elisa.models.mul#

Multiplicative models.

class Constant(f: 'Parameter' | float | None = None, latex: str | None = None)[source]#

Bases: AnaIntMultiplicative

Energy-independent multiplicative factor.

\[M(E) = f.\]

Parameters:

fParameter, optional: The multiplicative factor \(f\), dimensionless.
latexstr, optional: \(\LaTeX\) format of the component. Defaults to class name.

Attributes

`eval`	Get side-effect free component evaluation function.
`f`	Constant parameter \(f\).
`latex`	\(\LaTeX\) format of the component.
`name`	Component name.
`param_names`	Component's parameter names.
`type`	Component type is multiplicative.

Methods

integral(egrid, params)

Calculate the average value of the model between the grid.

static integral(egrid: JAXArray, params: NameValMapping) → JAXArray[source]#

Calculate the average value of the model between the grid.

Parameters:

egridndarray: Photon energy grid in units of keV.
paramsdict: Parameter dict for the model.

Returns:

jax.Array: The model value, dimensionless.

property f: Parameter#: Constant parameter \(f\).

Bases: NumIntMultiplicative

Absorption edge.

\[\begin{split}M(E) = \begin{cases} \exp\left[-D \bigl(\frac{E}{E_\mathrm{c}}\bigr)^3\right], &\text{if } E \ge E_\mathrm{c}, \\\\ 1, &\text{otherwise.} \end{cases}\end{split}\]

Parameters:

EcParameter, optional: The threshold energy \(E_\mathrm{c}\), in units of keV.
DParameter, optional: The absorption depth \(D\) at the threshold energy, dimensionless.
latexstr, optional: \(\LaTeX\) format of the component. Defaults to class name.
method{‘trapz’, ‘simpson’}, optional: Numerical integration method. Defaults to ‘trapz’.

Attributes

`D`	Edge parameter \(D\).
`Ec`	Edge parameter \(E_\mathrm{c}\).
`eval`	Get side-effect free component evaluation function.
`latex`	\(\LaTeX\) format of the component.
`method`	Numerical integration method.
`name`	Component name.
`param_names`	Component's parameter names.
`type`	Component type is multiplicative.

Methods

continuum(egrid, params)

Calculate the model value at the energy grid.

static continuum(egrid: Array, params: dict[str, Array]) → Array[source]#

Calculate the model value at the energy grid.

Parameters:

egridndarray: Photon energy grid in units of keV.
paramsdict: Parameter dict for the model.

Returns:

jax.Array: The model value at egrid, dimensionless.

property D: Parameter#: Edge parameter \(D\).

property Ec: Parameter#: Edge parameter \(E_\mathrm{c}\).

class ExpAbs(Ec: 'Parameter' | float | None = None, latex: str | None = None, method=None)[source]#

Bases: NumIntMultiplicative

Low-energy exponential rolloff.

\[M(E) = \exp\left(-\frac{E_\mathrm{c}}{E}\right).\]

Parameters:

EcParameter, optional: The e-folding energy \(E_\mathrm{c}\) for the absorption, in units of keV.
latexstr, optional: \(\LaTeX\) format of the component. Defaults to class name.
method{‘trapz’, ‘simpson’}, optional: Numerical integration method. Defaults to ‘trapz’.

Attributes

`Ec`	ExpAbs parameter \(E_\mathrm{c}\).
`eval`	Get side-effect free component evaluation function.
`latex`	\(\LaTeX\) format of the component.
`method`	Numerical integration method.
`name`	Component name.
`param_names`	Component's parameter names.
`type`	Component type is multiplicative.

Methods

continuum(egrid, params)

Calculate the model value at the energy grid.

static continuum(egrid: Array, params: dict[str, Array]) → Array[source]#

Calculate the model value at the energy grid.

Parameters:

egridndarray: Photon energy grid in units of keV.
paramsdict: Parameter dict for the model.

Returns:

jax.Array: The model value at egrid, dimensionless.

property Ec: Parameter#: ExpAbs parameter \(E_\mathrm{c}\).

Bases: NumIntMultiplicative

Exponential modification.

\[\begin{split}M(E) = \begin{cases} 1 + A \exp\bigl(-\frac{f E}{E_0}\bigr), &\text{if } E \ge E_\mathrm{c}, \\\\ 1, &\text{otherwise,} \end{cases}\end{split}\]

where \(E_0\) is the pivot energy fixed at 1 keV.

Parameters:

AParameter, optional: The amplitude of effect \(A\), dimensionless.
fParameter, optional: The exponential factor \(f\), dimensionless.
EcParameter, optional: The start energy of modification \(E_\mathrm{c}\), in units of keV.
latexstr, optional: \(\LaTeX\) format of the component. Defaults to class name.
method{‘trapz’, ‘simpson’}, optional: Numerical integration method. Defaults to ‘trapz’.

Attributes

`A`	ExpFac parameter \(A\).
`Ec`	ExpFac parameter \(E_\mathrm{c}\).
`eval`	Get side-effect free component evaluation function.
`f`	ExpFac parameter \(f\).
`latex`	\(\LaTeX\) format of the component.
`method`	Numerical integration method.
`name`	Component name.
`param_names`	Component's parameter names.
`type`	Component type is multiplicative.

Methods

continuum(egrid, params)

Calculate the model value at the energy grid.

static continuum(egrid: Array, params: dict[str, Array]) → Array[source]#

Calculate the model value at the energy grid.

Parameters:

egridndarray: Photon energy grid in units of keV.
paramsdict: Parameter dict for the model.

Returns:

jax.Array: The model value at egrid, dimensionless.

property A: Parameter#: ExpFac parameter \(A\).

property Ec: Parameter#: ExpFac parameter \(E_\mathrm{c}\).

property f: Parameter#: ExpFac parameter \(f\).

Bases: NumIntMultiplicative

Gaussian absorption line.

\[M(E) = \exp\left[ -\frac{\tau}{\sqrt{2\pi} \sigma} \exp\left[ -\frac{\left(E - E_\mathrm{l}\right)^2}{2 \sigma^2} \right] \right].\]

The optical depth at line center is \(\frac{\tau}{\sqrt{2\pi}\sigma}\).

Parameters:

ElParameter, optional: The line energy \(E_\mathrm{l}\), in units of keV.
sigmaParameter, optional: The line width \(\sigma\), in units of keV.
tauParameter, optional: The line depth \(\tau\), in units of keV.
latexstr, optional: \(\LaTeX\) format of the component. Defaults to class name.
method{‘trapz’, ‘simpson’}, optional: Numerical integration method. Defaults to ‘trapz’.

Attributes

`El`	GAbs parameter \(E_\mathrm{l}\).
`eval`	Get side-effect free component evaluation function.
`latex`	\(\LaTeX\) format of the component.
`method`	Numerical integration method.
`name`	Component name.
`param_names`	Component's parameter names.
`sigma`	GAbs parameter \(\sigma\).
`tau`	GAbs parameter \(\tau\).
`type`	Component type is multiplicative.

Methods

continuum(egrid, params)

Calculate the model value at the energy grid.

static continuum(egrid: Array, params: dict[str, Array]) → Array[source]#

Calculate the model value at the energy grid.

Parameters:

egridndarray: Photon energy grid in units of keV.
paramsdict: Parameter dict for the model.

Returns:

jax.Array: The model value at egrid, dimensionless.

property El: Parameter#: GAbs parameter \(E_\mathrm{l}\).

property sigma: Parameter#: GAbs parameter \(\sigma\).

property tau: Parameter#: GAbs parameter \(\tau\).

Bases: NumIntMultiplicative

High-energy cutoff.

\[\begin{split}M(E) = \begin{cases} \exp\bigl(\frac{E_\mathrm{c}-E}{E_\mathrm{f}}\bigr), &\text{if } E \ge E_\mathrm{c}, \\\\ 1, &\text{otherwise.} \end{cases}\end{split}\]

Parameters:

EcParameter, optional: The cutoff energy \(E_\mathrm{c}\), in units of keV.
EfParameter, optional: The e-folding energy \(E_\mathrm{f}\), in units of keV.
latexstr, optional: \(\LaTeX\) format of the component. Defaults to class name.
method{‘trapz’, ‘simpson’}, optional: Numerical integration method. Defaults to ‘trapz’.

Attributes

`Ec`	HighECut parameter \(E_\mathrm{c}\).
`Ef`	HighECut parameter \(E_\mathrm{f}\).
`eval`	Get side-effect free component evaluation function.
`latex`	\(\LaTeX\) format of the component.
`method`	Numerical integration method.
`name`	Component name.
`param_names`	Component's parameter names.
`type`	Component type is multiplicative.

Methods

continuum(egrid, params)

Calculate the model value at the energy grid.

static continuum(egrid: Array, params: dict[str, Array]) → Array[source]#

Calculate the model value at the energy grid.

Parameters:

egridndarray: Photon energy grid in units of keV.
paramsdict: Parameter dict for the model.

Returns:

jax.Array: The model value at egrid, dimensionless.

property Ec: Parameter#: HighECut parameter \(E_\mathrm{c}\).

property Ef: Parameter#: HighECut parameter \(E_\mathrm{f}\).

Bases: AnaIntMultiplicative

Absorption as a power-law in energy. Useful for things like dust.

\[M(E) = K \left(\frac{E}{E_0}\right)^{-\alpha},\]

where \(E_0\) is the pivot energy fixed at 1 keV.

Parameters:

alphaParameter, optional: The power law index \(\alpha\), dimensionless.
KParameter, optional: The coefficient \(K\), dimensionless.
latexstr, optional: \(\LaTeX\) format of the component. Defaults to class name.

Attributes

`K`	PLAbs parameter \(K\).
`alpha`	PLAbs parameter \(\alpha\).
`eval`	Get side-effect free component evaluation function.
`latex`	\(\LaTeX\) format of the component.
`name`	Component name.
`param_names`	Component's parameter names.
`type`	Component type is multiplicative.

Methods

integral(egrid, params)

Calculate the average value of the model between the grid.

static integral(egrid: Array, params: dict[str, Array]) → Array[source]#

Calculate the average value of the model between the grid.

Parameters:

egridndarray: Photon energy grid in units of keV.
paramsdict: Parameter dict for the model.

Returns:

jax.Array: The model value, dimensionless.

property K: Parameter#: PLAbs parameter \(K\).

property alpha: Parameter#: PLAbs parameter \(\alpha\).

class PhAbs(nH: 'Parameter' | float | None = None, latex: str | None = None, abund=None, xsect=None, method=None)[source]#

Bases: PhotonAbsorption

Photoelectric absorption.

\[M(E) = \exp \left[ -\eta_\mathrm{H}\ \sigma(E) \right],\]

where \(\sigma(E)\) is the photo-electric cross-section, NOT including Thomson scattering.

Parameters:

nHParameter, optional

The equivalent hydrogen column density \(\eta_\mathrm{H}\), in units of 10²² cm⁻².

latexstr, optional

\(\LaTeX\) format of the component. Defaults to class name.

abundstr, optional

Abundance table to use. Available options are:

'angr' [1] (Photospheric, using Table 2)

'aspl' [2] (Photospheric, using Table 1)

'feld' [3]

'aneb' [4]

'grsa' [5]

'wilm' [6]

'lodd' [7] (Photospheric, using Table 1)

'lpgp' [8] (Photospheric, using Table 4)

'lpgs' [8] (Proto-solar, using Table 10)

The default is 'angr'.

xsectstr, optional

Photon cross-section to use. Available options are:

'bcmc' [9] with a new He cross-section [10]

'obcm' [9]

'vern' [11]

The default is 'vern'.

method{‘trapz’, ‘simpson’}, optional

Numerical integration method. Defaults to ‘trapz’.

Attributes

`abund`	Current abundance table.
`eval`	Get photon absorption model function.
`latex`	\(\LaTeX\) format of the component.
`method`	Numerical integration method.
`nH`	PhAbs parameter \(\eta_\mathrm{H}\).
`name`	Component name.
`param_names`	Component's parameter names.
`type`	Component type is multiplicative.
`xsect`	Current photon cross-section.

Methods

`abund_list`()	Get available abundance list.
`continuum`(egrid, params, abs_model, abund, xsect)	Photon absorption model.
`xsect_list`()	Get available photon cross-section list.

References

static abund_list() → list[str][source]#: Get available abundance list.

static xsect_list() → list[str][source]#: Get available photon cross-section list.

property nH: Parameter#: PhAbs parameter \(\eta_\mathrm{H}\).

class TBAbs(nH: 'Parameter' | float | None = None, latex: str | None = None, abund=None, xsect=None, method=None)[source]#

Bases: PhotonAbsorption

The Tuebingen-Boulder ISM absorption model.

This model calculates the cross-sections for X-ray absorption by the ISM as the sum of the cross-sections for X-ray absorption due to the gas-phase ISM, the grain-phase ISM, and the molecules in the ISM.

Parameters:

nHParameter, optional

The equivalent hydrogen column density \(\eta_\mathrm{H}\), in units of 10²² cm⁻².

latexstr, optional

\(\LaTeX\) format of the component. Defaults to class name.

abundstr, optional

Abundance table to use. Available options are:

'angr' [1] (Photospheric, using Table 2)

'aspl' [2] (Photospheric, using Table 1)

'feld' [3]

'aneb' [4]

'grsa' [5]

'wilm' [6]

'lodd' [7] (Photospheric, using Table 1)

'lpgp' [8] (Photospheric, using Table 4)

'lpgs' [8] (Proto-solar, using Table 10)

The default is 'wilm'.

xsectstr, optional

Always use cross-section 'vern' [9] as baseline.

method{‘trapz’, ‘simpson’}, optional

Numerical integration method. Defaults to ‘trapz’.

Attributes

`abund`	Current abundance table.
`eval`	Get photon absorption model function.
`latex`	\(\LaTeX\) format of the component.
`method`	Numerical integration method.
`nH`	TBAbs parameter \(\eta_\mathrm{H}\).
`name`	Component name.
`param_names`	Component's parameter names.
`type`	Component type is multiplicative.
`xsect`	Current photon cross-section.

Methods

`abund_list`()	Get available abundance list.
`continuum`(egrid, params, abs_model, abund, xsect)	Photon absorption model.
`xsect_list`()	Get available photon cross-section list.

References

[1]

Anders & Grevesse 1989, Geochimica et Cosmochimica Acta, 53, 1, 197-214

[2]

Asplund et al. 2009 ARAA, 47, 481

[3]

Feldman 1992, Phys. Scr. 46, 202

[4]

Anders & Ebihara 1982, Geochimica et Cosmochimica Acta, 46, 11, 2363-2380

[5]

Grevesse & Sauval 1998, Space Science Reviews, 85, 161–174

[6]

Wilms et al 2000, ApJ, 542, 914

[7]

Lodders 2003, ApJ, 591, 1220

[8] (1,2)

Lodders et al. 2009

[9]

Verner et al. 1996, ApJ, 465, 487

static abund_list() → list[str][source]#: Get available abundance list.

static xsect_list() → list[str][source]#: Get available photon cross-section list.

property nH: Parameter#: TBAbs parameter \(\eta_\mathrm{H}\).

class WAbs(nH: 'Parameter' | float | None = None, latex: str | None = None, abund=None, xsect=None, method=None)[source]#

Bases: PhotonAbsorption

A photo-electric absorption using Wisconsin cross-sections [1].

\[M(E) = \exp \left[ -\eta_\mathrm{H}\ \sigma(E) \right],\]

where \(\sigma(E)\) is the photo-electric cross-section, NOT including Thomson scattering.

Warning

The WAbs model is obsolete and is only included for comparison with historical results. The TBAbs model should be used for the ISM or PhAbs for general photoelectric absorption.

Parameters:

nHParameter, optional: The equivalent hydrogen column density \(\eta_\mathrm{H}\), in units of 10²² cm⁻².
latexstr, optional: \(\LaTeX\) format of the component. Defaults to class name.
abundstr, optional: Always use abundance table 'aneb' [2].
xsectstr, optional: Always use Wisconsin cross-sections [1].
method{‘trapz’, ‘simpson’}, optional: Numerical integration method. Defaults to ‘trapz’.

Attributes

`abund`	Current abundance table.
`eval`	Get photon absorption model function.
`latex`	\(\LaTeX\) format of the component.
`method`	Numerical integration method.
`nH`	WAbs parameter \(\eta_\mathrm{H}\).
`name`	Component name.
`param_names`	Component's parameter names.
`type`	Component type is multiplicative.
`xsect`	Current photon cross-section.

Methods

`abund_list`()	Get available abundance list.
`continuum`(egrid, params, abs_model, abund, xsect)	Photon absorption model.
`xsect_list`()	Get available photon cross-section list.

References

[1] (1,2)

Morrison & McCammon 1983, ApJ, 270, 119

[2]

Anders & Ebihara 1982, Geochimica et Cosmochimica Acta, 46, 11, 2363-2380

property nH: Parameter#: WAbs parameter \(\eta_\mathrm{H}\).

static abund_list() → list[str][source]#: Get available abundance list.

static xsect_list() → list[str][source]#: Get available photon cross-section list.