Luminous galaxy candidates at z > 10 revealed by JWST indicate “future deep JWST observations may identify relatively bright galaxies to much earlier epochs than might have been expected” [1]. As explained below, holographic analysis based on quantum mechanics, general relativity, thermodynamics, and Shannon information theory indicates galaxies with mass ~10⁹ solar masses should be expected at z = 10 - 20. The analysis does not assume or require a theory specifically relating arrangements of bits of information on holographic screens to distribution (as opposed to amount) of mass within such screens.

Behroozi et al. [2] listed some early predictions for what JWST will see, and then used a supercomputer simulation to predict JWST will find galaxies z > 10 with masses considerably below those revealed by early JWST data. In contrast, the prediction from holographic analysis below, ~10⁹ solar masses for average luminous mass of galaxies at z ≈ 10 - 20, is consistent with early JWST results.

Our post-inflationary universe, dominated by vacuum energy, has cosmological constant Λ = 1.088 × 10 − 56   cm − 2 [3] and event horizon radius R H = 3 Λ = 1.661 × 10 28   cm . Holographic analysis [4] finds only a finite number N = π ln ( 2 ) ( R H l P ) 2 = 4.741 × 10 122 of bits of information on the event horizon are available to describe our universe, where Planck length l P = ℏ G c 3 = 1.616 × 10 − 33   cm .

Friedmann’s general relativistic equation H 0 2 = 8 π G 3 ρ c r i t + Λ c 2 3 for a flat Euclidean universe with critical density and cosmological constant requires Ω Λ ≡ Λ c 2 3 H 0 2 . PDG 2022 [3] lists present day Hubble expansion rate H 0 = 67.4   km / ( sec ⋅ Mpc ) , critical density ρ c r i t = 3 H 0 2 8 π G = 8.53 × 10 − 30 g / cm 3 , dark energy density parameter Ω Λ = 0.685 , Hubble length c / H 0 = 1.37 × 10 28   cm , and matter density ρ m = ( 1 − Ω Λ ) ρ c r i t . PDG parameters result in Λ c 2 3 Ω Λ H 0 2 = 0.997 , so our universe is indistinguishable from flat Euclidean space to three significant figures. Mass within the event horizon M H = 4 3 π ( 1 − Ω Λ ) ρ c r i t R H 3 = ( 1 − Ω Λ ) c 2 2 G 3 Λ = 5.14 × 10 55   g is constant in time, and M H = [ ( 1 − Ω Λ ) c 2 2 G ( H 0 c ) 2 3 Λ ] R H 2 = ( 0.187   g / cm 2 ) R H 2 . The constant mass per bit of information m b i t = M H / N = 1.08 × 10 − 67   g .

In a fundamental sense, information specifies location of matter in space, and holographic analysis indicates 4.741 × 10¹²² bits of information on the spherical holographic screen (SHS) of the event horizon are associated with matter within our observable universe. Holographic analysis then indicates information and associated mass M within isolated gravitationally bound systems relates to radii R of spherical holographic screens around system centers of mass by M = ( 0.187   g / cm 2 ) R 2 .

Cosmic microwave background (CMB) radiation density at redshift z is ρ r ( z ) = ( 1 + z ) 4 ρ r ( 0 ) , where mass equivalent of today’s radiation energy density ρ r ( 0 ) = 4.59 × 10 − 34 g / cm 3 . Matter density ρ(z) is much greater than radiation density and Jeans mass [5] M J = π 48 ρ m 2 [ 2 c 3 π ρ r ( 0 ) G ] 3 = 2.30 × 10 50   g , the upper limit on mass of gravitationally bound systems stable against gravitational collapse, is independent of z . Large scale structures at z > 10 are gravitationally bound systems of individual stars with masses between Jeans mass M J and minimum stellar mass m ∗ min ( z ) at redshift z .

Minimum stellar mass m ∗ min ( z ) is estimated by setting escape velocity of protons at SHS radius R ∗ min for minimum stellar mass equal average velocity of protons in equilibrium with CMB radiation outside the SHS for m ∗ min ( z ) . Protons in equilibrium with CMB outside the SHS for stellar systems with mass < m ∗ min ( z ) can transfer energy to those systems until they reach m ∗ min ( z ) . Escape velocity v for protons of mass m p gravitationally bound at radius R from system center of mass M is calculated from 1 2 m p v 2 = G M m p R . Escape velocity of protons on the SHS for minimum mass stars with mass M at redshift z is velocity of protons in thermal equilibrium with CMB, so 3 2 k T ( z ) = G M m p R , where CMB temperature T ( z ) = ( 1 + z ) 2.725   K and Boltzmann constant k = 1.38 × 10 − 16 ( g ⋅ cm 2 / sec 2 ) / K . With radius R = M / ( 0.187   g / cm 2 ) for structures of mass M , m ∗ min ( z ) = 1 0.187 ( 1.5 k ( 1 + z ) 2.725 G m p ) 2 g , so m ∗ min ( 10 ) = 8.26 M ⊙ , m ∗ min ( 12 ) = 11.5 M ⊙ , and m ∗ min ( 20 ) = 30.1 M ⊙ , with solar mass M ⊙ = 2 × 10 33   g . If outgoing protons at the SHS are in thermal equilibrium with outgoing photon flow from minimum mass stars, stars must have mass > m ∗ min ( z ) to appear against the CMB background. Maximum star mass 6 × 10 35   g ≈ 300 M ⊙ [6] coincided with minimum star mass at z ≈ 65 , consistent with indications stars first formed at z ≈ 65 [7]. At z = 0 , minimum star mass ≈ 1.4 × 10 32   g = 0.07 M ⊙ , consistent with hydrogen burning mass threshold separating brown dwarfs from lowest mass stars [8].

With no good reason to suspect information describing gravitationally bound systems is not uniformly distributed between mass bins, the number of gravitationally bound systems of mass m at redshift z can be taken as n ( m ) = K / m with constant K . Then total mass of observable gravitationally bound systems at redshift z is M H ≈ ∫ m ∗ min ( z ) M J m ( K m ) d m = K ( M J − m ∗ min ( z ) ) and K ≈ M H / M J = 2.24 × 10 5 . The number of observable gravitationally bound structures in Jeans mass M J at redshift z is N ( z ) = ∫ m ∗ min ( z ) M J K m d m = K ln ( 2.30 × 10 50   g / m ∗ min ( z ) ) . Estimated average total mass of observable gravitationally bound structures at redshift z, M a v g ( z ) = M J / N ( z ) , at z = 10 - 20 is ~ 1.4 × 10 10 M ⊙ , between estimated Milky Way mass ~ 10 45   g ~ 10 12 M ⊙ and dwarf galaxy masses ~ 10 40   g ~ 10 7 M ⊙ .

PDG 2022 [3] lists baryon density fraction of the universe Ω b = 0.0493 , so stellar mass is Ω b / ( 1 − Ω Λ ) = 0.0720 times total galactic mass. Then stellar mass ~ 10 9 M ⊙ of galaxy candidates at redshift z ≈ 10 - 12 identified by Naidu et al. in JWST data is consistent with “early appearance of UV-luminous galaxies with stellar masses as high as ≈ 10 9 M ⊙ already at few 100 Myr after the Big Bang” [1].

Holographic analysis predicts the average galaxy detected by JWST space telescope at redshift z ≈ 10 - 12 will have luminous mass of about 10⁹ solar masses, consistent with early JWST data.

The author declares no conflicts of interest regarding the publication of this paper.

Mongan, T.R. (2023) Average Luminous Mass of Early Galaxies at z = 10 - 20 Predicted as ~10⁹ Solar Masses. Journal of Modern Physics, 14, 208-211. https://doi.org/10.4236/jmp.2023.143015