- δSi is a small area of a true surface, in terms that luminosity goes outside of one side of this surface. Then we can use that - δLi = δSσTi⁴ is the total luminosity of that small area of a true surface - d is a distance to an “observing” sphere δLi will be smeared over semi-sphere while producing energy density δfi = δLi/(2πd²). δLi = δSiσTi⁴ = 2pid²δfi At that sphere, total luminosity will be summation over all small true surfaces L = ∑iδSiσTi⁴ = 4πR²σT⁴. And from one side the area of a cell is πR². Here factor of 4 is justified. But if that is not a sphere but per say an accretion disk, total produced luminosity on the both sides of the disk is L = 2πRd²σT⁴ = ∑Ai, cellσT⁴. So, factor is 2 if you looked from one side, but infinity if one looks and integrated from an edge of the disk. If an object is a cube, L = 6a²σT⁴ = ∑Ai, cellσT⁴. Factor is 6 if one is looking from one side.
We compare the properties of giant molecular associations in the galaxy Messier 100 (M100) with those of the less massive giant molecular clouds in the Milky Way and Local Group, while also observing how those properties change within M100 itself. From this analysis of cloud mass, radius, and velocity dispersion, we determine that the clouds are in or near virial equilibrium and that their properties are consistent with the underlying trends for the Milky Way. We find differences between nuclear, arm and inter-arm M100 populations, such as the nuclear clouds being the most massive and turbulent, and arm and inter-arm populations having differently shaped mass distributions from one another. Through the analysis of velocity gradients, cloud motion can be attributed to turbulence rather than large scale shearing motion. This is supported by our comparison with turbulence regulated star formation models. Finally, we calculate ISM depletion times to see how quickly clouds turn gas into stars and found that clouds form stars more efficiently if they are turbulent or dense.
ABSTRACT The work of identified characteristic mass scales in the mass distributions of young massive clusters in the nearby galaxy M83. Here, here we present a cloud-based analysis of ALMA CO(1 → 0) data to search for such characteristic mass scales in the molecular cloud population. We identify a population of molecular clouds in M83 that is largely similar to those found in the Milky Way and Local Group galaxies, however clouds in the center of the galaxy show high surface densities and enhanced turbulence, as is common for clouds in high density nuclear environments. Like the work on young massive clusters, we find a characteristic mass scale for the populations that decreases radially in the galaxy. We find the most massive young massive cluster tracks the most massive molecular cloud radially with the cluster mass being ∼0.01 that of the most massive molecular cloud. The maximum mass of the molecular cloud distribution also corresponds well to the value expected from shear instabilities, particularly in regions outside the nuclear and bar regions, where our simple shear model is inappropriate. Outside the nuclear region of M83 (Rgal > 0.5), there is no evidence for changing internal conditions in the population of molecular clouds, with the average internal pressures, densities, and free-fall times remaining constant for the cloud population over the galaxy. Thus, the observed variation in the fraction of star formation that results in bound clusters must result from the changing fragmentation process of the molecular gas.
All molecular clouds are observed to be turbulent, but the origin, means of sustenance, and evolution of the turbulence remain debated. One possibility is that stellar feedback injects enough energy into the cloud to drive observed motions on parsec scales. Recent numerical studies of molecular clouds have found that feedback from stars, such as protostellar outflows and winds, injects energy and impacts turbulence. We expand upon these studies by analyzing magnetohydrodynamic simulations of winds interacting with molecular clouds which vary the stellar mass-loss rates and magnetic field strength. We generate synthetic ¹²CO(1-0) maps assuming that the simulations are at the distance of the nearby Perseus molecular cloud. By comparing the outputs from different initial conditions and evolutionary times, we identify differences in the synthetic observations and characterize these using common astrostatistics. We quantify the different statistical responses using a variety of metrics proposed in the literature. We find that multiple astrostatistics, such as principle component analysis, velocity component spectrum, and dendrograms, are sensitive to changes in stellar mass-loss rates and/or magnetic field strength. This demonstrates that stellar feedback influences molecular cloud turbulence and can be identified and quantified observationally using such statistics.
We have performed a series of rock physics measurements under various simulate confining and pore pressure and temperature states to test the seismic response of two tight reservoir samples of the sedimentary basin of the St. Lawrence Lowlands to different CO₂ phases. Results show that the seismic velocity and amplitude can be used to detect the CO₂ phase transition. Laboratory measurements were used to calibrate a stochastic geological model that was used to generate synthetic seimograms reproducing the response to CO₂ injection in the reservoir formations. The modeled CO₂ injection scenario included 15 years of injection followed by 35 years of CO₂ migration. Synthetic time-lapse seismograms were produced after 5, 15 and 50 years form the start of injection. Results show that substitution of brine by CO₂ is responsible of a time-delay in the seismic traces despite very low reservoir permeabilities and porosities. A comparison between a classical blocky model and our stochastic model shows that the blocky model leads to a misinterpretation of the CO₂ effect on the seismic response. Keywords: CO₂, ultrasonic measurements, seismic modeling, time-lapse VSP, low porosity sandstones, CO₂ injection modeling