Some simple scaling relations for heating of ballistic entry bodies
Scaling relations showing effects of ballistic coefficient, flight path angle and inverse atmospheric scale height on heating of ballistic entry bodies
Tauber, M. E.↗
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Implicit Priors in Galaxy Cluster Mass and Scaling Relation Determinations
Deriving the total masses of galaxy clusters from observations of the intracluster medium (ICM) generally requires some prior information, in addition to the assumptions of hydrostatic equilibrium and spherical symmetry. Often, this information takes the form of particular parametrized functions used to describe the cluster gas density and temperature profiles. In this paper, we investigate the implicit priors on hydrostatic masses that result from this fully parametric approach, and the implications of such priors for scaling relations formed from those masses. We show that the application of such fully parametric models of the ICM naturally imposes a prior on the slopes of the derived scaling relations, favoring the self-similar model, and argue that this prior may be influential in practice. In contrast, this bias does not exist for techniques which adopt an explicit prior on the form of the mass profile but describe the ICM non-parametrically. Constraints on the slope of the cluster mass-temperature relation in the literature show a separation based the approach employed, with the results from fully parametric ICM modeling clustering nearer the self-similar value. Given that a primary goal of scaling relation analyses is to test the self-similar model, the application of methods subject to strong, implicit priors should be avoided. Alternative methods and best practices are discussed.
Mantz, A.↗
Scaling Relations from Sunyaev-Zel'dovich Effect and Chandra X-ray Measurements of High-Redshift Galaxy Clusters
We present Sunyaev-Zel'dovich Effect (SZE) scaling relations for 38 massive galaxy clusters at redshifts 0.14 less than or equal to z less than or equal to 0.89, observed with both the Chandra X-ray Observatory and the centimeter-wave SZE imaging system at the BIMA and OVRO interferometric arrays. An isothermal ,Beta-model with central 100 kpc excluded from the X-ray data is used to model the intracluster medium and to measure global cluster properties. For each Cluster, we measure the X-ray spectroscopic temperature, SZE gas mass, total mass. and integrated Compton-gamma parameters within r(sub 2500). Our measurements are in agreement with the expectations based on a simple self-similar model of cluster formation and evolution. We compare the cluster properties derived from our SZE observations with and without Chandra spatial and spectral information and find them to be in good agreement: We compare our results with cosmological numerical simulations, and find that simulations that include radiative cooling, star formation and feedback match well both the slope and normalization of our SZE scaling relations.
Bonamente, Massimiliano↗
Scaling Relations from Sunyaev-Zel'dovich Effect and Chandra X-Ray Measurements of High-Redshift Galaxy Clusters
We present Sunyaev-Zel'dovich Effect (SZE) scaling relations for 38 massive galaxy clusters at redshifts 0.14 less than or equal to z less than or equal to 0.89, observed with both the Chandra X-ray Observatory and the centimeter-wave SZE imaging system at the BIMA and OVRO interferometric arrays. An isothermal Beta-model with the central 100 kpc excluded from the X-ray data is used to model the intracluster medium and to measure global cluster properties. For each cluster, we measure the X-ray spectroscopic temperature, SZE gas mass, total mass, and integrated Compton gamma-parameters within r(sub 2500). Our measurements are in agreement with the expectations based on a simple self-similar model of cluster formation and evolution. We compare the cluster properties derived from our SZE observations with and without Chandra spatial and spectral information and find them to be in good agreement. We compare our results with cosmological numerical simulations and find that simulations that include radiative cooling, star formation, and feedback match well both the slope and normalization of our SZE scaling relations.
Bonamente, Massimiliano↗
Scaling relations for heating during gliding entry at parabolic speed
The scaling relations presently derived illustrate the influence of ballistic coefficient and L/D primary vehicle parameters on the peak heating rate and total heating/unit area for gliding entry of the earth atmosphere at parabolic speed. Comparisons with stagnation-point and windward centerline laminar and turbulent heating during three Space Shuttle flights are presented. It is found that total heat input/unit area is reduced by decreasing both of the primary vehicle parameters.
Tauber, Michael E.↗
Resolved scaling relations and metallicity gradients on sub-kiloparsec scales at z ≈ 1
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V Patrício↗
Critical exponents and scaling relations for self-organized critical phenomena
Critical indices beta, gamma delta, nv, etc. are defined and calculated for self-organized critical phenomena. Scaling relations are derived and checked numerically. The order-parameter exponent beta describes the spontaneous current and the relaxation to the criticl point. The power spectrum has 'l/f' behavior with the exponent phi = nv x z, where z is the dynamical critical exponent.
Tang, Chao↗
X-ray Binary Luminosity Function Scaling Relations for Local Galaxies Based on Subgalactic Modeling
We present new Chandra constraints on the X-ray luminosity functions(XLFs)of X-ray binary(XRB)populations, as well as their scaling relations, for a sample of 38 nearby galaxies(D = 3.4–29 Mpc). Our galaxy sample is drawn primarily from the Spitzer Infrared Nearby Galaxies Survey(SINGS)and contains a wealth of Chandra(5.8 Ms total)and multiwavelength data, allowing for star formation rates(SFRs)and stellar masses(M⁎)to be measured on subgalactic scales. We divided the 2478 X-ray-detected sources into 21 subsamples in bins of specific SFR(sSFR ≡ SFR/M⁎)and constructed XLFs. To model the XLF dependence on sSFR, we fit a global XLF model, containing contributions from high-mass XRBs(HMXBs), low-mass XRBs(LMXBs), and background sources from the cosmic X-ray background that respectively scale with SFR, M⁎, and sky area. We find an HMXB XLF that is more complex in shape than previously reported and an LMXB XLF that likely varies with sSFR, potentially due to an age dependence. When applying our global model to XLF data for each individual galaxy, we discover a few galaxy XLFs that significantly deviate from our model beyond statistical scatter. Most notably, relatively low-metallicity galaxies have an excess of HMXBs above≈10^(38)erg/s, and elliptical galaxies that have relatively rich populations of globular clusters(GCs)show excesses of LMXBs compared to the global model. Additional modeling of how the XRB XLF depends on stellar age, metallicity, and GC specific frequency is required to sufficiently characterize the XLFs of galaxies.
Bret D. Lehmer↗
The Evolution of the Cluster X-ray Scaling Relations in the Wide Angle ROSAT Pointed Survey Sample at 0.6 < z < 1.0
The X-ray properties of a sample of 11 high-redshift (0.6 < z < 1 .O) clusters observed with Chardm and/or XMM-Newton are used to investigate the evolution of the cluster scaling relations. The observed evolution in the normalization of the L-T, M-T, M(sub 2)-T and M-L relations is consistent with simple self-similar predictions, in which the properties of clusters reflect the properties of the Universe at their redshift of observation. Under the assumption that the model of self-similar evolution is correct and that the local systems formed via a single spherical collapse, the high-redshift L-T relation is consistent with the high-z clusters having virialized at a significantly higher redshift than the local systems. The data are also consistent with the more realistic scenario of clusters forming via the continuous accretion of material. The slope of the L-T relation at high redshift (B = 3.32 +/- 0.37) is consistent with the local relation, and significantly steeper than the self-similar prediction of B = 2. This suggests that the same non-gravitational processes are responsible for steepening the local and high-z relations, possibly occurring universally at z is approximately greater than 1 or in the early stages of the cluster formation, prior to their observation. The properties of the intracluster medium at high redshift are found to be similar to those in the local Universe. The mean surface-brightness profile slope for the sample is Beta = 0.66 +/- 0.05, the mean gas mass fractions within R(sub 2500(z)) and R(200(z)) are 0.069 +/- 0.012 and 0.11 +/- 0.02, respectively, and the mean metallicity of the sample is 0.28 +/- 0.11 Z(sub solar).
Maughan, B. J.↗
Revisiting Empirical Solar Energetic Particle Scaling Relations. I. Solar Flares
Aims. The possible influence of solar superflares on the near-Earth space radiation environment are assessed through the investigation of scaling laws between the peak proton flux and fluence of solar energetic particle (SEP) events with the solar flare soft X-ray peak photon flux. Methods. We compiled a catalog of 65 well-connected (W20-90) SEP events during the last three solar cycles covering a period of ∼34 yr (1984–2020) that were associated with flares of class ≥C6.0, and investigated the statistical relations between the recorded peak proton fluxes (I p ) and the fluences (F p ) at a set of integral energies from E > 10, > 30, and > 60 to > 100 MeV versus the associated solar flare peak soft X-ray flux in the 1–8 Å band (F SXR ). Based on the inferred relations, we calculated the integrated energy dependence of the peak proton flux (I p ) and fluence (F p ) of the SEP events, assuming that they follow an inverse power law with respect to energy. Finally, we made use of simple physical assumptions, combining our derived scaling laws, and estimated the upper limits for I p and F p focusing on the flare associated with the strongest ground level enhancement (GLE) directly observed to date (GLE 05 on 23 February 1956), and that inferred for the cosmogenic radionuclide-based SEP event of AD774/775. Results. A scaling law relating I p and F p to the solar soft X-ray peak intensity (F SXR ) as ∝ F 5/6 SXR for a flare with a F SXR = X600 (in the revised scale) is consistent with values of FP inferred for the cosmogenic nuclide event of AD774/775.
Athanasios Papaioannou↗
The X-Ray Halo Scaling Relations of Supermassive Black Holes
We carry out a comprehensive Bayesian correlation analysis between hot halos and direct masses of supermassive black holes (SMBHs), by retrieving the X-ray plasma properties (temperature, luminosity, density, pressure, and masses) over galactic to cluster scales for 85 diverse systems. We find new key scalings, with the tightest relation being −, followed by −. The tighter scatter (down to 0.2 dex) and stronger correlation coefficient of all the X-ray halo scalings compared with the optical counterparts (as the −) suggest that plasma halos play a more central role than stars in tracing and growing SMBHs (especially those that are ultramassive). Moreover, correlates better with the gas mass than dark matter mass. We show the important role of the environment, morphology, and relic galaxies/coronae, as well as the main departures from virialization/self-similarity via the optical/X-ray fundamental planes. We test the three major channels for SMBH growth: hot/Bondi-like models have inconsistent anticorrelation with X-ray halos and too low feeding; cosmological simulations find SMBH mergers as subdominant over most of cosmic time and too rare to induce a central-limit-theorem effect; the scalings are consistent with chaotic cold accretion, the rain of matter condensing out of the turbulent X-ray halos that sustains a long-term self-regulated feedback loop. The new correlations are major observational constraints for models of SMBH feeding/feedback in galaxies, groups, and clusters (e.g., to test cosmological hydrodynamical simulations), and enable the study of SMBHs not only through X-rays, but also via the Sunyaev–Zel'dovich effect (Compton parameter), lensing (total masses), and cosmology (gas fractions).
Supermassive black holes↗
Revisiting Scaling Relations for Giant Radio Halos in Galaxy Clusters
Many galaxy clusters host megaparsec-scale radio halos, generated by ultrarelativistic electrons in the magnetized intracluster medium. Correlations between the synchrotron power of radio halos and the thermal properties of the hosting clusters were established in the last decade, including the connection between the presence of a halo and cluster mergers. The X-ray luminosity and redshift-limited Extended GMRT Radio Halo Survey provides a rich and unique dataset for statistical studies of the halos. We uniformly analyze the radio and X-ray data for the GMRT cluster sample, and use the new Planck Sunyaev-Zel'dovich (SZ) catalog to revisit the correlations between the power of radio halos and the thermal properties of galaxy clusters. We find that the radio power at 1.4 GHz scales with the cluster X-ray (0.1-2.4 keV) luminosity computed within R(sub 500) as P(sub 1.4) approx. L(2.1+/-0.2) - 500). Our bigger and more homogenous sample confirms that the X-ray luminous (L(sub 500) > 5 × 10(exp 44) erg/s)) clusters branch into two populations-radio halos lie on the correlation, while clusters without radio halos have their radio upper limits well below that correlation. This bimodality remains if we excise cool cores from the X-ray luminosities. We also find that P(sub 1.4) scales with the cluster integrated SZ signal within R(sub 500), measured by Planck, as P(sub 1.4) approx. Y(2.05+/-0.28) - 500), in line with previous findings. However, contrary to previous studies that were limited by incompleteness and small sample size, we find that "SZ-luminous" Y(sub 500) > 6×10(exp −5) Mpc(exp 2) clusters show a bimodal behavior for the presence of radio halos, similar to that in the radio-X-ray diagram. Bimodality of both correlations can be traced to clusters dynamics, with radio halos found exclusively in merging clusters. These results confirm the key role of mergers for the origin of giant radio halos, suggesting that they trigger the relativistic particle acceleration.
radiation mechanisms↗
Scaling Relation for Occulter Manufacturing Errors
An external occulter is a spacecraft own along the line-of-sight of a space telescope to suppress starlight and enable high-contrast direct imaging of exoplanets. The shape of an external occulter must be specially designed to optimally suppress starlight and deviations from the ideal shape due to manufacturing errors can result loss of suppression in the shadow. Due to the long separation distances and large dimensions involved for a space occulter, laboratory testing is conducted with scaled versions of occulters etched on silicon wafers. Using numerical simulations for a flight Fresnel occulter design, we show how the suppression performance of an occulter mask scales with the available propagation distance for expected random manufacturing defects along the edge of the occulter petal. We derive an analytical model for predicting performance due to such manufacturing defects across the petal edges of an occulter mask and compare this with the numerical simulations. We discuss the scaling of an extended occulter test-bed.
Sirbu, Dan↗
Scaling Relation for Occulter Manufacturing Errors
For directly imaging exoplanets, NASA is considering space mission designs that use an external occulter as the principal starlight suppression system. These occulter designs range in diameter from 16 to 40 meters and separation distance from 8,000 to 60,000 kilometers for telescopes with primary diameters of 0.5 to 4 meters. Occulter shapes are solutions to an optimization problem which seeks to maximize suppression in the shadow subject to constraints such as size, separation, and wavelengths. These designs are based on scalar diffraction theory and must be verified experimentally to demonstrate predicted on-orbit performance. Due to the large sizes and separations involved the experiment must be scaled to lab size. We are currently expanding the existing experimental test-bed at Princeton to enable scaling of occulters operating at flight Fresnel sizes. Here we examine the effect on suppression performance of edge defects and their scaling to test-bed size.
Scalar Diffraction↗
Limited cavitation and the related scale effects problem.
It is indicated that the study of limited cavitation can be divided into two parts, namely, the factors which influence the pressure field, and those which influence the bubble dynamics. Major aspects of cavitation nuclei and bubble dynamics are summarized. An analysis is presented of the effects of velocity, size and fluid properties, including the thermodynamic effect. The effects of turbulence, roughness and polymer additives are presented. These include new data on roughness and estimates of the effects of turbulence and polymer additives on jets. An analysis of nonvaporous cavitation with new data on vortex cavitation is presented. Implications concerning scale effects are given.
Holl, J. W.↗
Scaling relations in the equation of state, thermal expansion, and melting of metals
A simple and yet quite accurate prediction of volume as a function of pressure for metals and alloys is presented. Thermal expansion coefficients and melting temperatures are predicted by simple, analytic expressions and results compare favorably with experiment for a broad range of metals. All of these predictions are made possible by the discovery of universality in binding energy relations for metals.
Guinea, F.↗
An Experimental Investigation of the Scale Relations for the Impinging Water Spray Generated by a Planing Surface
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Mcbride, Ellis E↗