Welcome to the website belonging to the paper 'Disentangling galaxy environment and host halo mass' by Marcel R. Haas, Joop Schaye and Akila Jeeson-Daniel. On this page, we provide the reader with tabulated polynomial fits for the host halo mass as a function of several environmental parameters for galaxies. We strongly encourage the users of these tables to read our paper. Below we repeat the abstract, after which we explain the contents of the tables.

## Abstract

The properties of both observed galaxies and dark matter haloes in simulations depend on their environment. The term `environment' has, however, been used to describe a wide variety of measures that may or may not correlate with each other. Popular measures of environment include, for example, the distance to the N'th nearest neighbour, the number density of objects within some distance, or, for the case of galaxies, the mass of the host dark matter halo. Here we use results from the Millennium simulation and a semi-analytic model for galaxy formation to quantify the relations between different measures of environment and halo mass. We show that the environmental parameters used in the observational literature are in effect measures of halo mass, even if they are measured for a fixed stellar mass. The strongest correlation between environmental density and halo mass arises when the number of objects is counted out to a distance of 1.5 - 2 times the virial radius of the host halo and when the galaxies/haloes are required to be relatively bright/massive. For observational studies this virial radius is not easily determined, but the number of neighbours out to 1 - 2 Mpc/h gives a similarly strong correlation with halo mass. For the distance to the N'th nearest neighbour the (anti-)correlation with halo mass is nearly as strong provided N >= 2. We demonstrate that this environmental parameter becomes insensitive to halo mass if it is constructed from dimensionless quantities. This can be achieved by scaling the minimum luminosity/mass of neighbours to that of the object that the environment is determined for and by dividing the distance to a length scale associated with either the neighbour or the galaxy under consideration. We show how such a halo mass independent environmental parameter can be defined for both observational and numerical studies. The results presented here will help future studies to disentangle the effects of halo mass and external environment on the properties of galaxies and dark matter haloes.

## The environmental parameters

The tables we provide below contain 3^{rd}order polynomial fits for the host halo mass of galaxies as a function of environmental parameters. Specifically, we fit a function of the form

Log

_{10}[M

_{halo}(h

^{-1}M

_{sun})] = A + B P + C P

^{2}+ D P

^{3}(1)

Where P is the logarithm of the environmental parameter in question. All logarithms here are in base 10. All tables provide such fits for the following environmental parameters:

_{10}[r

_{1}(Mpc/h)]: The logarithm of the projected distance on the sky to the first nearest neighbour.

_{10}[r

_{4}(Mpc/h)]: The logarithm of the projected distance on the sky to the fourth nearest neighbour.

_{10}[r

_{10}(Mpc/h)]: The logarithm of the projected distance on the sky to the tenth nearest neighbour.

_{10}[n

_{0.5 Mpc/h}]: The logarithm of the number of neighbours within a projected distance on the sky of 0.5 Mpc/h.

_{10}[n

_{1 Mpc/h}]: The logarithm of the number of neighbours within a projected distance on the sky of 1 Mpc/h.

_{10}[n

_{2 Mpc/h}]: The logarithm of the number of neighbours within a projected distance on the sky of 2 Mpc/h.

_{10}[n

_{1 Rvir}]: The logarithm of the number of neighbours within a projected distance equal to 1 times the virial radius of the host halo.

_{10}[n

_{1.5 Rvir}]: The logarithm of the number of neighbours within a projected distance equal to 1.5 times the virial radius of the host halo.

_{10}[n

_{2 Rvir}]: The logarithm of the number of neighbours within a projected distance equal to 2 times the virial radius of the host halo.

In the neighbour search we include all galaxies above a given flux or stellar mass limit, with a maximum redshift difference of 1000 km/s between the neighbour and the galaxy we determine the environmental parameter for. All tables have the flux/mass limit fixed for the neighbour search (indicated in the list below and in the file name). Note that in the fits only galaxies at redshift zero are included. The fits will therefore be only precise at very low redshift. For higher redshift a similar anaysis should be carried out. You can contact the authors if you so desire.

## Tables

The tables are structured as follows:- Some explanation of the fits provided in that table, including the lower limit on the K-band flux or stellar mass.
- For the first environmental parameter, we provide the fits for:
- All galaxies in the sample.
- Galaxies in the sample in small bins of K-band magnitude or stellar mass (note that the neighbour search still contains all galaxies in the full sample). An upper flux limit correpsonding to a K-band magnitude of -999 means that there is no upper limit on the K-band flux. Similarly, a Log
_{10}[M_{*}(h^{-1}M_{sun})] = 100 means there is no upper stellar mass limit.

- The same for all following environmental parameters.

We provide tables for samples of galaxies that are limited in the K-band flux, and that are limited in stellar mass. We include, in all columns respectively, the lower and upper flux or stellar mass limit for the galaxies for which we perform the fit, the parameters A-D (eq. 1) for the best fit to the median of the distribution of galaxies and the parameters A-D (eq. 1) for fits to 16

^{th}and 84

^{th}percentiles of the data (these would describe the +/- one sigma for a gaussian distribution. Note that the distribution of host halo masses at fixed environment is neither gaussian nor symmetric). The last number we provide is the Spearman rank correlation coefficient between halo mass and environmental parameter S(M

_{halo}, P). All lines in the tables that do not contain numbers are comments that help navigation through the files and start with a '#'.

_{10}[M

_{*}(h

^{-1}M

_{sun})] > 10.

_{10}[M

_{*}(h

^{-1}M

_{sun})] > 10.2

_{10}[M

_{*}(h

^{-1}M

_{sun})] > 10.4

_{10}[M

_{*}(h

^{-1}M

_{sun})] > 10.6

_{10}[M

_{*}(h

^{-1}M

_{sun})] > 10.8

_{10}[M

_{*}(h

^{-1}M

_{sun})] > 11.

Or download all tables in one tarball.

If you have any comments and/or questions, please do not hesitate to contact the authors using the contact details provided here.