ScienceProblem: EvolutionOfBias

PrimaryActor:

Research astronomer

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ScienceGoal:

Determine the evolution with redshift of 'bias' (e.g.Blanton et al, 2000), the relationship between the spatial distribution of galaxies and that of the underlying cosmological density field.

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DataSets:

A very large galaxy catalogue (e.g. from VISTA) and a weak lensing mass map previously derived from it (see separate ScienceProblem).

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ProblemDescription:

Theoretical models suggest that galaxies may be biased tracers of the cosmological density field - i.e. that galaxies cluster differently from the matter in general. The form, and evolution with redshift, of this bias is provides a handle on galaxy formation, so it is important to try and constrain it. This can be done, in principle, by cross-correlating the galaxy distrbution (either projected on the sky, or in redshift slices, thanks to spectroscopic measurements or photometric estimates) with a projected mass map derived from the same imaging dataset by a weak lensing analysis.

Several possible ways exist for doing this, but all are computationally expensive, on account of the inversions of huge covariance matrices required to perform the likelihood maximisation procedure necessary to derive the parameters describing the bias model. Since these covariance matrices are to be derived from the galaxy catalogue data, it is likely that any analysis like this will have to be performed at a data centre holding the catalogue.

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CurrentSolution:

No current solution, because nobody has attempted this yet: in part this is because the imaging datasets are not sufficiently large to make this a very interesting analysis, but also because nobody has thought seriously about the design of the algorithms needed for the job.

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VOSolution:

The VO solution envisages a significant computational resource sitting next to the archive server for the galaxy catalogue. A map would be created by binning the distribution of galaxies projected on the sky, or, alternatively, a series of such maps would be produced, for a series of slices of redshift space.

The covariance matrix between that map (or one of the set of them) and the mass map from the weak lensing analysis would be constructed, either analytically or using numerical simulations, under the assumption of a particular parametric form for the bias model. This covariance matrix would then be repeatedly inverted for different sets of bias parameter values, to find the set that maximised the likelihood of the observed mass and galaxy maps. That set of bias model parameters (or the series of such sets coming from the analysis of each redshift slice) would be the output from the analysis.

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KeyReferences:

Blanton et al, 2000, ApJ, 531, 1

Andy Taylor (IfA, Edinburgh), private communication.

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GoodStyle: Please add comments below. This area should be used for refinement of the above document. If you want to ask questions or start a dialogue with the author, please use (or create) a topic in the Science Problems Forum. For other ScienceProblems, refer to the ScienceProblemList.
Author: Once the refinements here and comments in the forum die down, perhaps you could rewrite the problem, incorporating the comments and refinements.

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Key algorithms and large multi-lambda datasets are not yet (or will be in the nearterm) available. But this could be a key longer term driver - especially the aqua-bility to run complex user supplied algorithms.

-- NicholasWalton - 17 Apr 2002

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-- BobMann - 07 Feb 2002