Historical research guide · 1058 · 2021
Axial Anomaly in Galaxies and the Dark Universe
Janning Meinert · Ralf Hofmann
In one minute
Janning Meinert and Ralf Hofmann propose that the dark universe is not a new particle waiting to be found but a consequence of something particle physics already has: the axial anomaly. In their picture gravity at the Planck scale breaks a chiral symmetry, and each of three SU(2) Yang-Mills theories — one per lepton family — gives the resulting boson a tiny mass equal to that theory’s energy scale squared divided by the Planck mass. The result is three species of ultralight axion, each condensing into self-gravitating lumps: a dense quantum core wrapped in a virialised halo. Fitting the rotation curves of first seventeen and then eighty low-surface-brightness galaxies from the SPARC catalogue, they read off the lightest axion’s mass, about 0.675 times ten to the minus twenty-third of an electronvolt, and from it the lump masses of the other two species, which follow from the charged-lepton mass ratios alone. Those land on the mass of the compact object at the centre of the Milky Way, and on the mass of a globular cluster.
Connection
This is chapter 13’s programme carried out to the end: one gauge principle asked to deliver the leptons, the dark matter and the dark energy together, with numbers you can check against galaxy rotation curves. It matters to chapter 2 because it identifies dark energy with a condensate that has simply never broken up, and to chapter 12 because the authors name a fusion-machine test — an electron temperature of 9.49 keV — that would settle the underlying gauge theory in a laboratory rather than a telescope.
From the source
The mass formula is the hinge of the paper. If chiral fermions gain mass through gravitational torsion at the Planck scale and are charged under a gauge group, the axial anomaly generates a mass for what would otherwise be a massless Nambu-Goldstone boson, and that mass is the square of the Yang-Mills scale divided by the Planck mass, the Planck mass being 1.221 times ten to the twenty-eighth electronvolts. Matching one such SU(2) theory to each of the three lepton families then fixes three ultralight axion species from three Yang-Mills scales. Because the anomaly is a firmly established feature of particle physics rather than a new postulate, the authors argue this would demystify the dark universe rather than deepen it.Section 1, Introduction, equation 1
The lightest axion mass is read off real rotation curves, twice, by two different models. Fitting the Soliton-Navarro-Frenk-White profile to seventeen SPARC low-surface-brightness galaxies with a reduced chi-squared below one gives a mass of 0.72 plus or minus 0.5 times ten to the minus twenty-third electronvolts. Fitting the Burkert profile to eighty galaxies and converting through the gravitational Bohr radius gives 0.65 plus or minus 0.4, and the virial masses cluster around 5 times ten to the tenth solar masses. The authors take the mean, 0.675 times ten to the minus twenty-third electronvolts, which confirms an independent earlier extraction of 0.554.Sections 3.2 and 3.3, equations 22 and 24, figures 2, 5 and 8
One measured lump predicts the other two. The mass of an isolated, unmerged lump is the cube of the Planck mass divided by a universal constant and by the square of that species’ Yang-Mills scale, so the ratios of lump masses are fixed by the squares of the ratios of the charged-lepton masses and by nothing else. With a typical electron-family lump at 6.3 times ten to the tenth solar masses, the muon-family lump comes out at 1.5 times ten to the sixth and the tau-family lump at 5.2 times ten to the third. The authors then note where those numbers land: allowing for the Milky Way’s dark disk being a merger of a few electron-family lumps, the implied muon-lump mass is 4.7 to 7 times ten to the sixth solar masses, and the central compact object of the Milky Way is measured at 4.31 to 4.5 times ten to the sixth.Section 4, equations 10, 11, 30 and 33
Dark energy becomes dark matter by depercolation, at named redshifts. While a condensate’s gravitational Bohr radius exceeds the Hubble radius it behaves as a homogeneous energy density, that is as dark energy; once the Hubble radius grows far larger, the condensate breaks into self-gravitating islands that dilute as pressureless matter. Anchoring on the electron-family transition at redshift 53 and promoting the ratio of the two radii there, about 55,500, to a universal constant, the authors obtain redshift 40,000 for the muon family and 685,000 for the tau family. The fourth theory, the one proposed for the CMB itself, never depercolates: its Bohr radius today is 2.4 times ten to the tenth megaparsecs against a Hubble radius of 4038 megaparsecs — so its condensate simply is the dark energy we still measure.Section 4, equations 34 and 35, and figures 10 and 11
The lumps are far from being black holes, and the paper says how far. The ratio of the gravitational Bohr radius to the Schwarzschild radius is half the square of the universal constant, which with a value of 314 for that constant gives 4.92 times ten to the fourth. Reaching the critical mass for black-hole formation therefore requires a merger of at least 222 isolated lumps. For the Milky Way that rules out a muon-lump route, since the central object is only about four million solar masses; a merger of several hundred tau-lumps, possibly catalysed by a few muon-lumps, is the viable candidate, and it is consistent with stellar orbits that fit a single point mass extremely well.Section 4, equations 31 and 32 and figure 9, and section 5.1
Two terrestrial tests, named by the authors. First, the underlying gauge-theory pattern predicts a low-frequency black-body anomaly at low temperatures, around 5 kelvin, which could be searched for with relatively low instrumental effort. Second, and more striking, an experimental link to the electron-family theory would be the detection of its Hagedorn transition in a plasma at an electron temperature of 9.49 kiloelectronvolts, together with the stabilisation of a macroscopically large plasma ball at 1.3 times that temperature. The authors state that such electron temperatures should be attainable by state-of-the-art nuclear-fusion experiments such as ITER, or by fusion experiments with inertial plasma confinement.Section 5.2, closing paragraph
The way in
https://doi.org/10.3390/universe7060198How to cite it
Janning Meinert, Ralf Hofmann (2021) Axial Anomaly in Galaxies and the Dark Universe doi:10.3390/universe7060198