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At least 307 records · Page 17

SU-E-T-220: Investigation of Intrafraction Changes to Photon Beam Profiles

Purpose: Treatment Planning Systems model beam profiles to be static and independent of gantry angle. This work investigates how beam profiles change over time, with varying gantry angle. Methods: 200 cGy was delivered to ICProfiler (Sun Nuclear) on 2 Elekta Synergys and 1 Varian 21EX linacs at 8 gantry angles and 1 clockwise arc. Measurements were recorded 8 times per second. To investigate the initial portion of the beams, single-shot and multi-control-point beams were measured. The differences in beam profiles were analyzed as well as the length of time for the beam to stabilize. Symmetry was calculated 5cm from the central axis at 100cm SSD. Field sizes ranged from 30×30 cm{sup 2} to 40×40 cm{sup 2}. Results: The beam profiles changed over time and were dependent on gantry angle. The composite profile for each beam met 1% tolerance described in TG-142. It took up to 14.7, 3.7 and 11.3 cGy for the two Elektas and Varian respectively to satisfy the tolerance. All linacs had the most flat, symmetric, and stable beam profile with the gantry at 0 degrees, where the symmetry was 100.5%±0.55, 101.0%±0.52 and 101.1%±0.44 respectively. The symmetry was 100.7%±1.06, 101.1%±1.05 and 101.2%±0.64 at the gantry angle with the biggest discrepancy (90, 180 and 180 degrees respectively). Symmetry was better in the X direction for the Elektas and the Y for the Varian. Fluctuations in beam profiles corresponded to changes in dose rate. Conclusion: Flatness and symmetry changed over time and with gantry angle. Because Treatment Planning Systems do not account for these changes, it may be necessary to limit certain beams from clinical use, for example, beams with low MU. It may also be necessary to add additional QA procedures beyond those suggested in TG-142 to account for these changes.

07 ISOTOPE AND RADIATION SOURCES↗

A Physical Model Enhanced Data Driven Method for High-Resolution Residential Load Profile Generation

Residential buildings account for significant energy consumption, creating opportunities to offer grid services. As electric utilities seek to implement effective system operation strategies, understanding residential energy consumption patterns becomes essential; However, the time intervals of load profiles measured by utilities' smart meters are typically from 15 minutes to 60 minutes. The low-resolution data make it hard to extract appliance-level load information, which is critical for providing grid services. This paper presents a load profile generator designed to produce synthetic load profiles for residential buildings that emphasizes the importance of accurate representations of realistic energy consumption patterns. The generator takes realistic low-resolution residential load measurements and weather data as inputs, producing 1-minute interval profiles that match the characteristics of the original profiles. Further, this generator can be used to populate load profiles in areas where actual measurements are limited to improve the ability of utilities to analyze their distribution systems. By providing more high-resolution residential building load profiles, this tool supports electric utilities to enhance their residential building load control strategies and improve overall grid stability.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Data-driven analysis of neutron diffraction line profiles: application to plastically deformed Ta

Abstract Non-destructive evaluation of plastically deformed metals, particularly diffraction line profile analysis (DLPA), is valuable both to estimate dislocation densities and arrangements and to validate microstructure-aware constitutive models. To date, the interpretation of whole line diffraction profiles relies on the use of semi-analytical models such as the extended convolutional multiple whole profile (eCMWP) method. This study introduces and validates two data-driven DLPA models to extract dislocation densities from experimentally gathered whole line diffraction profiles. Using two distinct virtual diffraction models accounting for both strain and instrument induced broadening, a database of virtual diffraction whole line profiles of Ta single crystals is generated using discrete dislocation dynamics. The databases are mined to create Gaussian process regression-based surrogate models, allowing dislocation densities to be extracted from experimental profiles. The method is validated against 11 experimentally gathered whole line diffraction profiles from plastically deformed Ta polycrystals. The newly proposed model predicts dislocation densities consistent with estimates from eCMWP. Advantageously, this data driven LPA model can distinguish broadening originating from the instrument and from the dislocation content even at low dislocation densities. Finally, the data-driven model is used to explore the effect of heterogeneous dislocation densities in microstructures containing grains, which may lead to more accurate data-driven predictions of dislocation density in plastically deformed polycrystals.

36 MATERIALS SCIENCE↗

Planck intermediate results (Corrigendum) : V. Pressure profiles of galaxy clusters from the Sunyaev-Zeldovich effect

Figure 7 of our original publication (Planck Collaboration 2013) is flawed. The correct figure is presented here and we stress that our original conclusion on the radial distribution of the gas fraction remains unchanged. There was an error in the reconstruction of the temperature profiles used to derive the gas mass distribution from the joint Planck and XMM-Newton pressure profile, and thereby a prediction for the gas fraction profiles. The error in the temperature profile reconstruction applies to this paper only. The predicted gas fraction profiles for both hypothesis on the temperature profiles, i.e., from hypothesis H1 and H2, were affected similarly. Now corrected, they are in better agreement at R 500 with the measurement by Pratt et al. (2009) on the REXCESS sample and with the expectations from the CMB. The Perseus profile (Simionescu et al. 2011) is still marginally compatible with our prediction within our large dispersion (shaded blue and red area on the figure).

79 ASTRONOMY AND ASTROPHYSICS↗

TDCOSMO - IV. Hierarchical time-delay cosmography – joint inference of the Hubble constant and galaxy density profiles

The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of H0 = 73.3−1.8+1.7 km s−1 Mpc−1, describing deflector mass density profiles by either a power-law or stars (constant mass-to-light ratio) plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in H0. We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with H0. Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured H0 = 74.5−6.1+5.6 km s−1 Mpc−1. Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured H0 = 67.4−3.2+4.1 km s−1 Mpc−1. This measurement assumes that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of H0. While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the H0 measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on H0 derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data.Key words: gravitational lensing: strong / galaxies: general / galaxies: kinematics and dynamics / distance scale / cosmological parameters / cosmology: observations⋆ The full analysis is available at https://github.com/TDCOSMO/hierarchy_analysis_2020_public.

79 ASTRONOMY AND ASTROPHYSICS↗

Performance and data analysis aspects of the new DIII-D monostatic profile reflectometer system

A new frequency-modulated profile reflectometer system, featuring a monostatic antenna geometry (using one microwave antenna for both launch and receive), has been installed on the DIII-D tokamak, providing a first experimental test of this measurement approach for profile reflectometry. Significant features of the new system are briefly described in this paper, including the new monostatic arrangement, use of overmoded, broadband transmission waveguide, and dual-polarization combination/demultiplexing. Updated data processing and analysis, and in-service performance aspects of the new monostatic profile reflectometer system are also presented. By using a raytracing code (GENRAY) to determine the approximate trajectory of the probe beam, the electron density (n{sub e}) profile can be successfully reconstructed with L-mode plasmas vertically shifted by more than 10 cm off the vessel midplane. Specifically, it is demonstrated that the new system has a capability to measure n{sub e} profiles with plasma vertical offsets of up to ±17 cm. Examples are also presented of accurate, high time and spatial resolution density profile measurements made over a wide range of DIII-D conditions, e.g., the measured temporal evolution of the density profile across a L-H transition.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Understanding and predicting profile structure and parametric scaling of intrinsic rotation

This study reports on a recent advance in developing physical understanding and a first-principles-based model for predicting intrinsic rotation profiles in magnetic fusion experiments. It is shown for the first time that turbulent fluctuation-driven residual stress (a non-diffusive component of momentum flux) along with diffusive momentum flux can account for both the shape and magnitude of the observed intrinsic toroidal rotation profile. Both the turbulence intensity gradient and zonal flow E×B shear are identified as major contributors to the generation of the k ∥ -asymmetry needed for the residual stress generation. The model predictions of core rotation based on global gyrokinetic simulations agree well with the experimental measurements of main ion toroidal rotation for a set of DIII-D ECH discharges. The validated model is further used to investigate the characteristic dependence of residual stress and intrinsic rotation profile structure on the multi-dimensional parametric space covering the turbulence type, q-profile structure, and up-down asymmetry in magnetic geometry with the goal of developing the physics understanding needed for rotation profile control and optimization. It is shown that in the flat-q profile regime, intrinsic rotations driven by ITG and TEM turbulence are in the opposite direction (i.e., intrinsic rotation reverses). The predictive model also produces reversed intrinsic rotation for plasmas with weak and normal shear q-profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Probing nonlinear velocity profiles of shear-thinning, nematic platelet dispersions in Couette flow using x-ray photon correlation spectroscopy

In this study, we report experiments employing x-ray photon correlation spectroscopy (XPCS) to characterize the velocity profiles of complex fluids in Couette flow. The approach involves modeling the XPCS correlation functions obtained with the incident x-ray beam passing tangentially through the Couette cell gap at various distances from the inner wall. We first demonstrate the technique with measurements on a dilute colloidal dispersion in the Newtonian liquid glycerol, where the expected linear velocity profiles are recovered. We then employ the technique to map the shear-rate-dependent velocity profiles of a shear-thinning dispersion of nematically ordered Gibbsite platelets. The nonlinear velocity profiles of the Gibbsite dispersion include a narrow slip region adjacent to the outer wall and a band with a small velocity gradient in the interior of the gap that evolves into a region increasingly resembling plug flow with increasing shear rate. Variations in the velocity profile along the vorticity direction indicate an instability in the interface between this region of small velocity gradient and a region of high velocity gradient near the inner wall. The analysis of the small-angle scattering patterns provides information about the spatial and temporal variations in the nematic order of the Gibbsite dispersion and their coupling to the velocity profile. Additional potential applications of this XPCS-based technique and comparisons with established methods for characterizing velocity profiles are discussed.

42 ENGINEERING↗

Equilibrium reconstruction of DIII-D plasmas using predictive modeling of the pressure profile

New workflows have been developed for predictive modeling of magnetohydrodynamic (MHD) equilibrium in tokamak plasmas. The goal of this work is to predict the MHD equilibrium in tokamak discharges without having measurements of the kinetic profiles. The workflows include a cold start tool, which constructs all the profiles and power flows needed by transport codes; a Grad–Shafranov equilibrium solver; and various codes for the sources and sinks. For validation purposes, a database of DIII-D tokamak discharges has been constructed that is comprised of scans in the plasma current, toroidal magnetic field, and triangularity. Initial efforts focused on developing a workflow utilizing an empirically derived pressure model tuned to DIII-D discharges with monotonic safety factor profiles. This workflow shows good agreement with experimental kinetic equilibrium calculations, but is limited in that it is a single fluid (equal ion and electron temperatures) model and lacks H-mode pedestal predictions. The best agreement with the H-mode database is obtained using a theory-based workflow utilizing pressure profile predictions from a coupled TGLF turbulent transport and EPED pedestal models together with external magnetics and Motional Stark Effect (MSE) data to construct the equilibrium. Here, we obtain an average root mean square error of 5.1% in the safety factor profile when comparing the predicted and experimental kinetic equilibrium. We also find good agreement with the plasma stored energy, internal inductance, and pressure profiles. Including MSE data in the theory-based workflow results in noticeably improved agreement with the q-profiles in high triangularity discharges in comparison with the results obtained with magnetic data only. The predictive equilibrium workflow is expected to have wide applications in experimental planning, between-shot analysis, and reactor studies.

Kinsey, J. E. (ORCID:0000000193347473)↗

THE ACS FORNAX CLUSTER SURVEY. IV. DEPROJECTION OF THE SURFACE BRIGHTNESS PROFILES OF EARLY-TYPE GALAXIES IN THE VIRGO AND FORNAX CLUSTERS: INVESTIGATING THE 'CORE/POWER-LAW DICHOTOMY'

Although early observations with the Hubble Space Telescope (HST) pointed to a sharp dichotomy among early-type galaxies in terms of the logarithmic slope {gamma}' of their central surface brightness profiles, several studies in the past few years have called this finding into question. In particular, recent imaging surveys of 143 early-type galaxies belonging to the Virgo and Fornax Clusters using the Advanced Camera for Surveys (ACS) on board HST have not found a dichotomy in {gamma}', but instead a systematic progression from central luminosity deficit to excess relative to the inward extrapolation of the best-fitting global Sersic model. Given that earlier studies also found that the dichotomy persisted when analyzing the deprojected density profile slopes, we investigate the distribution of the three-dimensional luminosity density profiles of the ACS Virgo and Fornax Cluster Survey galaxies. Having fitted the surface brightness profiles with modified Sersic models, we then deproject the galaxies using an Abel integral and measure the inner slopes {gamma}{sub 3D} of the resulting luminosity density profiles at various fractions of the effective radius R{sub e} . We find no evidence of a dichotomy, but rather, a continuous variation in the central luminosity profiles as a function of galaxy magnitude. We introduce a parameter, {Delta}{sub 3D}, that measures the central deviation of the deprojected luminosity profiles from the global Sersic fit, showing that this parameter varies smoothly and systematically along the luminosity function.

79 ASTRONOMY AND ASTROPHYSICS↗

ANALYSIS OF CORONAL GREEN LINE PROFILES: EVIDENCE OF EXCESS BLUESHIFTS

Coronal green line (Fe XIV 5303 A) profiles were obtained from Fabry-Perot interferometric observations of the solar corona during the total solar eclipse of 2001 June 21 from Lusaka, Zambia. The instrumental width is about 0.2 A and the spectral resolution is about 26,000. About 300 line profiles were obtained within a radial range of 1.0-1.5 R{sub sun} and a position angle coverage of about 240{sup 0}. The line profiles were fitted with single Gaussians, and their intensities, Doppler velocities, and line widths were obtained. Also obtained were the centroids of the line profiles, which give a measure of line asymmetry. The histograms of Doppler velocity show excess blueshifts, while the centroids reveal a predominant blue wing in the line profiles. It was found that the centroids and the Doppler velocities are highly correlated. This points to the presence of multiple components in the line profiles, with an excess of blueshifted components. We then obtained the (Blue-Red) wing intensities, which clearly reveal the secondary components, the majority of which are blueshifted. This confirms that the coronal green line profiles often contain multicomponents with excess blueshifts, which also depend on the solar activity. The magnitude of the Doppler velocity of the secondary components is in the range of 20-40 km s{sup -1} and shows an increase toward the poles. Possible explanations of the multicomponents are the type II spicules that were recently found to be important to coronal heating or the nascent solar wind flow, but the cause of the blue asymmetry in the coronal lines above the limb remains unclear.

79 ASTRONOMY AND ASTROPHYSICS↗

THE STELLAR MASS STRUCTURE OF MASSIVE GALAXIES FROM z = 0 TO z = 2.5: SURFACE DENSITY PROFILES AND HALF-MASS RADII

We present stellar mass surface density profiles of a mass-selected sample of 177 galaxies at 0.5 < z < 2.5, obtained using very deep Hubble Space Telescope optical and near-infrared data over the GOODS-South field, including recent CANDELS data. Accurate stellar mass surface density profiles have been measured for the first time for a complete sample of high-redshift galaxies more massive than 10{sup 10.7} M {sub Sun }. The key advantage of this study compared to previous work is that the surface brightness profiles are deconvolved for point-spread function smoothing, allowing accurate measurements of the structure of the galaxies. The surface brightness profiles account for contributions from complex galaxy structures such as rings and faint outer disks. Mass profiles are derived using radial rest-frame ug color profiles and a well-established empirical relation between these colors and the stellar mass-to-light ratio. We derive stellar half-mass radii from the mass profiles, and find that these are on average {approx}25% smaller than rest-frame g-band half-light radii. This average size difference of 25% is the same at all redshifts, and does not correlate with stellar mass, specific star formation rate, effective surface density, Sersic index, or galaxy size. Although on average the difference between half-mass size and half-light size is modest, for approximately 10% of massive galaxies this difference is more than a factor of two. These extreme galaxies are mostly extended, disk-like systems with large central bulges. These results are robust, but could be impacted if the central dust extinction becomes high. ALMA observations can be used to explore this possibility. These results provide added support for galaxy growth scenarios wherein massive galaxies at these epochs grow by accretion onto their outer regions.

79 ASTRONOMY AND ASTROPHYSICS↗

THE DENSITY PROFILES OF MASSIVE, RELAXED GALAXY CLUSTERS. II. SEPARATING LUMINOUS AND DARK MATTER IN CLUSTER CORES

We present stellar and dark matter (DM) density profiles for a sample of seven massive, relaxed galaxy clusters derived from strong and weak gravitational lensing and resolved stellar kinematic observations within the centrally located brightest cluster galaxies (BCGs). In Paper I of the series, we demonstrated that the total density profile derived from these data, which span three decades in radius, is consistent with numerical DM-only simulations at radii {approx}> 5-10 kpc, despite the significant contribution of stellar material in the core. Here, we decompose the inner mass profiles of these clusters into stellar and dark components. Parameterizing the DM density profile as a power law {rho}{sub DM}{proportional_to}r {sup -{beta}} on small scales, we find a mean slope ({beta}) = 0.50 {+-} 0.10(random){sup +0.14} {sub -0.13}(systematic). Alternatively, cored Navarro-Frenk-White (NFW) profiles with (log r {sub core}/kpc) = 1.14 {+-} 0.13{sup +0.14} {sub -0.22} provide an equally good description. These density profiles are significantly shallower than canonical NFW models at radii {approx}< 30 kpc, comparable to the effective radii of the BCGs. The inner DM profile is correlated with the distribution of stars in the BCG, suggesting a connection between the inner halo and the assembly of stars in the central galaxy. The stellar mass-to-light ratio inferred from lensing and stellar dynamics is consistent with that inferred using stellar population synthesis models if a Salpeter initial mass function is adopted. We compare these results to theories describing the interaction between baryons and DM in cluster cores, including adiabatic contraction models and the possible effects of galaxy mergers and active galactic nucleus feedback, and evaluate possible signatures of alternative DM candidates.

79 ASTRONOMY AND ASTROPHYSICS↗

Galaxy halo formation in the absence of violent relaxation and a universal density profile of the halo center

While N-body simulations testify to a cuspy profile of the central region of dark matter halos, observations favor a shallow, cored density profile of the central region of at least some spiral galaxies and dwarf spheroidals. We show that a central profile, very close to the observed one, inevitably forms in the center of dark matter halos if we make a supposition about a moderate energy relaxation of the system during the halo formation. If we assume the energy exchange between dark matter particles during the halo collapse is not too intensive, the profile is universal: it depends almost not at all on the properties of the initial perturbation and is very akin, but not identical, to the Einasto profile with a small Einasto index n ∼ 0.5. We estimate the size of the 'central core' of the distribution, i.e., the extent of the very central region with a respectively gentle profile, and show that the cusp formation is unlikely, even if the dark matter is cold. The obtained profile is in good agreement with observational data for at least some types of galaxies but clearly disagrees with N-body simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

A dynamically driven, universal thermal profile of galaxy groups and clusters

Large scale structures such as groups and clusters of galaxies show a universal, nearly linear entropy radial profile K(r). Using deprojected 16 clusters and 12 groups from the literature, we find that K∝r{sup 0.96±0.01}, consistent with the mean power-law index (0.9–1.1) of previous studies. A similarly good fit is given by a τ∝r{sup 0.72±0.01} ratio between cooling and free-fall times. Both profiles slightly flatten at small radii, as τ becomes of order unity. The entropy profile is usually attributed to self-similar shock accretion (shown to be inconsistent with the data), to non-standard heat conduction, or to turbulent heating. We argue that a dynamical mechanism is needed to sustain such a universal profile, oblivious to the temperature peak at the edge of the core and to the virial shock at the outskirts, and robust to the presence of ongoing cooling, merger, and active galactic nucleus activity. In particular, we show that such a profile can be naturally obtained in a spiral flow, which is likely to underlie most galaxy aggregates according to the ubiquitous spiral patterns and cold fronts observed. Generalizing a two-phase spiral flow model out to the virial radius surprisingly reproduces the thermal profile. A generalized Schwarzschild criterion indicates that observed spiral patterns must involve a convective layer, which may regulate the thermal profile.

79 ASTRONOMY AND ASTROPHYSICS↗

Improved profile fitting and quantification of uncertainty in experimental measurements of impurity transport coefficients using Gaussian process regression

The need to fit smooth temperature and density profiles to discrete observations is ubiquitous in plasma physics, yet the prevailing techniques for this have many shortcomings that cast doubt on the statistical validity of the results. This issue is amplified in the context of validation of gyrokinetic transport models (Holland et al 2009 Phys. Plasmas 16 052301), where the strong sensitivity of the code outputs to input gradients means that inadequacies in the profile fitting technique can easily lead to an incorrect assessment of the degree of agreement with experimental measurements. In order to rectify the shortcomings of standard approaches to profile fitting, we have applied Gaussian process regression (GPR), a powerful non-parametric regression technique, to analyse an Alcator C-Mod L-mode discharge used for past gyrokinetic validation work (Howard et al 2012 Nucl. Fusion 52 063002). We demonstrate that the GPR techniques can reproduce the previous results while delivering more statistically rigorous fits and uncertainty estimates for both the value and the gradient of plasma profiles with an improved level of automation. Moreover, we discuss how the use of GPR can allow for dramatic increases in the rate of convergence of uncertainty propagation for any code that takes experimental profiles as inputs. The new GPR techniques for profile fitting and uncertainty propagation are quite useful and general, and we describe the steps to implementation in detail in this paper. These techniques have the potential to substantially improve the quality of uncertainty estimates on profile fits and the rate of convergence of uncertainty propagation, making them of great interest for wider use in fusion experiments and modelling efforts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Non-power law behavior of the radial profile of phase-space density of halos

We study the pseudo phase-space density, ρ(r)/σ{sup 3}(r), of ΛCDM dark matter halos with and without baryons (baryons+DM, and pure DM), by using the model introduced in Del Popolo (2009), which takes into account the effect of dynamical friction, ordered and random angular momentum, baryons adiabatic contraction and dark matter baryons interplay. We examine the radial dependence of ρ(r)/σ{sup 3}(r) over 9 orders of magnitude in radius for structures on galactic and cluster of galaxies scales. We find that ρ(r)/σ{sup 3}(r) is approximately a power-law only in the range of halo radius resolved by current simulations (down to 0.1% of the virial radius) while it has a non-power law behavior below the quoted scale, with inner profiles changing with mass. The non-power-law behavior is more evident for halos constituted both of dark matter and baryons while halos constituted just of dark matter and with angular momentum chosen to reproduce a Navarro-Frenk-White (NFW) density profile, are characterized by an approximately power-law behavior. The results of the present paper lead to conclude that density profiles of the NFW type are compatible with a power-law behavior of ρ(r)/σ{sup 3}(r), while those flattening to the halo center, like those found in Del Popolo (2009) or the Einasto profile, or the Burkert profile, cannot produce radial profile of the pseudo-phase-space density that are power-laws at all radii. The results argue against universality of the pseudo phase-space density and as a consequence argue against universality of density profiles constituted by dark matter and baryons as also discussed in Del Popolo (2009)

79 ASTRONOMY AND ASTROPHYSICS↗

The virialization density of peaks with general density profiles under spherical collapse

We calculate the non-linear virialization density, Δ{sub c}, of halos under spherical collapse from peaks with an arbitrary initial and final density profile. This is in contrast to the standard calculation of Δ{sub c} which assumes top-hat profiles. Given our formalism, the non-linear halo density can be calculated once the shape of the initial peak's density profile and the shape of the virialized halo's profile are provided. We solve for Δ{sub c} for halos in an Einstein de-Sitter and a ΛCDM universe. As examples, we consider power-law initial profiles as well as spherically averaged peak profiles calculated from the statistics of a Gaussian random field. We find that, depending on the profiles used, Δ{sub c} is smaller by a factor of a few to as much as a factor of 10 as compared to the density given by the standard calculation ( ≈ 200). Using our results, we show that, for halo finding algorithms that identify halos through an over-density threshold, the halo mass function measured from cosmological simulations can be enhanced at all halo masses by a factor of a few. This difference could be important when using numerical simulations to assess the validity of analytic models of the halo mass function.

79 ASTRONOMY AND ASTROPHYSICS↗