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Doppler Debacle

The Doppler effect is not applied correctly resulting in every galaxy and quasar having the wrong velocity.
One definition of debacle is: a sudden and ignominious failure; a fiasco.
The Doppler effect is very simple and yet it is universally (pun intended) misunderstood  by astronomers.

The Doppler effect:
At the moment the electromagnetic radiation is generated by the source, the radiation propagates like an expanding sphere and is measured as a spectrum. This spectrum is a continuum of wavelengths with each directly related to a proportional amount of energy by its measurement as a frequency.

The motion of the light source will shift this spectrum at that moment based on the direction of propagation.

There are only 2 simple equations involved.
1) calculating z,
2) calculating the wavelength change in this continuum caused by this factor called z.

The background for the 2 equations:

The spectrum being emitted by the radiation source in the direction of travel has its wavelengths reduced or toward the blue end of the spectrum; this is called a blue shift.

The spectrum being emitted by the source in the direction opposite of travel has its wavelengths increased or toward the red end of the spectrum; this is called a redshift.

The light source radiates this continuum in all directions so so this wavelength shifting occurs around the entire initial sphere. In the direction exactly in line with the motion there is the maximum increase in energy, or reduced wavelength, while in the opposite direction there is the maximum decrease in energy or increased wavelength.

Around the sphere of radiation, there is the corresponding continuum of the changes in z including its polarity based on that direction relative to the light source direction of travel.
The total energy emitted is maintained for the sphere, just its distribution is not uniform. The change in wavelength in one direction is exactly matched to the change in the opposite direction. Energy is conserved.

The equations:

1) The velocity, called v here, of the source is compared to the velocity of light by dividing that v value by the velocity of light, called the constant c.
The result is called z by convention (defined by astronomers long ago).

The simple equation is  z=v/c, making sure the units are the same (usually km/s).

2) The shift in a spectrum due to the motion of the light source is a simple equation,
where EWL is the emission wavelength,
NWL is the new wavelength, and:
NWL = EWL + ( EWL multiplied by  z)

where the z is the factor for the change in the new wavelength from that originally emitted. Where z is positive a red shift results (because NWL increased, while where z is negative a blue shift results (because NWL decreased).

The combination around the sphere of radiation  conforms to the principle of conservation of energy as there is no change in energy (from the light source to the entire sphere of radiation) from the object.

The same occurs with an atom or molecule absorbing its characteristic wavelength for the atom to change its internal energy state by electrons changing orbitals.
The difference with an absorption line shift is the wavelength is absorbed or missing only when the energy required for the state change is present in the energy continuum.
When the atom is moving the energy being absorbed is affected by the same amount as shown in the above equation, causing an absorption line shift.

Note: The spectrum of M31 exhibits this behavior in a blue shifted calcium absorption line from a negative z value.

When observing the spectrum of multiple light sources the interpretation of the continuum is different.

A gas of atoms is not a cohesive light source (because it has no surface for its radiation) so a capture of light from some or all of its atoms will not exhibit a redshift by the Doppler effect. In a gas, each atom is an individual light source whose motion will affect its individual sphere of radiation (and its spectrum) as described. Each atom's generated spectrum is only the atom's emission line from its change to a lower energy state.
The observed spectrum from a gas is the summation of all the individual atoms in the field of view.

If all the atoms were moving in the identical direction relative to the observer then that emission line would accumulate in intensity.
However with random motion, a spread of emission lines would be observed centered on the characteristic wavelength, because some atoms are in one direction and others are in the opposite direction.

A galaxy presents the similar scenario as the gas of atoms but with stars.

Unlike a star having a surface, a galaxy is not a cohesive light source but consists of many stars.
The spectrum of a galaxy depends on the observer's line of sight so it is not intrinsic to the galaxy.

The galaxy spectrum is just the summation of light from all its stars in the observer's field of view. Each individual star will exhibit the Doppler Effect in only its light when the star is moving.
The galaxy is NOT a single object radiating energy in a sphere as described above with the cohesive light sources.
To monitor a spiral galaxy rotation, narrow slices across the arms have spectra taken around the hydrogen emission line frequency. In these spectra, red and blue shifts indicate relative velocities of these atoms in the hydrogen gas clouds in the arms. One side of the galaxy will have red shifts while the other side will have blue shifts.

Perhaps an analysis of this data would reveal an overall tendency. It is difficult to find such research if published.

If the M31 galaxy velocity analysis disagreed with the accepted velocity of -301 km/s there are 2 choices:

1) this result becomes the new M31 velocity so the Cepheid calculation gave the wrong result, or

2) this conflicting result is ignored so it is impossible to find this result unless one knows where to find it.

For all galaxies:

When a velocity is published, the spectrum shift used is rarely identified (like which element). This lack of galaxy data was described in a February 8 post.

When a distance is published the method used is never identified (like a) which Cepheid, or b) which velocity value with which Hubble constant value.

A spiral galaxy has rotating disk arms with dust clouds among the stars; neither the stars nor clouds have a consistent distribution in the arms.
The measured spectrum of a galaxy will vary from:

a) the particular field of view (in other words, those stars within a specific 'piece' of the sky) with closer stars hiding the further stars,

b) directly above, sometimes called face on,

c) directly on edge to the galactic disk where many stars are obscured by dust in the field of view,

d) directly in line with the apparent axis of an elliptical galaxy which can be somewhat flattened, but viewing at just the correct  angle the elliptical galaxy becomes a sphere.
e) any other angle which gets that particular collection of stars in the spectrum,

f) line of sight through variations in the IGM, causing differences in absorption lines from those intervening atoms.

Unlike the other items in the list of candidates, a galaxy (or quasar) spectrum depends on the observer's location relative to the galaxy so the collection of stars (and dust) being summed in the spectrum will vary.

Neither a galaxy nor a quasar has an intrinsic radiation pattern.

That radiation propagates, some of it toward the observer, passing through space where intervening atoms can reside. An atom in this path can cause an absorption line (described above) in the object's observed spectrum.

The current practice by astronomers is using an absorption line shift for a galaxy's velocity, or the hydrogen emission line shift for a quasar's velocity.

This is simply the wrong use of the Doppler effect. The intervening atom's velocity is not necessarily the same as the galaxy or quasar. The light source is a summation, separate from the IGM.

From the observational history, the hydrogen absorption line appears to have its redshift affected by the density of hydrogen atoms in the line of sight. Regardless of the mechanism in the IGM, the absorption line does not apply to the object generating the radiation.

The result is velocities vary by their direction from Earth because the IGM is not uniform. At the time of writing this, the highest galaxy z is 11.09 and the highest quasar z is 7.54.
The galaxy z is determined by an absorption line never identified. If it is hydrogen, then the z is affected by hydrogen atoms in the IGM.

The M31 galaxy redshift is -301 km/s from the calcium absorption line so the calcium atom in the IGM has that velocity and direction.

When considering these values as distances in the universe but in a practical human time frame (one year), they are not as extreme as initially perceived.

At the M31 rate of -301 km/s, the atom is moving 1E-3 ly or 0.001 ly per year.
The distance to M31 via Cepheids is 2.54 E+6 ly or 2.54 Mly

At the GN-z11 rate of z=11.09, the atom is moving 11.09 ly per year.
The distance to GN-z11 as astronomers (via Wikipedia) call a 'light travel distance' is 13.39Gly.

It is reasonable to call either motion by an atom as 'barely visible' for annual observations.

A transverse velocity of anything requires many observations to record changes in a distant separation between objects to calculate that velocity.
The calculation of its motion requires the known distance of the object for the 'sine function' with the angular change in position.

Trivia:
Among the galaxies in the Messier list, M100 has the highest (atom) velocity at 10195 km/s, or a rate of 357 ly per year, with M100 assumed to be at 55 Mly.

This long post is a somewhat condensed version of a longer 26 page pdf.
If anyone is curious about more detail, a web search for "Clarifying Redshifts" should find that pdf in my web site archive.

Conclusion:

Astronomers incorrectly use absorption lines for galaxy velocities. This is the wrong application of the Doppler effect,

A galaxy has no surface emitting light but is a multitude of stars. The observed spectrum depends on both the line of sight and which stars are in the field of view for that measurement.

The Gaia probe measured spectra for a billion objects and its data accumulation continues. Most of these objects are in the Milky Way or near, like its globular clusters and Magellanic Clouds.
Other galaxies have billions of stars while at a greater distance.  I expect it unlikely with our current imaging capabilities to collect and analyze another galaxy's stars with this precision.

In the meantime, a galaxy's absorption line is used resulting in a wrong velocity.

The Hubble Constant, cosmological redshift, expanding fabric of space, and dark energy are based on the presence and motions of atoms, not on the motions of galaxies and quasars.

I consider this situation a debacle.

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