Wine and Cheese Fall 2014: Difference between revisions
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Abstract | Abstract | ||
== Cora Uhlemann == | == Cora Uhlemann == | ||
''' | '''Large scale structure formation with the Schrödinger method''' <br> | ||
When describing large-scale structure formation of collisionless dark matter one is interested in the dynamics of a large collection of identical point particles that interact only gravitationally. Via gravitational instability initially small density perturbations evolve into eventually bound structures, like dark matter halos that are distributed along the cosmic web. Even though this problem seems quite simple from a conceptual point of view, no sufficiently general solution of the underlying equation, the collisionless Boltzmann equation coupled to the Poisson equation, is known. Therefore one usually has to resort to N-body simulations which tackle the problem numerically. Analytical methods to describe structure formation are in general based on the dust model which describes cold dark matter as a pressureless fluid characterized by density and velocity. This model works quite well up to the quasi-linear regime but eventually fails when multiple streams form that are especially important for halo formation but lead to singularities in the model. We employ the so-called Schrödinger method, originally proposed by Widrow & Kaiser (1993) as a numerical tool, to develop a model which is able to describe multi-streaming and therefore can serve as theoretical N-body double. As a first application we study the coarse-grained dust model, which is a limiting case of the Schrödinger method, within Eulerian and Lagrangian perturbation theory. | |||
= 3 Nov 2014 = | = 3 Nov 2014 = | ||
Revision as of 18:27, 20 October 2014
Back to W&C Schedule
8 Sept 2014
K.G. Lee
The First z>2 Large-Scale Structure Map with Lyman-Alpha Forest Tomography from LBGs
The hydrogen Lyman-alpha forest is a long-established probe of large-scale structure at z>2, but is typically limited to 1D investigations along individual quasar sightlines. However, by instead targeting LBGs as background sources, the transverse separation between sources is ~Mpc and it becomes possible to do a 3D 'tomographic' reconstruction of the intergalactic medium. I will describe pilot observations using this technique, which has produced the first map of 3D large-scale structure at z~2.3 within the COSMOS field. Comparisons with coeval galaxies and simulations indicate that our map is truly tracing large-scale structure. This motivates the CLAMATO survey, which will map out a volume of (100 Mpc/h)^3 at z~2.3 and allow us to search for galaxy protoclusters, study the effect of environment on galaxy evolution, and constrain cosmological parameters.
Peter Behroozi
Close Pairs: Observational Probes for how Halo Accretion Impacts Galaxy Star Formation
We present a simple observational method for selecting galaxies whose host dark matter haloes have had significantly higher-than-average accretion rates. The method relies on using close pairs of galaxies to preferentially identify major dark matter halo mergers. Applying the method to central L∗ galaxies in the Sloan Digital Sky Survey (SDSS) DR10, we find no evidence for enhanced average or median star formation accompanying as much as an 0.3 dex increase in average halo accretion rates. However, population subsamples do show enhancements. Most interestingly, star-forming L∗ galaxies show a double peak in star formation enhancements as a function of the distance to the close pair. The larger (factor of 2) enhancement occurs for close pairs within 30 kpc, and the smaller (factor of 40%) enhancement occurs for pairs separated by 100-200 kpc (i.e., just within the virial radius of the larger galaxy’s halo). We discuss implications for conditional abundance matching models; while galaxy quenchedness cannot depend only on halo mass and recent accretion, reproducing the full behaviour of star-forming galaxies requires more advanced models than currently exist.
15 Sept 2014
Dheeraj Pasham
A 400 solar mass black hole revealed while mimicking a stellar-mass black hole
The brightest X-ray source in M82 has been thought to be an intermediate-mass black hole (100-10,000 solar masses) because of its extremely high X-ray luminosity and variability characteristics, although some models suggest that its mass may be only of the order of 20 solar masses. The previous mass estimates were based on scaling relations which used low-frequency characteristic timescales which have large intrinsic uncertainties. In stellar-mass black holes we know that the high frequency quasi-periodic oscillations that occur in a 3:2 ratio (100-450 Hz) are stable and scale inversely with black hole mass with a reasonably small dispersion. The discovery of such stable oscillations thus potentially offers an alternative and less ambiguous mass determination for intermediate-mass black
holes, but has hitherto not been realized. I will discuss the discovery of stable, twin-peak (3:2 frequency ratio) X-ray quasi-periodic oscillations from M82 X-1 at the frequencies of 3.32 Hz and 5.07 Hz and how this helps overcome the systematic uncertainties present in previous studies. Assuming we can extend the stellar-mass relationship, we estimate its black hole mass to be 428+/-105 solar masses. (See also this paper for more information.)
Alexander Mendez
AEGIS+PRIMUS: The Clustering of X-ray, mid-IR, and radio-selected AGN
We present a clustering study of X-ray, mid-IR, and radio-selected active galactic nuclei (AGN) at 0.2 < z < 1.2 using multi-wavelength imaging and spectroscopic redshifts from the PRIMUS and DEEP2 redshift surveys, covering 7 separate fields spanning ~10 square degrees. Using the cross-correlation of AGN with dense galaxy samples, we measure the clustering scale length and slope, as well as the bias, of AGN selected at different wavelengths. We compare the clustering of each AGN sample with galaxy samples with the same stellar mass, star formation rate, and redshift distributions as the AGN host galaxies and find no significant difference in the clustering of AGN with matched galaxy samples. The observed differences in the clustering of AGN selected at different wavelengths can therefore be explained by the clustering differences of their host populations. We further find no significant difference between the clustering of obscured and unobscured AGN, using IRAC or WISE colors or X-ray hardness ratio.
22 Sept 2014
Yacine Ali-Haïmoud
Rotational Spectroscopy of Interstellar PAHs
Polycyclic aromatic hydrocarbons (PAHs) are believed to be ubiquitous in the interstellar medium. Yet, to date no specific PAH molecule has been identified. In this talk I describe a new observational avenue to detect individual PAHs, using their rotational line emission at radio frequencies. Previous PAH searches based on rotational spectroscopy have only targeted the bowl-shaped corannulene molecule, with the underlying assumption that other polar PAHs are triaxial and have a complex and diluted spectrum unusable for identification purposes. I will show that the asymmetry of planar, nitrogen-substituted symmetric PAHs is small enough that their rotational spectrum, when observed with a resolution of about a MHz, has the appearance of a "comb" of evenly spaced stacks of lines. The simple pattern of these "comb" spectra allows for the use of matched-filtering techniques, which can result in a significantly enhanced signal-to-noise ratio. Detection forecasts are discussed for regions harbouring "anomalous microwave emission", believed to originate from the collective PAH rotational emission. A systematic search for PAH lines in various environments is advocated. If detected, PAH "combs" would allow to the conclusive and unambiguous identification of specific, free-floating interstellar PAHs.
Jim Green
Imaging in the FUSE Band: The Sub-Lyman alpha Explorer
I will present our concept for a Small Explorer that will provide 2 arc second imaging in the 1020 – 1200 angstrom bandpass. Our primary science goals are to directly measure the ionizing escape fraction at low redshift, to quantify the contribution of O stars to galactic energy cycles, and probe the physics of proto-planetary disks. There will be a guest investigator program after the prime science surveys have been completed. The design utilizes dispersive re-construction to create a tunable bandpass below Lyman alpha, so that sub-bandpasses can be created in the 1020 – 1200 angstrom region. I will review the science cases and the optical design. If selected, launch would be in 2020.
29 Sept 2014
Remco van den Bosch
Compact Galaxies and Super Massive Black Holes
Super-massive black holes reside at the center of galaxies. And the masses of these black holes correlate to various properties of their host galaxies. These correlations are the foundation for theories of the (co-)evolution of super-massive black holes and their host galaxies.
However, very few galaxies are nearby enough for direct black hole mass measurements. To find suitable galaxies, we surveyed a thousand galaxies with the Hobby-Eberly Telescope. The first results of this survey was the discovery of a dozen extremely compact, high-dispersion, galaxies, which are candidates to host extraordinary massive black holes. The prototype is NGC1277, which is a small, Re=1kpc, compact, lenticular galaxy which hosts a 10 billion solar mass black hole. Which is a significant fraction of this galaxies mass. These highly compact galaxies appear to be the passively evolved descendants of the red nuggets, sub-mm galaxies, and quasars found at high redshifts.
Omer Bromberg
Can We Really Trust All That We Know on Short GRBs?
The study of short GRBs took a great leap since the arrival of Swift, 10 years
ago. However still, a large part of our newly gained knowledge of these events,
rely on a relatively small sample of bursts with good enough localization. As
there is an overlap with the much more abundant population of long GRBs
(with different origin than the short GRBs), there is a risk that contamination by falsely identified long GRBs may alter some of these conclusions.
In this talk I will show evidence that such a contamination does exist in the
current sample of the short GRBs that are studied (chosen with the criterion
of T_90<2 sec). I will then quantify this contamination, based on our knowledge
of the nature of long GRBs, and demonstrate how it affects some of our conclusions
regarding short GRBs.
6 Oct 2014
Matthias Bartelmann
Joint reconstruction of galaxy clusters from all observables
Galaxy clusters provide five types of observables related to their matter distribution: strong and weak gravitational lensing, X-ray emission, the thermal Sunyaev-Zel'dovich effect, and galaxy kinematics. In the talk, I will show how all these observables can be combined in a non-parametric way into a joint reconstruction of the projected gravitational cluster potential. First examples of cluster potentials reconstructed from X-ray emission, the thermal SZ effect and galaxy kinematics will be given.
Elizabeth Fernandez
The Science of Deduction: Interpreting Observations of the Epoch of Reionization
Up until very recently, the Epoch of Reionization has been largely observationally unexplored . However, with advancements of modern telescopes, we are now able to observe this period of the Universe in multiple ways. While observations are still very challenging due to a host of foreground contaminants, combining observations at multiple wavelengths can lead to a greater understanding of the populations of stars and galaxies at these redshifts. I will describe two of these observables: the Cosmic Infrared Background, which is partially the integrated light from all stars and galaxies at high redshifts, and the 21cm Background, which results from emission from neutral gas. These observables, when paired with theory and simulations, can tell us about some of the first stars and galaxies that formed within our Universe.
13 Oct 2014
Amy Reines
Probing the Origin of Supermassive Black Holes with Dwarf Galaxies
Supermassive black holes (BHs) live at the heart of essentially all massive galaxies with bulges, power AGN, and are thought to be important agents in the evolution of their hosts. However, the origin of the first supermassive BH "seeds" is far from understood. While direct observations of these distant BHs in the infant Universe are unobtainable with current capabilities, massive BHs in present-day dwarf galaxies offer another avenue to observationally constrain the masses, host galaxies and formation path of supermassive BH seeds. Using optical spectroscopy from the SDSS, we have increased the number of known dwarf galaxies hosting massive BHs by more than an order of magnitude. These dwarf galaxies have stellar masses comparable to the Magellanic Clouds and contain some of the least-massive supermassive BHs known. I will present results from this study, and well as on-going efforts using radio and X-ray observations to reveal massive BHs in star-forming dwarfs that can be missed by optical diagnostics.
Nick Stone
Stellar Tidal Disruption: the Role of General Relativity
In tidal disruption events (TDEs), stars passing too close to supermassive black holes (SMBHs) are violently torn apart. I will discuss several recent findings about the light curves of these events, including the role of orbital pericenter, ways in which the spin of the SMBH can be imprinted into TDE light curves, and possible emission of high frequency gravitational waves. I will also discuss an ongoing project focused on how highly eccentric debris streams from a TDE can circularize into a luminous accretion disk. It appears likely that the circularization process is mediated by general relativistic effects: circularization is aided by apsidal precession and hindered by nodal precession due to Lense-Thirring torques.
20 Oct 2014
Roseanne Cheng
Hydrodynamic Circularization of Stellar Tidal Disruption Debris
Black holes in galaxies are powerful central engines capable of
generating accretion flares and jets. A star passing too close to one
will tidally disrupt with some of its debris ejected from the system
while the rest funnels towards the black hole forming an accretion
disk. The emission properties are likely dependent on the mass and
spin of the black hole. The process by which debris forms a disk and
generates flares and/or jets is not well-understood. We investigate
this process by simulating the circularization of stellar tidal
disruption debris. We combine a high-resolution relativistic
hydrodynamic simulation of the star itself as it is torn apart with a
well-resolved relativistic hydrodynamics simulation of the subsequent
motion of the stellar debris as it orbits the black hole. With these
tools, we track the evolution of such a system long enough for 80% of
the stellar mass bound to the black hole to join the accretion
flow. We find significant departures from classical expectations for
the lightcurve associated with tidal disruptions.
Marcio Melendez
Herschel Far-infrared Photometry of the Swift Burst Alert Telescope Active Galactic Nuclei Sample of the Local Universe. I. PACS Observations
Far-Infrared (FIR) photometry from the Photodetector Array Camera and Spectrometer on the Herschel Space Observatory is presented for 313 nearby, hard X-ray selected galaxies from the 58 month Swift Burst Alert Telescope (BAT) Active Galactic Nuclei catalog. The present data do not distinguish between the FIR luminosity distributions at 70 and 160 um for Seyfert 1 and Seyfert 2 galaxies. This result suggests that if the FIR emission is from the nuclear obscuring material surrounding the accretion disk, then it emits isotropically, independent of orientation. Alternatively, a significant fraction of the 70 and 160 um luminosity could be from star formation, independent of active galactic nucleus (AGN) type. Using a non-parametric test for partial correlation with censored data, we find a statistically significant correlation between the AGN intrinsic power (in the 14-195 keV band) and the FIR emission at 70 and 160 um for Seyfert 1 galaxies. We find no correlation between the 14-195 keV and FIR luminosities in Seyfert 2 galaxies. The observed correlations suggest two possible scenarios: (1) if we assume that the FIR luminosity is a good tracer of star formation, then there is a connection between star formation and the AGN at sub-kiloparsec scales, or (2) dust heated by the AGN has a statistically significant contribution to the FIR emission. Using a Spearman rank-order analysis, the 14-195 keV luminosities for the Seyfert 1 and 2 galaxies are weakly statistically correlated with the F70/F160 ratios.
27 Oct 2014
Sarah Hoerst
Title
Abstract
Cora Uhlemann
Large scale structure formation with the Schrödinger method
When describing large-scale structure formation of collisionless dark matter one is interested in the dynamics of a large collection of identical point particles that interact only gravitationally. Via gravitational instability initially small density perturbations evolve into eventually bound structures, like dark matter halos that are distributed along the cosmic web. Even though this problem seems quite simple from a conceptual point of view, no sufficiently general solution of the underlying equation, the collisionless Boltzmann equation coupled to the Poisson equation, is known. Therefore one usually has to resort to N-body simulations which tackle the problem numerically. Analytical methods to describe structure formation are in general based on the dust model which describes cold dark matter as a pressureless fluid characterized by density and velocity. This model works quite well up to the quasi-linear regime but eventually fails when multiple streams form that are especially important for halo formation but lead to singularities in the model. We employ the so-called Schrödinger method, originally proposed by Widrow & Kaiser (1993) as a numerical tool, to develop a model which is able to describe multi-streaming and therefore can serve as theoretical N-body double. As a first application we study the coarse-grained dust model, which is a limiting case of the Schrödinger method, within Eulerian and Lagrangian perturbation theory.
3 Nov 2014
Chun Ly
Title
Abstract
Jeff Cummings
Title
Abstract
10 Nov 2014
Dominika Wylezalek
Title
Abstract
Kevin Lewis
Title
Abstract
17 Nov 2014
Laura Blecha
Title
Abstract
Michael Kesden
Title
Abstract
24 Nov 2014
Leonardo Almeida
Title
Abstract
1 Dec 2014
Hsiang-Yi Karen Yang
Title
Abstract
Sjoert van Velzen
Title
Abstract
8 Dec 2014
Richard Anderson
Title
Abstract
Karrie Gilbert
Title
Abstract
15 Dec 2014
Yicheng Guo
Title
Abstract
The hydrogen Lyman-alpha forest is a long-established probe of large-scale structure at z>2, but is typically limited to 1D investigations along individual quasar sightlines. However, by instead targeting LBGs as background sources, the transverse separation between sources is ~Mpc and it becomes possible to do a 3D 'tomographic' reconstruction of the intergalactic medium. I will describe pilot observations using this technique, which has produced the first map of 3D large-scale structure at z~2.3 within the COSMOS field. Comparisons with coeval galaxies and simulations indicate that our map is truly tracing large-scale structure. This motivates the CLAMATO survey, which will map out a volume of (100 Mpc/h)^3 at z~2.3 and allow us to search for galaxy protoclusters, study the effect of environment on galaxy evolution, and constrain cosmological parameters.
The brightest X-ray source in M82 has been thought to be an intermediate-mass black hole (100-10,000 solar masses) because of its extremely high X-ray luminosity and variability characteristics, although some models suggest that its mass may be only of the order of 20 solar masses. The previous mass estimates were based on scaling relations which used low-frequency characteristic timescales which have large intrinsic uncertainties. In stellar-mass black holes we know that the high frequency quasi-periodic oscillations that occur in a 3:2 ratio (100-450 Hz) are stable and scale inversely with black hole mass with a reasonably small dispersion. The discovery of such stable oscillations thus potentially offers an alternative and less ambiguous mass determination for intermediate-mass black holes, but has hitherto not been realized. I will discuss the discovery of stable, twin-peak (3:2 frequency ratio) X-ray quasi-periodic oscillations from M82 X-1 at the frequencies of 3.32 Hz and 5.07 Hz and how this helps overcome the systematic uncertainties present in previous studies. Assuming we can extend the stellar-mass relationship, we estimate its black hole mass to be 428+/-105 solar masses. (See also this paper for more information.)
Polycyclic aromatic hydrocarbons (PAHs) are believed to be ubiquitous in the interstellar medium. Yet, to date no specific PAH molecule has been identified. In this talk I describe a new observational avenue to detect individual PAHs, using their rotational line emission at radio frequencies. Previous PAH searches based on rotational spectroscopy have only targeted the bowl-shaped corannulene molecule, with the underlying assumption that other polar PAHs are triaxial and have a complex and diluted spectrum unusable for identification purposes. I will show that the asymmetry of planar, nitrogen-substituted symmetric PAHs is small enough that their rotational spectrum, when observed with a resolution of about a MHz, has the appearance of a "comb" of evenly spaced stacks of lines. The simple pattern of these "comb" spectra allows for the use of matched-filtering techniques, which can result in a significantly enhanced signal-to-noise ratio. Detection forecasts are discussed for regions harbouring "anomalous microwave emission", believed to originate from the collective PAH rotational emission. A systematic search for PAH lines in various environments is advocated. If detected, PAH "combs" would allow to the conclusive and unambiguous identification of specific, free-floating interstellar PAHs.
I will present our concept for a Small Explorer that will provide 2 arc second imaging in the 1020 – 1200 angstrom bandpass. Our primary science goals are to directly measure the ionizing escape fraction at low redshift, to quantify the contribution of O stars to galactic energy cycles, and probe the physics of proto-planetary disks. There will be a guest investigator program after the prime science surveys have been completed. The design utilizes dispersive re-construction to create a tunable bandpass below Lyman alpha, so that sub-bandpasses can be created in the 1020 – 1200 angstrom region. I will review the science cases and the optical design. If selected, launch would be in 2020.
Super-massive black holes reside at the center of galaxies. And the masses of these black holes correlate to various properties of their host galaxies. These correlations are the foundation for theories of the (co-)evolution of super-massive black holes and their host galaxies.
The study of short GRBs took a great leap since the arrival of Swift, 10 years ago. However still, a large part of our newly gained knowledge of these events, rely on a relatively small sample of bursts with good enough localization. As there is an overlap with the much more abundant population of long GRBs (with different origin than the short GRBs), there is a risk that contamination by falsely identified long GRBs may alter some of these conclusions. In this talk I will show evidence that such a contamination does exist in the current sample of the short GRBs that are studied (chosen with the criterion of T_90<2 sec). I will then quantify this contamination, based on our knowledge of the nature of long GRBs, and demonstrate how it affects some of our conclusions regarding short GRBs.
Galaxy clusters provide five types of observables related to their matter distribution: strong and weak gravitational lensing, X-ray emission, the thermal Sunyaev-Zel'dovich effect, and galaxy kinematics. In the talk, I will show how all these observables can be combined in a non-parametric way into a joint reconstruction of the projected gravitational cluster potential. First examples of cluster potentials reconstructed from X-ray emission, the thermal SZ effect and galaxy kinematics will be given.
Up until very recently, the Epoch of Reionization has been largely observationally unexplored . However, with advancements of modern telescopes, we are now able to observe this period of the Universe in multiple ways. While observations are still very challenging due to a host of foreground contaminants, combining observations at multiple wavelengths can lead to a greater understanding of the populations of stars and galaxies at these redshifts. I will describe two of these observables: the Cosmic Infrared Background, which is partially the integrated light from all stars and galaxies at high redshifts, and the 21cm Background, which results from emission from neutral gas. These observables, when paired with theory and simulations, can tell us about some of the first stars and galaxies that formed within our Universe.
Supermassive black holes (BHs) live at the heart of essentially all massive galaxies with bulges, power AGN, and are thought to be important agents in the evolution of their hosts. However, the origin of the first supermassive BH "seeds" is far from understood. While direct observations of these distant BHs in the infant Universe are unobtainable with current capabilities, massive BHs in present-day dwarf galaxies offer another avenue to observationally constrain the masses, host galaxies and formation path of supermassive BH seeds. Using optical spectroscopy from the SDSS, we have increased the number of known dwarf galaxies hosting massive BHs by more than an order of magnitude. These dwarf galaxies have stellar masses comparable to the Magellanic Clouds and contain some of the least-massive supermassive BHs known. I will present results from this study, and well as on-going efforts using radio and X-ray observations to reveal massive BHs in star-forming dwarfs that can be missed by optical diagnostics.
In tidal disruption events (TDEs), stars passing too close to supermassive black holes (SMBHs) are violently torn apart. I will discuss several recent findings about the light curves of these events, including the role of orbital pericenter, ways in which the spin of the SMBH can be imprinted into TDE light curves, and possible emission of high frequency gravitational waves. I will also discuss an ongoing project focused on how highly eccentric debris streams from a TDE can circularize into a luminous accretion disk. It appears likely that the circularization process is mediated by general relativistic effects: circularization is aided by apsidal precession and hindered by nodal precession due to Lense-Thirring torques.
Black holes in galaxies are powerful central engines capable of generating accretion flares and jets. A star passing too close to one will tidally disrupt with some of its debris ejected from the system while the rest funnels towards the black hole forming an accretion disk. The emission properties are likely dependent on the mass and spin of the black hole. The process by which debris forms a disk and generates flares and/or jets is not well-understood. We investigate this process by simulating the circularization of stellar tidal disruption debris. We combine a high-resolution relativistic hydrodynamic simulation of the star itself as it is torn apart with a well-resolved relativistic hydrodynamics simulation of the subsequent motion of the stellar debris as it orbits the black hole. With these tools, we track the evolution of such a system long enough for 80% of the stellar mass bound to the black hole to join the accretion flow. We find significant departures from classical expectations for the lightcurve associated with tidal disruptions.
Far-Infrared (FIR) photometry from the Photodetector Array Camera and Spectrometer on the Herschel Space Observatory is presented for 313 nearby, hard X-ray selected galaxies from the 58 month Swift Burst Alert Telescope (BAT) Active Galactic Nuclei catalog. The present data do not distinguish between the FIR luminosity distributions at 70 and 160 um for Seyfert 1 and Seyfert 2 galaxies. This result suggests that if the FIR emission is from the nuclear obscuring material surrounding the accretion disk, then it emits isotropically, independent of orientation. Alternatively, a significant fraction of the 70 and 160 um luminosity could be from star formation, independent of active galactic nucleus (AGN) type. Using a non-parametric test for partial correlation with censored data, we find a statistically significant correlation between the AGN intrinsic power (in the 14-195 keV band) and the FIR emission at 70 and 160 um for Seyfert 1 galaxies. We find no correlation between the 14-195 keV and FIR luminosities in Seyfert 2 galaxies. The observed correlations suggest two possible scenarios: (1) if we assume that the FIR luminosity is a good tracer of star formation, then there is a connection between star formation and the AGN at sub-kiloparsec scales, or (2) dust heated by the AGN has a statistically significant contribution to the FIR emission. Using a Spearman rank-order analysis, the 14-195 keV luminosities for the Seyfert 1 and 2 galaxies are weakly statistically correlated with the F70/F160 ratios.
Abstract
When describing large-scale structure formation of collisionless dark matter one is interested in the dynamics of a large collection of identical point particles that interact only gravitationally. Via gravitational instability initially small density perturbations evolve into eventually bound structures, like dark matter halos that are distributed along the cosmic web. Even though this problem seems quite simple from a conceptual point of view, no sufficiently general solution of the underlying equation, the collisionless Boltzmann equation coupled to the Poisson equation, is known. Therefore one usually has to resort to N-body simulations which tackle the problem numerically. Analytical methods to describe structure formation are in general based on the dust model which describes cold dark matter as a pressureless fluid characterized by density and velocity. This model works quite well up to the quasi-linear regime but eventually fails when multiple streams form that are especially important for halo formation but lead to singularities in the model. We employ the so-called Schrödinger method, originally proposed by Widrow & Kaiser (1993) as a numerical tool, to develop a model which is able to describe multi-streaming and therefore can serve as theoretical N-body double. As a first application we study the coarse-grained dust model, which is a limiting case of the Schrödinger method, within Eulerian and Lagrangian perturbation theory.
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