¶
Table of Contents

1. Introduction
2. PBH formation and sequestration of baryon-photon fluid to form primordial dwarf galaxies (PDGs)
3. Tension in the Hubble constant and S8
4. Emergence of ultra puffs as the second epoch of baryonic DM
5. Secondary accretional galaxies
6. Super-puff planets and/or Planet Nine as former ultra puffs(?)
7. Tully-Fisher and the radial acceleration relation (RAR)
8. Discussion
References
¶

Abstract
¶

¶    Baryonic dark matter (DM) has an early universe problem. It apparently requires a 6-fold increased baryon-to-photon ratio, which is incompatible with Big Bang nucleosynthesis (BBN) and with the first acoustic peak in the cosmic microwave background (CMB) power spectrum. But, a canonical baryon-to-photon ratio, with sequestration of 5/6 of the baryon-photon fluid from the Hubble flow prior to recombination, may correspond with observations by creating globally canonical conditions at BBN and locally canonical conditions at recombination. This conceptual baryonic DM hypothesis proposes 2 epochs of baryonic DM, with the first epoch composed of photon-depleted proto dwarf galaxies (PDGs) prior to recombination, and the second epoch composed of free-floating super-puff-like planets following recombination.
¶    In the first epoch, 5/6 of the baryon-photon fluid was sequestered from the Hubble flow by primordial black holes (PBHs), and the associated primordial photons were sub-sequestered behind PBH event horizons, with sequestration running to completion by about the epoch of matter-radiation equality. In this scenario, rotating (Kerr) PBHs caused frame dragging of baryon-photon fluid in PBH ergospheres, which collimated the energetic and super-abundant primordial photons. Tangential kicks from collimated photons levitated charged particles (fermions and BBN nuclei) on a photon sea, preventing matter particles from crossing PBH event horizons, while promoting photon accretion. The levitated charged particles were presumably magnetically channeled to the PBH poles and ejected in polar jets, forming gravitationally-bound, photon-depleted baryonic halos around PBHs, which converted PBHs into PDGs. Accretion of primordial photons in their early energetic state swelled PBHs to supermassive black hole (SMBH) proportions, and in turn, these early SMBHs provided the horsepower to sequester 5/6 of the baryon-photon fluid by about the epoch of matter-radiation equality. Very early SMBHs appear to require a small degree of new physics. Roy Kerr proposes that singularities don’t physically exist in black holes, suggesting here that photons may continue to experience cosmic redshift after crossing black hole event horizons. This implies that primordial SMBHs underwent ‘black hole redshift’, wherein their photon-bloated early mass was redshifted away at a rate inversely proportional to the cosmic scale factor.
¶    The second and present epoch of baryonic DM emerged within PDGs following recombination, forming ‘ultra puff planet DM’, similar to stellar-system super-puff planets, but with still-lower density and ultra-low metallicity. Gravitational lensing of quasars detect variability by an apparently large population of objects with a mass of ∼10 M⊕. By contrast, gravitational lensing of stars in Galactic studies excludes the possibility of planets or planetary-mass black holes, “but objects that have a peak column-density Σ0<∼10⁵ g cm⁻² do not automatically violate the Galactic constraints because they’re not strong gravitational lenses in that context”. (Tuntsov, Lewis & Walker 2023) So pithy ultra puffs with a mass of ∼10 M⊕ could satisfy quasar microlensing findings, and may avoid violating Galactic microlensing null results.
¶    Photon decoupling at recombination released the external photon pressure on PDGs, which along with black hole redshift caused expansive cooling that presumably triggered ‘secondary recombination’ within PDGs; however, secondary recombination within PDGs was not accompanied by photon decoupling, since the associated primordial photons had already been sub-sequestered within PBHs. Cooling of ionized gas can lead to rapid, progressive thermal fragmentation, designated “shattering” for its rapidity. Shattering ceases at a characteristic length scale of ~ 0.1 pc/n, which is the scale at which fragmented cloudlets reach thermal equilibrium with their surroundings. (McCourt et al. 2016) Significantly, the mass of these shattered cloudlets is ~ 5.7 M⊕, which is within a factor of 2 of the estimated mass of quasar lenses (∼10 M⊕). Thermal fragmentation and Jeans instability required stellar metallicity to provide infrared cooling, which the very first stars, Population III (Pop III) stars, supplied. So, at least some Pop III stars must have expired in supernovae prior to secondary recombination in densified PDG halos. Jeans instability of planetary-mass cloudlets composed of atomic hydrogen was facilitated by the external pressure of the surrounding plasma, collapsing cloudlets to form ultra puff planet DM. Ultra puffs presumably acted as accretionary magnets, competing with stellar-mass Jeans instability for the residual gas. This competition transformed gaseous proto-dwarf galaxies (PDGs) into gas-free ‘primordial dwarf galaxies’, which may correspond to the very faintest modern ultra-faint dwarf galaxies (UFDs). Then ultra puffs went dark (transparent), due to condensation and sedimentation of their Pop III star metallicity, forming diminutive rocky-icy cores.
¶    Sequestration of 5/6 of the baryon-photon fluid by about the epoch of matter-radiation equality created a sub-canonical sound horizon at recombination, since less expansion was required to reach the canonical conditions of recombination with sequestration. And a sub-canonical sound horizon may resolve the tension in the Hubble constant in favor of the local distance ladder.
………………..

1. Introduction
¶

¶    The rotation curves of spiral galaxies require much-greater cohesive force than the gravitation of their visible baryonic matter alone, positing DM halos to provide the necessary extra mass. Lambda Cold Dark Matter (ΛCDM) theory presumes cold (non-relativistic) DM of an exotic particle composition, but so far, all experiments designed to detect exotic-particle DM have consistently yielded negative results.

¶    The empirical baryon-to-photon ratio of the universe predicts an almost miraculous concordance between observed and model light-element abundances from Big Bang nucleosynthesis (BBN), most notably for the deuterium to hydrogen (D/H) ratio. Canonical conditions at BBN are challenging for baryonic DM theories that appear to require a six-fold increased baryon-to-photon ratio. Despite this challenge, surely the most intuitive DM candidate is baryonic matter composed of primordial concentrations of hydrogen and helium, since it requires no new particles beyond the standard model. The baryonic DM version suggested here proposes a canonical baryon-to-photon ratio, consistent with BBN and the first acoustic peak of the cosmic microwave background (CMB) radiation. This conceptual baryonic DM hypothesis requires 2 epochs of baryonic DM, with sequestration of 5/6 of the baryon-photon fluid from the Hubble flow into ‘proto dwarf galaxies’ prior to recombination as the first epoch of baryonic DM, followed by the conversion of sequestered baryons into puffy gaseous planets (‘ultra puff planet DM’ or merely ‘ultra puffs’) following recombination as the second and present epoch of baryonic DM.

‘Proto dwarf galaxy’ vs. ‘primordial dwarf galaxy’:
¶    Two terms will be used throughout to describe dwarf galaxies formed by PBHs in the early universe that evolved into the smallest modern dwarf galaxies. ‘Proto dwarf galaxy’ (PDG) and ‘primordial dwarf galaxy’ will at times be used interchangeably, but PDG specifically refers to (primordial) dwarf galaxies in an early proto state, prior to evolving into mature dwarf galaxies consisting of Population II (Pop II) stars and ultra puff DM. The more general term, primordial dwarf galaxy, refers to dwarf galaxies formed primordially (prior to recombination) that are in any stage of their evolution, from PDGs to modern ultra faint dwarf galaxies (UFDs).

Sequestration as the first epoch of baryonic DM, § 2:
¶    Mechanisms for sequestering 5/6 of all baryons are not difficult to conceive, but there may be only one possible mechanism that could sub-sequester the associated primordial photons, which is behind the event horizons of primordial black holes (PBHs). Frame dragging of baryonic photon fluid in Kerr PBH ergospheres collimated the baryon photon fluid, forcing it to rotate. The collimated photons overtook the charged particles (fermions and BBN nuclei) from behind and scattered off them in a coordinated fashion, resulting in tangential kicks that levitated the charged particles on a photon sea, preventing matter from reaching PBH event horizons, while allowing primordial photon accretion. The levitated charged particles were ejected from PBHs in polar jets, but remained gravitationally bound to their respective PBHs to form densified, photon-depleted halos. The emergence of baryonic halos transformed PBHs into PDGs as the first epoch of baryonic DM, sequestered from the Hubble flow. At the interface between the densified photon-depleted halo and the surrounding baryon-photon fluid of the Hubble flow, the primordial photons from the Hubble flow were scattered back into the Hubble flow due to the greater charge density of the densified, photon depleted halo, as if reflecting off a mirror, which reduced inward photon diffusion.
¶    If the degree of baryon-photon-fluid sequestration had been insignificant at BBN, then BBN essentially occurred at globally canonical conditions. And if the residual baryon-photon fluid remaining in the Hubble flow experienced locally canonical conditions at recombination, including a locally canonical baryon-to-photon ratio, then the CMB power spectrum should be canonical as well.
¶    Sub-sequestration of 5/6 of all primordial photons in their early energetic state swelled PBHs to supermassive proportions, rivaling the mass of all other matter and radiation in the universe combined, which requires a small degree of new physics. If rotating black holes do not possess singularities, as hypothesized by Roy Kerr, then this raises the possibility, suggested here, that photons may continue to undergo cosmic redshift after crossing black hole event horizons. This raises the possibility of black holes having a new property designated, ‘black hole redshift’, wherein the photon bloated early mass of PBHs decreased asymptotically toward the matter content (actually, the blueshifting of photons falling into black holes results in a ‘black hole redshift’ mass that is less than its cumulative matter content § 2).

Tension in the Hubble constant, § 3:
¶    Sequestration of 5/6 of the baryon-photon fluid caused compressive heating in PDGs and expansive cooling in the residual fluid remaining in the Hubble flow.  Compton scattering by the chilled residual baryons cooled the associated primordial photons in the Hubble flow, and since photon temperature (wavelength) determined the onset of recombination, the artificial chilling of photons due to sequestration necessitated less cosmic expansion (redshift) to reach the canonical temperature of recombination, resulting in a sub-canonical sound horizon at recombination.
¶    The angular size on the sky of the sound horizon is an empirical fact that is not in dispute. But a sub-canonical sound horizon (which is assumed to be canonical by ΛCDM) that is projected onto the empirical angular size on the sky of the sound horizon results in a sub-canonical ‘angular diameter distance’ to the last scattering surface. And a sub-canonical angular diameter distance (which is assumed to be canonical by ΛCDM) results in a super-canonical Hubble constant, since there are fewer megaparsecs to the actual last scattering surface than in the assumed canonical case. Thus, a sub-canonical sound horizon at recombination resolves the Hubble tension in favor of the local distance ladder of the Hubble constant measured by supernovae, calibrated by Cepheid variables.
¶    In the simplified case where the baryon density is canonical at recombination, this study calculates that the redshift of ‘effective recombination’ (had sequestration occurred instantaneously) occurred at z_seq = 3165 for a 7% tension in the Hubble constant and at z_seq = 3446 for a 5.5% tension in the Hubble constant (§ 3). The redshift of matter-radiation equality is often quoted as z_EQ ≅ 3400, so for a 7% tension in the Hubble constant this study calculates a redshift for effective sequestration slightly after matter-radiation equality, while for a 5.5% tension in the Hubble constant, this study calculates that effective sequestration occurred at just about matter-radiation equality.

Ultra puffs as the second epoch of baryonic DM, § 4:
¶    The remarkably high dark matter-to-luminous matter (DM/LM) ratio that can exceed 1000:1 in the smallest dwarf galaxies requires great formational efficiency, suggesting formation during a global state change, presumably during ‘secondary recombination’ in PDGs. Thermal fragmentation associated with radiative cooling of plasma can occur so rapidly that it’s been coined “shattering’, with fragmentation progressively extending to smaller and smaller scales until the cooling time becomes so short that cloudlets reach thermal equilibrium with their surroundings before they can fragment further. Importantly, this characteristic minimum scale length is within a factor of 2 of the estimated mass of a large cosmological population of free-floating planets from quasar microlensing studies.
¶    Jeans instability of planetary-mass cloudlets must have accompanied shattering as part of the state change of secondary recombination in order to achieve the high conversion efficiency, promoted by the external plasma pressure on planetary-mass cloudlets composed of atomic hydrogen. But even considering the efficiency of a state change, ultra puffs presumably had the secondary property of being accretional magnets, that competed with stellar-mass Jeans instability for the residual gas following secondary recombination, converting gaseous PDGs into modern gas-free primordial dwarf galaxies composed of Pop II stars and ultra puff DM.
¶    Excess angular momentum during Jeans instability may have formed ultra puffs in binary pairs. And binary ultra puffs would be resistant to the type of core collapse that forms cuspy stellar densities in globular clusters, possibly explaining the cored DM configurations observed in some dwarf galaxies.

¶    In terms of baryonic DM candidates, most collapsed and condensed matter objects, such as rogue gas-giant planets, brown dwarfs, white dwarfs, neutron stars, and black holes have been effectively excluded as exclusive DM candidates by Galactic microlensing studies, examining starlight for microlensing variability, although very-low-mass PBHs may still be viable (Tuntsov, Lewis & Walker 2023). Objects with sufficiently-low column density, however, are not automatically excluded by Galactic microlensing studies.

It has been claimed that the variability of field quasars resembles gravitational lensing by a large cosmological population of free-floating planets with mass ∼ 10 M⊕. But Galactic photometric monitoring experiments, on the other hand, exclude a large population of such planetary-mass gravitational lenses. These apparently contradictory pieces of evidence can be reconciled if the objects under consideration have a mean column-density that lies between the critical column-densities for gravitational lensing in these two contexts.

Galactic photometric monitoring experiments exclude the possibility that the Galactic dark matter resides in either planets or planetary-mass black holes; but objects that have
a peak column-density Σ0<∼10⁵ g cm⁻² do not automatically violate the Galactic constraints because they’re not strong gravitational lenses in that context.

(Tuntsov, Lewis & Walker 2023)

While Bonner-Ebert spheres are not excluded by Galactic microlensing studies due to their low column density, they are too short lived to constitute a feasible DM candidate, although the thermodynamics of hypothesized hydrogen snow clouds (Walker & Wardle 2019) may alter the stability calculus. A hybrid object is indicated, with the stability characteristic of gas-giant planets and the low column density characteristic of gas globules. Indeed, an article on super-puff planets sparked the idea for a free-floating version as a possible DM candidate. However, to be a viable DM candidate requires calculations proving long-term stability with a column below 10⁵ g cm⁻² and a reasonable metallicity.

¶    TOI-1420b is a super-puff planet with a remarkably low density that has a calculated envelope mass of 82 +7 -6 %, which leaves only about 18% of the planetary mass in the form of a rocky-metallic core. TOI-1420b has a radius of Rp = 11.9 ± 0.3 R⊕ and a mass of Mp = 25.1±3.8 M⊕ in a 6.96 day orbit around a late G dwarf star. (Yoshida et al. 2023)
¶    Ultra puffs are extreme versions of super-puff planets that permanently exist in a puffy state due to ultra-low metallicity, even at the cryogenic temperatures of the Galactic halo. While only ~ 18% of the mass of the remarkably-low-density super-puff planet TOI-1420b is in its core, primordial ultra puffs, presumably formed with only Population III (Pop III) star metallicity, may be orders of magnitude below the 1% metallicity of our Sun.

¶    Detection of the expected diminutive core mass of ultra puffs by Galactic microlensing will presumably require higher cadence studies than those designed to detect planetary mass objects, and one high cadence study designed to detect interstellar objects (ISOs), such as Oumuamua, has reported results. The Subaru Hyper Suprime-Cam (HSC) study (DeRocco et al 2023) with 2-minute cadence has peak sensitivity at 10⁻⁴ M⊕ for Milky Way lenses and 10⁻¹ M⊕ for lenses in M31. For a fiducial mass distribution of ISOs that follows a power law with an exponent of −2, the abundance of unbound objects is constrained to less than 1.4 × 10⁷ pc⁻³ for masses within 1 dex of 10⁻⁴ M⊕. This study highlights the difficulty of discriminating between diminutive cores of ultra puffs and the background noise of ISOs, which are now known to exist; however, an ultra puff signal might stand out as a departure from the expected power law for ISOs in a specially designed study.

Possible evidence for indirect detection of ultra puffs:
¶    Ultra puffs will not come away from stellar encounters unscathed. The Hill spheres of ultra puffs are greatly curtailed by close encounters with stars, necessarily resulting in evaporative loss (§ 7), which may be strongly enhanced by the intense stellar wind of hot stars, such as A-type and earlier stars.
¶    Walker et al. (2017) have discovered likely connections between radio-wave scattering of radio quasars by ionized gas clouds and the Hill spheres of hot A-type stars. The sight lines of 2 scintillating quasars pass near (inside or just beyond the Hill spheres) of two A-type stars, and the parallax of Earth’s orbital baseline is able to place the scintillating screens at the distance of these 2 stars. The team calculates that the chance association between these quasars and stars is ~ 10⁻⁴.
¶    Perhaps the most curious aspect of the Walker et al. (2017) finding is the ‘azimuthal velocities’ of the scintillating gas clouds of up to 9.7 km s⁻¹. Azimuthal velocities are tangential velocities to the hot stars, which would be expected from the forward momentum of gas eroded (evaporated)from ultra puffs in hyperbolic trajectories during stellar close encounters. Ultra puffs on steeply-inclined halo orbits should have differential velocities to disk stars comparable to the Sun’s 240 km s⁻¹ Galactic orbital velocity, which is some 20 times higher than the observed maximum velocity of 9.7 km s⁻¹, although the speed of evaporated gas will slow due to frictional interaction with the stellar wind. But a more likely cause of the low azimuthal velocities is that only ultra puffs with low differential velocities with respect to hot stars shed sufficient plasma density to cause measurable radio scintillation of quasars. But even intense erosion of ultra puff atmospheres by hot stars should not cause sublimation of core metallicity, which predicts that the composition of ultra puff erosion in stellar Hill spheres should be very nearly pure hydrogen and helium, with a scant contribution of metallicity from the stellar wind.

Ultra puff characteristics promoting invisibility:
¶    Theoretical Bonner-Ebert spheres have vanishingly small pressure and density gradients between their outer perimeters and their gravitational centers. Haworth et al. (2014) calculates that 1 M⊙ gas globules at 18 K will have a center-to-perimeter density ratio of only 1.5, compared to many orders of magnitude in the collapsed state of gaseous planets, including ultra puffs. So, dust that remains suspended indefinitely in gas globules will undergo rapid sedimentation in ultra puffs, promoting transparency and invisibility. But once again, hypothesized hydrogen snow clouds may differ from Bonner-Ebert spheres (Walker & Wardle 2019).
¶    Primordial ultra puffs have had nearly 14 Gyr to cool down, reducing their thermal signature, and they were born with very little radioactivity due to ultra-low metallicity, resulting in scant radioactive heating. Additionally, the majority of their Pop III star radioisotopes have decayed away, even the long-lived radioisotopes: thorium-232 has undergone 1 half-life, uranium-238 more than 3 half-lives, potassium-40 more than 10 half-lives and uranium-235 more than 18 half-lives in the presumed 13.78 Gyr age of ultra puffs.
¶    Elevated gas pressure at depth within ultra puff atmospheres raises the partial pressure of volatile metallicity, promoting condensation. Thus, the vast majority of the volatile stellar metallicity, such as carbon monoxide, has likely condensed and fallen onto the core. Additionally, ultra puffs on highly-inclined halo orbits encounter very little stellar radiation, and even the cosmic ray intensity is lower than in the disk plane. So, with low incident radiation and scant radioactive heating, there should be almost no internal thermal turbulence to prevent sedimentation of dust and condensates, interior of the interstellar wind disturbance of their extended ionospheres.
¶    Finally the diameters of ultra puffs, which may be large even compared to gas giant planets like Jupiter, are tiny compared to gas globules of a similar mass, and if only the central regions are opaque due to Rayleigh scattering, their central opaque diameters may be tiny fractions of their overall diameters, greatly limiting the distance at which ultra puffs can be telescopically resolved.
¶    Not all ultra puffs, however, are on steeply-inclined halo orbits and some may even have been incorporated into stellar systems as planets (§ 6), but for ultra puffs to have long survived in star systems may require considerable accretion of elevated metallicity gas prior to star formation, since the truncation of ultra puff Hill spheres within the gravitational wells of stars would otherwise cause evaporation. Therefore, there may be more naked ultra puff cores as terrestrial planets in stellar systems than as gaseous planets in the super-Earth mass range and up.

Spiral and Elliptical secondary accretional galaxies, § 5:
¶    This study suggests that secondary accretional galaxies formed by gravitational clustering of PDGs, with gravitational fragmentation of PDG assemblages responsible for the specific configurations of spiral and elliptical galaxies.
¶    Gravitational assemblages formed ‘PDG clusters’ that spun-up into ‘PDG disks’, akin to stellar protoplanetary disks. In systems with the highest specific angular momentum these spin-up configurations may have had bilateral rather than radial symmetry, possibly forming bar-mode instability or dumbbell configurations that fragmented due to self-gravity to form twin-binary proto-galaxies. Then subsequent mergers of these twin-binary galaxies formed giant elliptical galaxies. This high-angular-momentum mechanism for forming giant elliptical galaxies is designated ‘galactic symmetrical flip-flop fragmentation’ (galactic symmetrical FFF).
¶    This study suggests that spiral galaxies form by an alternative flip-flop mechanism. When a PDG cluster spun-up into a PDG disk that was much more massive than its proto-galactic core at the center of rotation, the disk had inertial dominance of the system, such that the diminutive proto-galactic core could not damp down disk inhomogeneities from amplifying into full-fledged disk fragmentation. The resulting solitary disk-fragmentation objects were necessarily much more massive than their diminutive proto-galactic cores, resulting in an inertial flip-flop that injected the former proto-galactic cores into satellite orbits around the disk-fragmentation objects, as proto-spiral galaxies. In the Milky Way system, the Large Magellanic Cloud is presumably the former proto-galactic core of the PDG disk that was flip-flopped into a satellite orbit by the disk fragmentation that formed the spiral Milky Way Galaxy. This galactic flip-flop mechanism is designated ‘galactic asymmetrical flip-flop fragmentation’ (galactic asymmetrical FFF).

The radial acceleration relation (RAR), § 7:
¶    Surely the most intuitive foundation for the RAR would be the direct interconversion of luminous matter (LM) and DM in galaxies, controlled by the local radial acceleration. The total mass (LM + DM) contained within a galactic radius determines the local radial acceleration, and the local radial acceleration determines the Hill spheres of ultra puffs at that galactic radius. The outer layer of an ultra puff atmosphere is presumably ionized, due to incident radiation and cosmic rays and the headwind of interstellar gas. This headwind will distort an ionosphere into a bow shock and a trailing tail, like the bow shock and heliotail of the Sun’s heliosphere. If the tail of an ultra puff ionosphere nominally exceeds its Hill sphere, the ultra puff will experience evaporative mass loss.
¶    Evaporation of an ultra puff necessarily increases its (specific) metallicity, since its metallicity is sequestered in its rocky-icy core. Thus, evaporative mass loss increases the specific core mass, which increases the atmospheric density, which contracts the ionosphere faster than the evaporative mass loss contracts the Hill sphere until the tail of the ionosphere no longer exceeds the Hill sphere, terminating evaporation. So the inverse correlation between mass and metallicity in evaporating ultra puffs provides the regulation mechanism of the RAR.
¶    On the other side of the ledger, gas accretion by ultra puffs could convert LM to DM; however, accretion of high metallicity gas would interfere with the RAR regulation mechanism, because of the positive correlation of mass and metallicity when accreting high metallicity gas. An alternative possibility for converting LM to DM would be the creation of new young ultra puffs in the circumgalactic medium, similar to the formation of primordial ultra puffs in PDGs.

DM/LM ratio today:
¶    This baryonic DM hypothesis does not provide a neat answer to the DM/LM ratio today, where a canonical ratio of sequestered to unsequestered baryons at recombination may have drifted since then. Exotic particle DM that does not decay will have maintained the DM/LM ratio of creation by definition, but baryonic DM that has the ability to interconvert with LM is far more ambiguous.
¶    On the DM side of the ledger, a variable percentage of formerly sequestered gas in PDGs has evolved into stars in primordial dwarf galaxies, and a larger percentage of formerly sequestered gas has presumably converted to gas and stars in secondary accretional galaxies. On the LM side of the ledger, an unknown percentage of formerly unsequestered gas was presumably accreted by PDGs prior to secondary recombination and an additional percentage was presumably accreted by ultra puffs after secondary recombination.
¶    While the RAR regulates the local interconversion of LM and DM in galaxies, there is no imagined mechanism for controlling the global DM/LM ratio of the universe, and thus the global ratio has presumably drifted over time. This ultra puff DM hypothesis can offer no reason why the sequestered to unsequestered ratio at recombination should be similar, close or identical to the DM/LM ratio today other than fortuitously, and the “missing baryon problem” recognized by the standard model may indicate that there has indeed been evolution of this ratio over time.
………………..

2. PBH formation and sequestration of baryon-photon fluid to form primordial dwarf galaxies (PDGs)

¶
PBH formation at the QCD epoch:
¶    Garcia-Bellido et al. (2022) identifies the quantum chromodynamics epoch for the creation of PBHs. “The sound speed drops abruptly in the quantum chromodynamics (QCD) transition due to the creation of non-relativistic protons and neutrons from quarks and gluons. This means that the radiation pressure, which usually prevents the collapse of mild inhomogeneities, suddenly drops, lowering the critical curvature ζ_c needed for PBH formation.” “[T]he sound speed drops abruptly by 30% during the QCD transition.” PBHs formed in the QCD epoch are on the order of the Chandrasekhar mass, M_Ch
≈1.4M_⊙, formed at a temperature corresponding to 200 MeV. (Garcia-Bellido et al., 2022).
¶    The term ‘PBH’ will be apply broadly, here, to any black hole that can trace its lineage back to the QCD epoch, excluding only stellar remnant black holes.

Baryon-photon fluid sequestration from the Hubble flow, forming PDGs:
¶    The radiation-dominated early universe constituted a high-pressure realm, with event horizons around PBHs as low-pressure sinks that efficiently channeled baryon-photon fluid to the ergosphere and primordial photons to the event horizon. The super-high baryon-to-photon ratio (> 109:1) and super-energetic primordial photons of the radiation epoch created conditions quite distinct from those in modern active galactic nuclei (AGN), with a very-different outcome for PBH accretion in the early universe.
¶    The Lense–Thirring effect around rotating Kerr black holes is a relativistic phenomenon causing spacetime itself to be dragged around rotating massive objects.  In the ergospheres surrounding rotating black holes, the frame dragging effect is so powerful that even photons are forced to rotate with the black hole in a collimated fashion. In this context, the super-abundant, super-energetic collimated primordial photons overtook charged particles (fermions and BBN nuclei) from behind and scattered off them in a coordinated fashion, providing collimated kicks that levitated the charged particles on a sea of photons, largely preventing charged matter particles from reaching PBH event horizons, while promoting photon accretion. The levitated charged particles may have been magnetically channeled and ejected in polar jets by the same poorly understood mechanism that operates in modern AGN.  Matter accreted by black holes emits energy, up to 42% of its rest mass for maximally rotating Kerr black holes, limiting the matter accretion rate to the Eddington Limit. By comparison, blueshifted photons retain their energy and do not contribute to Eddington luminosity. Thus, a sorting mechanism that accreted photons while ejecting matter promoted gargantuan rates of photon accretion by avoiding the Eddington Limit. The polar jets of charged particles were quickly blunted in the early high-density regime, swirling back on themselves to form densified, photon-depleted baryonic halos around their respective PBHs, with the densified photon-depleted halos confined by the gravity of PBHs swelled to supermassive proportions by energetic primordial photon accretion.
¶    So, the high-pressure realm of the radiation epoch caused PBHs to sequester baryon-photon fluid from the Hubble flow, with primordial photon sub-sequestration behind PBH event horizons. And the matter content of sequestered baryon-photon fluid was ejected from PBH erogospheres to form densified, photon-depleted baryonic halos around PBHs as the first epoch of baryonic DM.

Black hole redshift:
¶    Accretion of 5/6 of all primordial photons during their early energetic state must have converted stellar-mass PBHs into supermassive black holes (SMBHs). And reciprocally, only SMBHs whose aggregate mass rivaled or exceeded the energy content of everything else in the universe combined could have sequestered 5/6 of all baryon-photon fluid during the radiation dominated epoch. But the formation of very-early SMBHs in the cores of PDGs appears to require a new property of black holes, wherein photons continue to experience cosmic redshift after crossing PBH event horizons in a property designated here as ‘black hole redshift’. Black hole redshift requires that photons persist within BHs event horizons and continue to be subject to the metric expansion of space. This implies that BHs do not contain singularities that could crush photons out of existence.
¶    Roy P. Kerr (2023) states that there is no proof that black holes contain singularities when they are generated by real physical bodies, for which he provides counterexamples through every point in the Kerr metric that are asymptotic to at least one event horizon and do not end in singularities. Additionally, a rotating star that collapses to form a black hole does not result in a singularity, since—

“Centrifugal forces will always dominate in the end as the radius of the body decreases. That is just Physics. The Kerr metric shows that there will be a region between the event shell and the central body where an eagle can fly if it flaps its wings hard enough. It will, of course, notice the outside universe spinning very quickly around it. It may also have a problem with the radiation building up between the star and inner horizon.”
(Kerr, R. P., 2023)

So, if there is no singularity to crush photons out of existence, then a logical consequence may be continuing photon redshift after crossing black hole event horizons, which affecting BH mass.
¶    Baryonic DM appears to require black hole redshift, but beyond this basic requirement, the gravitational blueshifting of photons falling into black holes appears to suggest that black hole redshift may carry off more the pre-blueshifted energy of accreted photons, since the entire blueshifted energy of accreted photons would be subject to cosmic redshift. A photon falling from infinity into a Chandrasekhar mass black hole will experience a 64.87% increase in energy at the event horizon from gravitational blueshift (GPT-4), and photon blueshifting may continue inside black hole event horizons. Thus, black hole redshift could ultimately decrease BH mass by more than the energy content of their accreted pre-blueshifted photons; however, the information content of BHs may ultimately limit black hole redshift.
¶    PBHs reached their peak mass sometime before the epoch of matter-radiation equality. The vast majority of black hole redshift occurred in the very early universe when the Hubble parameter was vastly higher than today, with black hole redshift approximately halving PBH mass for every doubling of the scale factor. But even today, continuing mass loss due to black hole redshift should greatly exceed mass loss from Hawking radiation.

Little red dots as black hole stars:
¶    Pacucci & Loeb (2025) propose that LRDs may be the lowest 1% of the spin distribution of high redshifted galaxies, but alternatively, perhaps they were the 1% highest mass distribution of PDGs, which largely failed to form ultra puff DM. Even if all PBHs formed in the twinkle of an eye during the QCD epoch, there would still be a mass distribution of PBHs formed across the fleeting duration of the QCD epoch. The Schwarzschild area of a BH event horizon is proportional to its mass squared, A ∝ M², and if the baryon-photon-fluid sequestration rate of PBHs were proportional to event horizon area, rather than the mass, then a small initial mass distribution would create an exponentially larger distribution in the sequestration flux, resulting in a dramatic mass distribution of PDGs. Thus, percent differences in the initial mass function of PBHs may have translated into magnitude differences in the PDG mass distribution by the end of the sequestration epoch.
¶    And the upper end of the PDG mass distribution may have failed to form ultra puff DM, continuing as dense concentrations of primordial hydrogen and helium cored by massive black holes that are effectively black hole stars, which we see as little red dots (LRDs). The most extreme LRD to date is called The Cliff (RUBIES-UDS-154183), with M_∗ ~ 10^10.4–10.6 M_☉, packed into a volume of only ~ 40 pc (de Graaff et al., 2025). It may be that the most massive PDGs failed to undergo ‘shattering’, attended by secondary recombination, due to excessive conditions, or at least failed to form ultra puff DM in their gaseous cores.
¶    If the sequestration epoch effectively ended with matter-radiation equality, then the duration between sequestration and recombination would have been sufficient for diffusion damping to have erased dwarf-galaxy scale inhomogeneities, caused by a wide distribution of sequestration flux.

Primordial dwarf galaxies (PDGs):
¶    Baryon-photon fluid sequestration from the Hubble flow, with photon sub-sequestration behind PBH event horizons, converted PBHs into primordial dwarf galaxies (PDGs) by about the epoch of matter-radiation equality, likely with a mass distribution spanning 3 orders of magnitude or greater that evolved into modern dwarf galaxies. The high matter density and high charge density of photon-depleted baryonic halos surrounding PBHs may have largely shielded PDGs from surrounding baryon-photon fluid of the Hubble flow, by reflecting primordial photons from the surrounding Hubble flow like a mirror.
¶    Baryon-photon-fluid sequestration presumably ran to virtual completion around the epoch of matter-radiation equality, when primordial photons were no longer sufficiently energetic to exclude charged particles from crossing PBH event horizons, beginning the era of Eddington-luminosity-limited PBH accretion.
¶    Black hole redshift caused the expansion of PDGs, and expansive cooling of primordial gas laced with Pop III star metallicity promoted shattering to form planetary-mass cloudlets that gravitationally collapsed to form DM reservoirs in the form of stealthy ultra puffs (§ 4). The conversion of primordial gas to ultra puff DM transformed gaseous PDGs to modern DM-dominated dwarf galaxies.

Cosmological lithium problem:
¶    Collimated kicks by primordial photons may have mass fractionated charged particles in PBH ergospheres, causing stratification, such that protons (protium) were levitated above alpha particles (helium) in PBH ergospheres, with electrons governed more by electrical neutrality rather than by mass fractionation.  A finer discrimination of the fractionation stratification may reveal that primordial deuterium was sandwiched between protium and helium, with primordial lithium-7 as a substratum under helium.  Then as cosmic redshift progressively decreased the energy of the primordial photons, the stratified charged particles may have sunk progressively deeper into PBH ergosheres until a large percentage of the underlying primordial lithium formed at big bang nucleosynthesis (BBN) was skimmed off by PBH event horizons prior to the advent of the modern era, where PBH gas accretion is only limited by Eddington luminosity.
¶    So, fractionation of charged particles in PBH ergospheres by primordial photons offers the possibility of explaining the cosmological lithium problem, defined by the observed deficiency in primordial lithium-7 by a factor of 3–4, compared to theoretical predictions of BBN.
………………..

3. Tension in the Hubble constant and S8

¶
Hubble constant tension:

¶    The apparent size of the sound horizon at recombination when viewed from our current position in the universe is about 1 degree on the sky, which is linked to the first acoustic peak in the CMB power spectrum.

¶    The model-dependent value of the Hubble constant derived from the Planck mission, H₀ = (67.4±0.5) km s⁻¹ Mpc⁻¹ (Planck Collaboration, 2018), has a 5-sigma discrepancy with direct measurement by the Hubble Space Telescope of Cepheid variables in the host galaxies of 42 Type Ia supernovae used to calibrate the Hubble constant, H₀ = 73.04 ± 1.04 km s⁻¹ Mpc⁻¹ (Reiss et al., 2022). A follow up study by the SHoES project arrives at somewhat lower figures of H0 of 72.31±1.42 km s⁻¹ Mpc⁻¹ in the J band and 72.34+1.33−1.25 km s⁻¹ Mpc⁻¹ in the H band. (Galbany et al. 2023)
¶    This tension in the Hubble constant is in the 7–8% range. Direct measurements by the SHoES project are assumed here to be actual values, uncorrupted by uncertainty in the sound horizon.

¶    Sequestration decreased the baryon-photon fluid density and the associated baryon density in the Hubble flow by a factor of 6, but without directly affecting the redshift of the residual photons. Thus, the residual photons in the Hubble flow following sequestration were super-energetic compared to canonical photons at the same baryon density without sequestration.  But photon frequency/temperature, not baryon density, determines the recombination of electrons and protons, such that primordial photons unaffected by sequestration would have created a canonical sound horizon with sub-canonical baryon density at recombination, were it not for the associated expansive cooling caused by sequestration.
¶    While sequestration did not have a direct effect on photon frequency, it caused expansive cooling of the residual plasma in the Hubble flow, which had an indirect effect on the photon frequency, by way of Compton scattering. The residual baryon-photon fluid in the Hubble flow performed work on the sequestered fluid by compressing it into the low-pressure sinks formed by PBHs, resulting in compressive heating of the sequestered plasma and expansive cooling of the residual plasma.  This expansive cooling indirectly reduced photon frequency by thermal coupling between plasma and photons by means of Compton scattering. This chilling of the residual photons acted like artificial redshift, slightly reducing the subsequent photon redshift necessary to reach the canonical conditions of recombination.  Thus, extrapolated out to recombination, sequestration resulted in slightly early recombination, with a slightly sub-canonical sound horizon.  And a sub-canonical sound horizon at recombination artificially boosted the residual baryon density at recombination, possibly raising it to a canonical baryon density at recombination.  Ironically, sequestration reduced baryon density without directly affecting photon frequency, but by the epoch of recombination the effects were reversed, with Compton chilled photons resulting in a sub-canonical sound horizon that artificially boosted the baryon density, possibly raising it to a canonical baryon density at recombination.
¶    Sequestration was an extended epoch, but its effects can be modeled by an instantaneous event that occurred at the redshift of ‘effective sequestration’. Sequestration reduced the baryon-photon fluid density and the associated baryon density by a factor of 6, which can be represented as a (6−1) × 100% = 500% faux expansion of space, where the absolute value of the faux expansion was carried through to recombination, becoming a progressively smaller percentage of the sound horizon as the sound horizon grew over time. Thus, a 500% instantaneous volume reduction at sequestration that translates to a 7% length-scale reduction in the sound horizon at recombination, corresponds to a 20% volume reduction at recombination.

The redshift of ‘effective sequestration’:
¶    The alteration in the sound horizon due to sequestration can presumably be calculated from first principles, which is a task far beyond the scope of this conceptual study. However, in the special case where the sub-canonical sound horizon (fortuitously?) resulted in a canonical baryon density at recombination, the effective volume expansion inherent in sequestration carried through to recombination is a straightforward ratio calculation. Effective sequestration is an artificial construct of dubious value, since the first half of sequestration resulted in less faux expansion than the second half of sequestration, since the faux expansion is absolute, not relative.
¶    For conceptual discussion, the round number of 5:1 has been used for the DM/LM ratio, but the Planck 2018 results will be used for the DM/LM ratio for the calculation of effective sequestration, which is DM/LM = 0.120/0.0224 = 5.357 (Planck Collaboration 2018).
¶    Sequestration can be considered a 535.7% faux expansion of space, reducing the baryon density by 84% at the redshift of effective sequestration, but this faux expansion had no effect on the sound speed or sound horizon and no direct effect on photon frequency. In this special case where we stipulate that recombination occurred at the canonical baryon density, we can ignore photon frequency and follow the baryon density through to a canonical baryon density at which we define recombination for this purpose.
¶    The 535.7% faux expansion of space of effective sequestration is equated to the deficit in scale length at recombination that corresponds to the tension in the Hubble constant, according to,
¶  4π/3(r₂³ – r₁³) = 4π/3(r₄³ – r₃³)
where r₁ is the radius of the sound horizon at effective sequestration; r₂ is the canonical radius of the sound horizon without sequestration when the baryon density without sequestration equals the baryon density at effective sequestration; r₃ is the radius of the sound horizon at recombination with sequestration, and r₄ is the canonical radius of the sound horizon at recombination without sequestration
A 6.357-fold reduction in the baryon density at effective sequestration results in,
¶    r₂³ = 6.357r₁³
and a 7% deficit in the sound horizon at recombination results in,
¶    r₄ = 1.07r₃
Substituting and dividing out the constants results in,
¶    6.357r₁³ – r₁³ = (1.07r₄)³ – r₃³
¶    5.357r₁³ = 0.225r₃³
¶    r₃/r₁ = ∛(5.357/0.225) = 2.877
So, a 7% sub-canonical sound horizon at recombination yields a 2.877 ratio in the sound horizon between effective sequestration and recombination, corresponding to a redshift of effective sequestration of z_seq = 2.877 * 1100 = 3165. This compares to the redshift of matter-radiation equality, which is often quoted as z_EQ ≅ 3400.
¶    By comparison, a 5.5% sub-canonical sound horizon at recombination yields a redshift of effective sequestration of z_seq = 3446, which is closer to z_EQ ≅ 3400.
¶    The chilling of residual photons by the expansive cooling of sequestration resulted in a sub-canonical sound horizon. Some, most or all of the 6.357-fold reduction in baryon density caused by sequestration was made up by a sub-canonical sound horizon, possibly resulting in a canonical baryon density at recombination. A percent deviation from canonical baryon density at recombination results in the same percent deviation in the redshift of effective recombination.
¶    Assuming canonical baryon density at recombination,
– a 7% sub-canonical sound horizon predicts z_seq = 3165, and
– a 5.5% sub-canonical sound horizon predicts z_seq = 3446,
with the redshift of matter-radiation equality often quoted as, z_EQ ≅ 3400.
So, the redshift of effective sequestration corresponding to a 5.5% sub-canonical sound horizon at recombination more closely corresponds to z_EQ than a 7% sub-canonical sound horizon at recombination.

Early-time confusion sowing:
¶    A mistaken assumption by the standard model is called confusion sowing, and confusion that occurred at or before recombination is called early-time confusion sowing.  The confusion suggested here is a sub-canonical actual sound horizon that is mistaken to be canonical.  The angular projection on the sky of the sound horizon θ_s is an empirical value which is not in dispute, so for a sub-canonical actual sound horizon to fit the empirical θ_s footprint requires a sub-canonical actual angular diameter distance D_A, according to the formula,
¶    θ_s = r_s/D_A
where θ_s is the angular size on the sky, r_s is the physical size of the sound horizon at recombination, and D_A is the angular diameter distance to the last scattering surface.
¶    A sub-canonical actual diameter distance D_A to the last scattering surface translates into a super-canonical actual Hubble constant H₀, since there are fewer megaparsecs in the denominator of the Hubble constant (km/s/Mpc).  By this relationship, the percent tension in the Hubble constant directly corresponds to the same percent tension in the sound horizon at recombination.
¶    Positing a sub-canonical sound horizon is a well-trodden means of explaining away the tension in the Hubble constant. The most straightforward method of creating a sound horizon deficit is a reduction in the sound speed in the baryon-photon fluid prior to recombination by increasing the baryon density to radiation density ratio, ρ_b/ρ_γ; however, this alters θ_s at matter-radiation equality, which runs into contradictions with the CMB power spectrum (Knox and Millea 2019).  Sequestration sidesteps this failing, since the sound speed in the baryon-photon fluid is only a function of the baryon density to radiation density ratio, ρ_b/ρ_γ , which was unaffected by sequestration; however, the determination of matter-radiation equality (EQ) may not be straightforward with sequestration.  For θ_s at EQ to have been canonical with sequestration appears to require another departure from conventional understanding, where the sub-sequestered photons within PBHs are excluded from the tally for determining EQ. By this alternative method of accounting, θ_s at EQ with sequestration may have been canonical, occurring when the energy content of the residual photons in the Hubble flow equaled the combined energy content of residual and sequestered baryons, and this also assumes that sequestration had run to completion by EQ, which is counter to the above calculation for the redshift of effective sequestration.

The Hubble constant derived from the galaxy distribution:
¶    The baryon drag epoch began prior to recombination and extended slightly beyond it, ending when baryons and photons fully decoupled. The drag epoch extended slightly beyond recombination due to residual baryon-photon interactions, allowing acoustic waves to continue traveling for 10,000 to 20,000 years after recombination. While the sound horizon at recombination r_⋆ is imprinted on the CMB, the slightly-larger sound horizon at the drag epoch r_d determines the characteristic clustering of galaxies, with a canonical characteristic galaxy separation distance of about 150 Mpc. The clustering of galaxies is about 2% (r_d = 1.0184r_⋆) larger than the sound horizon at recombination.
¶    Sequestration had the same sub-canonical effect on r_d that it had on r_⋆ , creating a sub-canonical BAO distribution of galaxies, but unsurprisingly, the Hubble constant calculated from the model-dependent two-point correlation function of galaxy redshift and angular separation gives a value of the Hubble constant consistent with the canonical Planck results from the CMB. The most recent and most extensive baryon acoustic oscillations (BAO) evaluation are the DESI 2024 results, which gives a value of H₀ = 68.52 ± 0.62 km s⁻¹ Mpc⁻¹ (DESI Collaboration 2024), which firmly supports the standard model.

S8 tension:

¶    The S8 parameter is a key cosmological quantity used to describe the clustering of matter on a scale of 8 h⁻¹ Mpc in the universe. If the actual sound horizon is sub-canonical due to sequestration, then the anisotropies derived from the CMB power spectrum would also be sub-canonical, which is suggested here to be the source of the S8 tension.
¶    The model-dependent Planck results for the S8 parameter is 0.832 (Planck Collaboration 2018). Alternatively, the measured value based on weak gravitational lensing from the Hyper Suprime-Cam survey of the Subaru telescope for the S8 parameter is 0.769 (Li et al. 2023), resulting in a 7.5% sub-canonical S8 value, compared to the Planck results.
………………..

4. Emergence of ultra puffs as the second epoch of baryonic DM

¶
Ultra puff origin story:
¶    For some primordial dwarf galaxies to have acquired a DM/LM ratio as high as 1000:1 presumably requires formation by means of a global transition in former PDGs, such as a state change. In this regard, the plasma-to-neutral state change within PDGs suggests itself, designated here as ‘secondary recombination’. Secondary recombination was not accompanied by significant photon decoupling, since the overwhelming majority of the primordial photons associated with sequestered baryon-photon fluid within PDGs had been sub-sequestered within their respective PBHs. For clarity, hydrogen recombination in the Hubble flow, occurring at z = 1100, will be called ‘primary recombination’ in this section.
¶    Photon decoupling in the Hubble flow released the external pressure on densified PDG halos, causing expansive cooling of the halo gas, which was enhanced by ongoing black hole redshift. Although primary recombination presumably triggered secondary recombination, there may have been considerable delay between the two, perhaps hundreds of thousands or even millions of years until PDG halos became optically thin and could cool by infrared radiation. Thus, secondary recombination was not a sudden universal event like primary recombination, particularly due to the presumed mass variation range of PDGs and their central black holes.
¶    The rapid cooling of plasma causes thermal fragmentation, which progresses to smaller and smaller scales until reaching a relatively stable length scale, whereupon fragmentation ceases due to the cooling time becoming so short that the fragments reach thermal equilibrium with their surroundings before they can fragment further, whereupon hydrogen recombines (secondary recombination).

We find that clouds of optically-thin, pressure-confined gas are prone to fragmentation as they cool below ∼ 10⁶ K. This fragmentation follows the lengthscale ∼ c_st_cool , ultimately reaching very small scales (∼ 0.1 pc/n) as they reach the temperature ∼ 10⁴ K at which hydrogen recombines.
(McCourt et al. 2016)

¶    The length scale at which fragmentation ceases is determined by ~ c_st_cool , where c_s is the speed of sound in the gas and t_cool is the cooling time. The ultimate length of the cloudlet fragmentation is ~ 0.1 pc/n, where n is the number density of the gas. Assuming a primordial concentration of atomic hydrogen and helium, the mass of a cloudlet with this characteristic length scale is 5.7 M⊕ (by GPT-4), which is within a factor of 2 of the estimated mass of quasar lenses (∼10 M⊕). This type of thermal fragmentation occurs so rapidly that the process is referred to as “shattering”, which McCourt et al. (2016) describes as occurring in the circumgalactic medium (CGM) today.
¶    Additionally, the conversion of planetary-mass cloudlets into ultra puffs requires Jeans instability, which must have occurred with a similar degree of efficiency as the shattering process itself. Jeans instability in primordial PDGs was promoted by the external plasma pressure on planetary-mass cloudlets composed of atomic gas. This study does not reject the possibility of new young ultra puffs forming in the CGM today by similar mechanisms to those that formed primordial ultra puffs in PDGs, but with vastly lower efficiency.
¶    A final mechanism was presumably required to reach the high DM/LM ratio observed in many primordial dwarf galaxies, which was the accretional mopping up of residual gas by ultra puffs following the epoch of secondary recombination. Gas accretion by ultra puffs presumably competed with stellar-mass Jeans instability for the residual gas, with stellar-mass Jeans instability forming Population II (Pop II) stars. And the same gas and dust accretion facility of ultra puffs in early PDGs presumably continues in large accretional galaxies today (§ 7).

Binary ultra puffs may resolve the core-cusp issue:
¶    Stars are often formed in binary pairs, and ultra puffs may likewise form in binary pairs, when the specific angular momentum of their shattered cloudlets was high.
¶    When globular clusters undergo core collapse, the central regions form a very steep density profile that could be described as ‘cuspy’, similar to the theorized Navarro-Frenk-White (NFW) profile ∝ 𝑟−1 that is known as cuspy DM.  But binary stars in globular clusters can delay core collapse by providing a source of dynamical energy, until the binary pairs are resolved by either separating or by spiraling in and merging.  Globular clusters that have not undergone core collapse have a flat density profile in their central regions that could be described as ‘cored’, similar to the cored DM found at the center of some dwarf galaxies.  Binary stars can delay gravothermal catastrophe (core collapse) in globular clusters until the binary pairs are resolved in the central regions by either separating or by spiraling in and merging.
¶    Stellar profiles in the cores of globular clusters may be a good analogy for DM profiles in the cores of dwarf galaxies, with binary ultra puffs delaying DM core collapse in dwarf galaxies the way binary stars delay core collapse in globular clusters.  So if binary ultra puffs are capable of resolving themselves into solitary ultra puffs in the same way as binary stars in globular clusters, then ultra puff DM could explain both cored and cuspy DM profiles in dwarf galaxies, most notably in dSphs. But ultra puff DM is also subject to evaporation according to the RAR (§ 7), limiting the maximum ultra puff density in a cuspy profile.
………………..

5. Secondary accretional galaxies

¶
¶    Secondary accretional galaxies, such as spiral and elliptical galaxies, formed from the hierarchical assembly of a broad mass distribution of primordial dwarf galaxies to form ‘PDG clusters’. And gravitational contraction of PDG clusters caused spin up to form ‘PDG disks’, or possibly bar-mode instabilites, in the case of systems with high specific angular momentum. This study suggests that high-specific-angular momentum bar-mode instabilites may have formed gravitationally-bound twin galaxies that were doomed to spiral in and merge to form giant elliptical galaxies. And PDG disks presumably evolved into solitary spiral galaxies, but only indirectly by means of a disk fragmentation mechanism that accelerated galactic evolution by catastrophically projecting mass inward.
¶    In the standard model of cosmology, hierarchical galactic mergers form thick disks in computer simulations, unlike the thin knife-edge disks typical of actual spiral galaxies. But if PDGs already existed in modern form at the time of large accretional galaxy formation, then the earliest gravitational aggregation could be grainier and less gassy than the standard model.

Modern Dwarf galaxies as former PDGs:
¶    Ultra faint dwarf galaxies are defined as galaxies with luminosity L ≤ 10⁵ L_⊙. UFDs are differentiated from star clusters in possessing significant quantities of DM, and with larger physical extents than any known star clusters. Additionally, UFDs follow a luminosity-metallicity relationship, while globular clusters do not. Confirmed UFDs have half-light radii ranging from 24–295 pc. (Simon, 2019) UFDs are the least massive and most DM dominated galaxies.
¶    Dwarf spheroidal galaxies have diameters of 0.1–0.5 kpc, a mass range of 10⁷–10⁸ M_⊙ (and have half-light radii ranging from 170–2660 pc (Simon, 2019)).
¶    Dwarf elliptical galaxies, like their giant elliptical namesakes, are elliptical in shape and typically devoid of gas and ongoing star formation. DEs have diameters of 1–10 kpc, with a mass range of 10⁷–10⁹ M_⊙.

Spiral galaxy formation by a flip-flop mechanism:
¶    This study suggests that spiral galaxies may form by the same flip-flop mechanism that has been proposed to form most star systems with gas-giant exoplanets. The stellar version of this flip-flop mechanism is designated, ‘asymmetrical flip-flop fragmentation’ (asymmetrical FFF) (STARS, PLANETS, MOONS, MINOR PLANETS AND COMETS). When the central protostar or prestellar object (prestellar/protostellar core) of a nascent stellar system is more massive than its overlying protostellar disk, disk stability is governed by Toomre’s Q-criterion, where a Q parameter less than 1 can cause local disk instability. But when an overlying disk is much more massive than its diminutive (planetary-mass) prestellar/protostellar core, the core is unable to damp down disk inhomogeneities from amplifying into global ‘disk fragmentation’. According to asymmetrical FFF, this form of disk fragmentation necessarily forms a stellar-mass ‘disk-fragmentation’ object that is much-more massive than its planetary-mass core, which inertially flip-flops the core into a planetary satellite orbit around the disk-fragmentation object, with the disk-fragmentation object becoming the new star at the center of rotation.
¶    This study proposes a galactic version of asymmetrical FFF, designated ‘galactic asymmetrical FFF’, as the formation mechanism of spiral galaxies. And similar to the stellar version, when the central core at the center of rotation is unable to damp down inhomogeneities in a much-more-massive overlying disk, the PDG disk is similarly subject to disk fragmentation, forming a galactic disk-fragmentation object that injects the core into a planetary satellite orbit as a dwarf satellite galaxy, conserving system angular momentum. This catastrophic galactic disk-fragmentation mechanism rapidly projects mass inward, accelerating galactic evolution, forming very-early proto spiral galaxies. In the Milky Way system, the Large Magellanic Cloud (LMC) was presumably the former central ‘proto-galactic core’ of the PDG disk, and in the Andromeda system, “M32 is likely to be the stripped core of the disrupted galaxy” that merged with Andromeda about 2 billion years ago with a mass of ~ 2.5 x 10¹⁰ M⊙ (D’Souza & Bell, 2018), as the former central proto-galactic core of the Andromeda Galaxy system.

Disk of satellites (DoS):
¶    Spiral galaxies and stellar systems formed by asymmetrical FFF may have another similarity in the form of satellites in polar orbits. The highly flattened disk of satellites (DoS), or vast polar structure (VPOS), of co-orbiting satellite galaxies surrounding the Milky Way resembles the affinity of hot Jupiters for polar orbits around their host stars. Hot Jupiters in polar orbits around their host stars (Rice et al. 2022), indicates that the rotational axes of collapsing disk fragmentation objects are sometimes torqued perpendicular to the plane of their protostellar disks. In asymmetrical FFF, a nascent disk-fragmentation object may compete with the residual protostellar disk and the inertially-displaced former prestellar/protostellar core for the center of rotation, which may interfere with the contraction of the disk-fragmentation object. In this context, the most efficient path to a minimum energy state which forms the most massive possible central star may involve torquing the spin axis of the contracting disk-fragmentation object perpendicular to the original protostellar disk axis by reacting against the greater moment of inertia of the residual protostellar disk and the inertially-displace former prestellar/protostellar core. This torquing may take the form of a progressively increasing precession of the collapsing disk-fragmentation object, which may stop short of perpendicularity.
¶    A galactic analogy suggests that proto-spiral galaxies may similarly torque themselves perpendicular to their PDG disks, creating polar orbits for the residual satellite galaxies in the former PDG disk (predominantly UFDs and dSphs) and for the inertially-displaced former proto-galactic core (the LMC in the Milky Way).
¶    The DoS is notably polar around the Milky Way, meriting the designation VPOS, but is merely inclined to the spiral disk in Andromeda Galaxy (M31). The DoS is called the ‘Great Plane of Andromeda’ (GPoA) in M31, and its edge-on perspective clearly reveals the coorbiting nature of its constituent satellite galaxies in their relative Doppler shifts. Additionally, a DoS also has been found around Centaurus A, which is described as either an elliptical or lenticular galaxy.
¶    By comparison, the standard model predicts an isotropic distribution of satellite galaxies, and even computer simulation studies that specifically select for high line-of-sight velocity correlation find satellite structures to be transient. (Pawlowski & Sohn, 2021)

Elliptical galaxies from high-specific-angular-momentum PDG clusters:
¶    PDG clusters with elevated specific angular momentum may have spun-up into bilaterally symmetrical bar-mode instabilities or dumbbell-shaped configurations, rather than radially symmetrical PDG disks, with self-gravity forming twin proto-galaxies, with or without a diminutive tertiary proto-galactic core at the center of rotation as with galactic asymmetrical FFF. The stellar version of this mechanism is designated ‘symmetrical FFF’ (STARS, PLANETS, MOONS, MINOR PLANETS AND COMETS), which forms twin-binary stars and binary asteroids, comets and Kuiper belt objects. While asymmetrical FFF is a new and novel star-planet formation mechanism, symmetrical FFF may not represent a departure from the standard model. The ternary Alpha Centauri star system presumably formed by asymmetrical FFF, with Proxima Centauri as the former protostellar core of the star system and Alpha Centauri A & B as the much-more-massive twin-binary components of the disk fragmentation.
¶    The galactic version of this mechanism is designated ‘galactic symmetrical FFF’, which presumably formed twin-binary proto-galaxies that went on to merge and form giant elliptical galaxies. Elliptical galaxies are also understood to form by random galactic mergers.

Low surface brightness galaxies (LSB):
¶    LSBs are characterized by poor star formation rates, low metallicities, diffuse stellar disks, and extended atomic hydrogen gas disks, with little or no molecular hydrogen.  LSBs come in two types, 1) dwarf and irregular galaxies and 2) disk galaxies, with the largest giant low surface brightness galaxies (GLSB) among the most massive of all spiral galaxies.  Studies of the optical spectra of Seyfert 1 type nuclei in GLSB galaxies suggest that central black hole masses lie in the range of 10⁵−10⁶ M⊙, in the intermediate mass black hole (IMBH) range, rather than the SMBH range.  Some LSB disk galaxies have bright central bulges, while others have no bulges at all.  LSB galaxies are some of the most DM-dominated of all galaxies, and large DM halos may be responsible for disk stability and a slower rate of galaxy evolution.  Finally, larger LSB galaxies are clustered toward the outer edges of void walls and filaments.  (Das, 2013)
¶    The clustering of larger LSB galaxies toward the outer edge of void walls and filaments may be significant in their evolution, due to having had fewer mergers and tidal interactions with other large accretional galaxies, and this pristine formation history may also bear on the low (IMBH) mass of their central black holes. But the main difference compared to typical spiral galaxies may have been a failure of PDG disks to undergo galactic FFF, or alternatively perhaps merely a failure to torque their spin axes perpendicular to the PDG disks, which would have retarded the collapse of galactic disk fragmentation disks. But if LSB galaxies have undergone galactic asymmetrical FFF, whether or not they torqued their spin axes, they should each be accompanied by their inertially-displaced (flip-flopped) former cores, akin to the Large Magellanic Cloud in the Milky Way system. But why galaxies formed toward the outer edge of void walls and filaments may fail to undergo galactic FFF or may fail to torque their galactic disk-fragmentation objects perpendicular to their PDG disks is unclear.
………………..

6. Super-puff planets and/or Planet Nine as former ultra puffs(?)

Kepler-51:
¶    The three super-puff planets in the Kepler-51 system in the mass range of < 10 M⊕ are suggestive of ultra puffs, but the 90° inclination of the orbits of 2 of the 3 planets to the rotational axis of Kepler-51 instead implies formation by asymmetrical FFF, similar to the suggested formation mechanism of Hot Jupiters, which are commonly found in polar orbits around their host stars. When nascent star systems form by asymmetrical FFF, the contracting gas of the nascent disk instability object may be induced to torque its angular momentum vector perpendicular to the axis of the protoplanetary disk, resulting in a polar orbit of the former stellar core as a hot Jupiter § 5.
¶    Another argument against an ultra puff origin of the Kepler-51 planets is proximity to their host star in low warm orbits with highly truncated Hill spheres, where ultra puffs could not long survive.

Planet Nine:
¶    A much better case can be made for the hypothesized Planet Nine in our own solar system as an ultra puff planet with a mass of ~ 6−12 M⊕, a semimajor axis of ~ 654 AU, and an inclination of 30° (Millholland and Laughlin 2016).  Planet Nine is in the right mass range, its significant semi-major axis results in a sizable Hill sphere, and its significant inclination to the invariable plane of the solar system would be expected for a fortuitously acquired object.
¶    As of 2022, 3,924 trans-Neptunian objects (TNOs) have been discovered, with Planet Nine theoretically being millions of times more massive than the median TNO, while being only 4–20 times as distant.  Significantly, two synoptic surveys, the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) and The Dark Energy Survey (DES) have failed to detect the theoretical Planet Nine, while discovering numerous TNOs.  The still more powerful Legacy Survey of Space and Time (LSST) by Vera C. Rubin Observatory is expected to see first light in January 2025, although its highest resolution will only be achieved over time by stacking images.
¶    Planet Nine as an ultra puff could either have been captured by the Sun or could have preexisted in the dark core that collapsed to form the solar system, with the latter possibility being more likely, allowing for accretion of high metallicity gas in the nebula that spawned the Sun prior to having its Hill sphere truncated by the Sun’s gravity well.
¶    A study of long-period, nearly planar, Neptune-crossing objects discovers that ” the P9-free scenario is statistically rejected at a ∼5σ confidence-level” (Batygin et al. 2024).  So, a trans-Neptunian planet dimmer than median TNOs with a confidence level (5σ) sufficient to constitute a discovery makes a good case for Planet Nine in the form of an ultra puff.
………………..

7. Tully-Fisher and the radial acceleration relation (RAR)

¶
¶    McGaugh and Lelli (2016) assess the possibilities for the RAR as follows:

Possible interpretations for the radial acceleration relation fall into three broad categories.
¶    1. It represents the end product of galaxy formation
¶    2. It represents new dark sector physics that leads to the observed coupling.
¶    3. It is the result of new dynamical laws rather than dark matter.
(McGaugh and Lelli, 2016 )

¶    Of the 3 possibilities, the second possibility in the form of the continuous interconversion of luminous and dark baryonic matter dependent on the local radial acceleration is surely the simplest and most intuitive.

Radial acceleration relation:
¶    The Tully-Fisher relation correlates the intrinsic luminosity of a galaxy with its rotational velocity determined from Doppler shifts, while the RAR correlates the observed radial acceleration (g_obs) to the radial acceleration of the luminous matter (“baryonic”) component (g_bar). The Tully-Fisher relation calculates a single rotational velocity value, V_f , for each galaxy from the flat portion of the rotation curve, while the RAR enables the determination of multiple local values of gobs vs. g_bar at specific galactic radii. Additionally, the Tully-Fisher relation is limited to spiral and lenticular galaxies, while the RAR works for all galaxy types.
¶    A study (Lelli et al. 2017) of the link between “baryonic matter” (LM) and DM in 240 galaxies, spanning 9 dex in stellar mass including all galactic morphological types, strengthens the RAR, finding a “radial acceleration relation that is tantamount to a Natural Law: when the baryonic contribution is measured, the rotation curve follows, and vice versa”. When gobs is plotted against g_bar , a tight correlation is observed that has a 1:1 slope for radial acceleration greater than ∼10⁻¹⁰ m s⁻², and which increasingly deviates from a 1:1 slope at progressively-lower radial acceleration (Fig. 2). The 1:1 slope, where g_obs = g_bar , represents galactic regions that are essentially devoid of DM, while the progressive deviation from a 1:1 slope at lower radial accelerations represents a progressively-increasing DM/LM ratio. Lelli et al. (2017) finds that late-type galaxies (irregulars and spirals), early-type galaxies (ellipticals and lenticulars) and 62 dSphs follow the same radial acceleration relation over 4 dex, with a remarkably small scatter of ≤ 0.13 dex, albeit with a possible flattening of the curve at g_bar ≤ 10⁻¹² m s⁻² in ultra faint dSphs. But when the radial acceleration contribution of the host galaxy (ghost of the Milky Way Galaxy) is added to g_bar of ultra faint dSphs, replacing g_bar with g_bar + g_host , this apparent flattening of the curve disappears, which may indicate that total radial acceleration (g_obs) is the origin of the RAR, rather than g_bar , as the relation is often stated. Finally, the ‘tiny’ residuals in the study show no correlation with radius (R), stellar surface density at R, gas fraction at R, “baryonic mass” (LM), effective radius, effective surface brightness, or global gas fraction.

Tully-Fisher justification for gas-globule DM:
¶    Walker (1999) states, “If dark halos are composed of dense gas clouds, as has recently been inferred, then collisions between clouds lead to galaxy evolution.” He calculated that collisions between gas clouds create a DM core configuration that results in a pseudo Tully-Fisher relation between circular speed and visible mass, based on a preferred cloud column density of Σ ≈ 140 g cm⁻² in an isothermal halo model.
¶    Dense gas clouds, however, suffer from short lifespans, making them a problematic candidate for DM. The much-greater stability of gaseous planets in a collapsed state, such as ultra puffs, may provide the necessary stability that gas globules lack, but their much-greater column densities make them too weakly collisional to explain the Tully-Fisher relation on that basis.

Conversion of DM to LM, governed by the RAR:
¶    The most intuitive basis for the RAR is the direct interconversion of dark and luminous baryonic matter based on the observed radial acceleration at a given galactic radius, such that gobs determines gbar , not vice versa as the relation is often stated. The total mass enclosed within the galactic semi-major axis of an ultra puff determines the local radial acceleration, which determines (the size of) its Hill sphere. A 10 M⊕ planet, such as an ultra puff, at the Galactic semimajor axis of the Sun enclosing a mass of 10¹¹ M⊙ has a Hill sphere of 7,648 AU (GPT-4).
¶    The following is a hypothesis for the RAR, dependent on the containment or overflow of ultra puff ionospheres relative to their Hill spheres. Ultra puffs are presumably surrounded by extended ionospheres, ionized by cosmic rays, UV radiation, and the interstellar wind. Ultra puffs in highly-inclined halo orbits experience interstellar wind speeds comparable to their galactic orbital speed, and the interstellar headwind distorts their ionospheres into long trailing tails, like the solar heliotail of the heliosphere. Supposition: if the tail of an ultra puff ionosphere nominally exceeds its Hill sphere, the ultra puff will undergo evaporative mass loss. And since the vast majority of ultra puff metallicity is locked up in the icy-rocky core, evaporative mass loss is effectively a fractionation process that will progressively increase its (specific) metallicity, providing a regulating mechanism.
¶    This proposed metallicity regulating mechanism for the RAR is based on a positive correlation between metallicity and atmospheric density. When an ultra puff, with its metallicity sequestered in its icy-rocky core undergoes evaporative mass loss of its hydrogen-helium ionosphere, its specific core mass increases, which increases its atmospheric density which reduces its atmospheric diameter, including its ionospheric diameter. If an ultra puff in equilibrium were to fall into a lower galactic orbit with a higher ambient radial acceleration, the ultra puff’s Hill sphere would automatically decrease, but without immediately affecting the size of its ionosphere, causing its ionosphere to overflow its Hill sphere. The evaporative mass loss resulting from the overflow of the ionosphere would decrease the size of its ionosphere faster than the evaporative mass loss would decrease the size of its Hill sphere, due to the additional factor of atmospheric densification. Evaporation would continue until the ultra puff once again reached equilibrium at a lower mass and higher metallicity. Thus, ultra puff metallicity provides a regulating mechanism of the RAR by means of evaporative mass loss.
¶    On a galactic scale, radial acceleration decreases monotonically with galactic radius in spiral galaxies (as in almost all other galaxies) from the central bulge through the spiral disk, including through the flat portion of the rotation curve, resulting in ultra puff mass being positively correlated with galactic radius, and ultra puff metallicity being inversely correlated with galactic radius. So, DM density in a galactic setting is a factor of average ultra puff mass times ultra puff number density.

Conversion of LM to DM:
¶    To maintain something close to the 5/6 sequestered/unsequestered ratio of recombination in today’s universe in the context of ultra puff evaporation controlled by the RAR appears to require a mirror mechanism for converting luminous gas into ultra puff DM. Two possibilities come to mind, which are the creation of new (young) ultra puffs and/or gas accretion by existing ultra puffs.
¶    If ultra puffs evaporate when the stellar-wind elongated tails of their ionospheres nominally exceed their Hill spheres, then the converse may also occur, wherein they may accrete interstellar gas when their ionospheres are completely contained within their Hill spheres. One effect of accreting high metallicity interstellar gas in large secondary accretional galaxies would be an increase in (specific) metallicity that would skew the RAR. But in mature secondary accretional galaxies, such as the Milky Way, most ultra puffs may be in equilibrium, neither accreting nor evaporating, with most evaporation and accretion having occurred during early evolution when the ambient metallicity was far lower.
¶    The more interesting alternative for converting LM gas to ultra puff DM is the possibility of forming new young ultra puffs in secondary accretional galaxies by much the same mechanism as in primordial PDGs. McCourt et al. (2016) discusses the apparent locations of shattering in modern galaxies, naming the CGM, high-velocity clouds (HVCs), and in the broad-line regions and broad-absorption line regions around AGN.  If ultra puffs form in the vicinity of AGN, they may require high metallicity to overcome the high radial acceleration near AGN. Interstellar gas in the CGM has variable metallicity, such that some ultra puffs formed in the CGM in general and in HVCs in particular could be much more stable than their primordial versions, due to elevated metallicity. Shattering forms cloudlets composed of neutral hydrogen (H I) and helium of a characteristic length scale, surrounded by high temperature plasma whose external pressure helps confine and prolong the lifespan of the cloudlets. Fortuitous collisions of clouds and cloudlets may provide sufficient shock to induce Jeans instability in planetary-mass cloudlets, facilitating the formation of new young ultra puffs, but at a far lower efficiency than during secondary recombination in PDGs.

A possible role for ultra puffs in galactic bulge formation:
¶    Ultra puffs may possess a minimum threshold mass below which they experience runaway evaporation, despite metallicity increasing with evaporation, resulting in an absence of ultra puff DM in galactic cores above a threshold radial acceleration. And if runaway ultra puff evaporation occurred faster than the gas could settle onto the disk plane in proto spiral galaxies, then the gas may have spawned stars in situ by Jeans instability in highly-inclined galactic orbits, forming galactic bulges. If so, then spiral galaxies without central bulges may lack sufficient radial acceleration in their cores to cause runaway ultra puff evaporation. This predicts that spiral galaxies without central bulges contain ultra puff DM all the way down to their nuclear star clusters, whereas spiral galaxies with galactic bulges either contain no ultra puff DM in their bulge regions, or may contain a small quantity of ultra puffs with anomalously-high metallicity.
¶    In this regard, the central ellipses of elliptical galaxies may be similar to the central bulge in spiral galaxies, where ultra puff planet DM is unstable due to excessive radial acceleration.
Intriguingly, it was reported that some elliptical galaxies have little dark mass [12] and that the dark mass of elliptical galaxies appears correlated with the galaxy ellipticity [13]: the rounder the galaxy, the less dark matter it seems to contain.
(Winters et al. 2022)
¶    Runaway evaporation of ultra puffs will leave behind their icy-rocky cores, creating a large population of moony-mass or low-planetary-mass ultra puff cores in the galactic bulges of large galaxies. A high-cadence microlensing study targeting the galactic bulge might be interesting in this regard.
………………..

8. Discussion

¶

¶    Surely the simplest and most intuitive DM candidate is sequestered concentrations of primordial hydrogen and helium, and surely the most intuitive explanation for the RAR is the interconversion of LM and DM, dependent on the local radial acceleration.
¶    A canonical baryon-to-photon ratio, with sequestration of 5/6 of the baryon-photon fluid and sub-sequestration of the associated photons may resolve early universe objections to baryonic DM, and ultra-low-density free-floating planets may fit the requirement for a remote population of ∼ 10 M⊕ lenses, with a peak column-density ≲ 105 g cm−2, satisfying quasar microlensing studies, while skirting rejection by Galactic stellar microlensing studies.

Predictions:
– Predicts PBHs that lack lack singularities and experience black hole redshift
– Predicts the formation of PDGs prior to recombination as the 1st epoch of baryonic DM
– Predicts ultra puff DM as the 2nd and present epoch of baryonic DM
– Predicts a sub-canonical sound horizon, explaining the tension in the Hubble constant
– Predicts interconversion of LM and DM as the origin of the RAR
– Predicts rapid large galaxy formation by galactic FFF
– Predicts the cause of the cosmological lithium problem

Issues:
– Requires new physics to form PBHs without singularities that experience black hole redshift
– Quibbles with the standard model on matter-radiation equality
– Unable to explain why the DM/LM ratio today appears to be coincident with the observed DM/LM ratio at recombination

Summary:
– Two epochs of baryonic DM
– – 1st epoch—PBHs sequester 5/6 of all baryon-photon fluid from the Hubble flow around the time of matter-radiation equality, creating PDGs with densified photon-depleted halos surrounding PBHs, and the associated photons were sub-sequestered behind PBH event horizons. A residual 1/6 of the baryon-photon fluid remained in the Hubble flow at recombination at locally canonical conditions.
– – 2nd epoch—Primary recombination triggered secondary recombination in PDGs, with thermal fragmentation forming planetary-mass cloudlets that collapsed to form ultra-puff planet DM, likely in the form of binary ultra puffs.
– Primordial dwarf galaxies gravitationally clustered and spun up into proto dwarf galaxy disks. Most proto dwarf galaxy disks underwent galactic FFF (disk instability), either by means of asymmetrical galactic FFF forming spiral galaxies, or symmetrical galactic FFF forming elliptical galaxies.
– LM gas and DM ultra puffs freely interconvert within galaxies today, based on the local radial acceleration, creating the RAR.
………………..

References

¶   
Batygin, Konstantin; Morbidelli, Alessandro; Brown, Michael; Nesvorny, David, (2024), The Astrophysical Journal Letters, Volume 966, Number 1

DeRocco, William; Smyth, Nolan; Profumo, Stefano, (2023), Constraints on sub-terrestrial free-floating planets from Subaru microlensing observations, MNRAS 000, 1–10 (2023)

DESI Collaboration, (2024), DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations, arXiv:2404.03002v2

García-Bellido, Juan, Bernard Carr, and Sébastien Clesse. 2022. “Primordial Black Holes and a Common Origin of Baryons and Dark Matter” Universe 8, no. 1: 12

Galbany, Lluis; de Jaeger, Thomas; Reiss, Adam G.; Muller-Bravo, Tomas E.; Dhawan, Suhail; Phan, Kim; Stritzinger, M. D.; Karamehmetogulu, E.; Leibundgut, Bruno; Burns, Chris; Peterson, Erik; Kenworthy, W. D’Arcy; Johansson, Joel; Maguire, Kate; Jha, Saurabh W., (2023), A&A 679, A95 (2023)

de Graaff, A., Rix, H.-W., Naidu, R. P., et al, (2025), A remarkable ruby: Absorption in dense gas, rather than evolved stars, drives the extreme Balmer break of a little red dot at z = 3.5, A&A, 701, A168, doi:10.1051/0004-6361/202554681

Gratton, Raffaele; Bragaglia, Angela; Carreta, Eugenio; D’Orazi, Valentina; Lucatello, Sara; Sollima, Antonio, (2019), What is a Globular Cluster? An observational perspective, Astron Astrophys Rev 27, 8 (2019)

Haworth, Thomas J.; Facchini, Stefano; Clarke, Cathie J., (2014), The theory of globulettes: candidate precursors of brown dwarfs and free floating planets in H II regions, Mon. Not. R. Astron. Soc. 000, 1–10 (2014)

Kerr, R. P., (2023), Do Black Holes have Singularities?, 10.48550/arXiv.2312.00841

Knox, L.; Millea, M., (2019), The Hubble Hunter’s Guide, Phys. Rev. D 101, 043533 (2020)

Li, Xiangchong et al., Hyper Suprime-Cam Year 3 Results, (2023), Hyper Suprime-Cam Year 3 Results: Cosmology from Cosmic Shear Two-point Correlation Functions, arXiv:2304.00702v2

Libby-Roberts, Jessica E.; Berta-Thompson, Zachory K.; Désert, Jean-Michel; Masuda, Kento; Morley, Caroline V.; Lopez, Eric D.; Deck, Katherine M.; Fabrycky, Daniel; Fortney, Jonathan J.; Line, Michael R., (2019), The Featureless Transmission Spectra of Two Super-puff Planets, The Astronomical Journal, Volume 159, Number 2

Lelli, Federico; McGaugh, Sgtacy S.; Schombret, James M.; Pawlowski, Marcel S., (2017), One Law To Rule Them All: The Radial Acceleration Relation of Galaxies, arXiv:1610.08981v2

Masuda, Kento, (2014), Very Low-Density Planets around Kepler-51 Revealed with Transit Timing Variations and an Anomaly Similar to a Planet-Planet Eclipse Event, Astrophys.J. 783 (2014) 53

McCourt, Michael; Oh, S. Peng; O’Leary, Ryan M.; Madigan, Ann-Marie, (2016), A Characteristic Scale for Cold Gas, 2018 MNRAS.473.5407M

McGaugh, Stacy S.; Lelli, Federico; Schombert, James M., (2016), The Radial Acceleration Relation in Rotationally Supported Galaxies, Phys Rev Lett, 2016 Nov 11

Millholland, Sarah; Laughlin, Gregory, (2016), Constraints on Planet Nine’s Orbit and Sky Position within a Framework of Mean Motion Resonances, The Astronomical Journal, Volume 153, Number 3

Pacucci, Fabio & Loeb, Abraham, (2025), Cosmic Outliers: Low-spin Halos Explain the Abundance, Compactness, and Redshift Evolution of the Little Red Dots, ApJL 989 L19

Pawlowski, Marcel S., (2018), The Planes of Satellite Galaxies Problem, Suggested Solutions, and Open Questions, arXiv:1802.02579v1

Planck Collaboration, (2018), Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209

Reiss, Adam G.; Yuan, Wenlong; Macri, Lucas M.; Scolnic, Dan; Brout Dillon, Castertano, Stefano; Jones, David O.; Murakami, Yukei; Andand, Gagandeep S.; Breuval, Louise; Brink, Thomas G.; Flippenko, Alexei V. Hoffmann, Samantha; Jha, Saurabh W.; Kenworthy, D’arch; Mackenty, John; Stahl, Benjamin E. Zheng, Weikang, (2022), A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s-1 Mpc-1 Uncertainty from the Hubble Space Telescope and the SHoES Team, ApJL 934 L7

Rice, Malena; Wang, Songhu; Laughlin, Gregory, (2022), Origins of Hot Jupiters from the Stellar Obliquity Distribution, The Astrophysical Journal Letters, Volume 926, Issue 2, id.L17, 8 pp.

Shibata, Masaru; Yoshino, Hirotaka, (2010), Bar-mode instability of rapidly spinning black hole in higher dimensions: Numerical simulation in general relativity, arXiv:1004.4970v1

Simon, Joshua D., (2019), The Faintest Dwarf Galaxies, arXiv:1901.05465v1

Tokuda, Kazuki et al., (2019), AN ALMA VIEW OF MOLECULAR FILAMENTS IN THE LARGE MAGELLANIC CLOUD II: AN EARLY STAGE OF HIGH-MASS STAR FORMATION EMBEDDED AT COLLIDING CLOUDS IN N159W-SOUTH

Tsujimoto, T., (2010), Turn-off of deuterium astration in the recent star formation of the Galaxy disc (2010), arXiv:1009.0952v1 [astro-ph.GA]

Tuntsov, Artem V.; Lewis, Geraint F.; Walker, Mark A., (2023), Free-floating “planets” in the macrolensed quasar Q2237+0305, MNRAS 000, 1–18 (2023)

Walker, Mark A., (1999), Collisional baryonic dark matter halos, Mon. Not. R. Astron. Soc. 000, 00–00 (1999)

Walker, Mark A.; Tuntsov, Artem V.; Bignall, Hayley; Reynolds, Cormac; Bannister, Keith W.; Johnston, Simon; Stevens, Jamie; Ravo, Vikram, (2017), EXTREME RADIO-WAVE SCATTERING ASSOCIATED WITH HOT STARS

Walker, Mark A.; and Warble, Mark J., (2019), Cosmic Snow Clouds: Self-gravitating Gas Spheres Manifesting Hydrogen Condensation, arXiv:1906.05702v1 [astro-ph.GA]

Winters, D. M.; Deur, A.; Zheng, X., (2022), New Analysis of Dark Matter in Elliptical Galaxies, MNRAS, 518, 2, 2845-2852 (2023)

Yoshida et al., (2023), TESS Spots a Super-Puff: The Remarkably Low Density of TOI-1420b, AJ 166 181