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Distance coefficients

In order perform multi-plane lensing computations, one need to take into account the relative distances between the lensing planes and the source planes. In our library, the distance-related coefficients are stored in special structures. For convenience, we separate the lens-plane coefficients from the source-plane ones. This corresponds to the different roles played by lens planes and source planes: often, we have only a single lens plane, but multiple sources located at different redshifts.

Note

All distance computations are strictly associated to a cosmological model. If no specific model is defined, the Gravity.default_cosmology model is used.

Lensing coefficients

Gravity.LensCoeff — Type
LensCoeff{T,V}

A structure to hold the β coefficients of a lens system.

Members

  • zᵢ: vector of the lens redshifts
  • dᵢ: vector of comoving transverse distances associated to each zᵢ, in Mpc
  • ρᵢ: vector of dᵢⱼ / (dᵢ dⱼ), with j = i+1; this vector has one element less than zᵢ and dᵢ

Note that the ρᵢ are related to the ϑᵢ from Eq. (2.17) of Seitz & Schneider 1992, being essentially the inverses (with a factor c missing).

Constructor

LensCoeff(zᵢ [, cosmology])

Create a LensCoeff structure for a given set of lens redshifts zᵢ.

The redshifts zᵢ must be sorted increasing. Optionally, one can specify the cosmological model cosmology (default is the standard cosmology).

Note

All distances are taken to be measured in mega parsecs (Mpc) (this is the default when using Cosmology), and are saved as floats.

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Gravity.critical_density — Function
critical_density(zₗ [, zₛ] [, cosmo])

Compute the critical density for a lens at redshift zₗ.

The source redshift is taken to be at zₛ; if that value is not provided, it is assumed that D(zₛ) = D(zₗ, zₛ). Note that the latter assumption is not equivalent to take the limit zₛ → ∞. The result is given as a Quantity, and is expressed in units of $\mbox{M}_\odot \, \mbox{pc}^{-2}$. If cosmology is unspecified, the default_cosmology is assumed.

This procedure can be useful to convert the output of convergence into physical units.

Example

julia> round(typeof(1.0u"Msun/pc^2"), Gravity.critical_density(1.0); digits=5)
979.47086 M⊙ pc⁻²

julia> round(typeof(1.0u"Msun/pc^2"), Gravity.critical_density(1.0, 2.0); digits=5)
2718.54608 M⊙ pc⁻²

julia> round(typeof(1.0u"kg/m^2"), Gravity.critical_density(0.5) |> u"kg/m^2"; digits=8)
2.67631585 kg m⁻²
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Source coefficients

Gravity.SourceCoeff — Type
SourceCoeff{T}

A structure to hold the lensing coefficients of a source.

Note that each SourceCoeff is always defined within a given LensCoeff.

Members

  • zₒ: source redshift
  • i: last lensing plane before the source
  • dₒ: comoving transverse distance of the source
  • dᵢ: comoving transverse distance to the last lensing plane before the source
  • ρᵢ: dᵢₒ / (dᵢ dₒ), with dᵢₒ the comoving transverse distance between the last lensing plane and the source

Constructors

SourceCoeff(z, λ [, cosmo])
SourceCoeff(z, sys)

Build a SourceCoeff object using the provided source redshift z and LensCoeff λ; optionally, one can specify also the cosmological model (if not specified Gravity.default_cosmology is used). Alternatively, one can just pass a LensSystem sys: in that case, the cosmological model is directly taken from sys.cosmo.

SourceCoeff(sys, i)
SourceCoeff(λ, i)

These two constructors build a SourceCoeff for a source located at the i-th plane of a LensSystem: this can be useful to perform lensing of lenses.

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Gravity.SourcesCoeff — Type
SourcesCoeff{T}

A structure to hold the lensing coefficients for many sources within a given LensCoeff.

This is the Structure of Array (SoA) version of SourceCoeff. The various coefficients correspond to sources located at different redshifts.

The use of SoucesCoeff is convenient when one needs to compute a lensmapping at the same location for many sources. This happens, for example, when modeling the surface brightness of merging sources at different redshifts.

Members

  • zₒ: vector with the sources' redshift
  • i: vector of last lensing planes before each source
  • dₒ: vector of comoving transverse distances of the sources
  • dᵢ: vector of comoving transverse distances to the last lensing planes before each source
  • ρᵢ: vector of dᵢₒ / (dᵢ dₒ), with dᵢₒ the comoving transverse distances between the last lensing planes and the sources

Constructors

SourcesCoeff(zₒ, λ [, cosmo])
SourcesCoeff(zₒ, sys)

Build a SourcesCoeff object using the provided vector or source redshifts zₒ and LensCoeff λ; optionally, one can specify also the cosmological model (if not specified Gravity.default_cosmology is used). Alternatively, one can just pass a LensSystem sys.

See also: SourceCoeff

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