Radial-orbit instability in modified Newtonian dynamics

The stability of radially anisotropic spherical stellar systems in modified Newtonian dynamics (MOND) is explored by means of numerical simulations performed with the N-body code N-MODY. We find that Osipkov-Merritt MOND models require for stability larger minimum anisotropy radius than equivalent Newtonian systems (ENSs) with dark matter, and also than purely baryonic Newtonian models with the same density profile. The maximum value for stability of the Fridman-Polyachenko-Shukhman parameter in MOND models is lower than in ENSs, but higher than in Newtonian models with no dark matter. We conclude that MOND systems are substantially more prone to radial-orbit instability than ENSs with dark matter, while they are able to support a larger amount of kinetic energy stored in radial orbits than purely baryonic Newtonian systems. An explanation of these results is attempted, and their relevance to the MOND interpretation of the observed kinematics of globular clusters, dwarf spheroidal and elliptical galaxies is briefly discussed.Comment: 9 pages, 4 figures, accepted for publication in MNRA

The alignment of the second velocity moment tensor in galaxies

We show that provided the principal axes of the second velocity moment tensor of a stellar population are generally unequal and are oriented perpendicular to a set of orthogonal surfaces at each point, then those surfaces must be confocal quadric surfaces and the potential must be separable or Stäckel. This is true under the mild assumption that the even part of the distribution function (DF) is invariant under time reversal vi → −vi of each velocity component. In particular, if the second velocity moment tensor is everywhere exactly aligned in spherical polar coordinates, then the potential must be of separable or Stäckel form (excepting degenerate cases where two or more of the semiaxes of ellipsoid are everywhere the same). The theorem also has restrictive consequences for alignment in cylindrical polar coordinates, which is used in the popular Jeans Anisotropic Models (JAM) of Cappellari. We analyse data on the radial velocities and proper motions of a sample of ∼7300 stars in the stellar halo of the Milky Way. We provide the distributions of the tilt angles or misalignments from both the spherical polar coordinate systems. We show that in this sample the misalignment is always small (usually within 3°) for Galactocentric radii between ∼6 and ∼11 kpc. The velocity anisotropy is very radially biased (β ≈ 0.7), and almost invariant across the volume in our study. Finally, we construct a triaxial stellar halo in a triaxial NFW dark matter halo using a made-to-measure method. Despite the triaxiality of the potential, the velocity ellipsoid of the stellar halo is nearly spherically aligned within ∼6° for large regions of space, particularly outside the scale radius of the stellar halo. We conclude that the second velocity moment ellipsoid can be close to spherically aligned for a much wider class of potentials than the strong constraints that arise from exact alignment might suggest

The MOND Fundamental Plane

Modified Newtonian Dynamics (MOND) has been shown to be able to fit spiral galaxy rotation curves as well as giving a theoretical foundation for empirically determined scaling relations, such as the Tully - Fisher law, without the need for a dark matter halo. As a complementary analysis, one should investigate whether MOND can also reproduce the dynamics of early - type galaxies (ETGs) without dark matter. As a first step, we here show that MOND can indeed fit the observed central velocity dispersion $\sigma_0$ of a large sample of ETGs assuming a simple MOND interpolating functions and constant anisotropy. We also show that, under some assumptions on the luminosity dependence of the Sersic n parameter and the stellar M/L ratio, MOND predicts a fundamental plane for ETGs : a log - linear relation among the effective radius $R_{eff}$, $\sigma_0$ and the mean effective intensity $\langle I_e \rangle$. However, we predict a tilt between the observed and the MOND fundamental planes.Comment: 16 pages, 2 figures, 2 tables, accepted for publication on MNRA

Mid-J CO Emission From NGC 891: Microturbulent Molecular Shocks in Normal Star Forming Galaxies

We have detected the CO(6-5), CO(7-6), and [CI] 370 micron lines from the nuclear region of NGC 891 with our submillimeter grating spectrometer ZEUS on the CSO. These lines provide constraints on photodissociation region (PDR) and shock models that have been invoked to explain the H_2 S(0), S(1), and S(2) lines observed with Spitzer. We analyze our data together with the H_2 lines, CO(3-2), and IR continuum from the literature using a combined PDR/shock model. We find that the mid-J CO originates almost entirely from shock-excited warm molecular gas; contributions from PDRs are negligible. Also, almost all the H_2 S(2) and half of the S(1) line is predicted to emerge from shocks. Shocks with a pre-shock density of 2x10^4 cm^-3 and velocities of 10 km/s and 20 km/s for C-shocks and J-shocks, respectively, provide the best fit. In contrast, the [CI] line emission arises exclusively from the PDR component, which is best parameterized by a density of 3.2x10^3 cm^-3 and a FUV field of G_o = 100 for both PDR/shock-type combinations. Our mid-J CO observations show that turbulence is a very important heating source in molecular clouds, even in normal quiescent galaxies. The most likely energy sources for the shocks are supernovae or outflows from YSOs. The energetics of these shock sources favor C-shock excitation of the lines.Comment: 18 pages, 2 figures, 6 tables, accepted by Ap

The outcome of arthroscopic treatment of temporomandibular joint arthoropathy

The document attached has been archived with permission from the Australian Dental Association. An external link to the publisher’s copy is included.Ninety patients underwent arthroscopic temporomandibular joint surgery to 124 joints for arthropathy which had failed to respond to at least six months of non-surgical treatment. They were surveyed at between 6 months and 5 years (mean 2.5 years) after surgery and 63 per cent responded to the survey. They reported an 82 per cent improvement for pain (50 to 100 per cent better), 80 per cent for clicking and 82 per cent for locking. There was no morbidity following the treatment. Arthroscopic surgery sould be considered for advanced temporomandibular joint arthropathy which is refractory to non-surgical treatment.I. Rosenburg and A. N. Gos

Testing Yukawa-like potentials from f(R)-gravity in elliptical galaxies

We present the first analysis of extended stellar kinematics of elliptical galaxies where a Yukawa-like correction to the Newtonian gravitational potential derived from f(R)-gravity is considered as an alternative to dark matter. In this framework, we model long-slit data and planetary nebula data out to 7 R eff of three galaxies with either decreasing or flat dispersion profiles. We use the corrected Newtonian potential in a dispersion-kurtosis Jeans analysis to account for the mass-anisotropy degeneracy. We find that these modified potentials are able to fit nicely all three elliptical galaxies and the anisotropy distribution is consistent with that estimated if a dark halo is considered. The parameter which measures the strength of the Yukawa-like correction is, on average, smaller than the one found previously in spiral galaxies and correlates both with the scale length of the Yukawa-like term and the orbital anisotropy

The velocity dispersion and mass function of the outer halo globular cluster Palomar 4

We obtained precise line-of-sight radial velocities of 23 member stars of the remote halo globular cluster Palomar 4 (Pal 4) using the High Resolution Echelle Spectrograph (HIRES) at the Keck I telescope. We also measured the mass function of the cluster down to a limiting magnitude of V~28 mag using archival HST/WFPC2 imaging. We derived the cluster's surface brightness profile based on the WFPC2 data and on broad-band imaging with the Low-Resolution Imaging Spectrometer (LRIS) at the Keck II telescope. We find a mean cluster velocity of 72.55+/-0.22 km/s and a velocity dispersion of 0.87+/-0.18 km/s. The global mass function of the cluster, in the mass range 0.55<=M<=0.85 M_solar, is shallower than a Kroupa mass function and the cluster is significantly depleted in low-mass stars in its center compared to its outskirts. Since the relaxation time of Pal 4 is of the order of a Hubble time, this points to primordial mass segregation in this cluster. Extrapolating the measured mass function towards lower-mass stars and including the contribution of compact remnants, we derive a total cluster mass of 29800 M_solar. For this mass, the measured velocity dispersion is consistent with the expectations of Newtonian dynamics and below the prediction of Modified Newtonian Dynamics (MOND). Pal 4 adds to the growing body of evidence that the dynamics of star clusters in the outer Galactic halo can hardly be explained by MOND.Comment: 17 pages, accepted for publication in MNRAS; Fig. 8 surface brightness/density data at github.com/matthiasjfrank/pal4_surface_brightnes