WALLABY Pilot Survey: HI gas kinematics of galaxy pairs in cluster environment

We examine the H I gas kinematics of galaxy pairs in two clusters and a group using Australian Square Kilometre Array Pathfinder (ASKAP) WALLABY pilot survey observations. We compare the H I properties of galaxy pair candidates in the Hydra I and Norma clusters, and the NGC 4636 group, with those of non-paired control galaxies selected in the same fields. We perform H I profile decomposition of the sample galaxies using a tool, BAYGAUD which allows us to de-blend a line-of-sight velocity profile with an optimal number of Gaussian components. We construct H I super-profiles of the sample galaxies via stacking of their line profiles after aligning the central velocities. We fit a double Gaussian model to the super-profiles and classify them as kinematically narrow and broad components with respect to their velocity dispersions. Additionally, we investigate the gravitational instability of H I gas disks of the sample galaxies using Toomre Q parameters and H I morphological disturbances. We investigate the effect of the cluster environment on the H I properties of galaxy pairs by dividing the cluster environment into three subcluster regions (i.e., outskirts, infalling and central regions). We find that the denser cluster environment (i.e., infalling and central regions) is likely to impact the H I gas properties of galaxies in a way of decreasing the amplitude of the kinematically narrow H I gas (⁠MnarrowHI role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3eMHInarrowMnarrowHI/MtotalHI role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3eMHItotalMtotalHI⁠), and increasing the Toomre Q values of the infalling and central galaxies. This tendency is likely to be more enhanced for galaxy pairs in the cluster environment

The KSBA compactification for the moduli space of degree two K3 pairs

Inspired by the ideas of the minimal model program, Shepherd-Barron, Koll\'ar, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest examples that fits into this framework: the case of pairs (X,H) consisting of a degree two K3 surface X and an ample divisor H. Specifically, we construct and describe explicitly a geometric compactification $\bar{P_2}$ for the moduli of degree two K3 pairs. This compactification has a natural forgetful map to the Baily-Borel compactification of the moduli space $F_2$ of degree two K3 surfaces. Using this map and the modular meaning of $\bar{P_2}$, we obtain a better understanding of the geometry of the standard compactifications of $F_2$.Comment: 45 pages, 4 figures, 2 table

Tangent lines, inflections, and vertices of closed curves

We show that every smooth closed curve C immersed in Euclidean 3-space satisfies the sharp inequality 2(P+I)+V >5 which relates the numbers P of pairs of parallel tangent lines, I of inflections (or points of vanishing curvature), and V of vertices (or points of vanishing torsion) of C. We also show that 2(P'+I)+V >3, where P' is the number of pairs of concordant parallel tangent lines. The proofs, which employ curve shortening flow with surgery, are based on corresponding inequalities for the numbers of double points, singularities, and inflections of closed curves in the real projective plane and the sphere which intersect every closed geodesic. These findings extend some classical results in curve theory including works of Moebius, Fenchel, and Segre, which is also known as Arnold's "tennis ball theorem".Comment: Minor revisions; To appear in Duke Math.

Double crystallographic groups and their representations on the Bilbao Crystallographic Server

A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin-dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single- and double-valued irreducible representations of the double space groups. The new section includes databases of symmetry operations (DGENPOS) and of irreducible representations of the double (point and space) groups (REPRESENTATIONS DPG and REPRESENTATIONS DSG). The tool DCOMPATIBILITY RELATIONS provides compatibility relations between the irreducible representations of double space groups at different k-vectors of the Brillouin zone when there is a group-subgroup relation between the corresponding little groups. The program DSITESYM implements the so-called site-symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the program BANDREP calculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results of BANDREP have been extensively applied in the description and the search of topological insulators.Comment: 32 pages, 20 figures. Two extra figures and minor typo mistakes fixed. Published versio

The bottleneck degree of algebraic varieties

A bottleneck of a smooth algebraic variety $X \subset \mathbb{C}^n$ is a pair of distinct points $(x,y) \in X$ such that the Euclidean normal spaces at $x$ and $y$ contain the line spanned by $x$ and $y$. The narrowness of bottlenecks is a fundamental complexity measure in the algebraic geometry of data. In this paper we study the number of bottlenecks of affine and projective varieties, which we call the bottleneck degree. The bottleneck degree is a measure of the complexity of computing all bottlenecks of an algebraic variety, using for example numerical homotopy methods. We show that the bottleneck degree is a function of classical invariants such as Chern classes and polar classes. We give the formula explicitly in low dimension and provide an algorithm to compute it in the general case.Comment: Major revision. New introduction. Added some new illustrative lemmas and figures. Added pseudocode for the algorithm to compute bottleneck degree. Fixed some typo

A Unified Description of Cuprate and Iron Arsenide Superconductors

We propose a unified description of cuprate and iron-based superconductivity. Consistency with magnetic structure inferred from neutron scattering implies significant constraints on the symmetry of the pairing gap for the iron-based superconductors. We find that this unification requires the orbital pairing formfactors for the iron arsenides to differ fundamentally from those for cuprates at the microscopic level.Comment: 12 pages, 10 figures, 2 table

Property (RD) for Hecke pairs

As the first step towards developing noncommutative geometry over Hecke C*-algebras, we study property (RD) (Rapid Decay) for Hecke pairs. When the subgroup H in a Hecke pair (G,H) is finite, we show that the Hecke pair (G,H) has (RD) if and only if G has (RD). This provides us with a family of examples of Hecke pairs with property (RD). We also adapt Paul Jolissant's works in 1989 to the setting of Hecke C*-algebras and show that when a Hecke pair (G,H) has property (RD), the algebra of rapidly decreasing functions on the set of double cosets is closed under holomorphic functional calculus of the associated (reduced) Hecke C*-algebra. Hence they have the same K_0-groups.Comment: A short note added explaining other methods to prove that the subalgebra of rapidly decreasing functions is smooth. This is the final version as published. The published version is available at: springer.co