arXiv subjects

III

Publications and source records attributed to III.

At least 37 records · Page 2Linked to original sources

arXiv2004

The topology, geometry and conformal structure of properly embedded minimal surfaces

This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff space, naturally ordered by the relative heights of the ends in space. One of our main results is that the middle ends of the surface have quadratic area growth, and are thus not limit ends. This implies, for instance, that the surface can have at most two limit ends (at the top and bottom of the ordering), which is a strong topological restriction. There are also restrictions on the asymptotic geometry and conformal structure of such a surface: for example, we prove that if the surface has exactly two limit ends (as do the classical Riemann Staircase examples), then it is recurrent (that is, almost all Brownian paths are dense in the surface, and in particular any positive harmonic function on the surface is constant). These results have played an important role in the proof of several recent advances in the theory, including the uniqueness of the helicoid, the invariance of flux for a coordinate function on a properly immersed minimal surface, and the topological classification of properly embedded minimal surfaces.

math.DG↗

arXiv2004

Field Strengths of Linearized 5D, N = 1 Superfield Supergravity On a 3-Brane

Recently a description of linearized 5D supergravity in 4D, N =1 superspace was presented. By analyzing the on-shell component Lagrangian, this description was proven to be Lorentz invariant in five dimensions. This paper describes a geometric formulation of the 5D supergravity in 4D, N =1 superspace. Using this new formalism, the on-shell structure of the previous description is verified from purely superspace methods. This geometric description provides a connection to dimensionally reduced manifestly supersymmetric 5D supergravity.

hep-th↗

arXiv2002

High-Resolution Optical Rotation Curves of Low-Luminosity Spiral Galaxies

We present optical longslit spectroscopic observations of 21 low-luminosity, extreme late-type spiral galaxies. Our sample is comprised of Sc-Sm Local Supercluster spirals with moderate-to-low optical surface brightnesses and with luminosities at the low end for spiral disk galaxies (M_V>-18.8). For each galaxy we have measured high spatial resolution position-velocity (P-V) curves using the H alpha emission line, and for 15 of the galaxies we also derive major axis rotation curves. In ~50% of our sample, the P-V curves show significant asymmetries in shape, extent, and/or amplitude on the approaching and receding sides of the disk. A number of the P-V curves are still rising to the last measured point, or reach a clear turnover on only one side. In most instances we find good agreement between the kinematic centers of extreme late-type spirals as defined by the global HI emission profile and by their optical continuum, although in a few cases we see evidence of possible real offsets. In spite of their shallow central gravitational potentials, at least 6 of the galaxies in our sample possess semi-stellar nuclei that appear to be compact nuclear star clusters; in 5 of these cases we see kinematic signatures in the P-V curves at the location of the nucleus. Finally, we find that like giant spirals, our sample galaxies have higher specific angular momenta than predicted by current cold dark matter models.

astro-ph↗

arXiv2000

The Fossil Starburst in M82

(Abridged) We present high-resolution HST imaging in the optical (WFPC2) and near-infrared (NICMOS) of a disk region 1 kpc NE of the starburst core in the nearby galaxy M82. This region, M82 ``B,'' has been suspected to be a fossil starburst site in which an intense episode of star formation occurred over 100 Myr ago, and our new observations confirm this intepretation. We find a large, evolved system of super star clusters in M82 B; we identify a total of 113 super star cluster candidates. The clusters range in absolute magnitude from M_V^0 = -6 to -10, with a peak at -7.5. The derived age distribution suggests steady, continuing cluster formation at a modest rate at early times (> 2 Gyr ago), followed by a concentrated formation episode ~600 Myr ago and more recent suppression of cluster formation. The peak episode coincides with independent dynamical estimates for the last tidal encounter with M81. Our J and H band observations resolve the bright giant population in M82's disk for the first time. Star formation evidently continued in M82 B until about 20-30 Myr ago, but none is found associated with the youngest generations in the nuclear starburst (age <= 15 Myr). After correcting the cluster luminosity function to a fiducial age of 50 Myr, we find that the bright end is characterized by a power-law slope with alpha = -1.2 +/- 0.3. Cluster sizes (2.34 <= Reff <= 10 pc, or 2.4 <= Rcore <= 7.9 pc) and estimated masses (a median of 10^5 Msun) are consistent with values found for young super star cluster populations in M82's core and other galaxies and with the progenitors of globular clusters.

astro-ph↗

arXiv2000

Time-Dependence of the Mass Accretion Rate in Cluster Cooling Flows

We analyze two time-dependent cluster cooling flow models in spherical symmetry. The first assumes that the intracluster gas resides in a static external potential, and includes the effects of optically thin radiative cooling and mass deposition. This corresponds to previous steady-state cooling flow models calculated by White & Sarazin (1987). Detailed agreement is found between steady-state models and time-dependent models at fixed times in the simulations. The mass accretion rate is found either to increase or remain nearly constant once flows reach a steady state. The time rate of change of the accretion rate is strongly sensitive to the value of the mass deposition parameter q, but only mildly sensitive to the ratio beta of gravitational binding energy to gas temperature. We show that previous scaling arguments presented by Bertschinger (1988) and White (1988) are valid only for mature cooling flows with weak mass deposition (q ~< 1). The second set of models includes the effects of a secularly deepening cluster potential and secondary infall of gas from the Hubble flow. We find that such heating effects do not prevent the flows from reaching a steady state within an initial central cooling time.

astro-ph↗

arXiv2000

Topology from the Simulated Sloan Digital Sky Survey

We measure the topology (genus curve) of the galaxy distribution in a mock redshift catalog designed to resemble the upcoming Sloan Digital Sky Survey (SDSS). The catalog, drawn from a large N-body simulation of a Lambda-CDM cos- mological model, mimics the anticipated spectroscopic selection procedures of the SDSS in some detail. Sky maps, redshift slices, and 3-D contour maps of the mock survey reveal a rich and complex structure, including networks of voids and superclusters that resemble the patterns seen in the CfA redshift survey and the Las Campanas Redshift Survey (LCRS). The 3-D genus curve can be measured from the simulated catalog with superb precision; this curve has the general shape predicted for Gaussian, random phase initial conditions, but the error bars are small enough to demonstrate with high significance the subtle departures from this shape caused by non-linear gravitational evolution. These distortions have the form predicted by Matsubara's (1994) perturbative anal- ysis, but they are much smaller in amplitude. We also measure the 3-D genus curve of the radial peculiar velocity field measured by applying distance- indicator relations (with realistic errors) to the mock catalog. This genus curve is consistent with the Gaussian random phase prediction, though it is of relatively low precision because of the large smoothing length required to overcome noise in the measured velocity field. Finally, we measure the 2-D topology in redshift slices, similar to early slices from the SDSS and to slices already observed in the LCRS. The genus curves of these slices are consistent with the observed genus curves of the LCRS, providing further evidence in favor of the inflationary CDM model with Omega_M~0.4. The catalog is publicly available at http://www.astronomy.ohio-state.edu/~dhw/sdss.html.

astro-ph↗

arXiv1999

WFPC2 Observations of Compact Star Cluster Nuclei in Low Luminosity Spiral Galaxies

We have used the Wide Field Planetary Camera 2 aboard the Hubble Space Telescope to image the compact star cluster nuclei of the nearby, late-type, low-luminosity spiral galaxies NGC 4395, NGC 4242, and ESO 359-029. We also analyze archival WFPC2 observations of the compact star cluster nucleus of M33. A comparative analysis of the structural and photometric properties of these four nuclei is presented. All of the nuclei are very compact, with luminosity densities increasing at small radii to the resolution limit of our data. NGC 4395 contains a Seyfert 1 nucleus with a distinct bipolar structure and bright associated filaments which are likely due to [OIII] emission. The M33 nucleus has a complex structure, with elongated isophotes and possible signatures of weak activity, including a jet-like component. The other two nuclei are not known to be active, but share similar physical size scales and luminosities to the M33 and NGC 4395 nuclei. The circumnuclear environments of all four of our program galaxies are extremely diffuse, have only low-to-moderate star formation, and appear to be devoid of large quantities of dust. The central gravitational potentials of the galaxies are also quite shallow, making the origin of these types of `naked' nuclei problematic.

astro-ph↗

arXiv1998

Stellar Populations and Ages of M82 Super Star Clusters

We present high signal-to-noise optical spectra of two luminous super star clusters in the starburst galaxy M82. The data for cluster F and the nearby, highly reddened cluster L were obtained with the William Herschel Telescope (WHT) at a resolution of 1.6A. The blue spectrum (3250-5540A) of cluster F shows features typical of mid-B stars. The red spectra (5730-8790A) of clusters F and L show the Ca II triplet and numerous F and G-type absorption features. Strong Ca II and Na I interstellar absorption lines arising in M82 are also detected, and the 6283A diffuse interstellar band appears to be present. The quality of the WHT spectra allows us to considerably improve previous age estimates for cluster F. By comparing the blue spectrum with theoretical model cluster spectra using the PEGASE spectral synthesis code (Fioc & Rocca-Volmerange 1997), we derive an age of 60+/-20 Myr. The strength of the Ca II triplet is also in accord with this age. Cluster L appears to have a similar age, although this is much less certain. The measured radial velocities for the two clusters differ substantially, indicating that they are located in different regions of the M82 disk. Cluster F appears to be deep in M82, slightly beyond the main starburst region while the highly obscured cluster L lies near the outer edges of the disk. We derive an absolute V magnitude of -16.5 for F indicating that it is an extremely massive cluster. The presence of such a luminous super star cluster suggests that the M82 starburst experienced an episode of intense star formation approximately 60 Myr ago.

astro-ph↗

arXiv1998

Evolutionary Status of Dwarf ``Transition'' Galaxies

We present deep B, R and Halpha imaging of 3 dwarf galaxies: NGC3377A, NGC4286, and IC3475. Based on previous broadband imaging and HI studies, these mixed-morphology galaxies were proposed by Sandage & Hoffman (1991) to be, respectively, a gas-rich low surface brightness Im dwarf, a nucleated dwarf that has lost most of its gas and is in transition from Im to dS0,N, and the prototypical example of a gas-poor ``huge low surface brightness'' early-type galaxy. From the combination of our broadband and Halpha imaging with the published information on the neutral gas content of these three galaxies, we find that (1) NGC3377A is a dwarf spiral; (2) NGC3377A and NGC4286 have comparable amounts of ongoing star formation, as indicated by their Halpha emission, while IC3475 has no detected HII regions to a very low limit; (3) the global star formation rates are at least a factor of 20 below that of 30 Doradus for NGC3377A and NGC4286; (4) while the amount of star formation is comparable, the distribution of star forming regions is very different between NGC3377A and NGC4286; (5) given their current star formation rates and gas contents, both NGC3377A and NGC4286 can continue to form stars for more than a Hubble time; (6) both NGC3377A and NGC4286 have integrated total B-R colors that are redder than the integrated total B-R color for IC3475, and thus it is unlikely that either galaxy will ever evolve into an IC3475 counterpart; and (7) IC3475 is too blue to be a dE. We thus conclude that we have not identified potential precursors to galaxies such as IC3475, and unless signifcant changes occur in the star formation rates, neither NGC3377A nor NGC4286 will evolve into a dwarf elliptical or dwarf spheroidal within a Hubble time.

astro-ph↗

arXiv1998

Inflation in Kaluza-Klein Theory: Relation between the Fine-Structure Constant and the Cosmological Constant

In this paper we investigate a model of an inflationary universe in Kaluza-Klein theory, which is a four-dimensional de Sitter space plus a one-dimensional compactified internal space. We find that the energy scale for inflation can be predicted from the fine-structure constant in a self-consistent solution of the semi-classical Einstein equations including the Casimir effect. From the observed value of the fine-structure constant, we obtain an energy scale for inflation of $ε=1.84\times 10^{16}g_*^{1/4}$ Gev, where $g_*$ is a dimensionless number depending on the spin and number of matter fields existing in the universe. This value is consistent with the values often discussed for inflation and grand unification. The wave function for this model predicts a high probability for forming such universes, independent of the value of the cosmological constant. The tunneling probability favors the creation of inflationary universes with a compactified dimension, over those with all macroscopic dimensions.

astro-ph↗

arXiv1997

Can the Universe Create Itself?

The question of first-cause has troubled philosophers and cosmologists alike. Now that it is apparent that our universe began in a Big Bang explosion, the question of what happened before the Big Bang arises. Inflation seems like a very promising answer, but as Borde and Vilenkin have shown, the inflationary state preceding the Big Bang must have had a beginning also. Ultimately, the difficult question seems to be how to make something out of nothing. This paper explores the idea that this is the wrong question --- that that is not how the Universe got here. Instead, we explore the idea of whether there is anything in the laws of physics that would prevent the Universe from creating itself. Because spacetimes can be curved and multiply connected, general relativity allows for the possibility of closed timelike curves (CTCs). Thus, tracing backwards in time through the original inflationary state we may eventually encounter a region of CTCs giving no first-cause. This region of CTCs, may well be over by now (being bounded toward the future by a Cauchy horizon). We illustrate that such models --- with CTCs --- are not necessarily inconsistent by demonstrating self-consistent vacuums for Misner space and a multiply connected de Sitter space in which the renormalized energy-momentum tensor does not diverge as one approaches the Cauchy horizon and solves Einstein's equations. We show such a Universe can be classically stable and self-consistent if and only if the potentials are retarded, giving a natural explanation of the arrow of time. Some specific scenarios (out of many possible ones) for this type of model are described. For example: an inflationary universe gives rise to baby universes, one of which turns out to be itself. Interestingly, the laws of physics may allow the Universe to be its own mother.

astro-ph↗

arXiv1997

A Self-Consistent Vacuum for Misner Space and the Chronology Protection Conjecture

In this paper we find a self-consistent vacuum for Misner space. For this "adapted" Rindler vacuum the renormalized stress-energy tensor is zero throughout the Misner space. A point-like particle detector traveling on a timelike geodesic in a Misner space with this vacuum detects nothing. Misner space with this vacuum thus creates no problems for time travel in and of itself but a time traveler may pose a danger to himself and to the spacetime.

gr-qc↗

arXiv1997

The Nature of the X-Ray Point Source in the Bar of NGC 6822

We have analysed archival ROSAT PSPC and Einstein HRI data for the x-ray point source in the bar of NGC 6822. The source decreased in x-ray flux by at least half an order of magnitude in the 13 years between the HRI and PSPC observations. It has a PSPC flux of f_X = 8 x 10E-14 erg/cm^2/s, giving L_X = 2.4 x 10E36 erg/s for a distance of 500 kpc. The source appears to be related to the optical emission-line object Ho 12. It is unclear if Ho 12 is an HII region or a supernova remnant, although the latter interpretation is better supported by the available optical data. The x-rays are unlikely to be direct emission from a supernova remnant, due to the observed strong x-ray variability. The x-ray spectrum of the source is very soft. Acceptable fits are found for either a Raymond-Smith thermal model with kT = 0.56 keV, or a blackbody model with kT = 0.06 keV. The latter model would place the source amongst the class of Super-Soft x-ray sources first found in the Magellanic Clouds. If the thermal model is correct, the source appears similar to Galactic and Magellanic Cloud stellar-mass black hole binary candidates. We have identified a list of potential optical counterparts from published photometry. However, for either model discussed above, we expect the apparent magnitude of the optical counterpart to be in the range 21.5 < V < 24.0. Thus the optical counterpart may be below the limit of published photometry.

astro-ph↗

arXiv1997

A Robust Determination of the Time Delay in 0957+561A,B and a Measurement of the Global Value of Hubble's Constant

Photometric monitoring of the gravitational lens system 0957+561A,B in the g and r bands with the Apache Point Observatory (APO) 3.5 m telescope during 1996 shows a sharp g band event in the trailing (B) image light curve at the precise time predicted from the observation of an event during 1995 in the leading (A) image with a delay of 415 days. This success confirms the "short delay," and the lack of any feature at a delay near 540 days rejects the "long delay" for this system, resolving a long-standing controversy. A series of statistical analyses of our light curve data yield a best fit delay of 417 +/- 3 days (95% confidence interval). Recent improvements in the modeling of the lens system (consisting of a galaxy and cluster) allow us to derive a value of the global (at z = 0.36) value of Hubble's constant H_0 using Refsdal's method, a simple and direct distance determination based on securely understood physics and geometry. The result is H_0 = 63 +/- 12 km/s/Mpc (for Omega = 1) where this 95% confidence interval is dominated by remaining lens model uncertainties.

astro-ph↗

arXiv1996

An Iterative Approach to Twisting and Diverging, Type N, Vacuum Einstein Equations: A (Third-Order) Resolution of Stephani's `Paradox'

In 1993, a proof was published, within ``Classical and Quantum Gravity,'' that there are no regular solutions to the {\it linearized} version of the twisting, type-N, vacuum solutions of the Einstein field equations. While this proof is certainly correct, we show that the conclusions drawn from that fact were unwarranted, namely that this irregularity caused such solutions not to be able to truly describe pure gravitational waves. In this article, we resolve the paradox---since such first-order solutions must always have singular lines in space for all sufficiently large values of $r$---by showing that if we perturbatively iterate the solution up to the third order in small quantities, there are acceptable regular solutions. That these solutions become flat before they become non-twisting tells us something interesting concerning the general behavior of solutions describing gravitational radiation from a bounded source.

gr-qc↗

arXiv1996

Topology of COBE Microwave Background Fluctuations

We have measured the topology (genus) of the fluctuations in the cosmic microwave background seen in the recently completed (four-year) data set produced by the COBE satellite. We find that the genus is consistent with that expected from a random-phase Gaussian distribution, as might be produced naturally in inflationary models.

astro-ph↗

arXiv1995

Estabrook-Wahlquist Prolongations and Infinite-Dimensional Algebras

Detailed mappings between zero-curvture equations for prolongation structures of nonlinear pde's and Estabrook-Wahlquist algorithms for same are given. The differences are exemplified by studies of the sine-Gordon equation. An example where the prolongation structure must be infinite-dimensional is given by the Robinson-Trautman equation, where the minimal algebra is $K_2$. In general these algorithms require integration of vector-field valued pde's; solutions of simultaneous flow equations are given. Applications to coupled systems of flow equations are given, where the result describes Lie algebras of vector fields vertical over fibers of pseudopotentials over a jet bundle appropriate for a given system of pde's; algebras invariant under sl(2,C) are of special interest.

solv-int↗

arXiv1995

A Sharp Event in the Image a Light Curve of the Double Quasar 0957+561 and Prediction of the 1996 Image B Light Curve

CCD photometry of the gravitational lens system 0957+561A,B in the g and r bands was obtained on alternate nights, weather permitting, from December 1994 through May 1995 using the Double Imaging Spectrograph (DIS) on the Apache Point Observatory (APO) 3.5-meter telescope. The remote observing and fast instrument change capabilities of this facility allowed accumulation of light curves sampled frequently and consistently. The Honeycutt ensemble photometry algorithm was applied to the data set and yielded typical relative photometric errors of approximately 0.01 magnitudes. Image A exhibited a sharp drop of about 0.1 magnitudes in late December 1994; no other strong features were recorded in either image. This event displays none of the expected generic features of a microlensing-induced flux variation and is likely to be intrinsic to the quasar; if so, it should also be seen in the B image with the lensing differential time delay. We give the expected 1996 image B light curves based on two values of the time delay and brightness ratio which have been proposed and debated in the literature. Continued monitoring of the system in the first half of 1996 should easily detect the image B event and thus resolve the time-delay controversy.

astro-ph↗