Iris 1.0 Models

The following models are provided by Iris 1.0, for fitting to SED data. Models can be combined together in more 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.

absorptionedge

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

absorptiongaussian

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

absorptionlorentz

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

absorptionvoigt

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

accretiondisk

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

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

Parameters:

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

atten

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)

beta1d

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

blackbody

The blackbody function, taking the functional form:

       f(x) = (amp * 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

box1d

A box model:

       f(x) = A if x_low <= x <= x_hi

       f(x) = 0 otherwise

Parameters:

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

bremsstrahlung

The bremsstrahlung function, taking the functional form:

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

Parameters:

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

brokenpowerlaw

A broken power law, taking the functional form:

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

if x < refer, and

       f(x) = amp * (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

ccm

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

Parameters:

  ebv		E(B-V)		
  r		R

const1d

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

cos

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

dered

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)

edge

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.

emissiongaussian

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

emissionlorentz

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

emissionvoigt

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

erf

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)

erfc

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)

exp

The exponential function:

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

Parameters:

  offset	offset x_off
  coeff		coefficient C
  ampl		amplitude A

exp10

The exponential function, base 10:

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

Parameters:

  offset	offset x_off
  coeff		coefficient C
  ampl		amplitude A

gauss1d

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.

log

The natural logarithm function:

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

Parameters:

  offset	offset x_off
  coeff		coefficient C
  ampl		amplitude A

log10

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

logabsorption

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

logemission

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
  limit

logparabola

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

Parameters:

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

lorentz1d

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.

normbeta1d

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.

normgauss1d

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.

opticalgaussian

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

poisson

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

polynomial

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

powerlaw

A power law function, taking the functional form:

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

Parameters:

  refer		Position of the break, in Angstroms
  ampl		Amplitude
  index		Index of power law

recombination

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

If x >= refer,

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

and if x < refer,

       f(x) = amp * (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

sin

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

sqrt

A square-root model:

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

Parameters:

  offset	offset x_off
  ampl		amplitude A

stephi1d

A step model:

       f(x) = A if x > x_cut

and

       f(x) = 0 otherwise.

Parameters:

  xcut		cut-off x_cut
  ampl		amplitude A

steplo1d

A step model:

       f(x) = A if x < x_cut

and

       f(x) = 0 otherwise.

Parameters:

  xcut		cut-off x_cut
  ampl		amplitude A

tan

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

xgal

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

Parameters:

  ebv		E(B-V)

seaton

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)

smc

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)

sm

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

Parameters:

  ebv		E(B-V)

lmc

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

Parameters:

  ebv		E(B-V)

fm

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