## Optimal linear reconstruction of dark matter from halo catalogues

## Abstract

The dark matter lumps (or "halos") that contain galaxies have locations in the Universe that are to some extent random with respect to the overall matter distributions. We investigate how best to estimate the total matter distribution from the locations of the halos. We derive the weight function w(M) to apply to dark-matter haloes that minimizes the stochasticity between the weighted halo distribution and its underlying mass density field. The optimal w(M) depends on the range of masses of halos being used. While the standard biased-Poisson model of the halo distribution predicts that bias weighting is optimal, the simple fact that the mass is comprised of haloes implies that the optimal w(M) will be a mixture of mass-weighting and bias-weighting. In N-body simulations, the Poisson estimator is up to 15× noisier than the optimal. Optimal weighting could make cosmological tests based on the matter power spectrum or cross-correlations much more powerful and/or cost effective.

- Authors:

- Univ. of Pennsylvania, Philadelphia, PA (United States)

- Publication Date:

- Research Org.:
- Univ. of Pennsylvania, Philadelphia, PA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1203600

- Grant/Contract Number:
- FG02-95ER40893

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Monthly Notices of the Royal Astronomical Society

- Additional Journal Information:
- Journal Volume: 412; Journal Issue: 2; Journal ID: ISSN 0035-8711

- Publisher:
- Royal Astronomical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; dark-matter halos; halos-cosmology; theory-dark matter; gravitational lensing; analytical-methods; numerical

### Citation Formats

```
Cai, Yan -Chuan, Bernstein, Gary, and Sheth, Ravi K. Optimal linear reconstruction of dark matter from halo catalogues. United States: N. p., 2011.
Web. doi:10.1111/j.1365-2966.2010.17969.x.
```

```
Cai, Yan -Chuan, Bernstein, Gary, & Sheth, Ravi K. Optimal linear reconstruction of dark matter from halo catalogues. United States. doi:10.1111/j.1365-2966.2010.17969.x.
```

```
Cai, Yan -Chuan, Bernstein, Gary, and Sheth, Ravi K. Fri .
"Optimal linear reconstruction of dark matter from halo catalogues". United States. doi:10.1111/j.1365-2966.2010.17969.x. https://www.osti.gov/servlets/purl/1203600.
```

```
@article{osti_1203600,
```

title = {Optimal linear reconstruction of dark matter from halo catalogues},

author = {Cai, Yan -Chuan and Bernstein, Gary and Sheth, Ravi K.},

abstractNote = {The dark matter lumps (or "halos") that contain galaxies have locations in the Universe that are to some extent random with respect to the overall matter distributions. We investigate how best to estimate the total matter distribution from the locations of the halos. We derive the weight function w(M) to apply to dark-matter haloes that minimizes the stochasticity between the weighted halo distribution and its underlying mass density field. The optimal w(M) depends on the range of masses of halos being used. While the standard biased-Poisson model of the halo distribution predicts that bias weighting is optimal, the simple fact that the mass is comprised of haloes implies that the optimal w(M) will be a mixture of mass-weighting and bias-weighting. In N-body simulations, the Poisson estimator is up to 15× noisier than the optimal. Optimal weighting could make cosmological tests based on the matter power spectrum or cross-correlations much more powerful and/or cost effective.},

doi = {10.1111/j.1365-2966.2010.17969.x},

journal = {Monthly Notices of the Royal Astronomical Society},

number = 2,

volume = 412,

place = {United States},

year = {2011},

month = {4}

}

*Citation information provided by*

Web of Science

Web of Science