The glowing gas at the surface (photosphere) of the star radiates the smooth
linefree light like a "black body" (continuum). The intensity distribution
of that light obeys rawly the Planck's
law. Intensity and intensity-wavelength distribution of the black
body radiation are strongly dependent on temperature.
Then the smooth photosperic continuum spectrum in the outer layers of gas of
the star will be modified (under other physical conditions) by absorption and
emission processes, which can be seen due to the low pressures in these layers
usually as relatively sharp lines (absorption
and emission lines,
see eg the Fraunhofer
lines of the sun).
The star-light is then changed in the earth atmosphere (for example, scattering
and terrestrial lines by absorption of water and oxygen molecules). These physically
real starlight passes through our telescope, is dispersed in the spectrograph
and the resulting spectrum is recorded by the CCD camera. The physical intensity
distribution is superimposed the sensitivity of the CCD pixel. The sensivity
is quite variable for different wavelengths (see sensitivity curves of different
CCD chips). Therefore, the measured raw spectrum not linearly corresponds to
the actual physical distribution of intensity, but the plot in the y axis is
a relative flux (albeit with knowledge of the "response function" of the apparatus
the relative flux can be converted).
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On the left side we see the calibrated raw spectrum near the H alpha
line of the supergiant eps Aur (spectral class FI). The dominant, relatively
sharp H alpha line has an emission shoulder at the short wavelength edge
component (these shoulders ar very variabel). The many sharp lines are
water lines, caused by the water molecules in the lower atmosphere (humidity).
The starlight continuum (the component of the black body) is clearly seen
as constantly smooth curved line interrupted by the narrow absorptions
and emission. But here caution is needed. The H alpha line center sits
in a fairly flat broad bump (6550 to 6575 angstroms). That's the photospheric
H alpha absorption line. The sharp central absorption is due to the sorrounding
gas shell.
The relative flux of the ordinate was determined in a rather unwieldy
numbers around 25,000 ADU. This is simply the result of integration of
pixel columns, which have formed the spectral strip in the spectrum extraction.
With a gain of 2.3 e / ADU were involved about 2.3 * 25,000 = 56,000 photons
causing the signal in the pixels.
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Dividing all ADC values from the above figure
by a constant, here for example by 28,000 (the value at 6550 angstrom) the
relative flux is normalized to values close to 1, without the spectrum is
physically changed (it was only a linear transformation in the relative
flux carried out). Up to this point have yet been any individually affected
transformations. The spectrum is a pure measurement result (with the usual
physical factors such as statistical effects, inaccuracies, etc.). |
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If one is interested in effects for the star continuum, the continuum
of black body, play no role, we can eliminate the continuum. You only
have to specify a continuum function, ie, it is formed by defining
grid points that lie on the continuum. That's a spline (function), which
represents the continuum. Wherever be bridged the lines, we establishe
a quasi-continuum. It implicitly assumes that the continuum continues
as assumed, although it has in these places do not really measured. The
graph at left side shows such a quasi continuum in form of a solid
line, let's call it "nor". It was created by clicking on several
continuum points within a MIDAS procedure. The next step is normalizion
of the raw spectrum using this "nor" by dividing the raw spectrum
through "nor".
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Calculation of the normalized spectrum:
Normalized spectrum = raw spectrum / 'nor'.
The result is shown in the graph on the left side. Normalized Flux F
/ Fc is plotted against the wavelength. Now, throughout the continuum
is on level 1 and the flux 'F / Fc of the absorption lines are <1 and
the emission components > 1.
Without knowledge of the normalization function 'nor' is the original
spectrum no longer be reconstructable. Caution: the normalized spectrum
is already an interpretation of the editor , because a non linear transformation
of the measurement result (raw spectrum) is done by the observer with
a bona fide set 'nor'
- Fc (i) = flux of the quasi continuum in the pixel i of the calibrated
raw spectrum.
- F (i) = flux of each pixel i of the calibrated raw spectrum.
- F (i) / Fc (i) is the normalized value (normalized flux) of the pixel
i.
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The normalization of the above calibrated raw spectrum was relatively
easy because the continuum was highly visible. Here's an example where
this is no longer so trivial.
The H alpha line of zet Tau is in emission and also very wide
(shown a not calibrated sum spectrum on the left side). The rise flanks
on both sides of the line run out wide, so that the establishment of the
quasicontinuum "below the line" requires some experience. It must be the
"real" spectrum of the star have in mind (literature).
In such broad emission lines is in the flanks the Raleygh-scattered light
of the H alpha line. This is a light intensity that belongs to the H alpha
emission and can not be omitted !
Following the same spectrum calibrated and normalized.
: 
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In this example (the region around the H alpha line of lam
Cep) is a normalization in good conscience carry out any more, because
the line profile is much too complex. The establishment of a quasi continuum
in the central part of the spectrum runs on arbitrarity. The line profile
is quite variable in time. Possibly succeed by attracting a middle range
(mean over many spectra from a longer period, with all the line profile
variations must be recorded), an approximate normalization function (polynomial)
to be determined. |
Normalization
of spectra (continuum normalization)
