arXiv subjects

M. Milgrom

Publications and source records attributed to M. Milgrom.

13 recordsLinked to original sources

arXiv2018

MOND and the dynamics of NGC1052-DF2

The dwarf galaxy NGC1052-DF2 has recently been identified as potentially lacking dark matter. If correct, this could be a challenge for MOND, which predicts that low surface brightness galaxies should evince large mass discrepancies. However, the correct prediction of MOND depends on both the internal field of the dwarf and the external field caused by its proximity to the giant elliptical NGC1052. Taking both into consideration under plausible assumptions, we find $σ_{\rm MOND} = 13.4^{+4.8}_{-3.7}\;\mathrm{km}\,\mathrm{s}^{-1}$. This is only marginally higher than the claimed 90\% upper limit on the velocity dispersion ($σ< 10.5\;\mathrm{km}\,\mathrm{s}^{-1}$), and compares well with the observed root mean square velocity dispersion ($σ= 14.3\;\mathrm{km}\,\mathrm{s}^{-1}$). We also discuss a few caveats on both the observational and theoretical side. On the theory side, the internal virialization time in this dwarf may be longer that the time scale of variation of the external field. On the observational side, the paucity of data and their large uncertainties call for further analysis of the velocity dispersion of NGC1052-DF2, to check whether it poses a challenge to MOND or is a success thereof.

astro-ph.GA↗

arXiv2007

Unruh Effect for General Trajectories

We consider two-level detectors coupled to a scalar field and moving on arbitrary trajectories in Minkowski space-time. We first derive a generic expression for the response function using a (novel) regularization procedure based on the Feynmann prescription that is explicitly causal, and we compare it to other expressions used in the literature. We then use this expression to study, analytically and numerically, the time dependence of the response function in various non-stationarity situations. We show that, generically, the response function decreases like a power in the detector's level spacing, $E$, for high $E$. It is only for stationary world-lines that the response function decays faster than any power-law, in keeping with the known exponential behavior for some stationary cases. Under some conditions the (time dependent) response function for a non-stationary world-line is well approximated by the value of the response function for a stationary world-line having the same instantaneous acceleration, torsion, and hyper-torsion. While we cannot offer general conditions for this to apply, we discuss special cases; in particular, the low energy limit for linear space trajectories.

gr-qc↗

arXiv2007

Pair Winds in Schwarzschild Spacetime with Application to Strange Stars

We present the results of numerical simulations of stationary, spherically outflowing, electron-positron pair winds, with total luminosities in the range 10^{34}--10^{42} ergs/s. In the concrete example described here, the wind injection source is a hot, bare, strange star, predicted to be a powerful source of pairs created by the Coulomb barrier at the quark surface. We find that photons dominate in the emerging emission, and the emerging photon spectrum is rather hard and differs substantially from the thermal spectrum expected from a neutron star with the same luminosity. This might help distinguish the putative bare strange stars from neutron stars.

astro-ph↗

arXiv2006

Structure of pair winds from compact objects with application to emission from bare strange stars

We present the results of numerical simulations of stationary, spherically outflowing, electron-positron pair winds, with total luminosities in the range 10^{34}- 10^{42} ergs/s. In the concrete example described here, the wind injection source is a hot, bare, strange star, predicted to be a powerful source of electron-positron pairs created by the Coulomb barrier at the quark surface. We find that photons dominate in the emerging emission, and the emerging photon spectrum is rather hard and differs substantially from the thermal spectrum expected from a neutron star with the same luminosity. This might help distinguish the putative bare strange stars from neutron stars.

astro-ph↗

arXiv2005

Pair winds in Schwarzschild space-time with application to hot bare strange stars

We consider a time dependent, spherically outflowing wind, in Schwarzschild space-time, consisting of electron-positron pairs and photons . Without assuming thermal equilibrium, we account for the microphysics, including two-body processes and their radiative three-body variants. We present a finite-difference scheme for solving the general relativistic kinetic Boltzmann equations for electron-positron pairs and photons. We apply this to the concrete example of a wind from a hot, bare, strange star, predicted to be a powerful source of hard X-ray photons and pairs created by the Coulomb barrier at the quark surface. We study the kinetics of the wind particles and the emerging emission in photons and pairs for stationary winds with total luminosities in the range 10^{34}-10^{39} ergs/s, for different values of the injected photon-to-pair ratio. The wind parameters--such as the mean optical depth for photons, the rates of particle number and energy outflows, bulk velocity, and number density of the pair plasma--are presented as functions of the distance from the stellar surface, as well as characteristics of the emergent radiation. We find that photons dominate in the emerging emission, and the emerging photon spectrum is rather hard and differs substantially from the thermal spectrum expected from a neutron star with the same luminosity. This might help distinguish the putative bare strange stars from neutron stars.

astro-ph↗

arXiv2004

Structure of pair winds from compact objects with application to emission from hot bare strange stars

We consider a stationary, spherically outflowing wind consisting of electron-positron pairs and photons. We do not assume thermal equilibrium, and include the two-body processes that occur in such a wind: Moller and Bhaba scattering of pairs, Compton scattering, two-photon pair annihilation, and two-photon pair production, together with their radiative three-body variants: bremsstrahlung, double Compton scattering, and three-photon pair annihilation, with their inverse processes. In the concrete example described here, the wind injection source is a hot, bare, strange star. Such stars are thought to be powerful sources of pairs created by the Coulomb barrier at the quark surface. We present a new, finite-difference scheme for solving the relativistic kinetic Boltzmann equations for pairs and photons. Using this method we study the kinetics of the wind particles and the emerging emission for total luminosities of L=10^{34}-10^{42} ergs/s. We find the rates of particle number and energy outflows, outflow velocities, number densities, energy spectra, and other parameters for both photons and pairs as functions of the distance. We find that for L>2x10^{35} ergs/s, photons dominate the emerging emission. As L increases from ~ 10^{34} to 10^{42} ergs/s, the mean energy of emergent photons decreases from ~400-500 keV to 40 keV, as the spectrum changes in shape from that of a wide annihilation line to nearly a blackbody spectrum with a high energy (> 100 keV) tail. These results are pertinent to the deduction of the outside appearance of hot bare strange stars, which might help discern them from neutron stars.

astro-ph↗

arXiv2003

Radiation from hot bare strange stars

We present the results of numerical simulations of stationary, spherically outflowing, pair winds, with total luminosities of L=10^{35}- 10^{42} ergs/s. These results have direct relevance to the emission from hot, bare, strange stars, which are thought to be powerful sources of electron-positron pairs created by the Coulomb barrier at the quark surface. The spectra of emergent photons and pairs are calculated. For L > 2x10^{35} erg/s, photons dominate the emerging emission. As L increases from 10^{35} to 10^{42} ergs/s, the mean photon energy decreases from ~ 400-500 keV to 40 keV, while the spectrum changes in shape from a wide annihilation line to being nearly blackbody with a high energy (> 100 keV) tail. Such a correlation of the photon spectrum with the luminosity, together with the fact that super-Eddington luminosities can be achieved, might be a good observational signature of hot, bare, strange stars.

astro-ph↗

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.

astro-ph↗

arXiv1994

Finite Disks with Power-Law Potentials

We describe a family of circular, and elliptical, finite disks with a disk potential that is a power of the radius. These are all flattened ellipsoids, obtained by squashing finite spheres with a power-law density distribution, and cutoff at some radius Ro. First we discuss circular disks whose circular rotation speed v is proportional to r^alpha, with any alpha> -1/2. The surface-density of the disks is expressed in terms of hypergeometric functions of 1-(Ro/r)^2. We give closed expressions for the full 3-D potentials in terms of hypergeometric functions of two variables. We express the potential and acceleration in the plane at r>Ro, and along the rotation axis, in terms of simple hypergeometric functions. All the multipoles of the disk are given. We then generalize to non-axisymmetric disks. The potential in the midplane is given in terms of the hypergeometric function of two variables. For integer values of 2 alpha the above quantities are given in more elementary terms. All these results follow straightforwardly from formulae we derive for the general, cutoff, power-law, triaxial ellipsoid.

astro-ph↗

arXiv1994

Exact Solutions and Approximations of Mond Fields of Disk Galaxies

We Consider models of thin disks (with and without bulges) in the Bekenstein-Milgrom formulation of MOND as a modification of Newtonian gravity. Analytic solutions are found for the full gravitational fields of Kuzmin disks, and of disk-plus-bulge generalizations of them. For all these models a simple algebraic relation between the MOND potential field and the Newtonian potential holds everywhere outside the disk. We give exact expressions for the rotation curves for these models. We also find that the algebraic relation is a very good approximation for exponential disks. The algebraic relation outside the disk is then extended into the disk to derive an improved approximation for the MOND rotation curve of disk galaxies that requires only knowledge of the Newtonian curve and the surface density.

astro-ph↗

arXiv1994

The virial theorem for action-governed theories

We describe a simple derivation of virial relations (VR) for arbitrary action-governed systems. These follow directly from the action with no need to go via the equations of motion. When some of the degrees of freedom are of the same type a tensor virial theorem presents itself. Further generalizations are discussed. Symmetries of the action may lead to identities involving the VR. Beside pointing to a unified provenance of the VR, and affording general systematics of them, our method is a simple prescription for deriving such relations. It is particularly useful for treating high-derivative and non-local theories. We demonstarte the procedure with several examples.

astro-ph↗

arXiv1993

Modified-dynamics predictions agree with ovservations of the HI kinematics in faint dwarf galaxies contrary to the conclusions of Lo Sargent and Young

Lo, Sargent, and Young (1993) have recently concluded that the masses of some dwarf galaxies, as deduced by the modified dynamics (MOND) from the observed velocity dispersions, are systematically smaller than the observed masses, by a factor of ten or more. We show here that the MOND mass estimator used by Lo et al. is smaller than the proper expression, by a factor of about twenty. We derive the proper mass estimator as an exact virial-like relation between the 3-D rms velocity, Vs, and the total mass, M, of an arbitrary, self-gravitating system, made of light constituents, that is everywhere in the very-low-acceleration regime of MOND. This reads M=(9/4)Vs^2/G a0. (For a system that is not stationary, Vs involves also an average over time.) We further generalize this relation to cases with constituent masses that are not small compared with that of the whole system. We discuss various applications of the M-V relation. With the correct estimator the predictions of MOND are, by and large, in good agreement with the total observed masses (the observed gas mass plus a stellar mass corresponding to an M/L of order one solar unit).

astro-ph↗

arXiv1993

Dynamics with a non-standard inertia-acceleration relation: an alternative to dark matter

We investigate particle laws of motion derived from nonstandard kinetic actions of a special form. We are guided by a phenomenological scheme--the modified dynamics (MOND)--that imputes the mass discrepancy observed in galactic systems to a departure from Newtonian dynamics below a certain acceleration scale a0. In the limit a0 goes to 0 the theory goes to Newtonian dynamics. In the opposite limit the action becomes proportional to 1/a0. Galilei-invariant such theories must be strongly non-local; this is a blessing, as such theories need not suffer from the illnesses that are endemic to higher-derivative theories. We discuss the possibility that such a modified law of motion is an effective theory resulting from the elimination of degrees of freedom pertaining to the universe at large (the near equality a0=cH0 being a trace of that connection). A virial relation for bounded trajectories is derived. Exact solutions are obtained for circular orbits, which pertain to rotation curves of disk galaxies. We also explore, in passing, theories that depart from the conventional Newtonian dynamics for very low frequencies. The present formulation contrasts, on important accounts, with earlier, modified-gravity formulations.

astro-ph↗