Is Self Creation Cosmology a Viable Alternative to the Standard Model?

[SpaceTiger]

I will obviously have to start thinking about a theory of Super-Eddington accretion...

Even in the mainstream model, there have been observations that suggest a possible need for this and, I'll tell you now, it's not easy to get more than a factor of order unity above Eddington. The standard derivation of the Eddington luminosity assumes spherical symmetry, so it's not exactly applicable to accretion from a disk, but the geometrical correction factors are not large (and I'm not immediately sure which direction they go). There's a great deal of literature on this, so you might try a search.

 

[Garth]

The problem is a bit more complicated in the Jordan frame.

The calculation of the Eddington mass limit from the Eddington luminosity uses the observational relationship

$$\frac{L}{L_\odot} \sim (\frac{M}{M_\odot})^3$$

which cannot be depended upon when masses and G are varying cosmologically. Basically the luminosity created by the same stellar core will be less at earlier times because of the lesser atomic masses relative to the present day.

It is easier to calculate physical processes, such as nuclear luminosity, in the Einstein frame of the theory in which particle masses and G are constant. In which case the Eddington luminosity and mass limit are the same as in the mainstream theory. It is the way that gravitational orbits varies over cosmological time that is better described in the Jordan frame

Garth.

 

[SpaceTiger]

The calculation of the Eddington mass limit from the Eddington luminosity uses the observational relationship

$$\frac{L}{L_\odot} \sim (\frac{M}{M_\odot})^3$$

We're talking about quasars (i.e. black holes). The relationship you're quoting is for main sequence stars. I meant that a quasar observed to have a particular luminosity must at least be massive enough that it doesn't blow itself apart with its own radiation. This fact doesn't rely on the observed mass-luminosity relation of anything. The Eddington luminosity doesn't come from any fancy physics, just radiation pressure, Thomson scattering, and gravity.

 

[Garth]

Agreed, but I understood you to be saying that one problem was how such SMBHs formed in the first place, (i.e. via massive PopIII stars) once formed the Eddington limit would not apply to a black hole, would it?

As I said in my post #37, the problem with doing such calculations in the Jordan frame is the whole of nuclear and astro physics has to be reworked with the variable particle mass scenario. It is much easier to work it in the Einstein frame, with standard physics and a modified GR gravitational field. As, for example, in BBN where the cosmology and BBN becomes that of the Freely Coasting Model.




Garth

 

[SpaceTiger]

Agreed, but I understood you to be saying that one problem was how such SMBHs formed in the first place, (i.e. via massive PopIII stars) once formed the Eddington limit would not apply to a black hole, would it?

No, the problem is both how the SMBHs grew and how quasars can be so bright at high redshift. Yes, the Eddington limit does apply to a black hole, just as it does to any gravitating radiator. I suggest reviewing the derivation of the Eddington limit (if you can't find it, I'll be happy to reproduce it).

 

[Garth]

No, the problem is both how the SMBHs grew and how quasars can be so bright at high redshift. Yes, the Eddington limit does apply to a black hole, just as it does to any gravitating radiator. I suggest reviewing the derivation of the Eddington limit (if you can't find it, I'll be happy to reproduce it).

Yes, thank you. I am interested in how the Eddington limit applies to a BH accretion disk and jet, the quasar 'engine'.

Garth

 

[SpaceTiger]

Yes, thank you. I am interested in how the Eddington limit applies to a BH accretion disk and jet, the quasar 'engine'.

The easiest way to derive it is to just consider the force of radiation pressure versus the gravitational force. Assume a gas made of purely ionized hydrogen in the Newtonian approximation, the gravitational force on a hydrogen atom is given by:

$$F_g=\frac{GM_{BH}m_H}{r^2}$$

If the hydrogen atom is to remain in orbit around the black hole (in the disk), this force must be greater than that provided by radiation pressure. The free electrons present a greater cross section to the radiation than the hydrogen ions, but electromagnetic forces will couple the ions and electrons, so a force on the electron is effectively a force on the protons as well. The radiation force on an electron is:

$$F_r=Flux \times \sigma_T / c = \frac{L\sigma_T}{4\pi r^2c}$$

where c is the speed of light and $\sigma_T$ is the Thomson cross section. The point at which the radiation force overwhelms gravity is found by equating these two forces:

$$\frac{L\sigma_T}{4\pi r^2c}=\frac{GM_{BH}m_H}{r^2}$$

leading to...

$$L_{Edd}=\frac{4\pi GM_{BH}m_Hc}{\sigma_T}$$

There are several complications that arise in real accretion disks. First of all, the chemical composition is not entirely hydrogen. It is mostly hydrogen, though, so this won't be a big correction. Second of all, gravity isn't exactly Newtonian in the inner accretion disk. Again, an order unity correction. Finally, it assumes isotropic emission from the accretion, which is just a geometrical correction factor. None of these things, it turns out, make a big difference. The Eddington luminosity is still a good approximation to the maximum luminosity of an accreting black hole. If it radiates more strongly than this, then the surrounding matter is expelled and cannot accrete any further.

 

[Garth]

Thank you ST, very clear and the same as the Eddington luminosity of the envelope of a large star. Of course - we are talking about a 'thick disk', I keep thinking of an accretion disk as a thin affair!

The Thomson cross section is given by:

$$\sigma_T = \frac{8\pi}{3}\frac{e^4}{c^4m_e^2}$$
so the luminosity is proportional to particle masses cubed, thank you.

As I said in SCC it is easier to do the gravitational physics in the Jordan frame and leave everything else to the Einstein frame and be careful how you integrate the two. I make no claim that i understand this problem fully in the SCC scenario but you have given me some good pointers. Thank you again.

Garth

 

[Garth]

Putting some numbers in

$$\sigma_T = \frac{8\pi}{3}\frac{e^4}{c^4m_e^2} = 6.7 \times 10^{-29} m^2$$

$$L_{Edd}=\frac{4\pi GM_{BH}m_Hc}{\sigma_T}$$
$$c = 3 \times 10^8$$ km/sec
$$G = 6.7 \times 10^{11}$$ MKS
$$m_H = 1.7 \times 10^{-27}$$ Kg
so

$$L_E = \frac{4 \pi \times 3 \times 10^8 \times 6.7 \times 10^{-11} \times 1.7 \times 10^{-27} M}{6.7 \times 10^{-29}}$$ MKS

$$L_E \sim 17 M$$ MKS

now $$M_\odot = 2 \times 10^{30}$$ kg.
and $$L_\odot = 3.8 \times 10^{26}$$ MKS.
so
$$\frac{L_E}{L_\odot} = \frac{17 \times 2 \times 10^{30}}{3.8 \times 10^{26}} \frac{M}{M_\odot}$$
i.e. $$\frac{L_E}{L_\odot} \sim 10^5 \frac{M}{M_\odot}$$,
which if the variable mass ~ 1/(1 + z) effect is taken into account, becomes:
$$\frac{L_E}{L_\odot} \sim 10^5 \frac{M}{M_\odot}\frac{1}{(1 + z)^2}$$,

Now for the most luminous quasars $L \sim 10^{12} L_\odot$ out at z = 6, we have for the standard theory:
$$M = 10^7 M_\odot$$
and for SCC

$$M = 5 \times 10^8 M_\odot$$

not too outrageous?

I hope I have counted all the OOMs correctly!

Garth

 

[SpaceTiger]

Now for the most luminous quasars $L \sim 10^{12} L_\odot$ out at z = 6, we have for the standard theory:
$$M = 10^7 M_\odot$$
and for SCC

$$M = 5 \times 10^8 M_\odot$$

not too outrageous?

Actually, the most massive quasar that has been reported at high-z (by SDSS) has ~3 x 10⁹ M_sun in standard theory. With the same correction factor, that brings your most massive SMBH to ~1.5 x 10¹¹ M_sun. That's pretty tough to reconcile with local observations of central black holes.

 

[Garth]

Actually, the most massive quasar that has been reported at high-z (by SDSS) has ~3 x 10⁹ M_sun in standard theory. With the same correction factor, that brings your most massive SMBH to ~1.5 x 10¹¹ M_sun. That's pretty tough to reconcile with local observations of central black holes.

Thank you ST, as a point of information, that most massive quasar has a mass 300 x my estimate, does it therefore have a luminosity of $3 \times 10^{14}M_\odot$ or are my numbers out? (i.e. $$\frac{L_E}{L_\odot} \sim 10^5 \frac{M}{M_\odot}$$).

Your final point is interesting to study in the SCC Jordan frame. If the mass of the SMBH is decoupled from the scalar field then it should not grow cosmologically whereas ordinary matter will. (Ordinary matter: $m = m_0 exp(Ht)$).

However, our measurements define particle masses to be constant, in which case we are working in the Einstein conformal frame of SCC. In this case degenerate matter will appear to decrease in mass as time progresses as measured against a standard non-degenerate mass, such as that of the Sun.

This means that a SMBH that had a mass of $M \sim 1.5 \times 10^{11}$ at ~ z = 6 will today appear to have a mass of
$$M \sim \frac{1.5 \times 10^{11}}{1 + z}M_\odot = \sim 2 \times 10^{10}M_\odot$$

Is the core of M87 at $3 \times 10^{9}M_\odot$ the present observed SMBH? In which case I am about one OOM out, however, that object is still 'local' cosmologically speaking and more massive BHs could be lurking further away.

On the other hand, in my 'hand waving' mode: might this just give another explanation for the end of the 'quasar epoch', apart from them simply running out of accreted 'fuel', i.e. that epoch lies that between the earliest time such a large object could form and the time before their mass 'decreased' below some critical lower limit?

Garth

 

[SpaceTiger]

Thank you ST, as a point of information, that most massive quasar has a mass 300 x my estimate, does it therefore have a luminosity of $3 \times 10^{14}M_\odot$ or are my numbers out? (i.e. $$\frac{L_E}{L_\odot} \sim 10^5 \frac{M}{M_\odot}$$).

I get $\frac{L_E}{L_\odot} = 38,000 \frac{M}{M_\odot}$, leading to ~$10^{14} L_\odot$.

So which is the "real" mass in your model? In other words, how much mass has been accreted from ordinary matter?

 

[Garth]

Yes I must have pushed a key on my calculator twice or something -I have the same problem with mobile phones, my fingers are too big - I was brought up on the slide rule, this calculation would have been a doddle!

I have reworked it making no approximations until the last and get the figure

$$\frac{L_E}{L_\odot} = 3.28 \times 10^4 \frac{M}{M_\odot}$$

So which is the "real" mass in your model? In other words, how much mass has been accreted from ordinary matter?

Mass is measured by comparing it to a standard, e.g. the Sun, at the epoch of the measurement.

So actually $1.5 \times 10^{11} M_\odot$ real mass was accreted at z ~ 6, which in the FCM occurs at t = 2Gyr. The Sun continues to grow in mass (and G diminish) by a factor (1 + z) from the time @ z until the present day. Comparing the old quasar with the modern Sun the quasar (with no further accretion) will appear to have a mass today of $M \sim 2 \times 10^{10} M_\odot$ as I said above.

Garth

 

[SpaceTiger]

So actually $1.5 \times 10^{11} M_\odot$ real mass was accreted at z ~ 6, which in the FCM occurs at t = 2Gyr. The Sun continues to grow in mass (and G diminish) by a factor (1 + z) from the time @ z until the present day. Comparing the old quasar with the modern Sun the quasar (with no further accretion) will appear to have a mass today of $M \sim 2 \times 10^{10} M_\odot$ as I said above.

I don't really buy this argument. If the black hole's actual mass is remaining constant, then we should measure the same mass at two epochs when comparing to the same standard (e.g. the present-day sun). The fact that the sun's mass is changing is irrelevant, since we're only using it as a standard at one epoch.

Either way, though, you still have to explain how you built up over 100 billion solar masses in under two billion years with a strongly diminished Eddington limit.

 

[Garth]

I don't really buy this argument. If the black hole's actual mass is remaining constant, then we should measure the same mass at two epochs when comparing to the same standard (e.g. the present-day sun). The fact that the sun's mass is changing is irrelevant, since we're only using it as a standard at one epoch.

What actually changes in the Jordan frame is the rest mass of non-degenerate atomic particles from which the http://pda.physorg.com/lofi-news-standard-silicon-mass_3244.html is made, the Sun's mass, as a collection of such particles, is a convenient unit in which to express stellar, galactic & BH masses.

Remember in this conformal frame the rate of atomic clocks is also changing relative both to the (inverse) frequency of a photon sampled from the peak emission of the CMB, and also to ephemeris time.

Atomic clocks depend on the conservation of energy-momentum, i.e. rest mass (SCC Einstein frame), standard photon clocks (carefully defined), and ephemeris clocks (in SCC but not GR), depend on energy being locally conserved (SCC Jordan frame).

Such a clock drift between atomic and ephemeris time would reveal itself as an apparent sunwards acceleration of cH of the Pioneer spacecraft .

Either way, though, you still have to explain how you built up over 100 billion solar masses in under two billion years with a strongly diminished Eddington limit.

Agreed.

Working in the Einstein frame of constant atomic masses.

The process is by Jean's mass gravitational homogolous collapse of a baryonic density of ~20% closure, without the benefit of DM, in a linearly expanding universe.

As I have posted elsewhere:

In a Jean's collapse it is an overdensity that is important to get a nebula to collapse out of a homogeneous cosmological background.

In the FCM at the Surface of Last Scattering (SLS) at z ~ 1000, with
h = 0.71 and T = 3000⁰K, the density is $\rho = 3 \times 10^{-21}$ gms/cc.
With anisotropy fluctuations at the 10^-5 level the overdensity at the SLS is
$\rho = 3 \times 10^{-26}$ gms/cc.

The Jeans' Mass

$$M_J = 10^{-10}\sqrt{\frac{T^3}{\rho}}M_\odot$$
so the raw Jean's mass is [itex]3 \times 10^5 M_\odot[/tex] and the intial collapsing halos from the overdensity will be masses of $10^8 M_\odot$ forming and fragmenting 10⁶ yrs after Last Scattering at t = 13 Myrs i.e. forming at t = 14 Myrs, the process finishing t ~ 10⁸yrs. at ~ z = 100.

The Jeans Length works out as 12000 lgt.yrs, i.e roughly one halo per ~ 10⁴ lgt.yrs, or an average of one every 10⁷ lgt.yrs. today.

If the density anisotropies are at the ~ 10^-5 level and kinetic energies of forming halos follows the potential energy of these wells, their relative velocities would be expected to be of the order 10^-2.5c, which is the OOM of our own galaxy's motion relative to the CMB.

To an OOM I take a lower limit typical velocity for these halos to be ~ 10^-3c, (300 km/sec), collisions between them would be expected every ~ 10⁷ yrs.

About 10⁴ mergers would be required to make up a typical spiral halo, or elliptical galactic, mass of 10¹² M_Solar.

Thus such halo masses might form after, a very hand waving estimate, ~ $\sqrt N$ of 10⁷ x 10² = 10⁹ yrs, which would be seen today in the FCM model at z = 13, and onwards at lower z towards the present. This is where the earliest galaxies appear to have formed Detecting Reionization in the Star Formation Histories of High-Redshift Galaxies

To form the object discussed above about 10% of such a galactic halo mass of $10^{12} M_\odot$ would then be required to collapse right down to a black hole and quasar; there is about another $10^{9}$ years for this to happen.

The fine details I will have to leave to you!

Thank you for your continued constructive criticisms they are much appreciated.

Garth

 

[SpaceTiger]

What actually changes in the Jordan frame is the rest mass of non-degenerate atomic particles from which the http://pda.physorg.com/lofi-news-standard-silicon-mass_3244.html is made

I understand that, but it doesn't address the point. Our standard is at z=0, not z=6. The fact that its mass changes with time seems to be irrelevant. Our standards will not change significantly during the course of our observations and we can safely use it to interpret our observations at z=6, z=3, or z=2, as long as we account for the other changes in physical system (that is, G, the particle masses at z=6, the clocks, etc.).

To form the object discussed above about 10% of such a galactic halo mass of $10^{12} M_\odot$ would then be required to collapse right down to a black hole and quasar; there is about another $10^{9}$ years for this to happen.

The fine details I will have to leave to you!

That would be quite a task, considering that Pop III stars are thought to be limited to about 1000 $M_\odot$.

You also might want to look into trying to fit the WMAP data. Models without non-baryonic matter have been shown to be a very bad fit, particularly at the third peak.

 

[Garth]

I understand that, but it doesn't address the point. Our standard is at z=0, not z=6. The fact that its mass changes with time seems to be irrelevant. Our standards will not change significantly during the course of our observations and we can safely use it to interpret our observations at z=6, z=3, or z=2, as long as we account for the other changes in physical system (that is, G, the particle masses at z=6, the clocks, etc.).

The standard is at z = 0 in the laboratory 'here and now' on Earth. We out from our laboratory back in time to the limits of the universe and interpret what we see there by what we know here. The mass of that object was estimated from its luminosity:

$$\frac{L_E}{L_\odot} = 3.28 \times 10^4 \frac{M}{M_\odot}$$
so

$$M_E \geq 3 \times 10^{-5} \frac{L_q}{L_\odot}M_\odot$$

this is the standard theory mass, in the SCC Jordan frame we have to allow for a diminished m_H and an increased G, so the mass necessary to 'contain' the quasar's luminosity L_q is:

$$M_E \geq 3 \times 10^{-5} (1 + z)^2 \frac{L_q}{L_\odot}M_\odot$$

This is the mass of a distant supermassive quasar seen as it crossed our light cone in the distant past. We ask what about a similar but much nearer quasar of equal amount of accreted matter, which we might observe as it crossed out light cone at a much later time and therefore much closer to us?

In the SCC Jordan frame, during the time between the events of these two quasars crossing our light cone, atomic masses increased, rulers shrank and clocks 'speeded up' all relative to the energy, wavelength and inverse frequency of a photon sampled from the CMB. The effect of that would be that the second quasar would appear to be reduced in mass by the $\frac{1}{1+z}$ factor.

The difference between the SCC Jordan frame and GR is that masses genuinely do increase with gravitational potential energy, it is not simply an effect of measurement in an inconvenient coordinate system.

That would be quite a task, considering that Pop III stars are thought to be limited to about 1000 $M_\odot$.

In which case we need a merger of 10⁸ of them, or 10³ proto-halos of 10⁸M_Solar;with distances and velocities mentioned above this might take less than 10⁹ years, but my hands are going like windmills at this point!

You also might want to look into trying to fit the WMAP data. Models without non-baryonic matter have been shown to be a very bad fit, particularly at the third peak.

Yes I have no expertise here except to point out that that intepretation is model dependent, I wonder what the third and other peaks look like in the conformally flat, 'cylindrical 'universe of the SCC Jordan frame?

Garth

 

[SpaceTiger]

T In the SCC Jordan frame, during the time between the events of these two quasars crossing our light cone, atomic masses increased, rulers shrank and clocks 'speeded up' all relative to the energy, wavelength and inverse frequency of a photon sampled from the CMB. The effect of that would be that the second quasar would appear to be reduced in mass by the $\frac{1}{1+z}$ factor.

Again, I already know that your theory makes the first statement, but I don't see how it leads to the second. We've accounted for the increase in atomic masses. Are you perhaps referring to the effective time dilation that goes into measuring a "luminosity"? Remember that, in the standard model, luminosities are inferred with a time correction and redshift correction built in, so you should make sure that this is consistent with the corrections you expect in your model.

I have no expertise except to point out that the interpretation is model-dependent.

Yes, but the point is obvious, and most of the models that are significantly different from $\Lambda CDM$ (e.g. relativistic MOND) have been ruled out at large confidence levels. Considering that the CMB is the strongest single test of standard cosmology, I'd say this is pretty important. Even without a detailed fit, you'll need to figure out how you could produce a large third peak in the power spectrum without non-baryonic dark matter.

 

[Garth]

Again, I already know that your theory makes the first statement, but I don't see how it leads to the second. We've accounted for the increase in atomic masses. Are you perhaps referring to the effective time dilation that goes into measuring a "luminosity"? Remember that, in the standard model, luminosities are inferred with a time correction and redshift correction built in, so you should make sure that this is consistent with the corrections you expect in your model.

Of course! L_q in my post above is the luminosity uncorrected for red shift. If the mass has been derived from the corrected cosmological luminosity then that effect has already been accounted for.

The $(1 + z)^2$ factor, which is a time dilation effect in GR and the SCC Einstein frame, is the variable mass and G effect in the SCC Jordan frame.

In the SCC Jordan frame there is no detectable time dilation caused by the curvature/expansion of space, hence no 'quasar variablity time dilation', red shift is a varying mass effect. The universe is static.

Consequently the most massive SDSS quasar has a mass of just $3 \times 10^9M_\odot$ as in GR, so we just require 0.3% of a galactic halo to collapse down into a black hole. [Note 0.3% is $\sim \sqrt{10^{-5}}$, equal to the 'overdensity' Jeans' mass factor]

I believe you may well be correct about the mass reduction effect. Comparing the BH with a solar mass both at z = 6 and then both at
z = 0 will produce such an effect, but as you rightly point out we are not doing that.

Even without a detailed fit, you'll need to figure out how you could produce a large third peak in the power spectrum without non-baryonic dark matter.

Is that the same third peak around which the power spectrum data goes "a bit 'wobbly'"?

Garth

 

[SpaceTiger]

Is that the same third peak around which the power spectrum data goes "a bit 'wobbly'"?

From WMAP data alone, yes, but actually there have been several other experiments that did a better job of measuring the high-l multipoles and found a very clear peak (which is, by the way, consistent with WMAP). See the WMAP paper for the overlay with power spectra from other experiments. The third peak is detected at very high significance by several experiments.

I'll comment on the rest when I get back later. I could only think of one factor of (1+z) difference in the luminosity inference from the models. Note also that this doesn't solve the growth problem that arises from the low Eddington luminosity.

 

[Garth]

I'll comment on the rest when I get back later. I could only think of one factor of (1+z) difference in the luminosity inference from the models. Note also that this doesn't solve the growth problem that arises from the low Eddington luminosity.

The standard cosmological luminosity takes two factors of (1 + z) into account, one for the fact that from an object at red shift z the photons are arriving less frequently by a factor of (1 + z), and the second because each photon carries less energy by a factor of (1 + z).

Your reference to "low Eddington luminosity" is where I became confused and assumed that you had not taken the (1 + z)² factor into account in the luminosity. There is no further "low Eddington luminosity" effect in the SCC Jordan frame, it is the (1 + z)² luminosity correction in GR.

Garth

 

[SpaceTiger]

Your reference to "low Eddington luminosity" is where I became confused and assumed that you had not taken the (1 + z)² factor into account in the luminosity. There is no further "low Eddington luminosity" effect in the SCC Jordan frame, it is the (1 + z)² luminosity correction in GR.

Well, I should say "low" in the sense that your theory decreases the amount of matter the black hole can accrete, even if it doesn't increase the inferred mass of the black hole. I'm not 100% confident we've accounted for all of the quirks of your cosmology, but it's clear that this asymmetry between the masses of relativistic degenerate matter and non-relativistic matter still exists.

 

[Garth]

Well, I should say "low" in the sense that your theory decreases the amount of matter the black hole can accrete, even if it doesn't increase the inferred mass of the black hole. I'm not 100% confident we've accounted for all of the quirks of your cosmology, but it's clear that this asymmetry between the masses of relativistic degenerate matter and non-relativistic matter still exists.

Well, I said I'm not sure I fully understand the behaviour of BHs in my theory!

It is necessary to solve the Schwarzschild solution with a SCC/BD scalar field in the strong gravity case and let the central mass collapse. I have not yet had the time to do that, and I'm not sure I would get it right even if I did without outside help.

However I do understand that in the case of high z BH accretion the amount of matter, i.e. number of atoms, a BH can accrete is the same as in GR, however the amount of mass is reduced because of the variable mass effect. There is no other red shift to worry about, so the effect of this reduced mass, and increased G, in the SCC Jordan frame is the same as the $(1 + z)^2$ red shift effect on the luminosity in GR . The two SCC/GR scenarios are conformally equivalent.

Thank you for the discussion it has been illuminating.

Garth.

 

[Nereid]

Not to take this interesting exchange off track, but, as Garth mentioned earlier, in SCC it rests on the assumption that the variability observed/observable in the optical part of the EM spectrum of QSOs arises essentially from just one component - the accretion disk.

Don't you, Garth, also need to establish that the jet, broad line region, etc are negligible contributors to the observed variability, in all stages of the quasars' evolution? Also, whatever the SMBH is, in SCC, don't you also need to establish - in some detail - the behaviour of the accretion disk? For example, no matter which theory (or combo of theories) is used to model such disks, the integrated emission includes significant contributions from very different (physical) regimes, doesn't it?

 

[Garth]

Hi Nereid, yes a good point. It is instructive to note that of all the energy produced by matter falling into the BH of a quasar that roughly half goes into the jet and half 'falls down the plughole' into the event horizon and only a small proportion is emitted as radiation. The jet and consequent radio lobes are powerful emitters, however the time scale of variability, and the Hawkins paper was looking at between 1 week to 1 year, depends on the size of the emitter. My understanding is the jet is much larger than the disc, extending many 1000's of light years and the structure within it ~ light years across, so would not the jet vary on a longer time scale?

Of course it is claimed by Baganoff & Malkan, ApJ. 444 1995, Gravitational microlensing is not required to explain quasar variability that because wavelength is inversely proportional to temperature, which depends inversely with the radius from the BH, that the variability is not expected to show dilation. However Hawkins refutes this.

To make it clear, I do agree that you need to not only to understand the behaviour of the accretion disk, but also you first need to fully understand the black hole in the SCC theory. All I have been engaged in is some 'back of the envelope' calculations to see how the land lies.

My basic point is simply that if it can be established that distant S/N and GRB light curves show time dilation and the variability of quasars do not, then my suggestion is the significant difference between them is that the 'engines' of former class consist of non-degenerate matter and the 'engine' of the BH is degenerate. SCC offers a ready distinction in the predicted behaviour between the two classes.

Garth

 

[Garth]

Is that the same third peak around which the power spectrum data goes "a bit 'wobbly'"?

From WMAP data alone, yes, but actually there have been several other experiments that did a better job of measuring the high-l multipoles and found a very clear peak (which is, by the way, consistent with WMAP). See the WMAP paper for the overlay with power spectra from other experiments. The third peak is detected at very high significance by several experiments.

Such as here? (You have to press <Page Down> once.)

Garth

 

[SpaceTiger]

Such as here? (You have to press <Page Down> once.)

Sorry Garth, I can't load it on this computer. Could you just summarize it briefly or give me a paper reference?

 

[Garth]

Sorry Garth, I can't load it on this computer. Could you just summarize it briefly or give me a paper reference?

http://cosmologist.info/notes/Moriond2006.ppt
is a series of lecture slides by Antony Lewis of the IoA, Cambridge, England. The second slide shows the power spectrum and the WMAP3 data with Acbor, Boomerang, CBI & VSA readings superimposed.
Whereas the other experiments do trace the predicted $\Lambda CDM$ third and even fourth peaks and beyond fairly well, the WMAP3 data goes, as I said "a bit wobbly". In particular the errors bars at l= ~870 and beyond do not even reach the predicted curve. I know that in this region the WMAP3 data has a problem with noise, but I wondered how those error bars were determined? Either the power spectrum here is less well determined than declared or there seems to be an inconsistency between WMAP3 and the different experiments and the predicted model.

Garth

 

[SpaceTiger]

http://cosmologist.info/notes/Moriond2006.ppt
is a series of lecture slides by Antony Lewis of the IoA, Cambridge, England. The second slide shows the power spectrum and the WMAP3 data with Acbor, Boomerang, CBI & VSA readings superimposed.
Whereas the other experiments do trace the predicted $\Lambda CDM$ third and even fourth peaks and beyond fairly well, the WMAP3 data goes, as I said "a bit wobbly".

That's right, WMAP isn't the primary constraint on the third peak. They use ACBAR, CBI, etc. to fit to the high multipoles, though none of the experiments (including WMAP) are inconsistent with one another. See the WMAP parameters paper for more detail.

 

[Garth]

In their paper Cosmic Conspiracies Scott & Frolop point out:

The now standard vanilla-flavoured LambdaCDM model has gained further confirmation with the release of the 3-year WMAP data combined with several other cosmological data-sets. As the parameters of this standard model become known with increasing precision, more of its bizarre features become apparent. Here we describe some of the strangest of these ostensible coincidences. In particular we appear to live (within 1sigma) at the precise epoch when the age of the Universe multiplied by the Hubble parameter H₀ t₀ = 1.

Note that in the http://en.wikipedia.org/wiki/Self_creation_cosmology linearly expanding model
R(t) ~ t, H₀ x t₀ = 1 at all epochs.

Garth

 

[SpaceTiger]

In their paper Cosmic Conspiracies Scott & Frolop point out:

That paper is hilarious. Check out some of the references.

(and in case you haven't already, check the date of submission)

 

[Garth]

Cosmic coincidences

That paper is hilarious. Check out some of the references.

(and in case you haven't already, check the date of submission)

Well of course:

(Dated: 1st April 2006)

Douglas Scott = http://www.astro.ubc.ca/people/scott/"
Ali Frolop = April Fool ,
They were obviously sponsored by the Church of Scientology

H₀t₀ = 1.03 ± 0.04 needs no further explanation, but nevertheless is consistent with a linearly expanding model.

Garth

 

[hellfire]

A question for my understanding. The fact that the theory contains a frame in which mass evolves and the universe is static, is this a direct consequence of conformal invariance, or is it also related to that principle of energy conservation in the preferred frame? What if you do not impose that second principle?

 

[Garth]

A question for my understanding. The fact that the theory contains a frame in which mass evolves and the universe is static, is this a direct consequence of conformal invariance, or is it also related to that principle of energy conservation in the preferred frame?

Yes, both, the conformal transformation is chosen so that energy is locally conserved. However, it is not an invariant conformal transformation, which is where SCC differs from other conformal gravity and scalar field theories.

What if you do not impose that second principle?

Then you are in another theory, if you now impose conformal invariance then you end up with either the standard Brans Dicke or one of the other conformal gravity theories.

Garth

 

[hellfire]

I was under the impression that in oder to claim that there exists an equivalent description of expansion, with static space and evolving masses, one has to rely on conformal invariance. It seams I am wrong. May be you could elaborate a bit.