A Radial Velocity Study of Composite-Spectra Hot Subdwarf Stars with the Hobby-Eberly Telescope

Many hot subdwarf stars show composite spectral energy distributions indicative of cool main sequence companions. Binary population synthesis (BPS) models demonstrate such systems can be formed via Roche lobe overflow or common envelope evolution but disagree on whether the resulting orbital periods will be long (years) or short (days). Few studies have been carried out to assess the orbital parameters of these spectroscopic composite binaries; current observations suggest the periods are long. To help address this problem, we selected fifteen moderately-bright (V~13) hot subdwarfs with F-K dwarf companions and monitored their radial velocities (RVs) from January 2005 to July 2008 using the bench-mounted Medium Resolution Spectrograph on the Hobby-Eberly Telescope (HET). Here we describe the details of our observing, reduction, and analysis techniques and present preliminary results for all targets. By combining the HET data with recent observations from the Mercator telescope, we are able to calculate precise orbital solutions for three systems using more than 6 years of observations. We also present an up-to-date period histogram for all known hot subdwarf binaries, which suggests those with F-K main sequence companions tend to have orbital periods on the order of several years. Such long periods challenge the predictions of conventional BPS models, although a larger sample is needed for a thorough assessment of the models' predictive success. Lastly, one of our targets has an eccentric orbit, implying some composite-spectrum systems might have formerly been hierarchical triple systems, in which the inner binary merged to create the hot subdwarf.Comment: Published in The Astrophysical Journal, Volume 758, Issue 1, article id. 58 (2012). References updated and Equation (5) corrected. 12 pages, 5 figures, 5 table

Tulczyjew Triples in Higher Derivative Field Theory

The geometrical structure known as Tulczyjew triple has been used with success in analytical mechanics and first order field theory to describe a wide range of physical systems including Lagrangian/Hamiltonian systems with constraints and/or sources, or with singular Lagrangian. Starting from the first principles of the variational calculus we derive Tulczyjew triples for classical field theories of arbitrary high order, i.e. depending on arbitrary high derivatives of the fields. A first triple appears as the result of considering higher order theories as first order ones with configurations being constrained to be holonomic jets. A second triple is obtained after a reduction procedure aimed at getting rid of nonphysical degrees of freedom. This picture we present is fully covariant and complete: it contains both Lagrangian and Hamiltonian formalisms, in particular the Euler-Lagrange equations. Notice that, the required Geometry of jet bundles is affine (as opposed to the linear Geometry of the tangent bundle). Accordingly, the notions of affine duality and affine phase space play a distinguished role in our picture. In particular the Tulczyjew triples in this paper consist of morphisms of double affine-vector bundles which, moreover, preserve suitable presymplectic structures.Comment: 29 pages, v2: minor revisions. Accepted for publication in J. Geom. Mec

3-nets realizing a diassociative loop in a projective plane

A \textit{$3$-net} of order $n$ is a finite incidence structure consisting of points and three pairwise disjoint classes of lines, each of size $n$, such that every point incident with two lines from distinct classes is incident with exactly one line from each of the three classes. The current interest around $3$-nets (embedded) in a projective plane $PG(2,K)$, defined over a field $K$ of characteristic $p$, arose from algebraic geometry. It is not difficult to find $3$-nets in $PG(2,K)$ as far as $0<p\le n$. However, only a few infinite families of $3$-nets in $PG(2,K)$ are known to exist whenever $p=0$, or $p>n$. Under this condition, the known families are characterized as the only $3$-nets in $PG(2,K)$ which can be coordinatized by a group. In this paper we deal with $3$-nets in $PG(2,K)$ which can be coordinatized by a diassociative loop $G$ but not by a group. We prove two structural theorems on $G$. As a corollary, if $G$ is commutative then every non-trivial element of $G$ has the same order, and $G$ has exponent $2$ or $3$. We also discuss the existence problem for such $3$-nets

The order of the automorphism group of a binary qq-analog of the Fano plane is at most two

It is shown that the automorphism group of a binary $q$-analog of the Fano plane is either trivial or of order $2$.Comment: 10 page

Spiral spin-liquid and the emergence of a vortex-like state in MnSc2_2S4_4

Spirals and helices are common motifs of long-range order in magnetic solids, and they may also be organized into more complex emergent structures such as magnetic skyrmions and vortices. A new type of spiral state, the spiral spin-liquid, in which spins fluctuate collectively as spirals, has recently been predicted to exist. Here, using neutron scattering techniques, we experimentally prove the existence of a spiral spin-liquid in MnSc$_2$S$_4$ by directly observing the 'spiral surface' - a continuous surface of spiral propagation vectors in reciprocal space. We elucidate the multi-step ordering behavior of the spiral spin-liquid, and discover a vortex-like triple-q phase on application of a magnetic field. Our results prove the effectiveness of the $J_1$-$J_2$ Hamiltonian on the diamond lattice as a model for the spiral spin-liquid state in MnSc$_2$S$_4$, and also demonstrate a new way to realize a magnetic vortex lattice.Comment: 10 pages, 11 figure

Quantum geometry of moduli spaces of local systems and representation theory

Let G be a split semi-simple adjoint group, and S an oriented surface with punctures and special boundary points. We introduce a moduli space P(G,S) parametrizing G-local system on S with some boundary data, and prove that it carries a cluster Poisson structure, equivariant under the action of the cluster modular group M(G,S), containing the mapping class group of S, the group of outer automorphisms of G, and the product of Weyl / braid groups over punctures / boundary components. We prove that the dual moduli space A(G,S) carries a M(G,S)-equivariant cluster structure, and the pair (A(G,S), P(G,S)) is a cluster ensemble. These results generalize the works of V. Fock & the first author, and of I. Le. We quantize cluster Poisson varieties X for any Planck constant h s.t. h>0 or |h|=1. First, we define a *-algebra structure on the Langlands modular double A(h; X) of the algebra of functions on X. We construct a principal series of representations of the *-algebra A(h; X), equivariant under a unitary projective representation of the cluster modular group M(X). This extends works of V. Fock and the first author when h>0. Combining this, we get a M(G,S)-equivariant quantization of the moduli space P(G,S), given by the *-algebra A(h; P(G,S)) and its principal series representations. We construct realizations of the principal series *-representations. In particular, when S is punctured disc with two special points, we get a principal series *-representations of the Langlands modular double of the quantum group Uq(g). We conjecture that there is a nondegenerate pairing between the local system of coinvariants of oscillatory representations of the W-algebra and the one provided by the projective representation of the mapping class group of S.Comment: 199 pages. Minor correction