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Supernova Luminosity Curve Stretching in Time

Astronomers can use a supernova as a standard candle.
An innovation in 1998 used the supernova data in conjunction with an assumed distance for its host galaxy to derive conclusions about the universe expansion over time.

When this distance is wrong then the conclusions are wrong.

I hope this is not too long but details are important.

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The accelerated expansion was discovered during 1998, by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which both used distant type Ia supernovae to measure the acceleration.
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The comments below apply to that prestigious project. I am not a career physicist but perhaps an alternate view is interesting. That is up to the reader.

From the DOE Lawrence Berkeley National Laboratory:

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The surprising discovery that the expansion of the universe is accelerating, and thus is likely to go on expanding forever, is based on observations of type Ia supernovae, very bright astronomical "standard candles" that all have the same intrinsic brightness. Thus how bright they appear reveals their distance.

By comparing the distance of these exploding stars with the redshifts of their home galaxies, researchers can calculate how fast the universe was expanding at different times in its history. Good results depend upon observing many type Ia supernovae, both near and far. Employing supercomputer facilities at the National Energy Research Scientific Computing Center (NERSC) located at Berkeley Lab, the Supernova Cosmology Project has fully analyzed the first 42 out of the more than 80 supernovae it has discovered, and more analysis is in progress.

He adds, "Type Ia supernovae are so similar, whether nearby or far away, that the time at which an explosion started can be determined just from looking at its spectrum. Type Ia supernovae which exploded when the universe was half its present age behave the same as they do today."
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More details and comments  will follow.

The assumption is the supernova luminosity is always reliable.

The red shift in a galaxy's hydrogen absorption line can be affected by hydrogen atoms in the intergalactic medium, or even hydrogen gas clouds in the galaxy's cluster, often observed by Chandra.
The distance calculated from this red shift using Hubble's constant means the distance could be too far away.


The Supernova Cosmology Project document is attached (pdf from 2001).

This technical document is 'deep', but hopefully my excerpts and comments help at first. I hope I was not 'in over my head.'

excerpt:
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The basic idea is that you want to find an object of known brightness, a “standard candle," and then plot it on the astronomer’s Hubble diagram (Fig. 1), which is a plot of brightness (magnitude) against redshift. We should interpret this graph as follows: for an object of known brightness, the fainter the object the farther away it is and the further back in time you are looking, so you can treat the y-axis as the time axis. The x-axis, the redshift, is a very direct measurement of the relative expansion of the universe, because as the universe expands the wavelengths of the photons travelling to us stretch exactly proportionately—and that is the redshift. Thus the Hubble diagram is showing you the “stretching" of the universe as a function of time. As you look farther and farther away, and further back in time, you can find the deviations in the expansion rate that are caused by the cosmological parameters.
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my comment:
I thought the universe expansion resulted in increasing red shift values, caused by the relative velocity of the light source, which is assumed to be zooming away at the moment of the light emission, where a normal wavelength value has a higher value when observed in the spectrum like it could show a shift from from 200 Angstroms to 300 A (or whatever). A line shift is not the same as a wavelength stretching longer so after stretching the original wavelength at 200 A now stretched to 300A).

Since the wavelength is related to the energy of light (or a photon) proposing an increasing wavelength occurs during the light travel over the expanse of the universe means energy is being lost, contrary to the conservation of energy. This is not happening.

Perhaps the scientists did not make this mistake, just the author, but the text is very distracting given that problematic result. Red shifts come from relative velocity, the Doppler Effect, not stretching over distance.

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Figure 1: The Hubble plot: A history of the “size" of the Universe.
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my comments:
Figure 1 in my opinion is a very interesting conclusion. In the past for cosmology, the luminosity of the supernova was used to calculate the distance for that dimming. It is called a 'standard candle' for that purpose.
Figure 1 indicates the luminosity reduction (y-axis) is directly proportional to the red shift of the host galaxy (x-axis ).

because the graph shows dimming increases with red shift (or distance), the graph claims this conclusion:  'More redshift = Faster expansion in past= Expansion is slowing = More mass'

Dimming with distance does not necessarily justify a conclusion about the past.

excerpt of the 'new' step in this analysis:

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Before this high-redshift supernova data can be plotted on the Hubble diagram [probably a reference to Figure 1] and the cosmological parameters fitted, there are two small additional analysis steps necessary in order to compare the distant supernovae to the nearby supernovae on the same Hubble plot. First of all, although most type Ia supernovae follow a very similar light curve, there are a few outliers that are a little bit brighter or a little bit fainter. In the early 1990s, it was pointed out by Mark Phillips that there is an easy way to distinguish these supernovae, and recognize the slightly brighter ones and slightly fainter ones, using the timescale of the events. Phillips  noted that the decline rate in the first 15 days after maximum provides a good parameterization of the timescale, and that this is a good predictor of how bright the supernova will be.

Later, [they] showed another elegant statistical method which effectively added and subtracted shoulders on the light curve to achieve the same sort of timescale characterization. Finally, our group developed a third method, which we call the timescale stretch factor method, in which we simply stretch or contract the timescale of the event by a linear stretch factor, s. This also predicts very nicely the brightness of the supernova: The s > 1 supernovae are the brighter ones and the s < 1 supernovae are the fainter ones.
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my comment:
The new step involves a linear stretch factor, so this 'predicts very nicely' the brightness.
It is not clear if this stretch factor is the problematic stretch mentioned above.

excerpt:
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Figure 5: Upper panel: The range of lightcurve for low-redshift supernovae discovered by the Calan/Tololo Supernova Survey. At these redshifts, the relative distances can be determined (from redshift), so their relative brightnesses are known. Lower panel: The same lightcurves after calibrating the supernova brightness using the “stretch” of the timescale of the lightcurve as an indicator of brightness (and the color at peak as an indicator of dust absorption).
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my comment:
The supernova  light curve is 'calibrated' by the host galaxy distance, however reliable that is.

Figure 6 is a comparison of two spectra, B and R.

excerpt:
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Figure 6: Slightly different parts of the supernova spectrum are observed through the “B filter” transmission function at low redshift (upper panel) and through the “R filter” transmission function at high redshift (lower panel). This small difference is accounted for by the “cross-filter K-correction”
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my comment:
I hope my interpretation of this figure 6 is correct. These are not emission lines or synchrotron radiation with absorption lines. This wavelength distribution looks like thermal radiation with the peak indicating a temperature so curve B is hotter than curve R, with the B peak at a shorter wavelength.
If the peaks and patterns in thermal radiation were different between B and R I would have assumed different temperatures.
Instead the difference in spectra is treated as a red shift, not a different temperature.
The supernova has no red shift in an absorption line or emission line for this analysis. Only the red shift in the galaxy absorption line is used. In this figure  the red shift is observed in comparing the range of wavelengths for thermal radiation, assuming both have the same temperature, but then shifted by a different z.

I am not a physicist but this approach seems innovative (in other words, is it justified?).

From the document I cannot determine the consequences of figure 6. The term red shift is used many times, but '1+z' is immediate.

excerpt:
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This is one of the most dramatic examples of a macroscopic time dilation that you will get to see. If you take out that (1+z) time dilation, and also remove the small variations in the stretch factor, the low redshift and high redshift composite light curves now lay right on top of each other. This shows that the supernovae are very similar across redshifts and that the K-correction does an excellent job in bringing them in line with each other.
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my comment:

When the luminosity curves do not match, this stretch factor from the expanding universe reconciles the difference - and the supernova confirms the expanding universe.

This stretch factor assumes a relativistic time dilation, in this expanding universe spacetime.

excerpt from below figure 9:

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This result can also be interpreted as a measurement of the age of the universe,
if you know the current expansion rate (i.e., the current Hubble constant).
This is shown on the plot with isochrons of age for a given mass density and cosmological constant (see Fig. 9). The supernova confidence region picks off a value of about 14.5 billion years, or 15 billion years along the flat universe line.
These values are for a Hubble constant of 65 km/s/Mpc; if we had chosen a Hubble constant that was 10 percent higher we would have found an age that was 10 percent lower. In either case, there no longer appears to be an “age crisis" in which the oldest stars seemed to be older than the age of universe.
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This comment is very interesting when knowing many cosmologists met in July 2019 to discuss this 'crisis' and could not agree on the 'correct' Hubble's Constant; they still disagree by 'only a few percent' around 70 or 73, but not 65 as above. This uncertain value is absolutely critical for cosmology as noted in the paper.

a subsequent excerpt:

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These results can also be compared with those from other methods for measuring the cosmological parameters. In particular, we can ask to what extent do we know that we live along the flat universe line, because our measurement does not constrain that very well. The cosmic microwave background, the leftover glow from the very dense period at the beginning of the big bang, is a very good indicator of how curved the universe is. We are beginning to see CMB data coming in that is starting to constrain the curvature. Although much better data should be available within the next few years, we can already begin to rule out the upper right (“over-closed") and lower left (very “open") regions . This has been taken by some as suggestive that we will find the answer to be a flat universe. If you put the CMB data together with the supernova data, you find a result that centers quite close to the flat universe line, with mass density approximately 0.3 and vacuum energy density approximately 0.7.
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my comment:
Since the CMB has been shown to be the background noise from the Earth's oceans, it is not reassuring to know there is a common conclusion with CMB analysis.



The paper concludes with a question about the level of confidence.

excerpt:
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Given the surprising nature of this result, it is important to ask how strongly it
can be believed. First of all, if you believe that we have evidence for a flat universe
from the cosmic microwave background data—or if you like the inflationary universe
model which predicts a flat universe—then the supernova results are very strong.

such higher redshifts are useful in addressing both loopholes, evolution and gray dust. This is because the curve on the Hubble diagram that is predicted for a cosmology with a positive cosmological constant is fainter at z = 0.5 than the curve for a universe with no cosmological constant, but at much higher redshifts the two curves come back together and cross. This behavior is very difficult to mimic with an evolutionary effect.
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My conclusion to a long post:

The level of confidence does not convey certainty, but the effort was rewarded.

I hope my comments are useful. References to a Hubble diagram are suspicious given uncertainty about red shifts.
When I began this topic I did not expect the CMB reference in this study's conclusion so perhaps I made a few good points.

link to pdf


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