eqwidth

determine equivalent width

Determine the equivalent width of a model component.

Syntax: eqwidth [[range <frac range>] [<model name>:]<model component number>] [err <number><level>|noerr]

The command calculates the integrated photon flux produced by an additive model component (combined with its multiplicative and/or convolution pre-factors) (FLUX), the location of the peak of the photon spectrum (E), and the flux (photons per keV) at that energy of the continuum (CONTIN). The equivalent width is then defined as {EW = FLUX / CONTIN} in units of keV. New for XSPEC12: the continuum is defined to be the contribution from all other components of the model.

There are certain models with a lot of structure where, were they the continuum, it might be inappropriate to estimate the continuum flux at a single energy. The continuum model is integrated (from $E(1-<frac range>)$ to $E(1+<frac range>)$. The initial value of <frac range> is 0.05 and it can changed using the range keyword.

The err/noerr switch sets whether errors will be estimated on the equivalent width. The error algorithm is to draw parameter values from the distribution and calculate an equivalent width. <number> of sets of parameter values will be drawn. The resulting equivalent widths are ordered and the central <level> percent selected to give the error range. You can get the full array of simulated equivalent width values by calling tclout eqwidth with the errsims option (see tclout command).

When Monte Carlo Markov Chains are loaded (see chain command), they will provide the distribution of parameter values for the error estimate. Otherwise the parameter values distribution is assumed to be a multivariate Gaussian centered on the best-fit parameters with sigmas from the covariance matrix. This is only an approximation in the case that fit statistic space is not quadratic.

Examples:

The current model is assumed to be $M_1(A_1+A_2+A_3+A_4+M_2(A_5))$, where the $M_x$ models are multiplicative and the $A_x$ models are additive.

XSPEC12> eqwidth 3
// Calculate the total flux of component M1A2 (the third 
// component of the model with its multiplicative pre-factor)
// and find its peak energy (E). The continuum flux is
// found by the integral flux of M1(A1+A3+A4+M2(A5)), using the 
// range of 0.95E to 1.05E to estimate the flux.
XSPEC12> eqwidth range .1 3
// As before, but now the continuum is estimated from 
// its behavior over the range 0.9E to 1.1E.
XSPEC12> eqwidth range 0 3
// Now the continuum at the single energy range (E) 
// will be used.
XSPEC12> eqwidth range .05 2
// Now the component M1A1 is used as the feature, and 
// M1(A2+A3+A4+M2(A5)) are used for the continuum.  The range 
// has been reset to the original value.
XSPEC12> eqwidth 1
// Illegal, as M1 is not an additive component.

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