Tutorial: Warm dark matter halo mass function

In this tutorial we'll use Galacticus to compute and output the mass function of warm dark matter halos. You should first follow the CDM halo mass function tutorial which explains how to run a halo mass function calculation, and describes the outputs.

Running the calculation

To run an example of a warm dark matter halo mass function calculation, do the following:

$ ./Galacticus.exe parameters/tutorials/haloMassFunctionWarmDarkMatter.xml

If everything is working a file haloMassFunctionWarmDarkMatter.hdf5 will have been created.

Understanding the input

You can look at the entire parameter file for this tutorial here. Below we'll explore just those sections of the parameter file specific to the warm dark matter calculation - everything else is just as it would be for the equivalent CDM calculation.

  <!-- Specify tasks to perform -->
  <task value="haloMassFunction">
    <haloMassMinimum value="1.0e7"/>    
  </task>

The only difference with respect to the CDM case here is that we specify the minimum halo mass at which to compute the halo mass function. By default a minimum mass of 10¹⁰M_☉ is used, but here we want to go to lower masses to see the effects of warm dark matter.

  <!-- Use a thermal WDM particle - mass is in keV -->
  <darkMatterParticle value="WDMThermal">
    <degreesOfFreedomEffective value="1.5" />
    <mass value="3.0" />
  </darkMatterParticle>

In the above we explicitly specify a thermal warm dark matter particle, with effective degrees of freedom g_X=1.5 and a mass of m_X=3.0 keV. In the CDM case we didn't specify the type of dark matter particle, since CDM is the default.

  <!-- Use the Bode et al. (2001) transfer function for thermal WDM -->
  <transferFunction value="bode2001">
    <epsilon value="0.359" />
    <eta value="3.810" />
    <nu value="1.100" />
    <!-- Bode2001 transfer function works by modifying a CDM transfer function - so feed it a CDM transfer function here -->
    <transferFunction value="eisensteinHu1999">
      <!-- Feed this transfer function a CDM particle - otherwise it will see the WDM particle defined above and complain that it
           can not compute WDM transfer functions -->
      <darkMatterParticle value="CDM" />
      <neutrinoNumberEffective value="3.046"/>
      <neutrinoMassSummed value="0.000"/>
    </transferFunction>
  </transferFunction>
  <!-- When computing sigma(M) for power spectra with a cut off it's better to use a filter that is sharp in k-space, instead of
       the usual real-space top-hat (which introduces artificial halos below the cut-off scale -->
  <cosmologicalMassVariance value="filteredPower">
    <monotonicInterpolation value="true" />
    <nonMonotonicIsFatal value="false" />
    <powerSpectrumWindowFunction value="sharpKSpace">
      <normalization value="2.5" />
    </powerSpectrumWindowFunction>
    <sigma_8 value="0.8111" />
    <tolerance value="3.0e-4" />
    <toleranceTopHat value="3.0e-4" />
  </cosmologicalMassVariance>

Here we use the Bode et al. (2001) fitting function for the warm dark matter transfer function. Note that this works by modifying the CDM transfer function (supplied here using the eisensteinHu1999 method), and that we explicitly pass a CDM dark matter particle to this class (otherwise it would find the WDM particle class and refuse to work, since it doesn't know how to compute the transfer function for WDM). For warm dark matter, we switch to using a sharp-in-k-space filter to compute σ(M), as it avoids spurious halos below the cut-off scale which result for warm dark matter power spectra using the usual top-hat-in-real-space filter (see Benson et al. (2013)).

  <!-- Use the Barkana et al. (2001) method for the critical overdensity for collapse for WDM -->
  <criticalOverdensity value="barkana2001WDM">
    <!-- Barkana2001 critical overdensity works by modifying a CDM critical overdensity - so feed it a CDM critical overdensity
         here -->
    <criticalOverdensity value="sphericalCollapseClsnlssMttrCsmlgclCnstnt">
      <!-- Feed this critical overdensity a CDM particle - otherwise it will see the WDM particle defined above and complain that
           it can not compute WDM critical overdensities-->
      <darkMatterParticle value="CDM" />
    </criticalOverdensity>
  </criticalOverdensity>

For the critical overdensities for collapse of halos (as used in Press-Schechter-type models) we make use of the results from Barkana et al. (2001) for warm dark matter. Note that this works by modifying the CDM critical overdensities (supplied here using the sphericalCollapseClsnlssMttrCsmlgclCnstnt method), and that we explicitly pass a CDM dark matter particle to this class (otherwise it would find the WDM particle class and refuse to work, since it doesn't know how to compute critical overdensities for WDM).

  <darkMatterProfileConcentration value="schneider2015">
    <reference>
      <darkMatterParticle value="CDM" />
      <darkMatterProfileConcentration value="gao2008"/>
      <criticalOverdensity value="sphericalCollapseClsnlssMttrCsmlgclCnstnt"/>
      <cosmologicalMassVariance value="filteredPower">
	<sigma_8 value="0.807"/>
	<monotonicInterpolation value="true" />
	<nonMonotonicIsFatal value="false" />
	<powerSpectrumWindowFunction value="sharpKSpace">
	  <normalization value="2.5" />
	</powerSpectrumWindowFunction>
	<transferFunction value="eisensteinHu1999">
	  <darkMatterParticle value="CDM" />
	  <neutrinoNumberEffective value="3.046"/>
	  <neutrinoMassSummed value="0.000"/>
	</transferFunction>
      </cosmologicalMassVariance>
    </reference>
  </darkMatterProfileConcentration>

For dark matter halo concentrations, we make use of the Schneider et al. (2015) algorithm, which computes the concentration by matching halo formation epochs to a "reference" CDM universe. The properties of the reference universe are described in the above in the reference section.

Understanding the output

The output file haloMassFunctionWarmDarkMatter.hdf5 has exactly the same format as for the CDM case, described in the halo mass function tutorial.