Dark Matter Profile Scale Radii¶
Class providing the scale radius \(r_\mathrm{s}\) of dark matter halo density profiles. The scale radius sets the characteristic transition scale between the inner and outer slopes of the density profile (e.g. at \(r_\mathrm{s}\) the NFW profile transitions from \(\rho \propto r^{-1}\) to \(\rho \propto r^{-3}\)). Implementations may derive the scale radius from a concentration parameter, from energy conservation arguments, or from other empirical relations.
Default implementation: darkMatterProfileScaleRadiusConcentration
Methods¶
radius→double precisionReturns the scale radius \(r_\mathrm{s}\) (in Mpc) of the dark matter halo density profile for the halo in
node, the characteristic radius at which the logarithmic slope of the density profile transitions between inner and outer power laws.type(treeNode), intent(inout), target :: node
darkMatterProfileScaleRadiusBinary¶
A dark matter halo profile scale radii class which switches between two methods based on a filter.
darkMatterProfileScaleRadiusConcentration¶
Dark matter halo scale radii are computed from the concentration.
(Default implementation)
Parameters
[correctForConcentrationDefinition](default.false.) — If true, then when computing dark matter profile scale radii using concentrations, any difference between the current definition of halo scales (i.e. typically virial density contrast definitions) and density profiles and those assumed in measuring the concentrations will be taken into account. If false, the concentration is applied blindly.[useMeanConcentration](default.false.) — If true, then when computing dark matter profile scale radii using concentrations do not account for any possible scatter in the concentration-mass relation.[useLastIsolatedTime](default.false.) — If true, evaluate the concentration using a the virial density definition at the last isolated time of the halo.
darkMatterProfileScaleRadiusConcentrationLimiter¶
Dark matter halo scale radii from another class are limited to enforce bounds on concentration.
Parameters
[concentrationMinimum]— The minimum allowed concentration parameter \(c = r_\mathrm{virial}/r_\mathrm{scale}\) for dark matter halos; scale radii that would imply concentrations below this floor are adjusted upward to enforce the constraint.[concentrationMaximum]— The maximum allowed concentration parameter \(c = r_\mathrm{virial}/r_\mathrm{scale}\) for dark matter halos; scale radii that would imply concentrations above this ceiling are adjusted downward to enforce the constraint.
darkMatterProfileScaleRadiusJohnson2021¶
A dark matter profile scale radius class that computes scale radii based on the energy conservation approach of Johnson et al. (2021), with some modifications and improvements.
Specifically, for “well-resolved” halos (see below for discussion of this point), the concentration is found by computing the total energy of the halo as the sum over the energies (internal and orbital) of its progenitor halos. The halo is assumed to have virialized at this energy, and the scale radius is then solved for such that the energy of the assumed density profile (e.g. Galacticusnfw) is equal to the computed energy of the halo.
In detail, the energy, \(E_\mathrm{int}\), of a node is assumed to be given by:
where \(E_{\mathrm{int}, 0}\) is the internal energy of the primary progenitor halo, \(E_{\mathrm{int}, i}\) is the internal energy of the \(i^\mathrm{th}\) non-primary progenitor halo, \(E_{\mathrm{orb}, i,0}\) is the orbital energy of the \(i^\mathrm{th}\) non-primary progenitor halo about the primary progenitor halo, \(\mu = M_i/M_0\) is the mass ratio of the \(i^\mathrm{th}\) non-primary progenitor and the primary progenitor ratio, \(\nu\) is the peak height parameter for the primary progenitor halo, \(w_i\) is the subsampling weight of the \(i^\mathrm{th}\) non-primary progenitor, \(\mathcal{N}(0,1)\) is a standard normal deviate, \(\alpha=\)[massExponent], \(\beta=\)[peakHeightExponent], \(b=\)[energyBoost], and \(\sigma=\)[scatterExcess].
To account for the contribution to the energy from unresolved accretion, we proceed as follows. First, the unresolved mass is determined by subtracting the mass of all progenitors from the halo mass:
This mass will be accreted in halos spanning a range of masses below the unresolved mass scale, \(M_\mathrm{unres}\). We assume the mass function of these unresolved halos follows a power-law, \(n(M) \propto M^\delta\), with \(\delta = -1.8\). We further assume that the mean orbit energy of an unresolved halo is simply proportional to \(M\) (i.e. the distribution of orbital parameters is independent of mass), and that the internal energy of an unresolved halo scales as \(E_\mathrm{int} \propto M^{5/3+\epsilon}\) where the \(5/3\) exponent is the expected scaling for halos assuming a self-similar structure, and \(\epsilon = -0.02\) accounts for the non-self-similarity (e.g. that concentration is a function of mass) and was estimated for typical CDM halos.
The mean energy (orbital or internal) per unit mass of unresolved halos is then found by averaging these scalings over the mass function. Dividing these by the energy of an unresolved halo of mass \(M_\mathrm{unres}\) then gives a correction factor that can be applied to the energy computed for halos of \(M_\mathrm{res}\) to account for the spectrum of unresolved halo masses. That is, for an energy that scales as \(x^p\) where \(x = M/M_0\), the correction factor is:
This evaluates to:
We further compute correction factors to account for the fact that this unresolved mass is accreted over some interval of time, during which mean halo properties (e.g. virial density) will evolve. For internal energies we have \(E_\mathrm{int} \propto M^2/r \propto M^{5/3}/\rho \propto M^{5/3}/a(t)\) where \(a(t)\) is the expansion factor. If the current halo exists at time \(t\), and the primary progenitor at time \(t_0\), we therefore compute a correction factor to the midpoint of this interval,
where the second term in the parentheses is the ratio of the internal energy of a halo of fixed mass at \(t\) and \(t_0\). For orbital energy we expect a scaling \(E_\mathrm{orb} \propto M M_\mathrm{host}/r_\mathrm{host} \propto M M_\mathrm{host}^{2/3}/\rho \propto M M_\mathrm{host}^{2/3}/a(t)\) where \(M_\mathrm{host}\) and \(r_\mathrm{host}\) are the virial mass and radius of the host (current) halo, respectively. Computing a correction factor to the midpoint of the time interval we find,
We next estimate the mean and root-variance, \(\bar{E}_\mathrm{unres}\) and \(\sigma_\mathrm{unres}\), respectively, of the energy of a halo of mass \(M_\mathrm{unres}\) via a Monte Carlo approach. We generate \(N_\mathrm{MC}=\)[countSampleEnergyUnresolved] such halos, each with scale radii set using the fall-back darkMatterHaloScaleClass object with an added scatter of \(\sigma^\prime=\)[scatter] dex, and a randomly selected orbit. For each such halo, the energy is computed as
where \(u =\)[unresolvedEnergy].
To estimate the deviation from the mean unresolved energy we again consider the contributions from a spectrum of unresolved halo masses. For simplicity we here ignore the internal energies (which are typically small relative to the orbital energy assuming that the unresolved halo masses are small compared to that of the primary progenitor. The mean energy of unresolved halos is then
while the variance in this energy is
The fractional variance is then
We therefore add to the energy of the halo an unresolved contribution of
where \(\sigma_\mathrm{e}=\)[scatterExcess] accounts for scatter missed by this model.
The scale radius which corresponds to this energy is then solved for.
For halos with mass less than \(f_\mathrm{res} M_\mathrm{res}\), where \(f_\mathrm{res}=\)[factorMassResolution] and \(M_\mathrm{res}\) is the mass resolution of the merger tree, and for any halo which has no progenitors (a leaf node), the scale radius is instead computed using an alternative methodfootnoteFor leaf nodes, there are no progenitors for which to apply the above energy calculation, and for halos sufficiently close to the mass resolution the energy calculation may not be reliable due to the poorly-resolved formation history of the node.. In these cases, the entire extent of the branch for which this criterion applies is first determined. Each halo in this sub-branch is first assigned a scale radius from a fall-back darkMatterHaloScaleClass object which should be configured to return a scatter-free scale radius for halos of given mass and redshiftfootnoteAs scatter will be added directly by the present class. Then, a correlated set of random, log-normal deviates are applied to the scale radii of these nodes. That is, the scale radius of the \(i^\mathrm{th}\) node in such a sub-branch will be \(r_\mathrm{s} = \bar{r}_{\mathrm{s}, i} 10^{x_i}\) where \(x_i\) is a normally-distributed random variate with mean zero and dispersion \(\sigma^\prime=\)[scatter]. The deviates \(x_i\) are assumed to be correlated with correlation matrix:
wherefootnoteThese values were found by fitting to results from this class. \(\gamma =\)[correlationRateDecay], \(\mu =\)[correlationExponent] and \(M_i\) is the mass of the \(i^\mathrm{th}\) halo in the sub-branch. This results in a scale radius along the sub-branch with the correct mean and scatter, but correlated over mass increment scales in a way that matches the predictions of this algorithm.
Parameters
[energyBoost](default0.797d0) — A multiplicative boost factor applied to the orbital energy in the (Johnson et al., 2021) scale radius model, calibrated to match the energy budget of merging halos in N-body simulations.[massExponent](default2.168d0) — The exponent of mass ratio appearing in the orbital energy term.[peakHeightExponent](default0.0d0) — The exponent of the peak height \(\nu\) (a dimensionless measure of halo rarity relative to the mass function) in the orbital energy term of the (Johnson et al., 2021) scale radius model; controls the dependence of scale radius on halo formation epoch.[unresolvedEnergy](default0.550d0) — Factor multiplying the estimate of the internal energy of unresolved accretion.[factorMassResolution](default1.0d2) — The Johnson et al. (2021) model is applied only for halos with mass greater than \(f M_\mathrm{res}\) where \(f=\)[factorMassResolution]. Below this mass the fall-back method is used, with correlated scatter along the branch.[scatter](default0.16d0) — The scatter in scale radius (in dex) to be applied to halos that are too low mass for the Johnson et al. (2021) model to be applied.[scatterExcess](default0.116d0) — The additional scatter radius (in dex) to be applied to the energies of merging halos to account for the fact that the Johnson et al. (2021) underpredicts the scatter in concentrations.[correlationRateDecay](default3.8361d0) — The decay rate for the exponential correlation model for scale radii.[correlationExponent](default1.6198d0) — The exponent for the exponential correlation model for scale radii.[countSampleEnergyUnresolved](default100) — The number of samples to use in Monte Carlo estimates of the mean and scatter in the energy of unresolved halos.[mainBranchOnly](default.false.) — If true, the Johnson et al. (2021) algorithm is applied to the main branch only, with other branches using the fall-back method.[applySubsamplingWeights](default.true.) — If true, account for halo subsampling weights when computing population-averaged quantities in the (Johnson et al., 2021) model, necessary when the merger tree was constructed using subsampled halo catalogs.[acceptUnboundOrbits](default.false.) — If true, allow unbound orbits when sampling orbits for unresolved halos.[includeUnresolvedVariance](default.false.) — If true, account for the variance in the energy of unresolved halos.
darkMatterProfileScaleRadiusLudlow2014¶
Dark matter halo scale radii are computed using the algorithm of Ludlow et al. (2014).
darkMatterProfileScaleRadiusLudlow2016¶
Dark matter halo scale radii are computed using the algorithm of Ludlow et al. (2016). While Ludlow et al. (2016) used \(\Delta = 200 \rho_\mathrm{crit}\) to define halos, their model actually predicts the scale radius, \(r_{-2}\), rather than the concentration. Therefore, here we report that the Ludlow et al. (2016) concentrations are defined using the model’s own virial density contrast definition — this ensures that the predicted scale radii are applied directly to model halos.
Methods
tabulate— Tabulate the virial density contrast as a function of mass and time.restoreTable— Restore a tabulated solution from file.storeTable— Store a tabulated solution to file.
Parameters
[velocityCharacteristic](default250.0d0) — The velocity scale at which the SNe-driven outflow rate equals the star formation rate in disks.[exponent](default3.5d0) — The velocity scaling of the SNe-driven outflow rate in disks.[fraction](default0.01d0) — The normalization \(f\) of the outflow rate relative to the star formation rate at a reference halo velocity of 200 km/s and expansion factor of 1, setting the overall mass-loading amplitude of the halo-scaling feedback model.[exponentVelocity](default-2.0d0) — The exponent of virial velocity in the outflow rate in disks.[exponentRedshift](default0.0d0) — The power-law exponent of the cosmological expansion factor \((1+z)\) in the halo-scaling outflow rate, allowing the mass-loading factor to evolve with redshift; a value of zero gives no redshift evolution.[toleranceRelativeVelocityDispersion](default1.0d-6) — The relative tolerance to use in numerical solutions for the velocity dispersion in dark-matter-only density profiles.[toleranceRelativeVelocityDispersionMaximum](default1.0d-3) — The maximum relative tolerance to use in numerical solutions for the velocity dispersion in dark-matter-only density profiles.[radiusNormalization](default3.3d-6) — The initial value appearing in the radius-mass relation[toleranceAbsoluteMass](default1.0d-6) — The mass tolerance used to judge whether the nuclear star cluster is physically plausible.[toleranceRelativeMetallicity](default1.0d-4) — The metallicity tolerance for ODE solution.[inactiveLuminositiesStellar](default.false.) — Specifies whether or not nuclear star cluster stellar luminosities are inactive properties (i.e. do not appear in any ODE being solved).[scaleRelativeMass](default1.0d-2) — The mass scale, relative to the total mass of the node, below which calculations in the delayed very simple hot halo component are allowed to become inaccurate.[starveSatellites](default.false.) — Specifies whether or not the hot halo should be removed (“starved”) when a node becomes a satellite.[starveSatellitesOutflowed](default.false.) — Specifies whether or not the outflowed hot halo should be removed (“starved”) when a node becomes a satellite.[outflowReturnOnFormation](default.false.) — Specifies whether or not outflowed gas should be returned to the hot reservoir on halo formation events.[angularMomentumAlwaysGrows](default.false.) — Specifies whether or not negative rates of accretion of angular momentum into the hot halo will be treated as positive for the purposes of computing the hot halo angular momentum.[fractionBaryonLimitInNodeMerger](default.false.) — Controls whether the hot gas content of nodes should be limited to not exceed the universal baryon fraction at node merger events. If set totrue, hot gas (and angular momentum, abundances, and chemicals proportionally) will be removed from the merged halo to the unaccreted gas reservoir to limit the baryonic mass to the universal baryon fraction where possible.[scaleAbsoluteMass](default100.0d0) — The absolute mass scale below which calculations in the very simple disk component are allowed to become inaccurate.[toleranceAbsoluteMass](default1.0d-6) — The mass tolerance used to judge whether the disk is physically plausible.[toleranceAbsoluteMass](default1.0d-6) — The mass tolerance used to judge whether the disk is physically plausible.[toleranceRelativeMetallicity](default1.0d-4) — The metallicity tolerance for ODE solution.[radiusStructureSolver](default1.0d0) — The radius (in units of the standard scale length) to use in solving for the size of the disk.[structureSolverUseCole2000Method](default.false.) — If true, use the method described in Cole et al. (2000) to correct for difference between thin disk and spherical mass distributions when solving for disk radii.[diskNegativeAngularMomentumAllowed](default.true.) — Specifies whether or not negative angular momentum is allowed for the disk.[inactiveLuminositiesStellar](default.false.) — Specifies whether or not disk stellar luminosities are inactive properties (i.e. do not appear in any ODE being solved).[postStepZeroNegativeMasses](default.true.) — If true, negative masses will be zeroed after each ODE step. Note that this can lead to non-conservation of mass.[ratioAngularMomentumSolverRadius](defaultratioAngularMomentumSolverRadiusDefault) — The assumed ratio of the specific angular momentum at the structure solver radius to the mean specific angular momentum of the standard disk component.[scaleAbsoluteMass](default100.0d0) — The absolute mass scale below which calculations in the very simple spheroid component are allowed to become inaccurate.[toleranceAbsoluteMass](default1.0d-6) — The mass tolerance used to judge whether the spheroid is physically plausible.[efficiencyEnergeticOutflow](default1.0d-2) — The proportionality factor relating mass outflow rate from the spheroid to the energy input rate divided by \(V_\mathrm{spheroid}^2\).[toleranceRelativeMetallicity](default1.0d-4) — The metallicity tolerance for ODE solution.[toleranceAbsoluteMass](default1.0d-6) — The mass tolerance used to judge whether the spheroid is physically plausible.[inactiveLuminositiesStellar](default.false.) — Specifies whether or not spheroid stellar luminosities are inactive properties (i.e. do not appear in any ODE being solved).[postStepZeroNegativeMasses](default.true.) — If true, negative masses will be zeroed after each ODE step. Note that this can lead to non-conservation of mass.[ratioAngularMomentumScaleRadius](defaultratioAngularMomentumScaleRadiusDefault) — The assumed ratio of the specific angular momentum at the scale radius to the mean specific angular momentum of the standard spheroid component.[outputMergers](default.false.) — Determines whether or not properties of black hole mergers will be output.[fileNames]— The name of the file(s) from which merger tree data should be read when using the[mergerTreeConstruct]\(=\)readtree construction method.[forestSizeMaximum](default0_c_size_t) — The maximum number of nodes allowed in a forest before it will be broken up into trees and processed individually. A value of 0 implies that forests should never be split.[presetMergerTimes](default.true.) — Specifies whether merging times for subhalos should be preset when reading merger trees from a file.[presetMergerNodes](default.true.) — Specifies whether the target nodes for mergers should be preset (i.e. determined from descendant nodes). If they are not, merging will be with each satellite’s host node.[presetSubhaloMasses](default.true.) — Specifies whether subhalo mass should be preset when reading merger trees from a file.[subhaloAngularMomentaMethod](defaultvar_str('summation')) — Specifies how to account for subhalo angular momentum when adding subhalo mass to host halo mass.[presetSubhaloIndices](default.true.) — Specifies whether subhalo indices should be preset when reading merger trees from a file.[presetPositions](default.true.) — Specifies whether node positions should be preset when reading merger trees from a file.[presetScaleRadii](default.true.) — Specifies whether node scale radii should be preset when reading merger trees from a file.[scaleRadiiFailureIsFatal](default.true.) — Specifies whether failure to set a node scale radii should be regarded as a fatal error. (If not, a fallback method to set scale radius is used in such cases.)[presetScaleRadiiConcentrationMinimum](default3.0d0) — The lowest concentration (\(c=r_\mathrm{vir}/r_\mathrm{s}\)) allowed when setting scale radii, \(r_\mathrm{s}\).[presetScaleRadiiConcentrationMaximum](default60.0d0) — The largest concentration (\(c=r_\mathrm{vir}/r_\mathrm{s}\)) allowed when setting scale radii, \(r_\mathrm{s}\).[presetScaleRadiiMinimumMass](default0.0d0) — The minimum halo mass for which scale radii should be preset (if[presetScaleRadii]\(=\)true).[presetUnphysicalAngularMomenta](default.false.) — When reading merger trees from file and presetting halo angular momenta, detect unphysical (<=0) angular momenta and preset them using the selected halo spin method.[presetAngularMomenta](default.true.) — Specifies whether node angular momenta should be preset when reading merger trees from a file.[presetAngularMomenta3D](default.false.) — Specifies whether node 3-D angular momenta vectors should be preset when reading merger trees from a file.[presetOrbits](default.true.) — Specifies whether node orbits should be preset when reading merger trees from a file.[presetOrbitsSetAll](default.true.) — Forces all orbits to be set. If the computed orbit does not cross the virial radius, then select one at random instead.[presetOrbitsAssertAllSet](default.true.) — Asserts that all virial orbits must be preset. If any can not be set, Galacticus will stop.[presetOrbitsBoundOnly](default.true.) — Specifies whether only bound node orbits should be set.[beginAt](default-1_kind_int8) — Specifies the index of the tree to begin at. (Use -1 to always begin with the first tree.)[outputTimeSnapTolerance](default0.0d0) — The relative tolerance required to “snap” a node time to the closest output time.[missingHostsAreFatal](default.true.) — Specifies whether nodes with missing host nodes should be considered to be fatal—see the discussion of missing host nodes in the class description above.[treeIndexToRootNodeIndex](default.false.) — Specifies whether tree indices should always be set to the index of their root node.[allowBranchJumps](default.true.) — Specifies whether nodes are allowed to jump between branches.[allowSubhaloPromotions](default.true.) — Specifies whether subhalos are permitted to be promoted to being isolated halos.[alwaysPromoteMostMassive](default.false.) — If true, the most massive progenitor is always promoted to be the primary progenitor even if it is a subhalo. Otherwise, isolated progenitors are given priority over subhalo progenitors, even if they are less massive.[presetNamedReals]— Names of real datasets to be additionally read and stored in the nodes of the merger tree when using the[mergerTreeConstruct]\(=\)readtree construction method.[presetNamedIntegers]— Names of integer datasets to be additionally read and stored in the nodes of the merger tree when using the[mergerTreeConstruct]\(=\)readtree construction method.[fatalMismatches](default.true.) — Specifies whether mismatches in cosmological parameter values between Galacticus and “Sussing Merger Trees” format (Srisawat et al., 2013) merger tree files should be considered fatal.[fatalNonTreeNode](default.true.) — Specifies whether nodes in snapshot files but not in the merger tree file should be considered fatal when importing from the “Sussing Merger Trees” format (Srisawat et al., 2013).[subvolumeCount](default1) — Specifies the number of subvolumes along each axis into which a “Sussing Merger Trees” format (Srisawat et al., 2013) merger tree files should be split for processing through Galacticus.[subvolumeBuffer](default0.0d0) — Specifies the buffer region (in units of Mpc\(/h\) to follow the format convention) around subvolumes of a “Sussing Merger Trees” format (Srisawat et al., 2013) merger tree file which should be read in to ensure that no halos are missed from trees.[subvolumeIndex](default[0,0,0]) — Specifies the index (in each dimension) of the subvolume of a “Sussing Merger Trees” format (Srisawat et al., 2013) merger tree file to process. Indices range from 0 to[subvolumeCount]\(-1\).[badValue](default-0.5d0) — Use for bad value detection in “Sussing” merger trees. Values for scale radius and halo spin which exceed this threshold are assumed to be bad.[badValueTest](defaultvar_str('lessThan')) — Use for bad value detection in “Sussing” merger trees. Values which exceed the threshold in ths specified direction are assumed to be bad.[treeSampleRate](default1.0d0) — Specify the probability that any given tree should processed (to permit subsampling).[massOptions](defaultvar_str('default')) — Mass option for Sussing merger trees.[mergeProbability](default0.1d0) — The largest probability of branching allowed in a timestep in merger trees built by the Cole et al. (2000) method.[accretionLimit](default0.1d0) — The largest fractional mass change due to subresolution accretion allowed in a timestep in merger trees built by the Cole et al. (2000) method.[redshiftMaximum](default1.0d5) — The highest redshift to which merger trees will be built in the Cole et al. (2000) method.[toleranceTimeEarliest](default2.0d-6) — The fractional tolerance used to judge if a branch is at the earliest allowed time in the tree.[branchIntervalStep](default.true.) — Iffalseuse the original Cole et al. (2000) method to determine whether branching occurs in a timestep. Iftruedraw branching intervals from a negative exponential distribution.[toleranceResolutionSelf](default1.0d-6) — The fractional tolerance in node mass at the resolution limit below which branch mis-orderings will be ignored.[toleranceResolutionParent](default1.0d-3) — The fractional tolerance in parent node mass at the resolution limit below which branch mis-orderings will be ignored.[ignoreNoProgress](default.false.) — If true, failure to make progress on a branch will be ignored (and the branch terminated).[ignoreWellOrdering](default.false.) — If true, non-well-ordered tree branches are pruned away instead of causing errors..[redshiftBase](default0.0d0) — The redshift at which to plant the base node when building merger trees.[timeSnapTolerance](default1.0d-6) — The fractional tolerance within which the tree base time will be snapped to a nearby output time.[treeBeginAt](default0) — The index (in order of increasing base halo mass) of the tree at which to begin when building merger trees. A value of “0” means to begin with tree number 1 (if processing trees in ascending order), or equal to the number of trees (otherwise).[processDescending](default.true.) — If true, causes merger trees to be processed in order of decreasing mass.[splitTrees](default.false.) — If true, prune away any nodes of the tree that are not needed to determine evolution up to the latest time at which a node is present inside the lightcone. This typically leads to a tree splitting into a forest of trees.[label]— A label for the mass function.[comment]— A descriptive comment for the mass function.[starFormationRates]— The star formation rates corresponding to bin centers.[covarianceBinomialBinsPerDecade](default10) — The number of bins per decade of star formation rate to use when constructing star formation rate function covariance matrices for main branch galaxies.[covarianceBinomialMassHaloMinimum](default1.0d10) — The star formation rate to consider when constructing star formation rate function covariance matrices for main branch galaxies.[covarianceBinomialMassHaloMaximum](default1.0d12) — The maximum star formation rate to consider when constructing star formation rate function covariance matrices for main branch galaxies.[targetLabel]— Label for the target dataset.[functionValueTarget]— The target function for likelihood calculations.[functionCovarianceTarget]— The target function covariance for likelihood calculations.[likelihoodBins]— Controls which bins in the stellar mass–halo mass relation will be used in computing the likelihood: * not present: all bins are included in the likelihood calculation; * list of integers: use only the mass bin(s) given in this list in the likelihood calculation; *auto: use only bins which have a non-zero number of halos contributing to them in the likelihood calculation.[fileNameTarget]— The name of the file containing the target data.[redshiftInterval](default1) — The redshift interval to use.[likelihoodNormalize](default.false.) — If true, then normalize the likelihood to make it a probability density.[computeScatter](default.false.) — If true, the scatter in log10(stellar mass) is computed. Otherwise, the mean is computed.[systematicErrorPolynomialCoefficient](default[0.0d0]) — The coefficients of the systematic error polynomial for stellar mass in the stellar vs halo mass relation.[systematicErrorMassHaloPolynomialCoefficient](default[0.0d0]) — The coefficients of the systematic error polynomial for halo mass in the stellar vs halo mass relation.[errorTolerant](default.false.) — Error tolerance for the N-body spin distribution operator.[logNormalRange](default100.0d0) — The multiplicative range of the log-normal distribution used to model the distribution of the mass and energy terms in the spin parameter. Specifically, the lognormal distribution is truncated outside the range \((\lambda_\mathrm{m}/R,\lambda_\mathrm{m} R\), where \(\lambda_\mathrm{m}\) is the measured spin, and \(R=\)[logNormalRange][fileName]— The name of the file from which to read spin distribution function parameters.[comment]— A comment describing this analysis.[label]— A label for this analysis.[label]— A label for the spin distribution function.[comment]— A descriptive comment for the spin distribution function.[redshift]— The redshift at which to compute the spin distribution function.[massMinimum]— Minimum halo mass for the spin distribution function.[massMaximum]— Maximum halo mass for the spin distribution function.[spinMinimum]— Minimum spin for the spin distribution function.[spinMaximum]— Maximum spin for the spin distribution function.[countSpinsPerDecade]— Number of spins per decade at which to compute the spin distribution function.[timeRecent]— Halos which experienced a major node merger within a time \(\Delta t=\)[timeRecent]of the analysis time will be excluded from the analysis.[particleCountMinimum]— The minimum particle count to assume when computing N-body errors on spins.[massParticle]— The mass of the particle used in the N-body simulation from which spins were measured.[energyEstimateParticleCountMaximum]— The maximum number of particles used in estimating halo energies when measuring spins from the N-body simulation.[targetLabel]— Label for the target dataset.[functionValueTarget]— The target function for likelihood calculations.[functionCovarianceTarget]— The target function covariance for likelihood calculations.[label]— A label for the mass function.[comment]— A descriptive comment for the mass function.[masses]— The masses corresponding to bin centers.[covarianceBinomialBinsPerDecade](default10) — The number of bins per decade of halo mass to use when constructing HI mass function covariance matrices for main branch galaxies.[covarianceBinomialMassHaloMinimum](default1.0d8) — The minimum halo mass to consider when constructing HI mass function covariance matrices for main branch galaxies.[covarianceBinomialMassHaloMaximum](default1.0d16) — The maximum halo mass to consider when constructing HI mass function covariance matrices for main branch galaxies.[targetLabel]— Label for the target dataset.[functionValueTarget]— The target function for likelihood calculations.[functionCovarianceTarget]— The target function covariance for likelihood calculations.[label]— A label for the luminosity function.[comment]— A descriptive comment for the luminosity function.[magnitudesAbsolute]— The absolute magnitudes corresponding to bin centers.[covarianceBinomialBinsPerDecade](default10) — The number of bins per decade of halo mass to use when constructing luminosity function covariance matrices for main branch galaxies.[covarianceBinomialMassHaloMinimum](default1.0d8) — The minimum halo mass to consider when constructing luminosity function covariance matrices for main branch galaxies.[covarianceBinomialMassHaloMaximum](default1.0d16) — The maximum halo mass to consider when constructing luminosity function covariance matrices for main branch galaxies.[targetLabel]— Label for the target dataset.[functionValueTarget]— The target function for likelihood calculations.[functionCovarianceTarget]— The target function covariance for likelihood calculations.[label]— A label for the luminosity function.[comment]— A descriptive comment for the luminosity function.[luminosities]— The luminosities corresponding to bin centers.[covarianceBinomialBinsPerDecade](default10) — The number of bins per decade of halo mass to use when constructing luminosity function covariance matrices for main branch galaxies.[covarianceBinomialMassHaloMinimum](default1.0d8) — The minimum halo mass to consider when constructing luminosity function covariance matrices for main branch galaxies.[covarianceBinomialMassHaloMaximum](default1.0d16) — The maximum halo mass to consider when constructing luminosity function covariance matrices for main branch galaxies.[includeNitrogenII](default.false.) — If true, include contamination by the [NII] (6548AA \(+\) 6584AA) doublet.[depthOpticalISMCoefficient](default1.0d0) — Multiplicative coefficient for optical depth in the ISM.[targetLabel]— Label for the target dataset.[functionValueTarget]— The target function for likelihood calculations.[functionCovarianceTarget]— The target function covariance for likelihood calculations.[label]— A label for the mass function.[comment]— A descriptive comment for the mass function.[masses]— The masses corresponding to bin centers.[covarianceBinomialBinsPerDecade](default10) — The number of bins per decade of halo mass to use when constructing stellar mass function covariance matrices for main branch galaxies.[covarianceBinomialMassHaloMinimum](default1.0d8) — The minimum halo mass to consider when constructing stellar mass function covariance matrices for main branch galaxies.[covarianceBinomialMassHaloMaximum](default1.0d16) — The maximum halo mass to consider when constructing stellar mass function covariance matrices for main branch galaxies.[targetLabel]— Label for the target dataset.[functionValueTarget]— The target function for likelihood calculations.[functionCovarianceTarget]— The target function covariance for likelihood calculations.[rootVarianceFractionalMinimum](default0.0d0) — The minimum fractional root variance (relative to the target dataset).[fileName]— The name of the file from which to read concentration distribution function parameters.[comment]— A comment describing this analysis.[label]— A label for this analysis.[label]— A label for the concentration distribution function.[comment]— A descriptive comment for the concentration distribution function.[redshift]— The redshift at which to compute the concentration distribution function.[massMinimum]— Minimum halo mass for the concentration distribution function.[massMaximum]— Maximum halo mass for the concentration distribution function.[concentrationMinimum]— Minimum concentration for the concentration distribution function.[concentrationMaximum]— Maximum concentration for the concentration distribution function.[countConcentrationsPerDecade]— Number of concentrations per decade at which to compute the concentration distribution function.[timeRecent]— Halos which experienced a major node merger within a time \(\Delta t=\)[timeRecent]of the analysis time will be excluded from the analysis.[massParticle]— The particle mass in the source N-body simulation.[targetLabel]— Label for the target dataset.[functionValueTarget]— The target function for likelihood calculations.[functionCovarianceTarget]— The target function covariance for likelihood calculations.[fileName]— The name of the file from which to read star forming main sequence function parameters.[comment]— A comment describing this analysis.[label]— A label for this analysis.[label]— A label for the star forming main sequence function.[comment]— A descriptive comment for the star forming main sequence function.[massMinimum]— Minimum stellar mass for the star forming main sequence function.[massMaximum]— Maximum stellar mass for the star forming main sequence function.[countMassesPerDecade]— Number of masses per decade at which to compute the star forming main sequence function.[targetLabel]— Label for the target dataset.[meanValueTarget]— The target function for likelihood calculations.[meanCovarianceTarget]— The target function covariance for likelihood calculations.[label]— A label for the mass function.[comment]— A descriptive comment for the mass function.[separations]— The separations corresponding to bin centers.[massMinima]— The minimum mass of each mass sample.[massMaxima]— The maximum mass of each mass sample.[massHaloBinsPerDecade](default10) — The number of bins per decade of halo mass to use when constructing the mass function covariance matrix for main branch galaxies.[massHaloMinimum](default1.0d8) — The minimum halo mass to consider when constructing the mass function covariance matrix for main branch galaxies.[massHaloMaximum](default1.0d16) — The maximum halo mass to consider when constructing the mass function covariance matrix for main branch galaxies.[wavenumberCount](default60_c_size_t) — The number of bins in wavenumber to use in computing the correlation function.[wavenumberMinimum](default1.0d-3) — The minimum wavenumber to use when computing the correlation function.[wavenumberMaximum](default1.0d4) — The maximum wavenumber to use when computing the correlation function.[integralConstraint]— The integral constraint for these correlation functions.[depthLineOfSight]— The line-of-sight depth over which the correlation function was projected.[halfIntegral]— Set to true if the projection integrand should be over line-of-sight depths greater than zero.[binnedProjectedCorrelationTarget]— The target function for likelihood calculations.[binnedProjectedCorrelationCovarianceTarget]— The target function covariance for likelihood calculations.[targetLabel](defaultvar_str('')) — A label for the target dataset in a plot of this analysis.[starFormationRateSpecificQuiescentLogarithmic]— The base-10 logarithm specific star formation rate (in units of Gyr\(^{-1}\)) separating quiescent and star-forming galaxies.[starFormationRateSpecificLogarithmicError]— The observational fractional error in specific star formation rate (in units of dex) of galaxies.[fileName]— The name of the file from which to read quiescent fraction function parameters.[comment]— A comment describing this analysis.[label]— A label for this analysis.[label]— A label for the star forming main sequence function.[comment]— A descriptive comment for the star forming main sequence function.[massMinimum]— Minimum stellar mass for the star forming main sequence function.[massMaximum]— Maximum stellar mass for the star forming main sequence function.[countMassesPerDecade]— Number of masses per decade at which to compute the star forming main sequence function.[targetLabel]— Label for the target dataset.[meanValueTarget]— The target function for likelihood calculations.[meanCovarianceTarget]— The target function covariance for likelihood calculations.[nonAnalyticSolver](defaultvar_str('fallThrough')) — Selects how solutions are computed when no analytic solution is available. If set to “fallThrough” then the solution ignoring heating is used, while if set to “numerical” then numerical solvers are used to find solutions.[radiusFractionalTruncateMinimum](default2.0d0) — The minimum radius (in units of the virial radius) to begin truncating the density profile.[radiusFractionalTruncateMaximum](default4.0d0) — The maximum radius (in units of the virial radius) to finish truncating the density profile.[nonAnalyticSolver](defaultvar_str('fallThrough')) — Selects how solutions are computed when no analytic solution is available. If set to “fallThrough” then the solution ignoring heating is used, while if set to “numerical” then numerical solvers are used to find solutions.[velocityDispersionApproximate](default.true.) — Iftrue, radial velocity dispersion is computed using an approximate method in which we assume that \(\sigma_\mathrm{r}^2(r) \rightarrow \sigma_\mathrm{r}^2(r) - (2/3) \epsilon(r)\), where \(\epsilon(r)\) is the specific heating energy. Iffalsethen radial velocity dispersion is computed by numerically solving the Jeans equation.[tolerateEnclosedMassIntegrationFailure](default.false.) — Iftrue, tolerate failures to find the mass enclosed as a function of radius.[tolerateVelocityDispersionFailure](default.false.) — Iftrue, tolerate failures to compute the velocity dispersion.[tolerateVelocityMaximumFailure](default.false.) — Iftrue, tolerate failures to find the radius of the maximum circular velocity.[toleratePotentialIntegrationFailure](default.false.) — Iftrue, tolerate numerical failures when computing the gravitational potential of a heated dark matter profile, allowing the calculation to continue with a fallback result rather than aborting.[toleranceRelativeVelocityDispersion](default1.0d-6) — The relative tolerance to use in numerical solutions for the velocity dispersion in dark-matter-only density profiles.[toleranceRelativeVelocityDispersionMaximum](default1.0d-3) — The maximum relative tolerance to use in numerical solutions for the velocity dispersion in dark-matter-only density profiles.[fractionRadiusFinalSmall](default1.0d-3) — The initial radius is limited to be no smaller than this fraction of the final radius. This can help avoid problems in profiles that are extremely close to being disrupted.[toleranceRelativePotential](default1.0d-3) — The maximum allowed relative tolerance to use in numerical solutions for the gravitational potential in dark-matter-only density profiles before aborting.[tolerateVelocityMaximumFailure](default.true.) — If true, tolerate failures to find the radius of the peak in the rotation curve.[lengthResolution]— The gravitational softening length \(\Delta x\) (in Mpc) of the N-body simulation, which sets the minimum spatial scale below which the dark matter profile is smoothed to avoid artificial two-body effects.[massResolution]— The mass resolution \(\Delta M\) (in \(\mathrm{M}_\odot\)) of the N-body simulation, representing the minimum halo mass that can be resolved; profiles of halos near this limit are softened to account for particle discreteness effects.[resolutionIsComoving]— If true, the resolution length is assumed to be fixed in comoving coordinates, otherwise in physical coordinates.[nonAnalyticSolver](defaultvar_str('fallThrough')) — Selects how solutions are computed when no analytic solution is available. If set to “fallThrough” then the solution ignoring heating is used, while if set to “numerical” then numerical solvers are used to find solutions.[C](default400.0d0) — The parameter \(C\) appearing in the halo concentration algorithm of Ludlow et al. (2016).[f](default0.02d0) — The parameter \(f\) appearing in the halo concentration algorithm of Ludlow et al. (2016).[timeFormationSeekDelta](default0.0d0) — The parameter \(\Delta \log t\) by which the logarithm of the trial formation time is incremented when stepping through the formation history of a node to find the formation time. If set to zero (or a negative value) the cumulative mass histories of nodes are assumed to be monotonic functions of time, and the formation time is instead found by a root finding algorithm,[massBoundIsInactive](default.false.) — Specifies whether or not the bound mass of the satellite component is inactive (i.e. does not appear in any ODE being solved).[useLastIsolatedTime](default.false.) — If true, evaluate the halo virial radius using a the virial density definition at the last isolated time of the halo.[filterName]— The filter to select.[filterType]— The filter type (rest or observed) to select.[redshiftBand]— The redshift of the band (if not the output redshift).[postprocessChain]— The postprocessing chain to use.[cloudyTableFileName](defaultvar_str('%DATASTATICPATH%/hiiRegions/emissionLineLuminosities_BC2003_highResolution_imfChabrier.hdf5')) — The file of emission line luminosities to use.[lineNames]— The emission lines to extract.[component]— The component from which to extract star formation rate.[toleranceRelative](default1.0d-3) — The relative tolerance used in integration over stellar population spectra.[component]— The component from which to extract star formation rate.[radiusCore]— The soliton core radius (in Mpc) characterizing the size of the quantum pressure-supported central core of the fuzzy dark matter halo; the density profile flattens inside this scale.[densitySolitonCentral]— The central density (in \(\mathrm{M}_\odot\)/Mpc\(^3\)) of the solitonic core at \(r=0\), which sets the overall normalization of the density profile \(\rho(r) = \rho_\mathrm{c} [1+(r/r_c)^2]^{-8}\).[toleranceRelativePotential](default1.0d-3) — The relative tolerance used in numerical ODE solutions for the gravitational potential of the solitonic core profile.[dimensionless](default.true.) — If true the soliton profile is treated as dimensionless (scale-free), allowing its radial and density quantities to be specified in arbitrary units.[componentType](defaultvar_str('unknown')) — The galactic structure component type (e.g.dark matter halo, disk, spheroid) represented by this mass distribution, used for component-specific queries.[massType](defaultvar_str('unknown')) — The mass type (e.g.dark matter, baryonic, total) represented by this mass distribution, used for mass-type-specific queries.[radiusTransition]— The transition radius (in Mpc) at which the density profile smoothly switches from the halo profile to the accretion flow, controlled by the fourth-order transition function \(f_\mathrm{trans}(r)\).[nonAnalyticSolver](defaultvar_str('fallThrough')) — Selects how solutions are computed when no analytic solution is available. If set to “fallThrough” then the solution ignoring heating is used, while if set to “numerical” then numerical solvers are used to find solutions.[componentType](defaultvar_str('unknown')) — The component type that this mass distribution represents.[massType](defaultvar_str('unknown')) — The mass type that this mass distribution represents.[timeAge]— The age of the halo (in Gyr) since its formation, determining the total time available for SIDM self-interactions to thermalize the inner halo and produce an isothermal core.[velocityRelativeMean]— Mean relative velocity to calculate self interaction cross section.[nonAnalyticSolver](defaultvar_str('fallThrough')) — Selects how solutions are computed when no analytic solution is available. If set to “fallThrough” then the solution ignoring heating is used, while if set to “numerical” then numerical solvers are used to find solutions.[componentType](defaultvar_str('unknown')) — The component type that this mass distribution represents.[massType](defaultvar_str('unknown')) — The mass type that this mass distribution represents.[nonAnalyticSolver](defaultvar_str('fallThrough')) — Selects how solutions are computed when no analytic solution is available. If set to “fallThrough” then the solution ignoring heating is used, while if set to “numerical” then numerical solvers are used to find solutions.[componentType](defaultvar_str('unknown')) — The component type that this mass distribution represents.[massType](defaultvar_str('unknown')) — The mass type that this mass distribution represents.[tolerateVelocityMaximumFailure](default.false.) — If true, tolerate failures to find the radius of the peak in the rotation curve.[tolerateEnclosedMassIntegrationFailure](default.false.) — Iftrue, tolerate failures to find the mass enclosed as a function of radius.[toleratePotentialIntegrationFailure](default.false.) — Iftrue, tolerate failures to compute the potential.[fractionRadiusFinalSmall](default1.0d-3) — The initial radius is limited to be no smaller than this fraction of the final radius. This can help avoid problems in profiles that are extremely close to being disrupted.[toleranceRelativePotential](default1.0d-3) — The maximum allowed relative tolerance to use in numerical solutions for the gravitational potential in dark-matter-only density profiles before aborting.[lengthResolution]— The spatial resolution length scale (in Mpc) below which the underlying density profile is softened to a flat core, mimicking the finite force resolution of an N-body simulation.[nonAnalyticSolver](defaultvar_str('fallThrough')) — Selects how solutions are computed when no analytic solution is available. If set to “fallThrough” then the solution ignoring heating is used, while if set to “numerical” then numerical solvers are used to find solutions.[componentType](defaultvar_str('unknown')) — The component type that this mass distribution represents.[massType](defaultvar_str('unknown')) — The mass type that this mass distribution represents.[massMinimum]— The minimum halo mass (in \(\mathrm{M}_\odot\)) below which halos are excluded from the mass function histogram.[massMaximum]— The maximum halo mass (in \(\mathrm{M}_\odot\)) above which halos are excluded from the mass function histogram.[massCountPerDecade]— The number of logarithmic bins per decade of halo mass used when constructing the halo mass function.[description]— A human-readable description of this mass function dataset, stored as metadata in the output file.[simulationReference]— A bibliographic reference for the N-body simulation from which this mass function is derived, stored as metadata.[simulationURL]— A URL pointing to the publicly accessible dataset or documentation for the N-body simulation, stored as metadata.[bootstrapSampleCount](default30_c_size_t) — The number of bootstrap resamples of the particles that should be used.[representativeMinimumCount](default10_c_size_t) — Minimum number of representative particles used to compute the center of a halo.[tolerance](default1.0d-2) — The tolerance in the summed weight of bound particles which must be attained to declare convergence.[bootstrapSampleRate](default1.0d0) — The sampling rate for particles.[representativeFraction](default0.05d0) — Fraction of bound particles used to compute the center of a halo.[analyzeAllParticles](default.true.) — If true, all particles are assumed to be self-bound at the beginning of the analysis. Unbound particles at previous times are allowed to become bound in the current snapshot. If false and the self-bound information from the previous snapshot is available, only the particles that are self-bound at the previous snapshot are assumed to be bound at the beginning of the analysis.[useVelocityMostBound](default.false.) — If true, the velocity of the most bound particle in velocity space is used as the representative velocity of the satellite. If false, use the mass weighted mean velocity (center-of-mass velocity) of self-bound particles instead.[orderRotation](defaultvar_str('none')) — The order in which evaluation of likelihoods should be rotated as a function of process number.[logLikelihoodAccept](defaulthuge(0.0d0)) — The log-likelihood which should be “accepted”—once the log-likelihood reaches this value (or larger) no further updates to the chain will be made.[report](default.false.) — If true, report on the log-likelihood obtained.[means]— The mean of the multivariate normal distribution.[covariance]— The covariance matrix for the of the multivariate normal distribution.[countForestsMaximum](default-1_c_size_t) — If set to a positive number, this is the maximum number of forests that will be evolved.[walltimeMaximum](default-1_kind_int8) — If set to a positive number, this is the maximum wall time for which forest evolution is allowed to proceed before the task gives up.[tolerateFailures](default.false.) — If true then failures to evolve a forest are tolerated. The forest is evolved no further, but evolution of other forests continues.[evolveForestsInParallel](default.true.) — If true then each forest is evolved by a separate OpenMP thread. Otherwise, a single thread evolves all forests.[suspendToRAM](default.true.) — Specifies whether trees should be suspended to RAM (otherwise they are suspend to file).[suspendPath]— The path to which tree suspension files will be stored.[timeIntervalCheckpoint](default-1_kind_int8) — If positive, gives the time in seconds between storing of checkpoint files. If zero or negative, no checkpointing is performed..[fileNameCheckpoint]— The path to which checkpoint data will be stored.[logM0](default10.0d0) — The parameter \(\log_{10} M_0\) (with \(M_0\) in units of \(\mathrm{M}_\odot\)) appearing in the star formation rate threshold expression for the star formation rate galactic filter class.[logSFR0](default9.0d0) — The parameter \(\alpha_0\) appearing in the star formation rate threshold expression for the star formation rate galactic filter class.[logSFR1](default0.0d0) — The parameter \(\alpha_1\) appearing in the star formation rate threshold expression for the star formation rate galactic filter class.[cW](default3.78062835d0) — The parameter \(c_\mathrm{W}\) in the Bohr et al. (2021) power spectrum window function.[beta](default3.4638743d0) — The parameter \(\beta\) in the Bohr et al. (2021) power spectrum window function.[transferFunctionType](defaultvar_str('darkMatter')) — Specifies whether to use thedarkMatterortotaltransfer function.[fileName]— The name of the file from which to read a tabulated transfer function.[redshift](default0.0d0) — The redshift of the transfer function to read.[factorWavenumberSmoothExtrapolation](default0.0d0) — If positive, and extrapolation is used at high wavenumbers, the slope for extrapolation will be set by averaging over wavenumbers from \(k_\mathrm{max}/f\) to \(k_\mathrm{max}\), where \(f=\)[factorWavenumberSmoothExtrapolation]and \(k_\mathrm{max}\) is the highest wavenumber tabulated. This avoids spurious extrapolation for highly oscillatory transfer functions.[acceptNegativeValues](default.false.) — If true, negative values in the transfer function are allowed (and the absolute value is taken prior to interpolation). Otherwise, negative values result in an error.[fractionalTimeStep](default0.01d0) — The fractional time step used when computing barrier crossing rates (i.e. the step used in finite difference calculations).[fileName](defaultvar_str('none')) — The name of the file to/from which tabulations of barrier first crossing probabilities should be written/read. If set to “none” tables will not be stored.[fractionalTimeStep](default0.01d0) — The fractional time step used when computing barrier crossing rates (i.e. the step used in finite difference calculations).[varianceNumberPerUnitProbability](default1000) — The number of points to tabulate per unit variance for first crossing probabilities.[varianceNumberPerUnit](default40) — The number of tabulation points per unit of \(\sigma^2\) used when building the rate look-up table for the Farahi excursion-set first-crossing distribution; higher values improve interpolation accuracy at the cost of memory and initialization time.[varianceNumberPerDecade](default400) — The number of points to tabulate per decade of progenitor variance for first crossing rates.[varianceNumberPerDecadeNonCrossing](default40) — The number of points to tabulate per decade of progenitor variance for non-crossing rates.[timeNumberPerDecade](default10) — The number of tabulation points per decade of cosmic time used when building the first-crossing rate look-up table as a function of time; higher values improve temporal interpolation accuracy for rapidly evolving cosmologies.[varianceIsUnlimited](default.false.) — If true, the variance is assumed to have no upper limit (e.g. as in the case of CDM). This allows the tabulated solutions to be extended arbitrarily. Otherwise, tables are extended to encompass just the range of variance requested.[linkingLength](default0.2d0) — The friends-of-friends linking length to use in computing virial density contrasts with the percolation analysis of More et al. (2011).
darkMatterProfileScaleRadiusLudlow2016Analytic¶
Dark matter halo scale radii are computed using the algorithm of Ludlow et al. (2016) with an analytic model for formation time.
Parameters
darkMatterProfileScaleRadiusPowerLaw¶
A dark matter profile scale radius class that uses simple power-law scalings. Specifically, the scale radius is given by:
where \(r(\nu)\), \(\alpha(\nu)\), and \(\beta(\nu)\) are sigmoid functions of the peak height, \(\nu\), of the form:
where \(r_0=\)[radiusLow], \(r_1=\)[radiusHigh], \(r_\nu=\)[radiusTransition], \(\Delta r=\)[radiusWidth], \(\alpha_0=\)[massLow], \(\alpha_1=\)[massHigh], \(\alpha_\nu=\)[massTransition], \(\Delta \alpha=\)[massWidth], \(\beta_0=\)[expansionFactorLow], \(\beta_1=\)[expansionFactorHigh], \(\beta_\nu=\)[expansionFactorTransition], and \(\Delta \beta=\)[expansionFactorWidth] , plus a random log-normal scatter of [scatter] dex.
Parameters
[exponent](default1.73d0) — Exponent of the differential luminosity function.[rateHydrogenIonizingPhotonsMinimum](default1.0d48) — The minimum ionizing photon production rate (\(Q_\mathrm{H,min}\), in photons/s) below which the power-law HII region luminosity function is truncated to zero.[rateHydrogenIonizingPhotonsMaximum](defaulthuge(0.0d0)) — The maximum ionizing photon production rate (\(Q_\mathrm{H,max}\), in photons/s) above which the power-law HII region luminosity function is truncated to zero.[exponent](default1.0d0) — Halo masses will be (pseudo-)uniformly distributed in \([\log(M)]^{1/(1+\alpha)}\) where \(\alpha=\)exponent.[wavelengthMinimum]— The minimum wavelength (in units of AA) for the power-law spectrum.[wavelengthMaximum]— The maximum wavelength (in units of AA) for the power-law spectrum.[exponent]— The exponent of the power-law spectrum.[normalization]— The normalization (in units of \(L_\odot / \AA\)) of the power-law spectrum.[normalization]— Parameter \(\sigma_{12}\) appearing in model for random errors in the halo mass function.[fractionalErrorHighMass]— Parameter \(\sigma_\infty\) appearing in model for random errors in the halo mass function.[exponent]— Parameter \(\gamma\) appearing in model for random errors in the halo mass function. Specifically, the fractional error is given by \(\sigma(M) = \left[ \sigma^2_{12} \left({M_\mathrm{halo} \over 10^{12}\mathrm{M}_\odot}\right)^{2\gamma} + \sigma^2_\infty \right]^{1/2}\), where \(\sigma_{12}=\)[normalization]and \(\gamma=\)[exponent].[correlationModelTrivial](default.true.) — If true, the correlation between mass errors of pairs of halos is unity for halos with identical mass and time, and zero otherwise. If false, a power-law correlation model in mass ratio and expansion factor ratio is used instead.[correlationNormalization](default0.0d0) — Variable \(C_0\) in the model for the correlation between halo mass errors: \(C_{12} = C_0 [M_2/M_1]^\alpha [(1+z_2)/(1+z_1)]^\beta\).[correlationMassExponent](default0.0d0) — Variable \(\alpha\) in the model for the correlation between halo mass errors: \(C_{12} = C_0 [M_2/M_1]^\alpha [(1+z_2)/(1+z_1)]^\beta\).[correlationRedshiftExponent](default0.0d0) — Variable \(\beta\) in the model for the correlation between halo mass errors: \(C_{12} = C_0 [M_2/M_1]^\alpha [(1+z_2)/(1+z_1)]^\beta\).[radiusLow](default+0.0154d0) — The low-mass limit of the characteristic scale radius \(r_0\) (in Mpc) in the power-law scale radius model, giving the scale radius normalization for low-mass halos as a function of peak height and expansion factor.[radiusHigh](default+0.0962d0) — The high-mass limit of the characteristic scale radius \(r_1\) (in Mpc) in the power-law scale radius model, giving the scale radius normalization for high-mass halos.[radiusTransition](default+1.2137d0) — The peak height \(\nu\) at which the characteristic scale radius transitions between its low-mass and high-mass limiting values in the power-law scale radius model.[radiusWidth](default+0.5482d0) — The parameter \(\Delta r\) in the power-law scale radius model.[massLow](default+0.3895d0) — The parameter \(\alpha_0\) in the power-law scale radius model.[massHigh](default+0.2984d0) — The parameter \(\alpha_1\) in the power-law scale radius model.[massTransition](default-0.2583d0) — The parameter \(\alpha_\nu\) in the power-law scale radius model.[massWidth](default+16.6050d0) — The parameter \(\Delta \alpha\) in the power-law scale radius model.[expansionFactorLow](default-0.6977d0) — The parameter \(\beta_0\) in the power-law scale radius model.[expansionFactorHigh](default+0.7972d0) — The parameter \(\beta_1\) in the power-law scale radius model.[expansionFactorTransition](default+0.5395d0) — The parameter \(\beta_\nu\) in the power-law scale radius model.[expansionFactorWidth](default+0.4282d0) — The parameter \(\Delta \beta\) in the power-law scale radius model.[scatter](default+0.1513d0) — The scatter (in dex) in the scale radius at fixed halo mass and redshift in the power-law scale radius model, representing the intrinsic halo-to-halo variation in concentration.[index](default0.9649d0) — The index of the power-law primordial power spectrum.[running](default0.0d0) — The running, \(\d n_\mathrm{s} / \d \ln k\), of the power spectrum index.[runningRunning](default0.0d0) — The running-of-the-running, \(\d^2 n_\mathrm{s} / \d \ln k^2\), of the power spectrum index.[wavenumberReference](default1.0d0) — When a running power spectrum index is used, this is the wavenumber, \(k_\mathrm{ref}\), at which the index is equal to[index].[runningSmallScalesOnly](default.false.) — Iftruethen the index runs only for \(k > k_\mathrm{ref}\), for smaller \(k\) the index is constant.
darkMatterProfileScaleRadiusRandomWalk¶
A dark matter profile scale radius class that assigns dark matter profile scale radii using a Weiner process random walk around the mean expectation, and then interpolates linearly between child and parent nodes. For primary progenitor nodes \(\dot{r}_\mathrm{s} = (r_{\mathrm{s},i+1}-r_{\mathrm{s},i})/(t_{i+1}-t_i)\), where \(r_{\mathrm{s},i}\) is the scale radius of the dark matter profile of the node in the initialized tree, \(r_{\mathrm{s},i+1}\) is the spin of its parent node, and \(t_i\) and \(t_{i+1}\) are the corresponding times. For non-primary progenitors the rate of change is set to zero, i.e. \(\dot{r}_\mathrm{s}=0\).
The energy of each halo is set to the energy expected from the mean scale radius for halos of the mass and epoch, plus a perturbation given by:
where \(J_\mathrm{v}(t) = M_\mathrm{v}(t) V_\mathrm{v}(t) R_\mathrm{v}(t)\) is the characteristic virial angular momentum, \(M_\mathrm{v}(t)\), \(V_\mathrm{v}(t)\), and \(R_\mathrm{v}(t)\) are the virial mass, velocity, and radius respectively, \(\sigma^2\) represents the variance in angular momentum per unit increase in \(J_\mathrm{v}^2\), and \(N(0,1)\) is a random variable distributed as a standard normal.
Parameters
[energyVarianceSpecific](default0.006d0) — The variance in the difference in the energy of a halo per unit energy growth.
darkMatterProfileScaleRadiusZero¶
Dark matter halo scale radii class in which are assumed to be zero.