Friday, April 22, 2005

Jim Peebles & formation

Yesterday, Jim Peebles gave a nice talk about possible anomalies in the standard model of structure formation and possible remedies in the dark sector. He showed many pictures of colliding and other galaxies, and so forth. The main technical hypothesis was that there is an equivalence-principle violating fifth force caused by a massive scalar that only couples to the dark sector. The inverse mass is comparable to 1 megaparsec. Such a new force would allow to empty the voids more efficiently. I've already described these ideas after Steve Gubser's talk.

What I found really new, interesting, and simple enough was the autocorrelation of galaxies. If you draw the number of galaxies with a given angular separation theta as a function of theta, you will find that for moderately small angles, you obtain an almost exact power law with the exponent -1.77. This means that the distribution of galaxies behaves as a fractal whose Hausdorff dimension is another fractional number. In my opinion, there could exist a rather robust explanation of this exponent. Any ideas?


  1. Hi Lubos,

    I probably misunderstand your very brief explanation somehow, but what exactly is new? I agree that the result you mention is incredibly important, but it seems standard.

    When you plot the speed of objects circling a galaxy as a function of their distance from the galaxy's center, you find that for large distances the speed does not drop off as much as one should expect. This is the strongest and most widely accepted evidence for the existence of dark matter we have today.

    A related issue is that of clusters of galaxies. If it weren't for the presence of dark matter, such clusters shouldn't exist and the individual galaxies wouldn't interact enough to form clusters.

    Now, if you accept the explanation of anomalously high orbiting speeds due to dark matter, you have already solved the mystery of why galaxies form clusters. This is a strong and non-trivial consistency check on the hypothesis that dark matter exists.

    Finally, your power law for the galaxy density is presumably nothing but a description of the "bunching up" of galaxies in a cluster. You wouldn't have a need to restrict to small angles if it weren't for the finite size of clusters.

    Isn't the real question what kind of particle *is* the dark matter? I think it's the neutralino! ;))

  2. Dear Psychiatrist,

    I did not claim that the talk was the most original talk. The purpose of this short article was to summarize a talk by Jim Peebles.


  3. By the way, I apologize for my ambiguous user name.

    I am Quantoken's psychiatrist, which is a full time job. And yes, I dearly hate it!

  4. Lubos:

    Why is it so hard for you to realize that 1.77 = SQRT(PI), I realize it before I even finish reading the last decimal place of the number. There is a very natural explanation by simple geometry. I will leave it to you as math homework.

    Plus it is completely stupid to suggest a "MASSIVE" scalar field that corresponds to length scale of 1 megaparsec. Give some physics intuition, please. More massive scales should correspond to much smaller length scale. One megaparsec is a very very long length scale, which corresponds to a mass very very light, not massive at all.

    Such a light mass scale will contribute virtually no energy to anything at all to have any observable effect. So it's pure illusions.


  5. The anomalous exponent associated with the scaling of the correlation function as a function of separation angle might be modelled using a conformal field theory applied at the "heavenly sphere" with radius given by the distance of objects. Perhaps some minimal model could predict the exponent correctly. Also ut would
    be interesting to see whether the model in question is a "cosmological constant of motion".

    There is an article about cosmic conformal invariance. I. Antoniadis, P. O. Mazur, and E. Mottola (1996), Conformal Invariance and Cosmic Background Radiation, astro-ph/9611208.

    Matti Pitkanen

  6. On a closer examination, I think I would rule 1.77 = SQRT(PI) as pure coincidence with no significance, although it is indeed very close. I can not find a rational reason why PI or any combination of PI should occur in the exponent.

    Where exactly is the source of the -1.77 number? How was it obtained? Computer simulation or statistics of real observational data?

    Too bad Jim Peebles has no idea of complex systems. He did not cite a single paper by Per Bak. If he know anything Per Bak had done he would not be puzzling about the 1.77 number.

    I think it is actualy 16/9, square of 4/3. The -4/3 is a very important power exponent occuring in many catastropic system like sand pile model, avalanche model, and earth quake models, as first revealed by Gutenberg and Richter in 1956. Richter is certain the famous guy for him the scale of earthquakes, the Richter Scale, was named. They discovered that the frequency distribution of earth quakes is porportional to the (-4/3) power of the energy released. So that's just one of many catastropic systems where the fractional dimention -4/3 occured.

    The same thing occurs considering how little droplets of water (fog) forms out of the water vapor in the air. It's a random process but droplets close by tend to merge into bigger ones. If you consider the distribution you find the -4/3 power index, too.

    And galaxy formation works the same way. Galaxies form out of the uniformly distributed cosmic dust clouds, the same way water droplets form from the water vapor. So, clearly they follow the same physics rules that govern catastropic systems. That's where the -16/9 power index came from!!!


  7. Could you really provide the source of the -1.77 numebr? I think it clearly a strong observational support of my theory of cosmic dusts.