École Euclid de cosmologie 2018

Date: August 20 - September 1, 2018

Venue: Roscoff, Bretagne, France

Website: http://ecole-euclid.cnrs.fr/accueil-session-2018


Lecture ``Weak gravitational lensing'' (Le lentillage gravitationnel), Martin Kilbinger.

Find here links to the lecture notes, TD exercises, "tables rondes" topics, and other information.

  • Resources.
    • A great and detailed introduction to (weak) gravitational lensing are the 2005 Saas Fee lecture notes by Peter Schneider. Download Part I (Introduction to lensing) and Part III (Weak lensing) from my homepage.
    • Check out Sarah Bridle's video lectures on WL from 2014.
  • TD cycle 1+2, Data analysis.
    1.  We will work on a rather large (150 MB) weak-lensing catalogues from the public CFHTLenS web page. During the TD I will show instructions how to create and download this catalogue. These catalogues will also be available on the virtual machine for the school.
      If you like, you can however download the catalogue on your laptop at home. Please have a look at the instructions in the TD slides.
    2. If you want to do the TD on your laptop, you'll need to download and install athena (the newest version 1.7). Available on the VM.
    3.  For one of the bonus TD you'll need a new version of pallas.py (v 1.8beta). Download it here. Available on the VM.
  • Lecture notes and exercise classes.  You can already download the slides in one file (40 - 60 MB), but be ware that the content will still change slightly until the classes.
    • Part I (Cycle 1):    [all | day 1 (1/6)  |   day 2 (2/6) |  day 3 (3/6)]
    • Part II (Cycle 2):  [all | day 1 (4/6)   |   day 2 (5/6)  | day 3 (6/6)]
    • TD:                             [1/2 and 2/2]
    • Table Ronde sujet
  • Slack channel: ede2018.slack.com

Athena

 

Authors: M. Kilbinger
Language: C
Download: athena_1.7.tgz
Description: A tree code for calculating second-order correlation functions.
Notes:  


athena: Tree code for second-order correlation functions

athena olive tree Martin Kilbinger, CEA Saclay, Service d'Astrophysique (SAp), France

METHOD athena is a 2d-tree code written in C, which estimates second-order correlation functions from input galaxy catalogues. These include shear-shear correlations (cosmic shear), position-shear (galaxy-galaxy lensing) and position-position (spatial angular correlation).

  DOWNLOAD Get the latest version athena_1.7.tgz. A readme file is available. Run the code on the test data set. New features and bug fixes in version 1.7 (Mar 2014):

  • General
    • Added FITS file support. Input catalogues and output correlation function files can be both in ascii or fits format.
      (Note: If reading a FITS file causes a segmentation fault, remove the compiler option "-std=c99", either from CMakeLists.txt or src/Makefile.athena".)
    • Format of resample files changed, only relevant columns are output.
    • Compilation of code automated using cmake. Alternatively, the traditional Makefile is still usable.
    • Directory structure changed.

To compile and run the code, you need a C-compiler. To calculate the angular correlation function, including reading mask files and creating random catalogues, gsl and perl and required. The library cfitsio is optional (for FITS file support).


Further scripts are part of the athena package:

  • The python script pallas.py calculates (band-)power spectrum by integrating over the correlation function using an estimator from this paper. Further, the aperture-mass dispersion is compuated, also via integrating the correlation function.
  • The perl script woftheta_xcorr.pl is the master script for angular correlation function calculations. It creates random catalogues and calls athena for all necessary combinations of data and random catalogues, including redshift bins, and outputs the Landy & Szalay (1993) and Hamilton (1993) estimators of the correlation function.
  • Two perl scripts (cat2gal.pl and center_gal.pl) calculate projections of an input catalogue in spherical coordinates, and transform an arbitrary (ascii) input catalogue into an athena-readable format.
  • The python script test_suite_athena.py runs a series of tests for easy comparison with expected results.
  • Various scripts to transform and plot resampled data (e.g. Jackknife)

  • For older versions of athena please contact me (martin.kilbinger at cea.fr).

REFERENCES

AUTHORS
Martin Kilbinger
Christopher Bonnett (gal-gal lensing)
Jean Coupon (venice)

With helpful suggestions from Henry McCracken, Lance Miller, and Barnaby Rowe. Ami Choi, Jonathan Benjamin, Matthieu Béthermin, and Shahab Joudaki are thanked for testing the code and bug-hunting.

CONTACT
Please feel free to send questions, feedback and bug reports to martin.kilbinger@cea.fr. If you want to be added to the athena mailing list, to get updates about new versions and bug-fixes, send me a mail to martin.kilbinger@cea.fr

LINKS
CosmoPMC (cosmology sampling with Population Monte Carlo [PMC])
nicaea (cosmology and lensing package)
reduced-shear corrections home

Last updated February 2017.

Camelus

 

Authors: Chieh-An Lin
Language: C
Download: GitHub
Description: A code for fast weak lensing peak count modelling.
Notes:  


Counts of Amplified Mass Elevations from Lensing with Ultrafast Simulations
Chieh-An Lin (University of Edinburgh)

Camelus

Description

Camelus is a fast weak lensing peak count modeling in C. It provides a prediction on peak counts from input cosmological parameters.

Here is the summary of the algorithm:

  • Sample halos from a mass function
  • Assign density profiles, randomize their positions
  • Compute the projected mass, add noise
  • Make maps and create peak catalogues

For a more detailed description, please take a look at Lin & Kilbinger (2015a).

Downloads

Please check the GitHub page of Camelus.

Requirements

The following softwares are required:

Updates

Current release: Camelus v1.31

New features in v1.31 - Mar 22, 2016:

  • Made installation more friendly by removing the dependency on cfitsio and mpi
  • Added the routine for computing 1-halo & 2-halo terms of the convergence profile
  • Flexible parameter space for PMC ABC
  • Remove files: FITSFunctions.c/.h

New features in v1.3 - Dec 09, 2015:

  • New files: constraint.c/.h
  • Allowed multiscale peaks in one data vector
  • Allowed a data matrix from several realizations
  • Used the local galaxy density as the noise level in the S/N
  • Increased the parameter dimension for PMC ABC
  • Changed the summary statistic options for PMC ABC

New features in v1.2 - Apr 06, 2015:

  • Improved the computation speed by a factor of 6~7
  • Converted the halo array structure into a binned structure, called "halo_map"
  • Converted the galaxy tree structure into a binned structure, called "gal_map"
  • Added the population Monte Carlo approximate Monte Carlo (PMC ABC) algorithm

New features in v1.1 - Jan 19, 2015:

  • Fixed the bug from calculating halo radii

New features in v1.0 - Oct 24, 2014:

  • Fast weak lensing peak count modeling

References

Contact information

Authors:

Please feel free to send questions, feedback and bug reports to calin AT roe DOT ac DOT uk.

Last updated Jun 26, 2015.

École Euclid de cosmologie 2017

Date: June 27 - July 8 2017

Venue: Fréjus, France

Website: http://ecole-euclid.cnrs.fr/programme-2017


Lecture ``Weak gravitational lensing'' (Le lentillage gravitationnel), Martin Kilbinger.

Find here links to the lecture notes, TD exercises, "tables rondes" topics, and other information.

  • Resources.
    • A great and detailed introduction to (weak) gravitational lensing are the 2005 Saas Fee lecture notes by Peter Schneider. Download Part I (Introduction to lensing) and Part III (Weak lensing) from my homepage.
    • Check out Sarah Bridle's video lectures on WL from 2014.
  • TD cycle 1+2, Data analysis.
    1.  We will work on a rather large (150 MB) weak-lensing catalogue from the public CFHTLenS web page. During the TD I will show instructions how to create and download this catalogue. For faster access, it will be available on the server during the school, and I will bring a few USB sticks.
      If you like, you can however download the catalogue on your laptop at home. Please have a look at the instructions (available soon).
    2. If you want to do the TD on your laptop, you'll need to download and install athena (the newest version 1.7).
    3.  For one of the bonus TD you'll need a new version of pallas.py (v 1.8beta). Download it here.
  • Lecture notes and exercise classes:

Quantifying systematics from the shear inversion on weak-lensing peak counts

Authors: C. Lin, M. Kilbinger
Journal: Submitted to A&A letters
Year: 2017
Download: ADS | arXiv

 


Abstract

Weak-lensing (WL) peak counts provide a straightforward way to constrain cosmology, and results have been shown promising. However, the importance of understanding and dealing with systematics increases as data quality reaches an unprecedented level. One of the sources of systematics is the convergence-shear inversion. This effect, inevitable from observations, is usually neglected by theoretical peak models. Thus, it could have an impact on cosmological results. In this letter, we study the bias from neglecting the inversion and find it small but not negligible. The cosmological dependence of this bias is difficult to model and depends on the filter size. We also show the evolution of parameter constraints. Although weak biases arise in individual peak bins, the bias can reach 2-sigma for the dark energy equation of state w0. Therefore, we suggest that the inversion cannot be ignored and that inversion-free approaches, such as aperture mass, would be a more suitable tool to study weak-lensing peak counts.

Weak-lensing projections

Authors: M. Kilbinger, C. Heymans et al.
Journal: submitted to MNRAS
Year: 2017
Download: ADS | arXiv


Abstract

We compute the spherical-sky weak-lensing power spectrum of the shear and convergence. We discuss various approximations, such as flat-sky, and first- and second- order Limber equations for the projection. We find that the impact of adopting these approximations are negligible when constraining cosmological parameters from current weak lensing surveys. This is demonstrated using data from the Canada-France-Hawaii Lensing Survey (CFHTLenS). We find that the reported tension with Planck Cosmic Microwave Background (CMB) temperature anisotropy results cannot be alleviated, in contrast to the recent claim made by Kitching et al. (2016, version 1). For future large-scale surveys with unprecedented precision, we show that the spherical second-order Limber approximation will provide sufficient accuracy. In this case, the cosmic-shear power spectrum is shown to be in agreement with the full projection at the sub-percent level for l > 3, with the corresponding errors an order of magnitude below cosmic variance for all l. When computing the two-point shear correlation function, we show that the flat-sky fast Hankel transformation results in errors below two percent compared to the full spherical transformation. In the spirit of reproducible research, our numerical implementation of all approximations and the full projection are publicly available within the package nicaea at http://www.cosmostat.org/software/nicaea.


Summary

We discuss various methods to calculate projections for weak gravitational lensing: Since lenses galaxies pick up matter inhomogeneities of the cosmic web along the line of sight while photons from the galaxies propagate through the Universe to the observer, these inhomogeneities have to be projected to a 2D observable, the cumulative shear or convergence. The full projection involves three-dimensional integrals over highly oscillating Bessel functions, and can be time-consuming to compute numerically to high accuracy. Most previous work have therefore used approximations such as the Limber approximation, that reduce the integrals to 1D, and thereby neglecting modes along the line of sight.

The authors show that these projections are more than adequate for present surveys. Sub-percent accuracy is reached for l>20, for example as shown by the pink curve, which is the ratio of the case 'ExtL1Hyb' to the full projection. The abbreviation means 'extended', corresponding to the improved approximation introduced by LoVerde & Afshordi (2008), first-order Limber, and hybrid, since this is a hybrid between flat-sky and spherical coordinates. This case has been used in most of the recent publications (e.g. for KiDS), whereas the cast 'L1Fl' (first-order Limber flat-sky) was popular for most publications since 2014.

These approximations are sufficient for the small areas of current observations coming from CFHTLenS, KiDS, and DES, and well below cosmic variance of even future surveys (the figure shows Euclid - 15,000 deg2 and Kids -1,500 deg2).

K17_Fig1b

The paper then discusses the second-order Limber approximation, introduced in a general framework by LoVerde & Afshordi (2008), and applied to weak lensing in the current paper. The best 2nd-order case 'ExtL2Sph' reaches sub-percent accuracy down to l=3, sufficient for all future surveys.

The paper also computes the shear correlation function in real space, and shows that those approximations have a very minor influence.

We then go on to re-compute the cosmological constraints obtained in Kilbinger et al. (2013), and find virtually no change when choosing different approximations. Only the depreciated case 'ExtL1Fl' makes a noticeable difference, which is however still well within the statistical error bars. This case shows a particular slow convergence to the full projection.

Similar results have been derived in two other recent publications, Kitching et al. (2017), and Lemos, Challinor & Efstathiou (2017).
Note however that Kitching et al. (2017) conclude that errors from projection approximations of the types we discussed here (Limber, flat sky) could make up to 11% of the error budget of future surveys. This is however assuming the worst-case scenario including the deprecated cast 'ExtL1Fl', and we do not share their conclusion, but think that for example the projection 'ExtL2Sph' is sufficient for future surveys such as LSST and Euclid.