Energy Density Driven Cosmology – a ΛCDM Alternative

Abstract

This work advances a conceptual cosmological model as presented in the original publication, “Energy Density Driven Galactic Formation and Evolution” (La Fortune 2015). Termed the Rotation Curve-Spin Parameter (RC-SP) model, it describes a singular, universal relativistically driven process providing for very early and rapid galactic disk formation in agreement with latest high red-shift astrophysical observations. In stark contrast to ΛCDM’s hierarchical accretion scenario, RC-SP completes nearly all galactic formation and significant evolution within the first 500Myr and greatly simplifies the understanding of galactic morphologies, kinematics and currently misunderstood gravitational “anomalies.”

Cosmological Energy Density and Gravitational Force Law

RC-SP dynamics agree with the general consensus that in the very early universe, conditions were highly relativistic in part due to extreme energy density that existed immediately following the big bang. It is only during this time that energy levels were high and distances short enough to drive complete formation of relatively ‘mature’ disks. Perhaps the most controversial aspect of this proposal is the assumption of relativistically driven non-Keplerian gravitational forces governing matter and structure creation in this very early environment. Per RC-SP, highly relativistic conditions immediately following the big band were governed by a pseudo 1/r force law. As the energy density rapidly declined and relativistic effects waned, the universe transformed to one governed by Keplerian gravitational dynamics and 1/r2 force law that is in effect now.

Why is 1/r-based force law associated with proto-galactic formation and rapid evolution? Based on RC-SP cosmology, this effective force law is the result of dimensional reduction (Lorentz contraction, relativistic velocities and/or geometric influence) and its physical impact on flux behavior and conservative scalar forces. This view requires no extra dimensions, ‘new-physics,’ nor dark entities, just an appreciation of the remarkable physics that can occur at this unique epoch of history. If a dimensionally reduced (2+1) and 1/r-governed early universe created galaxies immediately following the big bang, what would their expected properties be? The answer lies in the morphological and kinematic characteristics disk galaxies exhibit in the current universe; highly planar exponential surface mass density profiles, constant / flat rotation curves and non-Keplerian dynamics. In fact, 1/r force law has been a central tenet of MOdified Newtonian Dynamics (MOND) for over forty-years as a functional means to reproduce asymptotically flat galactic rotation curves. Unfortunately, MOND has been hampered as fundamental for lack of a satisfactory physical explanation for this particular force law. On the other hand, ΛCDM relies exclusively on Newtonian mechanics and massive dark matter halos. This non-relativistic approach does not describe conditions during this very early epoch of galaxy formation when energy densities were ten million of times greater than today.

Galactic Formation and Evolution – Interpreting New Evidence

What if any evidence supports this early, intense and rapid galaxy formation? As we can peer into the more distant past, there has been a trend in finding extremely old “fully developed spiral galaxies” inhabiting the universe at a very early stage (Steinhardt 2015). Steinhardt’s title of his paper is, “The Impossibly Early Galaxy Problem,” implying galaxies like these should not exist in a ΛCDM governed universe – but they do and in great numbers. What are the favored properties and evolutionary fate for this these very early galaxies? An H-ATLAS/GAMA calorimetry survey has already answered this question (Eales 2015). Their findings show highly red shift galaxies are “disk-dominated” and undergo significant morphological transformation in the early universe. This study was given support by another survey of 10 billion year old galaxies in which over ninety-percent had rotational signatures (Price 2015). This implies angular momentum was present and played a significant role right from the start.

In addition to proto-galactic formation, star formation has also been regulated via the RC-SP process described above. Figure 1 shows observed the galactic Star Formation Rate (SFR) over the life of the universe. (Snaith 2014). This figure is meant to be illustrative indicating there is correspondence between SFR and the decline in cosmic energy density over time.

Figure 1: Radiation Energy Density vs. Observed Star Formation Rate (Snaith 2014). Georgia State University Hyper Physics App for radiation energy density calculation.

Nearly all primordial galaxy formation occurs in the extremely condensed time frame on the right-side of the plot. At around 250 million years, stars are physically able to form in the emerging Keplerian dynamic (1/r → 1/r2) and fully realized in three “isotropic” dimensional "space" in the form of truly spheroidal entities. This transition to Keplerian dynamics and elevated SFR rates following the ‘knee’ in the energy density curve is evidence of this association. Stars continued to form at high rates for a couple billion years afterwards until secular and environmental processes began to dominate galactic evolution. Perhaps just as important, Price found little evidence of significant evolution over the past several billion years as suggested by the SFR tracking of cosmological energy density’s slow decline to present day.

The Dark Matter Halo and Galactic Rotational Velocity Support

This section gives a very brief overview of ΛCDM dynamics and dark matter influence on galactic kinematics. This provides a direct comparison between RC-SP dynamics and dark matter halo rotational velocity and angular momentum support. Figure 2 below depicts an idealized ΛCDM velocity curve scaled to the dimensions of the (Milky Way) MW.

Figure 2:  Idealized Dark Matter Halo Contribution to the MW’s Rotation Curve.

This figure shows the MW with a flat disk rotation velocity of 230 km/s represented by the horizontal blue dashed line. Halo velocity support is denoted by the thick black curve and the baryonic velocity contribution by the peaked thin curve near the left side of the plot. The vertical double light-blue arrows highlight the extent of rotational support. We see that halo velocity support becomes progressively prominent at larger radii and is almost entirely responsible for flat rotation beyond 40 kpc (the stellar disk’s edge). The red dotted curve is the Keplerian velocity expectation for a 5x1011Mʘ point mass, the importance of which will be covered in the next sections.

RC-SP Dynamics – Reinterpreting the Physical Evidence

This section presents a dark matter free alternative based on the latest, most advanced observations of the MW and M31. First, we challenge the notion of highly extended flat galactic rotation velocities against new findings indicating a Keplerian decline outside the baryonic disk. Figure 3 below represents the latest estimate of rotation velocities inside 25 kpc for the MW, versus the calculated baryonic (gray band/thin black curve) contribution as reproduced in the previous figure (Pato 2015).

Figure 3: Milky Way “Actual” Rotation Curve vs. Estimated Baryonic Contribution (Pato 2015).

These latest measurements clearly indicate a flat rotation curve (red points with error bars). We definitely observe flat rotation inside 25 kpc, but can this be arbitrarily extended to the edge of the dark matter halo? New data is increasingly suggesting flat rotation does not extend to the halo’s edge, but terminates at the edge of the baryonic disk.

Figure 4 shows a combined extended view of MW satellite data out to 200 kpc (Küpper 2015). The Keplerian rotation curve (red dashed curve) represents an equivalent point mass of 5x1011Mʘ (Moffat 2015), the same as shown in Figure 2.

Figure 4: Measured Circular Velocities of Extended Milky Way Satellites (Küpper 2015).

The horizontal blue dashed line in Figure 4 is the same shown in the previous figure, but drawn “to scale” highlighting the limited extent of Pato’s data set. Blue data points represent MW satellite galaxy orbital radius against circular velocity. Note that these satellites define a Keplerian curve, not the ΛCDM flattened asymptotic rotation curves depicted by the black solid lines extending to the far right. A fact that can be drawn from this data is that at least for the MW, flat rotation does not extend past the disk.

Figure 5 reconfigures the data presented in Figures 3 and 4 to create an idealized full rotation curve for the MW per RC-SP. Similar to previous figures, the vertical blue arrows represent rotational velocity support.

Figure 5: Idealized RC-SP Velocity Contribution to the Milky Way’s Rotation Curve.

Compared to the ΛCDM/dark matter halo depiction in Figure 2, we see an entirely new phenomenon - rotational velocity suppression (represented by vertical red arrows). We find flat disk rotation is the net action of imparted/retained angular momentum inherent in the baryonic disk. Maximal Keplerian suppression occurs near the galactic core, declining toward the disk’s edge tracking with the decline in baryonic surface mass density. Beyond the baryonic disk, rotational velocity follows the Keplerian point mass equivalent and MW satellite galaxy kinematics.

Note that velocity suppression is not possible for dark matter as its contribution is always additive to the overall rotation curve. Even MOND proponents have acknowledged this velocity decline and have modified their models to account for this fact (Hees 2015).

RC-SP Dynamics - MW and M31 Physical Evidence

This bold restating of the galactic dynamics in Figure 5 requires one to ask, where is the physical evidence for suppressed rotation velocities? Evidence is revealed in a recent paper investigating the influence of dark matter halos within the Local Group (Sofue 2015). In this work, Sofue updated rotational velocity data for MW and M31 and termed them the new “Grand Rotation Curves” (GRCs). The updated MW GRC is reproduced in Figure 6 below.

Figure 6: The New GRC of the Milky Way and Kinematic Disruption (Sofue 2015), inset (King 2015).

In the above figure, we fit the same 5x1011Mʘ point mass equivalent Keplerian decline obtained from the satellite data to the GRC and find it matches the GRC data. We see that the RC-SP dynamic mass estimate (red dash) is corroborated by two independent measures. As the MW is a real system and not idealized as depicted in previous figure, the light gray data points indicate partial suppression / velocity lift in the outer disk toward the Keplerian curve. In addition to gross velocity deviation, the inset shows a significant disruption in velocity dispersion, as described by the Anisotropy Coefficient “β” (King 2015). These exceptionally negative velocity anisotropy coefficients (β < -3) correspond to very fast, highly tangential orbits that boarder on the “unphysical” for well equilibrated, relaxed systems. Neither ΛCDM nor MOND proponents have advanced any plausible (internally consistent) solutions for this particular significant kinematic signature. In fact, this signature has been downplayed or dismissed by the mainstream due to inability to explain this feature within their frameworks.

We now turn our attention to the GRC for M31, as reproduced below in Figure 7 to demonstrate the applicability of this method beyond a single galaxy.

Figure 7: The GRC of M31 and the RC-SP Fit to Rotation Curve (Sofue 2015). Log-log format linearizes the Keplerian decline.

As with the MW, we visually fit a Keplerian curve to M31’s GRC providing a dynamic mass at 14x1011M ʘ. Although Figures 6 and 7 indicate little or no dark matter halo velocity support beyond the baryonic disk, the GRC curve fit is consistent with other estimated dynamic masses for the local pair, MW at 6x1011Mʘ and M31 at 12x1011Mʘ (Fattahi 2015).

Disk Galaxies - Fundamental Physical Parameters and Constraints

RC-SP dynamics assumes disk galaxies are inherently fully self-gravitating and rotationally supported baryonic entities. The early-era transformation process, although not perceptible in today’s static, low energy environment, maintains maximal angular momentum over galactic lifetimes. Based on this assumption, what is the guiding physical and dynamical relationship that drives galaxies to a common morphology and similar phenomena? We find galaxies are governed and constrained by the dimensionless ratio termed Spin Parameter (λ). This particular equation is the fundamental relationship for fully self-gravitating disks having axisymmetric exponentially declining mass density profiles, a useful description for rotationally supported disk (spiral) galaxies:

Where J = Angular Momentum, E = Total Energy, MDyn = Dynamic mass, and Total E = K + PE.

The concept of assuming maximal, self-gravitating disks is not new and has been used by others in the past. This approach employing the Spin Parameter to characterize spiral galaxies has recently been revived substituting a galactic disk log-normal surface density profile for the standard exponential parameter shown above (Marr 2015). Marr found the log-normal disk model may provide a better fit than the exponential model with observations supporting a value with very little deviation (λ = 0.423±0.014).

The Spin Parameter is a simple relation/equation that obeys the concept of simple proportionality. With this capability, we can estimate the total baryonic content of other disk galaxies within this broad class of rotationally supported galaxies. Also, by combining the Spin Parameter with the GRC, it constrains dynamic to baryonic mass ratios. In other words, if we can determine the baryonic mass for one galaxy, we can apply this same ratio to others and can estimate many disk galaxy properties from a few examples.

By most recent estimates, the stellar baryonic mass of the MW disk is ~5x1010Mʘ (McGaugh 2015). The MW is considered an unremarkable quiescent disk galaxy, perfectly suited for our analysis (Mutch 2011). Using the dynamic mass estimate of 5x1011Mʘ obtained from the GRC fit, we find the dynamic to stellar baryonic mass ratio for the MW:

Since both MW and M31 adhere to the same Spin Parameter class, we calculate M31’s disk to contain 14x1010Mʘ baryons, 3x the baryonic mass of the MW:

Note that this 10:1 ratio is based on the stellar disk mass where the majority of angular momentum resides. If all bound galactic baryons: bulge, thick disk, thin disk, stellar halo, and neutral/ionized gas are considered, this ratio would naturally be reduced. This type of baryonic accounting, so important for ΛCDM is a simple bookkeeping exercise for RC-SP.

As RC-SP dynamics predict proportionality between galactic properties, we expect a consistent mass-size ratio for all baryonic constituents in the disk. Our Local Group pair provides an excellent example to estimate the stellar disk mass-size ratio:

Note this 3:2 (m=1.5) ratio correspond to total galactic dynamic mass, including all angular momentum and energy carried by the baryons according to the spin parameter equation. We can compare the stellar disk ratio with measurements obtained for the physical properties of HI disk inhabiting spiral galaxies (Martinsson 2015). Figure 8 provides the relationship between HI disk mass and diameter and a demonstration how the gas content of the Milky Way is estimated from a first order perspective.

Figure 8: The HI mass-size relationship [fig 6 (Martinsson 2015)]. The estimated HI percentage for the MW is determined from the standard D25 photometric value (blue square). The arrow to the left of D25 is the ratio of the diameter of HI disks compared to the D25 values (DHI ≈ 1.35D25) obtained from Martinsson. This figure illustrates how direct observation provides a realistic HI gas proportion for the Milky Way.

We can obtain a reasonable estimate of the MW’s HI disk mass by employing the DHI/D25 = 1.35 ± 0.22 relationship obtained by Martinsson. Using a Küpper derived dynamic mass of 2.1x1011Mʘ inside a radius of 19 kpc (close to 27 kpc for an estimate). The MW HI gas fraction is estimated made using the RC-SP inferred baryonic (stellar) mass 2.1x1010Mʘ is approximately 15%, wholly consistent with observational expectations. Applying the standard ratio of HI to total gas (x1.33), the estimated gas content is close to 20% for the MW.

The next section compares results obtained from RC-SP from a ΛCDM perspective. We point out several issues with the current paradigm and suggest RC-SP based solutions without the need for a dark matter placeholder. With equivalency between M200 and MRC-SP already established, the RC-SP 10:1 ratio can be directly related to ΛCDM’s “baryonic fraction,” fb ≡ (MBaryons/M200) = 0.1.

RC-SP Dynamics: Comparisons to ΛCDM (Dark Matter Halo) Simulations

As ΛCDM simulations become more sophisticated, we are beginning to see a convergence of physically observed and simulated baryonic properties. HI gas is now considered an integral component in the accurate reproduction of baryon physics and is incorporated in the latest EAGLE ΛCDM-based hydrodynamical simulations summarized below in Figure 9 (Bah´e 2015). This figure from Bah´e depicts neutral hydrogen (HI + H2) gas fraction as a function of galactic stellar mass for EAGLE simulations and GASS observations.

Figure 9: EAGLE simulation for neutral gas (HI+H2) gas fractions (blue line and shade) for a wide range of galactic stellar mass [Fig 1. (Bah´e 2015)]. The MW RC-SP estimated mass and gas fraction is depicted in red.

The blue curve denotes simulation results (blue solid/shade) and GASS observations (gray triangles). The RC-SP disk HI gas fraction is shown in red. We find the simulations match observations well as does the RC-SP value for the MW. EAGLE results depict a smooth but substantial fall-off in neutral gas fraction for more massive galaxies. This substantial decline in HI gas with galactic mass appears to be an artifact of the simulation. Based on the estimated gas fraction of M31 (log stellar mass = 11.1), the simulation returns a HI gas fraction of less than three-percent, an unrealistically low value based on observation.

Now we begin to investigate ΛCDM simulation results beyond the Local Group and compare RC-SP expectations for a broad class of disk galaxies.

A basic tenet of ΛCDM simulations is that baryonic matter receives its angular momentum directly from the dark matter halo. Simulations and numerical methods have shown dark matter halos exhibit a median Spin Parameter λ ≈ 0.04 which is ten times lower than baryonic disks with Spin Parameter λ ≈ 0.425. Therefore, the halo must at least be ten times more massive than the baryons to satisfy the total disk moment, leading to an expected galactic baryonic fraction of ≈0.1, the same as the RC-SP dynamic/stellar mass ratio. Employing the assumption of angular momentum conservation between the halo and disk, GADGET-3 simulations were performed focusing on momentum transfer and its effect on baryonic constituents – stars and gas shown in Figure 10 (Pedrosa 2015). These simulations results provide a theoretical angular momentum-mass relationship for the dark matter halo   based on the proposition that all baryons receive their observed angular momentum (and total energy) from the dark matter halo - exclusively. This basic tenet has not been proved to be physical, but is mathematically required to reproduce the baryonic spin parameter.

Figure 10: Specific Angular Momentum versus Galactic Component Mass [Fig 2, z=0, Pedrosa 2015: Relation ji − mi medians for the stellar (red dashed lines) and gaseous (green dashed lines) disc components, the stellar spheroidal components (pink dashed lines), the total stellar component (blue line) and the total baryonic component (black lines). The solid black line represents the relation in the case of angular momentum conservation for the dark matter halos. The dashed black line is the Total Baryonic Spin Parameter expectation (added to original figure).

GADGET-3 results presented in Figure 10 confirm the anticipated ΛCDM-based relationship for individual baryonic constituents. However, when the total baryonic content is accounted for, it shifts to the fundamental Spin Parameter relationship already provided - .

Next, we return to results obtained from the EAGLE simulation from a larger perspective (Schaller 2015). Figure 11 compares EAGLE simulation output with RC-SP derived MW and M31 ‘baryonic fractions’ and dynamic masses. We show the differences (and similarities) between ɅCDM models and the RC-SP prescription.

Figure 11: The median ratio of stellar (M*) and DM halo mass (M200) (Schaller 2015).

The above figure reproduces Shaller’s results for the baryonic fraction (M*(stellar)/M200) as a function of M200 (equivalent to MRC-SP dynamic mass values). We observe a short horizontal plateau near baryon fraction fb = 0.1, decreasing on either side. Setting MRC-SP M200 and normalizing Ωbm ≡ 1 (no dark matter) the results of RC-SP and ΛCDM can be compared in the same plot. Open circles represent MW and M31 dynamic masses with a dynamic/stellar ratio of 10:1 or the equivalent baryonic fraction fb = 0.1. Included in Figure 11 are Sofue’s values for the MW and M31 (orange triangles) via ΛCDM. It is interesting to note that the same reference providing the new GRCs (Figures 6 and 7) also report viral mass and baryonic fraction for the pair of galaxies. We see Sofue’s MW and M31 values deviate from the models and almost appear to be outliers indicating the methodology is amiss or that both MW and M31 do not represent typical disk galaxies in the ΛCDM universe.

Please note that RC-SP results span a very short mass range delimited by the two data points, MW and M31. The full RC-SP expectation is that fb = 0.1 should remain consistent over a wide range of dynamic mass, not just the narrow plateau depicted above. With RC-SP, it is expected that the galactic baryonic fraction to remain reasonably consistent over a much broader range of dynamic mass. We need to look beyond this specific simulation result to determine if the plateau near fb = 0.1 is realistic or an artifact of the methodology. This question can be answered by comparing ΛCDM simulation results (Gadget2-SPH + Ref in Figure 10) with galactic survey data as provided in Figure 12 below reproduced from a more recent publication from Sofue (Y.Sofue 2015).

Figure 12: GADGET2-SPH ΛCDM Simulation (Schaller 2015) and RC-SP Results Comparison. Figure from (Y.Sofue 2015)

The above plot depicts the observed halo/baryon relationship for dwarf and spiral (disk) galaxies spanning a wide range of galactic mass. Using this format provided by Sofue, we can determine the general accuracy and interpretation of ΛCDM simulations results against observation. From a simple visual analysis, we observe an obvious flaw in the simulation. It directly links spiral to dwarfs by a falling baryonic fraction curve extending between the two populations. The open white circles represent RC-SP dynamics for the MW and M31 for baryonic fractions equivalent to 0.11 (dashed blue line intersecting MW and M31). The GADGET2-SPH + Ref result is interesting in that it attempts to directly link spirals and dwarf galaxies through a decreasing baryonic fraction. This linkage might make sense computationally, but highlights a cognitive disconnect existing between fundamental physics and unresolved galactic phenomena.

We reinterpret the data in Figure 12 by fitting the correct baryonic fraction to the dwarf galaxy population (fb 0.1) and see that the dwarf population parallels the more massive spiral galaxies. This suggests all rotationally supported galaxies regardless of mass are governed by the same Spin Parameter constraint. An Occam’s razor argument directs us to conclude this vertical offset is due to an incomplete inventory (probably gas) of total baryonic mass for these dwarf galaxies. Nothing “dark” is required to harmonize both low and high mass galaxies.

To finish up the discussion, we are beginning to witness ΛCDM simulations starting to deliver real-world results for some of the basic baryonic properties of galactic disks. The downside is ΛCDM is has achieved convergence using very complex assumptions and tortuous logic when more simple methods are available to arrive at the same result. Moreover, we show dark matter can be completely eliminated from the cosmological process using a RC-SP dynamical approach. As precision astrophysical observations continue to tighten physical constraints and relationships for all theories, we need to remember it is not the what, but the how that is crucial to understanding galactic phenomena.

Conclusion

A new galactic formation and evolution process (RC-SP Dynamics) has been proposed. This process, driven by the extreme energy density decline within the very early universe results in the morphological and kinematic properties of the Milky Way and other rotationally supported galaxies. RC-SP side-steps “angular momentum catastrophe” and “missing mass” problems inflicting ΛCDM and provides alternative classically obtained solutions. The goal of this letter is to bring substance and structure to the original RC-SP proposition through improved discussion, evidence and examples. Thanks to the Winnower for the opportunity to share my thoughts to a wide audience and a means for public response and review.

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Showing 2 Reviews

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    Jeffrey La Fortune
    0

    Follow-up Notes:
    It appears the focus on ‘dark’ solutions has altered our perceptional framework toward actual physical processes and properties governing the universe. Astrophysics is becoming a dynamic scientific endeavor again with the availability of improved physical observation coupled with highly comprehensive modeling techniques. It is now possible to expressly challenge key assumptions and predictions related to dark matter in the galactic setting. As examples, I cite three papers recently published over a ten day span on arXiv as support for a dark matter free galactic cosmology.
    1.) “The link between the assembly of the inner dark matter halo and the angular momentum evolution of galactic in the EAGLE simulation,” by J. Zavala, et al, published Dec 8, 2015 http://arxiv.org/pdf/1512.02636v1.pdf suggests that baryons inform the evolutionary history of dark matter halos. Advanced ΛCDM hydrodynamical simulations such as EAGLE/GADGET-3 are providing a new look into the dynamics of evolution for the dark matter halo and baryonic constituents as co-evolving processes. They discovered that the baryonic galactic “end-state” at z=0 can be used to infer and potentially predict dark matter accretion history. Another crucial finding in this paper is the importance of including both stellar and gas components in providing realistic galactic models. The authors concluded that galactic dynamics are best elucidated from the total baryonic content of the galaxy, not just the stellar component that has preoccupied past ɅCDM simulation results and analysis. Through comprehensive accounting of baryonic constituents and their motions, fundamental tenets underpinning ‘dark’ based solutions are becoming increasingly uncertain and confusing.
    2.) “The Small Scatter of the Baryonic Tully-Fisher Relation,” by Lelli, et al, published Dec 14, 2015 http://arxiv.org/pdf/1512.04543v1.pdf states there is no correlation between the BFTR and ‘galactic structural parameters.’ This finding directly contradicts ɅCDM formalism where dark matter interacts (co-evolves) with baryonic matter throughout the life of the galaxy. The authors sum it up, “…the stochastic process of galaxy formation needs to reproduce a global relation with little (if any) intrinsic scatter and no dependence on structural parameters,” concluding ɅCDM models cannot meet this empirically determined physical constraint. Rather than hierarchal accretion, the BTFR is a signature of a global process that can physically generate this highly refined relationship. In fact, this process needs to be both global and primordial in order to maintain this high degree of galactic conformity across the observable universe.
    3.) “Andromeda IV, a solitary gas-rich dwarf galaxy,” by Karachentsev, et al, published Dec 18, 2015 http://arxiv.org/pdf/1512.05907v1.pdf provides a comprehensive analysis of an irregular dwarf galaxy. The authors measured its baryonic-to-dark mass ratio (Mgas + M*)/MT at ≈0.11 (equivalent to a baryonic fraction of the same value). Although this dwarf galaxy is considered to be one of the ‘darkest’ of its type, this relatively high baryonic-to-dark mass ratio does not support this inference. In fact, the Milky Way and Andromeda galaxies both exhibit ≈0.11 ratios. Neither galaxy has been considered exceptionally ‘dark.’ Although ɅCDM expects a significant difference in dark matter content between host spirals and irregular dwarf satellite galaxies, this is not the case. As this very recent paper demonstrates, there is little (or in this case, no) corroborating evidence linking dark matter to baryonic physics of rotationally supported galaxies. The fact that the measured baryonic-to-dark matter ratio is very close to the global value obtained from rotation curve/spin parameter considerations. For an extended discussion, I refer readers to the final section of my paper and especially Figure 11. This figure provides a simple physical interpretation of observed galactic dynamics in a dark matter free context.

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