Average Expansion Velocity Research Articles

Slip distribution of the 11 March 2011 Tohoku-Oki earthquake (Mw 9.0) inferred from the refined homomorphic deconvolution method

The kinematic rupture process of the 2011 Tohoku-Oki earthquake (Mw 9.0) was derived given apparent source time functions (ASTFs) retrieved from Rayleigh waves using a refined homomorphic deconvolution method. The total duration of the rupture process was about 165s. Three slip-concentrated areas were identified based on images of static slip distribution. The largest asperity, located up-dip from the hypocenter with an area of 250km×110km extending to the trench on the fault, had a maximum slip of about 54m. The other asperities with smaller slip down-dip from the hypocenter were centered on the north and south of the hypocenter, respectively. The preferred average rupture expansion velocity was 1.2km/s within 130km from the hypocenter and up to 2.3km/s over other areas on the fault. Thus, the region near the vicinity of the hypocenter with lower rupture velocity had higher slip amplitude, strongly suggesting brittle failure on a high friction fault. Based on ASTF results, our proposed method offers another way of directly detecting the kinematic source parameters of earthquakes.

EXPANDED VERY LARGE ARRAY OBSERVATIONS OF THE RADIO EVOLUTION OF SN 2011dh

We report on Expanded Very Large Array (EVLA) observations of the Type IIb supernova 2011dh, performed over the first 100 days of its evolution and spanning 1-40 GHz in frequency. The radio emission is well-described by the self-similar propagation of a spherical shockwave, generated as the supernova ejecta interact with the local circumstellar environment. Modeling this emission with a standard synchrotron self-absorption (SSA) model gives an average expansion velocity of v \approx 0.1c, supporting the classification of the progenitor as a compact star (R_* \approx 10^11 cm). We find that the circumstellar density is consistent with a {\rho} \propto r^-2 profile. We determine that the progenitor shed mass at a constant rate of \approx 3 \times 10^-5 M_\odot / yr, assuming a wind velocity of 1000 km / s (values appropriate for a Wolf-Rayet star), or \approx 7 \times 10^-7 M_\odot / yr assuming 20 km / s (appropriate for a yellow supergiant [YSG] star). Both values of the mass-loss rate assume a converted fraction of kinetic to magnetic energy density of {\epsilon}_B = 0.1. Although optical imaging shows the presence of a YSG, the rapid optical evolution and fast expansion argue that the progenitor is a more compact star - perhaps a companion to the YSG. Furthermore, the excellent agreement of the radio properties of SN 2011dh with the SSA model implies that any YSG companion is likely in a wide, non-interacting orbit.

Very intense geomagnetic storms and their relation to interplanetary and solar active phenomena

We revisit previous studies in which the characteristics of the solar and interplanetary sources of intense geomagnetic storms have been discussed. In this particular analysis, using the Dst time series, we consider the very intense geomagnetic storms that occurred during Solar Cycle 23 by setting a value of Dstmin⩽-200nT as threshold. After carefully examining the set of available solar and in situ observations from instruments aboard the Solar and Heliospheric Observatory (SOHO) and the Advanced Composition Explorer (ACE), complemented with data from the ground, we have identified and characterized the solar and interplanetary sources of each storm. That is to say, we determine the time, angular width, plane-of-the-sky, lateral expansion, and radial velocities of the source coronal mass ejection (CME), the type and heliographic location of the CME solar source region (including the characteristics of the sunspot groups), and the time duration of the associated flare. After this, we investigate the overall characteristics of the interplanetary (IP) main-phase storm driver, including the time arrival of the shock/disturbance at 1AU, the type of associated IP structure/ejecta, the origin of a prolonged and enhanced southward component (Bs) of the IP field, and other characteristics related to the energy injected into the magnetosphere during the storm (i.e. the solar wind maximum convected electric field, Ey). The analyzed set consists of 20 events, some of these are complex and present two or more Dst minima that are, in general, due to consecutive solar events. The 20 storms are distributed along Solar Cycle 23 (which is a double-peak cycle) in such a way that 15% occurs during the rising phase of the cycle, 45% during both cycle maxima, and, surprisingly, 40% during the cycle descending phase. This latter set includes half of the superstorms and the only cycle extreme event. 85% of the storms are associated to full halo CMEs and 10% to partial halo events. One of the storms occurred at the time contact with SOHO was lost. The CME solar sources of all analyzed storms, but one, are active regions (ARs). The source of the remaining CME is a bipolar low-field region where a long and curved filament erupts. The ARs where the CMEs originate show, in general, high magnetic complexity; δ spots are present in 74% of the ARs, 10% are formed by several bipolar sunspot groups, and only 16% present a single bipolar sunspot group. All CMEs are associated to long duration events (LDEs), exceeding 3h in all cases, with around 75% lasting more than 5h. The associated flares are, in general, intense events, classified as M or X in soft X-rays; only 3 of them fall in the C class, with the one happening in the bipolar low field region hardly reaching the C level. We calculate the lateral expansion velocity for most of the CMEs. The values found exceed in all cases but one the fast solar wind speed (≈750kms−1). The average lateral expansion velocity is 2400kms−1. The spatial distribution of the solar CME sources on the solar disk shows an evident asymmetry; while there are no sources located more eastward than 12° in longitude, there are 7 events more westward than 12°. Nevertheless, the bulk of the solar sources are located near Sun center, i.e. at less than 20° in longitude or latitude. Considering the IP structures responsible for a long and enhanced Bs, we find that 35% correspond to magnetic clouds (MCs) or ICME fields, 30% to sheath fields, and 30% to combined sheath and MC or ICME fields. For only one storm the origin of Bs is related to the back compression of an ICME by a high speed stream coming from a coronal hole in the neighborhood of the corresponding CME source region. We have also found that for this particular set of storms the linear relation between Ey and the storm intensity holds (with a correlation coefficient of 0.73). These results complement and extend those of other works in the literature.

EXPANSION VELOCITY OF EJECTA IN TYCHO's SUPERNOVA REMNANT MEASURED BY DOPPLER BROADENED X-RAY LINE EMISSION

We show that the expansion of ejecta in Tycho's supernova remnant (SNR) is consistent with a spherically symmetric shell, based on Suzaku measurements of the Doppler broadened X-ray emission lines. All the strong K_alpha line emission show broader widths at the center than at the rim, while the centroid energies are constant across the remnant (except for Ca). This is the pattern expected for Doppler broadening due to expansion of the SNR ejecta in a spherical shell. To determine the expansion velocities of the ejecta, we applied a model for each emission line feature having two Gaussian components separately representing red- and blue-shifted gas, and inferred the Doppler velocity difference between these two components directly from the fitted centroid energy difference. Taking into account the effect of projecting a three-dimensional shell to the plane of the detector, we derived average spherical expansion velocities independently for the K_alpha emission of Si, S, Ar, and Fe, and K_beta of Si. We found that the expansion velocities of Si, S, and Ar ejecta of 4700+/-100 km/s are distinctly higher than that obtained from Fe K_alpha emission, 4000+/-300 km/s, which is consistent with segregation of the Fe in the inner ejecta. Combining the observed ejecta velocities with the ejecta proper-motion measurements by Chandra, we derived a distance to the Tycho's SNR of 4+/-1 kpc.

Is there a mildly relativistic jet in SN2007gr?

AbstractSN2007gr was an ordinary type Ic supernova, with a hint of asymmetric explosion seen in the optical polarization spectrum. This type of SNe is occasionally associated with long duration gamma-ray bursts which generate ultra-relativistic jets; no relativistic outflows have yet been found by direct imaging in SNe Ib/c explosions. High resolution very long baseline interferometry (VLBI) data and simultaneous total radio flux density measurements indicated that SN2007gr has expanded mildly relativistically. We performed late time Westerbork Synthesis Radio Telescope (WSRT) observations to measure the level of the underlying extended emission. Comparison of the VLBI and the background-subtracted WSRT and independent VLA data indicate an at least partially resolved source with an average expansion velocity of ≥0.4c, although the VLBI data could be consistent with a fainter source with an expansion velocity of ~0.2c as well.

A mildly relativistic radio jet from the otherwise normal type Ic supernova 2007gr

The class of type Ic supernovae have drawn increasing attention since 1998 owing to their sparse association (only four so far) with long duration gamma-ray bursts (GRBs). Although both phenomena originate from the core collapse of a massive star, supernovae emit mostly at optical wavelengths, whereas GRBs emit mostly in soft gamma-rays or hard X-rays. Though the GRB central engine generates ultra-relativistic jets, which beam the early emission into a narrow cone, no relativistic outflows have hitherto been found in type Ib/c supernovae explosions, despite theoretical expectations and searches. Here we report radio (interferometric) observations that reveal a mildly relativistic expansion in a nearby type Ic supernova, SN 2007gr. Using two observational epochs 60 days apart, we detect expansion of the source and establish a conservative lower limit for the average apparent expansion velocity of 0.6c. Independently, a second mildly relativistic supernova has been reported. Contrary to the radio data, optical observations of SN 2007gr indicate a typical type Ic supernova with ejecta velocities approximately 6,000 km s(-1), much lower than in GRB-associated supernovae. We conclude that in SN 2007gr a small fraction of the ejecta produced a low-energy mildly relativistic bipolar radio jet, while the bulk of the ejecta were slower and, as shown by optical spectropolarimetry, mildly aspherical.

Nonstationarity of the α CYG atmosphere: IV. Some peculiarities of time variation in line profiles

We use 240 CCD spectra taken in 1998–2000 with the coude echelle spectrograph of the 2-m telescope of the National Academy of Sciences of Azerbaijan to study temporal radial velocity and line profile variations of the ion, HeI, and Hβ lines in the spectrumof the α Cyg supergiant. We demonstrate that these variations are caused by pulsation-type motions in the star’s atmosphere. Ion and HeI lines oscillate in the main fundamental mode with a period of about 12.0 ± 0.5d and an amplitude of 5.0 ± 0.5 km/s. These ion-line oscillations continue for about 35 days. Then the difference between the radial velocities of strong and weak ion lines results in a gradual decay of oscillations over a time interval of about 5.0 ± 1.0d. Thereafter the process repeats itself. For the Hβ line we found two significant periods, two amplitudes, and three characteristic radial velocity variability behaviors for the blue and red halves of the absorption profile: with equal variability parameters (period P and amplitude A); with equal P and A, but with a phase shift between the radial velocity variations of the blue and red halves of the absorption profile; with different P and A for the two halves of the absorption profile. The star’s center of mass radial velocity as inferred from the γ-velocity is −4.5 ± 0.5 km/s. The average expansion velocity of the atmospheric layers, where the Hβ line forms, amounts to about −16.5 ± 0.5 km/s and varies temporally with an amplitude of about 3.0 km/s.

IMPROVED DISTANCES TO TYPE Ia SUPERNOVAE WITH TWO SPECTROSCOPIC SUBCLASSES

We study the observables of 158 relatively normal Type Ia supernovae (SNe Ia) by dividing them into two groups in terms of the expansion velocity inferred from the absorption minimum of the Si II ?6355 line in their spectra near B-band maximum brightness. One group (Normal) consists of normal SNe Ia populating a narrow strip in the Si II velocity distribution, with an average expansion velocity v = 10, 600 ? 400 km?s?1 near B maximum; the other group (HV) consists of objects with higher velocities, v 11, 800 km s?1. Compared with the Normal group, the HV one shows a narrower distribution in both the peak luminosity and the luminosity decline rate ?m 15. In particular, their B?V colors at maximum brightness are found to be on average redder by ~ 0.1 mag, suggesting that they either are associated with dusty environments or have intrinsically red B?V colors. The HV SNe Ia are also found to prefer a lower extinction ratio RV 1.6 (versus ~ 2.4 for the Normal ones). Applying such an absorption-correction dichotomy to SNe Ia of these two groups remarkably reduces the dispersion in their peak luminosity from 0.178 mag to only 0.125 mag.

23 GHz VLBI observations of SN 2008ax

We report on phase-referenced 23 GHz Very-Long-Baseline-Interferometry (VLBI) observations of the type IIb supernova SN 2008ax, made with the Very Long Baseline Array (VLBA) on 2 April 2008 (33 days after explosion). These observations resulted in a marginal detection of the supernova. The total flux density recovered from our VLBI image is 0.8 <i>±<i/> 0.3 mJy (one standard deviation). As it appears, the structure may be interpreted as either a core-jet or a double source. However, the supernova structure could be somewhat confused with a possible close by noise peak. In such a case, the recovered flux density would decrease to 0.48 <i>±<i/> 0.12 mJy, compatible with the flux densities measured with the VLA at epochs close in time to our VLBI observations. The lowest average expansion velocities derived from our observations are (1.90 <i>±<i/> 0.30) 10<sup>5<sup/> km s<sup>-1<sup/> (case of a double source) and (5.2 <i>±<i/> 1.3) 10<sup>4<sup/> km s<sup>-1<sup/> (taking the weaker source component as a spurious, close by, noise peak, which is the more likely interpretation). These velocities are 7.3 and 2 times higher, respectively, than the maximum ejecta velocity inferred from optical-line observations.

Optical Imaging and Spectroscopy of the Galactic Supernova Remnant 3C 58 (G130.7+3.1)

We present a comprehensive imaging and spectroscopic survey of optical emission knots associated with the young Galactic supernova remnant 3C 58. Hα images show hundreds of clumpy filaments and knots arranged in a complex structure covering a nearly circular area roughly 400'' in diameter. A quite different emission structure is seen in [O III], where the brightest features are less clumpy and largely confined to the remnant's northwest quadrant. Measured radial velocities of over 450 knots reveal two distinct kinematic populations; one with average and peak expansion velocities of 770 and 1100 km s−1, respectively, forming a thick shell, and the other showing |v| ≤ 250 km s−1. High-velocity knots (|v| ≥ 500 km s−1) exhibit a strong bipolar expansion pattern with redshifted and blueshifted knots located in northeastern and southwestern regions, respectively. These knots also show strong [N II]/Hα line emission ratios, suggesting enhanced N/H. In contrast, the slower expanding knot population shows much lower [N II]/Hα line ratios and likely represents circumstellar mass loss material from the 3C 58 progenitor. Proper-motion estimates using images spanning a 28 yr time interval suggest positional shifts of between 0.5'' and 2.0'', implying proper motions of 0.02''-0.07'' yr−1. These values agree with previous estimates but are much less than the ≈0.2'' yr−1 expected if 3C 58 were associated with historic guest star of 1181 CE.

Time-resolved measurements of desorbed gas during 1-MeVK+pulsed beam deposition in a stainless steel target

Measurements were made of the density, species, and velocity of the desorbed gas cloud on intense ${\mathrm{K}}^{+}$ beam bombardment of a stainless steel target. Residual gas analyzer measurements indicate that the gas cloud consists of predominantly ${\mathrm{H}}_{2}$. Energy analyzer measurements of doubly ionized beam ions show that the ratio of hydrogen gas production to beam density was approximately $3000\text{ }\text{ }\mathrm{\text{molecules}}/\mathrm{\text{ion}}$ at normal incidence. Optical measurements of the evolution of the gas cloud during the beam pulse show a distribution with an average expansion velocity of about $0.5\text{ }\text{ }\mathrm{mm}/\ensuremath{\mu}\mathrm{s}$. Comparison is made with a simple model of the gas cloud behavior.

The Chemical Distribution in a Subluminous Type Ia Supernova:Hubble Space TelescopeImages of the SN 1885 Remnant

SN 1885 was a probable subluminous SN Ia that occurred in the bulge of the Andromeda galaxy, M31, at a projected location 16'' from the nucleus. Here we present and analyze Hubble Space Telescope images of the SN 1885 remnant seen in absorption against the M31 bulge via the resonance lines of Ca I, Ca II, Fe I, and Fe II. Viewed in Ca II H and K line absorption, the remnant appears as a nearly black circular spot with an outermost angular radius of 0.40'' ± 0.025'', implying a maximum linear radius of 1.52 ± 0.15 pc at M31's estimated distance of 785 ± 30 kpc and hence a 120 yr average expansion velocity of 12,400 ± 1400 km s-1. The strongest Ca II absorption is organized in a broken ring structure with a radius of 0.2'' (=6000 km s-1) with several apparent absorption "clumps" of an angular size around that of the image pixel scale of 0.05'' (=1500 km s-1). Ca I and Fe I absorption structures appear similar except for a small Fe I absorption peak displaced 0.1'' off-center of the Ca II structure by a projected velocity of about 3000 km s-1. Analyses of these images using off-center, delayed-detonation models suggest a low 56Ni production similar to the subluminous SN Ia explosion of SN 1986G. The strongly lopsided images of Ca I and Fe I can be understood as resulting from an aspherical chemical distribution, with the best agreement found using an off-center model viewed from an inclination of ~60°. The images require a central region of no or little Ca but with iron group elements indicative for burning under sufficiently high densities for electron capture to take place, i.e., burning prior to a significant preexpansion of the WD.

Time scales of membrane fusion revealed by direct imaging of vesicle fusion with high temporal resolution

Membrane fusion is a vital process of life involved, for example, in cellular secretion via exocytosis, signaling between nerve cells, and virus infection. In both the life sciences and bioengineering, controlled membrane fusion has many possible applications, such as drug delivery, gene transfer, chemical microreactors, or synthesis of nanomaterials. Until now, the fusion dynamics has been elusive because direct observations have been limited to time scales that exceed several milliseconds. Here, the fusion of giant lipid vesicles is induced in a controlled manner and monitored with a temporal resolution of 50 micros. Two different fusion protocols are used that are based on synthetic fusogenic molecules and electroporation. For both protocols, the opening of the fusion necks is very fast, with an average expansion velocity of centimeters per second. This velocity indicates that the initial formation of a single fusion neck can be completed in a few hundred nanoseconds.

Comparison of average radial expansion velocity from impacted liquid filled cylinders

In this paper, the average radial expansion velocity of an impacted fluid filled cylindrical target is investigated. Theoretical and numerical predictions of the radial expansion velocity are compared to the experimentally measured radial expansion velocity. The primary objective of this work is to assess the ability of these theoretical and numerical techniques to predict the radial expansion velocity. A secondary objective of this work is to quantify the effect of changes in dimensional scale on the radial expansion velocity and to construct a simple physics based model which incorporates these scaling effects. Two-dimensional numerical hydrocode simulations accurately predict the measured ejection velocity for tests with low projectile–target misalignment. However, three-dimensional numerical calculations, which account for this misalignment, accurately predict all experimental tests. A theoretical formulation, based on a simple conservation of energy principle, yields a zero-dimensional model which accurately predicts the two-dimensional hydrocode simulations. Thus for experimental simulations which have low projectile–target misalignment, the simple theoretical model developed here accurately predicts the average radial expansion velocity. A dimensional analysis of this theoretical formulation yields a scaling relationship which accurately predicts the effect of dimensional scale between two different experimental test series.

Expansion and Collapse in the Cosmic Web

We study the kinematics of the gaseous cosmic web at high redshift using Lyα forest absorption in multiple QSO sight lines. Observations of the projected velocity shifts between Lyα absorbers common to the lines of sight to a gravitationally lensed QSO and three more widely separated QSO pairs are used to directly measure the expansion of the cosmic web in units of the Hubble velocity, as a function of redshift and spatial scale. The lines of sight used span a redshift range from about 2 to 4.5 and represent transverse scales from the subkiloparsec range to about 300 h physical kpc. Using a simple analytic model and a cosmological hydrodynamic simulation, we constrain the underlying three-dimensional distribution of expansion velocities from the observed line-of-sight distribution of velocity shear across the plane of the sky. The shape of the shear distribution and its width (14.9 km s-1 rms for a physical transverse separation of 61 h kpc at z = 2, 30.0 km s-1 for 261 h kpc at z = 3.6) are found to be in good agreement with the IGM undergoing large-scale motions dominated by the Hubble flow, making this one of the most direct observations possible of the expansion of the universe. However, modeling the Lyα clouds with a simple expanding pancake model, the average expansion velocity of the gaseous structures causing the Lyα forest in the lower redshift (z ~ 2) smaller separation (61 kpc) sample appears about 20% lower than the local Hubble expansion velocity. In order to understand the observed velocity distribution further we investigated the statistical distribution of expansion velocities in cosmological Lyα forest simulations. The mean expansion velocity in the (z ~ 2, separation ~ 60 kpc) simulation is indeed somewhat smaller than the Hubble velocity, as found in the real data. We interpret this finding as tentative evidence for some Lyα forest clouds breaking away from the Hubble flow and undergoing the early stages of gravitational collapse. However, the distribution of velocities is highly skewed, and the majority of Lyα forest clouds at all redshifts from 2 to 3.8 expand with super-Hubble velocities, typically about 5%-20% faster than the Hubble flow. This behavior is explained if most Lyα forest clouds in the column density range typically detectable are expanding filaments that stretch and drain into more massive nodes. The significant difference seen in the velocity distributions between the high- and low-redshift samples may conceivably reflect actual peculiar deceleration, the differences in spatial scale, or our selecting higher densities at lower redshift for a given detection threshold for Lyα forest lines. We also investigate the alternative possibility that the velocity structure of the general Lyα forest could have an entirely different, local origin, as expected if the Lyα forest were produced or at least significantly modified by galactic feedback, e.g., winds from star-forming galaxies at high redshift. However, we find no evidence that the observed distribution of velocity shear is significantly influenced by processes other than Hubble expansion and gravitational instability. To avoid overly disturbing the IGM, galactic winds may be old and/or limp by the time we observe them in the Lyα forest, or they may occupy only an insignificant volume fraction of the IGM. We briefly discuss the observational evidence usually presented in favor of an IGM afflicted by high-redshift extragalactic superwinds and find much of it ambiguous. During the hierarchical buildup of structure, galaxies are expected to spill parts of their interstellar medium and to heat and stir the IGM in ways that make it hard to disentangle this gravitational process from the effects of winds.

Spectrophotometric Variability of Mira

Data from the Pulkovo spectrophotometric data base on the absolute quasimonochromatic fluxes from oCet in the 320–1080 nm range are used to determine the physical parameters of this star in different phases of its light curve. The continuum emission layer is found to expand between the phases of the cycle corresponding to the rising and falling branches of the light curve. The average expansion velocity is 32 km/s. By the time the star’s brightness has fallen by roughly three magnitudes, its radius has increased by almost a factor of three. Over this same time the temperature of the layer has fallen from 3000 K to 2200 K. For this expansion velocity, the calculated mass rate loss is ⊙ M /year.

The Nature of SN 1961V

The nature of SN 1961V has been uncertain. Its peculiar optical light curve and slow expansion velocity are similar to those of superoutbursts of luminous blue variables (LBVs), but its nonthermal radio spectral index and declining radio luminosity are consistent with decades-old supernovae (SNe). We have obtained Hubble Space Telescope STIS images and spectra of the stars in the vicinity of SN 1961V and find object 7 identified by Filippenko and coworkers to be closest to the optical and radio positions of SN 1961V. Object 7 is the only point source detected in our STIS spectra, and only its Hα emission is detected; it cannot be the SN or its remnant because of the absence of forbidden lines. While the Hα line profile of object 7 is remarkably similar to that of η Carinae, the blue color (similar to an A2 Ib supergiant) and lack of appreciable variability are unlike known postoutburst LBVs. We have also obtained Very Long Baseline Array observations of SN 1961V at 18 cm. The nondetection of SN 1961V places a lower limit on the size of the radio-emitting region, 7.6 mas or 0.34 pc, which implies an average expansion velocity in excess of 4400 km s-1, much higher than the optical expansion velocity measured in 1961. We conclude the following: (1) An SN occurred in the vicinity of SN 1961V a few decades ago. (2) If the SN 1961V light maximum originates from a giant eruption of a massive star, object 7 is the most probable candidate for the survivor, but its blue color and lack of significant variability are different from a postoutburst η Car. (3) The radio SN and object 7 could be physically associated with each other through a binary system. (4) Object 7 needs to be monitored to determine its nature and relationship to SN 1961V.

Study of angular dependences of ion component parameters in CO2-laser-produced plasma

CO2-laser-produced plasma ion component parameters were studied for aluminium and lead targets at laser intensity of P = 4×1013 W cm−2 and pulse duration of τ = 15 ns experimentally and numerically. Angular dependences of ion number density for different charge states, average velocity and its spread were measured by time-of-flight method. Ion charge state distribution shows high-charge and low-charge state groups at normal expansion direction. Ions in these groups have different average expansion velocity and longitudinal velocity spread. Angular distribution of high-charge states is narrower than that of the low-charge state ion group, maximum yield of low-charge states occur at some angle from normal. For Al target results show similar trends as for Pb target, but simulations have indicated that the effect of laser ponderomotive force is more pronounced in this case.

Millimetre observations of infrared carbon stars

Dust- and gas mass loss rates and distances are determined for a sample of about 330 infra-red carbon stars that probe a distance up to about 5.5 kpc. The dependence of the dust- and gas mass loss rates, and the expansion velocity upon galactic longitude (l) are studied. It is found that the expansion velocity significantly depends on l, but that the absolute bolometric magnitude, the dust mass loss rate and the gas-to-dust ratio depend on l marginally, if at all, and the gas mass loss rate does not depend on l. Beyond the solar circle, the expansion velocity (as well as the luminosity, dust-to-gas ratio, dust mass loss rate) is lower than inside the solar circle, as expected from the overall gradient in metallicity content of the Galaxy. Combining the average expansion velocity inside and beyond the solar circle with the theoretically predicted relation between expansion velocity and gas-to-dust ratio, we find that the metallicity gradient in the solar neighbourhood is about 0:034 dex/kpc, well within the quoted range of values in the literature.

Analyses of transverse momentum spectra in central C+C and C+Ta interactions at4.2A GeV/cbeam momentum within a collective flow model and a boundary model

The transverse momentum spectra of secondary ${\ensuremath{\pi}}^{\ensuremath{-}}$ mesons and participant protons in central C+C and C+Ta interactions at $4.2A$ GeV/c beam momentum have been analyzed within a collective flow model and a boundary model. All the particle spectra within a collective flow model at a given beam energy can be reproduced with a single set of intensive parameters for the initial state of fireball. As typical freeze-out parameters in this beam energy region we find a freeze-out temperature $T=(55--100) \mathrm{MeV},$ and an average transverse expansion velocity at freeze-out $〈\ensuremath{\beta}〉=0.30--0.39.$ The pion spectra within a boundary model including the quantum mechanical effects can be described well. To fit the proton spectra well, within a boundary model, one will need to introduce the transverse collective expansion.