Velocity Dispersion Estimates Research Articles

A Closer Look at the Extended Edge-on Low-surface Brightness Galaxies

To understand the origin of extended disks of low-surface brightness (LSB) galaxies, we studied in detail four such systems with large disks seen edge on. Two of them are edge-on giant LSB galaxies (gLSBGs) recently identified by our team. The edge-on orientation of these systems boosts their surface brightnesses that provided an opportunity to characterize stellar populations spectroscopically and yielded the first such measurements for edge-on gLSBGs. We collected deep images of one galaxy using the 1.4 m Milanković Telescope, which we combined with the archival Subaru Hyper Suprime-Cam and DESI Legacy Surveys data available for the three other systems, and measured the structural parameters of the disks. We acquired deep long-slit spectra with the Russian 6 m telescope and the 10 m Keck II telescope and estimated stellar population properties in the high-surface brightness and LSB regions as well as the gas-phase metallicity distribution. The gas metallicity gradients are shallow to flat in the range between 0 and −0.03 dex per exponential disk scale length, which is consistent with the extrapolation of the gradient–scale length relation for smaller disk galaxies. Our estimates of stellar velocity dispersion in the LSB disks as well as the relative thickness of the disks indicate the dynamical overheating. Our observations favor mergers as the essential stage in the formation scenario for massive LSB galaxies.

Escape Velocity Mass of A1063

We measure the radius–velocity phase-space edge profile of A1063 using galaxy redshifts from Karman et al. and Mercurio et al. Combined with a cosmological model and after accounting for interlopers and sampling effects, we infer the escape velocity profile. Using the Poisson equation, we then directly constrain the gravitational potential profile and find excellent agreement between three different density models. For the Navarro–Frenk–White profile, we find log10(M 200,crit) = 15.40−0.12+0.06 M ⊙, consistent to within 1σ of six recently published lensing masses. We argue that this consistency is due to the fact that the escape technique shares no common systematics with lensing other than radial binning. These masses are 2–4σ lower than estimates made using X-ray data, in addition to the Gómezet al. velocity dispersion estimate. We measure the 1D velocity dispersion within r 200 to be σv=1477−99+87 km s−1, which combined with our escape velocity mass, brings the dispersion for A1063 in-line with hydrodynamic cosmological simulations for the first time.

Dynamically cold disks in the early Universe: Myth or reality?

Context. Theoretical models struggle to reproduce dynamically cold disks with significant rotation-to-dispersion support (Vrot/σ) observed in star-forming galaxies in the early Universe at redshift z > 4. Aims. We aim to explore the possible emergence of dynamically cold disks in cosmological simulations and to understand whether different kinematic tracers can help reconcile the tension between theory and observations. Methods. We used 3218 galaxies from the SERRA suite of zoom-in simulations, with 8 ≤ log(M⋆/M⊙) ≤ 10.3 and star formation rates SFR ≤ 128 M⊙/yr, within the 4 ≤ z ≤ 9 range. We generated hyperspectral data cubes for 2 × 3218 synthetic observations of Hα and [CII]. Results. We find that the choice of kinematic tracer strongly influences gas velocity dispersion (σ) estimates. In Hα ([C II]) synthetic observations, we observe a strong (mild) correlation between σ and M⋆. This difference mostly arises for M⋆ > 109 M⊙ galaxies, for which σHα > 2σ[CII] for a significant fraction of the sample. Regardless of the tracer, our predictions suggest the existence of massive (M⋆ > 1010 M⊙) galaxies with Vrot/σ > 10 at z > 4, maintaining cold disks for > 10 orbital periods (∼ 200 Myr). Furthermore, we find no significant redshift dependence for the Vrot/σ ratio in our sample. Conclusions. Our simulations predict the existence of dynamically cold disks in the early Universe. However, different tracers are sensitive to different kinematic properties. While [C II] effectively traces the thin gaseous disk of galaxies, Hα includes the contribution from ionized gas beyond the disk region, characterized by prevalent vertical or radial motions that may be associated with outflows. We show that Hα halos could be a signature of these galactic outflows. This result emphasizes the importance of combining ALMA and JWST/NIRspec studies of high-z galaxies.

Imposters among us: globular cluster kinematics and the halo mass of ultra-diffuse galaxies in clusters

ABSTRACT The velocity dispersion of globular clusters (GCs) around ultra-diffuse galaxies (UDGs) in the Virgo cluster spans a wide range, including cases where GC kinematics suggest haloes as massive as (or even more massive than) that of the Milky Way around these faint dwarfs. We analyse the catalogues of GCs derived in post-processing from the TNG50 cosmological simulation to study the GC system kinematics and abundance of simulated UDGs in galaxy groups and clusters. UDGs in this simulation reside exclusively in dwarf-mass haloes with M200 ≲ 1011.2 M⊙. When considering only GCs gravitationally bound to simulated UDGs, we find GCs properties that overlap well with several observational measurements for UDGs. In particular, no bias towards overly massive haloes is inferred from the study of bound GCs, confirming that GCs are good tracers of UDG halo mass. However, we find that contamination by intracluster GCs may, in some cases, substantially increase velocity dispersion estimates when performing projected mock observations of our sample. We caution that targets with less than 10 GC tracers are particularly prone to severe uncertainties. Measuring the stellar kinematics of the host galaxy should help confirm the unusually massive haloes suggested by GC kinematics around some UDGs.

Extreme Tidal Stripping May Explain the Overmassive Black Hole in Leo I: A Proof of Concept

A recent study found dynamical evidence of a supermassive black hole of ∼3 × 106 M ⊙ at the center of Leo I, the most distant dwarf spheroidal galaxy of the Milky Way. This black hole, comparable in mass to the Milky Way’s Sgr A*, places the system >2 orders of magnitude above the standard M •–M ⋆ relation. We investigate the possibility, from a dynamical standpoint, that Leo I’s stellar system was originally much more massive and, thus, closer to the relation. Extreme tidal disruption from one or two close passages within the Milky Way’s virial radius could have removed most of its stellar mass. A simple analytical model suggests that the progenitor of Leo I could have experienced a mass loss in the range 32%–57% from a single pericenter passage, depending on the stellar velocity dispersion estimate. This mass-loss percentage increases to the range 66%–78% if the pericenter occurs at the minimum distance allowed by current orbital reconstructions. Detailed N-body simulations show that the mass loss could reach ∼90% with up to two passages, again with pericenter distances compatible with the minimum value allowed by Gaia data. Despite very significant uncertainties in the properties of Leo I, we reproduce its current position and velocity dispersion, as well as the final stellar mass enclosed in 1 kpc (∼5 × 106 M ⊙) within a factor <2. The most recent tidal stream is directed along our line of sight toward Leo I, making it difficult to detect. Evidence from this extreme tidal disruption event could be present in current Gaia data in the form of extended tidal streams.

Velocity dispersions of clusters in the Dark Energy Survey Y3 redMaPPer catalogue

ABSTRACT We measure the velocity dispersions of clusters of galaxies selected by the red-sequence Matched-filter Probabilistic Percolation (redMaPPer) algorithm in the first three years of data from the Dark Energy Survey (DES), allowing us to probe cluster selection and richness estimation, λ, in light of cluster dynamics. Our sample consists of 126 clusters with sufficient spectroscopy for individual velocity dispersion estimates. We examine the correlations between cluster velocity dispersion, richness, X-ray temperature, and luminosity, as well as central galaxy velocity offsets. The velocity dispersion–richness relation exhibits a bimodal distribution. The majority of clusters follow scaling relations between velocity dispersion, richness, and X-ray properties similar to those found for previous samples; however, there is a significant population of clusters with velocity dispersions that are high for their richness. These clusters account for roughly 22 per cent of the λ &amp;lt; 70 systems in our sample, but more than half (55 per cent) of λ &amp;lt; 70 clusters at z &amp;gt; 0.5. A couple of these systems are hot and X-ray bright as expected for massive clusters with richnesses that appear to have been underestimated, but most appear to have high velocity dispersions for their X-ray properties likely due to line-of-sight structure. These results suggest that projection effects contribute significantly to redMaPPer selection, particularly at higher redshifts and lower richnesses. The redMaPPer determined richnesses for the velocity dispersion outliers are consistent with their X-ray properties, but several are X-ray undetected and deeper data are needed to understand their nature.

Velocity dispersion and dynamical mass for 270 galaxy clusters in the Planck PSZ1 catalogue

We present the velocity dispersion and dynamical mass estimates for 270 galaxy clusters included in the first Planck Sunyaev-Zeldovich (SZ) source catalogue, the PSZ1. Part of the results presented here were achieved during a two-year observational program, the ITP, developed at the Roque de los Muchachos Observatory (La Palma, Spain). In the ITP we carried out a systematic optical follow-up campaign of all the 212 unidentified PSZ1 sources in the northern sky that have a declination above −15° and are without known counterparts at the time of the publication of the catalogue. We present for the first time the velocity dispersion and dynamical mass of 58 of these ITP PSZ1 clusters, plus 35 newly discovered clusters that are not associated with the PSZ1 catalogue. Using Sloan Digital Sky Survey archival data, we extend this sample, including 212 already confirmed PSZ1 clusters in the northern sky. Using a subset of 207 of these galaxy clusters, we constrained the MSZ–Mdyn scaling relation, finding a mass bias of (1 − B) = 0.83 ± 0.07(stat) ± 0.02(sys). We show that this value is consistent with other results in the literature that were obtained with different methods (X-ray, dynamical masses, or weak-lensing mass proxies). This result cannot dissolve the tension between primordial cosmic microwave background anisotropies and cluster number counts in the ΩM–σ8 plane.

Central velocity dispersion catalogue of LAMOST-DR7 galaxies

ABSTRACT The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) is a major facility to carry out spectroscopic surveys for cosmology and galaxy evolution studies. The seventh data release of the LAMOST ExtraGAlactic Survey (LEGAS) is currently available and including redshifts of 193 361 galaxies. These sources are spread over $\sim 11\, 500$ deg2 of the sky, largely overlapping with other imaging (SDSS and HSC) and spectroscopic (BOSS) surveys. The estimated depth of the galaxy sample, r ∼ 17.8, the high signal-to-noise ratio, and the spectral resolution R = 1800, make the LAMOST spectra suitable for galaxy velocity dispersion (VD) measurements, which are invaluable to study the structure and formation of galaxies and to determine their central dark matter content. We present the first estimates of central VD of $\sim 86\, 000$ galaxies in LAMOST footprint. We have used a wrap-up procedure to perform the spectral fitting using ppxf, and derive VD measurements. Statistical errors are also assessed by comparing LAMOST VD estimates with the ones of SDSS and BOSS over a common sample of $\sim 51\, 000$ galaxies. The two data sets show a good agreement, within the statistical errors, in particular when VD values are corrected to 1 effective radius aperture. We also present a preliminary mass–σ relation and find consistency with previous analyses based on local galaxy samples. These first results suggest that LAMOST spectra are suitable for galaxy VD measurements to complement the available catalogues of galaxy internal kinematics in the Northern hemisphere. We plan to expand this analysis to next LAMOST data releases.

Biases in galaxy cluster velocity dispersion and mass estimates in the small Ngal regime

Aims. We present a study of the statistical properties of three velocity dispersion and mass estimators: biweight, gapper, and standard deviation for a small number of galaxies (Ngal ≤ 75). Methods. Using a set of 73 numerically simulated galaxy clusters, we first characterised the statistical bias and the variance for each one of the three estimators (biweight, gapper, and standard deviation) in the determination of the velocity dispersion and the dynamical mass of the clusters through the σ–M relation. These results were used to define a new set of unbiased estimators that are able to correct for these statistical biases with a minimum increase in associated variance. We also used the same set of numerical simulations to characterise two other physical biases that affect the estimates: the effect of velocity segregation on the selection of cluster members, and the effect of using cluster members within different physical radii from the cluster centre. Results. The standard deviation (and its unbiased counterpart) is the estimator with the lowest variance estimator after the biweight and gapper. The effect of velocity segregation in the selection of galaxies within the sub-sample of the most massive galaxies in the cluster introduces a bias of 2% in the velocity dispersion estimate when it is calculated using a quarter of the most massive cluster members. We also find a dependence of the velocity dispersion estimate on the aperture radius as a fraction of R200. This is consistent with previous results in the literature. Conclusions. The proposed set of unbiased estimators effectively provides a correction of the velocity dispersion and mass estimates from the statistical and physical effects discussed above for small numbers of cluster members. When these new estimators are applied to a subset of simulated observations, they can retrieve bias-corrected values for the mean velocity dispersion and the mean mass; the standard deviation has the lowest variance. Although for a single galaxy cluster the statistical and physical effects discussed here are comparable to or slightly smaller than the bias introduced by interlopers, they are relevant when ensemble properties and scaling relations for large number of clusters are studied.

Nonlinear FAVO Dispersion Quantification Based on the Analytical Solution of the Viscoelastic Wave Equation

Wave-induced fluid flow is the main cause of seismic attenuation and dispersion. So the estimated velocity dispersion information can be used to identify reservoir fluid and effectively reduce the risk of reservoir drilling. Using equivalence of dispersion and attenuation between poroelastic and viscoelastic media, we developed the method of FAVO (frequency-dependent amplitude variation with offset) dispersion quantitative estimation based on the analytical solution of 1D viscoelastic wave equation. Compared with the current single-interface velocity dispersion estimation method, the new nonlinear approach uses the analytical solution of 1D viscoelastic wave equation as the forward modeling engine. This method can conveniently handle the attenuation and generate the full-wave field response of a layered medium. First, the compound matrix method (CMM) was applied to rapidly obtain the analytical solution by vectorization. Further, we analyzed the seismic response characteristics through the model data to clarify the effectiveness of the forward modeling method. Then, the more reliable P-wave velocity, S-wave velocity, and density were recovered based on prestack viscoelastic waveform inversion (PVWI). Combining with the inversion results, the derivative matrix was calculated to perform nonlinear velocity dispersion estimation. Finally, the new estimation method was tested with the model and actual data. The experiments show that the developed method is clearly superior to the single-interface dispersion estimation method in accuracy and resolution. This approach can be used as a new choice reservoir fluid identification.

Hubble Space Telescope Astrometry in the Orion Nebula Cluster: Census of Low-mass Runaways

Abstract We present a catalog of high-precision proper motions in the Orion Nebula Cluster (ONC), based on Treasury Program observations with the Hubble Space Telescope’s (HST) ACS/WFC camera. Our catalog contains 2454 objects in the magnitude range of 14.2 &lt; m F775W &lt; 24.7, thus probing the stellar masses of the ONC from ∼0.4 M ☉ down to ∼0.02 M ☉ over an area of ∼550 arcmin2. We provide a number of internal velocity dispersion estimates for the ONC that indicate a weak dependence on stellar location and mass. There is good agreement with the published velocity dispersion estimates, although nearly all of them (including ours at and mas yr−1) might be biased by the overlapping young stellar populations of Orion A. We identified four new ONC candidate runaways based on HST and the Gaia DR 2 data, all with masses less than ∼1 M ☉. The total census of known candidate runaway sources is 10—one of the largest samples ever found in any Milky Way open star cluster. Surprisingly, none of them have tangential velocities exceeding 20 km s−1. If most of them indeed originated in the ONC, it may compel the re-examination of dynamical processes in very young star clusters. It appears that the mass function of the ONC is not significantly affected by the lost runaways.

The velocity field of the Lyra complex

Context. The formation of cosmic structures culminates with the assembly of galaxy clusters, a process that is quite different from cluster to cluster. Aims. We present the study of the structure and dynamics of the Lyra complex, consisting of the two clusters RXC J1825.3+3026 and CIZA J1824.1+3029, which was very recently studied by using both X-ray and radio data. Methods. This is the first analysis based on the kinematics of member galaxies. New spectroscopic data for 285 galaxies were acquired at the Italian Telescopio Nazionale Galileo and were used in combination with PanSTARRS photometry. The result of our member selection is a sample of 198 galaxies. Results. For RXCJ1825 and CIZAJ1824 we report the redshifts, z = 0.0645 and z = 0.0708, the first estimates of velocity dispersion, σv = 995+131−125 km s−1 and σv = 700 ± 50 km s−1, and of dynamical mass, M200 = 1.1 ± 0.4 × 1015 M⊙ and M200 = 4 ± 0.1 × 1014 M⊙. The past assembly of RXCJ1825 is traced by the two dominant galaxies, which are both aligned with the major axis of the galaxy distribution along the east–west direction, and by a minor northeast substructure. We also detect a quite peculiar high velocity field in the southwest region of the Lyra complex. This feature is likely related to a very luminous galaxy, which is characterized by a high velocity. This galaxy is suggested to be the central galaxy of a group that is in interaction with RXCJ1825 according to very recent studies based on X-ray and radio data. The redshift of the whole Lyra complex is z = 0.067. Assuming that the redshift difference between RXCJ1825 and CIZAJ1824 is due to the relative kinematics, the projected distance between the cluster centers is D ∼ 1.3 Mpc and the line–of–sight velocity difference is ∼1750 km s−1. A dynamical analysis of the system shows that the two clusters are likely to be gravitationally bound in a pre-merger phase, and that CIZAJ1824 is moving toward RXCJ1825. Conclusions. Our results corroborate a picture where the Lyra region is the place of a very complex scenario of cluster assembly.

Biases in the estimation of velocity dispersions and dynamical masses for galaxy clusters

Using a set of 73 numerically simulated galaxy clusters, we have characterised the statistical and physical biases for three velocity dispersion and mass estimators, namely biweight, gapper and standard deviation, in the small number of galaxies regime (Ngal ≤ 75), both for the determination of the velocity dispersion and the dynamical mass of the clusters via the σ–M relation. These results are used to define a new set of unbiased estimators, that are able to correct for those statistical biases. By applying these new estimators to a subset of simulated observations, we show that they can retrieve bias-corrected values for both the mean velocity dispersion and the mean mass.

Optical validation and characterization of Planck PSZ2 sources at the Canary Islands observatories

Context. The second legacy catalog of Planck Sunyaev–Zeldovich (SZ) sources, hereafter PSZ2, provides the largest galaxy cluster sample selected by means of the SZ signature of the clusters in a full sky survey. In order to fully characterize this PSZ2 sample for cosmological studies, all the members should be validated and the physical properties of the clusters, including mass and redshift, should be derived. However, at the time of its publication, roughly 21% of the 1653 PSZ2 members had no known counterpart at other wavelengths. Aims. Here, we present the second and last year of observations of our optical follow-up program 128-MULTIPLE-16/15B (hereafter LP15), which has been developed with the aim of validating all the unidentified PSZ2 sources in the northern sky with declinations higher than −15° that have no correspondence in the first Planck catalog PSZ1. The description of the program and the first year of observations have been presented previously. Methods. The LP15 program was awarded 44 observing nights that were spread over two years with the Isaac Newton Telescope (INT), the Telescopio Nazionale Galileo (TNG), and the Gran Telescopio Canarias (GTC), all at Roque de los Muchachos Observatory (La Palma). Following the same method as described previously, we performed deep optical imaging for more than 200 sources with the INT and spectroscopy for almost 100 sources with the TNG and GTC at the end of the LP15 program. We adopted robust confirmation criteria based on velocity dispersion and richness estimates for the final classification of the new galaxy clusters as the optical counterparts of the PSZ2 detections. Results. Here, we present the observations of the second year of LP15, as well as the final results of the program. The full LP15 sample comprises 190 previously unidentified PSZ2 sources. Of these, 106 objects were studied before, while the remaining sample (except for 6 candidates) has been completed in the second year and is discussed here. In addition to the LP15 sample, we here study 42 additional PSZ2 objects that were originally validated as real clusters because they matched a WISE or PSZ1 counterpart, but they had no measured spectroscopic redshift. In total, we confirm the optical counterparts for 81 PSZ2 sources after the full LP15 program, 55 of them with new spectroscopic information. Forty of these 81 clusters are presented in this paper. After the LP15 observational program the purity of the PSZ2 catalog has increased from 76.7% originally to 86.2%. In addition, we study the possible reasons for false detection, and we report a clear correlation between the number of unconfirmed sources and galactic thermal dust emission.

Two Point Method For Robust Shear Wave Phase Velocity Dispersion Estimation of Viscoelastic Materials

Ultrasound shear wave elastography (SWE) is an imaging modality used for noninvasive, quantitative evaluation of tissue mechanical properties. SWE uses an acoustic radiation force to produce laterally propagating shear waves that can be tracked in spatial and temporal domains in order to obtain the wave velocity. One of the ways to study the viscoelasticity is through examining the shear wave velocity dispersion curves. In this paper, we present an alternative method to two-dimensional Fourier transform (2D-FT). Our unique approach (2P-CWT) considers shear wave propagation measured in two lateral locations only and uses wavelet transformation analysis. We used the complex Morlet wavelet function as the mother wavelet to filter two shear waves at different locations. We examined how the first signal position and the distance between the two locations affect the shear wave velocity dispersion estimation in 2P-CWT. We tested this new method on a digital phantom data created using the local interaction simulation approach (LISA) in viscoelastic media with and without added white Gaussian noise to the wave motion. Moreover, we tested data acquired from custom made tissue mimicking viscoelastic phantom experiments and ex vivo porcine liver measurements. We compared results from 2P-CWT with the 2D-FT technique. 2P-CWT provided dispersion curves estimation with lower errors over a wider frequency band in comparison to 2D-FT. Tests conducted showed that the two-point technique gives results with better accuracy in simulation results and can be used to measure phase velocity of viscoelastic materials.

HALO7D I. The Line-of-sight Velocities of Distant Main-sequence Stars in the Milky Way Halo

Abstract The Halo Assembly in Lambda-CDM: Observations in 7 Dimensions (HALO7D) data set consists of Keck II/DEIMOS spectroscopy and Hubble Space Telescope–measured proper motions of Milky Way halo main-sequence turnoff stars in the CANDELS fields. In this paper, we present the spectroscopic component of this data set and discuss target selection, observing strategy, and survey properties. We present a new method of measuring line-of-sight (LOS) velocities by combining multiple spectroscopic observations of a given star, utilizing Bayesian hierarchical modeling. We present the LOS velocity distributions of the four HALO7D fields and estimate their means and dispersions. All of the LOS distributions are dominated by the “hot halo”: none of our fields are dominated by substructure that is kinematically cold in the LOS velocity component. Our estimates of the LOS velocity dispersions are consistent across the different fields, and these estimates are consistent with studies using other types of tracers. To complement our observations, we perform mock HALO7D surveys using the synthetic survey software Galaxia to “observe” the Bullock &amp; Johnston accreted stellar halos. Based on these simulated data sets, the consistent LOS velocity distributions across the four HALO7D fields indicate that the HALO7D sample is dominated by stars from the same massive (or few relatively massive) accretion event(s).

Depth-Dependent Geoacoustic Inferences With Dispersion at the New England Mud Patch via Reflection Coefficient Inversion

Depth-dependent geoacoustic properties are inferred from wide-angle frequency-domain reflection-coefficient data at two sites with different mud-layer thicknesses on the New England Mud Patch. A trans-dimensional Bayesian inversion is employed to estimate geoacoustic properties and uncertainties from these data using the viscous grain shearing sediment model and spherical-wave reflection-coefficient predictions. Results near the thick-mud (SWAMI) site show a nearly uniform sound velocity over the upper approximately 9.2 m, followed by a transition layer with velocity increasing nonlinearly by $\sim$ 280 m/s over 1.8 m. At the thin-sediment (VC31-2) site, the velocity profile exhibits a similar transition layer. Estimates of intrinsic velocity and attenuation dispersion are also obtained. Over the measurement band of about 400–1300 Hz, the velocity in the fine-grained sediments (mud) at both sites varies by only a few meters per second, i.e., velocity is nearly independent of frequency. The attenuation of the fine-grained sediments at both sites follows a nearly linear frequency dependence. The geoacoustic inferences compare reasonably closely with independent measurements including core measurements, chirp-reflection data, and angle of intromission data.

Gaia DR 2 and VLT/FLAMES search for new satellites of the LMC

A wealth of tiny galactic systems populates the surroundings of the Milky Way. However, some of these objects might have originated as former satellites of the Magellanic Clouds, in particular of the Large Magellanic Cloud (LMC). Examples of the importance of understanding how many systems are genuine satellites of the Milky Way or the LMC are the implications that the number and luminosity-mass function of satellites around hosts of different mass have for dark matter theories and the treatment of baryonic physics in simulations of structure formation. Here we aim at deriving the bulk motions and estimates of the internal velocity dispersion and metallicity properties in four recently discovered distant southern dwarf galaxy candidates, Columba I, Reticulum III, Phoenix II, and Horologium II. We combined Gaia DR2 astrometric measurements, photometry, and new FLAMES/GIRAFFE intermediate-resolution spectroscopic data in the region of the near-IR Ca II triplet lines; this combination is essential for finding potential member stars in these low-luminosity systems. We find very likely member stars in all four satellites and are able to determine (or place limits on) the bulk motions and average internal properties of the systems. The systems are found to be very metal poor, in agreement with dwarf galaxies and dwarf galaxy candidates of similar luminosity. Of these four objects, we can only firmly place Phoenix II in the category of dwarf galaxies because of its resolved high velocity dispersion (9.5 −4.4+6.8 km s−1) and intrinsic metallicity spread (0.33 dex). For Columba I we also measure a clear metallicity spread. The orbital pole of Phoenix II is well constrained and close to that of the LMC, suggesting a prior association. The uncertainty on the orbital poles of the other systems is currently very large, so that an association cannot be excluded, except for Columba I. Using the numbers of potential former satellites of the LMC identified here and in the literature, we obtain for the LMC a dark matter mass of M200 = 1.9 −0.9+1.3 × 1011 M⊙.

Phase velocity dispersion estimation of viscoelastic materials by two-point wavelet-based method

Ultrasound shear wave elastography (SWE) is a promising imaging modality used for noninvasive, quantitative evaluation of tissue mechanical properties. This method uses an acoustic radiation force to produce laterally propagating shear waves that can be tracked to obtain the wave velocity. One of the ways to explore the viscoelasticity is through examining the shear wave velocity dispersion curves. In this paper, we present an alternative method to the classical two-dimensional Fourier transform (2D-FT), a two-point wavelet transformation method. We use the Morlet wavelet function as the mother wavelet to filter two shear waves at different locations. We examined how starting distance from the push and distance between the two locations affected the shear wave velocity dispersion. We tested this method on digital phantom data created using local interaction simulation approach (LISA) in viscoelastic media and on data acquired from phantom experiments. We compared results from the two-point method with the 2D-FT technique. The two-point method provided dispersion curves estimation with lower errors over a wider frequency band. Tests conducted showed that the two-point technique gives results with better accuracy in simulation results and can be used to measure phase velocity of viscoelastic materials.

Robust Phase Velocity Dispersion Estimation of Viscoelastic Materials Used for Medical Applications Based on the Multiple Signal Classification Method.

Ultrasound shear wave elastography (SWE) is emerging as a promising imaging modality for the noninvasive evaluation of tissue mechanical properties. One of the ways to explore the viscoelasticity is through analyzing the shear wave velocity dispersion curves. To explore the dispersion, it is necessary to estimate the shear wave velocity at each frequency. An increase of the available spectrum to be used for phase velocity estimation is significant for a tissue dispersion analysis in vivo. A number of available methods suffer because the available spectrum that one can work with is limited. We present an alternative method to the classical 2-D Fourier transform (2D-FT) that uses the multiple signal classification (MUSIC) technique to provide robust estimation of the -space and phase velocity dispersion curves. We compared results from the MUSIC method with the 2D-FT technique twofold: by searching for maximum peaks and gradient-based strategy. We tested this method on digital phantom data created using finite-element methods (FEMs) in viscoelastic media as well as on the experimental phantoms used in the Radiological Society of North America Quantitative Imaging Biomarker Alliance effort for the standardization of shear wave velocity in liver fibrosis applications. In addition, we evaluated the algorithm with different levels of added noise for FEMs. The MUSIC algorithm provided dispersion curves estimation with lower errors than the conventional 2D-FT method. The MUSIC method can be used for the robust evaluation of shear wave velocity dispersion curves in viscoelastic media.