arXiv subjects

Mordehai Milgrom

Publications and source records attributed to Mordehai Milgrom.

At least 55 records · Page 3Linked to original sources

arXiv2013

MOND laws of galactic dynamics

MOND predicts a number of laws that galactic systems should obey irrespective of their complicated, haphazard, and mostly unknowable histories -- as Kepler's laws are obeyed by planetary systems. The main purpose of this work is to show how, and to what extent, these MOND laws follow from only the paradigm's basic tenets: departure from standard dynamics at accelerations a<~a0, and space-time scale invariance in the limit a<<a0. Such predictions will be shared by all MOND theories that embody these premises. This is important because we do not know which of the existing MOND theories, if any, is a step in the right direction. In the Newtonian-dynamics-plus-dark-matter paradigm, the validity of such clear-cut laws -- which tightly constrain baryons, `dark matter', and their mutual relations -- is contrary to expectations.

astro-ph.CO↗

arXiv2013

MOND and its bimetric formulation

I first give a succinct account of the MOND paradigm--emphasizing the centrality of scale invariance in the nonrelativistic, deep-MOND limit--and describing rudiments of its phenomenology. I then present my credo, and some generalities, concerning existing MOND theories. Then I concentrate on one relativistic formulation of MOND in the form of a bimetric theory (BIMOND). I describe its various limits: the weak field, with application to gravitational waves, the nonrelativistic limit, and their further deep-MOND (low acceleration) limits, which are scale invariant. Other aspects of BIMOND that have been explored are aspects of cosmology, matter fluctuations in cosmology, and matter-twin-matter interactions. BIMOND remains largely unexplored, despite its promise in several regards: It tends to GR for a0 goes to 0 (a0 is the MOND constant); it has a simple nonrelativistic limit; it describes gravitational lensing correctly; and, it has a generic appearance of a cosmological-constant term that is of order a0^2/c^4, as observed.

gr-qc↗

arXiv2013

Testing the MOND Paradigm of Modified Dynamics with Galaxy-Galaxy Gravitational Lensing

MOND predicts that the asymptotic gravitational potential of an isolated, bounded (baryonic) mass, M, is phi(r)=(MGa0)^{1/2}ln(r); a0 is the MOND constant. Relativistic MOND theories predict that the lensing effects of M are dictated by phi(r) as general-relativity lensing is dictated by the Newtonian potential. Thus, MOND predicts that the asymptotic Newtonian potential deduced from galaxy-galaxy gravitational lensing will have: (1) a logarithmic r dependence, and (2) a normalization (parametrized standardly as 2s^2) that depends only on M: s=(MGa0/4)^{1/4}. I compare these predictions with recent results of galaxy-galaxy lensing, and find agreement on all counts. For the "blue"-lenses subsample ("spiral" galaxies) MOND reproduces the observations well with an r'-band M/L of 1-3 solar units, and for "red" lenses ("elliptical" galaxies) with M/L of 3-6 solar units, both consistent with baryons only. In contradistinction, Newtonian analysis requires, typically, M/L values of about 130 solar units, bespeaking a mass discrepancy of a factor of about 40. Compared with the staple, rotation-curve tests, MOND is here tested in a wider population of galaxies, through a different phenomenon, using relativistic test objects, and is probed to several-times-lower accelerations--as low as a few percent of a0.

astro-ph.CO↗

arXiv2013

Andromeda Dwarfs in Light of MOND

We compare the recently published velocity dispersions for seventeen Andromeda dwarf spheroidals with estimates of the MOND predictions, based on the luminosities of these dwarfs, with reasonable stellar M/L values, and no dark matter. We find that the two are consistent within the uncertainties. We further predict the velocity dispersions of another ten dwarfs for which only photometric data are currently available.

astro-ph.CO↗

arXiv2013

The failures of the standard model of cosmology require a new paradigm

Cosmological models that invoke warm or cold dark matter can not explain observed regularities in the properties of dwarf galaxies, their highly anisotropic spatial distributions, nor the correlation between observed mass discrepancies and acceleration. These problems with the standard model of cosmology have deep implications, in particular in combination with the observation that the data are excellently described by Modified Newtonian Dynamics (MOND). MOND is a classical dynamics theory which explains the mass discrepancies in galactic systems, and in the universe at large, without invoking dark entities. MOND introduces a new universal constant of nature with the dimensions of acceleration, a0, such that the pre-MONDian dynamics is valid for accelerations a >> a0, and the deep MONDian regime is obtained for a << a0, where space-time scale invariance is invoked. Remaining challenges for MOND are (i) explaining fully the observed mass discrepancies in galaxy clusters, and (ii) the development of a relativistic theory of MOND that will satisfactorily account for cosmology. The universal constant a0 turns out to have an intriguing connection with cosmology: \bar a0 == 2 pi a0 \approx c H_0 \approx c^2(Lambda/3)^{1/2}. This may point to a deep connection between cosmology and internal dynamics of local systems.

astro-ph.CO↗

arXiv2012

Global Deep-MOND Parameter as a Theory Discriminant

Different formulations of MOND predict somewhat different rotation curves for the same mass distribution. Here I consider a global attribute of the rotation curve that might provide a convenient discriminant between theories when applied to isolated, pure-disk galaxies that are everywhere deep in the MOND regime. This parameter is Q= /V0^2, where is the mean squared rotational speed of the galaxy, and V0 is the asymptotic (constant) rotational speed. The comparison between the observed and predicted values of Q is oblivious to the distance, the inclination, the mass, and the size of the disk, and to the form of the interpolating function. For the known modified-gravity theories Q is predicted to be a universal constant (independent of the mass distribution in the disk): Q=2/3. The predicted Q value for modified-inertia theories does depend on the mass distribution. However, surprisingly, I find here that it varies only little among a very wide range of mass distributions, Q=0.73+-0.01. While the difference between the theories amounts to only about 5 percent in the predicted RMS velocity, a good enough sample of galaxies may provide the first discerning test between the two classes of theories.

astro-ph.CO↗

arXiv2012

Testing MOND Over a Wide Acceleration Range in X-Ray Ellipticals

The gravitational fields of two isolated ellipticals, NGC 720 and NGC 1521, have been recently measured to very large galactic radii (~100 and ~200 kpc), assuming hydrostatic balance of the hot gas enshrouding them. They afford, for the first time to my knowledge, testing MOND in ellipticals with force and quality that, arguably, approach those of rotation-curve tests in disk galaxies. In the context of MOND, it is noteworthy that the measured accelerations span a wide range, from more than 10a0 to about a0/10, unprecedented in individual ellipticals. I find that MOND predicts correctly the measured dynamical mass runs (apart from a possible minor tension in the inner few kpc of NGC 720, which might be due to departure from hydrostatic equilibrium): The predicted mass discrepancy increases outward from none, near the center, to ~10 at the outermost radii. The implications for the MOND-vs-dark-matter controversy go far beyond the simple fact of two more galaxies conforming to MOND.

astro-ph.CO↗

arXiv2012

A novel MOND effect in isolated high-acceleration systems

I discuss a novel MOND effect that entails a correction to the dynamics of isolated mass systems even when they are deep in the Newtonian regime: systems whose extent R< 0 is a numerical factor that depends on the interpolating function. For example, the correction to the Newtonian force between two masses, m and M, a distance L apart (L<<Rm), is Fa=2q(L/Rm)^3(mM)^2(M+m)^{-3}a0 (attractive). For generic MOND theories, which approach Newtonian dynamics quickly for accelerations beyond a0, the predicted strength of the effect in the Solar system is rather much below present testing capabilities. In MOND theories that become Newtonian only beyond k*a0, the effect is enhanced by k^2.

astro-ph.CO↗

arXiv2012

Practically linear analogs of the Born-Infeld and other nonlinear theories

I discuss theories that describe fully nonlinear physics, while being practically linear (PL), in that they require solving only linear differential equations. These theories may be interesting in themselves as manageable nonlinear theories. But, they can also be chosen to emulate genuinely nonlinear theories of special interest, for which they can serve as approximations. The idea can be applied to a large class of nonlinear theories, exemplified here with a PL analogs of scalar theories, and of Born-Infeld (BI) electrodynamics. The general class of such PL theories of electromagnetism are governed by a Lagrangian L=-(1/2)F_mnQ^mn+ S(Q_mn), where the electromagnetic field couples to currents in the standard way, while Qmn is an auxiliary field, derived from a vector potential that does not couple directly to currents. By picking a special form of S(Q_mn), we can make such a theory similar in some regards to a given fully nonlinear theory, governed by the Lagrangian -U(F_mn). A particularly felicitous choice is to take S as the Legendre transform of U. For the BI theory, this Legendre transform has the same form as the BI Lagrangian itself. Various matter-of-principle questions remain to be answered regarding such theories. As a specific example, I discuss BI electrostatics in more detail. As an aside, for BI, I derive an exact expression for the short-distance force between two arbitrary point charges of the same sign, in any dimension.

gr-qc↗

arXiv2012

Light and Dark in the Universe

Translation of a popular article on MOND vs. dark matter that appeared, in Hebrew, in the Israeli magazine "Odyssea", dedicated to "thoughts and ideas in the forefront of science and philosophy".

physics.pop-ph↗

arXiv2011

MOND--particularly as modified inertia

After a succinct review of the MOND paradigm--with its phenomenology, and its various underlying theories--I concentrate on so called modified inertia (MI) formulations of MOND, which have so far received only little attention. These share with all MOND theories the salient MOND predictions, such as asymptotically flat rotation curves, and the universal mass-asymptotic-speed relation. My emphasis here is, however, on the fact that MI theories can differ substantially from their "modified-gravity" (MG) kin in predicting other phenomena. Because MI theories are non local in time, MOND effects depend on the full trajectory of a system, not only on its instantaneous state, as in MG theories. This may lead to rather different predictions for, e.g., the external-field effect (EFE): A subsystem, such as a globular cluster or a dwarf galaxy, moving in the field of a mother galaxy, or a galaxy in a cluster, may be subject to an EFE that depends on the accelerations all along its orbit, not only on the instantaneous value. And, it is even possible to construct MI theories with practically no EFE. Other predictions that may differ are also discussed. Since we do not yet have a full fledged, modified-inertia formulation, simple, heuristic models have been used to demonstrate these points.

astro-ph.CO↗

arXiv2011

MOND and the unique void galaxy KK246

MOND predictions are compared with the mass discrepancy, Gamma (the dynamical-to-baryon mass ratio) deduced from the recently measured rotation curve, for the gas-rich, dwarf galaxy KK246, "the only galaxy observed in the local void". KK246 is special in at least two regards: a. It is, to my knowledge, the record holder for the largest mass discrepancy deduced from a rotation curve, Gamma= 15. b. It is very isolated, residing in a large, very empty void. I also discuss another extreme case: Andromeda IV, a dwarf considered here for the first time in light of MOND, with a very large mass discrepancy, Gamma =12, also conforming accurately to the MOND prediction. In both cases, MOND predicts Gamma, or the total dynamical mass at the last observed radius, from only the knowledge of the small mass of baryons. If MOND is accepted as the root of the mass discrepancy, these are just two more expected, albeit reassuring, conformities. However, in the framework of the dark-matter paradigm--where the mass discrepancy is strongly dependent on the buildup history of a galaxy--every new such conformity with a tight law is another difficult-to-understand surprise, and does carry a new import: What, in the LCDM paradigm, would prevent such galactic baryons from residing in a halo of half, or twice, the observed rotational velocities, instead of selecting exactly the velocities predicted by MOND? This conundrum is especially poignant for KK246, whose great isolation points to a relatively unique buildup history. This note underscores the individual importance of each galaxy as a new test, as opposed to the view of them all as a statistical ensemble.

astro-ph.CO↗

arXiv2011

Gravitational Cherenkov losses in MOND theories

Survival of high-energy cosmic rays (HECRs) against gravitational Cherenkov losses is shown not to cast strong constraints on MOND theories that are compatible with general relativity (GR): theories that coincide with GR in the high-acceleration limit. The energy-loss rate, L, is shown to be many orders smaller than those derived in the literature for theories with no extra scale. The gravitational acceleration produced by a HECR in its vicinity is much higher than the MOND acceleration a0. So, modification to GR, which underlies L, enters only beyond the MOND radius of the particle, within which GR holds sway: r_M=sqrt(Gp/c a0). The spectral cutoff, which enters L quadratically, is thus 1/r_M, not the particle's, much larger, de Broglie wavenumber: k_{dB}= p/hbar. Thus, L is smaller than published rates, which use k_{dB}, by a factor (r_M k_{dB})^2~10^{39}(cp/3.10^{11}Gev)^3. With 1/r_M as cutoff, the distance a HECR can travel without major losses is q l_M, where l_M=c^2/a0 is the MOND length, and q is a dimensionless function of parameters of the problem. Since l_M is ~2 pi times the Hubble distance, survival of HECRs does not strongly constrain GR-compatible, MOND theories. Such theories also easily satisfy existing preferred-frame limits, inasmuch as these limits are gotten in high-acceleration systems. I exemplify the results with MOND adaptations of Einstein-Aether theories.

astro-ph.CO↗

arXiv2011

MD or DM? Modified dynamics at low accelerations vs dark matter

The MOND paradigm posits a departure from standard Newtonian dynamics, and from General Relativity, in the limit of small accelerations. The resulting modified dynamics aim to account for the mass discrepancies in the universe without non-baryonic dark matter. I briefly review this paradigm with its basic tenets, and its underlying theories--nonrelativistic and relativistic--including a novel, bimetric MOND gravity theory. I also comment on MOND's possible connection to, and origin in, the cosmological state of the universe at large. Some of its main predictions, achievements, and remaining desiderata are listed. I then succinctly pit MOND against the competing paradigm of standard dynamics with cold, dark matter. (Abridged)

astro-ph.CO↗

arXiv2010

New Physics at Low Accelerations (MOND): an Alternative to Dark Matter

I describe the MOND paradigm, which posits a departure from standard physics below a certain acceleration scale. This acceleration as deduced from the dynamics in galaxies is found mysteriously to agree with the cosmic acceleration scales defined by the present day expansion rate and by the density of `dark energy'. I put special emphasis on phenomenology and on critical comparison with the competing paradigm based on classical dynamics plus cold dark matter. I also describe briefly nonrelativistic and relativistic MOND theories.

astro-ph.CO↗

arXiv2010

Cosmological fluctuation growth in bimetric MOND

I look at the growth of weak density inhomogeneities of nonrelativistic matter, in bimetric-MOND (BIMOND) cosmology. I concentrate on matter-twin-matter-symmetric versions of BIMOND, and assume that, on average, the universe is symmetrically populated in the two sectors. MOND effects are absent in an exactly symmetric universe, apart from the appearance of a cosmological constant, Lambda~(a0/c)^2. MOND effects-local and cosmological-do enter when density inhomogeneities that differ in the two sectors appear and develop. MOND later takes its standard form in systems that are islands dominated by pure matter. I derive the nonrelativistic equations governing small-scale fluctuation growth. The equations split into two uncoupled systems, one for the sum, the other for the difference, of the fluctuations in the two sectors. The former is governed strictly by Newtonian dynamics. The latter is governed by MOND dynamics, which entails stronger gravity, and nonlinearity even for the smallest of perturbations. These cause the difference to grow faster than the sum, conducing to matter-twin-matter segregation. The nonlinearity also causes interaction between nested perturbations on different scales. Because matter and twin matter (TM) repel each other in the MOND regime, matter inhomogeneities grow not only by their own self gravity, but also through shepherding by flanking TM overdensitie. The relative importance of gravity and pressure in the MOND system depends also on the strength of the perturbation. The development of structure in the universe, in either sector, thus depends crucially on two initial fluctuation spectra: that of matter alone and that of the matter-TM difference. I also discuss the back reaction on cosmology of BIMOND effects that appear as "phantom matter" resulting from inhomogeneity differences between the two sectors.

astro-ph.CO↗

arXiv2010

Matter and twin matter in bimetric MOND

Bimetric MOND (BIMOND) theories, propounded recently, predict peculiar gravitational interactions between matter and twin matter (TM). Twin matter is hypothetical matter that might couple directly only to the second metric of the theory. Considerations of cosmology in the BIMOND framework suggest that such TM might exist and copy matter in its attributes. Here I investigate the indirect interactions that BIMOND theories predict between nonrelativistic masses of matter and TM. The most salient result is that in the deep-MOND regime of the matter-TM-symmetric theories, TM behaves as if it has a negative gravitational mass. To wit, interaction within each sector is attractive MOND gravity, but between matter and TM it is repulsive MOND gravity. In the high-acceleration regime, the interaction depends on a parameter, beta. For the favored value beta=1, matter and TM do not interact in this regime; for beta<1 they attract; and for beta>1 they repel each other. Such interactions may have substantial ramifications for all aspects of structure formation, such as matter distribution, peculiar velocities, and effects on the CMB. The repulsive interactions probably lead to segregation of matter and TM structures, leading, in turn, to intermeshing of the respective cosmic webs, with high-density nodes of one sector residing in the voids of the other (possibly conducing to efficient evacuation of the voids). Weak lensing by TM seems the best way to constrain its attributes. In the MOND regime a TM body acts on matter photons as a diverging lens. Strong lensing occurs in the high acceleration regime, and thus depends on the value of beta. For beta=1 no strong lensing effects of TM are expected. I also discuss briefly asymmetric theories (abridged).

astro-ph.CO↗

arXiv2010

Quasi-linear formulation of MOND

A new formulation of MOND as a modified-potential theory of gravity is propounded. In effect, the theory dictates that the MOND potential phi produced by a mass distribution rho is a solution of the Poisson equation for the modified source density rho*=-(1/4 pi G)divergence(g), where g=nu(|gN|/a0)gN, and gN is the Newtonian acceleration field of rho. This makes phi simply the scalar potential of the algebraic acceleration field g. The theory thus involves solving only linear differential equations, with one nonlinear, algebraic step. It is derivable from an action, satisfies all the usual conservation laws, and gives the correct center-of-mass acceleration to composite bodies. The theory is akin in some respects to the nonlinear Poisson formulation of Bekenstein and Milgrom, but it is different from it, and is obviously easier to apply. The two theories are shown to emerge as natural modifications of a Palatini-type formulation of Newtonian gravity, and are members in a larger class of bi-potential theories.

astro-ph.CO↗