On the second homology group of the Torelli subgroup of Aut(F_n)

Let IA_n be the Torelli subgroup of Aut(F_n). We give an explicit finite set of generators for H_2(IA_n) as a GL_n(Z)-module. Corollaries include a version of surjective representation stability for H_2(IA_n), the vanishing of the GL_n(Z)-coinvariants of H_2(IA_n), and the vanishing of the second rational homology group of the level l congruence subgroup of Aut(F_n). Our generating set is derived from a new group presentation for IA_n which is infinite but which has a simple recursive form.Comment: 39 pages; minor revision; to appear in Geom. Topo

A Birman exact sequence for the Torelli subgroup of Aut(F_n)

We develop an analogue of the Birman exact sequence for the Torelli subgroup of Aut(F_n). This builds on earlier work of the authors who studied an analogue of the Birman exact sequence for the entire group Aut(F_n). These results play an important role in the authors' recent work on the second homology group of the Torelli group.Comment: 31 pages, minor revision; to appear in Int. J. Algebr. Compu

The Smith Cloud: HI associated with the Sgr dwarf?

The Smith high velocity cloud (V(LSR) = 98 kms) has been observed at two locations in the emission lines [OIII]5007, [NII]6548 and H-alpha. Both the [NII] and H-alpha profiles show bright cores due to the Reynolds layer, and red wings with emission extending to V(LSR) = 130 kms. This is the first simultaneous detection of two emission lines towards a high velocity cloud, allowing us to form the ratio of these line profiles as a function of LSR velocity. At both cloud positions, we see a clear distinction between emission at the cloud velocity, and the Reynolds layer emission (V(LSR) = 0). The [NII]/H-alpha ratio (=0.25) for the Reynolds layer is typical of the warm ionised medium. At the cloud velocity, this ratio is enhanced by a factor of 3-4 compared to emission at rest with respect to the LSR. A moderately deep upper limit at [OIII] (0.12R at 3-sigma) was derived from our data. If the emission arises from dilute photoionisation from hot young stars, the highly enhanced [NII]/H-alpha ratio, the [OIII] non-detection and weak H-alpha emission (0.24-0.30R) suggest that the Smith Cloud is 26+/-4 kpc from the Sun, at a Galactocentric radius of 20+/-4 kpc. This value assumes that the emission arises from an optically thick slab, with a covering fraction of unity as seen by the ionizing photons, whose orientation is either (a) parallel to the Galactic disk, or (b) such as to maximize the received flux from the disk. The estimated mass and size of the cloud are 4x10^6 Msun and 6 kpc. We discuss a possible association with the much larger Sgr dwarf, at a galactocentric radius of 16+/-2 kpc, which lies within 35 degrees (~12 kpc) of the Smith Cloud.Comment: 18 pages, 14 figures, mn.sty. Our first application of a new method for establishing distances to high velocity clouds. This version matches paper to appear in MNRAS, 299, 611-624 (Sept. 11 issue

The scattered debris of the Magellanic Stream

Searching the HI Parkes All-Sky Survey (HIPASS) and its northern extension, we detected a population of very compact high-velocity clouds (HVCs) with similar velocities in the Galactic standard-of-rest frame which appear to be arranged in several filaments aligned with the nearby Magellanic Stream. A comparison with published OVI/CaII absorption and HI emission line measurements suggests that the HVCs are condensations within an extended and mainly ionised component of the Magellanic Stream. They coincide in position with a faint gas stream predicted in numerical simulations of the Magellanic Clouds by Gardiner & Noguchi (1996). Consequently, the Magellanic Stream could be much more extended than generally believed.Comment: 5 pages, 4 figures, accepted for publication in MNRA

Stability of Localized Wave Fronts in Bistable Systems

Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation, and spatially inhomogeneous activating agents. We determine the conditions under which wave-front localization is possible and analyze the stability thereof with respect to extrinsic perturbations and internal noise. It is found that stability is enhanced upon regulating a positional signal and, surprisingly, also for a low degree of binding cooperativity. We further show a contrasting impact of self-activation to the stability of these two sources of destabilization. DOI: 10.1103/PhysRevLett.110.03810