- Probing dark matter caustics with weak lensing
- 1 Online Material
- 1 Smooth halo density profile
- 2 Caustics density profile and weak lensing
- 3 Consequences

A&A 454, 715 (2006)

DOI: 10.1051/0004-6361:20053557e

*Erratum*

**R. Gavazzi ^{1,3} - R. Mohayaee^{2} - B. Fort^{2}**

1 - Laboratoire d'Astrophysique, UMR 5572 CNRS & Université Paul Sabatier, 14 Av. Edouard Belin, 31400 Toulouse, France

2 - Institut d'Astrophysique de Paris, UMR 7095 CNRS & Université Pierre & Marie Curie, 98bis Bd. Arago, 75014 Paris, France

3 -
Oxford University, Astrophysics,
Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK

A&A, 445, 43-49 (2006), DOI:10.1051/0004-6361:20053557

**Abstract**

We correct two errors that were present in the former version of
this paper. First, a factor 1/3 was missing in the expression of
the smooth density profile of the dark matter halo (Eq. (1)) that
propagates into the expression of the projected smooth
density profile (Eq. (9)). Second, the numerical integration of
the caustics' density profile also misses a factor of 2, although the
equations are correct. The former error has no effect on the
analysis but the latter makes the weak lensing signal twice stronger
than previously published. Therefore, the detection of dark matter
caustics through weak lensing is made easier. Instead of a
superposition of about 200 cluster-size halos, one would require
only 100 such systems for the caustics to show up in
ground-based observations. Similarly, space-based weak lensing data
would achieve the same detection threshold with 30 galaxy
clusters.

**Key words: **dark matter - gravitational lensing - errata, addenda

1 Online Material

(1) |

This factor 1/3 is also missing in the approximation of the projected halo density profile (Eq. (9) in the previous version). It then reads:

(2) |

Therefore the only consequences of this error for the remainder of the paper is that the smooth black solid curves of Fig. 1 (previous version) should now look like Fig. 1 here (both are lowered by a factor 1/3).

Let us first consider the ideal case in which we have perfect knowledge
of the virial (or turnaround) radius of every stacked halo.
The required number of cluster-size halos is lowered to .
If the dark matter temperature is non zero, with *N*=100 (resp. 250)
clusters, one could achieve a limit
(resp.
)
at a 95% confidence level. If one considers galaxies instead of cluster-size
haloes, the number of such systems to be stacked is divided by two
in the same way. For space-based weak lensing observations,
the factor of 3 gain in sensitivity is conserved.
If we now turn back to the realistic situation in which the virial
radius of individual clusters is known with a
accuracy,
the results are also changed in the same way. One now needs only
stacked clusters to be observed both in weak lensing and X-ray.

To conclude, the main changes due to the errors present in the previous version make the possibility of detecting dark matter caustics even less challenging.

Figure 3:
Difference between the
contribution
of cold caustics and the smooth component. We illustrate the blurring
effect of an imperfect knowledge of the turnaround radius of stacked
halos. The solid black line, dashed green line, and dot-dashed
blue line correspond to zero, 3%, and 10% uncertainties, respectively.
As in Fig. 2, the binned curve represents
the noise level achieved with 200 stacked halos. The convolution effect
of error in the assumed/measured value of
is important and a
significant detection of caustics requires well-determined turnaround
radii (
a few percents relative accuracy). The very small-scale
wiggles in the plot are numerical artifacts and ideally the only
sawtooth patterns are those due to caustics. |

Copyright ESO 2006