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Michael A. Singer

Publications and source records attributed to Michael A. Singer.

13 recordsLinked to original sources
arXiv2018

The first super-Earth Detection from the High Cadence and High Radial Velocity Precision Dharma Planet Survey

The Dharma Planet Survey (DPS) aims to monitor about 150 nearby very bright FGKM dwarfs (within 50 pc) during 2016$-$2020 for low-mass planet detection and characterization using the TOU very high resolution optical spectrograph (R$\approx$100,000, 380-900nm). TOU was initially mounted to the 2-m Automatic Spectroscopic Telescope at Fairborn Observatory in 2013-2015 to conduct a pilot survey, then moved to the dedicated 50-inch automatic telescope on Mt. Lemmon in 2016 to launch the survey. Here we report the first planet detection from DPS, a super-Earth candidate orbiting a bright K dwarf star, HD 26965. It is the second brightest star ($V=4.4$ mag) on the sky with a super-Earth candidate. The planet candidate has a mass of 8.47$\pm0.47M_{\rm Earth}$, period of $42.38\pm0.01$ d, and eccentricity of $0.04^{+0.05}_{-0.03}$. This RV signal was independently detected by Diaz et al. (2018), but they could not confirm if the signal is from a planet or from stellar activity. The orbital period of the planet is close to the rotation period of the star (39$-$44.5 d) measured from stellar activity indicators. Our high precision photometric campaign and line bisector analysis of this star do not find any significant variations at the orbital period. Stellar RV jitters modeled from star spots and convection inhibition are also not strong enough to explain the RV signal detected. After further comparing RV data from the star's active magnetic phase and quiet magnetic phase, we conclude that the RV signal is due to planetary-reflex motion and not stellar activity.

astro-ph.EP↗
arXiv2007

Constant scalar curvature Kaehler surfaces and parabolic polystability

A complex ruled surface admits an iterated blow-up encoded by a parabolic structure with rational weights. Under a condition of parabolic stability, one can construct a Kaehler metric of constant scalar curvature on the blow-up according to math.DG/0412405. We present a generalization of this construction to the case of parabolically polystable ruled surfaces. Thus we can produce numerous examples of Kaehler surfaces of constant scalar curvature with circle or toric symmetry.

math.DG↗
arXiv2005

Continued fractions and Einstein manifolds of infinite topological type

We present a construction of complete self-dual Einstein metrics of negative scalar curvature on an uncountable family of manifolds of infinite topological type, which are enumerated by continued fraction expansions of irrational numbers. These manifolds may be regarded as limits of the resolutions of cyclic quotient singularities (governed by continued fraction expansions of rational numbers) on which we constructed complete self-dual Einstein metrics in previous work.

math.DG↗
arXiv2005

Toric selfdual Einstein metrics on compact orbifolds

We prove that any compact selfdual Einstein 4-orbifold of positive scalar curvature whose isometry group contains a 2-torus is, up to an orbifold covering, a quaternion Kaehler quotient of (k-1)-dimensional quaternionic projective space by a (k-2)-torus for some $k\geq 2$. We also obtain a topological classification in terms of the intersection form of the 4-orbifold.

math.DG↗
arXiv2004

Non-minimal scalar-flat Kaehler surfaces and parabolic stability

A new construction is presented of scalar-flat Kaehler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable holomorphic bundles. This rather general construction is shown also to give new examples of low genus: in particular, it is shown that CP^2 blown up at 10 suitably chosen points, admits a scalar-flat Kaehler metric; this answers a question raised by Claude LeBrun in 1986 in connection with the classification of compact self-dual 4-manifolds.

math.DG↗
arXiv2003

Gerbes, Clifford modules and the index theorem

The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators can be given natural interpretations using this language and that the resulting formula is still an identity.

math.DG↗
arXiv2003

A note on monopole moduli spaces

We discuss the structure of the framed moduli space of Bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact Lie groups. We show that each stratum is a union of submanifolds for which we conjecture that the natural $L^2$ metric is hyperKahler. The dimensions of the strata and of these submanifolds are calculated, and it is found that for the latter, the dimension is always a multiple of four.

math-ph↗
arXiv2002

Einstein metrics and complex singularities

This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkaehler gravitational instantons, but we focus on a different class of singularities. We show that any resolution X of an isolated cyclic quotient singularity admits a complete scalar-flat Kaehler metric (which is hyperkaehler if and only if c_1(X)=0), and that if c_1(X)<0 then X also admits a complete (non-Kaehler) self-dual Einstein metric of negative scalar curvature. In particular, complete self-dual Einstein metrics are constructed on simply-connected non-compact 4-manifolds with arbitrary second Betti number. Deformations of these self-dual Einstein metrics are also constructed: they come in families parameterized, roughly speaking, by free functions of one real variable. All the metrics constructed here are toric (that is, the isometry group contains a 2-torus) and are essentially explicit. The key to the construction is the remarkable fact that toric self-dual Einstein metrics are given quite generally in terms of linear partial differential equations on the hyperbolic plane.

math.DG↗
arXiv2000

An L^2-Index Theorem for Dirac Operators on S^1 * R^3

An expression is found for the $L^2$-index of a Dirac operator coupled to a connection on a $U_n$ vector bundle over $S^1\times{\mathbb R}^3$. Boundary conditions for the connection are given which ensure the coupled Dirac operator is Fredholm. Callias' index theorem is used to calculate the index when the connection is independent of the coordinate on $S^1$. An excision theorem due to Gromov, Lawson, and Anghel reduces the index theorem to this special case. The index formula can be expressed using the adiabatic limit of the $η$-invariant of a Dirac operator canonically associated to the boundary. An application of the theorem is to count the zero modes of the Dirac operator in the background of a caloron (periodic instanton).

math.DG↗
arXiv1999

On the complete integrability of the discrete Nahm equations

The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-bundle over the spectral curve, such that the discrete-time DN evolution corresponds to walking in the Jacobian of the spectral curve in a straight line through the line-bundle with steps of a fixed size. Some of the implications for hyperbolic monopoles are also discussed.

math-ph↗
arXiv1998

A momentum construction for circle-invariant Kahler metrics

An ansatz of Calabi allows construction of Kahler metrics in an Hermitian disk bundle over a Kahler manifold. We attempt to give a definitive treatment of this ansatz, with the following results: We give curvature conditions on the disk bundle that guarantee existence of families of complete Kahler metrics of constant scalar curvature, including some Einstein-Kahler metrics. These curvature conditions are somewhat weaker than those used by prior authors, and are shown to give rise to large families of metrics that seem to be new. Further, these curvature hypotheses are necessary, in the sense that if the ansatz gives two distinct metrics of constant scalar curvature in a disk bundle, then the curvature hypotheses are satisfied.

math.DG↗