The following models are provided by Iris for fitting to SED data. Models can be combined together in complex mathematical expressions to better model features of a SED. Models are assumed to be suitable for modeling the continuum, unless it is specifically noted that the model is for modeling spectral lines.

The *Custom Model Manager interface* allows you to import into Iris your custom table, template, and Python user models, for use with the Iris Fitting Tool. Refer to the “Modeling and Fitting SED Data” section of the Iris How-to Guide to learn how to load your own models into Iris and use them to fit SED data in Iris.

A model of interstellar absorption, taking the functional form:

f(x) = exp[-tau * (x / edgew)**index], where x > edgew f(x) = 0, where x <= edgew

Parameters:

edgew Absorption edge (in Angstroms) tau Optical depth index index

[Back to top] |

A Gaussian model of an absorption feature (i.e., equivalent width), taking the functional form:

sigma = pos * fwhm / c / 2.354820044 ampl = ewidth / sigma / 2.50662828 f(x) = 1 - ampl * exp [-((x - pos) / sigma)**2 / 2]

Parameters:

fwhm The FWHM in Angstroms pos Center of the Gaussian, in Angstroms ewidth Equivalent width

[Back to top] |

A Lorentz model of an absorption feature, taking the functional form:

f(x) = 1.0 - ewidth / ((1.0 + 4.0 * ((1.0/x - 1.0/pos) * pos * 2.9979e5/fwhm)**2) * 1.571 * fwhm * pos/2.9979e5)

Parameters:

fwhm The FWHM in Angstroms pos Center of the feature, in Angstroms ewidth Equivalent width

[Back to top] |

A Voigt model of an absorption feature; using the absorbed Gaussian to model the core, and the absorbed Lorentzian to model the wings of an absorption feature.

The approximation presented in Astrophysical Formulae (K. R. Lang, 1980, 2nd ed., p. 220) is used. This approximation works best when the ratio between the FWHM of the Gaussian and Lorentzian sub-components is near unity.

Parameters:

center Center of the feature, in Angstroms ew Equivalent width fwhm The FWHM in Angstroms lg Ratio of Lorenztian to Gaussian FWHMs

[Back to top] |

A model of emission due to an accretion disk, taking the functional form:

f(x) = ampl * (x / 200000.0)**(-beta) * exp (-ref / x)

Parameters:

ref Center of the spectral feature, in Angstroms beta index ampl Amplitude of the feature

[Back to top] |

This model calculates the transmission of the interstellar medium using the description of the ISM absorption of Rumph, Bowyer, & Vennes 1994, AJ 107, 2108. It includes neutral He autoionization features. Between 1.2398 and 43.655 Angstroms (i.e. in the 0.28-10 keV range) the model also accounts for metals as described in Morrison & MacCammon 1983, ApJ 270, 119.

The code uses the best available photoionization cross-sections to date from the atomic data literature and combines them in an arbitrary mixture of the three ionic species: HI, HeI, and HeII.

The model assumes that the data are expressed in Angstroms.

This model provided courtesy of Pat Jelinsky.

Parameters:

hcol N(HI) column (atoms cm^-2) heiRatio N(HeI)/N(HI) heiiRatio N(HeII)/N(HI)

[Back to top] |

A Lorentz model with a varying power law, also known as a 1-D Beta model:

f(x) = f(r) = A*(1+[(x-xpos)/r_o]**2)**(-3*beta+1/2)

Parameters:

r0 core radius r_o beta beta index xpos offset from x = 0 ampl amplitude A at x = xpos

[Back to top] |

The blackbody function, taking the functional form:

f(x) = (ampl * refer**5 * [exp(1.438786E8 / T / refer) - 1]) / (x**5 * [exp(1.438786E8 / T / x) - 1])

Parameters:

refer Position of peak of blackbody curve, in Angstroms ampl Amplitude of the blackbody function temperature Temperature of the blackbody, in Kelvins

[Back to top] |

A box model:

f(x) = A if xlow <= x <= xhi

f(x) = 0 otherwise

Parameters:

xlow low cut-off xhi high cut-off ampl amplitude A

[Back to top] |

The bremsstrahlung function, taking the functional form:

f(x) = ampl * (refer / x)**2 * exp (-1.438779E8 / x / T)

Parameters:

refer Reference position, in Angstroms ampl Amplitude of the bremsstrahlung function temperature Temperature, in Kelvins

[Back to top] |

A broken power law, taking the functional form:

f(x) = ampl * (x / refer) ** index1

if x < refer, and

f(x) = ampl * (x / refer) ** index2

if x >= refer.

Parameters:

refer Position of the break, in Angstroms ampl Amplitude index1 Index of first power law index2 Index of second power law

[Back to top] |

The interstellar extinction function, according to Cardelli, Clayton, and Mathis extinction curve (ApJ, 1989, 345, 245).

Parameters:

ebv E(B-V) r R

[Back to top] |

A constant amplitude model:

f(x) = A

A is limited to being > 0. To model negative constant amplitudes, multiply by -1.

Parameters:

c0 amplitude A

[Back to top] |

A cosine model:

f(x) = A cos[2pi(x-x_off)/P]

Parameters:

period period P, in same units as x offset x offset x_off ampl amplitude A

[Back to top] |

This dereddening model uses the analytic formula for the mean extension law described in Cardelli, Clayton, & Mathis 1989, ApJ 345, 245:

A(lambda) = E(B-V) (aR_v+b) = 1.086 tau(lambda)

where tau(lambda) is the wavelength-dependent optical depth,

I(lambda) = I(0) exp[-tau(lambda)] ,

and a and b are computed using wavelength-dependent formulae which we will not reproduce here, for the wavelength range 1000 A - 3.3 microns. The relationship between the color excess and the column density is

E(B-V) = [ N_(Hgal) (10^20 cm^-2) ]/58.0

(Bohlin, Savage, & Drake 1978, ApJ 224, 132). The value of the ratio of total to selective extinction, R_v, is initially set to 3.1, the standard value for the diffuse ISM. The final model form is:

I(lambda) = I(0) exp[-N_(Hgal)(aR_v+b)/58.0/1.086]

This model provided courtesy of Karl Forster. The model assumes that the data are expressed in Angstroms.

Parameters:

rv total to selective extinction ratio R_v nhgal absorbing column density N(H_gal)

[Back to top] |

A phenomenological photoabsorption edge model as a function of wavelength:

f'(x) = f(x)

if x > lambda_b, and

f'(x) = f(x) exp[-A(x/lambda_b)**3]

otherwise.

space energy (0) or wavelength (1) thresh edge position E_b or lambda_b abs absorption coefficient A

Note: the "space" parameter should be kept equal to 1, as Iris always fits models to data using wavelength (in Angstroms) as the spectral coordinate.

[Back to top] |

A Gaussian model of an emission feature, where:

sigma = pos * fwhm / c / 2.354820044 delta = (x - pos) / sigma

if skew = 1,

f(x) = flux * exp (- delta**2 / 2) / sigma / 2.50662828

and, if skew != 1 and x <= pos,

f(x) = 2 * flux * exp(- delta**2 /2)/ sigma /2.50662828/(1+skew)

and, if skew != 1 and x > pos,

f(x) = 2 * flux * exp(- delta**2 /2/ skew**2)/ sigma /2.50662828/(1+skew)

Parameters:

fwhm FWHM, in Angstroms pos Center of feature, in Angstroms flux Amplitude of Gaussian skew skew

[Back to top] |

A Lorentz model of an emission feature, where:

f(x) = flux * pos * fwhm / c / ([abs(x - pos)]**kurt + (pos * fwhm / c / 2)**2) / 6.283185308

Parameters:

fwhm FWHM, in Angstroms pos Center of feature, in Angstroms flux Amplitude of Lorentzian kurt kurtosis

[Back to top] |

A model of an emission feature, where a Gaussian modeling the core is added to a Lorentzian modeling the wings. The approximation presented in Astrophysical Formulae (K. R. Lang, 1980, 2nd ed., p. 220) is used. This approximation works best when the ratio between the FWHM of the Gaussian and Lorentzian sub-components is near unity.

Parameters:

center Center of the emission feature, in Angstroms flux Amplitude of Voigt function fwhm FWHM, in Angstroms lg Ratio of Lorenztian to Gaussian FWHMs

[Back to top] |

The error function:

f(x) = A erf[(x-x_0)/sigma]

where

erf(y)=(2/sqrt(pi)) Int_0**y (exp(-t**2)) dt

Parameters:

ampl amplitude A offset offset x_off sigma scaling factor sigma

erf is the complement of erfc, the complementary error function:

erfc(y) = 1 - erf(y)

[Back to top] |

The complementary error function:

f(x) = A erfc[(x-x_0)/sigma]

where

erfc(y)=(2/sqrt(pi)) Int_y**Inf (exp(-t**2)) dt

Parameters:

ampl amplitude A offset offset x_off sigma scaling factor sigma

erfc is the complement of erf, the error function:

erfc(y) = 1 - erf(y)

[Back to top] |

The exponential function:

f(x) = A exp[C(x-x_off)]

Parameters:

offset offset x_off coeff coefficient C ampl amplitude A

[Back to top] |

The exponential function, base 10:

f(x) = A 10**[C(x-x_off)]

Parameters:

offset offset x_off coeff coefficient C ampl amplitude A

[Back to top] |

An unnormalized Gaussian model:

f(x) = A exp[-f(x-x_o/F)**2]

The constant f = 2.7725887 = 4log2 relates the full-width at half-maximum F to the Gaussian sigma so that F=sqrt(8log2)*sigma.

Parameters:

fwhm full-width at half-maximum F pos mean position x_o ampl amplitude A

This model is suitable for modeling spectral lines.

[Back to top] |

The natural logarithm function:

f(x) = A log[C(x-x_off)]

Parameters:

offset offset x_off coeff coefficient C ampl amplitude A

[Back to top] |

The common (base 10) logarithm function:

f(x) = A log_10[C(x-x_off)]

Parameters:

offset offset x_off coeff coefficient C ampl amplitude A

[Back to top] |

A logarithmic absorption model, taking the functional form:

alpha = log(2) / log(1 + fwhm / 2 / c)

if x >= pos,

f(x) = exp [-(tau * (x / pos)**alpha)]

and if x < pos,

f(x) = exp [-(tau * (x / pos)**(-1.0*alpha))]

Parameters:

fwhm FWHM of the feature, in Angstroms pos Center of the feature, in Angstroms tau Optical depth

[Back to top] |

A logarithmic emission model, taking the functional form:

arg = log (2) / log(1 + fwhm / 2 / c) fmax = (arg - 1) * flux / 2 / c

If skew = 1 and x < pos,

f(x) = fmax * (x / pos)**arg

and, if skew = 1 and x >= pos,

f(x) = fmax * (x / pos)**(-1.0*arg)

If skew != 1,

arg1 = log (2) / log (1 + skew * fwhm / 2 / c) fmax = (arg - 1) * flux / c / [1 + (arg - 1) / (arg1 - 1)]

and if x <= pos,

f(x) = f = fmax * (x / pos)**arg

and if x > pos

f(x) = fmax * (x / pos)**(-1.0*arg1)

Parameters:

fwhm FWHM of the feature, in Angstroms pos Center of the feature, in Angstroms flux Amplitude of the function skew skew

[Back to top] |

The logparabola function, particularly useful for modeling high-energy continuum for blazars.

f(x) = ampl * (x / ref)**[-(c1 + c2 * log10(x / ref))]

Parameters:

ref Reference position, in Angstroms c1 Index c2 Curvature of parabola ampl Amplitude of logparabola function

[Back to top] |

The normalized Lorentz function:

f(x) = (A/pi) (F/2)/[(F/2)**2 + (x-x_o)**2] ,

where

Int_(-Inf)**(+Inf) f(x) dx = A

This means the normalization is equal to the total flux integrated under the curve.

Parameters:

fwhm full-width at half-maximum F pos mean position x_o ampl amplitude A

This model is suitable for modeling spectral lines.

[Back to top] |

A normalized 1-D beta function appropriate for use fitting line profiles:

f(x) = A * [1 + ((x-x_0)**2/w**2)] ** (-alpha)

Parameters:

pos line centroid x_0 width line width w index index alpha ampl line amplitude A - equal to the value of the constant for which the integral of the model is equal to 1

This model is suitable for modeling spectral lines.

[Back to top] |

The normalized Gaussian function:

f(x) = [A/sqrt(pi/f)/F] exp[-f(x-x_o/F)**2]

where

Int_(-Inf)**(+Inf) dx f(x) = A

This means the normalization is equal to the total flux integrated under the curve.

The constant f = 2.7725887 = 4log2 relates the full-width at half-maximum F to the Gaussian sigma so that F=sqrt(8log2)*sigma.

Parameters:

fwhm full-width at half-maximum F pos mean position x_o ampl amplitude A

This model is suitable for modeling spectral lines.

[Back to top] |

A Gaussian model of an absorption feature, with optical depth as a parameter, taking the functional form:

sigma = pos * fwhm / c / 2.354820044 ampl = equiv_width / sigma / 2.50662828

f(x) = exp(-tau * exp(-((x - pos) / sigma)**2 / 2))

Parameters:

fwhm The FWHM in Angstroms pos Center of the Gaussian, in Angstroms tau Optical depth limit

[Back to top] |

A model expressing the ratio of two Poisson distributions of mean mu, one for which the random variable is x, and the other for which the random variable is equal to mu itself:

f(x) = A (mu!/x!) mu**(x-mu)

Parameters:

mean mean mu ampl amplitude A

[Back to top] |

A 1-D polynomial of order <= 5:

f(x) = sum_(i=0)**5 c_i (x-x_off)**i ,

where the coefficients c_i are the parameters numbered i+1, and x_off is parameter number 7.

Note that there is a degeneracy in the parameters, so it is recommended to set at least one of c_0 or x_off to zero and freeze it; thawing both may lead to unpredicted results.

Note also that all coefficients except c_0 are default frozen, so that the default polynomial model is a constant.

Parameters:

c0 coefficient c_0 c1 coefficient c_1 c2 coefficient c_2 c3 coefficient c_3 c4 coefficient c_4 c5 coefficient c_5 offset offset for x x_off

[Back to top] |

A power law function, taking the functional form:

f(x) = ampl * (x / refer) ** index

Parameters:

refer Reference position, in Angstroms ampl Amplitude index Index of power law

[Back to top] |

A model of the continuum emission due to recombination, taking the functional form:

If x >= refer,

f(x) = ampl * exp(-(x - refer)**2 / (refer * fwhm / c / 2.354820044)**2 / 2)

and if x < refer,

f(x) = ampl * (refer / x)**2 * exp -(1.440E8 * (1/x - 1/refer)/T)

Parameters:

refer Reference position, in Angstroms ampl Amplitude temperature Temperature, in Kelvins fwhm FWHM, in Angstroms

[Back to top] |

A sine model:

f(x) = A sin[2pi(x-x_off)/P]

Parameters:

period period P, in same units as x offset x offset x_off ampl amplitude A

[Back to top] |

A square-root model:

f(x) = A sqrt(x-x_off)

Parameters:

offset offset x_off ampl amplitude A

[Back to top] |

A step model:

f(x) = A if x > x_cut

and

f(x) = 0 otherwise.

Parameters:

xcut cut-off x_cut ampl amplitude A

[Back to top] |

A step model:

f(x) = A if x < x_cut

and

f(x) = 0 otherwise.

Parameters:

xcut cut-off x_cut ampl amplitude A

[Back to top] |

A tangent model:

f(x) = A sin[2pi(x-x_off)/P]

Parameters:

period period P, in same units as x offset x offset x_off ampl amplitude A

[Back to top] |

This model is the extragalactic extinction function of Calzetti, Kinney and Storchi-Bergmann, 1994, ApJ, 429, 582.

Parameters:

ebv E(B-V)

[Back to top] |

This model is the galactic extinction from Seaton, M. J. 1979, MNRAS 187, 73P. The formulae are based on an adopted value of R = 3.20.

This function implements Seaton's function as originally implemented in STScI's Synphot program.

For wavelengths > 3704 Angstrom, the function interpolates linearly in 1/lambda in Seaton's table 3. For wavelengths < 3704 Angstrom, the class uses the formulae from Seaton's table 2. The formulae match at the endpoints of their respective intervals. There is a mismatch of 0.009 mag/ebmv at nu=2.7 (lambda=3704 Angstrom). Seaton's tabulated value of 1.44 mag at 1/lambda = 1.1 may be in error; 1.64 seems more consistent with his other values.

Wavelength range allowed is 0.1 to 1.0 microns; outside this range, the class extrapolates the function.

Parameters:

ebv E(B-V)

[Back to top] |

This model is the extinction curve for the SMC, as given in Prevot et al., 1984, A&A, 132, 389-392.

Parameters:

ebv E(B-V)

[Back to top] |

This model is the galactic extinction curve according to Savage & Mathis, 1979, ARA&A, 17, 73-111.

Parameters:

ebv E(B-V)

[Back to top] |

This model is the extinction curve for the LMC, as given in Howart, 1983 MNRAS, 203, 301.

Parameters:

ebv E(B-V)

[Back to top] |

This model is the Fitzpatrick and Massa extinction curve with Drude UV bump (ApJ, 1988, 328, 734).

Parameters:

ebv E(B-V) x0 Offset width Width of Drude bump c1 Coefficient 1 c2 Coefficient 2 c3 Coefficient 3 c4 Coefficient 4

[Back to top] |