Smooth and analytic actions of SL(n,R)SL(n,{\bf R}) and SL(n,Z)SL(n,{\bf Z}) on closed nn-dimensional manifolds

The main result is a classification of smooth actions of $SL(n,{\bf R})$, $n \geq 3$, or connected groups locally isomorphic to it, on closed $n$-manifolds, extending a theorem of Uchida. We construct new exotic actions of $SL(n,{\bf Z})$ on the $n$-torus and connected sums of $n$-tori, and we formulate a conjectural classification of actions of lattices in $SL(n,{\bf R})$ on closed $n$-manifolds. We prove some results about invariant rigid geometric structures for $SL(n,{\bf R})$-actions.Comment: 29 pp.; In memory of Fuichi Uchida (1938--2021). Minor changes in second versio

Spitzer spectral line mapping of supernova remnants: I. Basic data and principal component analysis

We report the results of spectroscopic mapping observations carried out toward small (1 x 1 arcmin) regions within the supernova remnants W44, W28, IC443, and 3C391 using the Infrared Spectrograph of the Spitzer Space Telescope. These observations, covering the 5.2 - 37 micron spectral region, have led to the detection of a total of 15 fine structure transitions of Ne+, Ne++, Si+, P+, S, S++, Cl+, Fe+, and Fe++; the S(0) - S(7) pure rotational lines of molecular hydrogen; and the R(3) and R(4) transitions of hydrogen deuteride. In addition to these 25 spectral lines, the 6.2, 7.7, 8.6, 11.3 and 12.6 micron PAH emission bands were also observed. Most of the detected line transitions have proven strong enough to map in several sources, providing a comprehensive picture of the relative distribution of the various line emissions observable in the Spitzer/IRS bandpass. A principal component analysis of the spectral line maps reveals that the observed emission lines fall into five distinct groups, each of which may exhibit a distinct spatial distribution: (1) lines of S and H2 (J > 2); (2) the H2 S(0) line; (3) lines of ions with appearance potentials less than 13.6 eV; (4) lines of ions with appearance potentials greater than 13.6 eV, not including S++; (5) lines of S++. Lines of group (1) likely originate in molecular material subject to a slow, nondissociative shock that is driven by the overpressure within the supernova remnant, and lines in groups (3) - (5) are associated primarily with dissociative shock fronts with a range of (larger) shock velocities. The H2 S(0) line shows a low-density diffuse emission component, and - in some sources - a shock-excited component.Comment: 43 pages, including 21 figures. Accepted for publication in Ap

SWAS observations of comet 9P/Tempel 1 and Deep Impact

On 4 July 2005 at 1:52 UT the Deep Impact mission successfully completed its goal to hit the nucleus of 9P/Tempel 1 with an impactor, forming a crater on the nucleus and ejecting material into the coma of the comet. The 370 kg impactor collided with the sunlit side of the nucleus with a relative velocity of 10.2 km/s. NASA's Submillimeter Wave Astronomy Satellite (SWAS) observed the 1(10)-1(01) ortho-water ground-state rotational transition in comet 9P/Tempel 1 before, during, and after the impact. No excess emission from the impact was detected by SWAS. However, the water production rate of the comet showed large natural variations of more than a factor of three during the weeks before the impact.Comment: to appear in the proceedings of the IAU Symposium No. 231: "Astrochemistry - Recent Successes and Current Callenges". Typo corrected in author affiliation lis

Distribution of Water Vapor in Molecular Clouds

We report the results of a large-area study of water vapor along the Orion Molecular Cloud ridge, the purpose of which was to determine the depth-dependent distribution of gas-phase water in dense molecular clouds. We find that the water vapor measured toward 77 spatial positions along the face-on Orion ridge, excluding positions surrounding the outflow associated with BN/KL and IRc2, display integrated intensities that correlate strongly with known cloud surface tracers such as CN, C2H, 13CO J =5-4, and HCN, and less well with the volume tracer N2H+. Moreover, at total column densities corresponding to Av < 15 mag., the ratio of H2O to C18O integrated intensities shows a clear rise approaching the cloud surface. We show that this behavior cannot be accounted for by either optical depth or excitation effects, but suggests that gas-phase water abundances fall at large Av. These results are important as they affect measures of the true water-vapor abundance in molecular clouds by highlighting the limitations of comparing measured water vapor column densities with such traditional cloud tracers as 13CO or C18O. These results also support cloud models that incorporate freeze-out of molecules as a critical component in determining the depth-dependent abundance of water vapor

The Role of Context in the Evolution of a Serial Entrepreneur

Entrepreneurial research often focuses on the psychological traits of the entrepreneur but rarely on the notion that under certain circumstances entrepreneurship may be equally driven by external factors beyond the founder's control. This paper looks at the 40-year history of a serial entrepreneur and identifies five types of business ventures driven by contextual factors and the personal attributes of the entrepreneur. These five types are the “advised” venture, the “safe harbor” venture, the “accidental” venture, the “greener grass” venture, and the “passion” venture. The paper closes with a call for future research to include situational context in defining what creates and motivates entrepreneurs

An independent determination of the local Hubble constant

The relationship between the integrated H$\beta$ line luminosity and the velocity dispersion of the ionized gas of HII galaxies and giant HII regions represents an exciting standard candle that presently can be used up to redshifts z ~ 4. Locally it is used to obtain precise measurements of the Hubble constant by combining the slope of the relation obtained from nearby ($z \leq$ 0.2) HII galaxies with the zero point determined from giant HII regions belonging to an `anchor sample' of galaxies for which accurate redshift-independent distance moduli are available. We present new data for 36 giant HII regions in 13 galaxies of the anchor sample that includes the megamaser galaxy NGC 4258. Our data is the result of the first four years of observation of our primary sample of 130 giant HII regions in 73 galaxies with Cepheid determined distances. Our best estimate of the Hubble parameter is $71.0\pm2.8(random)\pm2.1(systematic)$ km /s Mpc This result is the product of an independent approach and, although at present less precise than the latest SNIa results, it is amenable to substantial improvement.Comment: 30 pages, 28 figures, Accepted to be published in MNRA

The L - \sigma\ relation for HII galaxies in green

The correlation between emission-line luminosity (L) and profile width (sigma) for HII Galaxies provides a powerful method to measure the distances to galaxies over a wide range of redshifts. In this paper we use SDSS spectrophotometry to explore the systematics of the correlation using the [OIII]5007 lines instead of Halpha or Hbeta to measure luminosities and line widths. We also examine possible systematic effects involved in measuring the profile-widths and the luminosities through different apertures. We find that the green L-sigma relation defined using [OIII]5007 luminosities is significantly more sensitive than Hbeta to the effects of age and the physical conditions of the nebulae, which more than offsets the advantage of the higher strength of the [OIII]5007 lines. We then explore the possibility of mixing [OIII]5007 profile-widths with SDSS Hbeta luminosities using the Hubble constant H0 to quantify the possible systematic effects. We find the mixed L(Hbeta) sigma[OIII] relation to be at least as powerful as the canonical L-sigma relation as a distance estimator, and we show that the evolutionary corrections do not change the slope and the scatter of the correlation, and therefore, do not bias the L-sigma distance indicator at high redshifts. Locally, however, the luminosities of the Giant HII Regions that provide the zero-point calibrators are sensitive to evolutionary corrections and may bias the Hubble constant if their mean ages, as measured by the equivalent widths of Hbeta, are significantly different from the mean age of the HII Galaxies. Using a small sample of 16 ad-hoc zero point calibrators we obtain a value of H0 = 66.4\pm4.5 km s^-1 Mpc^-1 for the Hubble constant, which is fully consistent with the best modern determinations, and that is not biased by evolutionary corrections.Comment: 14 pages, 7 figures. Accepted for publication by A&

Ultraluminous infrared galaxies: mergers of sub-L* galaxies?

A sample of 27 low-redshift, mostly cool, ultraluminous infrared galaxies (ULIRGs) has been imaged at 1.6 μm with the Hubble Space Telescope (HST) Near-Infrared Camera and Multi-Object Spectrometer (NICMOS). The majority (67%) of the sample's galaxies are multiple-nucleus galaxies with projected separations of up to 17 kpc, and the rest of the sample (33%) are single-nucleus galaxies, as determined by the NICMOS angular resolution limit. The average observed, integrated (host+nucleus) H magnitude of our HST H sample ULIRGs is -24.3, slightly above that of an L* galaxy (MH = -24.2), and 52% of the sample's galaxies have sub-L* luminosities. The ULIRGs in the HST H sample are not generated as a result of the merging of two luminous (i.e., ≥L*) spiral galaxies. Instead, the interactions and mergers occur in general between two, or in some cases more, less massive sub-L* (0.3-0.5L*) galaxies. Only one out of the 49 nuclei identified in the entire HST H sample has the properties of a bright quasar-like nucleus. On average, the brightest nuclei in the HST H sample galaxies (i.e., cool ULIRGs) are 1.2 mag fainter than warm ULIRGs and low-luminosity Bright Quasar Survey quasars (BQS QSOs) and 2.6 mag fainter than high-luminosity BQS QSOs. Since the progenitor galaxies involved in the merger are sub-L* galaxies, the mass of the central black hole in these ULIRGs would be only about (1-2) × 107 M☉, if the bulge-to-black hole mass ratio of nearby galaxies holds for ULIRGs. The estimated mass of the central black hole is similar to that of nearby Seyfert 2 galaxies but at least 1 order of magnitude lower than the massive black holes thought to be located at the center of high-luminosity QSOs. Massive nuclear starbursts with constant star formation rates of 10-40 M☉ yr-1 could contribute significantly to the nuclear H-band flux and are consistent with the observed nuclear H-band magnitudes of the ULIRGs in the HST H sample. An evolutionary merging scenario is proposed for the generation of the different types of ULIRGs and QSOs on the basis of the masses of the progenitors involved in the merging process. According to this scenario, cool ULIRGs would be the end product of the merging of two or more low-mass (0.3L*-0.5L*) disk galaxies. Warm ULIRGs and low-luminosity QSOs would be generated by a merger involving intermediate-mass (0.5 L*) disk galaxies. Under this scenario, warm ULIRGs could still be the dust-enshrouded phases of UV-bright low-luminosity QSOs, but cool ULIRGs, which are most ULIRGs, would not evolve into QSOs