Sunday, March 24, 2013

Reading - Seeing Red: Redshifts, Cosmology & Academic Science. Part 1.

Reading -  "Seeing Red: Redshifts, Cosmology & Academic Science"

I came across Halton Arp's book some months ago while perusing my local technical library.  Since  Arp's work is referenced by virtually every crank claim (often in way contradictory to what the crank claim is trying to support!), I thought maybe it was time I finally read this book.  I had read a number of Arp's papers over the years and been repeatedly frustrated by the number of questions left unanswered by Arp and others claiming that quasar redshifts were not due to cosmological expansion.

The nature of the redshifts of extragalactic objects has been a source of controversy since their discovery in the early part of the 20th century.  Our understanding of the distant cosmos depends very strongly on an accurate understanding of the distance scale from which many other cosmic parameters depend.  The amount of energy we detect at the Earth emitted by an object is dependent on its intrinsic luminosity and the distance.  This is critical to understanding other aspects of the phenomenon.

While the Hubble Law (Wikipedia) has reigned as the dominant explanation that fit the great majority of the data, occasional discovery of a new class of objects would almost always present some challenges.   Numerous alternative explanations for the redshift have been explored.  When quasars (Wikipedia) were discovered in the 1960s, the distances inferred from their red-shifts and the Hubble law suggested that they must be incredible sources of energy.  The difficulting explaining such energy output generated some concern that perhaps for this class of objects, the redshift was not a reliable indicator of distances.

When Arp and others first brought attention to quasars very close to regular galaxies on the sky, there was a flurry of interest.  Arp (wikipedia), Geoffrey Burbidge (wikipedia), Jayant Narlikar (wikipedia), Fred Hoyle (wikipedia) and others developed a cosmological model derived from Hoyle's earlier steady-state cosmology. Arp pursued the idea that quasars were actually ejected objects from the nearby galaxy and that much of the redshift observed was intrinsic to the quasar and not due to distance.  For a time, Arp's observations suggesting that the red-shift might not apply the quasars received a lot of attention. 

Eventually, it was realized that these 'alignments' were not actual associations, but due to chance placements on the sky.  The great majority of the astronomical community found the cosmological redshift had far more successful predictions than Arp's model.

Beyond the scientific issues, of my greatest complaints about this book is it's somewhat chaotic organization.  It is not organized historically or by objects, or even thematically.  Each chapter seems to drift into discussions that might be better served collected together.  It reads almost like a set of essays originally written as separate pieces which were subsequently published together.  I'll attempt to consolidate some of the themes, which better illustrates some of the errors.

Arp often discusses how ideas changed - what we used to believe, vs what is believed now.  However, he fails to mention that these new ideas often had associated problems which had to be solved before the idea became accepted.  Arp's ideas failed to solve many of their problems.

The Chapters:
Chapter 1: X-ray observations confirm intrinsic redshifts
Chapter 2: Seyfert Galaxies as Quasar Factories
Chapter 3: Excess Redshifts all the Way Down
Chapter 4: Intrinsic redshifts in stars
Chapter 5: The Local Supercluster
Chapter 6: Clusters of Galaxies
Chapter 7: Gravitational Lenses
Chapter 8: Quantization of redshifts
Chapter 9: Cosmology
Chapter 10: Academia

The Odds Must be Crazy (with apologies to the Website & Podcast)

One of the greatest potential pitfalls of Arp's hypothesis was that these alignments could be perfectly ordinary chance alignments between bright foreground galaxies and more distant, but brighter, background objects.  Arp and supporters were always very quick to quote some small probablity (usually < 1 in 100) that the alignments were chance.  When I first started reading these papers, I was often frustrated that many of these authors did not publish just what assumptions went into the probability calculation or did not provide clear direct references to the papers that did.  I eventually found the methodologies, but it took quite a bit of digging.

Humans have a lousy sense of probabilities.  If they understood probabilities well, Las Vegas would be a ghost town and lotteries would fold for lack-of-interest.  Yet a huge part of Arp's evidence is based on his computations of these probabilities, claiming that the odds of any two or more of these objects being so close by chance is very low. 

Perhaps the simplest problem to illustrate part of Arp's probability errors is the Birthday Problem (Wikipedia).  In this problem, the probability that YOU share a birthday with anyone in a roomful of some number, N, other people is significantly lower than the probability that any two people in that same room will share a birthday.  Yet most people think these two probabilities should be equal.  If you were searching a room of 23 people for matching birthdays, you'd express suprise if you found two people that matched, yet the real probability is about 50% that you would find two matching birthdays in the room.

Arp continued to draw attentions to correlations he finds while ignoring the far larger quantities of uncorrelated galaxies, which made his probabilities seem more significant than they actually were.  If a probability of an alignment is 1%, then in a catalog of 100 randomly distributed objects, you would expect one or even two alignments.  If you went looking for alignments, any one you found would be significant.  As galaxy catalogs grew significantly larger than a few hundred, it was becoming clear that chance alignments were a significant probability.  Arp attempts to dismiss these by arguing that you can turn any alignment into a chance correlation if you go to sufficiently deep magnitudes, a tactic which Arp calls the 'Pleiadies maneuver' (pg 103). 

There was also this apparent correlation that the closer the quasar was to the galaxy, the larger it's redshift.  Arp argued that if galaxies were truly spread randomly on the sky, there should be no correlation between these two quantities.  That these two quantities should have this interesting correlation was strong evidence to Arp that the quasar-galaxy association was real. 

But Arp never really properly tested this against the cosmological redshift interpretation.  This is only strictly true for a 2-dimensional sky - as if Earth were inside a sphere an all the universe were on the surface of that sphere.  It would fall to Noerdlinger (ADS) to give a surprisingly simple, GEOMETRIC, explanation of this correlation for a 3-dimensional universe where redshift was proportional to the radial distance.  Below I've generated a view of a few degrees of sky from one of my simple cosmology models illustrating what you would see.
Click to Enlarge
Click the plot to look at a larger version.  In this simulation, each dot represents a galaxy sampled from a volume of randomly distributed points.  The colors are assigned based on distance from the observer, with blue being nearest, and red being furthest.  Size of the dot is also based on distance, with the closer dots being larger.  One characteristic we immediately notice is that the bluer dots tend to be larger but fewer, while the orange and red dots are consistently smaller and far more numerous.  It turns out that the mean angular distance we see between the galaxies gets smaller the further away they are.  This is the origin of the angular distance-redshift relationship - a simple example of visual perspective (wikipedia).

My simulation above was generated with a uniform poisson distribution in space of the same mean density, no there is no clumping of galaxies due to gravity.  Yet how many close associations can you find, in this one sample plot, of a (large, blue) foreground galaxy with a more distant (small, red) background galaxies?  What about objects in a line of three or more?  The Noerdlinger paper was an interesting discovery which I will explore  more in a future post.

But while Arp tried to make a point that is was the nearness of quasars to galaxies, measures of a few arc-minutes and less, that was the important characteristic (Table 1-1, 1-2, figure 1-5, 1-9, 1-11, 1-20, 2-3, 2-4, ), he also claimed associations for quasars and galaxies a degree or more apart.  Many of fields of view in Arp's book are 1-3 degrees wide to show the association (Figures 1-6, 1-17, 2-5, 2-6, 2-10, 2-20).  What's up with that?

Arp's statistical computations were subjected to continual scrutiny (1977ApJ…211..311R, 1978ApJ…223..747S, 1978A&A….70..219N, 1980ApJ…237..326W), but even when legitimate biases were pointed out which dramatically increased the probabilities of chance alignments significanlty larger than Arp's estimates, Arp continued to ignore these corrections.  There are very few papers where these issues are actually addressed.  As more of these errors were pointed out to him, it seemed that Arp began adjusting his probability calculations with a smaller a priori probabilities which were used to drive his alignment probabilities to even lower (1981ApJ…250…31A), and more dubious values (1982ApJ…263L…7B).

Numerous additional researchers questioned Arp's probability computations for associations (1983ApL….23..155P, 1983MNRAS.204..675Z) and claimed quasar alignments (1982MNRAS.200P..47W, 1982MNRAS.201..179W). 

And Arp and a few of his supporters continued to ignore these results. 

But as the galaxy and quasar surveys grew larger with more complete coverage of the sky, more problems were found with Arp's interpretation.  We were also finding regular galaxies near quasars of the same redshift (1972ApJ...171L..83R, 1972ApJ...176L..47O).  It was becoming clear to the rest of the astronomical community that the alignments were due to chance.

Distances vs. Brightness
One of the more annoying claims in the book was Arp stating that the redshift-distance relationship implies a strict redshift-apparent magnitude relationship (pg 153-154).  This is only strictly true when the objects in question are reasonably 'standard candles' (Hyperphysics).  As a population, galaxies can range in brightness over several magnitudes which can create significant spread in the result.  Below is a plot from one of my model universes with just a few galaxies.  The model has a gaussian distribution of galaxies in absolute magnitude with a half-width of 1.2 magnitudes.  What kind of correlation can you see?  I've plotted more galaxies in this sample than Arp does in his book.

With small numbers of data points, sampled over a short range, it is easy to make the correlation undetectable.  In Figure 6-14, Arp plots a handful of galaxies over a very narrow range of redshift, making the plot look almost random.  Arp says that such a broad range of brightness for galaxies (4 magnitudes, or a factor of 40) is unrealistic.  However, an even broader magnitude range exists for stars, a factor of about 10^10 =10^(0.4*25) or 25 magnitudes! 

What makes galaxies exempt from a broad range of brightness? Is Arp just dismissing this possibility because of the problem it creates for his particular interpretation of the data?

2-Dimensional Thinking
"He is intelligent, but not experienced.  His pattern indicates two-dimensional thinking" -- Capt. Spock, ST: TWOK
I had this suspicion some years ago when I was reading Arp's papers individually, but seeing Arp's arguments in his book, while exploring the papers, reinforced my suspicions. 

I can find none of Arp's probablility calculations that treat the sky as a 3-dimensional volume with the viewer's proper perspective.

Most of Arp's arguments treat the universe as if it were a 2-dimensional spherical surface centered on the Earth.  His probability calculations are strictly for random points scattered on a 2-dimensional sphere.  This error is intimately related to the error pointed out by Noerdlinger in paper mentioned above and which I will cover more in a future post. 

When Arp tries to argue for redshift 'quantization', he treats the sky as 1-dimensional, but this time in redshift space.  This is a problem with many advocates of redshift-quantization.  These researchers who simply run a histogram of number of galaxies as a function of redshift (actually a 3-d dataset) through a simple 1-dimensional Fast Fourier Transform.  This is not a true 3-D power spectrum.  If the quantization were real, why do the power spectra of individual separate catalogs peak at different frequencies?  (see Quantized Redshifts. VII. Common Power Spectral Density "Bloopers")

If you keep these three dimensions separate, all kinds of strangeness can be found.  Yet, a consistent picture emerges when redshift is proxy for third dimension and you treat space as a full 3-D structure.

I've been assembling this writeup for a number of months now and it just seems to keep getting longer.  I'll have more about Arp's book, and his cosmological & quasar model, in part II.

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