Resolving the beta-discrepancy for clusters of galaxies

Neta A. Bahcall, Lori M. Lubin

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Previous comparisons of optical and X-ray observations of clusters of galaxies have led to the so-called β-discrepancy that has persisted for the last decade. The standard hydrostatic-isothermal model for clusters predicts that the parameter βspec = σr2(kT/μmp), which describes the ratio of energy per unit mass in galaxies to that in the gas, should equal the parameter βfit, (where pgas(r) ∝ ρgal(r)βfit) determined from the X-ray surface brightness distribution. The observations suggest an apparent discrepancy: βspec ∼ 1.2 (i.e., the galaxies are "hotter" than the gas), while βfit ∼ 0.65 (i.e., the gas is "hotter" and more extended than the galaxies). Here we show that the discrepancy is resolved when the actual observed galaxy distribution in clusters is used, ρgal(r)∝ r -2.4±0.2 instead of the previously assumed steeper King approximation, ρgal(r) ∝ r-3. Using the correct galaxy profile in clusters, we show that the standard hydrostatic-isothermal model predicts βspec = βfitc ≃ (1.25 ± 0.1)βfit, rather than βspec ≃ βfit (where βfit is the standard parameter using the King approximation, and βfitc is the corrected parameter using the proper galaxy distribution). Using a large sample of clusters, we find best-fit mean values of βspec = 0.94 ± 0.08 and βfitc = 1.25βfit = 0.84 ± 0.1. These results resolve the β-discrepancy and provide additional support for the hydrostatic cluster model.

Original languageEnglish (US)
Pages (from-to)513-515
Number of pages3
JournalAstrophysical Journal
Issue number2
StatePublished - May 10 1994

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Galaxies: clustering
  • X-rays: galaxies


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