FittingFunction

Band(E,α,β,E₀,A)

Compute the so-called 'Band function'

#Arguments

• E input energy.
• α low-energy index.
• β high-energy index.
• E₀ break energy.
• A normalization.

The peak-energy is then $Ep = (2+α)E₀$.

Examples

Band(300.,-2.,-1.,200.,1.)

# output

-0.45304697140984085

CPL(E,N,α,Ec;E0=1.)

Compute a cut-off power-law.

Arguments

• α spectral index.
• N normalization.
• E input energy.
• Ec cut-off energy.
• E0 energy for power-law normalization.

Examples

CPL(3.,1.,-1.,2.)

# output

0.0743767200494766

Counts2Mag(cts,ects;zp=25.0,ezp=0.0)

Convert counts (or flux) to magntudes,

Arguments

• cts counts.
• ects count uncertainty.
• zp magnitude zero-point
• zp zero-point uncertainty.

Examples

Counts2Mag(100,10)

# output

(20.0, 0.10857362047581294)

Ecm2sA2Jy(fluden, lambd)

Convert flux densities in $erg~s^{-1} cm^{-2} Angstrom^{-1}$ to $Jy$.

Arguments

• fluden flux density ($erg~s^{-1} cm^{-2} Angstrom^{-1}$).
• lambd wavelength ($Angstrom$).

Examples

Ecm2sA2Jy([1.2e-15,2e-15,2.5e-15],[5000,5500,6000])

# output

3-element Vector{Float64}:
 0.001
 0.002016666666666667
 0.0029999999999999996

Extinction(wave,EBV;gal="SMC",Rv=FFGals["SMC"],z=0.)

Compute the UV/optical/extinction.

Argguments

• wave input wavelengths (Angstrom).
• EBV color excess E(B-V) (magnitude).
• gal one of the galaxy extinction recipes listed in the 'FFGals' (exported) dictionary.
• Rv selective extinction.
• z redshift of the absorpber.

References about the adopted extinction curves are discussed in the documentation of the DustExtinction package.

Examples

Extinction(5500.,1,gal="MW",Rv=FFGals["MW"],z=0.)

# output

0.06017150537641227

FourierPeriodogram(signal,fs;zerofreq=true)

Compute the discrete Fourier periodogram for the inpout signal.

Arguments

• signal array of input data.
• fs sampling in frequency of the input data (1/dt).
• 'zerofreq' is true (false) to (not) include the zero frequency in the output.

Outputs are two arrays: the frequencies and the powers.

Examples

FourierPeriodogram([1.,2.,3.,4.],1.)

# output

([0.0, 0.25], [100.0, 8.000000000000002])

GaussAbs(E,Ed,σ,El)

Compute a Gaussian absorption.

Arguments

• Ed depth. at
• E input energy.
• El absorption center.
• σ absorption width ($FWHM/2.35$).
• A normalization.

Examples

GaussAbs(2.,1.,0.1,2.)

# output

0.018510395162776326

Gaussian(E,A,σ,El)

Compute a Gaussian.

Arguments

• E input energy.
• El Gussian center.
• σ absorption width ($FWHM/2.35$).
• A normalization.

Examples

Gaussian(3.,1.,0.1,2.)

# output

4.009419869036418

GetAtomicData(table::String="")::DataFrame

Return a table with atomic data among those available.

Calling the function with no parameter shows the available tables. At present we have:

• "FitLyman". This is the original table generated for the "FitLyman" ESO-MIDAS package.
• "JitrikBunge04". This is a collection of atomic data prepared by Jitrik & Bunge (2004).
• "VALD03". This is a collection of atomic data extracted from the VALD3 database.

Examples

fly = GetAtomicData("FitLyman")

Jy2Ecm2sA(fluden, lambd)

Convert flux densities in $Jy$ to $erg~s^{-1} cm^{-2} Angstrom^{-1}$.

Arguments

• fluden flux density ($Jy$).
• lambd wavelength ($Angstrom$).

Examples

Jy2Ecm2sA([1e-3,2e-3,3e-3],[5000,5500,6000])

# output

3-element Vector{Float64}:
 1.2000000000000002e-15
 1.9834710743801656e-15
 2.5e-15

Mag2Counts(mag,emag;zp=25.0)

Convert magnitudes to counts (or flux).

Arguments

• mag input magnitude.
• emag magnitude uncertainty.
• zp zero-point.

Examples

Mag2Counts(20,0.1)

# output

(100.0, 9.210340371976184)

NorrisPulse(x;pulsNorm,tmax,σ_rise,σ_decay,pulsSharpness,base)

Compute an asymmetric pulse shape according to the recipe reported in Norris et al. (1996)..

Arguments

• x input vector.
• pulsNorm the nornalization of the pulse.
• tmax the maximum of the pulse.
• σ_rise the time-scale of the rising phase.
• σ_decay the time-scale of the decaying phase.
• pulsSharpness pulse sharpness parameter.
• base signal level without the pulse.

Examples

NorrisPulse([1.,2.,3.,4.,5.],pulsNorm=1.5,tmax=3.,σ_rise=1.,σ_decay=2.,pulsSharpness=1.1,base=0.3)

# output

5-element Vector{Float64}:
 0.47585740398559895
 0.8518191617571635
 1.8
 1.2407748943132098
 0.8518191617571635

PL(E,N,α;E0=1.)

Compute a power-law with.

Arguments

• α spectral index.
• N normalization.
• E input energy.
• E0 power-law energy normalization.

Examples

PL(3.,1.,-1.)

# output

0.3333333333333333

Pol2Stokes(i, p, t, c; ep=0.0, et=0.0, ec=0.0)

Compute the Stokes parameters for a given polarisation degree and position angle.

Arguments

• i total intensity.
• p polarisation degree.
• t position angle (randians).
• c the circular polarisation.
• ep polarization uncertainty.
• et position angle uncertainty.
• ec circular polarization uncertainty.

The ouput is: intensity q, u, v Stokes parameters and respective errors.

Examples

Pol2Stokes(1.,0.1,0.1,0.)

# output

(1.0, 0.09800665778412417, 0.019866933079506124, 0.0, 0.0, 0.0, 0.0)

SBPL(E,N,α,β,Eb)

Compute a smoothly joint broken power-law.

Arguemnts

• α pre-break spectral index.
• β post-break spectral index.
• Eb break energy.
• N normalization.
• E input energy.

Examples

SBPL(6.,1.,-1.,-1.5,5.)

# output

0.15214515486254615

SBPL2(E,N,α,β,γ,Eb1,Eb2)

Compute a smoothly joint double broken power-law.

Arguments

• α pre-break spectral index.
• β inter-break spectral index.
• γ post-break spectral index.
• Eb1 first break energy.
• Eb2 second break energy.
• N normalization.
• E input energy.

Examples

SBPL2([4.,6.,8.],1.,-1.,-1.5,-2.,5.,7.)

# output

3-element Vector{Float64}:
 0.25
 0.06804138174397717
 0.04133986423538423

SigmaClip(x, ex=ones(size(x)); sigmacutlevel=2)

Sigma-clipping filtering of an input array,

Arguments

• x input array.
• ex uncertainties.
• sigmacutlevel sigma-clipping level.

It performs a one-iteration sigma clipping and reports a mask to select the surviving elements in the input arrays or other related arrays.

Examples

x = [4.,6.,8.,1.,3.,5.,20.]
mask = SigmaClip(x)
x[mask]

# output

6-element Vector{Float64}:
 4.0
 6.0
 8.0
 1.0
 3.0
 5.0

Stokes2Pol(i, q, u, v; eq=0.0, eu=0.0, ev=0.0)

Compute the polarisation degree and position angle from the Stokes parameters.

Arguments

• i total intensity.
• q verical/horizontal polarization.
• u oblique polarization.
• v circular polarisation.
• eq uncertainty on the q parameter.
• eu uncertainty on the u parameter.
• ev uncertainty on the v parameter.

The ouput is given by the intensity i, polarisation degree, p, position angle (randians) theta and circular polarisation chi, with respective errors.

Examples

Stokes2Pol(1.,0.1,0.1,0.)

# output

(1.0, 0.14142135623730953, 0.39269908169872414, 0.0, 0.0, 0.0, 0.0)

TauVoigt(λ,NHI,DopplerBroadening,z,transition)

Compute the opacity due to a given absorption transition.

Arguments

• λ is the wavelenghths ($cm$).
• N the column density ($cm^{-2}$).
• DopplerBroadening is the Doppler broadening ($cm~s^{-1}$).
• z is the source redshift.
• transition is a tuple formed by the central wawelength ($cm$), the oscillator strength and the damping coefficient ($s^{-1}$) for the given transition.

The Doppler broadening factor is typicaly due to either an intrinsic thermal broadening ($b_K = \sqrt{2KT/m}$) or to a turbulent motion of the gas ($b_T = \sqrt{σ_T}$, where $σ_T$ is the inner velocity dispersion). These two factors can be summed in quadrature, i.e. $b = \sqrt{b_K^2 + b_T^2}$.

Examples

TauVoigt(range(start=1494.5,stop=1495.5,step=0.1) .* 1e-8,1e18,1e5,0.,[1495.05*1e-8,0.54,8.106e8])

# output

11-element Vector{Float64}:
  0.5408331361420329
  0.8079604230648749
  1.3357686994197793
  2.618871809580839
  7.282358478732964
 66.40911467182524
 66.40911467182524
  7.282358478732964
  2.618871809580839
  1.3357686994184856
  0.8079604230648749

VoigtFuncTG(a,v)

Approximate the Voigt (or line broadening function) function.

It was introduced by Tepper-Garcia (2006). It is of high accuracy provided that $a \le 10^{-4}$. The $a$ and $v$ parameters are defined as: $a = \frac{\Gamma \lambda_c}{4\pi b 10^{13}}$ and $v = \frac{(\lambda_c - \lambda)c}{b \lambda_c \sqrt{2 \log 2}}$, where $\lambda_c$ is the central wavelength of the transition, $c$ the speed of light, $b$ the Doppler broadening factor and $\Gamma$ the damping coefficient.

Examples

FittingFunction.VoigtFunctTG(1e-5,1.)

# output

0.36788094737611143

XAbs(E; NH=1e20, z=0)

Compute the effective absorption cross section per hydrogen atom.

It is based on the Morrison & McCammon (1983) recipe.

Arguments

• E is the energy (KeV, in the 0.03-10 KeV range).
• N is the column density (particle per square cm).
• z is the redshift.

Examples

XAbs([0.5,1.25,2.], NH=1e20, z=0)

# output

3-element Vector{Float64}:
 0.9290803992951834
 0.9868927382232576
 0.9957079871273042

Z2N(freqs, time)

Compute the Rayleigh power spectrum of a time series in a given range of frequencies.

Arguments

• freqs is an array with frequencies in units of 1/[time].
• time is an array with the time series where to find a period.
• harm is the number of harmonics to be used in the analysis.

Examples

Z2N([1.,0.5,0.25], [1.,2.,2.5,3.5,5.])

# output

3-element Vector{Any}:
 0.4
 0.4000000000000002
 0.537258300203048