SPEX User's Manual - SRON

66 Spectral Models
• type=3: b 1 is the lower wavelength in Å, b 2 is the upper wavelength in Å, and the grid is linear in
wavelength in between.
• type=4: b 1 is the lower wavelength in Å, b 2 is the upper wavelength in Å, and the grid is logarithmic
in wavelength in between.
Note that the logarithmic grids can also be used if one wants to keep a fixed velocity resolution (for
broadened line features for example). Further, each time that the model is being evaluated, the relevant
values of the x i grid points are evaluated.
Warning: Be aware that if you just set b 1 , b 2 and n but do not issue the ”calc” command or the ”fit”
command, the x i values have not yet been calculated and any listed values that you get with the ”par
show” command will be wrong. After the first calculation, they are right.
Warning: If at any time you change one of the parameters type, b 1 , b 2 or n, the y i values will not be
appropriate anymore as they correspond to the previous set of x i values.
The maximum number n of grid points that is allowed is 999, for practical reasons. Should you wish to
have a larger number, then you must define multiple spln components, each spanning its own (disjunct)
b 1 –b 2 range.
It should be noted, however, that if you take n very large, spectral fitting may become slow, in particular
if you take your initial guesses of the y i parameters not too close to the true values. The reason for the
slowness is two-fold; first, the computational time for each fitting step is proportional to the number of
free parameters (if the number of free parameters is large). The second reason is unavoidable due to our
spectral fitting algorithm: our splines are defined in log photon spectrum space; if you start for example
with the same value for each y i , the fitting algorithm will start to vary each parameter in turn; if it
changes for example parameter x j by 1, this means a factor of 10; since the neighbouring points (like
x j−1 and x j+1 however are not adjusted in thid step, the photon spectrum has to be drawn as a cubic
spline through this very sharp function, and it will show the well-known over-and undershooting at the
intermediate x-values between x j−1 and x j and between x j and x j+1 ; as the data do not show this strong
oscillation, χ 2 will be poor and the fitting algorithm will decide to adjust the parameter y j only with a
tiny amount; the big improvement in χ 2 would only come if all values of y i were adjusted simultaneously.
The parameters of the model are:
type - The parameter type defined above; allowed values are 1–4. Default value: 1.
n - The number of grid points n. Should be at least 2.
low - Lower x-value b 1 .
upp - Upper x-value b 2 . Take care to take b 2 > b 1 .
x001 - First x-value, by definition equal to b 1 . x-values are not allowed to vary (i.e. you may not fit
them).
x002 - Second x-value
x003 - Third x-value
. . . - Other x-values
x999 - last x-value, by definition equal to b n . If n < 999, replace the 999 by the relevant value (for
example, if n = 237, then the last x-value is x237).
y001 - First y-value. This is a fittable parameter.
y002 - Second y-value
y003 - Third y-value
. . . - Other y-values
y999 - last y-value. If n < 999, replace the 999 by the relevant value (for example, if n = 237, then the
last y-value is y237).
3.26 Vblo: Rectangular velocity broadening model
This multiplicative model broadens an arbitrary additive component with a rectangular Doppler profile,
characterized by the half-width v. Therefore if a delta-line at energy E is convolved with this component,
its full energy width will be 2Ev/c, and line photons get a rectangular distribution between E − Ev/c