Redshift of solar limb and in cosmology

In message , Robin Whittle
writes


Philip Helbig wrote:

Presumably, you mean that this theory could have a cosmological
redshift with no expansion.

Yes. If we find plasma redshift under our noses in the solar
corona, its reasonable to expect it in the inter-cluster medium.
There, I guess the inter-particle spacing is a metre or so, which
should be long enough to redshift both the main black-body light
and its absorption and emission lines by about the same amount.
I wouldn't expect much redshift of microwave emission lines, since
their coherence length is likely to be many metres. Nor would I
expect much plasma redshift of X-rays because they have such a
short wavelength that they experience the Universe as being very
empty.


The problem is that you find visible-light and radio redshifts which are
the same. Here's an example
http://adsabs.harvard.edu/abs/1987ApJ...319..683C
And red shifted X-ray lines have also been observed
http://xmm.vilspa.esa.es/external/xmm_science/1st_results/pdf/xmm11.pdf

Thanks Jonathan for your critique and references. I can't
fault these papers.

In my tentative theory, the similar or identical redshift of
visible light along with 21cm or X-rays can't be explained by
plasma redshift. So if the redshifts reported by these papers
are real then I figure the BBT is correct, since I can't
imagine anything other than Doppler creating them.

Still, there are so many problems with the BBT that I am not
inclined to abandon this project so easily. Maybe plasma
redshift or something similar will turn out to be part of the
final picture. I won't bug you or other people to consider it
as a cause of the cosmological redshift, since these papers
seem to rule that out.

I still think some process such as this needs to be considered
for the heating and acceleration of the solar corona and wind.
Something is depositing energy and momentum all the way out to
the outer planets and beyond. Something consistently raises
the temperature of the corona to a million degrees very close
to the Sun's surface, no matter what is happening with
large-scale magnetic fields. This is not explicable by
conventional theories. The momentum is always away from the
Sun, and what is continually streaming out of the Sun? Short
coherence length (~1 to 3 microns) wavefronts of light.

I think we should develop a really solid understanding of the
solar corona and wind before we can be confident that the
cosmological redshift is purely Doppler shift.

I have noted your critique at my site:

http://astroneu.com/simmering/#critique_2

along with two critiques from Craig Markwardt:

http://astroneu.com/simmering/#critique_1

- Robin

As you may have seen, I started a separate thread about my own theory
regarding a possible plasma redshift mechanism
(http://groups.google.co.uk/group/sci...a41d46c3744cee
), but I just wanted to briefly comment on a few points here

Robin Whittle wrote:
Thanks Jonathan for your critique and references. I can't
fault these papers.

In my tentative theory, the similar or identical redshift of
visible light along with 21cm or X-rays can't be explained by
plasma redshift. So if the redshifts reported by these papers
are real then I figure the BBT is correct, since I can't
imagine anything other than Doppler creating them.

I don't think that the reference Jonathan gave above
(http://adsabs.harvard.edu/cgi-bin/np....319..683C&amp
) is in any way conclusive here.
First of all, the redshift considered is very small (of the order of
z=0.01) and could, at least for one of the two cases considered in the
paper, even be due to a peculiar velocity of the absorbing galaxy.

Secondly, the lines considered are absorption lines. The light being
observed is actually that of the quasar lying behind the galaxy, and it
is anybody's guess what the coherency of this light in either
wavelength region is.

Thirdly, as indicated on my web page
http://www.plasmaphysics.org.uk/research/redshift.htm , both the
coherence length and/or the wavelength could be a limiting factor here
with regard to the redshift mechanism, and a wavelength of 21 cm is
presumably still significantly shorter than the average particle
distance in the intergalactic plasma. One would need data for a
wavelength of more than 1m in order to definitely notice any threshold
effect.

Another possibility is that in this case the redshift is actually not
caused by the random electric field of the intergalactic plasma, but by
a systematic electric field associated with the plasma halo that
surrounds all stars, galaxies and galaxy clusters. The point is that
this field has scale of the order of the objects involved, and the
wavelength/coherence length issue is thus not relevant here (as shown
on my page http://www.plasmaphysics.org.uk/research/lensing.htm , this
could at least explain the redshift of solar spectral lines, and may be
also the redshift and lensing associated with galaxies (although I have
not made a quantitative estimate yet for the latter case)).

X-ray redshifts should anyway not be affected by the field scale as
both the wavelength and coherence length are much shorter.


I still think some process such as this needs to be considered
for the heating and acceleration of the solar corona and wind.
Something is depositing energy and momentum all the way out to
the outer planets and beyond. Something consistently raises
the temperature of the corona to a million degrees very close
to the Sun's surface, no matter what is happening with
large-scale magnetic fields. This is not explicable by
conventional theories.

The temperature of the corona can simply be explained in terms of the
gravitational energy of the sun. What needs to be explained is the
lowered temperature of the photosphere, and I have suggested that
inelastic collisions of the original high energy protons with neutral
hydrogen in the photosphere is responsible for this. The small amount
of protons which does not suffer from inelastic collisions forms then
the corona and solar wind (see my page
http://www.plasmaphysics.org.uk/research/sun.htm ).

Thomas

Thomas Smid suggested that a redshift of 0.01 could be
explained by "peculiar motion" of galaxies. 3,000 km/s is a
lot higher than a few figures I found Googling, such as 90
and 130 km/s from astro-ph/9705224 . I haven't looked at
how such figures are calculated. As far as I know, it would
take a major revision of conventional theories to arrive at
galaxy motions approaching 1% the speed of light.

Thomas Smid wrote:

Secondly, the lines considered are absorption lines. The
light being observed is actually that of the quasar lying
behind the galaxy, and it is anybody's guess what the
coherency of this light in either wavelength region is.

This raises a difficult and unconventional question about
light - but it they must be faced when considering a
mechanism which depends on "coherence length". In this
context, I use "coherence length" to refer to the thickness
(length in the direction of travel) of a planar wavefront
of a single impulse, if we consider that the total light
signal can be considered as being composed of many such
wavefronts.

I think the best approach is to consider the total light
signal as the sum of a variety of signals. Short coherence-
length light can be thought of as many short wavefronts -
because one could generate a very short impulse with the
right shape to create the observed spectrum, and then create
something identical to the original light by launching many
such short impulse wavefronts with random phases. Then, we
could analyse the behaviour of the light by considering just
one such short impulse (unless there were non-linear
processes at work).

This model of light, emr etc. as being made of myriads of
short coherence length wavefronts, would apply to black body
light or broadband synchrotron light etc. from a quasar.

An emission line is clearly an additional signal, of longer
coherence length. The tricky question is how to think about
an absorption line. I think it is best to consider it as
a long coherence length signal (long wavefront like a sine
wave which rises and falls over hundreds or thousands of
sine wave cycles) which is generated by the narrow filter
(band reject in this instance) as the filter is stimulated
by each of the short coherence length input signals.

The sum of this signal and the input signals has the
spectrum we expect - the signal which constitutes the
absorption line is out of phase with the components of the
input signal only at those frequencies which are being
rejected.

I think this is a more satisfactory approach than trying
to imagine the final filtered signal as consisting of
highly coherent components near the edges of the absorption
line. The original light had no such coherency, so how
could a band reject filter alter the light in neighbouring
frequencies so that they were more coherent?

On this basis, I expect the broad spectrum of black body,
or quasar, light to be redshifted in the plasma, as long as
the coherence length is less than the inter-particle
spacing, and the long coherence length absorption (or
emission) lines should not be redshifted much or at all.
I regret I can't describe this more mathematically.


. . . both the coherence length and/or the wavelength
could be a limiting factor here with regard to the
redshift mechanism, and a wavelength of 21 cm is
presumably still significantly shorter than the average
particle distance in the intergalactic plasma.

I figure the width (in terms of frequency, for instance)
of these 21cm absorption lines is probably 1,000 to 100,000
times narrower than their frequency, so I figure the
coherence length of the signal which constitutes such a line
(emission or absorption) must have a coherence length 100 to
100,000 times 21 cm.

I don't understand the paragraph "Another possibility ...".

The temperature of the corona can simply be explained
in terms of the gravitational energy of the sun. What
needs to be explained is the lowered temperature of the
photosphere, . . .

Maybe there is an explanation for temperature rise as cold
particles fall towards the Sun, but that is not what is
occurring.

Can you formulate your theory in terms of the experience of
particles at the photosphere? I see no problem in
explaining why the photosphere is at its current temperature.
Can you explain why a small proportion of these atoms, H2
molecules, He etc. atoms and ions are lifted up, against the
Sun's gravity, and heated to a million k and beyond, all the
while being lifted faster and faster? The lifting continues
out to Pluto and beyond, even though the temperature of the
particles drops considerably by then. Heavier ions are
accelerated faster than light ions and electrons:

http://astroneu.com/plasma-redshift-1/#Cranmer

My plasma redshift theory, such as it is, does explain this
once the inter-particle distance gets above the approximate
coherence length of the main body of sunlight - which I
figure is just a few microns, since the ~0.5 micron centre
of the emission is so broad.

If I had more mathematical chops I would do a Fourier
transform of the blackbody spectrum of the Sun to produce a
short impulse signal which has the same spectrum. If we
arbitrarily cut off the spectrum to ignore wavelengths
longer than 2 microns, we have still got more than 95% of
the Sun's energy. An impulse such as:

*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*

should reproduce the spectrum, and I guess it is only
2 or 3 microns long. The length of this impulse is
what I also call the "coherence length" and it could
be thought of as the depth of a planar wavefront.

Robin Whittle wrote:
Thomas Smid suggested that a redshift of 0.01 could be
explained by "peculiar motion" of galaxies. 3,000 km/s is a
lot higher than a few figures I found Googling, such as 90
and 130 km/s from astro-ph/9705224 . I haven't looked at
how such figures are calculated. As far as I know, it would
take a major revision of conventional theories to arrive at
galaxy motions approaching 1% the speed of light.


There is an unarguable instance in the Perseus galaxy cluster.
The cluster has a redshift of about cz=5000 km/s. Partially
silhouetted in frontof the active central galaxy NGC 1275 is
a gas-rich galaxy (I can just about convince myself I see a
disorganized spiral pattern) complete with dust lanes, star
clusters, and cold gas. It appears in absorption against NGC 1275
in the optical (dust lanes), soft X-rays, and 21-cm H I absorption.
The demonstrably foreground object has cz=8000 km/s (frommemory, not
too exact). It's just possible for it to have picked up that
much peculiar velocity from a 3-sigma set of encounters with
other cluster members, but whatever, the cause, the peculiar
velocity component is there.

Bill Keel

Robin Whittle wrote:
Thomas Smid suggested that a redshift of 0.01 could be
explained by "peculiar motion" of galaxies. 3,000 km/s is a
lot higher than a few figures I found Googling, such as 90
and 130 km/s from astro-ph/9705224 . I haven't looked at
how such figures are calculated. As far as I know, it would
take a major revision of conventional theories to arrive at
galaxy motions approaching 1% the speed of light.

According to http://www.seds.org/messier/more/virgo_gal.html , there
are galaxies which deviate from the 'Hubble flow' by almost 2000
km/sec. That's more than one of the galaxies considered in the paper
Jonathan referenced above.


I don't understand the paragraph "Another possibility ...".

What I meant here is that the observed redshift of individual galaxies
might also to a certain degree be intrinsic due to a large scale steady
state electric field (plasma polarization field) being produced by a
plasma halo surrounding the galaxy (analogous to the effect I suggested
on my page http://www.plasmaphysics.org.uk/research/lensing.htm in
order to explain the redshift and bending of light by the sun). The
scale of this field would be the same as the size of the galaxy itself
and thus the coherency would not be an issue here (in contrast to the
random field of the intergalactic plasma which merely has a scale of 1m
or so).



Thomas Smid wrote:

Secondly, the lines considered are absorption lines. The
light being observed is actually that of the quasar lying
behind the galaxy, and it is anybody's guess what the
coherency of this light in either wavelength region is.

This raises a difficult and unconventional question about
light - but it they must be faced when considering a
mechanism which depends on "coherence length". In this
context, I use "coherence length" to refer to the thickness
(length in the direction of travel) of a planar wavefront
of a single impulse, if we consider that the total light
signal can be considered as being composed of many such
wavefronts.

I think the best approach is to consider the total light
signal as the sum of a variety of signals. Short coherence-
length light can be thought of as many short wavefronts -
because one could generate a very short impulse with the
right shape to create the observed spectrum, and then create
something identical to the original light by launching many
such short impulse wavefronts with random phases. Then, we
could analyse the behaviour of the light by considering just
one such short impulse (unless there were non-linear
processes at work).

This model of light, emr etc. as being made of myriads of
short coherence length wavefronts, would apply to black body
light or broadband synchrotron light etc. from a quasar.

An emission line is clearly an additional signal, of longer
coherence length. The tricky question is how to think about
an absorption line. I think it is best to consider it as
a long coherence length signal (long wavefront like a sine
wave which rises and falls over hundreds or thousands of
sine wave cycles) which is generated by the narrow filter
(band reject in this instance) as the filter is stimulated
by each of the short coherence length input signals.

The sum of this signal and the input signals has the
spectrum we expect - the signal which constitutes the
absorption line is out of phase with the components of the
input signal only at those frequencies which are being
rejected.

I think this is a more satisfactory approach than trying
to imagine the final filtered signal as consisting of
highly coherent components near the edges of the absorption
line. The original light had no such coherency, so how
could a band reject filter alter the light in neighbouring
frequencies so that they were more coherent?

On this basis, I expect the broad spectrum of black body,
or quasar, light to be redshifted in the plasma, as long as
the coherence length is less than the inter-particle
spacing, and the long coherence length absorption (or
emission) lines should not be redshifted much or at all.
I regret I can't describe this more mathematically.


. . . both the coherence length and/or the wavelength
could be a limiting factor here with regard to the
redshift mechanism, and a wavelength of 21 cm is
presumably still significantly shorter than the average
particle distance in the intergalactic plasma.

I figure the width (in terms of frequency, for instance)
of these 21cm absorption lines is probably 1,000 to 100,000
times narrower than their frequency, so I figure the
coherence length of the signal which constitutes such a line
(emission or absorption) must have a coherence length 100 to
100,000 times 21 cm.
........
.........


My plasma redshift theory, such as it is, does explain this
once the inter-particle distance gets above the approximate
coherence length of the main body of sunlight - which I
figure is just a few microns, since the ~0.5 micron centre
of the emission is so broad.

If I had more mathematical chops I would do a Fourier
transform of the blackbody spectrum of the Sun to produce a
short impulse signal which has the same spectrum. If we
arbitrarily cut off the spectrum to ignore wavelengths
longer than 2 microns, we have still got more than 95% of
the Sun's energy. An impulse such as:

*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*

should reproduce the spectrum, and I guess it is only
2 or 3 microns long. The length of this impulse is
what I also call the "coherence length" and it could
be thought of as the depth of a planar wavefront.

You seem to assume that the overall width of a spectrum is always a
measure of the coherency of the radiation. This is in fact usually not
so. The continuum of the stars is not produced by a single wave-train
with a very short duration, but by long wave-trains which merely have
different frequencies: if a free electron recombines into a certain
atomic level, it produces a sharp line according to the difference of
the energy of the free electron and the atomic level, and it is only
the fact that the free electron energies are distributed continuously
over a rather wide range which lead to the apparent continuum. You
should consider the latter therefore rather as a blend of a large
number of sharp lines (which are actually even more coherent than
spectral lines arising from discrete transitions within the atom).
Essentially the same can be said when discrete atomic levels are
broadened by the plasma field fluctuations (Stark broadening) for
instance: also here the broadening does not imply a reduction of the
coherency, but you should consider it merely as a widening of the range
of frequencies possible for a transition. Neither of course does
Doppler broadening imply a change in coherency.

Although essentially the radiation in the apparent continuum is
therefore at least as coherent as line radiation, the point is that
during the emission the atoms undergo collisions with free electrons in
the plasma, and the associated phase jumps during the emission reduce,
according to my estimate, the coherence time to about 10^-12 sec in the
photosphere (for visible light) which translates into a coherence
length of about 10^-2 cm.

So you really can not tell anything about the coherency of a radiation
field just by looking at the width of the spectrum. The coherency of
the spectrum at a given frequency (as defined by the effective length
of the wavetrains at this frequency) is solely determined by the
physics in the emission region i.e. a) the intrinsic decay constants
for the atomic transitions and b) the collision frequencies.

Anyway, a coherence length of about 1 micron, as you suggested, would
mean that the coherence length is about the same as the wavelength. I
doubt actually that this kind of radiation would still be detectable.


The temperature of the corona can simply be explained
in terms of the gravitational energy of the sun. What
needs to be explained is the lowered temperature of the
photosphere, . . .

Maybe there is an explanation for temperature rise as cold
particles fall towards the Sun, but that is not what is
occurring.

Can you formulate your theory in terms of the experience of
particles at the photosphere? I see no problem in
explaining why the photosphere is at its current temperature.
Can you explain why a small proportion of these atoms, H2
molecules, He etc. atoms and ions are lifted up, against the
Sun's gravity, and heated to a million k and beyond, all the
while being lifted faster and faster? The lifting continues
out to Pluto and beyond, even though the temperature of the
particles drops considerably by then. Heavier ions are
accelerated faster than light ions and electrons:

The photospheric temperature is irrelevant for the corona and the solar
wind. The latter arise from material that penetrates *through* the
photosphere from the region below (which has a temperature of 10^7 K
according to the gravitational energy of the sun). Note that this only
a very small amount of material, which, according to the arguments on
my page http://www.plasmaphysics.org.uk/research/sun.htm , is just a
fraction 10^-15 or less of what would escape without the presence of
the photosphere (which would actually potentially be a factor 1/e of
all the material, as this the fraction of particles with an energy
higher than the escape energy in a self-gravitating volume of gas).

You could probably compare the situation to the case of lava on the
earth's surface. You don't invoke fancy theories like magnetic
reconnection here either in order to explain the appearance of material
with a temperature of 1500 K in an environment having only a
temperature of 300 K. As everybody knows, the lava comes through cracks
from a region with a higher temperature below the earth's crust, and
this is essentially also what happens on the sun, with the only
difference that the photosphere is overall 'porous' to the high energy
particles from below.

Thomas

Thanks Bill for pointing out this apparently foreground
object having a redshift about 0.01 higher than a background
object:

http://www.astr.ua.edu/keel/agn/ngc1275hst.html
http://antwrp.gsfc.nasa.gov/apod/ap030505.html

I can't imagine an explanation other than the two objects
moving towards each other at 0.01 the speed of light.

Thanks too for your extensive site!

In a message I wrote in the thread "Plasma Theory of
Galactic Redshifts and 'Gravitational Lensing' of Light" I
cite three papers by David G. Russell which argue for higher
redshift differences between members of the same cluster.
However, he argues these are not due, primarily, to velocity
differences but to some kind of intrinsic redshift mechanism.

Thanks Thomas for your response.

I can't imagine how a very large scale electric field could
develop between a galaxy and its surrounding plasma, or how
such a field could redshift light.

You wrote:

You seem to assume that the overall width of a spectrum is
always a measure of the coherency of the radiation.

Yes. I think of light like radio waves and signals in
audio and RF circuits. I do not think of it as "photons" -
I think the radiation is not quantized, but it seems that
its interaction with matter often, or always, is.

If I had electronic circuits small enough and fast enough I
could generate a perfect facsimile of the Sun's black-body
radiation by sending a randomly phased series of impulses to
a small antenna. The impulse would look something like I
sketched in my previous message. Each such impulse would
have the spectrum of the black body light. A single such
impulse of sufficient energy would deposit energy in lots of
"photons" distributed over the detector of a spectrograph
with the same statistics as the black body light from the
Sun. I argue that since I can make light which is
indistinguishable from that of the Sun (not counting
absorption lines etc.) out of a bunch of tiny impulses, and
that since we can predict many aspects of the behaviour of
the entire stream of impulses by thinking about just one
impulse, that it is valid to think of the light being made
up of such impulses. I know this may seem a little forced,
but it makes no sense to me what you suggest:

The continuum of the stars is not produced by a single
wave-train with a very short duration, but by long
wave-trains which merely have different frequencies: if a
free electron recombines into a certain atomic level, it
produces a sharp line according to the difference of the
energy of the free electron and the atomic level, and it
is only the fact that the free electron energies are
distributed continuously over a rather wide range which
lead to the apparent continuum.

I don't believe that the maelstrom of atoms, ions and
electrons at the photosphere, or the vibrations in a hot
filament, can usefully be seen in terms of neat transitions
between clearly defined quantum energies of atoms. It looks
to me like a vast number of antennae all of which are
radiating in "random" ways, according to some common
conditions.

Theoretically I think you could make black body light with
an infinitely (or near infinitely) large number of narrow
transmitters as you suggest - but this seems less physically
satisfying to me than the idea of lots of tiny impulses.

. . . broadening does not imply a reduction of the
coherency.

An eternal sine wave is infinitely coherent. Any random
or regular modulation of its amplitude or frequency produces
a broader spectrum which is inherently less coherent. I
don't think one has to consider how the signal was made -
just see it as an electrical signal in space and subject
it to spectrum analysis, electronically, with a prism or via
some other method such as a diffraction grating or an attempt
to detect it with a narrow filter such as an atom or
molecule which is ready to absorb this particular wavelength.

. . . during the emission the atoms undergo collisions
with free electrons in the plasma, and the associated
phase jumps during the emission reduce, according to my
estimate, the coherence time to about 10^-12 sec in the
photosphere (for visible light) which translates into a
coherence length of about 10^-2 cm.

So you really can not tell anything about the coherency of
a radiation field just by looking at the width of the
spectrum.

I completely disagree. I have already tried to explain why
I estimate the coherence length of black body sunlight is
just a few microns. I don't think it is necessary to
consider how the light is made. The spectrum alone tells us
how coherent it is.

If I get some random noise - white noise, which is
completely random values per sample (in a sampled digital
signal processing system) - this has no coherence at all.
Its coherence length is zero. If I filter it to give it
a spectrum identical to a black body spectrum, I introduce
some correlation between the value of one sample the values
of the samples which precede it. This gives it some
coherency - probably a few samples long, depending on
exactly how "coherence length" is defined.

If I then take this sample and pass it through a band-reject
filter, say one which only reduces frequencies in a range
of 0.0001 of the entire frequency range, as happens when
black body light passes through a gas or plasma which absorbs
narrow lines, then the result can be seen as the original
unfiltered signal plus a second, very narrow spectrum,
highly coherent, signal. That second signal nulls out the
energy which was in the original signal only in a very
narrow range of frequencies. A similar narrow (long
coherence length) signal is added if I use a narrow band
pass filter - its just that its phase constructively adds
to a narrow range of frequencies in the original.


The photospheric temperature is irrelevant for the corona
and the solar wind. The latter arise from material that
penetrates *through* the photosphere from the region below
(which has a temperature of 10^7 K according to the
gravitational energy of the sun).

OK - I understand you see the photosphere as a kind of
barrier with a few particles passing through it, carrying
their thermal and kinetic energy. I had assumed you were
invoking your plasma redshift theory to account for the
heating and acceleration of the corona and wind.

I can't imagine how this penetration of the photosphere
could occur, and I can't see how any such process could
explain the rising temperature gradient, the thinning plasma
and the increasing velocity well into the corona. Nor do I
see how your theory could explain delivery of momentum to
ions etc. in the wind, way out past the Earth's orbit. I
understand they are still being accelerated all through the
distances we have so far been able to observe, such as with
the Pioneer spacecraft.

With volcanoes, we observe the lava getting cooler and
slowing down with gravity as it emerges. Completely the
opposite occurs with the solar corona and wind.

- Robin http://astroneu.com

Robin Whittle wrote:

I can't imagine how a very large scale electric field could
develop between a galaxy and its surrounding plasma, or how
such a field could redshift light.

The point is that electrons tend to escape from any plasma volume due
to the fact that a) they have a much higher velocity than ions of the
same energy (due to their much smaller mass) and b) they are
gravitationally practically unbound. Electrons will therefore diffuse
to larger distances or some will escape altogether until an electric
field (plasma polarization field) is set up such that further electrons
will be prevented from escaping (or strictly speaking until the field
results in a zero net electron current).
The redshift mechanism would essentially be the same as for the
intergalactic plasma i.e. the field would 'stretch' the light wave. The
point is that the galactic halo field would be a steady field with a
much larger scale than the random field of the intergalactic plasma,
and thus the coherence length or wavelength would not present any
threshold.



You wrote:

You seem to assume that the overall width of a spectrum is
always a measure of the coherency of the radiation.

Yes. I think of light like radio waves and signals in
audio and RF circuits. I do not think of it as "photons" -
I think the radiation is not quantized, but it seems that
its interaction with matter often, or always, is.

.......

An eternal sine wave is infinitely coherent. Any random
or regular modulation of its amplitude or frequency produces
a broader spectrum which is inherently less coherent. I
don't think one has to consider how the signal was made -
just see it as an electrical signal in space and subject
it to spectrum analysis, electronically, with a prism or via
some other method such as a diffraction grating or an attempt
to detect it with a narrow filter such as an atom or
molecule which is ready to absorb this particular wavelength.

I don't think is correct (not in this context anyway):
the Fourier theorem (which you are apparently applying here) assumes
actually that all the frequencies in the spectrum are waves which not
only extend from -infinity to +infinity in time, but also are all
locked in phase: I am sure you know for instance that the frequency
spectrum of a rectangular pulse of duration T is given by the
sinc-function sin(f*T/2)/(f*T/2) where f is the frequency. The
pulse is exactly reconstructed if you superpose waves (ranging
continuously in frequency from -infinity to +infinity) with this
amplitude, but this is obviously only possible if all the sub-waves
belonging to the individual frequencies f are locked in phase somehow.
If the phases of the waves are however randomly uncorrelated, they
could never produce the constructive and destructice interference
required to reconstitute the rectangular pulse.
The point here is that for all natural light sources the phases of the
individual waves *are* randomly uncorrelated as they originate from
statistically independent atomic emissions.
So the Fourier theorem can not be applied here to obtain the coherence
length of the signal from the shape of the spectrum. The coherence
length must be physically determined by the atomic decay times and/or
collision times that are relevant for the radiation produced.

Thomas