*Halos*

12 to 15 million halos (with more than 100 particles) were detected on the light-cones with a Friends-of-Friends algorithm (with a linking-length b given in the table). The resulting relativistic catalogs (produced through ray-tracing) are provided here. The format is explained below.

FoF b=0.2 ASCII angle/red/WL | ||

Narrow 2500 deg^{2} LCDM | link (12M) | |

Narrow 2500 deg^{2} wCDM | link (13M) | |

Fullsky 41253 deg^{2} LCDM | link (13M) | |

Fullsky 41253 deg^{2} wCDM | link (15M) |

Remark: The deeper (z < 10) light-cone is available upon demand to Michel-Andrès Breton (breton at ice.csic.es). Beyond z > 3 one has to take extra care of finite resolution effects at scales of order few coarse cells.

*Particle subsample*

Subsamples of about 200 million particles, 400 million particles and 1.4 billion particles were ray-traced. The resulting relativistic catalogs are provided here (the format is explained below).

Narrow lightcone 2500 deg2 z<2.0 LCDM 400M particles (fits)

Narrow lightcone 2500 deg2 z<2.0 wCDM 400M particles (fits)

———————————————————————-

Fullsky lightcone 41253 deg2 z<0.5 LCDM 1400M particles (fits)

Fullsky lightcone 41253 deg2 z<0.5 LCDM 200M particles (light fits)

Fullsky lightcone 41253 deg2 z<0.5 wCDM 1400M particles (fits)

Fullsky lightcone 41253 deg2 z<0.5 wCDM 200M particles (light fits)

**FILE CONTENT AND FORMAT**

The catalogs are displayed as ASCII files for halo or FITS file for particles, the different columns refers to :

id β_{1} β_{2} θ_{1} θ_{2} error_{1} error_{2} z_{0} z_{1} z_{2} z_{3} z_{4} z_{5} a_{11} a_{12} a_{21} a_{22} n_{part}

id= pFoF id of the halo

β_{i} = undeflected angles (ie without lensing) in radian

θ_{i}= apparent angles (ie with lensing) in radian

The angles are defined as in spherical coordinates. The normalized comoving coordinates are recovered as :

x = cos(β_{1})*sin(β_{2})

y = sin(β_{1})*sin(β_{2})

z = cos(β_{2})

The same formula can be used (replacing β_{i }by θ_{i}) to convert apparent angles into apparent normalized coordinates.

The (perturbed) redshifts z_{i} are defined as follows:

1+z_{0} = a_{0}/a

1+z_{1} = a_{0}/a [ 1 – (φ-φ_{0})/c^{2} ]

1+z_{2} = a_{0}/a [ 1 – (φ-φ_{0})/c^{2} +v·n/c ]

1+z_{3} = a_{0}/a [ 1 – (φ-phi0)/c^{2} +v.n/c +0.5*|v.v|/c^{2} ]

1+z_{4} = a_{0}/a [ 1 – (φ-φ_{0})/c^{2} +v·n/c +0.5*|v·v|/c^{2} – 2 int(∂φ∂η dη)/c^{2} ]

z_{5} = exact redshift computation from GR definition (in principle the resulting redshift should be very close to z_{4})

a is the expansion factor, φ is the potential, c is the square of the speed of light, v is the peculiar velocity of the source, n the direction of observation and ∂φ∂η the derivative of the potential with respect to the conformal time η. The subscript 0 indicates quantities evaluated at the observer location, while those without subscript indicates quantities evaluated at the source location. The observer is assumed to have no velocity in the adopted system of coordinates.

a_{ij} are the components of the distortion matrix a_{ij}=dβ_{i}/dθ_{j}, to be read as :

a_{11} a_{12}

a_{21} a_{22}

n_{part} is the number of particles in the halo.

## How to read the file?

ASCII files are straightforward to read. For instance in Python

```
import numpy as np
data=np.loadtxt(filename)
```

Light fits files are straightforward to read. For instance in Python:

```
from astropy.io import fits
hdulist = fits.open(filename)
data = hdulist[0].data # This gives the same array as for ASCII files
```

Standard fits can be read column by column. For instance in Python:

```
from astropy.io import fits
hdulist = fits.open(filename)
c1 = hdulist[1].data['COLUMN_NAME_1']
c2 = hdulist[1].data['COLUMN_NAME_2']
```

where COLUMN_NAME_I can be id,beta1,beta2,theta1,theta2,error,iteration,z0,z1,z2,z3,z4,z5,a11,a12,a21,a22,npart