Surface Impedance Determination via Numerical Resolution of the Inverse Helmholtz Problem

Assigning boundary conditions, such as acoustic impedance, to the frequency domain thermoviscous wave equations (TWE), derived from the linearized Navier-Stokes equations (LNSE) poses a Helmholtz problem, solution to which yields a discrete set of complex eigenfunctions and eigenvalue pairs. The proposed method -- the inverse Helmholtz solver (iHS) -- reverses such procedure by returning the value of acoustic impedance at one or more unknown impedance boundaries (IBs) of a given domain, via spatial integration of the TWE for a given real-valued frequency with assigned conditions on other boundaries. The iHS procedure is applied to a second-order spatial discretization of the TWEs on an unstructured staggered grid arrangement. Only the momentum equation is extended to the center of each IB face where pressure and velocity components are co-located and treated as unknowns. The iHS is finally closed via assignment of the surface gradient of pressure phase over the IBs, corresponding to assigning the shape of the acoustic waveform at the IB. The iHS procedure can be carried out independently for different frequencies, making it embarrassingly parallel, and able to return the complete broadband complex impedance distribution at the IBs in any desired frequency range to arbitrary numerical precision. The iHS approach is first validated against Rott's theory for viscous rectangular and circular ducts. The impedance of a toy porous cavity with a complex geometry is then reconstructed and validated with companion fully compressible unstructured Navier-Stokes simulations resolving the cavity geometry. Verification against one-dimensional impedance test tube calculations based on time-domain impedance boundary conditions (TDIBC) is also carried out. Finally, results from a preliminary analysis of a thermoacoustically unstable cavity are presented.Comment: As submitted to AIAA Aviation 201

Numerical Solver for Multiphase Flows

The technological development of micro-scale electronic devices is bounded by the challenge of dissipating their heat output. Latent heat absorbed by a fluid during phase transition offers exceptional cooling capabilities while allowing for the design of compact heat exchangers. The understanding of heat transport dynamics in the context of multiphase flow physics is hampered by the limited access to detailed flow features offered by experimental measurements. Computational Fluid Dynamics (CFD) can overcome such difficulties by providing a complete description of the three-dimensional instantaneous flow field. Unfortunately, the majority of the numerical investigations in this field at Purdue are carried out with closed-source commercial CFD software which is computationally inefficient, (financially) expensive, and allows for extremely limited algorithmic development. The goal of this project is to initiate the development of an in-house code at Purdue that can simulate multiphase-flow physics that can exploit state-of-the-art supercomputing architectures, performing very large-size computations in a cost-efficient way. A first step has been the development of a simple 2D Python toy code relying on the volume of fluid (VOF) method coupled with a continuum surface force model (CSF), which treats surface tension effects as a localized body force. Results are compared with companion simulations carried out with the commercial software Fluent, revealing a noticeable improvement in the quality of the solution and a reduced computational cost. Future works involves the implementation of interface tracking methods and the extension of an existing highly-parallelized 3D incompressible Navier-Stokes code to include multi-phase problem capabilities

Self-Regulated Growth of Supermassive Black Holes in Galaxies as the Origin of the Optical and X-ray Luminosity Functions of Quasars

We postulate that supermassive black-holes grow in the centers of galaxies until they unbind the galactic gas that feeds them. We show that the corresponding self-regulation condition yields a correlation between black-hole mass (Mbh) and galaxy velocity dispersion (sigma) as inferred in the local universe, and recovers the observed optical and X-ray luminosity functions of quasars at redshifts up to z~6 based on the hierarchical evolution of galaxy halos in a Lambda-CDM cosmology. With only one free parameter and a simple algorithm, our model yields the observed evolution in the number density of optically bright or X-ray faint quasars between 2<z<6 across 3 orders of magnitude in bolometric luminosity and 3 orders of magnitude in comoving density per logarithm of luminosity. The self-regulation condition identifies the dynamical time of galactic disks during the epoch of peak quasar activity (z~2.5) as the origin of the inferred characteristic quasar lifetime of ~10 million years. Since the lifetime becomes comparable to the Salpeter e-folding time at this epoch, the model also implies that the Mbh-sigma relation is a product of feedback regulated accretion during the peak of quasar activity. The mass-density in black-holes accreted by that time is consistent with the local black-hole mass density of ~(0.8-6.3) times 10^5 solar masses per cubic Mpc, which we have computed by combining the Mbh-sigma relation with the measured velocity dispersion function of SDSS galaxies (Sheth et al.~2003). Applying a similar self-regulation principle to supernova-driven winds from starbursts, we find that the ratio between the black hole mass and the stellar mass of galactic spheroids increases with redshift as (1+z)^1.5 although the Mbh-sigma relation is redshift-independent.Comment: 10 pages, 5 figures, submitted to Ap

Looking for Distributed Star Formation in L1630: A Near-infrared (J, H, K) Survey

We have carried out a simultaneous, multi-band (J, H, K) survey over an area of 1320 arcmin^2 in the L1630 region, concentrating on the region away from the dense molecular cores and with modest visual extinctions (\leq 10 mag). Previous studies found that star formation in L1630 occurs mainly in four localized clusters, which in turn are associated with the four most massive molecular cores (Lada et al. 1991; Lada 1992). The goal of this study is to look for a distributed population of pre-main-sequence stars in the outlying areas outside the known star-forming cores. More than 60% of the pre-main-sequence stars in the active star forming regions of NGC 2024 and NGC 2023 show a near-infrared excess in the color-color diagram. In the outlying areas of L1630, excluding the known star forming regions, we found that among 510 infrared sources with the near-infrared colors ((J-H) and (H-K)) determined and photometric uncertainty at K better than 0.10 mag, the fraction of the sources with a near-infrared excess is 3%--8%; the surface density of the sources with a near-infrared excess is less than half of that found in the distributed population in L1641, and 1/20 of that in the young cluster NGC 2023. This extremely low fraction and low surface density of sources with a near-infrared excess strongly indicates that recent star formation activity has been very low in the outlying region of L1630. The sources without a near-infrared excess could be either background/foreground field stars, or associated with the cloud, but formed a long time ago (more than 2 Myrs). Our results are consistent with McKee's model of photoionization-regulated star formation.Comment: 30 pages, 10 figures To appear in ApJ Oct 1997, Vol 48

The Variation of Integrated Star IMFs among Galaxies

The integrated galaxial initial mass function (IGIMF) is the relevant distribution function containing the information on the distribution of stellar remnants, the number of supernovae and the chemical enrichment history of a galaxy. Since most stars form in embedded star clusters with different masses the IGIMF becomes an integral of the assumed (universal or invariant) stellar IMF over the embedded star-cluster mass function (ECMF). For a range of reasonable assumptions about the IMF and the ECMF we find the IGIMF to be steeper (containing fewer massive stars per star) than the stellar IMF, but below a few Msol it is invariant and identical to the stellar IMF for all galaxies. However, the steepening sensitively depends on the form of the ECMF in the low-mass regime. Furthermore, observations indicate a relation between the star formation rate of a galaxy and the most massive young stellar cluster in it. The assumption that this cluster mass marks the upper end of a young-cluster mass function leads to a connection of the star formation rate and the slope of the IGIMF above a few Msol. The IGIMF varies with the star formation history of a galaxy. Notably, large variations of the IGIMF are evident for dE, dIrr and LSB galaxies with a small to modest stellar mass. We find that for any galaxy the number of supernovae per star (NSNS) is suppressed relative to that expected for a Salpeter IMF. Dwarf galaxies have a smaller NSNS compared to massive galaxies. For dwarf galaxies the NSNS varies substantially depending on the galaxy assembly history and the assumptions made about the low-mass end of the ECMF. The findings presented here may be of some consequence for the cosmological evolution of the number of supernovae per low-mass star and the chemical enrichment of galaxies of different mass.Comment: 27 pages, accepted for publication by Ap

Large Area Mapping at 850 Microns. V. Analysis of the Clump Distribution in the Orion A South Molecular Cloud

We present results from a 2300 arcmin^2 survey of the Orion A molecular cloud at 450 and 850 micron using the Submillimetre Common-User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope. The region mapped lies directly south of the OMC1 cloud core and includes OMC4, OMC5, HH1/2, HH34, and L1641N. We identify 71 independent clumps in the 850 micron map and compute size, flux, and degree of central concentration in each. Comparison with isothermal, pressure-confined, self-gravitating Bonnor-Ebert spheres implies that the clumps have internal temperatures T_d ~ 22 +/- K and surface pressures log (k^-1 P cm^-3 K) = 6.0 +/- 0.2. The clump masses span the range 0.3 - 22 Msun assuming a dust temperature T_d ~ 20 K and a dust emissivity kappa_850 = 0.02 cm^2 g^-1. The distribution of clump masses is well characterized by a power-law N(M) propto M^-alpha with alpha = 2.0 +/- 0.5 for M > 3.0 Msun, indicating a clump mass function steeper than the stellar Initial Mass Function. Significant incompleteness makes determination of the slope at lower masses difficult. A comparison of the submillimeter emission map with an H_2 2.122 micron survey of the same region is performed. Several new Class 0 sources are revealed and a correlation is found between both the column density and degree of concentration of the submillimeter sources and the likelihood of coincident H_2 shock emission.Comment: 44 pages, 17 figures, accepted by Ap

The Stellar Populations and Evolution of Lyman Break Galaxies

Using deep near-IR and optical observations of the HDF-N from the HST NICMOS and WFPC2 and from the ground, we examine the spectral energy distributions (SEDs) of Lyman break galaxies (LBGs) at 2.0 < z < 3.5. The UV-to-optical rest-frame SEDs of the galaxies are much bluer than those of present-day spiral and elliptical galaxies, and are generally similar to those of local starburst galaxies with modest amounts of reddening. We use stellar population synthesis models to study the properties of the stars that dominate the light from LBGs. Under the assumption that the star-formation rate is continuous or decreasing with time, the best-fitting models provide a lower bound on the LBG mass estimates. LBGs with ``L*'' UV luminosities are estimated to have minimum stellar masses ~ 10^10 solar masses, or roughly 1/10th that of a present-day L* galaxy. By considering the effects of a second component of maximally-old stars, we set an upper bound on the stellar masses that is ~ 3-8 times the minimum estimate. We find only loose constraints on the individual galaxy ages, extinction, metallicities, initial mass functions, and prior star-formation histories. We find no galaxies whose SEDs are consistent with young (< 10^8 yr), dust-free objects, which suggests that LBGs are not dominated by ``first generation'' stars, and that such objects are rare at these redshifts. We also find that the typical ages for the observed star-formation events are significantly younger than the time interval covered by this redshift range (~ 1.5 Gyr). From this, and from the relative absence of candidates for quiescent, non-star-forming galaxies at these redshifts in the NICMOS data, we suggest that star formation in LBGs may be recurrent, with short duty cycles and a timescale between star-formation events of < 1 Gyr. [Abridged]Comment: LaTeX, 37 pages, 21 figures. Accepted for publication in the Astrophysical Journa

On the Similarity between Cluster and Galactic Stellar Initial Mass Functions

The stellar initial mass functions (IMFs) for the Galactic bulge, the Milky Way, other galaxies, clusters of galaxies, and the integrated stars in the Universe are composites from countless individual IMFs in star clusters and associations where stars form. These galaxy-scale IMFs, reviewed in detail here, are not steeper than the cluster IMFs except in rare cases. This is true even though low mass clusters generally outnumber high mass clusters and the average maximum stellar mass in a cluster scales with the cluster mass. The implication is that the mass distribution function for clusters and associations is a power law with a slope of -2 or shallower. Steeper slopes, even by a few tenths, upset the observed equality between large and small scale IMFs. Such a cluster function is expected from the hierarchical nature of star formation, which also provides independent evidence for the IMF equality when it is applied on sub-cluster scales. We explain these results with analytical expressions and Monte Carlo simulations. Star clusters appear to be the relaxed inner parts of a widespread hierarchy of star formation and cloud structure. They are defined by their own dynamics rather than pre-existing cloud boundaries.Comment: 22 pages, 2 figures, ApJ, 648, in press, September 1, 200

How many young star clusters exist in the Galactic center?

We study the evolution and observability of young compact star clusters within about 200pc of the Galactic center. Calculations are performed using direct N-body integration on the GRAPE-4, including the effects of both stellar and binary evolution and the external influence of the Galaxy. The results of these detailed calculations are used to calibrate a simplified model applicable over a wider range of cluster initial conditions. We find that clusters within 200 pc from the Galactic center dissolve within about 70 Myr. However, their projected densities drop below the background density in the direction of the Galactic center within 20 Myr, effectively making these clusters undetectable after that time. Clusters farther from the Galactic center but at the same projected distance are more strongly affected by this selection effect, and may go undetected for their entire lifetimes. Based on these findings, we conclude that the region within 200 pc of the Galactic center could easily harbor some 50 clusters with properties similar to those of the Arches or the Quintuplet systems.Comment: ApJ Letters in pres

The M/L ratio of massive young clusters

We point out a strong time-evolution of the mass-to-light conversion factor \eta commonly used to estimate masses of dense star clusters from observed cluster radii and stellar velocity dispersions. We use a gas-dynamical model coupled with the Cambridge stellar evolution tracks to compute line-of-sight velocity dispersions and half-light radii weighted by the luminosity. Stars at birth are assumed to follow the Salpeter mass function in the range [0.15--17 M_\sun]. We find that $\eta$, and hence the estimated cluster mass, increases by factors as large as 3 over time-scales of 20 million years. Increasing the upper mass limit to 50 M_\sun leads to a sharp rise of similar amplitude but in as little as 10 million years. Fitting truncated isothermal (Michie-King) models to the projected light profile leads to over-estimates of the concentration par ameter c of $\delta c\approx 0.3$ compared to the same functional fit applied to the proj ected mass density.Comment: Draft version of an ApJ lette