Cosmology of the local universe

Cosmology of the Local Universe

Mapping the local (z < 0.05) universe

Early work
A French-Finnish collaboration for mapping the local universe was started in the 1980's. A dataset of 400 spiral galaxies was collected and their distances were solved with the Tully-Fisher (TF) method. The selection effects were accounted for by a method of normalized distances: the distances of the galaxies were scaled so that the galaxies at small normalized distances were not affected by the Malmquist bias. Using this subsample the unbiased value of H₀ was calculated. See the results published by Bottinelli et al. (1986).

Kinematics of the Local Universe or KLUN project was launched in order to collect a larger TF sample. The data was extracted from the Lyon-Meudon Extragalactic Database (LEDA) and complemented with optical redshifts measured with ESO and OHP telescopes, and HI spectra obtained with Nancay and Parkes radio telescopes. According to LEDA precepts, all astrophysical parameters are homogenized and reduced to a standard and common system (Paturel et al., 1997). By the end of 1990's the KLUN sample consisted of 6600 galaxies with data on isophotal D₂₅ diameters, apparent B-magnitudes, HI line widths, and morphological types. Outside the zone of avoidance ( |b| < 15^o) and the declination limit of the Nancay telescope (dec < -38^o) the sample is complete in diameter down to D₂₅ = 1.6'.
A map showing the 6600 KLUN galaxies and the incomplete regions.

TF studies & the value of H₀
The KLUN sample was used to study the type (Theureau et al., 1997) and surface brightness (Theureau, 1998) dependence of the Tully-Fisher relation. Using the direct TF relation and the Normalized Distance correction, we derived the value of the Hubble constant ( Theureau et al., 1997). Our value, H₀ = 55 km/s/Mpc, is in the low side in the range of the lately published results. E.g. the HST key project team obtained, with TF and other methods, H₀ = 72 km/s/Mpc (Freedman et al., 2001). A discussion on the possible reasons for this discrepancy is included in my thesis (Hanski, 2001). The differing Malmquist corrections were not found responsible for the shift, but the calibration of the TF relation explained it partly; if the HST team calibration is used for KLUN galaxies, our H₀ would be 60 km/s/Mpc. The features of the datasets must be the cause for the additional difference. KLUN sample is larger than the one used by the HST team. However, the infrared magnitudes that they use are less affected by the interstellar dust, and have a smaller scatter in the TF relation than the B-magnitudes used in KLUN.

The Hubble diagram for KLUN galaxies

Inverse TF puzzle
The inverse TF relation is usually thought to be free from the Malmquist bias. However, when applied to the KLUN data, the inverse relation yields H₀ = 80 km/s/Mpc. The most logical reason for the higher value would be an incompleteness, similar to the observational magnitude limit, in the rotational velocity measurements. However, such an effect was not found in the KLUN sample, and if present, it would be not efficient enough to provide such a high value of H₀. The explanation for this puzzling problem was a new kind of bias, connected to the TF relation calibration; if the rotational velocity distribution of the calibrator galaxies differs from the corresponding distribution of the field galaxies, the resulting inverse TF relation is biased (Teerikorpi et al., 1999). When this effect is corrected, we get the same value of H₀ as with the unbiased direct relation ( Ekholm et al., 1999).

Observing the local cosmological structures
Tully-Fisher, Fundamental Plane and alike distances can be used to map the distribution and peculiar velocities of the galaxies. The dynamics and formation of the galaxy concentrations can then be observed. In Hanski et al. (2001), the Perseus-Pisces (PP) supercluster was studied with the KLUN galaxies and the Tolman-Bondi theoretical model. There the mass of the central PP, (~ 7 - 9 · 10¹⁵ h^-1 M_Sun) the Local Group infall towards it ( < 100 km/s) and the matter density of the universe (Omega = 0.2 - 0.4) were estimated. The method was to compare the radially averaged infall velocities of the KLUN galaxies towards the PP to the values predicted by the Tolman-Bondi equations, where a smoothed IRAS density map was used as an input.

Galaxies in the Perseus-Pisces region.

KLUN+, extension of the KLUN sample
The main problem of the KLUN sample is that it is limited to the B band luminosities. B band is more sensitive to the dust than the infrared (IR) wavelengths. The correspondence to the galaxy mass is also better in the IR. The TF relation in infrared luminosities therefore have a smaller scatter and give more accurate distances than the B band relation. An extension project, KLUN+ for adding several thousand new galaxies in our TF dataset, and adopting the IR (I-, J-, H-, and K-band) luminosities has begun in the beginning of 2001. With 25% of dedicated telescope time at the Nançay radio telescope, we expect to have a TF sample of 20.000 galaxies by the end of 2004.

Numerical modeling of the local structures

N-body simulations are the tools used in the numerical modeling of cosmological structure formation. The largest simulations consist of 10⁸ mass particles, distributed in a 100-1000 Mpc size periodic cube. The long range particle-particle interactions are approximated with interpolated gravitational potentials, using mesh, nested grid, refinement tree or other techniques, to speed up the calculations. A simulation is set up by creating an initial density field. A random realization from the power spectrum of perturbations for a given cosmology is used. This particle distribution is evolved with the numerical code and a statistical comparison of the results with observations is done.

ART
In refinement tree codes the computational domain is divided into hierarchical series of boxes, each having half the length of its parent. That is, a cube is divided into eight smaller cubes, each of them recursively divided into eight smaller ones, and so on. The refinement process continues until the wanted resolution is achieved. The tree structures partition the mass distribution into a hierarchy of localized regions, so that when calculating the force on a given particle, the "tree" region near the particle in question is explored in detail, and the more distant regions are explored more coarsely by treating distant clumps of particles as single massive pseudo-particles. Barnes and Hut (1986) were the first to apply the tree code on an astrophysical simulation. In the Adaptive Refinement Tree (ART) algorithm (Kravtsov et al., 1997), the refined structure is created in a fully adaptive manner in the regions where higher force resolution is desired. The tree is not created anew on each time step but is properly adjusted to the evolving particle distribution.

Refinement tree structure.

Constrained simulations of the real universe
The first attempts to study existing structures with simulations have been based on searching the simulated galaxy distribution for "something that looks like the Local Group" near "something that looks like the Virgo cluster". If lucky, such a look-alike environment can be found, but any correspondence to the physics of the real universe is speculative. In constrained simulations the initial conditions are calculated from the observed peculiar velocity data. A Wiener filter (WF) reconstruction of the mass and velocity distribution is derived first, using a prior density power spectrum and a linear gravitational instability approach. The WF, commonly used in image manipulation, attenuates the signal to the mean field in the noise-dominated regions. Thus the WF estimator is statistically inhomogeneous. To recover from this inhomogeneity, random realizations of the residual from the mean field are generated according to a priorly assumed model (Zaroubi et al., 1999). Using the MARK III data (Willick et al., 1997) for the WF constrained realization initial conditions, and the ART N-body simulation for the structure evolution, Klypin et al. (2001) were able to reproduce the nearby universe, including structures like the Local Group, the Coma and Virgo clusters, the Great Attractor, the Perseus-Pices, and the Local Supercluster in approximately correct locations.

Simulated local galaxy structures.

Future plans: KLUN+ application and parallel ART
MARK III data consists of 3400 galaxies with TF and fundamental plane distances. After the grouping procedure that is used for Malmquist bias correction, distances of 1200 objects remain. This is less than the number of KLUN distances, but, as mentioned above, the B band TF distances of KLUN have a large scatter, which is why the MARK III catalogue has been prefered in peculiar velocity studies. The KLUN+ data, combined with the new fundamental plane surveys (6dF, NFP) will be ~ ten times larger than MARK III, enabling the construction of a deeper and more detailed peculiar velocity map.
By summer of 2002, a cluster of 80 alpha computers will be installed in Nançay, for the use of a pulsar detection survey (P.I.: I. Cognard). KLUN+ team will have 20 % of the computing time on this cluster. The plan is to use these resources for a constrained simulation of the local universe, deriving the initial conditions from the KLUN+ data. Currently I am working on the parallelization of the ART code, using the MPI libraries for the message passing between the computational nodes. The first executable parallel version of ART is planned to be tested in Autumn 2002, the real applications will be done when more observational data is available, in 2003-2004.
The ultimate goal is to reproduce an accurate simulated version of the local cosmological structures. With the enhanced observational data and large parallel platform simulations this goal can be reached. A simulated model of the real universe will be a powerful tool. It can be used in many applications, including the study of structure formation, galaxy cluster dynamics, and selection effects.

Mikko Hanski 09/2001


Kinematics of the Local Universe or KLUN project was launched in order to collect a larger TF sample. The data was extracted from the Lyon-Meudon Extragalactic Database (LEDA) and complemented with optical redshifts measured with ESO and OHP telescopes, and HI spectra obtained with Nancay and Parkes radio telescopes. According to LEDA precepts, all astrophysical parameters are homogenized and reduced to a standard and common system (Paturel et al., 1997). By the end of 1990's the KLUN sample consisted of 6600 galaxies with data on isophotal D₂₅ diameters, apparent B-magnitudes, HI line widths, and morphological types. Outside the zone of avoidance ( \|b\| < 15^o) and the declination limit of the Nancay telescope (dec < -38^o) the sample is complete in diameter down to D₂₅ = 1.6'.
	A map showing the 6600 KLUN galaxies and the incomplete regions.


Observing the local cosmological structures Tully-Fisher, Fundamental Plane and alike distances can be used to map the distribution and peculiar velocities of the galaxies. The dynamics and formation of the galaxy concentrations can then be observed. In Hanski et al. (2001), the Perseus-Pisces (PP) supercluster was studied with the KLUN galaxies and the Tolman-Bondi theoretical model. There the mass of the central PP, (~ 7 - 9 · 10¹⁵ h^-1 M_Sun) the Local Group infall towards it ( < 100 km/s) and the matter density of the universe (Omega = 0.2 - 0.4) were estimated. The method was to compare the radially averaged infall velocities of the KLUN galaxies towards the PP to the values predicted by the Tolman-Bondi equations, where a smoothed IRAS density map was used as an input.
	Galaxies in the Perseus-Pisces region.


	ART In refinement tree codes the computational domain is divided into hierarchical series of boxes, each having half the length of its parent. That is, a cube is divided into eight smaller cubes, each of them recursively divided into eight smaller ones, and so on. The refinement process continues until the wanted resolution is achieved. The tree structures partition the mass distribution into a hierarchy of localized regions, so that when calculating the force on a given particle, the "tree" region near the particle in question is explored in detail, and the more distant regions are explored more coarsely by treating distant clumps of particles as single massive pseudo-particles. Barnes and Hut (1986) were the first to apply the tree code on an astrophysical simulation. In the Adaptive Refinement Tree (ART) algorithm (Kravtsov et al., 1997), the refined structure is created in a fully adaptive manner in the regions where higher force resolution is desired. The tree is not created anew on each time step but is properly adjusted to the evolving particle distribution.
Refinement tree structure.


Constrained simulations of the real universe The first attempts to study existing structures with simulations have been based on searching the simulated galaxy distribution for "something that looks like the Local Group" near "something that looks like the Virgo cluster". If lucky, such a look-alike environment can be found, but any correspondence to the physics of the real universe is speculative. In constrained simulations the initial conditions are calculated from the observed peculiar velocity data. A Wiener filter (WF) reconstruction of the mass and velocity distribution is derived first, using a prior density power spectrum and a linear gravitational instability approach. The WF, commonly used in image manipulation, attenuates the signal to the mean field in the noise-dominated regions. Thus the WF estimator is statistically inhomogeneous. To recover from this inhomogeneity, random realizations of the residual from the mean field are generated according to a priorly assumed model (Zaroubi et al., 1999). Using the MARK III data (Willick et al., 1997) for the WF constrained realization initial conditions, and the ART N-body simulation for the structure evolution, Klypin et al. (2001) were able to reproduce the nearby universe, including structures like the Local Group, the Coma and Virgo clusters, the Great Attractor, the Perseus-Pices, and the Local Supercluster in approximately correct locations.
	Simulated local galaxy structures.