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David Fisher

Publications and source records attributed to David Fisher.

At least 37 records · Page 2Linked to original sources
arXiv2018

Rigidity of warped cones and coarse geometry of expanders

We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian factors, then two such warped cones are quasi-isometric if and only if the actions are finite covers of conjugate actions. As a consequence, we produce continuous families of non-quasi-isometric expanders and superexpanders. The proof relies on the use of coarse topology for warped cones, such as a computation of their coarse fundamental groups.

math.MG↗
arXiv2017

Quasi-isometric embeddings of non-uniform lattices

Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $Γ<G$ and $Λ< G'$ be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of $Γ$ into $Λ$ is at bounded distance from a homomorphism. For example, any quasi-isometric embedding of $SL(n,\mathbb Z)$ into $SL(n, \mathbb Z[i])$ is at bounded distance from a homomorphism. We also include a discussion of some cases when this result is not true for what turn out to be purely algebraic reasons.

math.GR↗
arXiv2017

Quasi-Isometric Embeddings of Symmetric Spaces

We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric embeddings of higher rank symmetric spaces. In particular, we produce embeddings of $SL(n,\mathbb R)$ into $Sp(2(n-1),\mathbb R)$ when no isometric embeddings exist. A key ingredient in our proofs of rigidity results is a direct generalization of the Mostow-Morse Lemma in higher rank. Typically this lemma is replaced by the quasi-flat theorem which says that maximal quasi-flat is within bounded distance of a finite union of flats. We improve this by showing that the quasi-flat is in fact flat off of a subset of codimension $2$.

math.DG↗
arXiv2016

Large Molecular Gas Reservoirs in Ancestors of Milky Way-Mass Galaxies 9 Billion Years Ago

The gas accretion and star-formation histories of galaxies like the Milky Way remain an outstanding problem in astrophysics. Observations show that 8 billion years ago, the progenitors to Milky Way-mass galaxies were forming stars 30 times faster than today and predicted to be rich in molecular gas, in contrast with low present-day gas fractions ($<$10%). Here we show detections of molecular gas from the CO(J=3-2) emission (rest-frame 345.8 GHz) in galaxies at redshifts z=1.2-1.3, selected to have the stellar mass and star-formation rate of the progenitors of today's Milky Way-mass galaxies. The CO emission reveals large molecular gas masses, comparable to or exceeding the galaxy stellar masses, and implying most of the baryons are in cold gas, not stars. The galaxies' total luminosities from star formation and CO luminosities yield long gas-consumption timescales. Compared to local spiral galaxies, the star-formation efficiency, estimated from the ratio of total IR luminosity to CO emission,} has remained nearly constant since redshift z=1.2, despite the order of magnitude decrease in gas fraction, consistent with results for other galaxies at this epoch. Therefore the physical processes that determine the rate at which gas cools to form stars in distant galaxies appear to be similar to that in local galaxies.

astro-ph.GA↗
arXiv2016

ZFIRE: A KECK/MOSFIRE Spectroscopic Survey of Galaxies in Rich Environments at z~2

We present an overview and the first data release of ZFIRE, a spectroscopic redshift survey of star-forming galaxies that utilizes the MOSFIRE instrument on Keck-I to study galaxy properties in rich environments at $1.5<z<2.5$. ZFIRE measures accurate spectroscopic redshifts and basic galaxy properties derived from multiple emission lines. The galaxies are selected from a stellar mass limited sample based on deep near infra-red imaging ($\mathrm{K_{AB}<25}$) and precise photometric redshifts from the ZFOURGE and UKIDSS surveys as well as grism redshifts from 3DHST. Between 2013--2015 ZFIRE has observed the COSMOS and UDS legacy fields over 13 nights and has obtained 211 galaxy redshifts over $1.57<z<2.66$ from a combination of nebular emission lines (such as \Halpha, \NII, \Hbeta, \OII, \OIII, \SII) observed at 1--2\micron. Based on our medium-band NIR photometry, we are able to spectrophotometrically flux calibrate our spectra to \around10\% accuracy. ZFIRE reaches $5σ$ emission line flux limits of \around$\mathrm{3\times10^{-18}~erg/s/cm^2}$ with a resolving power of $R=3500$ and reaches masses down to \around10$^{9}$\msol. We confirm that the primary input survey, ZFOURGE, has produced photometric redshifts for star-forming galaxies (including highly attenuated ones) accurate to $Δz/(1+z\mathrm{_{spec})}=0.015$ with $0.7\%$ outliers. We measure a slight redshift bias of $<0.001$, and we note that the redshift bias tends to be larger at higher masses. We also examine the role of redshift on the derivation of rest-frame colours and stellar population parameters from SED fitting techniques. The ZFIRE survey extends spectroscopically-confirmed $z\sim 2$ samples across a richer range of environments, here we make available the first public release of the data for use by the community.\footnote{\url{http://zfire.swinburne.edu.au}}

astro-ph.GA↗
arXiv2016

Character varieties and actions on products of trees

It is well known that surface groups admit free and proper actions on finite products of infinite valence trees. In this note, we address the question of whether there can be a free and proper action on a finite product of bounded valence trees. We provide some obstructions and an arithmetic criterion for existence. The bulk of the paper is devoted to an approach to verifying the arithmetic criterion by studying the character variety of certain surface groups over fields of positive characteristic. The methods may be useful for attempting to determine when groups admit good linear representations in other contexts.

math.GR↗
arXiv2015

Electron paramagnetic resonance of the $\mathrm{N_{2}V^{-}}$ defect in $\mathrm{^{15}N}$-doped synthetic diamond

Nitrogen is the dominant impurity in the majority of natural and synthetic diamonds, and the family of nitrogen vacancy-type ($\mathrm{N_{n}V}$) defects are crucial in our understanding of defect dynamics in these diamonds. A significant gap is the lack of positive identification of $\mathrm{N_{2}V}^{-}$, the dominant charge state of $\mathrm{N_{2}V}$, in diamond that contains a significant concentration of electron donors. In this paper we employ isotopically-enriched diamond to identify the EPR spectrum associated with $^{15}\mathrm{N_{2}V}^{-}$ and use the derived spin Hamiltonian parameters to identify $^{14}\mathrm{N_{2}V}^{-}$ in a natural isotopic abundance sample. The electronic wavefunction of the $\mathrm{N_{2}V^{-}}$ ground state and previous lack of identification is discussed. The $\mathrm{N_{2}V}^{-}$ EPR spectrum intensity is shown to correlate with H2 optical absorption over an order of magnitude in concentration.

cond-mat.mtrl-sci↗
arXiv2013

The VIRUS-P Exploration of Nearby Galaxies (VENGA): Survey Design, Data Processing, and Spectral Analysis Methods

We present the survey design, data reduction, and spectral fitting pipeline for the VIRUS-P Exploration of Nearby Galaxies (VENGA). VENGA is an integral field spectroscopic survey, which maps the disks of 30 nearby spiral galaxies. Targets span a wide range in Hubble type, star formation activity, morphology, and inclination. The VENGA data-cubes have 5.6'' FWHM spatial resolution, ~5A FWHM spectral resolution, sample the 3600A-6800A range, and cover large areas typically sampling galaxies out to ~0.7 R_25. These data-cubes can be used to produce 2D maps of the star formation rate, dust extinction, electron density, stellar population parameters, the kinematics and chemical abundances of both stars and ionized gas, and other physical quantities derived from the fitting of the stellar spectrum and the measurement of nebular emission lines. To exemplify our methods and the quality of the data, we present the VENGA data-cube on the face-on Sc galaxy NGC 628 (a.k.a. M 74). The VENGA observations of NGC 628 are described, as well as the construction of the data-cube, our spectral fitting method, and the fitting of the stellar and ionized gas velocity fields. We also propose a new method to measure the inclination of nearly face-on systems based on the matching of the stellar and gas rotation curves using asymmetric drift corrections. VENGA will measure relevant physical parameters across different environments within these galaxies, allowing a series of studies on star formation, structure assembly, stellar populations, chemical evolution, galactic feedback, nuclear activity, and the properties of the interstellar medium in massive disk galaxies.

astro-ph.CO↗
arXiv2012

The VIRUS-P Exploration of Nearby Galaxies (VENGA): The Xco Gradient in NGC 628

We measure the radial profile of the 12CO(1-0) to H_2 conversion factor (Xco) in NGC 628. The Hαemission from the VENGA integral field spectroscopy is used to map the star formation rate surface density (Σ_{SFR}). We estimate the molecular gas surface density (Σ_{H2}) from Σ_{SFR} by inverting the molecular star formation law (SFL), and compare it to the CO intensity to measure Xco. We study the impact of systematic uncertainties by changing the slope of the SFL, using different SFR tracers (Hαvs. far-UV plus 24μm), and CO maps from different telescopes (single-dish and interferometers). The observed Xco profile is robust against these systematics, drops by a factor of 2 from R~7 kpc to the center of the galaxy, and is well fit by a gradient Δlog(Xco)=0.06\pm0.02 dex kpc^-1. We study how changes in Xco follow changes in metallicity, gas density, and ionization parameter. Theoretical models show that the gradient in Xco can be explained by a combination of decreasing metallicity, and decreasing Σ_{H2} with radius. Photoelectric heating from the local UV radiation field appears to contribute to the decrease of Xco in higher density regions. Our results show that galactic environment plays an important role at setting the physical conditions in star forming regions, in particular the chemistry of carbon in molecular complexes, and the radiative transfer of CO emission. We caution against adopting a single Xco value when large changes in gas surface density or metallicity are present.

astro-ph.GA↗
arXiv2012

Coarse differentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphs

In this paper, we prove that certain spaces are not quasi-isometric to Cayley graphs of finitely generated groups. In particular, we answer a question of Woess and prove a conjecture of Diestel and Leader by showing that certain homogeneous graphs are not quasi-isometric to a Cayley graph of a finitely generated group. This paper is the first in a sequence of papers proving results announced in [EFW0]. In particular, this paper contains many steps in the proofs of quasi-isometric rigidity of lattices in Sol and of the quasi-isometry classification of lamplighter groups. The proofs of those results are completed in [EFW1]. The method used here is based on the idea of "coarse differentiation" introduced in [EFW0].

math.GR↗
arXiv2012

Cross-wired lamplighter groups

We give a necessary and sufficient condition for a locally compact group to be isomorphic to a closed cocompact subgroup in the isometry group of a Diestel-Leader graph. As a consequence of this condition, we see that every cocompact lattice in the isometry group of a Diestel-Leader graph admits a transitive, proper action on some other Diestel-Leader graph. We also give some examples of lattices that are not virtually lamplighters. This implies the class of discrete groups commensurable to lamplighter groups is not closed under quasi-isometries and, combined with work of Eskin, Fisher and Whyte, gives a characterization of their quasi-isometry class.

math.GR↗
arXiv2011

Orbit-Based Dynamical Models of the Sombrero Galaxy (NGC 4594)

We present axisymmetric, orbit-based models to study the central black hole, stellar mass-to-light ratio, and dark matter halo of NGC 4594 (M104, the Sombrero Galaxy). For stellar kinematics, we use published high-resolution kinematics of the central region taken with the Hubble Space Telescope, newly obtained Gemini long-slit spectra of the major axis, and integral field kinematics from the SAURON instrument. At large radii, we use globular cluster kinematics to trace the mass profile and apply extra leverage to recovering the dark matter halo parameters. We find a black hole of mass M_{\bullet}=(6.6 +/- 0.4) x 10^8 M_{\odot}, and determine the stellar M/L_I=3.4 +/- 0.05 (uncertainties are the 68% confidence band marginalized over the other parameters). Our best fit dark matter halo is a cored logarithmic model with asymptotic circular speed V_c=376 +/- 12 km/s and core radius r_c= 4.7 +/- 0.6 kpc. The fraction of dark to total mass contained within the half-light radius is 0.52. Taking the bulge and disk components into account in our calculation of σ_e puts NGC 4594 squarely on the M-σrelation. We also determine that NGC 4594 lies directly on the M-L relation.

astro-ph.CO↗
arXiv2010

The VIRUS-P Exploration of Nearby Galaxies (VENGA): Survey Design and First Results

VENGA is a large-scale extragalactic IFU survey, which maps the bulges, bars and large parts of the outer disks of 32 nearby normal spiral galaxies. The targets are chosen to span a wide range in Hubble types, star formation activities, morphologies, and inclinations, at the same time of having vast available multi-wavelength coverage from the far-UV to the mid-IR, and available CO and 21cm mapping. The VENGA dataset will provide 2D maps of the SFR, stellar and gas kinematics, chemical abundances, ISM density and ionization states, dust extinction and stellar populations for these 32 galaxies. The uniqueness of the VIRUS-P large field of view permits these large-scale mappings to be performed. VENGA will allow us to correlate all these important quantities throughout the different environments present in galactic disks, allowing the conduction of a large number of studies in star formation, structure assembly, galactic feedback and ISM in galaxies.

astro-ph.CO↗