Posts Tagged three dimensional shape

Recent Postings from three dimensional shape

The intrinsic shapes of prestellar cores

Using observations of prestellar cores to infer their intrinsic properties requires the solution of several poorly constrained inverse problems. Here we address one of these problems, namely to deduce from the observed aspect ratios of prestellar cores their intrinsic three-dimensional shapes. Four models are proposed, all based on the standard assumption that prestellar cores are ellipsoidal, and on the further assumption that a core’s shape is not correlated with its absolute size. The first and simplest model, M1, has a single free parameter, and assumes that the relative axes of a prestellar core are drawn randomly from a log-normal distribution with zero mean and standard deviation \tauO. The second model, M2a, has two free parameters, and assumes that the log-normal distribution (with standard deviation \tauO) has a finite mean, \nuO, defined so that \nuO<0 means elongated (or filamentary) cores are favoured, whereas \nuO>0 means flattened (or disc-like) cores are favoured. Details of the third model (M2b, two free parameters) and the fourth model (M4, four free parameters) are given in the text. Markov chain Monte Carlo sampling and Bayesian analysis are used to map out the posterior probability density functions of the model paramaters, and the relative merits of the models are compared using Bayes factors. We show that M1 provides an acceptable fit to the data with \tauO=0.57+/-0.06; and that, although the other models sometimes provide an improved fit, there is no strong justification for the introduction of their additional parameters.

The Three-Dimensional Shapes of Galaxy Clusters

While clusters of galaxies are considered one of the most important cosmological probes, the standard spherical modelling of the dark matter and the intracluster medium is only a rough approximation. Indeed, it is well established both theoretically and observationally that galaxy clusters are much better approximated as triaxial objects. However, investigating the asphericity of galaxy clusters is still in its infancy. We review here this topic which is currently gathering a growing interest from the cluster community. We begin by introducing the triaxial geometry. Then we discuss the topic of deprojection and demonstrate the need for combining different probes of the cluster’s potential. We discuss the different works that have been addressing these issues. We present a general parametric framework intended to simultaneously fit complementary data sets (X-ray, Sunyaev Zel’dovich and lensing data). We discuss in details the case of Abell 1689 to show how different models/data sets lead to different haloe parameters. We present the results obtained from fitting a 3D NFW model to X-ray, SZ, and lensing data for 4 strong lensing clusters. We argue that a triaxial model generally allows to lower the inferred value of the concentration parameter compared to a spherical analysis. This may alleviate tensions regarding, e.g. the over-concentration problem. However, we stress that predictions from numerical simulations rely on a spherical analysis of triaxial halos. Given that triaxial analysis will have a growing importance in the observational side, we advocate the need for simulations to be analysed in the very same way, allowing reliable and meaningful comparisons. Besides, methods intended to derive the three dimensional shape of galaxy clusters should be extensively tested on simulated multi-wavelength observations.

The polar ring galaxy AM 2040-620 and its possible companion

Polar ring galaxies (PRGs) are peculiar systems where a gas-rich, nearly polar ring surrounds a host galaxy. They are the result of galaxy interactions that form mainly by tidal accretion of material from a gas rich donor galaxy. There is a number of formation mechanisms for PRGs: minor or major mergers, tidal accretion events, or direct cold gas accretion from filaments of the cosmic web. These objects can be used to probe the three-dimensional shape of dark matter haloes, provided that the ring is in equilibrium with the gravitational potential of the host galaxy. The polar ring galaxy, AM 2040-620, which has not yet been well studied, is the subject of this work. This galaxy contains an almost perpendicular warped ring and one possible companion galaxy to the NW. The radial velocity of this object is 3301\pm65 km/s and is part of a group of fifteen possible polar ring galaxies, according to the literature. In order to better understand this system, images and long slit spectra were observed with the 1.60 m OPD/LNA telescope. In the I band image, the outer parts of the ring are not symmetrical. A disturbance in the Eastern side and a faint plume were detected. Two small satellites are located to the north. The bulge is elliptical but not perfectly symmetrical in this image. The B-band image shows material that extends beyond the ring in the western and eastern directions. After processing, the B-image shows that the possible companion galaxy 2MASX J20441668-6158092 has a tidally disturbed disk. Its radial velocity is unknown, but the spectroscopy, which is still under analysis, will furnish this information.

Study of the three-dimensional shape and dynamics of coronal loops observed by Hinode/EIS

We study plasma flows along selected coronal loops in NOAA Active Region 10926, observed on 3 December 2006 with Hinode’s EUV Imaging Spectrograph (EIS). From the shape of the loops traced on intensity images and the Doppler shifts measured along their length we compute their three-dimensional (3D) shape and plasma flow velocity using a simple geometrical model. This calculation was performed for loops visible in the Fe VIII 185 Ang., Fe X 184 Ang., Fe XII 195 Ang., Fe XIII 202 Ang., and Fe XV 284 Ang. spectral lines. In most cases the flow is unidirectional from one footpoint to the other but there are also cases of draining motions from the top of the loops to their footpoints. Our results indicate that the same loop may show different flow patterns when observed in different spectral lines, suggesting a dynamically complex rather than a monolithic structure. We have also carried out magnetic extrapolations in the linear force-free field approximation using SOHO/MDI magnetograms, aiming toward a first-order identification of extrapolated magnetic field lines corresponding to the reconstructed loops. In all cases, the best-fit extrapolated lines exhibit left-handed twist (alpha < 0), in agreement with the dominant twist of the region.

Measuring the 3D shape of X-ray clusters

Observations and numerical simulations of galaxy clusters strongly indicate that the hot intracluster x-ray emitting gas is not spherically symmetric. In many earlier studies spherical symmetry has been assumed partly because of limited data quality, however new deep observations and instrumental designs will make it possible to go beyond that assumption. Measuring the temperature and density profiles are of interest when observing the x-ray gas, however the spatial shape of the gas itself also carries very useful information. For example, it is believed that the x-ray gas shape in the inner parts of galaxy clusters is greatly affected by feedback mechanisms, cooling and rotation, and measuring this shape can therefore indirectly provide information on these mechanisms. In this paper we present a novel method to measure the three-dimensional shape of the intracluster x-ray emitting gas. We can measure the shape from the x-ray observations only, i.e. the method does not require combination with independent measurements of e.g. the cluster mass or density profile. This is possible when one uses the full spectral information contained in the observed spectra. We demonstrate the method by measuring radial dependent shapes along the line of sight for CHANDRA mock data. We find that at least 10^6 photons are required to get a 5-{\sigma} detection of shape for an x-ray gas having realistic features such as a cool core and a double powerlaw for the density profile. We illustrate how Bayes’ theorem is used to find the best fitting model of the x-ray gas, an analysis that is very important in a real observational scenario where the true spatial shape is unknown. Not including a shape in the fit may propagate to a mass bias if the x-ray is used to estimate the total cluster mass. We discuss this mass bias for a class of spacial shapes.

Measuring the 3D shape of X-ray clusters [Replacement]

Observations and numerical simulations of galaxy clusters strongly indicate that the hot intracluster x-ray emitting gas is not spherically symmetric. In many earlier studies spherical symmetry has been assumed partly because of limited data quality, however new deep observations and instrumental designs will make it possible to go beyond that assumption. Measuring the temperature and density profiles are of interest when observing the x-ray gas, however the spatial shape of the gas itself also carries very useful information. For example, it is believed that the x-ray gas shape in the inner parts of galaxy clusters is greatly affected by feedback mechanisms, cooling and rotation, and measuring this shape can therefore indirectly provide information on these mechanisms. In this paper we present a novel method to measure the three-dimensional shape of the intracluster x-ray emitting gas. We can measure the shape from the x-ray observations only, i.e. the method does not require combination with independent measurements of e.g. the cluster mass or density profile. This is possible when one uses the full spectral information contained in the observed spectra. We demonstrate the method by measuring radial dependent shapes along the line of sight for CHANDRA mock data. We find that at least 10^6 photons are required to get a 5-{\sigma} detection of shape for an x-ray gas having realistic features such as a cool core and a double powerlaw for the density profile. We illustrate how Bayes’ theorem is used to find the best fitting model of the x-ray gas, an analysis that is very important in a real observational scenario where the true spatial shape is unknown. Not including a shape in the fit may propagate to a mass bias if the x-ray is used to estimate the total cluster mass. We discuss this mass bias for a class of spacial shapes.

Observing the Multiverse with Cosmic Wakes

Current theories of the origin of the Universe, including string theory, predict the existence of a multiverse containing many bubble universes. These bubble universes will generically collide, and collisions with ours produce cosmic wakes that enter our Hubble volume, appear as unusually symmetric disks in the cosmic microwave background (CMB) and disturb large scale structure (LSS). There is preliminary observational evidence consistent with one or more of these disturbances on our sky. However, other sources can produce similar features in the CMB temperature map and so additional signals are needed to verify their extra-universal origin. Here we find, for the first time, the detailed three-dimensional shape and CMB temperature and polarization signals of the cosmic wake of a bubble collision in the early universe consistent with current observations. The predicted polarization pattern has distinctive features that when correlated with the corresponding temperature pattern are a unique and striking signal of a bubble collision. These features represent the first verifiable prediction of the multiverse paradigm and might be detected by current experiments such as Planck and future CMB polarization missions. A detection of a bubble collision would confirm the existence of the Multiverse, provide compelling evidence for the string theory landscape, and sharpen our picture of the Universe and its origins.

The properties of asteroid (2867) Steins from Spitzer observations and OSIRIS shape reconstruction

We report on the thermal properties and composition of asteroid (2867) Steins derived from an analysis of new Spitzer Space Telescope (SST) observations performed in March 2008, in addition to previously published SST observations performed in November 2005. We consider the three-dimensional shape model and photometric properties derived from OSIRIS images obtained during the flyby of the Rosetta spacecraft in September 2008, which we combine with a thermal model to properly interpret the observed SST thermal light curve and spectral energy distributions. We obtain a thermal inertia in the range 100\pm50 JK-1m-2s-1/2 and a beaming factor (roughness) in the range 0.7-1.0. We confirm that the infrared emissivity of Steins is consistent with an enstatite composition. The November 2005 SST thermal light curve is most reliably interpreted by assuming inhomogeneities in the thermal properties of the surface, with two different regions of slightly different roughness, as observed on other small bodies, such as the nucleus of comet 9P/Tempel 1. Our results emphasize that the shape model is important to an accurate determination of the thermal inertia and roughness. Finally, we present temperature maps of Steins, as seen by Rosetta during its flyby, and discuss the interpretation of the observations performed by the VIRTIS and MIRO instruments.

Stellar disc-active galactic nucleus alignments in the SDSS-DR7

We determine the intrinsic shapes and orientations of 27,450 type I and II active galactic nucleus (AGN) galaxies in the spectroscopic sample of the Sloan Digital Sky Survey Data Release 7, by studying the distribution of projected axis ratios of AGN hosts. Our aim is to study possible alignments between the AGN and host galaxy systems (e.g. the accretion disc and the galaxy angular momentum) and the effect of dust obscuration geometry on the AGN type. We define control samples of non-AGN galaxies that mimic the morphology, colour, luminosity and concentration distributions of the AGN population, taking into account the effects of dust extinction and reddening. By assuming that AGN galaxies have the same underlying three-dimensional shape distribution as their corresponding control samples, we find that the spiral and elliptical type I AGN populations are strongly biased toward face-on galaxies, while ellipticals and spirals type II AGN are biased toward edge-on orientations. These findings rule out random orientations for AGN hosts at high confidence for type I spirals (delta chi^2~170) and type II ellipticals (delta chi^2~14), while the signal for type I ellipticals and type II spirals is weaker (delta chi^2~5 and delta chi^2~3, respectively). We obtain a much stronger tendency for the type II spirals to be edge-on when just high [OIII] equivalent width (EW) AGN are considered, meaning that >20% of low [OIII] EW edge-on type II AGN may be missing from the optical sample. The subset of AGN with point-like detections in the Faint Images of the Radio Sky at Twenty-Centimeters (FIRST) survey also tend to be face-on (delta chi^2>100), suggesting that radio jets are parallel to the galaxy disc angular momentum. [ABRIDGE]

Host galaxy-active galactic nucleus alignments in the SDSS-DR7 [Replacement]

We determine the intrinsic shapes and orientations of 27,450 type I and II active galactic nucleus (AGN) galaxies in the spectroscopic sample of the SDSS DR7, by studying the distribution of projected axis ratios of AGN hosts. Our aim is to study possible alignments between the AGN and host galaxy systems (e.g. the accretion disc and the galaxy angular momentum) and the effect of dust obscuration geometry on the AGN type. We define control samples of non-AGN galaxies that mimic the morphology, colour, luminosity and concentration distributions of the AGN population, taking into account the effects of dust extinction and reddening. Assuming that AGN galaxies have the same underlying three-dimensional shape distribution as their corresponding control samples, we find that the spiral and elliptical type I AGN populations are strongly skewed toward face-on galaxies, while ellipticals and spirals type II AGN are skewed toward edge-on orientations. These findings rule out random orientations for AGN hosts at high confidence for type I spirals (delta chi^2~230) and type II ellipticals (delta chi^2~15), while the signal for type I ellipticals and type II spirals is weaker (delta chi^2~3 and delta chi^2~6, respectively). We obtain a much stronger tendency for the type II spirals to be edge-on when just high [OIII] equivalent width (EW) AGN are considered, suggesting that >20% of low [OIII] EW edge-on type II AGN may be missing from the optical sample. Galactic dust absorption of the broad-line region alone cannot explain the observed inclination angle and projected axis ratio distributions of type I and II Seyfert types, implying that obscuration by a small-scale circumnuclear torus is necessary. These results favour a scenario in which the angular momentum of the material which feeds the black hole retains a memory of its original gas source at least to some small, non-negligible degree.

Shapes of Gas, Gravitational Potential and Dark Matter in Lambda-CDM Clusters [Replacement]

We present analysis of the three-dimensional shape of intracluster gas in clusters formed in cosmological simulations of the Lambda-CDM cosmology and compare it to the shape of dark matter distribution and the shape of the overall isopotential surfaces. We find that in simulations with radiative cooling, star formation and stellar feedback (CSF), intracluster gas outside the cluster core is more spherical compared to non-radiative (NR) simulations, while in the core the gas in the CSF runs is more triaxial and has a distinctly oblate shape. The latter reflects the ongoing cooling of gas, which settles into a thick oblate ellipsoid as it loses thermal energy. The shape of the gas in the inner regions of clusters can therefore be a useful diagnostic of gas cooling. We find that gas traces the shape of the underlying potential rather well outside the core, as expected in hydrostatic equilibrium. At smaller radii, however, the gas and potential shapes differ significantly. In the CSF runs, the difference reflects the fact that gas is partly rotationally supported. Interestingly, we find that in NR simulations the difference between gas and potential shape at small radii is due to random gas motions, which make the gas distribution more spherical than the equipotential surfaces. Finally, we use mock Chandra X-ray maps to show that the differences in shapes observed in three-dimensional distribution of gas are discernible in the ellipticity of X-ray isophotes. Contrasting the ellipticities measured in simulated clusters against observations can therefore constrain the amount of cooling of the intracluster medium and the presence of random gas motions in cluster cores.

Shapes of Gas, Gravitational Potential and Dark Matter in Lambda-CDM Clusters

We present analysis of the three-dimensional shape of intracluster gas in clusters formed in cosmological simulations of the Lambda-CDM cosmology and compare it to the shape of dark matter distribution and the shape of the overall iso-potential surfaces. We find that in simulations with radiative cooling, star formation and stellar feedback (CSF), intracluster gas outside the cluster core is more spherical compared to non-radiative (NR) simulations, while in the core the gas in the CSF runs is more triaxial and has a distinctly oblate shape. The latter reflects the ongoing cooling of gas, which settles into a thick oblate ellipsoid as it loses thermal energy. The shape of the gas in the inner regions of clusters can therefore be a useful diagnostic of gas cooling. We find that gas traces the shape of the underlying potential rather well outside the core, as expected in hydrostatic equilibrium. At smaller radii, however, the gas and potential shapes differ significantly. In the CSF runs, the difference reflects the fact that gas is partly rotationally supported. Interestingly, we find that in non-radiative simulations the difference between gas and potential shape at small radii is due to random gas motions, which make the gas distribution more spherical than the equi-potential surfaces. Finally, we use mock Chandra X-ray maps to show that the differences in shapes observed in three-dimensional distribution of gas are discernible in the ellipticity of X-ray isophotes. Contrasting the ellipticities measured in simulated clusters against observations can therefore constrain the amount of cooling of the intracluster medium and the presence of random gas motions in cluster cores.

Unveiling the three-dimensional structure of galaxy clusters: resolving the discrepancy between X-ray and lensing masses [Replacement]

[Abridged] We present the first determination of the intrinsic three-dimensional shapes and the physical parameters of both dark matter (DM) and intra-cluster medium (ICM) in a triaxial galaxy cluster. While most previous studies rely on the standard spherical modeling, our approach allows to infer the properties of the non-spherical intra-cluster gas distribution sitting in hydrostatic equilibrium within triaxial DM halos by combining X-ray, weak and strong lensing observations. We present an application of our method to the galaxy cluster MACS J1423.8+2404. This source is an example of a well relaxed object with a unimodal mass distribution and we infer shape and physical properties of the ICM and the DM for this source. We found that this is a triaxial galaxy cluster with DM halo axial ratios 1.53+/-0.15 and 1.44+/-0.07 on the plane of the sky and along the line of sight, respectively. We show that accounting for the three-dimensional geometry allows to solve the long-standing discrepancy between galaxy cluster masses determined from X-ray and gravitational lensing observations. We focus also on the determination of the inner slope of the DM density profile alpha, since the cuspiness of dark-matter density profiles is one of the critical tests of the cold dark matter (CDM) paradigm for structure formation: we measure alpha=0.94+/-0.09 by accounting explicitly for the 3D structure for this cluster, a value which is close to the CDM predictions, while the standard spherical modeling leads to the biased value alpha=1.24+/-0.07. Our findings provide further evidences that support the CDM scenario and open a new window in recovering the intrinsic shapes and physical parameters of galaxy clusters in a bias-free way. This has important consequences in using galaxy clusters as cosmological probes.

 

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