How to Measure Subdiffusion Parameters

We propose a method to measure the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_{\alpha}$ which are defined by means of the relation $=\frac{2D_\alpha} {\Gamma(1+\alpha)} t^\alpha$ where $$ denotes a mean square displacement of a random walker starting from $x=0$ at the initial time $t=0$. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. We experimentally study a diffusion of glucose and sucrose in a gel solvent, and we precisely determine the parameters $\alpha$ and $D_{\alpha}$, using a fully analytic solution of the fractional subdiffusion equation.Comment: short version of cond-mat/0309072, to appear in Phys. Rev. Let

Measuring subdiffusion parameters

We propose a method to extract from experimental data the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_\alpha$ which are defined by means of the relation $=2D_\alpha/\Gamma(1+\alpha) t^\alpha$ where $$ denotes a mean square displacement of a random walker starting from $x=0$ at the initial time $t=0$. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. Using such a system, we experimentally study a diffusion of glucose and sucrose in a gel solvent. We find a fully analytic solution of the fractional subdiffusion equation with the initial and boundary conditions representing the system under study. Confronting the experimental data with the derived formulas, we show a subdiffusive character of the sugar transport in gel solvent. We precisely determine the parameter $\alpha$, which is smaller than 1, and the subdiffusion coefficient $D_\alpha$.Comment: 17 pages, 9 figures, revised, to appear in Phys. Rev.

Arm & Interarm Star Formation in Spiral Galaxies

We investigate the relationship between spiral arms and star formation in the grand-design spirals NGC 5194 and NGC 628 and in the flocculent spiral NGC 6946. Filtered maps of near-IR (3.6 micron) emission allow us to identify "arm regions" that should correspond to regions of stellar mass density enhancements. The two grand-design spirals show a clear two-armed structure, while NGC 6946 is more complex. We examine these arm and interarm regions, looking at maps that trace recent star formation - far-ultraviolet (GALEX NGS) and 24 micron emission (Spitzer, SINGS) - and cold gas - CO (Heracles) and HI (Things). We find the star formation tracers and CO more concentrated in the spiral arms than the stellar 3.6 micron flux. If we define the spiral arms as the 25% highest pixels in the filtered 3.6 micron images, we find that the majority (60%) of star formation tracers occurs in the interarm regions; this result persists qualitatively even when considering the potential impact of finite data resolution and diffuse interarm 24 micron emission. Even with a generous definition of the arms (45% highest pixels), interarm regions still contribute at least 30% to the integrated star formation rate tracers. We look for evidence that spiral arms trigger star or cloud formation using the ratios of star formation rate (SFR, traced by a combination of FUV and 24 micron emission) to H_2 (traced by CO) and H_2 to HI. Any enhancement of SFR / M(H_2) in the arm region is very small (less than 10%) and the grand design spirals show no enhancement compared to the flocculent target. Arm regions do show a weak enhancement in H_2/HI compared to the interarm regions, but at a fixed gas surface density there is little clear enhancement in the H_2/HI ratio in the arm regions. Thus, it seems that spiral arms may only act to concentrate the gas to higher densities in the arms.Comment: 11 pages, 9 Figures, accepted by Ap

Starbursting Nuclear CO Disks of Early-type Spiral Galaxies

We have initiated the first CO interferometer survey of early-type spiral galaxies (S0-Sab). We observed five early-type spiral galaxies with HII nuclei (indicating circumnuclear starburst activities). These observations indicate gas masses for the central kiloparsec of \sim 1-5% of the dynamical masses. Such low gas mass fractions suggest that large-scale gravitational instability in the gas is unlikely to be the driving cause for the starburst activities. The Toomre Q values were >1 (mostly >3) within the central kiloparsec, indicating that the gas disks are globally gravitationally stable. The area filling factor of the gas disks is estimated to be about 0.05. This small value indicates the existence of lumpy structure, i.e. molecular clouds, in the globally-gravitationally stable disks. The typical surface density of the molecular clouds is as high as \sim 3000 Msun pc^{-2}. We reconsider the nature of the Toomre Q criterion, and conclude that the Q derived from CO observations indicates neither star formation nor molecular cloud formation. This argument should be valid not only for the circumnuclear disks but also for any region in galactic disks. We tentatively explore an alternative model, i.e. cloud-cloud collisions, as an initiating mechanism of star formation.Comment: 7pages, including 2 figures ; A&A accepted (19 Oct. 2004

Gaps in the cloud cover? Comparing extinction measures in spiral disks

Dust in galaxies can be mapped by either the FIR/sub-mm emission, the optical or infrared reddening of starlight, or the extinction of a known background source. We compare two dust extinction measurements for a set of fifteen sections in thirteen nearby galaxies, to determine the scale of the dusty ISM responsible for disk opacity: one using stellar reddening and the other a known background source. In our earlier papers, we presented extinction measurements of 29 galaxies, based on calibrated counts of distant background objects identified though foreground disks in HST/WFPC2 images. For the 13 galaxies that overlap with the Spitzer Infrared Nearby Galaxies Survey (SINGS), we now compare these results with those obtained from an I-L color map. Our goal is to determine whether or not a detected distant galaxy indicates a gap in the dusty ISM, and hence to better understand the nature and geometry of the disk extinction. We find that distant galaxies are predominantly in low-extinction sections marked by the color maps, indicating that their number depends both on the cloud cover of {\it Spitzer}-resolved dust structures --mostly the spiral arms--and a diffuse, unresolved underlying disk. We note that our infrared color map (E[I-L]) underestimates the overall dust presence in these disks severely, because it implicitly assumes the presence of a dust screen in front of the stellar distribution.Comment: 22 pages, 2 figures, 3 tables, accepted for publication in A

The Opacity of Spiral Galaxy Disks VIII: Structure of the Cold ISM

The quantity of dust in a spiral disk can be estimated using the dust's typical emission or the extinction of a known source. In this paper, we compare two techniques, one based on emission and one on absorption, applied on sections of fourteen disk galaxies. The two measurements reflect, respectively the average and apparent optical depth of a disk section. Hence, they depend differently on the average number and optical depth of ISM structures in the disk. The small scale geometry of the cold ISM is critical for accurate models of the overall energy budget of spiral disks. ISM geometry, relative contributions of different stellar populations and dust emissivity are all free parameters in galaxy Spectral Energy Distribution (SED) models; they are also sometimes degenerate, depending on wavelength coverage. Our aim is to constrain typical ISM geometry. The apparent optical depth measurement comes from the number of distant galaxies seen in HST images through the foreground disk. We measure the IR flux in images from the {\it Spitzer} Infrared Nearby Galaxy Survey in the same section of the disk that was covered by HST. A physical model of the dust is fit to the SED to estimate the dust surface density, mean temperature, and brightness in these disk sections. The surface density is subsequently converted into the average optical depth estimate. The two measurements generally agree. The ratios between the measured average and apparent optical depths of the disk sections imply optically thin clouds in these disks. Optically thick disks, are likely to have more than a single cloud along the line-of-sight.Comment: 31 pages, 5 figures, 4 tables, accepted for publication in A

The Calibration of Mid-Infrared Star Formation Rate Indicators

With the goal of investigating the degree to which the mid-infrared emission traces the star formation rate (SFR), we analyze Spitzer 8 um and 24 um data of star-forming regions in a sample of 33 nearby galaxies with available HST/NICMOS images in the Paschen-alpha (1.8756 um) emission line. The galaxies are drawn from the Spitzer Infrared Nearby Galaxies Survey (SINGS) sample, and cover a range of morphologies and a factor ~10 in oxygen abundance. Published data on local low-metallicity starburst galaxies and Luminous Infrared Galaxies are also included in the analysis. Both the stellar-continuum-subtracted 8 um emission and the 24 um emission correlate with the extinction-corrected Pa-alpha line emission, although neither relationship is linear. Simple models of stellar populations and dust extinction and emission are able to reproduce the observed non-linear trend of the 24 um emission versus number of ionizing photons, including the modest deficiency of 24 um emission in the low metallicity regions, which results from a combination of decreasing dust opacity and dust temperature at low luminosities. Conversely, the trend of the 8 um emission as a function of the number of ionizing photons is not well reproduced by the same models. The 8 um emission is contributed, in larger measure than the 24 um emission, by dust heated by non-ionizing stellar populations, in agreement with previous findings. Two SFR calibrations, one using the 24 um emission and the other using a combination of the 24 um and H-alpha luminosities (Kennicutt et al. 2007), are presented. No calibration is presented for the 8 um emission, because of its significant dependence on both metallicity and environment. The calibrations presented here should be directly applicable to systems dominated by on-going star formation.Comment: 67 pages, 15 figures, accepted for publication on the Astrophysical Journal; replacement contains: correction to equation 8; important tweaks to equation 9; various typos correcte

Particularly Efficient Star Formation in M33

The Star Formation (SF) rate in galaxies is an important parameter at all redshifts and evolutionary stages of galaxies. In order to understand the increased SF rates in intermediate redshift galaxies one possibility is to study star formation in local galaxies with properties frequently found at this earlier epoch like low metallicity and small size. We present sensitive observations of the molecular gas in M 33, a small Local Group spiral at a distance of 840 kpc which shares many of the characteristics of the intermediate redshift galaxies. The observations were carried out in the CO(2--1) line with the HERA heterodyne array on the IRAM 30 m telescope. A 11\arcmin$\times$22\arcmin region in the northern part of M 33 was observed, reaching a detection threshold of a few 10$^{3}$ \msol. The correlation in this field between the CO emission and tracers of SF (8\mum, 24\mum, \Ha, FUV) is excellent and CO is detected very far North, showing that molecular gas forms far out in the disk even in a small spiral with a subsolar metallicity. One major molecular cloud was discovered in an interarm region with no HI peak and little if any signs of SF -- without a complete survey this cloud would never have been found. The radial dependence of the CO emission has a scale length similar to the dust emission, less extended than the \Ha or FUV. If, however, the \ratioo ratio varies inversely with metallicity, then the scale length of the H$_2$ becomes similar to that of the \Ha or FUV. Comparing the SF rate to the H$_2$ mass shows that M 33, like the intermediate redshift galaxies it resembles, has a significantly higher SF efficiency than large local universe spirals.Comment: 16 pages, 15 figure

Molecular Gas in Spiral Galaxies

In this review, I highlight a number of recent surveys of molecular gas in nearby spiral galaxies. Through such surveys, more complete observations of the distribution and kinematics of molecular gas have become available for galaxies with a wider range of properties (e.g., brightness, Hubble type, strength of spiral or bar structure). These studies show the promise of both interferometers and single-dish telescopes in advancing our general understanding of molecular gas in spiral galaxies. In particular, I highlight the contributions of the recent BIMA Survey of Nearby Galaxies (SONG).Comment: 8 pages, 1 figure. To appear in the proceedings of the 4th Cologne-Bonn-Zermatt-Symposium, "The Dense Interstellar Medium in Galaxies", which was held in Zermatt, Switzerland in September 200