Engineering topics

Tsai, John C.

Publications and source records attributed to Tsai, John C..

9 records

NASA NTRS1995

Protostellar Collapse with a Shock

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(exp -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Tsai, John C.↗

NASA NTRS1995

The reliability of X-ray constraints of intrinsic cluster shapes

Using the simulation of Katz & White (1993) we have tested the viability of X-ray analysis for constraining the intrinsic shapes of clusters of galaxies considering the effects of both substructure and steep temperature gradients. We restrict our analysis to the aggregate shapes of clusters on scales of r approximately 1-2 Mpc in order to reduce our sensitivity to subclustering in the core. For low redshifts (z less than or approximately = 0.25) the X-ray method accurately measures the true ellipticity of the three-dimensional cluster dark matter provided the inclination of the cluster is known to within approximately 30 deg; assuming the gas is isothermal adds only small errors to the derived shapes. At higher redshifts the X-ray method yields unreliable results since the gas does not trace the cluster gravitational potential. We proffer some necessary conditions for the reliability of X-ray methods characterized by both the amount of substructure in the X-ray surface brightness images and the shapes of the isophotes. We conclude that measurements of the aggregate shapes of clusters on scales r approximately 1-2 Mpc are insensitive to core substructure representing scales of a few hundred kpc. Therefore our results suggest that the X-ray measurements of aggregate cluster shapes by Fabricant, Rybicki, & Gorenstein (1984) and Buote & Canizares (1992) are valid provided that they do not suffer from serious projection effects. A substantial number of Abell clusters observed with the ROSAT PSPC will be amenable to X-ray shape analysis.

Buote, David A.↗

NASA NTRS1995

Interstellar grains in elliptical galaxies

We consider the evolution and heating of dust embedded in the hot interstellar medium of isolated elliptical galaxies. We first construct a new set of galaxy models spanning a decade in luminosity which we use to study the evolution of dust as it is ejected by stellar sources, merges and flows with the interstellar gas, and is sputtered away due to the presence of the hot gas. We find that although grains can flow a considerable distance from the parent star in some cases before being sputtering away, the grain size distribution at a given location is accurately determined by assuming in situ sputtering of dust grains as they are ejected by the parent star. We find that dust heating is dominated by absorption of ambient starlight. Heating due to collisions with energetic electrons in the hot gas and absorption of thermal X-rays is smaller by orders of magnitude. We also find that for the largest galaxy considered (L(sub B) approximately 10 (exp 11) solar luminosity) the energy lost from the hot gas due to electronic collisions with the dust is about an order of magnitude less than that lost due to thermal emission in X-rays. The gas in smaller galaxies loses even less of its energy via heating of grains. In deriving this result, we find that the inclusion of grain sputtering is a crucial ingredient of the calculation. The presence of dust grains is therefore energetically unimportant for elliptical galaxy cooling flow models.

Tsai, John C.↗

NASA NTRS1995

Protostellar Collapse with a Shock

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(sup -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Tsai, John C.↗

NASA NTRS1994

Reanalysis of X-ray emission from M87. 2: The multiphase medium

In a previous paper, we showed that a single-phase model for the gas around M87 simultaneously explained most available X-ray data. Total enclosed masses derived from the model, however, fell well below the determinations from optical measurements. In this paper, we consider possible solutions to the inconsistency, including two multiphase medium models for the gas and the consequences of systematic errors of the Einstein Focal Point Crystal Spectrometer (FPCS). First, we find that when constraints from optical mass determinations are not considered, the best-fit model to the X-ray data is always the single-phase model. Multiphase models or consideration of FPCS systematic errors are required only when optical mass constraints are included. We find that the cooling time model of White & Sarazin adequately explains the available X-ray data and predicts total masses which agree with optical measurements. An ad hoc power-law multiphase does not. This shows both that the existence of mass dropping out of the ambient phase is consistent with the data and that the cooling-time model gives a reasonable parameterization of the dropout rate. Our derived mass accretion rate is similar to previous determinations. The implications of this result for cluster mass determinations in general are discussed. We then consider 'self absorbing' models where we assume that material dropping out of the ambient medium goes completely into X-ray absorbing gas. The resulting internal absorption is small compared to Galactic absorption at most radii. The models are therefore indistinguishable from models with only Galactic absorption. We finally show that it is alternatively possible to simultaneously fit optical mass measurements and X-ray data with a single-phase model if some of the observed FPCS line fluxes are too high by the maximum systematic error. This possiblity can be checked with new data from satellites such as ASCA.

Tsai, John C.↗

NASA NTRS1994

X-Ray Emission from a Simulated Cluster of Galaxies

Using the 1993 cluster simulation of Katz & White, we analyze the intracluster medium and investigate the accuracy of the standard hydrostatic method for determining cluster masses. We show that the simulated cluster gas is in hydrostatic equilibrium with a subsonic flow toward the center. Inside a radius of (approx.) 100 kpc, this flow is in a steady state. The cooling time is shorter than a Hubble time within the central 50 kpc. The flow rate is regulated by the gas sink in the middle of the cluster and the PdV work done as the gas flows in, verifying the standard cooling flow scenario. We simulate observations of the cluster using the instrument parameters of the EXOSAT ME detector and the Einstein IPC detector. Even though the intracluster gas is not isothermal, isothermal models of the cluster, excluding regions within 100 kpc of galaxies, fit the EXOSAT X-ray spectra as well as they fit real clusters. The X- ray surface brightness distribution is similar to that of real clusters, again excluding the galaxies. We simulate the procedure used to determine the masses of real clusters. We use the equation of hydrostatic equilibrium together with the temperature derived from an isothermal fit to the simulated EXOSAT spectrum and the density profile derived from a fit to the simulated IPC surface brightness profile to determine the mass. A comparison of the derived mass profile to the actual mass profile shows that errors of a factor of 2 are possible. If the actual temperature profile is used, the cluster mass is found to an accuracy of better than 25% within the virial radius.

Tsai, John C.↗

NASA NTRS1994

Reanalysis of X-ray emission from M87. 1: The single-phase medium

We reanalyze the density and temperature profiles of the X-ray-emitting gas around M87, assuming a spherically symmetric, single-phase model. For given assumed density and temperature profiles, we predict Einstein High Resolution Imager (HRI) and Imaging Proportional Counter (IPC) surface brightness distribution as well as Focal Point Crystal Spectrometer (FPCS) line fluxes, which we compare with the data. We find that a good fit to these data can be obtained and that, with a suitable adjustment of the abundances, the equivalent width of the iron complex at 7 keV as observed by wide-beam instruments can also be explained. In contrast to this, the Einstein Solid State Spectrometer (SSS) spectrum and optically determined mass profiles cannot be accounted for simultaneously with the previous X-ray data. We show that the disagreement of the Solid State Spectrometer with our models is due to an inconsistency of the Solid State Spectrometer data with that of the other X-ray instruments. Because of this, we find no evidence for the existence of absorption above the Galactic value, contrary to an earlier claim based on Solid State Spectrometer data. The disagreement of our models with optical mass data is due either to the assumption of a single-phase model, thus rendering the model unacceptable, or possibly to maximal systematic errors in the FPCS data. We also show that thermal conduction at the Spitzer rate is important in our models, although this conclusion is of limited importance in view of the poor fit of our models to the data.

Tsai, John C.↗

NASA NTRS1993

The dark matter distribution of M87 and NGC 1399

Recent X-ray observations of clusters of galaxies indicate that, outside the innermost about 100 kpc region, the ratio of dark matter density to baryonic matter density declines with radius. We show that this result is consistent with a cold dark matter simulation, suggesting the presence of dissipationless dark matter in the observed clusters. This is contrary to previous suggestions that dissipational baryonic dark matter is required to explain the decline in the density ratio. The simulation further shows that, in the inner 100 kpc region, the density ratio should rise with radius. We confirm this property in M87 and NGC 1399, which are close enough to allow the determination of the density ratio in the required inner region. X-ray mappings of the dark matter distribution in clusters of galaxies are therefore consistent with the presence of dissipationless dark matter.

Tsai, John C.↗

NASA NTRS1992

Reanalysis of x ray emission from M87 II: Multiphase models

In a previous paper by the authors (hereafter TB), it was shown that the hot intracluster gas around M87 could not be adequately explained in terms of a spherically symmetric, single phase model. It was found that although data from the Einstein satellite High Resolution Imager (HRI), Imaging Proportional Counter (IPC), and Focal Point Crystal Spectrometer (FPCS) could indeed be simultaneously explained by a single phase model, data from the Solid State Spectrometer (SSS) and optically determined mass estimates could not be similarly explained. A qualitative discussion was then given to indicate how the adoption of a specific multiphase model could plausibly improve upon the single phase model, but a detailed discussion was delayed until now. The x ray data is reanalyzed for the gas around M87 in the same spirit as the work in TB. That is, by assuming several cooling flow models, the shortcomings are improved upon. The procedure of TB was adopted and the data reanalyzed in the following manner: a multiphase model is assumed which can compute the surface brightness as seen by HRI and IPC. Also, the line fluxes can be computed of the lines seen by the FPCS and the mass profile after assuming hydrostatic equilibrium. The parameters of the model are then adjusted to fit the data. A check is then made to see whether the resulting model is consistent with the SSS spectrum and the equivalent width of the 7 keV complex of Fe lines as seen by large field of view instruments.

Tsai, John C.↗