Journal of Modern Physics, 2017, 8, 2179-2188 http://www.scirp.org/journal/jmp ISSN Online: 2153-120X ISSN Print: 2153-1196 Galactic Structure and Holography T. R. Mongan 84 Marin Avenue, Sausalito, CA, USA How to cite this paper: Mongan, T.R. Abstract (2017) Galactic Structure and Holography. Journal of Modern Physics, 8, 2179-2188. Galactic structure, involving bulk motion of matter conserving mass and an- https://doi.org/10.4236/jmp.2017.814133 gular momentum, is analyzed in a holographic large scale structure model. In isolated galaxies, baryonic matter inhabits dark matter halos with holographic Received: November 18, 2017 Accepted: December 17, 2017 radii determined by total galactic mass. The existence of bulgeless giant spiral Published: December 20, 2017 galaxies challenges previous models of galaxy formation. In sharp contrast, holographic analysis is consistent with the finding that 15% of a sample of Copyright © 2017 by author and 15,000 edge-on disk galaxies in the sixth SDSS data release are bulgeless. Ho- Scientific Research Publishing Inc. This work is licensed under the Creative lographic analysis also indicates that E7 ellipticals are less than 2% of elliptical Commons Attribution International galaxies. License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Keywords Open Access Galactic Structure, Holography 1. Introduction This paper does not address the wide range of processes, mechanisms, and mer- gers generating galactic structures and leading to the myriad galaxy types ob- served by astronomers. Instead, it identifies the range of isolated galactic struc- tures consistent with conservation of mass and angular momentum in a holo- graphic large scale structure (HLSS) model [1]. Current observations indicate that our universe can be approximated as a closed vacuum-dominated Friedmann universe. Futhermore, “the universe is dominated by an exotic nonbaryonic form of matter largely draped around the galaxies. It approximates an initially low pressure gas of particles that interact only with gravity…” [2]. The holographic principle [3] applied in a vacuum-dominated universe led to an approximate large scale structure model [1] where isolated structures with total mass M g inhabit spherical holographic screens with M radius S = g if the Hubble constant H =67.8 km ⋅⋅ sec−−11 Mpc . 0.183 g cm2 0 DOI: 10.4236/jmp.2017.814133 Dec. 20, 2017 2179 Journal of Modern Physics T. R. Mongan M The HLSS model considers galactic matter density distributions ρ (r) = g , 4πSr 2 where r is distance from the galactic center. Then, mass within radius R is (RS) Mg , and tangential velocity of stars or star clusters in circular orbits within M g the 1 r 2 density distribution around the galactic center is VG= , where S G =6.67 × 10−831 cm ⋅⋅ g −− sec 2. This analysis treats galaxies as spherical halos of dark matter with radius S and (1−α ) M g density distribution ρ (r) = surrounding total baryonic mass 4πSr 2 MMbary= α g . Cosmological data indicate matter fraction of total energy density of the universe is ≈ 0.31 and baryonic fraction of total energy desity is ≈ 0.05 , so baryonic fraction of matter is α ≈=0.05 0.31 0.16 and dark matter fraction is α −=1 0.84 . The analysis uses α = 0.16 , but a distribution of values centered around α = 0.16 could be used to assess galactic systems formed in parts of the universe with slightly higher or lower ratio of baryons to dark matter. This paper considers galactic structures at redshift z = 0 , but the analysis is readily extended to z > 0 using results in Ref. [1]. 2. Black Holes in the Galactic Core M There is no singularity in galactic matter density distribution ρ (r) = g 4πSr 2 because mass inside a core radius C at the galactic center is concentrated in a C central black hole with mass MM= , where C is the holographic radius CBH S g of star clusters that can inhabit circular orbits just outside the core without being disrupted and drawn into the central black hole [1]. The mass M St comprising the dark matter halo with mass M H plus baryonic matter with mass M bary is MSt=−=+= MM g CBH M H M bary 0.84 MSt + 0.16 MSt . Total angular momentum of a galaxy is estimated using the moment of inertia 2 I= MS2 of a rotating sphere with galactic holographic radius S and density gg9 M ρ (r) = g . From the holographic relation MS= 0.183 2 , total angular 4πSr 2 g 2 2 M J = g ω ω momentum of the galaxy is gg, where g is galactic angular 9 0.183 velocity. Galactic angular velocity ωg is estimated by considering a mass m fixed on the rotating holographic screen at radius S. Radial acceleration GmM aS= −ω 2 of that mass results from gravitational force F = − g attracting g S 2 it to the centroid of the structure. Then, (correcting a misprint in Ref. [1]) GM 3 0.5 22g G 2 2 G 2 ωg = = (0.183g cm ) and JMgg= . In the HLSS S 3 M 9 0.25 (0.183M g ) DOI: 10.4236/jmp.2017.814133 2180 Journal of Modern Physics T. R. Mongan model [1], average galactic mass at z = 0 is 8.3× 1043 g and average galactic −16 2 angular momentum is JMgg=9 × 10 , 15% higher than Paul Wesson’s [4] −16 2 empirical value JMgg=8 × 10 . Central black hole angular momentum JCBH max cannot exceed maximum 2 G22 GC Kerr black hole angular momentum JMCBH max =±=±KCBH Mg , c cS 2 J GC 2 G0.5 CBH = and ≤± 0.25 . In the HLSS model at z 0 , J cS 9 g (0.183M g ) 39 45 C galactic mass ranges from ≈×4 10 g to ≈10 g and ≤1. So S −4 −3 JJCBHmax g ranges from ≈×2 10 to ≈×5 10 , and central black hole angular momentum is negligible. Core radius C equals the holographic radius of star cluster sub-elements of the galaxy that can inhabit circular orbits around the galactic center without being disrupted by the central black hole. Maximum 39 HLSS star cluster mass is 4.64× 10 g , so Cmax = 0.052 kpc , and minimum star 34 cluster mass is 2.11× 10 g , so Cmin = 0.00011 kpc . 3. Spiral Galaxies Spiral galaxies predominate in underdense regions of the universe. This analysis treats baryonic matter in isolated spiral galaxies as disk structures with constant M g tangential velocity VG= surrounding a central sphere with constant S density. 4. Conservation of Mass and Angular Momentum Baryonic matter outside core radius C around the central black hole consists of a bulge, with mass M B in a hollow sphere with inner radius C and outer radius B, and a disk with mass M DS . So Mbary =0.16( MMg −=+ CBH) MM B DS . Total mass within B and outside the core in the 1 r 2 density distribution around the M galactic center is (BC− ) g and tangential velocity at B is S M M g V= GB = VG = . If M , the baryonic part of total mass within B, is B BSB in a hollow sphere with inner radius C and outer radius B, M M=0.16( BC − ) g (1) B S Conservation of mass then requires a disk mass M g B MDS =0.16 Mg − M CBH −−( BC) =0.16 1 − Mg (2) SS Angular momentum conservation in spiral galaxies requires JJgCBHHBDS= + J ++ JJ, where terms on the right of the equation are DOI: 10.4236/jmp.2017.814133 2181 Journal of Modern Physics T. R. Mongan respectively the angular moment of the central black hole ( JCBH ), the dark matter halo ( J H ), the central bulge ( J B ), and the disk ( J DS ). Since −3 JJCBH ≤×5 10 g , JJg≈ H ++ JJ B DS (3) β M A hollow sphere with density ρ (r) = g , inner radius C, and outer radius 4πSr 2 2 RC33− R has moment of inertia β M g , so angular momentum Jbary of 9 RC− galactic baryonic matter comprising the bulge and disk with mass Mbary= MM B + DS is 2 SC33− Jbary=+=− JJ B DS J g (0.84) Mg ωg (4) 9 SC− 5. Bulge Radius and Disk Thickness If the hollow sphere of baryonic matter constituting the bulge has constant M 4 ρ =−−g 33 density B 0.16(BC) π(BC) , tangential velocity of baryonic S 3 C matter in the bulge rises from VV= at core radius C to V at B. The hollow C B sphere of the bulge with constant density ρB has moment of inertia 55 2 (BC− ) M B . To approximate observed velocity curves, angular velocity of 5 (BC33− ) the constant density bulge is found by setting tangential velocity at the edge of V the bulge VBBB= ω equal to disk tangential velocity V, so ωB = and B 55 2 V (BC− ) JMBB= . (5) 5 B (BC33− ) From Equation (4), disk angular momentum is 22SC33−− V BC55 V =−− JJDS g (0.84) Mg MB 33. (6) 95SC− S BC− B Maximum bulge radius Bmax occurs when there is no disk and all baryonic JJ−= J SC BC> mass is bulge mass. From gH Bmax , using and max , 22 5 (0.16) M SV≈ (0.16) M B V and BSS≈=0.56 . 95ggmax max 9 Next, consider a disk extending from RB= to RS= with density (RB− ) − 2 z K ρρ(Rz,) = 4B sech e , approximating an isothermal disk with constant z0 scale height z0 . Setting scale height zH0 = 8 , the integral H zH 22 4sech2 dzz= 8 tanh= H tanh( 4) = 0.9993H.