The Caustic Ring Model of the Milky Way Halo

We present a proposal for the full phase space distribution of the Milky Way halo. The model is axially and reflection symmetric and its time evolution is self-similar. It describes the halo as a set of discrete dark matter flows with stated densities and velocity vectors everywhere. We first discuss the general conditions under which the time evolution of a cold collisionless self-gravitating fluid is self-similar, and show that symmetry is not necessary for self-similarity. When spherical symmetry is imposed, the model is the same as described by Fillmore and Goldreich, and by Bertschinger, twenty-three years ago. The spherically symmetric model depends on one dimensionless parameter $\epsilon$ and two dimensionful parameters. We set $\epsilon$ = 0.3, a value consistent with the slope of the power spectrum of density perturbations on galactic scales. The dimensionful parameters are determined by the Galactic rotation velocity (220 km/s) at the position of the Sun and by the age of the Galaxy (13.7 Gyr). The properties of the outer caustics are derived in the spherically symmetric model. The structure of the inner halo depends on the angular momentum distribution of the dark matter particles. We assume that distribution to be axial and reflection symmetric, and dominated by net overall rotation. The inner caustics are rings whose radii are determined in terms of a single additional parameter $j_{\rm max}$. We summarize the observational evidence in support of the model. The evidence is consistent with $j_{\rm max}$ = 0.18 in Concordance Cosmology, equivalent to $j_{\rm max,old}$ = 0.26 in Einstein - de Sitter cosmology. We give formulas to estimate the flow densities and velocity vectors anywhere in the Milky Way halo. The properties of the first forty flows at the location of the Earth are listed.Comment: 35 pages, 6 figure

The Distribution of Dark Matter in a Ringed Galaxy

Outer rings are located at the greatest distance from the galaxy center of any feature resonant with a bar. Because of their large scale, their morphology is sensitive to the distribution of the dark matter in the galaxy. We introduce here how study of these rings can constrain the mass-to-light ratio of the bar, and so the percentage of dark matter in the center of these galaxies. We compare periodic orbits integrated in the ringed galaxy NGC 6782 near the outer Lindblad resonance to the shape of the outer ring. The non-axisymmetric component of the potential resulting from the bar is derived from a near-infrared image of the galaxy. The axisymmetric component is derived assuming a flat rotation curve. We find that the pinched non-self-intersecting periodic orbits are more elongated for higher bar mass-to-light ratios and faster bars. The inferred mass-to-light ratio of the bar depends on the assumed inclination of the galaxy. With an assumed galaxy inclination of i=41 degrees, for the orbits to be consistent with the observed ring morphology the mass-to-light ratio of the bar must be high, greater than 70% of a maximal disk value. For i=45 degrees, the mass-to-light ratio of the bar is $75\pm 15$ of the maximal disk value. Since the velocity field of these rings can be used to constrain the galaxy inclination as well as which periodic orbit is represented in the ring, further study will yield tighter constraints on the mass-to-light ratio of the bar. If a near maximal disk value for the bar is required, then either there would be little dark matter within the bar, or the dark matter contained in the disk of the galaxy would be non-axisymmetric and would rotate with the bar.Comment: AAS Latex + jpg Figures, Accepted for publication in Ap

Accurate Determination of the Mass Distribution in Spiral Galaxies: II. Testing the Shape of Dark Halos

New high resolution CFHT Fabry-Perot data, combined with published VLA 21 cm observations are used to determine the mass distribution of NGC 3109 and IC 2574. The multi-wavelength rotation curves allow to test with confidence different dark halo functional forms from the pseudo-isothermal sphere to some popular halo distributions motivated by N-body simulations. It appears that density distribution with an inner logarithmic slope <= -1 are very hard to reconcile with rotation curves of late type spirals. Modified Newtonian Dynamics (MOND) is also considered as a potential solution to missing mass and tested the same way. The new higher resolution data show that MOND can reproduce in details the rotation curve of IC 2574 but confirm its difficulty to fit the kinematics of NGC 3109.Comment: 28 pages, accepted by AJ. New HI profile increases the compatibility of NGC 3109 rotation curve with MON

The Bar Pattern Speed of NGC 1433 Estimated Via Sticky-Particle Simulations

We present detailed numerical simulations of NGC 1433, an intermediate-type barred spiral showing strong morphological features including a secondary bar, nuclear ring, inner ring, outer pseudoring, and two striking, detached spiral arcs known as ``plumes.'' This galaxy is an ideal candidate for recreating the observed morphology through dynamical models and determining the pattern speed. We derived a gravitational potential from an $H$-band image of the galaxy and simulated the behavior of a two-dimensional disk of 100,000 inelastically colliding gas particles. We find that the closest matching morphology between a $B$-band image and a simulation occurs with a pattern speed of 0.89 km s$^{-1}$ arcsec$^{-1}$ $\pm$ 5-10%. We also determine that the ratio of corotation radius to the average published bar radius is 1.7 $\pm$ 0.3, with the ambiguity in the bar radius being the largest contributor to the error.Comment: Accepted for publication by The Astronomical Journal. 34 pages, 13 figures, 2 table

Searching for Dark Matter with Future Cosmic Positron Experiments

Dark matter particles annihilating in the Galactic halo can provide a flux of positrons potentially observable in upcoming experiments, such as PAMELA and AMS-02. We discuss the spectral features which may be associated with dark matter annihilation in the positron spectrum and assess the prospects for observing such features in future experiments. Although we focus on some specific dark matter candidates, neutralinos and Kaluza-Klein states, we carry out our study in a model independent fashion. We also revisit the positron spectrum observed by HEAT.Comment: 19 pages, 33 figure

Evidence for universal structure in galactic halos

The late infall of dark matter onto a galaxy produces structure (such as caustics) in the distribution of dark matter in the halo. We argue that such structure is likely to occur generically on length scales proportional to $l \sim t_0 v_{rot}$, where $t_0$ is the age of the universe and $v_{rot}$ is the rotation velocity of the galaxy. A set of 32 extended galactic rotation curves is analyzed. For each curve, the radial coordinate is rescaled according to $r\to \tilde r \equiv r (v_0 / v_{rot})$, where we choose $v_0 = 220 km/s$. A linear fit to each rescaled rotation curve is subtracted, and the residuals are binned and averaged. The sample shows significant features near $\tilde r = 40 kpc$ and $\tilde r = 20 kpc$. This is consistent with the predictions of the self-similar caustic ring model of galactic halos.Comment: 4 pages, LaTeX, 1 epsf figur

Open Questions in Classical Gravity

We discuss some outstanding open questions regarding the validity and uniqueness of the standard second order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of Newton's Law of Gravity can actually be extended to distances much larger than the solar system distance scales on which the law was originally established. On the theoretical side we identify some commonly accepted but actually still open to question assumptions which go into the formulating of the standard second order Einstein theory in the first place. In particular, we show that while the familiar second order Poisson gravitational equation (and accordingly its second order covariant Einstein generalization) may be sufficient to yield Newton's Law of Gravity they are not in fact necessary. The standard theory thus still awaits the identification of some principle which would then make it necessary too. We show that current observational information does not exclusively mandate the standard theory, and that the conformal invariant fourth order theory of gravity considered recently by Mannheim and Kazanas is also able to meet the constraints of data, and in fact to do so without the need for any so far unobserved non-luminous or dark matter.Comment: UCONN-93-1, plain TeX format, 22 pages (plus 7 figures - send requests to [email protected]). To appear in a special issue of Foundations of Physics honoring Professor Fritz Rohrlich on the occasion of his retirement, L. P. Horwitz and A. van der Merwe Editors, Plenum Publishing Company, N.Y., Fall 199

Mass Density Profiles of LSB Galaxies

We derive the mass density profiles of dark matter halos that are implied by high spatial resolution rotation curves of low surface brightness galaxies. We find that at small radii, the mass density distribution is dominated by a nearly constant density core with a core radius of a few kpc. For rho(r) ~ r^a, the distribution of inner slopes a is strongly peaked around a = -0.2. This is significantly shallower than the cuspy a < -1 halos found in CDM simulations. While the observed distribution of alpha does have a tail towards such extreme values, the derived value of alpha is found to depend on the spatial resolution of the rotation curves: a ~ -1 is found only for the least well resolved galaxies. Even for these galaxies, our data are also consistent with constant density cores (a = 0) of modest (~ 1 kpc) core radius, which can give the illusion of steep cusps when insufficiently resolved. Consequently, there is no clear evidence for a cuspy halo in any of the low surface brightness galaxies observed.Comment: To be published in ApJ Letters. 6 pages. Uses aastex and emulateapj5.sty Typo in Eq 1 fixe

Limits on Supersymmetric Dark Matter From EGRET Observations of the Galactic Center Region

In most supersymmetic models, neutralino dark matter particles are predicted to accumulate in the Galactic center and annihilate generating, among other products, gamma rays. The EGRET experiment has made observations in this region, and is sensitive to gamma rays from 30 MeV to $\sim$30 GeV. We have used an improved point source analysis including an energy dependent point spread function and an unbinned maximum likelihood technique, which has allowed us to significantly lower the limits on gamma ray flux from the Galactic center. We find that the present EGRET data can limit many supersymmetric models if the density of the Galactic dark matter halo is cuspy or spiked toward the Galactic center. We also discuss the ability of GLAST to test these models.Comment: 4 pages, 3 figure

Stellar and Gas properties of High HI Mass-to-Light Ratio Galaxies in the Local Universe

We present a multi-wavelength study (BVRI band photometry and HI line interferometry) of nine late-type galaxies selected from the HIPASS Bright Galaxy Catalog on the basis of apparently high HI mass-to-light ratios (3 M_sun/L_sun < M_HI/L_B < 27 M_sun/L_sun). We found that most of the original estimates for M_HI/L_B based on available photographic magnitudes in the literature were too high, and conclude that genuine high HI mass-to-light ratio (>5 M_sun/L_sun) galaxies are rare in the Local Universe. Extreme high M_HI/L_B galaxies like ESO215-G?009 appear to have formed only the minimum number of stars necessary to maintain the stability of their HI disks, and could possibly be used to constrain galaxy formation models. They may to have been forming stars at a low, constant rate over their lifetimes. The best examples all have highly extended HI disks, are spatially isolated, and have normal baryonic content for their total masses but are deficent in stars. This suggests that high M_HI/L_B galaxies are not lacking the baryons to create stars, but are underluminous as they lack either the internal or external stimulation for more extensive star formation.Comment: 29 Pages, 59 Figures. Accepted for publication in AJ (to be published ~April 2006