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.Comment: 6 page

The MOND limit from space-time scale invariance

The MOND limit is shown to follow from a requirement of space-time scale invariance of the equations of motion for nonrelativistic, purely gravitational systems; i.e., invariance of the equations of motion under (t,r) goes to (qt,qr), in the limit a0 goes to infinity. It is suggested that this should replace the definition of the MOND limit based on the low-acceleration behavior of a Newtonian-MOND interpolating function. In this way, the salient, deep-MOND results--asymptotically flat rotation curves, the mass-rotational-speed relation (baryonic Tully-Fisher relation), the Faber-Jackson relation, etc.--follow from a symmetry principle. For example, asymptotic flatness of rotation curves reflects the fact that radii change under scaling, while velocities do not. I then comment on the interpretation of the deep-MOND limit as one of "zero mass": Rest masses, whose presence obstructs scaling symmetry, become negligible compared to the "phantom", dynamical masses--those that some would attribute to dark matter. Unlike the former masses, the latter transform in a way that is consistent with the symmetry. Finally, I discuss the putative MOND-cosmology connection in light of another, previously known symmetry of the deep-MOND limit. In particular, it is suggested that MOND is related to the asymptotic de Sitter geometry of our universe. It is conjectured, for example, that in an exact de Sitter cosmos, deep-MOND physics would exactly apply to local systems. I also point out, in this connection, the possible relevance of a de Sitter-conformal-field-theory (dS/CFT) duality.Comment: 17 pages; Changed to match version to be published in The Astrophysical Journa

The central surface density of "dark halos" predicted by MOND

Prompted by the recent claim, by Donato et al., of a quasi-universal central surface density of galaxy dark matter halos, I look at what MOND has to say on the subject. MOND, indeed, predicts a quasi-universal value of this quantity for objects of all masses and of any internal structure, provided they are mostly in the Newtonian regime; i.e., that their mean acceleration is at or above a0. The predicted value is qSm, with Sm= a0/2 pi G= 138 solar masses per square parsec for the nominal value of a0, and q a constant of order 1 that depends only on the form of the MOND interpolating function. This gives in the above units log(Sm)=2.14, which is consistent with that found by Doanato et al. of 2.15+-0.2. MOND predicts, on the other hand, that this quasi-universal value is not shared by objects with much lower mean accelerations. It permits halo central surface densities that are arbitrarily small, if the mean acceleration inside the object is small enough. However, for such low-surface-density objects, MOND predicts a halo surface density that scales as the square root of the baryonic one, and so the range of the former is much compressed relative to the latter. This explains, in part, the finding of Donato et al. that the universal value applies to low acceleration systems as well. Looking at literature results for a number of the lowest surface-density disk galaxies with rotation-curve analysis, I find that, indeed, their halo surface densities are systematically lower then the above "universal" value. The prediction of Sm as an upper limit, and accumulation value, of halo central surface densities, pertains, unlike most other MOND predictions, to a pure "halo" property, not to a relation between baryonic and "dark matter" properties.Comment: 9 page

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.Comment: 23 pages. Published in MNRAS. Minor changes to match the published versio

Marriage \`a-la-MOND: Baryonic dark matter in galaxy clusters and the cooling flow puzzle

I start with a brief introduction to MOND phenomenology and its possible roots in cosmology--a notion that may turn out to be the most far reaching aspect of MOND. Next I discuss the implications of MOND for the dark matter (DM) doctrine: MOND's successes imply that baryons determine everything. For DM this would mean that the puny tail of leftover baryons in galaxies wags the hefty DM dog. This has to occur in many intricate ways, and despite the haphazard construction history of galaxies--a very tall order. I then concentrate on galaxy clusters in light of MOND, which still requires some yet undetected cluster dark matter, presumably in some baryonic form (CBDM). This CBDM might contribute to the heating of the x-ray emitting gas and thus alleviate the cooling-flow puzzle. MOND, qua theory of dynamics, does not directly enter the microphysics of the gas; however, it does force a new outlook on the role of DM in shaping the cluster gasdynamics: MOND tells us that the cluster DM is not cold dark matter, is not so abundant, and is not expected in galaxies; it is thus not subject to constraints on baryonic DM in galaxies. The mass in CBDM required in a whole cluster is, typically, similar to that in hot gas, but is rather more centrally concentrated, totally dominating the core. The CBDM contribution to the baryon budget in the universe is thus small. Its properties, deduced for isolated clusters, are consistent with the observations of the ``bullet cluster''. Its kinetic-energy reservoir is much larger than that of the hot gas in the core, and would suffice to keep the gas hot for many cooling times. Heating can be effected in various ways depending on the exact nature of the CBDM, from very massive black holes to cool, compact gas clouds.Comment: 11 pages. Talk given at "Jean-Pierre Lasota, X-ray binaries, accretion disks and compact stars" (October 2007); Abramowicz, M. Ed., New Astron. Rev., in pres

MOND effects in the inner solar system

I pinpoint a previously unrecognized MOND effect that may act in the inner solar system, and is due to the galactic acceleration, g_g=eta*a0: a byproduct of the MOND external-field effect. Predictions of the effect are not generic to the MOND paradigm, but depend on the particular MOND formulation at hand. However, the modified-Poisson formulation, on which I concentrate, uniquely predicts a subtle anomaly that may be detected in planetary and spacecraft motions (and perhaps in other precision systems, such as binary pulsars), despite their very high accelerations, and even if the MOND interpolating function is arbitrarily close to unity at high accelerations. Near the sun, this anomaly appears as a quadrupole field, with the acceleration at position u from the sun being g_i(u)=-q_{ij}u^j, with q_{ij} diagonal, axisymmetric, and traceless: -2q_{xx}=-2q_{yy}=q_{zz}=q(eta)*(a0/R_M), where R_M=(MG/a0)^{1/2}=8*10^3 au is the MOND radius of the sun. The anomaly is described and analyzed as the Newtonian field of the fictitious cloud of ``phantom matter'' that hovers around the sun. I find, for the relevant range of eta values, and for a range of interpolating functions, mu(x), values of 10^{-2}<-q< 0.3, which turn out to be sensitive to the form of mu(x) around the MOND-to-Newtonian transition. This range verges on the present bounds from solar system measurements. There might thus exist favorable prospects for either measuring the effect, or constraining the theory and the relevant parameters.Comment: 31 pages; accepted for publication in MNRAS. Minor changes to match published versio

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.Comment: 12 page

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.Comment: 15 pages, minor coorrections. proceedings of: "The Invisible Universe International Conference", Paris, June 2009 (J.M. Alimi et al. eds.