We explore both classical and quantum dynamics of a model potential exhibiting a caldera: that is, a shallow potential well with two pairs of symmetry related index one saddles associated with entrance/exit channels. Classical trajectory simulations
at several different energies confirm the existence of the `dynamical matching phenomenon originally proposed by Carpenter, where the momentum direction associated with an incoming trajectory initiated at a high energy saddle point determines to a considerable extent the outcome of the reaction (passage through the diametrically opposing exit channel). By studying a `stretched version of the caldera model, we have uncovered a generalized dynamical matching: bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly through the transition state opposite the reflection point. We also investigate the effects of dissipation on the classical dynamics. In addition to classical trajectory studies, we examine the dynamics of quantum wave packets on the caldera potential (stretched and unstretched). These computations reveal a quantum mechanical analogue of the `dynamical matching phenomenon, where the initial expectation value of the momentum direction for the wave packet determines the exit channel through which most of the probability density passes to product.
This work presents high spectral resolution observations of the CII line at 158 micron, one of the major cooling lines of the interstellar medium, taken with the HIFI heterodyne spectrometer on the Herschel satellite. In BCLMP 691, an HII region far
north (3.3 kpc) in the disk of M 33, the CII and CO line profiles show similar velocities within $0.5 kms$, while the HI line velocities are systematically shifted towards lower rotation velocities by $sim 5kms$. Observed at the same $12$ angular resolution, the CII lines are broader than those of CO by about 50% but narrower than the HI lines. The CII line to far-infrared continuum ratio suggests a photoelectric heating efficiency of 1.1%. The data, together with published models indicate a UV field $G_0 sim 100$ in units of the solar neighborhood value, a gas density $n_H sim 1000 cc$, and a gas temperature $Tsim 200$ K. Adopting these values, we estimate the C$^+$ column density to be $N_{C^+} approx 1.3 times 10^{17} cmt$. The CII emission comes predominantly from the warm neutral region between the HII region and the cool molecular cloud behind it. From published abundances, the inferred C$^+$ column corresponds to a hydrogen column density of $N_H sim 2 times 10^{21} cmt$. The CO observations suggest that $N_H = 2 N_{H_2} sim 3.2 times 10^{21} cmt$ and 21cm measurements, also at $12$ resolution, yield $N_HI approx 1.2 times 10^{21} cmt$ within the CII velocity range. Thus, some H$_2$ not detected in CO must be present, in agreement with earlier findings based on the SPIRE 250 -- 500 $mu$m emission.
Power spectra of de-projected images of late-type galaxies in gas and/or dust emission are very useful diagnostics of the dynamics and stability of their interstellar medium. Previous studies have shown that the power spectra can be approximated as t
wo power-laws, a shallow one at large scales (larger than 500 pc) and a steeper one at small scales, with the break between the two corresponding to the line-of-sight thickness of the galaxy disk. We present a thorough analysis of the power spectra of the dust and gas emission at several wavelengths in the nearby galaxy M33. In particular, we use the recently obtained images at five wavelengths by PACS and SPIRE onboard Herschel. The large dynamical range (2-3 dex in scale) of most images allow us to determine clearly the change in slopes from -1.5 to -4, with some variations with wavelength. The break scale is increasing with wavelength, from 100 pc at 24 and 100micron to 350 pc at 500micron, suggesting that the cool dust lies in a thicker disk than the warm dust, may be due to star formation more confined to the plane. The slope at small scale tends to be steeper at longer wavelength, meaning that the warmer dust is more concentrated in clumps. Numerical simulations of an isolated late-type galaxy, rich in gas and with no bulge, like M33, are carried out, in order to better interpret these observed results. Varying the star formation and feedback parameters, it is possible to obtain a range of power-spectra, with two power-law slopes and breaks, which nicely bracket the data. The small-scale power-law is indeed reflecting the 3D behaviour of the gas layer, steepening strongly while the feedback smoothes the structures, by increasing the gas turbulence. M33 appears to correspond to a fiducial model with an SFR of $sim$ 0.7 Mo/yr, with 10% supernovae energy coupled to the gas kinematics.
Context: The emission line of [CII] at 158 micron is one of the strongest cooling lines of the interstellar medium (ISM) in galaxies. Aims: Disentangling the relative contributions of the different ISM phases to [CII] emission, is a major topic of th
e HerM33es program, a Herschel key project to study the ISM in the nearby spiral galaxy M33. Methods: Using PACS, we have mapped the emission of [CII] 158 micron, [OI] 63 micron, and other FIR lines in a 2x2 region of the northern spiral arm of M33, centered on the HII region BCLMP302. At the peak of H-alpha emission, we have observed in addition a velocity resolved [CII] spectrum using HIFI. We use scatterplots to compare these data with PACS 160 micron continuum maps, and with maps of CO and HI data, at a common resolution of 12 arcsec or 50 pc. Maps of H-alpha and 24 micron emission observed with Spitzer are used to estimate the SFR. We have created maps of the [CII] and [OI] 63 micron emission and detected [NII] 122 micron and NIII 57 micron at individual positions. Results: The [CII] line observed with HIFI is significantly broader than that of CO, and slightly blue-shifted. In addition, there is little spatial correlation between [CII] observed with PACS and CO over the mapped region. There is even less spatial correlation between [CII] and the atomic gas traced by HI. Detailed comparison of the observed intensities towards the HII region with models of photo ionization and photon dominated regions, confirms that a significant fraction, 20--30%, of the observed [CII] emission stems from the ionized gas and not from the molecular cloud. The gas heating efficiency, using the ratio between [CII] and the TIR as a proxy, varies between 0.07 and 1.5%, with the largest variations found outside the HII region.
Within the key project Herschel M33 extended survey (HerM33es), we are studying the physical and chemical processes driving star formation and galactic evolution in the nearby galaxy M33, combining the study of local conditions affecting individual s
tar formation with properties only becoming apparent on global scales. Here, we present recent results obtained by the HerM33es team. Combining Spitzer and Herschel data ranging from 3.6um to 500um, along with HI, Halpha, and GALEX UV data, we have studied the dust at high spatial resolutions of 150pc, providing estimators of the total infrared (TIR) brightness and of the star formation rate. While the temperature of the warm dust at high brightness is driven by young massive stars, evolved stellar populations appear to drive the temperature of the cold dust. Plane-parallel models of photon dominated regions (PDRs) fail to reproduce fully the [CII], [OI], and CO maps obtained in a first spectroscopic study of one 2x2 subregion of M33, located on the inner, northern spiral arm and encompassing the HII region BCLMP302.
Aims: We aim at deriving the excitation conditions of the interstellar gas as well as the local FUV intensities in the molecular cloud surrounding NGC 3603 to get a coherent picture of how the gas is energized by the central stars. Methods: The NANTE
N2-4m submillimeter antenna is used to map the [CI] 1-0, 2-1 and CO 4-3, 7-6 lines in a 2 x 2 region around the young OB cluster NGC 3603 YC. These data are combined with C18O 2-1 data, HIRES-processed IRAS 60 and 100 micron maps of the FIR continuum, and Spitzer/IRAC maps. Results: The NANTEN2 observations show the presence of two molecular clumps located south-east and south-west of the cluster and confirm the overall structure already found by previous CS and C18O observations. We find a slight position offset of the peak intensity of CO and [CI], and the atomic carbon appears to be further extended compared to the molecular material. We used the HIRES far-infrared dust data to derive a map of the FUV field heating the dust. We constrain the FUV field to values of chi = 3 - 6 times 10^3 in units of the Draine field across the clouds. Approximately 0.2 to 0.3 % of the total FUV energy is re-emitted in the [CII] 158 {mu}m cooling line observed by ISO. Applying LTE and escape probability calculations, we derive temperatures (TMM1 = 43 K, TMM2 = 47 K), column densities (N(MM1) = 0.9 times 10^22 cm^-2, N(MM2) = 2.5 times 10^22 cm^-2) and densities (n(MM1) = 3 times 10^3 cm^-3, n(MM2) = 10^3 -10^4 cm^-3) for the two observed molecular clumps MM1 and MM2. Conclusions: The cluster is strongly interacting with the ambient molecular cloud, governing its structure and physical conditions. A stability analysis shows the existence of gravitationally collapsing gas clumps which should lead to star formation. Embedded IR sources have already been observed in the outskirts of the molecular cloud and seem to support our conclusions.
We present an analysis of the first space-based far-IR-submm observations of M 33, which measure the emission from the cool dust and resolve the giant molecular cloud complexes. With roughly half-solar abundances, M33 is a first step towards young lo
w-metallicity galaxies where the submm may be able to provide an alternative to CO mapping to measure their H$_2$ content. In this Letter, we measure the dust emission cross-section $sigma$ using SPIRE and recent CO and HI observations; a variation in $sigma$ is present from a near-solar neighborhood cross-section to about half-solar with the maximum being south of the nucleus. Calculating the total H column density from the measured dust temperature and cross-section, and then subtracting the HI column, yields a morphology similar to that observed in CO. The H$_2$/HI mass ratio decreases from about unity to well below 10% and is about 15% averaged over the optical disk. The single most important observation to reduce the potentially large systematic errors is to complete the CO mapping of M 33.
Within the framework of the HERM33ES Key Project, using the high resolution and sensitivity of the Herschel photometric data, we study the compact emission in the Local Group spiral galaxy M33 to investigate the nature of the compact SPIRE emission s
ources. We extracted a catalogue of sources at 250um in order to investigate the nature of this compact emission. Taking advantage of the unprecedented Herschel resolution at these wavelengths, we also focus on a more precise study of some striking Halpha shells in the northern part of the galaxy. We present a catalogue of 159 compact emission sources in M33 identified by SExtractor in the 250um SPIRE band that is the one that provides the best spatial resolution. We also measured fluxes at 24um and Halpha for those 159 extracted sources. The morphological study of the shells also benefits from a multiwavelength approach including Halpha, far-UV from GALEX, and infrared from both Spitzer IRAC 8um and MIPS 24um in order to make comparisons. For the 159 compact sources selected at 250um, we find a very strong Pearson correlation coefficient with the MIPS 24um emission (r24 = 0.94) and a rather strong correlation with the Halpha emission, although with more scatter (rHa = 0.83). The morphological study of the Halpha shells shows a displacement between far-ultraviolet, Halpha, and the SPIRE bands. The cool dust emission from SPIRE clearly delineates the Halpha shell structures. The very strong link between the 250um compact emission and the 24um and Halpha emissions, by recovering the star formation rate from standard recipes for HII regions, allows us to provide star formation rate calibrations based on the 250um compact emission alone. The different locations of the Halpha and far-ultraviolet emissions with respect to the SPIRE cool dust emission leads to a dynamical age of a few Myr for the Halpha shells and the associated cool dust.
Over the past few years several studies have provided estimates of the SFR (star-formation rate) or the total infrared luminosity from just one infrared band. However these relations are generally derived for entire galaxies, which are known to conta
in a large scale diffuse emission that is not necessarily related to the latest star-formation episode. We provide new relations to estimate the SFR from resolved star-forming regions at 100 mum and 160 mum. We select individual star-forming regions in the nearby (840 kpc) galaxy M33. We estimate the SFR combining the emission in Halpha and at 24 mum to calibrate the emission at 100 mum and 160 mum as SFR estimators, as mapped with PACS/Herschel. The data are obtained in the framework of the HERM33ES open time key project. There is less emission in the HII regions at 160 mum than at 100 mum. Over a dynamic range of almost 2 dex in Sigma(SFR) we find that the 100 mum emission is a nearly linear estimator of the SFR, whereas that at 160 mum is slightly superlinear. The behaviour of individual star-forming regions is surprisingly similar to that of entire galaxies. At high Sigma(SFR), star formation drives the dust temperature, whereas uncertainties and variations in radiation-transfer and dust-heated processes dominate at low Sigma(SFR). Detailed modelling of both galaxies and individual star forming regions will be needed to interpret similarities and differences between the two and assess the fraction of diffuse emission in galaxies.
To date the onset of large-scale star formation in galaxies and its link to gravitational stability of the galactic disk have not been fully understood. The nearby face-on spiral galaxy M51 is an ideal target for studying this subject. This paper com
bines CO, dust, HI, and stellar maps of M51 and its companion galaxy to study the H2/HI transition, the gas-to-dust ratios, and the stability of the disk against gravitational collapse. We combine maps of the molecular gas using 12CO 2--1 map HERA/IRAM-30m data and HI VLA data to study the total gas surface density and the phase transition of atomic to molecular gas. The total gas surface density is compared to the dust surface density from 850 micron SCUBA data. Taking into account the velocity dispersions of the molecular and atomic gas, and the stellar surface densities derived from the 2MASS K-band survey, we derive the total Toomre Q parameter of the disk. The gas surface density in the spiral arms is approximately 2-3 higher compared to that of the interarm regions. The ratio of molecular to atomic surface density shows a nearly power-law dependence on the hydrostatic pressure P_hydro. The gas surface density distribution in M51 shows an underlying exponential distribution with a scale length of h_gas=7.6 kpc representing 55% of the total gas mass, comparable to the properties of the exponential dust disk. In contrast to the velocity widths observed in HI, the CO velocity dispersion shows enhanced line widths in the spiral arms compared to the interarm regions. The contribution of the stellar component in the Toomre Q-parameter analysis is significant and lowers the combined Q-parameter Q_tot by up to 70% towards the threshold for gravitational instability. The value of Q_tot varies from 1.5-3 in radial averages. A map of Q_tot shows values around 1 on the spiral arms.
