produce a warp of the magnitude (and position) observed. Details of the warp geometry remain to be explained: we use a static configuration that can produce only warps with a straight line of nodes. In more realistic simulations one must reckon with the motion of the perturbing body, which sometimes occurs on time scales not much longer than the response time of the disk.

astro-ph↗

arXiv1999

Stability of disk galaxies in the modified dynamics

General analytic arguments lead us to expect that in the modified dynamics (MOND) self-gravitating disks are more stable than their like in Newtonian dynamics. We study this question numerically, using a particle-mesh code based on a multi-grid solver for the (nonlinear) MOND field equation. We start with equilibrium distribution functions for MOND disk models having a smoothly truncated, exponential surface-density profiles and a constant Toomre $Q$ parameter. We find that, indeed, disks of a given ``temperature'' are locally more stable in MOND than in Newtonian dynamics. As regards global instability to bar formation, we find that as the mean acceleration in the disk is lowered, the stability of the disk is increased as we cross from the Newtonian to the MOND regime. The degree of stability levels off deep in the MOND regime, as expected from scaling laws in MOND. For the disk model we use, this maximum degree of stability is similar to the one imparted to a Newtonian disk by a halo three times as massive at five disk scale lengths.

astro-ph↗

arXiv1999

The Modified Dynamics as a Vacuum Effect

Why does there appear in the modified dynamics (MOND) an acceleration constant, a0, of cosmological significance? An intriguing possibility is that MOND, indeed inertia itself--as embodied in the actions of free particles and fields, is due to effects of the vacuum. Either cosmology enters local dynamics by affecting the vacuum, and inertia in turn, through a0; or, the same vacuum effect enters both MOND (through a0) and cosmology (e.g. through a cosmological constant). For the vacuum to serve as substratum for inertia a body must be able to read in it its non-inertial motion; this indeed it can, by detecting Unruh-type radiation. A manifestation of the vacuum is also seen, even by inertial observers, in a non-trivial universe (marked, e.g., by curvature or expansion). A non-inertial observer in a nontrivial universe will see the combined effect. An observer on a constant-acceleration (a) trajectory in a de Sitter universe with cosmological constant L sees Unruh radiation of temperature T\propto [a^2+a0^2]^{1/2}, with a0=(Ł/3)^{1/2}. The temperature excess over what an inertial observer sees, T(a)-T(0), turns out to depend on a in the same way that MOND inertia does. An actual inertia-from-vacuum mechanism is still a far cry off.

astro-ph↗

arXiv1998

The modified dynamics (MOND) predicts an absolute maximum to the acceleration produced by `dark halos'

We have recently discovered that the modified dynamics (MOND) implies some universal upper bound on the acceleration that can be contributed by a `dark halo'--assumed in a Newtonian analysis to account for the effects of MOND. Not surprisingly, the limit is of the order of the acceleration constant of the theory. This can be contrasted directly with the results of structure-formation simulations. The new limit is substantial and different from earlier MOND acceleration limits (discussed in connection with the MOND explanation of the Freeman law for galaxy disks, and the Fish law for ellipticals): It pertains to the `halo', and not to the observed galaxy; it is absolute, and independent of further physical assumptions on the nature of the galactic system; and it applies at all radii, whereas the other limits apply only to the mean acceleration in the system.

astro-ph↗

arXiv1998

The Modified Dynamics--A Status Review

The Modified dynamics (MOND) has been propounded as an alternative to Dark matter. It imputes the mass discrepancy in galaxy systems to failure of standard dynamics in the limit of small accelerations. After a brief description of the MOND tenets, I discuss how its predictions now compare with the data. I put special emphasis on rotation-curve analysis--whence comes the most clear-cut support for MOND, and on the cores of rich x-ray clusters, where MOND does not yet explain away the mass discrepancy. I then outline the MOND program, especially work still left to do. This is followed by general comments on cosmology and structure formation in MOND. I conclude with some incomplete thoughts on the possible origin of MOND (as an effective theory); in particular on the possibility that it comes about as a vacuum effect.

astro-ph↗

arXiv1998

Suspension and levitation in nonlinear theories

I investigate stable equilibria of bodies in potential fields satisfying a generalized Poisson equation: divergence[m(grad phi) grad phi]= source density. This describes diverse systems such as nonlinear dielectrics, certain flow problems, magnets, and superconductors in nonlinear magnetic media; equilibria of forced soap films; and equilibria in certain nonlinear field theories such as Born-Infeld electromagnetism. Earnshaw's theorem, totally barring stable equilibria in the linear case, breaks down. While it is still impossible to suspend a test, point charge or dipole, one can suspend point bodies of finite charge, or extended test-charge bodies. I examine circumstances under which this can be done, using limits and special cases. I also consider the analogue of magnetic trapping of neutral (dipolar) particles.

cond-mat↗

arXiv1998

Galaxy groups and the modified dynamics

I estimate Modified-Dynamics (MOND), median M/L values for recently published catalogues of galaxy groups. While the median, Newtonian M/L values quoted for these catalogues are 110-200 solar units, the corresponding values for MOND are less than 10 solar units.

astro-ph↗

arXiv1997

Non-linear conformally invariant generalization of the Poisson equation to D>2 dimensions

I propound a non-linear generalization of the Poisson equation describing a "medium" in D dimensions with a "dielectric constant" proportional to the field strength to the power D-2. It is the only conformally invariant scalar theory that is second order, and in which the scalar $phi$ couples to the sources $ρ$ via a $ϕρ$ contact term. The symmetry is used to generate solutions for the field for some non-trivial configurations (e.g. for two oppositely charged points). Systems comprising N point charges afford further application of the symmetry. For these I derive e.g. exact expressions for the following quantities: the general two-point-charge force; the energy function and the forces in any three-body configuration with zero total charge; the few-body force for some special configurations; the virial theorem for an arbitrary, bound, many-particle system relating the time-average kinetic energy to the particle charges. Possible connections with an underlying conformal quantum field theory are mentioned.

gr-qc↗

arXiv1996

Models for anisotropic spherical stellar systems with a central point mass and Keplerian velocity dispersions

We add to the lore of spherical, stellar-system models a two-parameter family with an anisotropic velocity dispersion, and a central point mass (``black hole''). The ratio of the tangential to radial dispersions, is constant--and constitutes the first parameter--while each decreases with radius as r^{-1/2}. The second parameter is the ratio of the central point mass to the total mass. The Jeans equation is solved to give the density law in closed form: rho\propto (r/r0)^{-c}/[1+(r/r0)^{3-c}]^2, where r0 is an arbitrary scale factor. The two parameters enter the density law only through their combination c. At the suggestion of Tremaine, we also explore models with only the root-sum-square of the velocities having a Keplerian run, but with a variable anisotropy ratio. This gives rise to a more versatile class of models, with analytic expressions for the density law and the dispersion runs, which contain more than one radius-scale parameter.

astro-ph↗

arXiv1996

Large-scale filaments--Newtonian vs. modified dynamics

Eisenstein Loeb and Turner (ELT) have recently proposed a method for estimating the dynamical masses of large-scale filaments, whereby the filament is modeled by an axisymmetric, isothermal cylinder, for which ELT derive a global relation between the (constant) velocity dispersion and the total line density. We first show that the model assumptions of ELT can be relaxed materially: an exact relation between the velocity and line density is derived for any cylinder (not necessarily axisymmetric), with an arbitrary constituent distribution function (so isothermality need not be assumed). We then consider the same problem in the context of the modified dynamics (MOND). After a brief comparison between scaling properties in the two theories, we study idealized MOND model filaments. A preliminary application to the segment of the Perseus-Pisces filament treated by ELT, gives MOND M/L estimates of order 10 s.u., compared with the Newtonian value of about 450, which ELT find. In spite of the large uncertainties still besetting the analysis, this instance of MOND application is of particular interest because: 1. Objects of this geometry have not been dealt with before. 2. It pertains to large-scale structure. 3. The typical accelerations involved are the lowest so far encountered in a semi-virialized system.

astro-ph↗

arXiv1996

Exact results concerning multifield moduli of two-phase composites

Chen has recently shown how the response matrix of a two-phase composite can be written as linear combinations of products of the component matrices. We elaborate on Chen's expansions by deriving them in a different way, which a. shows them in a different light, and b. permits us to generalize them further. As an application of our results we find exact microstructure-independent relations between the moduli of the two components and those of any composite. The body of these relations is equivalent to the compatibility relations of Milgrom and Shtrikman (1989), but they are cast in a rather different form, which has certain advantages. As an example, we show how any modulus of an arbitrary two-phase composite can be written in closed form as a linear combination of any other $n$ of its moduli, with coefficients that depend only on the component moduli, but not on the volume fractions, or the microstructure.

cond-mat↗

arXiv1996

Low-surface-density galaxies and the modified dynamics

Very-low-surface-density galactic systems have very low mean accelerations. They thus provide quintessential tests of the Modified Dynamics (MOND), which predicts an increasing mass discrepancy with decreasing acceleration. We describe succinctly the results pertinent to several classes of such objects: Low-luminosity (dwarf) spirals, irregular dwarf spirals, normal-lumonosity-but -low-surface-density spirals, and dwarf-spheroidal satellites of the Milky Way.

astro-ph↗

arXiv1995

Gamma-ray bursters as sources of cosmic rays

The little we do know of the physical conditions in gamma-ray bursters makes them conducive to the acceleration of high-energy cosmic rays, especially if they are at cosmological distances. We find that, with the observed statistics and fluxes of gamma-ray bursts, cosmological bursters may be an important source of cosmic rays in two regions of the observed spectrum: 1. At the very-high-energy end (E>10^{19} eV), where cosmic rays must be of extragalactic origin. 2. Around and above the spectral feature that has been described as a bump and/or a knee, which occurs around 10^{15} eV, and starts at about 10^{14} eV. The occasional bursters that occur inside the Galaxy--about once in a few hundred thousand years if burst emission is isotropic; more often, if it is beamed--could maintain the density of galactic cosmic rays at the observed level in this range. These two energy ranges might correspond to two typical energy scales expected from bursters: one pertinent to acceleration due to interaction of a magnetized-fireball front with an ambient medium; the other to acceleration in the fireball itself (e.g. shock acceleration).

astro-ph↗

arXiv1995

Possible association of ultra-high-energy cosmic-ray events with strong gamma-ray bursts

We point out that each of the error boxes of the two highest-energy cosmic-ray shower events known, overlaps with that of a strong gamma-ray burst (GRB). The GRBs precede the cosmic rays by 5.5, and 11 months respectively. In one case the strongest known cosmic ray is paired with the strongest gamma-ray burst in the BATSE catalogue. The probability of this to have occurred by chance seems rather small. Without building on post-factum statistics, we think the above is remarkable enough to suggest that the cosmic ray and gamma-ray burst were produced by the same outburst. A time delay (and a small positional disparity) is expected, since the trajectory of a charged cosmic-ray particle is wriggled by intervening magnetic fields. We estimate that the Galaxy's field alone may produce a delay of the order observed. We discuss some of the implications that follow if such an association is confirmed. For example, the upper limit on the distance to the cosmic-ray source, combined with a much-better-determined position of the gamma-ray burst source, narrows greatly the volume in which to look for an optical counterpart. There is also useful information in the time delay regarding, e.g., intergalactic magnetic fields.

astro-ph↗