New Evidence of the Azimuthal Alignment of Quasars Spin vector in the LQG U1.28, U1.27, U1.11, Cosmologically Explained
AAstronomy & Astrophysics manuscript no. Slagter © ESO 2021February 26, 2021 L etter to the E ditor New Evidence of the Azimuthal Alignment of Quasars Spin vectorin the LQG U1.28, U1.27, U1.11, Cosmologically Explained.
R. J. Slagter
Asfyon, Astronomisch Fysisch Onderzoek Nederland, Bussum, The Netherlandsformer: University of Amsterdam, Department of Physics, The Netherlandse-mail: [email protected] feb 2021
ABSTRACT
Context.
There is observational evidence that the spin axes of quasars in large quasar groups are correlated over hundreds of Mpc.This is found in the radio sector as well as in the optical range. There is not yet a satisfactory explanation of this "spooky" alignment.
Aims.
This alignment cannot be explained by mutual interaction at the time that quasars manifest themselves optically. A cosmologicalexplanation could be possible by the formation of superconducting vortices (cosmic strings) in the early universe, just after thesymmetry breaking phase of the universe.
Methods.
We gathered from the NASA / IPAC and SIMBAD extragalactic databases the right ascension, declination, inclination,position angle and eccentricity of the host galaxies of 3 large quasar groups in order to obtain the azimuthal and polar angle of thespin vectors.
Results.
The alignment of the azimuthal angle of the spin vectors of quasars in their host galaxy is confirmed in the large quasargroup U1.27 and compared with two other groups in the vicinity, i.e., U1.11 and U1.28, investigated by Clowes (2013).
Conclusions.
It is well possible that the azimuthal angle alignment fits the predicted azimuthal angle dependency in the theoreticalmodel of the formation of general relativistic superconducting vortices, where the initial axially symmetry is broken just after thesymmetry breaking of the scalar-gauge field.
Key words. quasar groups – alignment spin vectors – host galaxy – cosmic strings – symmetry breaking – scalar-gauge field.
1. Introduction
Large quasar groups (LQG) are one the largest structures in theuniverse. Their sizes can be of the order of hundreds of Mpc.Astronomers are convinced that a quasar is nothing but an activegalactic nuclei (AGN) and consists of a violent eruption of radi-ation (in the optical as well as in the radio range), initiated by aspinning (Kerr-) black hole, surrounded by an accretion disk. Itis conjectured, that these LQG possess an internal non-uniformdistribution of spin vectors observed by Taylor & Jagannathan(2016) in the radio sector and by Hutsemekers (2014) in theoptical range. This mysterious coherence cannot be explainedby mutual interaction at a time scale where primordial galaxieswere formed. Several attempts were made to explain this phe-nomenon of cosmological origin. In a former study of Slagter &Miedema (2021), we found that the azimuthal angle of the spinvector of quasars in their host galaxies in six quasar groups, showpreferred directions. This could be explained by an emergentazimuthal angle dependency of the general relativistic Nielsen-Olesen (NO) vortices just after the symmetry breaking at grandunified theory (GUT)-scale. In this letter we investigated threeother LGQ, studied by Clowes (2012, 2013).
2. Results
From the NASA / IPAC extragalactic database and SIMBAD weextract for the three LQG U1.11, U1.27 and U.28 the RA, Dec,inclination, position angle and eccentricity of the host galaxies.The 3 dimensional orientation of the spin vectors can then be calculated (Pajowska (2019)). In figure 1 and 2 we plotted theazimuthal angle. Without statistical analysis one can concludethat the preferred orientations are evident. In the case of LQGU1.27, we fitted two trigonometric functions on the distribution,which can theoretically be explained (section 3).
Fig. 1.
Distribution of the azimuthal angle of the spin vectors in thelarge quasar group U1.27 (N =
71) with a best fit of two trigonometricfunctions with a phase shift of about o . Article number, page 1 of 3 a r X i v : . [ g r- q c ] F e b & A proofs: manuscript no. Slagter
Fig. 2.
Distribution of the azimuthal angle for the LQG U1.28 (N = =
3. The theoretical model
A linear approximation of wavelike solutions of the Einsteinequations is not adequate when one is dealing with high cur-vature (or high energy scale), i.e., close to the horizons of blackholes or in the early stage of the universe at the time of massformation by the Higgs mechanism. There will be a "back-reaction" on the background spacetime. There is a powerful ap-proximation method which can deal with these non linearities:the multiple-scale method. Pioneer work was done by Choquet-Bruhat (1968). One expands the relevant fields (Slagter (1986)) V i = ∞ (cid:88) n = ω n F ( n ) i ( x , ξ ) , (1)where ω represents a dimensionless parameter ("frequency"),which will be large. Further, ξ = ω Θ ( x ), with Θ a scalar (phase)function on the manifold. The small parameter ω can also be theratio of the characteristic wavelength of the perturbation to thecharacteristic dimension of the background. On warped space-times it could also be the ratio of the extra dimension to the back-ground dimension. In the vacuum case, we expand the metric g µν = ¯ g µν + ω h µν ( x , ξ ) + ω k µν ( x , ξ ) + ..., (2)where we defined dg µν dx σ = g µν,σ + ω l σ ˙ g µν , g µν,σ = ∂ g µν ∂ x σ , ˙ g µν = ∂ g µν ∂ξ , (3)with l µ = ∂ Θ x µ . One then says that V i = ∞ (cid:88) n = − m ω n F ( n ) i ( x , ξ ) (4)is an approximate wavelike solution of order n of the field equa-tion, if F ( n ) i = , ∀ n . One can substitute the expansion into thefield equations. The Ricci tensor then expands as R µν → ω R ( − µν + (cid:16) ¯ R µν + R (0) µν (cid:17) + ω R (1) µν + ... (5)By equating the subsequent orders to zero, we obtain R ( − µν = =
12 ¯ g βλ ( l λ l µ ¨ h βν + l ν l β ¨ h µλ − l λ l β ¨ h µν − l ν l µ ¨ h βλ ) , (6) R (0) µν + ¯ R µν = , R (1) µν = , .... (7)Here we used l µ l µ =
0. The rapid variation occur in the direc-tion of l µ . In the radiative outgoing Eddington-Finkelstein coor-dinates, we have x = u = Θ ( x ) = t − r and l µ = (1 , , , In a recent study of Slagter (2016, 2017, 2018) we applied thisnon-linear approximation scheme on a FLRW spacetime. Weconsidered the matter contribution of a gauged complex scalar(Higgs) field. Physicists are now convinced that this field plays afundamental role in the early universe and is responsible for thesymmetry breaking in the Standard Model of particle physics.The experimental verification came by the recently observedHiggs particle at CERN. The same field has lived up to its reputa-tion in superconductivity, where the field act as an order param-eter to describe the formation of Cooper pairs. The scalar fieldis combined with a gauge field, parameterized as
Φ = η X ( x ) e in ϕ and A µ ( x ) = ne ( P ( x ) − ∇ µ ϕ , with n the topological charge orwinding number. The trapped flux of the vortex is expressed as n π he . The formation of a lattice of quantized magnetic flux tubeswas first observed by Abrikosov (1957) and are described bythe famous equations of Ginzberg & Landau (1950). In thesemodels , one needs the quartic potential of the Higgs field, i.e., V ( Φ ) = λ (cid:16) ΦΦ ∗ − η (cid:17) , with η the vacuum expectation value.Further, m Φ m A = e λ is the ratio of the scalar to gauge masses. Thispotential leads to a nonzero η and spontaneous breaking of theU(1) symmetry (note that the parameters are in general temper-ature dependent). The forces between the vortices consist of theelectromagnetic force and the scalar force. When the vorticesare close together, the problem becomes non-linear and the re-sulting force depends also on the ratio e λ . For details, see, for ex-ample, the text books of Felsager (1998) and Weinberg (2012).Moreover, when the vortices are formed in the early stage of theuniverse, then gravity will come into play. These general rela-tivistic vortex solutions are known as "cosmic strings" (Garfin-kle (1985); Vilenkin & Shellard (1994)) when they extend tocosmological dimensions. They could possible explain the ob-served void and filament structures in the universe.We expand the scalar and gauge field to second order as A µ = ¯ A µ ( x ) + ω B µ ( x , ξ ) + ω C µ ( x , ξ ) + ..., (8) Φ = ¯ Φ ( x ) + ω Ψ ( x , ξ ) + ω Ξ ( x , ξ ) + ..., (9)where we write the subsequent orders of the scalar field as¯ Φ = η ¯ X ( t , r ) e in ϕ , Ψ = Y ( t , r , ξ ) e in ϕ , Ξ = Z ( t , r , ξ ) e in ϕ , (10)with n i the subsequent winding numbers. The azimuthal angle ϕ will not enter, of course, the PDE’s inthe unperturbed case. By quantum fluctuations, the vortex ex-cite in higher n -state and will dissociate into n well separated n = , because the energy of the configuration isproportional with n . The topological characterization is a setof isolated points with winding numbers n i (the zero’s of Φ ),with n = n , n , ... . This n-vortices solution represents a finiteenergy configuration. However, an imprint will be left over ofthe azimuthal dependency of the orientation of the clustering ofAbrikosov vortices lattice in the general relativistic situation. So the stability of the configuration depends on parameter λ (Weinberg(2012))Article number, page 2 of 3. J. Slagter: New evidence alignment quasars ... the axial symmetry is dynamically broken. The azimuthal de-pendency emerge already to first order in the approximation. Forexample, the energy-momentum tensor ¯ T t ϕ =
0, while the firstorder perturbation becomes T (0) t ϕ = ¯ X ¯ P ˙ Yn sin( n − n ) ϕ (11)However, in T (1) t ϕ there appears terms like cos( n − n ) ϕ andsin( n − n ) ϕ . The perturbative appearance of a non-zero energy-momentum component T t ϕ can be compared with the phe-nomenon of bifurcation along the Maclaurin-Jacobi sequence ofequilibrium ellipsoids of self-gravitating compact objects, sig-naling the onset of secular instabilities (Gondek-Rosinska &Gourgoulhon (2002)). There is a kind of similarity with theGoldstone-boson modes of spontaneously broken symmetries ofcontinuous groups. The recovery of the SO(2) symmetry fromthe equatorial eccentricity takes place on a time-scale compara-ble with the emission of gravitational waves.The particular orientation of the ellipsoid in the frame ( r , ϕ, z )expressed through ϕ ≡ ϕ ( t ), will be at t > t determined by thetransformation ϕ → ϕ − Jt , where J is the rotation frequency(circulation or "angular momentum") of the coordinate system.The angle ϕ is fixed arbitrarily at the onset of symmetry break-ing. In section 3.2 we found that temporarily o ff -diagonal terms ap-peared in the perturbative approach of the Einstein-scalar-gaugefield. One can wonder if this breaking of the axially symmetryalready appears in the vacuum case, for example, in the vicinityof a black hole spacetime. It is conjectured that the formation ofprimordial (Kerr-) black holes (and so quasars) took place in theearly stages of the evolution of the universe, even before the starformation. So let us consider the radiative Vaidya spacetime inEddington-Finkelstein coordinates ds = − (cid:16) − M ( u ) r (cid:17) du − dudr + r ( d θ + sin θ d ϕ ) , (12)which is the Schwarzschild black hole spacetime with u = t − r − M log( r M − l µ l µ =
0. In the radiativecoordinates, we have x = u = Θ ( x ) and l µ = (1 , , , h rr = h r θ = h r ϕ = , h ϕϕ = − sin θ h θθ (13)From the zero-order equations Eq.(7) we obtain¨ k rr = , ˙ h θθ = r ∂ r ˙ h θθ , ˙ h θϕ = r ∂ r ˙ h θϕ . (14)So one writes h θθ = r α ( u , θ, ϕ, ξ ) , h θϕ = r β ( u , θ, ϕ, ξ ) , h ϕϕ = − r α sin θ. (15)Further, we have¨ k r θ = r (cid:16) α cot θ + ∂ θ ˙ α + θ ∂ ϕ ˙ β (cid:17) , (16)¨ k r ϕ = r (cid:16) ˙ β cot θ − ∂ ϕ ˙ α + ∂ θ ˙ β (cid:17) , (17) This spacetime is also used to describe the evaporation of a blackhole by Hawking radiation in a quantum mechanical way dMdu = − ¨ k φφ + sin θ ¨ k θθ θ − r ˙ h uu − (cid:16) ˙ α + ˙ β sin θ (cid:17) + (cid:16) ¨ α + ¨ β sin θ (cid:17) . (18)Not all the components of h µν and k µν are physical, so one needssome extra gauge conditions. By suitable choice of α and β (Choquet-Bruhat uses, for example, α = , β = g ( u ) h ( ξ ) sin θ ),one then has a solution to second order which is in general notaxially symmetric. We can integrate these zero order equationswith respect to ξ . One obtains then some conditions on the back-ground fields, because terms like (cid:82) ˙ α d ξ disappear. From Eq.(18),we obtain dMdu = − τ (cid:90) τ (cid:16) ˙ α + ˙ β sin θ (cid:17) d ξ, (19)which is the back-reaction of the high-frequency disturbances onthe mass M . τ is the period of ˙ h µν . This expression can be sub-stituted back into Eq.(18). Note that in the non-vacuum case, theright-hand side will also contain contributions from the matterfields.In order to obtain propagation equations for h µν and k µν , oneproceeds with the next order equation R (1) µν =
0. First of all,Eq.(16), (17) are consistent with R (1) r ϕ = R (1) r θ =
0. Fur-ther, one obtains propagation equations for α and β and for somesecond order perturbations, such as k ϕϕ . Moreover, the ( ϕ, θ )-dependent part of the PDE’s for α and β (say A ( θ, ϕ ) , B ( θ, ϕ ))can be separated (for the case k θϕ (cid:44) ∂ ϕ B + θ cos θ A + sin θ∂ θ A = , (20)sin θ∂ θθ A + θ cos θ∂ θ A + θ∂ ϕ B + θ − A + ∂ θϕ B = . (21)A non-trivial simple solution is A = cos θ ( sin ϕ + cos ϕ ) sin θ , B = sin ϕ − cos ϕ sin θ + G ( θ ) , (22)with G ( θ ) arbitrary. So the breaking of the spherically and axiallysymmetry is evident.
4. Conclusions
We find new observational evidence for the alignment of the az-imuthal alignment of the spin vectors of quasars in three newinvestigated LQG. We present a new argument for the theoreti-cal explanation of the axial symmetry breaking in a non-linearperturbation scheme, by considering a vacuum black hole space-time in radiative coordinates.
References