Galactic Structure and Holography

Galactic structure, involving bulk motion of matter conserving mass and angular momentum, is analyzed in a holographic large scale structure model. In isolated galaxies, baryonic matter inhabits dark matter halos with holographic radii determined by total galactic mass. The existence of bulgeless giant spiral galaxies challenges previous models of galaxy formation. In sharp contrast, holographic analysis is consistent with the finding that 15% of a sample of 15,000 edge-on disk galaxies in the sixth SDSS data release are bulgeless. Holographic analysis also indicates that E7 ellipticals are less than 2% of elliptical galaxies.


Introduction
This paper does not address the wide range of processes, mechanisms, and mergers generating galactic structures and leading to the myriad galaxy types observed by astronomers.Instead, it identifies the range of isolated galactic structures consistent with conservation of mass and angular momentum in a holographic 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 The HLSS model considers galactic matter density distributions ( ) where r is distance from the galactic center.Then, mass within radius R is ( ) g R S M , and tangential velocity of stars or star clusters in circular orbits within the 2 1 r density distribution around the galactic center is , where 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 0 z = , but the analysis is readily extended to 0 z > using results in Ref. [1].

Black Holes in the Galactic Core
There is no singularity in galactic matter density distribution ( ) , where C is the holographic radius of star clusters that can inhabit circular orbits just outside the core without being disrupted and drawn into the central black hole [1].
Total angular momentum of a galaxy is estimated using the moment of inertia , total angular momentum of the galaxy is , where g ω is galactic angular velocity.Galactic angular velocity g ω is estimated by considering a mass m fixed on the rotating holographic screen at radius S. Radial acceleration ( )

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 tangential velocity surrounding a central sphere with constant density.

Conservation of Mass and Angular Momentum
, the baryonic part of total mass within B, is in a hollow sphere with inner radius C and outer radius B, ( ) Conservation of mass then requires a disk mass ( ) Angular momentum conservation in spiral galaxies requires , where terms on the right of the equation are respectively the angular moment of the central black hole ( CBH J ), the dark matter halo ( H J ), the central bulge ( B J ), and the disk ( DS J ).Since 3 5 10 A hollow sphere with density ( ) β ρ = , inner radius C, and outer radius R has moment of inertia , so angular momentum bary J of galactic baryonic matter comprising the bulge and disk with mass

Bulge Radius and Disk Thickness
If the hollow sphere of baryonic matter constituting the bulge has constant density ( ) ( ) ( ) ( ) From Equation (4), disk angular momentum is ( ) Maximum bulge radius max B occurs when there is no disk and all baryonic mass is bulge mass.From , approximating an isothermal disk with constant scale height 0 z .Setting scale height 0 8 z H = , the integral ( ) height H encompassing 99.9% of disk matter, disk mass is approximately and disk angular momentum is approximately ( ) Setting radial scale length K xS = , the following equation can be solved for x by trial and error If sufficient data are available, the model can be extended to consider situations where different stellar populations are in sub-disks with different radial scale lengths and scale heights This is relevant because analysis of the Milky Way [5] found different star populations in sub-disks with scale height inversely related to sub-disk radial scale lengths.

Percentage of Bulgeless Spiral Galaxies
Kormendy et al. [6]  1 10 g × are bulgeless.These estimates bracket the 15% estimate of bulgeless galaxies found among 15,127 edge-on disk galaxies in the sixth release of SDSS data [7].So, holographic analysis has no difficulty accounting for bulgeless giant spiral galaxies.

MOND Is Unnecessary
Dark matter can account for flat velocity curves in spiral galaxies, and observations of the colliding "bullet cluster" galaxies 1E0657-558 provide further evidence for dark matter.To avoid using dark matter to account for flat velocity curves, Modified Newtonian Dynamics (MOND) assumes the law of gravity is different at large distances.Ref. [8] cites the baryonic Tully-Fisher relation and mass discrepancy-acceleration (or observed Newtonian V V ) relation as "challenges for the ΛCDM model," and accounts for those relations using MOND with an acceleration threshold and at R sufficiently distant from the galactic center that total baryonic mass of the galaxy 0.16 can be treated as concentrated at the galactic center, Newtonian radial acceleration from baryonic matter is , and at that radius .So, ( ) , and , known as the baryonic Tully-Fisher relation.Fourth, if

Elliptical Galaxies
Elliptical galaxies predominate in overdense regions of the universe, and may result from mergers and collisions of progenitor galaxies.Baryonic matter interacts more strongly than dark matter, so collisions between galaxies can produce torques transferring angular momentum from baryonic matter to the composite halo, yielding baryonic ellipsoids with angular velocity less than the angular velocity of the halo and the galaxy as a whole.This analysis treats elliptical galaxies as constant density ellipsoids within a surrounding spherical isothermal dark matter halo.Dynamical instability of thin galaxies (the firehose instability) limits long axes of ellipsoids to about three times the length of short axes.So elliptical galaxies in this model range from oblate spheroids with radius A along the spin axis equal to one third the radius R ⊥ perpendicular to the spin axis to prolate spheroids with radius A along the spin axis equal to three times the radius R ⊥ perpendicular to the spin axis.
In the holographic approach, galaxies are arrangements of bits of information identifying the location of matter in the galaxy.There is no reason for one arrangement of information satisfying conservation of mass and angular momentum to be preferred over another.So, different configurations satisfying conservation of mass and angular momentum with the same total mass should be equally likely.A is A projected on the plane perpendicular to the line of sight.
When the angle between rotation axis of prolate elliptical galaxies and the line of sight decreases from 90˚ to 0˚, the projection ( ) sin

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galaxies as spherical halos of dark matter with radius S Cosmological data indicate matter fraction of total energy density of the universe is 0.31 ≈ and baryonic fraction of total energy desity is 0 a core radius C at the galactic center is concentrated in a central black hole with mass Baryonic matter outside core radius C around the central black hole consists of a bulge, with mass B M in a hollow sphere with inner radius C and outer radius B, and a disk with mass DS M tangential velocity of baryonic matter in the bulge rises from C C V V B = at core radius C to V at B. The hollow sphere of the bulge with constant density B ρ has moment of inertia observed velocity curves, angular velocity of the constant density bulge is found by setting tangential velocity at the edge of the bulge the HLSS model[1] within the ΛCDM paradigm readily accounts for the MOND acceleration threshold, baryonic Tully-Fisher relation, and mass discrepancy-acceleration ( observed Newtonian V V ) relation.First, radial acceleration at holographic radius S is , radial acceleration at radius R due to dark matter is the MOND hypothesis is unnecessary.
Baryonic ellipsoids outside the core radius C surrounding the central black hole have baryonic mass the moment of inertia around the spin axis so the spheroids fit within the holographic screen.Prolate and oblate spheroids with radius o AR along the spin axis have the same mass and angular momentum as spheres with radius o R R = .For prolate spheroids capable of avoiding firehose instability, radius along the spin axis ranges from o R to 3 o R , ( ) line of sight of the actual A along the axis of rotation gets smaller, so projected shape of the galaxy gets rounder and higher actual Hubble classes appear as lower projected Hubble classes as the axis of rotation gets closer to the line of sight.Hubble class distribution of prolate spheroid shapes projected on the plane perpendicular to the line of sight is found by integrating from 1 A = to 3 A = and from 0 θ = to π 2 θ = .As above, this analysis assumes information (matter), in prolate elliptical galaxies capable of avoiding firehose instability with a given mass and angular momentum and corresponding radius o R perpendicular to the rotation axis, is evenly distributed among prolate spheroids with radius .Total occupancy of prolate elliptical galaxies with given mass and angular momentum is class E0.The interval AE1 The mass HM plus baryonic matter with mass Hubble class E0 to E7.We only see projections of ellipsoids on the plane perpendicular to our line of sight, so actual Hubble class AEi of an elliptical galaxy and its projected (observed) Hubble class Ei are not the same.Prolate elliptical galaxies rotate around their major axis and oblate elliptical galaxies rotate around their minor axis, so results hold for oblate galaxies when 1 A is replaced by A, and the projection effect can be understood by considering only prolate spheroids.Table 1 shows i o A R major axis lengths marking transitions between Hubble classes for prolate spheroids, where i

Table 1 .
Major axis lengths i A marking transitions between Hubble classes for prolate spheroids.

Table 2 .
Projected Hubble class Ei of elliptical galaxies versus actual Hubble class AEi of elliptical galaxies.