Disk heating by more than one spiral density wave

We consider a differentially rotating, 2D stellar disk perturbed by two steady state spiral density waves moving at different patterns speeds. Our investigation is based on direct numerical integration of initially circular test-particle orbits. We examine a range of spiral strengths and spiral speeds and show that stars in this time dependent gravitational field can be heated (their random motions increased).This is particularly noticeable in the simultaneous propagation of a 2-armed spiral density wave near the corotation resonance (CR), and a weak 4-armed one near the inner and outer 4:1 Lindblad resonances. In simulations with 2 spiral waves moving at different pattern speeds we find: (1) the variance of the radial velocity, sigma_R^2, exceeds the sum of the variances measured from simulations with each individual pattern; (2) sigma_R^2 can grow with time throughout the entire simulation; (3) sigma_R^2 is increased over a wider range of radii compared to that seen with one spiral pattern; (4) particles diffuse radially in real space whereas they don't when only one spiral density wave is present. Near the CR with the stronger, 2-armed pattern, test particles are observed to migrate radially. These effects take place at or near resonances of both spirals so we interpret them as the result of stochastic motions. This provides a possible new mechanism for increasing the stellar velocity dispersion in galactic disks. If multiple spiral patterns are present in the Galaxy we predict that there should be large variations in the stellar velocity dispersion as a function of radius.Comment: 20 pages, 13 figures. Submitted to MNRA

New Constraints on the Galactic Bar

Previous work has related the Galactic Bar to structure in the local stellar velocity distribution. Here we show that the Bar also influences the spatial gradients of the velocity vector via the Oort constants. By numerical integration of test-particles we simulate measurements of the Oort C value in a gravitational potential including the Galactic Bar. We account for the observed trend that C is increasingly negative for stars with higher velocity dispersion. By comparing measurements of C with our simulations we improve on previous models of the Bar, estimating that the Bar pattern speed is Omega_b/Omega_0=1.87\pm0.04, where Omega_0 is the local circular frequency, and the Bar angle lies within 20<phi_0<45 deg. We find that the Galactic Bar affects measurements of the Oort constants A and B less than ~2 km/s/kpc for the hot stars.Comment: 4 pages, 2 figures, Accepted to ApJ Letters. Replaced with accepted versio

Chern classes and extraspecial groups

The mod-p cohomology ring of the extraspecial p-group of exponent p is studied for odd p. We investigate the subquotient ch(G) generated by Chern classes modulo the nilradical. The subring of ch(G) generated by Chern classes of one-dimensional representations was studied by Tezuka and Yagita. The subring generated by the Chern classes of the faithful irreducible representations is a polynomial algebra. We study the interplay between these two families of generators, and obtain some relations between them

The Effect of Spiral Structure on the Measurements of the Oort Constants

We perform test-particle simulations in a 2D, differentially rotating stellar disk, subjected to a two-armed steady state spiral density wave perturbation in order to estimate the influence of spiral structure on the local velocity field. By using Levenberg-Marquardt least-squares fit we decompose the local velocity field (as a result of our simulations) into Fourier components to fourth order. Thus we obtain simulated measurements of the Oort constants, A, B, C, and K. We get relations between the Fourier coefficients and some galactic parameters, such as the phase angle of the Solar neighborhood and the spiral pattern speed. We show that systematic errors due to the presence of spiral structure are likely to affect the measurements of the Oort constants. Moderate strength spiral structure causes errors of order 5 km/s/kpc in A and B. We find variations of the Fourier coefficients with velocity dispersion, pattern speed, and sample depth. For a sample at an average heliocentric distance of 0.8 kpc we can summarize our findings as follows:(i) if our location in the Galaxy is near corotation then we expect a vanishing value for C for all phase angles;(ii) for a hot disk, spiral structure induced errors for all Oort constants vanish at, and just inward of the corotation radius; (iii) as one approaches the 4:1 indblad resonances |C| increases and so does its variation with galactic azimuth; (iv) for all simulations |C|, on average, is larger for lower stellar velocity dispersions, contrary to recent measurements.Comment: 20p., 11 fig. Replaced with accepted version to be published in MNRA

Rigidification of quasi-categories

We give a new construction for rigidifying a quasi-category into a simplicial category, and prove that it is weakly equivalent to the rigidification given by Lurie. Our construction comes from the use of necklaces, which are simplicial sets obtained by stringing simplices together. As an application of these methods, we use our model to reprove some basic facts from Lurie's "Higher Topos Theory" regarding the rigidification process.Comment: 26 page

Radial Mixing due to Spiral-Bar Resonance Overlap: Implications to the Milky Way

We have recently identified a previously unknown radial migration mechanism resulting from the overlap of spiral and bar resonances in galactic discs (Minchev & Famaey 2010, Minchev et al. 2010). This new mechanism is much more efficient than mixing by transient spirals and its presence is unavoidable in all barred galaxies, such as our own Milky Way. The consequences of this are a strong flattening in the metallicity gradient in the disc, an extended disc profile, and the formation of a thick disc component, all taking place in only a couple of Gyr. This timescale is drastically shorter than previously expected and thus can put strong constraints on the longevity, strength and pattern speeds of the Galactic bar and Spiral Structure.Comment: 4 pages, 2 figures, presented at ELSA 2010: Gaia, at the frontiers of astrometry, 7-11 June 2010, S\`evres, Paris; To published in EAS Series; Proceedings editors: C. Turon, F. Arenou & F. Meynadie

A New Mechanism for Radial Migration in Galactic Disks: Spiral-Bar Resonance Overlap

While it has long been known that a large number of short-lived transient spirals can cause stellar migration, here we report that another mechanism is also effective at mixing disks of barred galaxies. The resonance overlap of the bar and spiral structure induces a nonlinear response leading to a strong redistribution of angular momentum in the disk. We find that, depending on the amplitudes of the perturbers, the changes in angular momentum, dL, could occur up to an order of magnitude faster than in the case of recurrent spirals. The signature of this mechanism is a bimodality in dL with maxima near the bar's corotation and its outer Lindblad resonance; this is independent of the properties of the spiral structure. For parameters consistent with the Milky Way the disk mixes in about 3 Gyr and the stellar velocity dispersion increases with time in a manner roughly consistent with observations. This new mechanism could account for both the observed age-velocity relation and the absence of age-metallicity relation in the solar neighborhood. Spiral-bar interaction could also explain observations showing that strongly barred galaxies have weaker metallicity gradients than weakly barred or non-barred galaxies.Comment: 10 pages, 7 figures. Substantially expanded. Main results remain the same. Accepted for publication in Ap

Gravitational torques in spiral galaxies: gas accretion as a driving mechanism of galactic evolution

The distribution of gravitational torques and bar strengths in the local Universe is derived from a detailed study of 163 galaxies observed in the near-infrared. The results are compared with numerical models for spiral galaxy evolution. It is found that the observed distribution of torques can be accounted for only with external accretion of gas onto spiral disks. Accretion is responsible for bar renewal - after the dissolution of primordial bars - as well as the maintenance of spiral structures. Models of isolated, non-accreting galaxies are ruled out. Moderate accretion rates do not explain the observational results: it is shown that galactic disks should double their mass in less than the Hubble time. The best fit is obtained if spiral galaxies are open systems, still forming today by continuous gas accretion, doubling their mass every 10 billion years.Comment: 4 pages, 2 figures, Astronomy and Astrophysics Letters (accepted