The missing baryon problem is NOT solved by the Sunyaev-Zel'dovich effect

Radio telescope measurements of micro-Kelvin temperatures in CMB radiation by the Sunyaev-Zeldovich effect are problematic as temperature fluctuations in dispersed WHIM atoms between galaxies are forbidden by the Planck law of quantum mechanics
Computer simulation of Dark Matter filaments between galaxiies
Computer simulation of Dark Matter filaments between galaxiies
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PITTSBURGH - Oct. 16, 2017 - PRLog -- .
The missing observable matter problem was recently claimed [1,2] solved by a hypothesized cosmic web of optically thin filaments of dark matter between galaxies. The filaments are comprised of ionized WHIM containing the missing baryonic atoms. WHIM stands for warm-hot intergalactic matter including free electrons produced upon ionization in million-degree temperature surroundings. Since the optically thin filaments are not observable, the WHIM atoms could be the missing mass in the observable Universe. Prior research [3] considered inferring missing mass from UV and X-ray emissions. Indeed, UV radiation emitted by WHIM and detected [1] by the Hubble Space Telescope has accounted for about 50 % of the missing gas baryons, still leaving about 50 % of the missing mass unknown.

Instead of inferring the remaining 50 % of the missing mas by X-ray and UV emissions, the search [1,2] relied on the SZE that occurs when CMB radiation passes through the hot ionized WHIM and interacts with free electrons. SZE stands for the thermal Sunyaev-Zel'dovich effect and CMB for cosmic microwave background. By the Compton effect, the SZE predicts the CMB photon gains a small amount of energy that corresponds to a temperature change ΔTSZE in the CMB temperature TCMB, the thermal emission of which measured with radio telescopes. In this way, the full 100 % of the missing mass was estimated from the free electron pressure and temperature.

But the CMB temperature change ΔTSZE is very small. For TCMB ≈ 2.725 K,  ΔTSZE ≈ 1 micro-Kelvin which is undetectable by radio telescopes. In order to get a detectable SZE, the  ΔTSZE from million pairs of galaxies separated by similar distances were simply stacked together.

Beyond the fact that stacked  ΔTSZE temperatures do not have any physical meaning, there is a far more fundamental problem. Based on the Stefan-Boltzmann law, radio telescopes measure the thermal emission power from macroscopic bodies. However, optically thin WHIM are not macroscopic, but are basically free atoms, and as such are quantum entities following the Planck law of QM and not classical physics. QM stands for quantum mechanics.

By the Planck law of QM, the kT heat capacity of isolated WHIM atoms and free electrons vanishes under the nanoscale EM confinement inherent in their high surface to volume ratios, and therefore SZE temperature changes ΔTSZE do not occur as shown in the thumbnail. For applications of  the Planck law see:, 2010 – 2017.

The SZE in the arguments [1,2] that the stacking of  ΔTSZE temperature changes in the CMB to detectable levels is simply NOT valid to support the claim the missing baryon mass in the Universe was found. This is not to say the WHIM atoms are not the missing mass as mechanisms other than the SZE may be shown valid.

In this PR, the WHIM atoms are proposed to be the missing baryons. The SZE is not invoked as  ΔTSZE fluctuations in the CMB do not exist. Lacking heat capacity, the intense heat from galaxies cannot increase temperatures of WHIM atoms, but rather is conserved by raising the core electron energy of the atom to X-ray levels. Once K-edges are reached, the X-rays are emitted, the process repeated ad infinitum. Assuming one X-ray emission per WHIM atom, X-ray telescopes may be used to measure the number of WHIM atoms and account for the missing baryons in the Universe.

The number of X-ray photons in the Universe as a measure of the number of WHIM atoms can be roughly estimated by assuming conservation with CMB photons in the Universe. The radius R of the Universe is, R ≈ 14 x 109 years x 3 x 108 m s-1 x 31.5 x  106 s year-1 = 1.32 x 1026 m. For a spherical volume, V = 4πR3 /3 ≈ 9.6 x 1078 m3. The number of CMB photons in the Universe is estimated as 37 x 106 m-3 x V = 3.5 x 1086. For WHIM atoms of nitrogen having a K-edge = 0.4 keV, the X-rays have wavelength λ = 3 x 10-9 m while the CMB photon wavelength is 1.8 x 10-3 m giving the ratio of the number of X-rays to CMB photons as 1.6 x 10-6, and therefore the number of WHIM atoms is 3.5 x 1086 x 1.6 x 10-6 = 5.8 x 1080. The number of atoms in the Universe has been estimated to be between 1078 and 1083 suggesting with more detailed the WHIM atoms do indeed explain the missing mass of the Universe.

QM by the Planck law precludes radio telescopes from measuring ΔTSZE temperature fluctuations in the CMB temperature by the SZE as the heat capacity of WHIM atoms vanishes. Instead, QM conserves the galaxy heat by raising the inner core electrons to K-edge levels whereupon the corresponding X-rays are emitted. The missing mass of the Universe is indeed the WHIM atoms and are detectable by X-ray telescopes.

Given WHIM atoms are the missing mass of the Universe, the Hubble redshift suggesting dark matter exists is no longer a valid explanation for the galaxy rotation problem and the expanding Universe. What this means is the Hubble redshifts are caused by another mechanism, e.g., see "Dark Matter does not exist if redshifts are corrected for cosmic dust" at 2017.

[1]H. Tanimura, et al., "A Search for Warm/Hot Gas Filaments Between Pairs of SDSS Luminous Red Galaxies," MNRAS 000, 1–10, 2017.
[2] A. de Graaff, et al., "Missing baryons in the cosmic web revealed by the
Sunyaev-Zel'dovich effect," arXiv:1709.10378v1 [astro-ph.CO] 29 Sep 2017.
[3] J. E. Carlstrom, et al., "Cosmology with the Sunyaev-zel'dovich effect," Annu. Rev. Astron. Astrophys. 40, 643–80, 2002.

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