Excursion Set Barrier

Class providing the collapse barrier \(B(\sigma^2, t)\) in the extended Press-Schechter excursion set formalism—the threshold overdensity that a random walk in the density field must first cross for a region of variance \(\sigma^2\) to collapse by cosmic time \(t\). The barrier height and its gradient with respect to variance control the halo mass function and merger rate: a constant barrier (spherical collapse) gives the Press-Schechter result, while a moving or stochastic barrier (ellipsoidal collapse) produces mass functions in better agreement with N-body simulations.

Default implementation: excursionSetBarrierCriticalOverdensity

Methods

barrier → double precision

Return the barrier height at the given variance and time. The rateCompute should be set to true if the barrier is being used in a calculation of barrier crossing rates, and to false otherwise.

• double precision , intent(in ) :: variance , time

• type (treeNode), intent(inout) :: node

• logical , intent(in ) :: rateCompute

barrierGradient → double precision

Return the gradient of the barrier with respect to variance at the given variance and time. The rateCompute should be set to true if the barrier is being used in a calculation of barrier crossing rates, and to false otherwise.

• double precision , intent(in ) :: variance , time

• type (treeNode), intent(inout) :: node

• logical , intent(in ) :: rateCompute

excursionSetBarrierCriticalOverdensity

A excursion set barrier class that adopts a barrier equal to the critical linear theory overdensity for halo collapse.

(Default implementation)

excursionSetBarrierLinear

A linear excursion set barrier class. The barrier is given by:

\[B(S) = B_0 + B_1 S,\]

where \(B_0=\)[coefficientConstant], and \(B_0=\)[coefficientLinear].

Parameters

• [coefficientConstant] (default 1.67d0) — The constant (zero-order) coefficient \(B_0\) in the linear excursion-set barrier \(B(\sigma^2) = B_0 + B_1\,\sigma^2\); corresponds to the spherical collapse threshold \(\delta_\mathrm{c} \approx 1.686\) in the simplest case.

• [coefficientLinear] (default 0.0d0) — The linear (first-order in \(\sigma^2\)) coefficient \(B_1\) in the excursion-set barrier \(B(\sigma^2) = B_0 + B_1\,\sigma^2\); a non-zero value produces a moving barrier that mimics ellipsoidal collapse corrections to the halo mass function.

excursionSetBarrierQuadratic

A quadratic excursion set barrier class. The barrier is given by:

\[B(S) = B_0 + B_1 S + B_2 S^2,\]

where \(B_0=\)[coefficientConstant], \(B_0=\)[coefficientLinear], and \(B_2=\)[coefficientQuadratic].

Parameters

• [coefficientConstant] (default 1.67d0) — The constant (zero-order) coefficient \(B_0\) in the quadratic excursion-set barrier \(B(\sigma^2) = B_0 + B_1\,\sigma^2 + B_2\,(\sigma^2)^2\); represents the flat threshold inherited from spherical collapse.

• [coefficientLinear] (default 0.0d0) — The linear (first-order in \(\sigma^2\)) coefficient \(B_1\) in the quadratic excursion-set barrier \(B(\sigma^2) = B_0 + B_1\,\sigma^2 + B_2\,(\sigma^2)^2\); encodes the leading ellipsoidal collapse correction to the collapse threshold.

• [coefficientQuadratic] (default 0.0d0) — The quadratic (second-order in \(\sigma^2\)) coefficient \(B_2\) in the excursion-set barrier \(B(\sigma^2) = B_0 + B_1\,\sigma^2 + B_2\,(\sigma^2)^2\); allows further curvature of the barrier to match simulation-calibrated mass functions.

excursionSetBarrierRemapScale

An excursion set barrier class which remaps the barrier values from another class by multiplying by a constant scaling factor given by [factor], allowing the effective collapse threshold to be rescaled uniformly. The rescaling can be applied selectively to barrier evaluations used in rate calculations, other calculations, or both, as controlled by [applyTo].

Parameters

• [factor] (default 1.0d0) — The multiplicative factor applied to the underlying excursion-set barrier value \(B(\sigma^2)\), uniformly rescaling the collapse threshold across all mass scales to adjust branching rates or halo abundances.

• [applyTo] (default var_str('nonRates')) — Specifies whether rescaling is to be applied to the barrier when used for rate calculation, for other calculations, or both.

excursionSetBarrierRemapShethMoTormen

An excursion set barrier class which remaps another class using the Sheth et al. (2001) ellipsoidal collapse parameterization:

\[B(S) \rightarrow \sqrt{A} B(S) \left(1 + b \left[ {S \over A B^2(S)}\right]^c\right),\]

where \(A=0.707\), \(b=0.5\), and \(c=0.6\).

Parameters

• [a] (default 0.707d0) — The parameter \(a\) in the Sheth et al. (2001) ellipsoidal collapse excursion set barrier remapping.

• [b] (default 0.500d0) — The parameter \(b\) in the Sheth et al. (2001) ellipsoidal collapse excursion set barrier remapping.

• [c] (default 0.600d0) — The parameter \(c\) in the Sheth et al. (2001) ellipsoidal collapse excursion set barrier remapping.

• [applyTo] (default var_str('nonRates')) — Specifies whether rescaling is to be applied to the barrier when used for rate calculation, for other calculations, or both.