Why does the peak of quasar distribution move from near to far with increasing magnitude?

[mikehelland]

I made a little tool to examine the distribution of quasars in various catalogs, including SDSS DR16Q:

https://mikehelland.github.io/hubbles-law/other/sdss.htm

If you check the +/- box, and move the magnitude slider from low (-20) to high (-30), the peak of the quasars moves from z=0 to about z=3.3.

Here's the results summarized:

One obvious factor is that the quasars on the dimmer end won't show up at high-z, simply because they're too dim. And very bright quasars ceased to exist recently.

But can that really explain this picture?

Is there something else going on? Seems odd the peak would move so linearly with magnitude.

[mikehelland]

GN-z11 has an estimated absolute magnitude of -22.1.

https://iopscience.iop.org/article/1...637X/819/2/129

If we can see galaxies of that magnitude at z=11... surely quasars of that magnitude should be detectable as well?

But the population of quasars of that magnitude doesn't exist at z > 1.6.

Here is what I suspect.

1. K-corrections

The K-corrections used are from 2006. Richards, et al:

https://ui.adsabs.harvard.edu/abs/2006AJ....131.2766R/abstract

Page 45:

This is where things get really weird. The DR16 paper says this:

2. (DR12Q) Absolute i-band magnitudes were incorrectly calculated. K-corrections were only done to the continuum and did not include emission line corrections. Additionally it appears the set cosmology parameters used was not either of the two sets published in the paper.

https://ui.adsabs.harvard.edu/abs/2020ApJS..250....8L/abstract

Since the Richards table includes both emission line and continuum, and it's the same table used for all the data releases, how is that even possible? They would have had to explicitly remove the emission lines. Here is the code to generate DR16Q:

https://github.com/bradlyke/dr16q/blob/master/abs_mag.py

But there really is no way they would have only applied the continuum and not the emission lines. Unless the continuum was applied further up the pipeline in DR12. Which means there's a possibility "fixing" it in DR16, by applying the K-corrections, double dips the continuum. This might explain why low-z get assign dimmer magnitudes and high-z are calculated to be brighter.

That's assuming the almost 20 year old table is even accurate.

2. Cosmological parameters

The bug report for DR12 also says the wrong parameters were used, and that's fixed, but they don't say what the old parameters were.

Line 125 is this:

h0 = 67.6 #Hubble constant at current time in km/s/Mpc

Here they are using the CMB (z~1100) measurement of Hubble's constant, 67.6, and applying this to the 0 < z < 5. Wouldn't it make more sense to use the value of Hubble's constant measured by supernovae in that range?

That's a small thing. But on top of the K-corrections, it forces magnitudes to be a little brighter than they should be too.

3. False readings

Another suspicion is that the brighter than -25 quasars are false readings. These videos explain that some of the brightest, when examined, are actually:

• double quasars
• a quasar with intermingled starlight
• gravitationally lensed

https://youtu.be/FCLv6W-D5hY?si=w-eBHo-70FXN2qkv&t=410
https://www.youtube.com/watch?v=pJ08d6vIcAw

When we examine individual quasars closely... they turn out to be more than quasars.

Aside: z > 5

Line 142 of that code has this.

rfile['Z_PCA']>5.0

Basically since this 2006 table only goes up to z ~ 5, anything z > 5 is simply omitted from the dataset. Does anyone know that's actually there? It doesn't seem to be disclosed anywhere. It took me actually contacting SDSS to find the code for this. It took even them a few days to find the GitHub repo.

[mikehelland]

Does anyone have a guess as to why quasars of absolute magnitude -22 don't exist in the early universe?

[mikehelland]

Using the DESI survey, and applying my bins (which represent equal volumes in non-expanding space) it seems the bright galaxy survey objects (BGS) jumps up exactly where the quasars fall off. This is at z=1.6, the alleged angular diameter turnaround.

Maybe that has something to do with it.

[ExpEarth]

Mike, your graphs and tools are not clearly enough explained, at least for me. An intro might have helped. There are questions throughout.

[mikehelland]

The x-axis are redshifts (z) and y-axis is quasar counts.

So in this graph for example:

There are about 12,000 quasars between z=0 and z=0.2.

[ExpEarth]

You mentioned that you are assuming non-expansion, but how are the quasar magnitudes in these charts estimated? Do they use the Big Bang assumption that surface brightness is weakened by (1 + z)^-4 ? I don't see how you can have a good analysis on this until you use a static model recalibration of these magnitudes.

[mikehelland]

For SDSS DR16Q, there is an absolute I band magnitude in the dataset:

M_I Absolute i-band magnitude, H0 = 67.6 km s-1 Mpc-1, ΩM = 0.31, ΩL = 0.69,
ΩR = 9.11x10-5. K-corrections taken from Table 4 of Richards et al. (2006). Z_PCA used for redshifts

https://data.sdss.org/datamodel/files/BOSS_QSO/DR16Q/DR16Q_v4.html

You can see specifically how it's done at the link in my first reply:

https://github.com/bradlyke/dr16q/blob/master/abs_mag.py

#Find the absolute magnitude given the previously calculated values and data
#taken from the fits file.
def abs_Mag(imag,ext,dm,kc):
    #imag is the apparent i-band magnitude, ext is i-band galactic extinction
    #dm is distance modulus from dist_mod(), and kc is k correction from kcorr_find().
    return imag - ext - dm - kc #unitless

My tool also has a select box, which allows you to use the data given, or for $H_0 = 73$, which I produced with cosmolopy, and z to find a luminosity distance, or for my non-expanding model $H = 70.5$ (no subscript zero in this model), also using luminosity distance, but this time from my model (not LCDM).

As I note, I think it might be these estimations (along with K-corrections) that give the magnitudes that show the moving peaks.

If you have any more questions, or if I did not address those well enough, let me know. Thanks.

[ExpEarth]

I can't easily navigate your panels and some of them don't display well. However, assuming everything is fine with your data, I think your basic question can be answered using the idea of an intrinsic quasar redshift which scales with the magnitude. A model which illustrates this possibility was given by Hansen:

https://arxiv.org/abs/1506.08784

The idea of an intrinsic quasar redshift was proposed much earlier by Arp and others, to account for the high redshift quasar being attached to a lower redshift galaxy. A number of mechanisms have been proposed for the quasar intrinsic redshift. Hansen attributes the redshift to an effect of light moving through a dense plasma. While his mechanism might not be correct, there are several important aspects of it which relate to your question.

First, the idea that the intrinsic quasar redshift is a plasma effect is compatible with a redshift which scales with quasar magnitude: more plasma = more redshift. Images of nearby supermassive black holes (or AGNs) show them to be essentially rings of plasma and so quasar phenomena associated with such AGNs would be related to their size.

Secondly, when more than one redshift is present, you can't just add the redshifts together. Instead, you have to multiply them, as in Eq. 3 of Hansen's paper. (This was emphasized by Arp also.) Thus, if we write the combined redshift as z3, the Hubble redshift as z1 and the intrinsic quasar redshift as z2, the corrected redshift is:

(1 + z3) = (1 + z1) (1 + z2) , which gives

z3 = z1 + z2 + z1z2

Now in Fig. 4 of Hansen's paper, he shows the intrinsic quasar redshifts ranging from roughly 0.1 to 1. Let's calculate the combined redshift for a .1 redshift quasar and a 1.0 redshift quasar for two separate Hubble redshifts, 0 and 1.

For the quasar type with z2 = .1 and z1 = 0 we have the combined redshift z3 = 0 + .1 + 0 = .1 For the same quasar type at z1 = 1, we have a combined redshift z3 = 1 + .1 + .1 = 1.2. The peak will have shifted just a slight amount from the point where we just added the redshifts.

The situation changes markedly for the quasar type with z2 = 1.0. For these quasars, if z1 = 0, we have z3 = 0 + 1 + 0 = 1. If z1 = 1, we have z3 = 1 + 1 + 1 = 3 !

To sum up, the low magnitude quasars for a Hubble redshift range of 0-1.0 are shifted to a range of .1-1.2. This is just a small change. But the high magnitude quasars will have been shifted to a range of 1-3, a large change.

You mentioned that bright quasars stopped existing recently. From the above considerations, this might not be so. We don't see them at low redshift because the intrinsic redshift moves them out to a higher redshift. We would tend to see only the low magnitude quasars at very low redshifts.

[HanDeBruijn]

With Intrinsic Redshift as explained by the Variable Mass Theory the energy $E$ of spectral lines is directly proportional to variable mass $m$:

$$ \frac{E}{E_0} = \frac{m}{m_0} $$

Conclusions of my writings in the section Length Contraction consist of (1) a sentence and (2) a formula. (1) Length Contraction [of matter] is observationally equivalent with the Expansion of Empty Space, (2) Length $L$ (e.g. Bohr radius of an atom / wavelength of light $\lambda$) is inversely proportional to variable mass $m$:

$$ \frac{L}{L_0} = \frac{m_0}{m} = \frac{\lambda}{\lambda_0} = 1+z $$

If the quasar is a compact object then we have that the net brightness is the product of the energy $E$ emitted and an area $L^2$. The latter is proportional to the size squared of its atoms. The end-result would be the following proportionality, with intrinsic redshift according to the VMT only.

$$ \mbox{bright} \sim \frac{E}{E_0}\left(\frac{L}{L_0}\right)^2 = \frac{m_0}{m} = 1+z $$

Inspiration comes from the ideas of @ExpEarth as uttered above.
I have no clue if this result is indeed applicable to the features as described by @mikehelland .

[mikehelland]

Hi Matt,

So I think you are saying the redshifts are over-estimated? Which means the magnitudes must be over-estimated as well?

But they are still brighter than, say M87 at M = -22, just not all the way up to M = -28 or something like that?

[ExpEarth]

Yes, the magnitudes must also be over-estimated, since the actual distances of the sources are not as great as their redshift distances suggest. If the correction could be made, perhaps the spread of intrinsic luminosities of quasars would then not be so great. It's also important to know what assumptions are going into estimating the luminosities. The estimates would be different in static versus expanding models.

[RedshiftDrift]

Your little tool is wonderful @mikehelland ! There is a lot to unpack here. Some quick comments:

1. The Karlsson periodicity is clearly visible here, although with different coefficients for the formula:
   $$\log_{10}(1+z) \simeq 0.0875 n - 0.01$$

2. The exact value of the Hubble constant doesn't make much of a difference.

3. rfile['Z_PCA']>5.0 is actually mentioned in the paper... "The full sample consists only of quasars where $0 &lt; Z &lt; 5$..." (p. 11 in http://arxiv.org/abs/2007.09001).

4. K-corrections are too complex to track what they have done... However this should not cause a distortion as large as what you see.

5. It has been known for a long time that there are no quasars closer than $z \simeq 0.3$. This is explained with "evolution": quasars all died 10.3 Gyr after the Big Bang... getting fainter and fainter with time, as your plots show.

Seems odd the peak would move so linearly with magnitude.

By sheer coincidence, the evolution (according to the BB model) of a complex system such as a quasar happens to follow a simple function of the redshift. Another coincidence that shows the Big Bang model cannot be correct.

[HanDeBruijn]

In view of a previous reply: here is a numerical / graphical simulation of an (idealized) Einstein cross. It is assumed that observation by a telescope is imperfect, as modelled mathematically by a webpage called Fuzzy Optics.
The first picture displays the quasars "in reality". The second picture displays the quasars as "observed", the third picture is a contouring of the second one. It is clearly seen that artificial "luminous bridges" appear. So it seems to me too that these are questionable.

     

[budrap00]

Hi Han,

It seems to me that this argument offers no basis for deciding the issue; the conclusion that the luminous bridges are artificial is entirely dependent on the assumption that the quasars are at their redshift distances. If you assume that the quasars are co-located with the central galaxy then the bridges are not artificial.

[HanDeBruijn]

Hi Bud,

With (our version of) the VMT it is not assumed that the quasars are at their redshift distances.

[RedshiftDrift]

The luminous bridge between NGC 4319 and Markarian 205 is a filament coming out of NGC 4319. It can even be seen on the more modern image of the galaxy if the contrast is increased dramatically (below is shown the wiki photo I rotated and contrast-enhanced). There are many such filaments around galaxies.

If another galaxy happens to be behind and lined-up with a filament, its redshift is enhanced by a tired-light effect caused by the gas in the filament. That's why "quasars" are always redshifted relative to their "putative parent" galaxy and appear to be "connected" with the galaxy.

It's an illusion, they are not physically connected to the filament, they are just behind it from our point of view. Moreover, quasars do not have an "extremely high intrinsic luminosity". The quasar is bright because it is a lot closer than the distance incorrectly inferred (using Hubble law) from their redshift.

[budrap00]

I don't see any conclusive evidence for either the near or far interpretation. The argument that there is a non-velocity component of redshift is more supportive of the close-by position but it is also inconclusive since the actual distance to the quasar would have to be known independent of redshift or there would need be a way of directly differentiating intrinsic from cosmological redshift.

That said, Arp's evidence is far more robust than that one image. The repeated pattern of quasars aligned across a central galaxy and other associations can't all be waived off as chance alignment. Not all the associations in the catalogue are equally compelling but in the aggregate they comprise robust observational evidence for the proposition that quasars are not at their redshift-implied distance and represent an evolutionary stage of galaxy formation.

It is certainly fair to say this interpretation of observed associations and their galaxy formation implications are arguable but it is scientific malfeasance to ignore or dismiss a such significant body of empirical observations simply because they are disruptive to the presently favored consensus model.

In particular the fact that these observations of Arp and others can be assembled into a coherent qualitative picture of galaxy formation is a direct challenge to the standard account of galaxy formation by accretion. The accretion model has no comparable body of empirical observations to support it. A cosmology that studiously avoids empirical observations in favor of searching for hypothetical, invisible-by-definition, dark matter particles has no valid claim to being a science. The standard model of cosmology is simply a self-deluded nerd fantasy. It is a scientific disgrace.

[Francois-Zinserling]

@budrap00 some comments don't seem to add up.
Unless the proposal includes a new mechanism which is not observed elsewhere, and limited to quasars?

"A quasar can be thought of as the end product of a gravitational collapse."
I get that. A quasar might be a unique object or stage just before a star or even a galaxy collapses to produce a black hole.

The computation of redshift I don't get. It's counter-intuitive. Please explain if there are specific mechanisms at play here?

As that evolution proceeds, the total mass-energy of the quasar increases (via gravitational attraction/infall)

• yes

in proportion to the surface area which is growing

• surface grows, yes, but in proportion, no

as while the mass-energy density decreases because the volume is increasing as ,

• no, mass = density * volume. Has this changed?

which results in a diminishing intrinsic redshift.

• still no

If a collapsing object (e.g the proposed quasar) is already a GR object, then adding mass will not reduce the density, even if the added mass is very low density. Electron degeneracy has already set in, else it is nowhere near a GR object. So the new mass will not lie on the surface like a fluffy cloud. An increase in mass still results in an increase in redshift, not a diminishing redshift.

[HanDeBruijn]

@Francois-Zinserling , @budrap00 :

just before a star or even a galaxy collapses to produce a black hole.

Black Holes don't exist - the pictures of Sgr A* and M87*?

the total mass-energy of the quasar increases (via gravitational attraction/infall)

• yes

• no. It increases because matter becomes more aged (: VMT ) .

which results in a diminishing intrinsic redshift.

• still no

• yes

[budrap00]

@HanDeBruijn @Francois-Zinserling, The mechanism that prevents gravitational collapse is provided by the confluence of two known facts regarding the nature of physical reality:

1. The speed of light varies with position in a gravitational field; the stronger the field the slower the SOL. This is an empirically verified prediction of General Relativity.
2. $\frac {E}{m}=c^2$

It is an unavoidable consequence of those two facts that, in an increasing gravitational field strength, a unit of matter such as a proton will have to shed energy in accord with relationship 2. That in turn means that the proton is losing rest mass; in the aggregate this means that the gravitating body is losing rest mass and therefore the gravitational field cannot increase without limit because of this countervailing loss of mass. This precludes a one-way gravitational collapse to a "black hole". Gravitational collapse is self-limiting under basic GR physics. Since both 1 & 2 derive from GR, GR is a variable mass theory.

As a gravitationally collapsing body stabilizes through loss of mass it emits copious amounts of electromagnetic radiation. On a galactic scale such a stabilized body would resemble a quasar.

A quasar is a compact, luminous, gravitating body. As such its matter-energy content will increase through infall/gravitational attraction. Assuming the quasar to be approximately spherical and an average density IGM in its immediate vicinity, there will be a constant infall of new matter onto the sphere, increasing its radius and therefore its surface area as $r^2$ and its volume as $r^3$.

Because the quasar is gravitationally stable (not collapsing) the new matter is acquired at the surface which in turn increases the surface area. The total amount of matter arriving at the surface area is proportional to the surface area - the larger the surface area the greater the amount of matter collected there (assuming a constant IGM source). Since matter-density = matter/volume and the matter is increasing as $r^2$ with the surface area while the volume is increasing as $r^3$ there is a consequent reduction in matter density.

This reduction in matter density further contributes to the reduction of the gravitational field already reduced by the initial mass loss which had achieved a stable quasar. So the original collapse process, first stabilized by the required mass loss, is then reversed by the infall of new matter. The gravitational gradient is no longer increasing, it is decreasing and therefore the SOL is no longer decreasing but increasing back toward the theoretical inertial field maximum. This would also result in a decreasing gravitational (intrinsic) redshift.

Also consequent on the decreasing gradient, as per item 2, the original matter that had shed mass to stabilize the system begins to increase its mass by absorbing the infalling energy from the ambient electromagnetic radiation that permeates the Cosmos. This overall scenario fits with Arp's observations and the general picture that galaxies are self-replicating phenomena. This model contains no metaphysical or mathematical assumptions that lie outside the bounds of known physics.

[budrap00]

Hi Han, I received this message in the email thread for this topic but it is not on the GitHub thread. Did you delete it or???

[HanDeBruijn]

Yes Bud, I deleted it. It was a rather thoughtless reply. Han

[mikehelland]

Which argument in particular? Photons should lose energy climbing out of a gravitational well. Gravitational redshift has been measured for stars near our galaxy's center:

https://www.aanda.org/articles/aa/abs/2018/07/aa33718-18/aa33718-18.html

[Francois-Zinserling]

Technical correction - photons in a gravity well are released with longer wavelengths, (or lower frequency) due to atoms in the well having slower clock speeds. (GR effect)

Coming out the gravity well, the photon does not lose energy, but depends on where you are measuring:

• if you measue at the source, frequency appears unaffected because your own clock is also slow
• if you measure 'out in space' your clock is faster (GR effect) and the measured clock appears to be slow.

It doesn't change your point though, but the photon has lower energy from the moment it is released in the well.

[ExpEarth]

It's from Bud's argument higher up. I transcribed his math symbols, which don't come through in quotes:

A quasar can be thought of as the end product of a gravitational collapse. The collapse stabilizes prior to the formation of a theoretical black hole and begins emitting copious amounts of electromagnetic radiation because the speed of light diminishes in an increasing gravitational field (an observed fact) and E = m/c^2. In other words because of two known facts of standard physics, gravitational collapse is self-limiting.

A quasar then is a highly compact gravitating body and consequently exhibits a GR gravitational (intrinsic) redshift as well a distance related cosmological redshift. Quasars evolve over an extended time period as viewed by an external observer (GR time dilation). As that evolution proceeds, the total mass-energy of the quasar increases (via gravitational attraction/infall) in proportion to the surface area which is growing as r^2 , while the mass-energy density decreases because the volume is increasing as r^3, which results in a diminishing intrinsic redshift. Quasars evolve over cosmological time scales into active galaxies which in turn produce new quasars. Quasars are nascent galaxies.

I don't see where it has been proved that masses shed rest mass as radiation when they enter a gravitational field. I also notice that Bud has the quasar rest mass decreasing due to this effect and then somehow increasing again. I don't get that part.

Photons should lose energy climbing out of a gravitational well. Gravitational redshift has been measured for stars near our galaxy's center

We had a long discussion in the old ACG with Doug Marrett about whether a photon actually loses energy climbing out of the well, or whether it is just a frame effect. I was the only one who actually thought it was losing energy. I wish we could get that thread transferred over to the new ACG.

P.S. Where's Doug?

[mikehelland]

The integrated Sachs-Wolfe effect says photons gain a bit of energy entering a gravitational well, and losing a bit leaving the well.

Although, if I'm reading it right, on Page 27 of @budrap00 's reference:

https://archive.org/details/halton-arp-catalogue-of-discordant-redshift-associations/page/27/mode/2up

Arp seems to be ruling out gravitational redshift and tired light as the intrinsic galaxy redshift.

[budrap00]

@ExpEarth

I don't see where it has been proved that masses shed rest mass as radiation when they enter a gravitational field.

I said nothing about "proof" which is a mathematical or logical concept. My argument is simply that since the varying SOL and $\frac {E}{m}=c^2$ are established scientific facts a loss of rest mass is necessitated under conditions where both facts are in play, or at least that is the most logical and obvious way of reconciling the two. It is entirely possible that the effect is observable under the right circumstances. To the best of my knowledge no effort has been made to test this idea and therefore the lack of "experimental evidence" cannot fairly be counted as evidence against the proposition.

@Francois-Zinserling
I agree with you that GR (not SR) time dilation accounts for gravitational redshift.

@mikehelland
Arp's argument doesn't seem convincing to me. If a galaxy with intrinsic redshift is undergoing an evolutionary process from quasar to "normal" AGN galaxy, the gravitational gradient of the galaxy should also be evolving from the quasar state toward the normal. Arp seems to assume that since the galaxy (intrinsically redshifted) has evolved some structure it should have the same gravitational gradient as a fully evolved galaxy.