arXiv subjects

Max Tegmark

Publications and source records attributed to Max Tegmark.

277 records · Page 16Linked to original sources

arXiv1995

Doppler peaks and all that: CMB anisotropies and what they can tell us

The power spectrum of fluctuations in the cosmic microwave background (CMB) depends on most of the key cosmological parameters. Accurate future measurements of this power spectrum might therefore allow us to determine h, Omega, Omega_b, Lambda, n, T/S, etc, with hitherto unprecedented accuracy. In these lecture notes, which are intended to be readable without much prior CMB knowledge, I review the various physical processes that generate CMB fluctuations, focusing on how changes in the parameters alters the shape of the power spectrum. I also discuss foregrounds and real-world data analysis issues and how these affect the accuracy with which the parameters can be measured.

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arXiv1995

A method for extracting maximum resolution power spectra from galaxy surveys

The power spectrum estimated from a galaxy redshift survey is the real spectrum convolved with a window function, so when estimating the power on very large scales (for small k), it is important that this window function be as narrow as possible. A method that achieves this is presented. The optimal estimate of P(k) is found to be the Fourier transform of the number density fluctuations (n/nbar - 1) weighted by a function psi_0, and the optimal psi_0 is found to be the ground-state solution of the Schoedinger equation, with the inverse selection function as the potential. This quantum mechanics analogy occurs basically because we want the weight function to be narrow both in Fourier space (to give a narrow window) and in real space (to minimize the variance from shot noise). An optimal method for averaging the estimates at different k-vectors is also presented, generalizing the standard procedure of averaging over shells in k-space. Finally, a discrete version of the method is presented, dividing space into ``fuzzy pixels", which has the advantage of being able to handle redshift distortions in a straightforward way.

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arXiv1995

Improved limits on gamma ray burst repetition

We tighten previous upper limits on gamma ray burst repetition by analyzing the angular power spectrum of the BATSE 3B catalog of 1122 bursts. At 95% confidence, we find that no more than 2% of all observed bursts can be labeled as repeaters, even if no sources are observed to repeat more than once. If a fraction f of all observed bursts can be labeled as repeaters that are observed to burst v times each, then all models with (v-1)f>0.05 are ruled out at 99% confidence, as compared to the best previous 99% limit (v-1)f>0.27. At 95% confidence, our new limit is (v-1)f>0.02. Thus even a cluster of 6 events from a single source would have caused excess power above that present in the 3B catalog. We conclude that the current BATSE data are consistent with no repetition of classical gamma ray bursts, and that any repeater model is severely constrained by the near perfect isotropy of their angular distribution.

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arXiv1995

The Angular Power Spectrum of BATSE 3B Gamma-Ray Burst

We compute the angular power spectrum C_l from the BATSE 3B catalog of 1122 gamma-ray bursts, and find no evidence for clustering on any scale. These constraints bridge the entire range from small scales (which probe source clustering and burst repetition) to the largest scales (which constrain possible anisotropies from the Galactic halo or from nearby cosmological large scale structures). We develop an analysis technique that takes the angular position errors into account, which enables us to place tight upper limits on the clustering down to scales l\approx 60, corresponding to a few degrees on the sky. The minimum-variance burst weighting that we employ is graphically visualized as an all-sky map where each burst is smeared out by an amount corresponding to its position uncertainty. We also present separate band-pass filtered sky maps for the quadrupole term and for the multipole-ranges l=3-10 and l=11-30, so that the fluctuations on different angular scales can be separately inspected for visual features such as localized ``hot spots" or structures aligned with the Galactic plane. These filtered maps reveal no apparent deviations from isotropy.

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arXiv1995

Using the kinematic Sunyaev-Zeldovich effect to determine the peculiar velocities of clusters of galaxies

We have investigated the possibility of inferring peculiar velocities for clusters of galaxies from the Doppler shift of scattered cosmic microwave background (CMB) photons. We find that if the core radius of the gas distribution or the beam size of the instrument is larger than 3-7 arcminutes, then the maximum attainable signal-to-noise ratio is determined by confusion with primary fluctuations. For smaller angular scales, ``cosmic confusion'' is less important and instrumental noise and/or foreground emission will be the limiting factor. For a cluster with the optical depth of the Coma cluster and for an optimal filtering technique, typical one-sigma errors span the wide range from 400 to 1600 km/s, depending on the cosmological model, the resolution of the instrument and the core radius of the cluster. The results have important implications for the design of future high-resolution surveys of the CMB. Individual peculiar velocities will be measurable only for a few fast moving clusters at intermediate redshift unless cosmic fluctuations are smaller than most standard cosmological scenarios predict. However, a reliable measurement of bulk velocities of ensembles of X-ray bright clusters will be possible on very large scales (100-500 Mpc/h).

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arXiv1995

ESTIMATING MICROWAVE POWER SPECTRA

A new method for estimating the power spectrum $C_l$ from cosmic microwave background (CMB) maps was recently presented by the author and applied to the 2 year COBE data. It was found that the spectral resolution $Δl$ for COBE could be more than doubled at $l=15$, thereby revealing previously unresolved features in the power spectrum. Whereas that paper was rather technical, the present paper shows that all qualitative features of this method can be understood from a simple analogy with quantum mechanics.

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arXiv1993

Power Spectrum Independent Constraints on Cosmological Models

A formalism is presented that allows cosmological experiments to be tested for consistency, and allows a simple frequentist interpretation of the resulting significance levels. As an example of an application, this formalism is used to place constraints on bulk flows of galaxies using the results of the microwave background anisotropy experiments COBE and SP91, and a few simplifying approximations about the experimental window functions. It is found that if taken at face value, with the quoted errors, the recent detection by Lauer and Postman of a bulk flow of 689 km/s on scales of 150$h^{-1}$Mpc is inconsistent with SP91 at a 95\% confidence level within the framework of a Cold Dark Matter (CDM) model. The same consistency test is also used to place constraints that are completely model-independent, in the sense that they hold for any power spectrum whatsoever --- the only assumption being that the random fields are Gaussian. It is shown that the resulting infinite-dimensional optimization problem reduces to a set of coupled non-linear equations that can readily be solved numerically. Applying this technique to the above-mentioned example, we find that the Lauer and Postman result is inconsistent with SP91 even if no assumptions whatsoever are made about the power spectrum.

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