Rms Density Fluctuation Research Articles

Approximating Density Probability Distribution Functions Across Cosmologies

Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is well-described by a function of two parameters: n s , the spectral slope, and σ L , the linear rms density fluctuation. For redshift-space density and the geometric mean of real- and redshift-space densities, we introduce a third parameter, . We find that density PDFs for the LCDM cosmology is also well-parameterized by these three parameters. As a result, we are able to use a suite of self-similar cosmological simulations to approximate density PDFs for a range of cosmologies. We make the density PDFs publicly available and provide an analytical fitting formula for them.

Growth of structures and redshift-space distortion data in scale-dependent gravity

This study is devoted to the implications of scale-dependent gravity in Cosmology. Redshift-space distortion data indicate that there is a tension between $\Lambda$CDM and available observations as far as the value of the rms density fluctuation, $\sigma_8$, is concerned. It has been pointed out that this tension may be alleviated in alternative theories in which gravity is weaker at red-shift $z \sim 1$. We study the evolution of density perturbations for non-relativistic matter on top of a spatially flat FLRW Universe, and we compute the combination $A=f \sigma_8$ in the framework of scale-dependent gravity, where both Newton's constant and the cosmological constant are allowed to vary with time. Upon comparison between available observational data (supernovae data as well as redshift-space distortion data) and theoretical predictions of the model, we determine the numerical value of $\sigma_8$ that best fits the data.

Turbulence in the intracluster medium: simulations, observables, and thermodynamics

We conduct two kinds of homogeneous isotropic turbulence simulations relevant for the intracluster medium (ICM): (i) pure turbulence runs without radiative cooling; (ii) turbulent heating$+$radiative cooling runs with global thermal balance. For pure turbulence runs in the subsonic regime, the rms density and surface brightness (SB) fluctuations vary as the square of the rms Mach number ($\mathcal{M}_{\text{rms}}$). However, with thermal balance, the density and SB fluctuations $(\delta SB/SB)$ are much larger. These scalings have implications for translating SB fluctuations into a turbulent velocity, particularly for cool cores. For thermal balance runs with large (cluster core) scale driving, both the hot and cold phases of the gas are supersonic. For small scale (one order of magnitude smaller than the cluster core) driving, multiphase gas forms on a much longer timescale but $\mathcal{M}_{\text{rms}}$ is smaller. Both small and large scale driving runs have velocities larger than the Hitomi results from the Perseus cluster. Thus turbulent heating as the dominant heating source in cool cluster cores is ruled out if multiphase gas is assumed to condense out from the ICM. Next we perform thermal balance runs in which we partition the input energy into thermal and turbulent parts and tune their relative magnitudes. The contribution of turbulent heating has to be $\lesssim 10\%$ in order for turbulence velocities to match Hitomi observations. If the dominant source of multiphase gas is not cooling from the ICM (but say uplift from the central galaxy), the importance of turbulent heating cannot be excluded.

Density distribution of the cosmological matter field

The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering, massive production of mock galaxy catalogs, and testing predictions of cosmological models. Here we make a comprehensive analysis of the dark matter PDF using a suite of 7000 N-body simulations that covers a wide range of numerical and cosmological parameters. We find that the PDF has a simple shape: it declines with density as a power-law P~rho**(-2), which is exponentially suppressed on both small and large densities. The proposed double-exponential approximation provides an accurate fit to all our N-body results for small filtering scales R< 5Mpc/h with rms density fluctuations sigma>1. In combination with the spherical infall model that works well for small fluctuations sigma<1, the PDF is now approximated with just few percent errors over the range of twelve orders of magnitude -- a remarkable example of precision cosmology. We find that at 5-10% level the PDF explicitly depends on redshift (at fixed sigma) and on cosmological density parameter Omega_m. We test different existing analytical approximations and find that the often used log-normal approximation is always 3-5 times less accurate than either the double-exponential approximation or the spherical infall model.

MassiveNuS: cosmological massive neutrino simulations

The non-zero mass of neutrinos suppresses the growth of cosmic structure on small scales. Since the level of suppression depends on the sum of the masses of the three active neutrino species, the evolution of large-scale structure is a promising tool to constrain the total mass of neutrinos and possibly shed light on the mass hierarchy. In this work, we investigate these effects via a large suite of N-body simulations that include massive neutrinos using an analytic linear-response approximation: the Cosmological Massive Neutrino Simulations (MassiveNuS). The simulations include the effects of radiation on the background expansion, as well as the clustering of neutrinos in response to the nonlinear dark matter evolution. We allow three cosmological parameters to vary: the neutrino mass sum Mν in the range of 0–0.6 eV, the total matter density Ωm, and the primordial power spectrum amplitude As. The rms density fluctuation in spheres of 8 comoving Mpc/h (σ8) is a derived parameter as a result. Our data products include N-body snapshots, halo catalogues, merger trees, ray-traced galaxy lensing convergence maps for four source redshift planes between zs=1–2.5, and ray-traced cosmic microwave background lensing convergence maps. We describe the simulation procedures and code validation in this paper. The data are publicly available at http://columbialensing.org.

Measurements of ICRF wave-induced density fluctuations in LHD by a microwave reflectometer

An O-mode microwave reflectometer has been developed to measure ICRF wave induced electron density fluctuations in LHD plasmas. The system has two probing frequencies (28.8 and 30.1 GHz) to measure two spatial points simultaneously. The rms density fluctuation levels are typically 0.01%. The linearity between the measured density fluctuation amplitude and the square root of the RF power is discussed. The decay length of the RF field was estimated to be 1 to 7 m under the operational condition investigated. A typical spatial distance between the two measurement points corresponding to the two probing frequencies is a few centimeters, and the fluctuation amplitudes at the two points are similar in amplitude. The phase difference between the two fluctuations show in-phase relationship on average. Out-of phase relationships, which implies a standing wave structure, are often observed when the wave absorption is expected to be poor.

A comparison of the galaxy peculiar velocity field with the PSCz gravity field - a Bayesian hyper-parameter method

We constructed a Bayesian hyper-parameter statistical method to quantify the difference between predicted velocities derived from the observed galaxy distribution in the IRAS-PSCz (Point Source Catalogue Redshift) survey and peculiar velocities measured using different distance indicators. In our analysis, we find that the model–data comparison becomes unreliable beyond 70 h−1 Mpc because of the inadequate sampling by the IRAS survey of prominent, distant superclusters, like the Shapley Concentration. On the other hand, the analysis of the velocity residuals shows that the PSCz gravity field provides an adequate model to the local, ≤70 h−1 Mpc, peculiar velocity field. The hyper-parameter combination of ENEAR, SN, A1SN and SFI++ catalogues in the Bayesian framework constrains the amplitude of the linear flow to be β = 0.53 ± 0.014. For an rms density fluctuation in the PSCz galaxy number density , we obtain an estimate of the growth rate of density fluctuations fσ8(z ∼ 0) = 0.42 ± 0.033, which is in excellent agreement with independent estimates based on different techniques.

Nonlinearities in modified gravity cosmology: Signatures of modified gravity in the nonlinear matter power spectrum

A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter \zeta, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution (\zeta = 1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance to include the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size and initial redshift). We find that, the nonlinear power spectra can differ by ~30% for 10% deviation from GR (|\zeta-1| = 0.1) where the rms density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.

The size distribution of void filaments in a ΛCDM cosmology

The size distribution of mini-filaments in voids has been derived from the Millennium Run halo catalogs at redshifts z=0,0.5,1 and 2. It is assumed that the primordial tidal field originated the presence of filamentary substructures in voids and that the void filaments have evolved only little, keeping the initial memory of the primordial tidal field. Applying the filament-finding algorithm based on the minimal spanning tree (MST) technique to the Millennium voids, we identify the mini-filaments running through voids and measure their sizes at each redshift. Then, we calculate the comoving number density of void filaments as a function of their sizes in the logarithmic interval and determine an analytic fitting function for it. It is found that the size distribution of void mini-filaments in the logarithmic interval has an almost universal shape, insensitive to the redshift: In the short-size section it is well approximated as a power-law, while in the long-size section it decreases exponentially. We expect that the universal size distribution of void filaments may provide a useful cosmological probe without resorting to the rms density fluctuations.

Galaxy groups in the 2dF Galaxy Redshift Survey: the number density of groups

The abundance of galaxy clusters as a function of mass is determined from the 2dF Galaxy Redshift Survey (2dFGRS) Percolation-Inferred Galaxy Group (2PIGG) catalogue. This is used to estimate the amplitude of the matter fluctuation spectrum, parametrized by the linear theory rms density fluctuations in spheres of radius 8h -1 Mpc, σ 8 . The best-fitting value for this parameter is highly correlated with the mean matter density in the Universe, Ω m , and is found to satisfy σ 8 = 0.25 Ω -0.92-4.5(Ω m -0.22)2 m ± 10 per cent (statistical) ±20 per cent (systematic) for 0.18 ≤ Ω m ≤ 0.50, assuming that Ω m + Ω ^ = 1. This gives σ 8 = 0.89 when evaluated at Ω m = 0.25. A ∼20 per cent correction has been applied to undo the systematic bias inherent in the measurement procedure. Mock catalogues, constructed from large cosmological N-body simulations, are used to help understand and model these systematic errors. The abundance of galaxy groups as a function of group b J -band luminosity is also determined. This is used in conjunction with the halo mass function, determined from simulations, to infer the variation of halo mass-to-light ratio over four orders of magnitude in halo mass. The mass-to-light ratio shows a minimum value of 100 h M ⊙ /L ⊙ in the bj band at a total group luminosity of L bJ ≈ 5×10 9 h -2 L ⊙ . Together with the observed Tully-Fisher (TF) relation, this implies that the observed rotation speed of TF galaxies with L bJ 10 10 h -2 L ⊙ is within ∼10 per cent of the typical circular speed of the haloes that host them.

WMAP constraints on the Cardassian model

We have investigated the constraints on the Cardassian model using the recent results from the Wilkinson Microwave Anisotropy Probe (WMAP) for the locations of the peaks of the Cosmic Microwave Background (CMB) anistropy spectrum. We find that the model is consistent with the recent observational data for certain range of the model parameter $n$ and the cosmological parameters. We find that the Cardassian model is favoured compared to $\Lambda$CDM model, for a higher spectral index ($n_s \approx 1$) together with lower value of Hubble parameter $h$ ($h\leq 0.71$). But for smaller values of $n_s$, both $\Lambda$CDM and Cardassian are equally favoured. Also, irrespective of Supernova constraint, CMB data alone predicts current acceleration of the universe in this model. We have also studied the constraint on the $\sigma_{8}$, the rms density fluctuations at $8h^{-1}$ Mpc scale.

Numerical Analysis of Compressible Turbulent Channel Flow between Adiabatic and Isothermal Wall. 2nd Report. Profiles of Turbulence Statistics.

The effects of the variable-property on the profiles of the turbulence statistics and the near-wall asymptotic behavior for the compressible turbulent channel flows are investigated using direct numerical simulation (DNS). Two cases of DNS are carried out. The first case is the compressible turbulent flow between isothermal walls, and the second case is one between adiabatic and isothermal walls. In the DNS, the Mach number based on the bulk velocity and sound speed at the isothermal wall is 1.5 and the Reynolds number based on the bulk density, bulk velocity, channel half-width, and viscosity at the isothermal wall is 3000. The main results are as follows : (1) When the velocity fluctuations, kinetic energy, and turbulent dissipation profiles are scaled by the wall variables, these profiles are larger near the isothermal wall and smaller near the adiabatic wall, comparing with those of the incompressible turbulent channel flow. On the other hand, these profiles agree well with the data of the incompressible turbulent channel flow, when these profiles are scaled by the local mean variables. It means Morkovin's hypothesis is applicable to these profiles. (2) The rms temperature fluctuation profile scaled by the mean temperature is almost the same as the rms density fluctuation profile scaled by the mean density, except that the rms temperature fluctuation on the isothermal wall is zero. (3) Differences between Favre and Reynolds averages on the Reynolds stresses are negligible in the wall bounded flow. (4) Morkovin's hypothesis is not applicable to the wall asymptotic behavior. (5) The rms temperature fluctuation profile scaled by the wall temperature varies linearly with the wall unit y+ near the isothermal wall and approaches a constant non-zero value with the decrease of y+ near the adiabatic wall.

Probability Distribution of Density Fluctuations in the Nonlinear Regime

We present a general procedure for obtaining the present density fluctuation probability distribution given the statistics of the initial conditions. The main difficulties faced with regard to this problem are those related to the non-linear evolution of the density fluctuations and those posed by the fact that the fields we are interested in are the result of filtering an underlying field with structure down to scales much smaller than that of filtering. The solution to the latter problem is discussed here in detail and the solution to the former is taken from a previous work. We have checked the procedure for values of the rms density fluctuation as large as 3/2 and several power spectra and found that it leads to results in excellent agreement with those obtained in numerical simulations. We also recover all available exact results from perturbation theory.

Light Propagation in Inhomogeneous Universes. II. Cosmological Parameter Survey

Using a multiple-lens plane algorithm, we study light propagation in inhomogeneous universes, for 43 different COBE-normalized Cold Dark Matter models, with various values of the density parameter 0, cosmological constant λ0, Hubble constant H0, and rms density fluctuation σ8. This is the largest cosmological parameter survey ever done in this field. We performed a total of 3,798 experiments, each experiment consisting of propagating a square beam of angular size 21.9 ′′ × 21.9 ′′ composed of 116,281 light rays from the observer up to redshift z = 3. These experiments provide statistics of the magnification, shear, and multiple imaging of distant sources. The results of these experiments can be compared with observations, and eventually help constraining the possible values of the cosmological parameters. Additionally, they provide insight into the gravitational lensing process and its complex relationship with the various cosmological parameters. Our main results are the following: (1) The magnification distribution depends mostly upon λ0 and σ8. As σ8 increases, the low-tail of the magnification distribution shifts toward lower magnifications, while the high-tail is hardly affected. The magnification distribution also becomes wider as λ0 increases. This effect is particularly large for models with λ0 = 0.8. (2) The magnification probability Pm is almost independent of σ8, for any combination of 0, λ0, H0, indicating that Pm does not depend strongly on the amount of largescale structure. (3) The shear distribution, like the magnification distribution, depends mostly upon λ0 and σ8. The shear distribution becomes wider with increasing σ8 and increasing λ0. The similarities between the properties of the magnification and shear distributions suggests that both phenomena are caused by weak lensing. (4) About 0.3% of sources have multiple images. The double-image probability P2 increases strongly with λ0 and is independent of 0, H0, and σ8. (5) The distribution of image separations depends strongly upon λ0, and is independent of σ8. Summarizing these results, we find that (1) The properties of gravitational lensing, both weak and strong, depend much more strongly upon λ0 than any other cosmological parameter, (2) magnification and shear are examples of weak lensing caused primarily by the distribution of background matter, with negligible contribution form galaxies, while multiple images and rings are examples of strong lensing, caused by direct interaction with galaxies, with negligible contribution from the background matter. Observations of weak lensing can be used to determine the cosmological constant and the density structure of the universe, while observations of strong lensing can be used to determine the cosmological constant and the internal structure of galaxies and clusters. Gravitational lensing depends much more weakly upon 0 and H0 than σ8 and λ0, making a determination of these parameters from observations more difficult.

Visible imaging of turbulence in the SOL of the Alcator C-Mod tokamak

Measurements of fluctuations in the scrape-off layer (SOL) of Alcator C-Mod plasmas were made using visible emission from the plasma edge. Line emissions from a local gas jet of He atoms were imaged along radially separated, toroidally viewing chords and provided local measurements (AR, ΔZ = 3.4 mm, RΔO ∼ 20) mm) of density fluctuations. The RMS emission fluctuation amplitudes, normalized by the average emission, ranged from 10% to 60%, depending on distance from the separatrix, and increased sharply beyond ρ from LCFS = 20 mm. These intensity fluctuations imply that radial profile of the normalized RMS density fluctuations varies from ∼20% to 90%. Typical fluctuation spectra show turbulence out to frequencies of ∼ 150 kHz, although most of the spectral power is below 20 kHz. The radial correlation length for the <20 kHz fluctuations is ∼7 mm. No essential differences were seen in the SOL fluctuations when plasmas with Enhanced D α ' (EDA) H-mode confinement were compared with those having L-mode confinement. In addition, fluctuations in natural' D α light, due to recycling at an outboard poloidal limiter, were imaged by a gated fast-framing camera and provided measurements of the poloidal size scale of the SOL fluctuations. Snapshots of D α emission were obtained with exposures of 2 and 10 μs. Typical fluctuation size in the poloidal dimension was 0.01-0.03 m. These striations/fluctuations were randomly located in the successive gated frames taken at 1000 Hz, as expected for edge turbulence.

Cosmological Parameter Survey Using the Gravitational Lensing Method

AbstractUsing a multiple-lens plane algorithm, we study light propagation in inhomogeneous universes for 43 different COBE-normalized Cold Dark Matter models, with various values of the density parameter Ω0, cosmological constant λ0, Hubble constant H0, and rms density fluctuation σ8.We performed a total of 3798 experiments, each experiment consisting of propagating a square beam of angular size 21.9″ 21.9″ composed of 116 281 light rays from the observer up to redshift z = 3. These experiments provide statistics of the magnification, shear, and multiple imaging of distant sources. The results of these experiments might be compared with observations, and eventually help constrain the possible values of the cosmological parameters. Additionally, they provide insight into the gravitational lensing process and its complex relationship with the various cosmological parameters.

Determining the Geometry and the Cosmological Parameters of the Universe through Sunyaev‐Zeldovich Effect Cluster Counts

We study Sunyaev-Zeldovich effect (SZE) cluster counts in different cosmologies. We find that even without full knowledge of the redshift distribution of SZE clusters, one can still readily distinguish a flat universe with a cosmological constant from an open universe. We divide clusters into a low-redshift group (with redshift z ≤ 0.5) and a high-redshift group (with z ≥ 1), and compute the ratio of r = N(z ≤ 0.5)/N(z ≥ 1), where N(z ≤ 0.5) is the number of flux-limited (S) SZE clusters with z ≤ 0.5, and N(z ≥ 1) is the number of flux-limited SZE clusters with z ≥ 1. With about the same total number of SZE clusters N(z ≥ 0), the r values for a flat universe with a nonzero cosmological constant and for an open universe occupy different regions in the S-r plot for the most likely cosmological parameters 0.25 ≤ Ω0 ≤ 0.35 and 0.2 ≤ Γ ≤ 0.3, where Ω0 is the matter density parameter of the universe and Γ is the shape parameter of the power spectrum of linear density fluctuations. Thus, with a deep SZE cluster survey, the ratio r can reveal independently of the normalization of the power spectrum whether we are living in a low-density flat universe or in an open universe. Within the flat universe scenario, the SZE cluster-normalized σ8 is studied, where σ8 is the rms density fluctuation within the top-hat scale 8 Mpc h-1, where h is the Hubble constant in units of 100 km s-1 Mpc-1. A functional relation of σ8 ∝ Ω is found. Combined with the X-ray cluster-normalized σ8 ∝ Ω, one can put constraints on both Ω0 and σ8 simultaneously.

Testing the Convergence of the Multiple Lens Plane Algorithm

We perform a series of ray-tracing experiments to test the convergence of the multiple lens plane algorithm. We consider six COBE-normalized cold dark matter (CDM) models with various values of the density parameter, Ω0, cosmological constant, λ0, Hubble constant, H0, and rms density fluctuation, σ8. For each model, we choose one ray-tracing experiment and perform that experiment six times, with six different numbers of lens planes. We study how the results of these experiments depend upon the number of planes used. For each experiment, we compute the magnification distribution, the magnification probability, and the location of the beam on the source plane. We also compute a stringent pointwise cross-correlation between the magnification maps generated for the same model with different numbers of planes. The cross-correlations converge as the number of planes is increased, but only for relatively large numbers of planes, ~100-200 planes, because the magnification maps suffer shifts in position due to small shifts in ray position in examples with different numbers of planes. Other results, such as the magnification distribution, are quite reliable even with only one experiment per model. We find that all the results converge as the number of planes increases, and that, for sources at redshifts zs ~ 2.5, 14 planes are sufficient to obtain reliable results for all cosmological models. This is significantly smaller than the number of planes typically used in such experiments.

A Database ofCOBE‐normalized Cold Dark Matter Simulations

We have simulated the formation and evolution of large-scale structure in the universe, for 68 different COBE-normalized cosmological models. For each cosmological model, we have performed between one and three simulations, for a total of 160 simulations. This constitutes the largest database of cosmological simulations ever assembled, and the largest cosmological parameter space ever covered by such simulations. We are making this database available to the astronomical community. We provide instructions for accessing the database and for converting the data from computational units to physical units. The database includes tilted cold dark matter (TCDM) models, tilted open cold dark matter (TOCDM) models, and tilted Λ cold dark matter (TΛCDM) models. (For several simulations, the primordial exponent n of the power spectrum is near unity, hence these simulations can be considered as untilted.) The simulations cover a four-dimensional cosmological parameter phase space, the parameters being the present density parameter Ω0, cosmological constant λ0, and Hubble constant H0, and the rms density fluctuation σ8 at scale 8 h-1 Mpc. All simulations were performed using a P3M algorithm with 643 particles on a 1283 mesh, in a cubic volume of comoving size 128 Mpc. Each simulation starts at a redshift of 24 and is carried up to the present. More simulations will be added to the database in the future. We have performed a limited amount of data reduction and analysis of the final states of the simulations. We computed the rms density fluctuation, the two-point correlation function, the velocity moments, and the properties of clusters. Our results are the following: 1. The numerical value σ of the rms density fluctuation differs from the value σ obtained by integrating the power spectrum at early times and extrapolating linearly up the present. This results from the combined effects of discreteness in the numerical representation of the power spectrum, the presence of a Gaussian factor in the initial conditions, and late-time nonlinear evolution. The first of these three effects is negligible. The second and third are comparable, and can both modify the value of σ8 by up to 10%. Nonlinear effects, however, are important only for models with σ8 > 0.6, and can result in either an increase or a decrease in σ8. 2. The observed galaxy two-point correlation function is well reproduced (assuming an unbiased relation between galaxies and mass) by models with σ8 ~ 0.8, nearly independently of the values of the other parameters, Ω0, λ0, and H0. For models with σ8 > 0.8, the correlation function is too large and its slope is too steep. For models with σ8 0.9, it has a U shape, which is probably a numerical artifact caused by the finite number of particles used in the simulations. For all models, clusters have densities in the range 100-1000 times the mean background density, the spin parameters λ are in the range 0.008-0.2, with the median near 0.05, and about of the clusters are prolate. Rotationally supported disks do not form in these simulations.

The Effects of Clumping and Substructure on Intracluster Medium Mass Measurements

We examine an ensemble of 48 simulated clusters to determine the effects of small-scale density fluctuations and large-scale substructure on X-ray measurements of the intracluster medium (ICM) mass. We measure rms density fluctuations in the ICM that can be characterized by a mean mass-weighted clumping factor C ≡ ρ2/ρ2 between 1.3 and 1.4 within a density contrast of 500. These fluctuations arise from the cluster history of accretion shocks and major mergers, and their presence enhances the cluster's luminosity relative to the smooth case. We expect, therefore, that ICM mass measurements utilizing models that assume uniform density at a given radius carry a bias of order ≈ 1.16. We verify this result by performing ICM mass measurements on X-ray images of the simulations and finding the expected level of bias. The varied cluster morphologies in our ensemble also allow us to investigate the effects of departures from spherical symmetry on our measurements. We find that the presence of large-scale substructure does not further bias the resulting gas mass unless it is pronounced enough to produce a second peak in the image of at least 1% the maximum surface brightness. We analyze the subset of images with no secondary peaks and find a bias of 9% and a Gaussian random error of 4% in the derived mass.