Dark matter

Clowe, Douglas et al.  “A Direct Empirical Proof of the Existence of Dark Matter.”  ApJ Letters 648:L109–L113.  2006.  A 2006 observation of the merging cluster 1E0657−558 that maps its total mass by weak gravitational lensing, the bending of light from distant galaxies, and compares that map with the hot X-ray gas.  The authors report that the mass follows the galaxies rather than the gas, with an 8σ offset (eight standard deviations of statistical significance) that a change to the law of gravity cannot explain.  The article uses it as the central observation of the Bullet Cluster.  Mirror:  arXiv

1. 1a.

   Section Abstract:  “An 8σ significance spatial offset of the center of the total mass from the center of the baryonic mass peaks cannot be explained with an alteration of the gravitational force law, and thus proves that the majority of the matter in the system is unseen.” ↩ ↩ ↩

2. 1b.

   Section 1:  “The cluster has two primary galaxy concentrations separated by 0.72 Mpc on the sky, a less massive (T ∼ 6 keV) western subcluster and a more massive (T ∼ 14 keV) eastern main cluster… The X-ray image also shows a prominent bow shock on the western side of the western plasma cloud, indicating that the subcluster is currently moving away from the main cluster at ∼4700 km/s.” ↩

3. 1c.

   Section 3:  “Plasma masses were computed from a multicomponent 3-dimensional cluster model fit to the Chandra X-ray image… Because of the simplicity of this cluster's geometry, especially at the location of the subcluster, this mass estimate is quite robust (to a 10% accuracy).” ↩

4. 1d.

   Table 2:  The paragraph after the table reads:  “The total of the two visible mass components of the subcluster is greater by a factor of 2 at the plasma peak than at the BCG;  however, the center of the lensing mass is located near the BCG.” ↩

5. 1e.

   Section 3:  The subcluster peak is.  “detected at 8σ significance (as compared to 3σ in (Clowe et al. 2004))”.  and the main-cluster peak is.  “detected at 12σ.”  “Both peaks are also offset at ∼ 8σ from the center of mass of their respective plasma clouds.” ↩

6. 1f.

   Section 1:  “None of the results of this paper are dependent on this assumption;  changing the assumed cosmology will result in a change of the distances and absolute masses measured, but the relative masses of the various structures in each measurement remain unchanged.” ↩

7. 1g.

   Section 3, table 2:  “Note that both the plasma mass and the stellar mass are determined directly from the X-ray and optical images, respectively, independently of any gravity or dark matter models.” ↩

8. 1h.

   Section 3:  “The assumed mass-to-light ratio is highly uncertain (can vary between 0.5 and 3)… however even in the case of an extreme deviation, the X-ray plasma is still the dominant baryonic component in all of the apertures.” ↩

9. 1i.

   Section 4:  The two-unrelated-structures probability is.  “∼ 10⁻⁷”.  The two-filament probability is.  “∼ 10⁻⁶”.  times.  “an additional factor of ∼ 10⁻⁵ reduction”.  for the alignment with the moving galaxy concentrations, so.  “two such projections would still have a ≪ 10⁻⁸ probability.” ↩

10. 1j.

    Section 4:  “Our κ map, however, has no evidence of any mass concentration between the two galaxy subclusters other than the small perturbations consistent with the gas mass contribution in Newtonian gravity… In 1E0657−558, however, the X-ray plasma, which would provide the central peak, lies north of the line connecting the two κ peaks.  Further, the absolute κ levels of the peaks observed in 1E0657−558 are in good agreement with those in systems with similar velocity dispersions and X-ray temperatures.”  “Any non-standard gravitational force that scales with baryonic mass will fail to reproduce these observations.” ↩

11. 1k.

    Section 4:  “While the existence of dark matter removes the primary motivation for alternative gravity models, it does not preclude non-standard gravity.” ↩

Frenk, Carlos S., and Simon D. M. White.  “Dark matter and cosmic structure.”  Annalen der Physik 524:507–534.  2012.  A review of the standard model of how cosmic structure formed, covering forty years of work, with its focus on computer simulations and on the nature of dark matter.  The article quotes its epilogue, because the authors, who helped build the cold dark matter model, say there that the dark matter particle is still unconfirmed.  Mirror:  arXiv

1. 2a.

   Section 9 Epilogue, page 24:  Preprint page.  “Time and again when astronomical data seemed to conflict with the model (for example, the clustering of galaxy clusters, large-scale streaming data, galaxies at very high redshift) the conflict has been resolved either by revisions of the data or by refinments of the theory.  Nevertheless, even the most ardent supporters of the cold dark matter idea must remain sceptical until the dark matter particles are finally and conclusively discovered.”  "refinments" is the preprint's spelling.  The page also says:  “The third proposal, that the dark matter consists of non-baryonic, weakly interacting elementary particles, still awaits independent comfirmation.” ↩ ↩ ↩

Planck Collaboration.  “Planck 2018 results. VI. Cosmological parameters.”  A&A 641:A6.  2020.  A 2020 paper by a very large team, presenting the final analysis of the full Planck mission's measurements of the cosmic microwave background, the faint glow left from the early universe.  It fits the standard six-parameter cosmological model, ΛCDM, to the glow's temperature, polarization and lensing patterns, and reports the density of each kind of matter.  It reports densities; it does not argue from the third acoustic peak, a peak in the pattern of hot and cold spots.  The article uses its two densities, for matter that clumps without shining and for ordinary matter, as the strongest single numbers for how much dark matter there is.  Mirror:  arXiv

1. 3a.

   Table 2:  The column is TT,TE,EE+lowE+lensing.  Ω_bh² = 0.02237 ± 0.00015;  Ω_ch² = 0.1200 ± 0.0012.  The ratio is 5.36.  Derived Ω_m = 0.3153 ± 0.0073. ↩ ↩

LUX-ZEPLIN (LZ) Collaboration.  “Dark Matter Search Results from 4.2 Tonne-Years of Exposure of the LUX-ZEPLIN (LZ) Experiment.”  Physical Review Letters 135:011802.  2025.  A dark matter search by the LUX-ZEPLIN (LZ) Collaboration, a large group of universities and laboratories, using the LZ detector, a tank of liquid xenon in the Sanford Underground Research Facility in South Dakota that records the flashes made when particles strike it.  It reports 4.2 tonne-years of exposure over 280 live days, finds no evidence for an excess over expected background, and sets the world's strongest limits on heavy dark matter particles interacting with xenon nuclei.  The article uses it as the best direct-search limit, and as the latest step in a search that has found nothing.  Mirror:  arXiv

1. 4a.

   Section Abstract:  “The strongest SI exclusion set is 2.2 × 10⁻⁴⁸ cm² at the 90% confidence level and the best SI median sensitivity achieved is 5.1 × 10⁻⁴⁸ cm², both for a mass of 40 GeV/c².”  The arXiv v1 gave 2.1 × 10⁻⁴⁸ at 36 GeV; the published v3 numbers are the ones quoted. ↩

2. 4b.

   Section Abstract:  “This analysis uses a total exposure of 4.2 ± 0.1 tonne-years from 280 live days of LZ operation… After removal of artificial signal-like events injected into the data set to mitigate analyzer bias, we find no evidence for an excess over expected backgrounds.  World-leading constraints are placed on spin-independent (SI) and spin-dependent WIMP-nucleon cross sections for masses ≥9 GeV/c².” ↩

Bertone, Gianfranco, and Dan Hooper.  “History of dark matter.”  Reviews of Modern Physics 90:045002.  2018.  A historical review of how dark matter came to be accepted as part of cosmology, built largely from 19th- and 20th-century papers and books and from discussions with some of the pioneering scientists.  The arXiv preprint is titled A History of Dark Matter.  The article uses it for how far the direct searches have improved since the late 1980s.  Mirror:  arXiv

1. 5a.

   Figure 8, page 66:  “The past and projected evolution of the spin-independent WIMP-nucleon cross section limits for a 50 GeV dark matter particle”.  The limits run from about 10⁻⁴⁰ cm² in the late 1980s to below 10⁻⁴⁷ cm² by the mid-2010s, with the coherent-neutrino-scattering floor marked near 10⁻⁴⁹ cm².  Against LZ's 2025 value of 2.2 × 10⁻⁴⁸ cm² that is roughly eight orders of magnitude of improvement.  The same section records the technology history: CDMS and EDELWEISS improved sensitivity.  “by more than two orders of magnitude”.  through the 2000s, and XENON100 and LUX by.  “approximately two orders of magnitude”.  between 2010 and 2015. ↩ ↩ ↩

LUX-ZEPLIN (LZ) Collaboration.  “Searches for Light Dark Matter and Evidence of Coherent Elastic Neutrino-Nucleus Scattering of Solar ⁸B Neutrinos with the LUX-ZEPLIN Experiment.”  Physical Review Letters.  2026.  A 2026 search by the LUX-ZEPLIN (LZ) Collaboration for light dark matter, using the xenon detector in the Sanford Underground Research Facility.  Alongside that search it reports evidence that the detector is seeing neutrinos from the Sun strike xenon nuclei, at 4.5 standard deviations (sigma), using a 5.7 tonne-year exposure.  The article uses it because this solar neutrino background cannot be shielded away, so a search of this kind stops improving at that point.  Mirror:  arXiv

1. 6a.

   Section Abstract:  “This analysis uses a 5.7 tonne-year exposure with data collected between March 2023 and April 2025… In the no-dark-matter scenario, we observe a signal consistent with ⁸B CEνNS events, corresponding to a 4.5σ statistical significance.  This is the most significant evidence of ⁸B CEνNS interactions.”  Section Conclusions:  The conclusion notes that LZ.  “continues to take data towards a target 1000-day exposure that will allow for further dark matter searches into the neutrino fog.” ↩ ↩

2. 6b.

   Section Experiment:  “The LZ experiment […] operates underground in the Sanford Underground Research Facility (SURF) in Lead, South Dakota, USA, with a 4300 meter water-equivalent overburden to shield from cosmic radiation.” ↩

Adhikari, G. et al.  “Strong constraints from COSINE-100 on the DAMA dark matter results using the same sodium iodide target.”  Science Advances 7:eabk2699.  2021.  A report from the COSINE-100 Collaboration, a team that runs sodium iodide crystal detectors deep underground in South Korea.  It tests the yearly rise and fall in detection rate that the DAMA experiment claims as a dark matter signal, using 1.7 years of data from 106 kg of crystal, and finds no signal consistent with dark matter interactions.  Its conclusion holds within the standard halo model, the usual assumed picture of how dark matter is spread through a galaxy.  The article counts it as one of two experiments that use the same sodium iodide material and contradict DAMA's claim.  Mirror:  arXiv

1. 7a.

   Section Abstract:  “No signal consistent with the dark matter interaction is identified, and rules out model-dependent dark matter interpretations of the DAMA signals in the specific context of standard halo model with the same NaI(Tl) target for various interaction hypotheses.” ↩ ↩

Amaré, J., and et al. (ANAIS-112 Collaboration).  ANAIS-112 three years data: a sensitive model independent negative test of the DAMA/LIBRA dark matter signal.  Oct 14, 2024.  A 2024 arXiv preprint, version 2, that reanalyses three years of data from ANAIS-112, a detector of 112.5 kg of sodium iodide crystals.  The DAMA/LIBRA experiment reports a yearly rise and fall in its count rate, called annual modulation, which it reads as a sign of dark matter, and the claimed signal depends on the target material, so ANAIS-112 uses the same material to test it.  The article uses it as the one long-running positive claim that two experiments with the same target material have contradicted.

1. 8a.

   Section Abstract:  The abstract says the results.  “are consistent with the absence of modulation and inconsistent with DAMA's observation at nearly 3σ confidence level, with the potential to reach a 5σ level within 8 years from the beginning of the data collection.”  Section Results, page 3:  “The results are compatible with the null hypothesis and incompatible with the DAMA/LIBRA signal at 3.7σ and 2.6σ confidence level (C.L.) for the [1–6] and [2–6] keV energy”.  The two energy regions are [1–6] and [2–6] keV. ↩ ↩

Sales, Laura V. et al.  “Baryonic solutions and challenges for cosmological models of dwarf galaxies.”  Nature Astronomy 6:897–910.  2022.  A review of the problems that the standard model of cosmology (ΛCDM, cold dark matter plus dark energy) has with dwarf galaxies.  It shows how recent simulations that include ordinary (baryonic) matter, such as gas and stars, explain many of them, and it ranks the problems that remain by how strong a tension each one still is.  The article uses that ranking to decide which dwarf-galaxy problems are strong tensions, which are uncertain and which are solved.  Mirror:  arXiv

1. 9a.

   Page 6:  Page of the arXiv preprint.  “Barring significant systematics in the observations, the diversity of rotation curves (and enclosed dark-matter mass) is arguably one of the strongest current tensions with theoretical models without a clear and consistent baryonic solution to date.  In particular, it seems that the same baryonic feedback solutions that appear to solve some of the other tensions that we discuss in this review, also tend to lower the inner dark-matter density in dwarfs too uniformly, driving a strong tension with the degree of diversity observed.  This warrants its placement as 'strong tension' in Fig. 1.” ↩ ↩

2. 9b.

   Page 10:  Page of the arXiv preprint.  MW is the Milky Way and M31 is Andromeda.  “Nearly all of the satellites around the MW and about half of the satellites around M31 are in a kinematically coherent, thin planar distribution… The nature of these planes of satellites has persisted as one of the strongest tensions between theory and observations.” ↩ ↩

3. 9c.

   Page 6:  Page of the arXiv preprint.  “With firm evidence from several independent numerical codes and analytical models showing that it is possible to form cores at the centers of the dark-matter halos of dwarf galaxies from feedback effects, the core-cusp tension with ΛCDM is, at this point, only uncertain (as listed in fig. 1) and awaiting larger samples of observed dwarfs with better observations of inner kinematics.” ↩ ↩

4. 9d.

   Page 9:  Page of the arXiv preprint.  TBTF is too-big-to-fail.  “In summary, there is a consensus among current cosmological simulations of MW/M31-mass halos that there is no TBTF problem for MW and M31 satellites, regardless of whether the simulations produce cuspy or cored dark-matter profiles.”  On the field version of the problem:  “We therefore assess this problem as a weak tension in Fig. 1.” ↩

Ibata, Rodrigo A. et al.  “A Vast Thin Plane of Co-rotating Dwarf Galaxies Orbiting the Andromeda Galaxy.”  Nature 493:62–65.  2013.  A Nature paper by Rodrigo Ibata and a team of astronomers, based on the Pan-Andromeda Archaeological Survey, which imaged about 400 square degrees of sky around the Andromeda galaxy with the Canada-France-Hawaii Telescope.  It reports a thin plane of 13 satellite galaxies, at least 400 kpc across and 12.6 kpc thick, whose members rotate the same way, with a total significance of 99.998 percent.  The article uses it as the main example of satellite galaxies lying in planes, and notes that the paper itself calls the structure a challenge to explain.  Mirror:  arXiv

1. 10a.

   Section Abstract:  “Here we report the existence (99.998% significance) of a planar sub-group of satellites in the Andromeda galaxy, comprising ≈ 50% of the population.  The structure is vast:  at least ∼ 400 kpc in diameter, but also extremely thin, with a perpendicular scatter < 14.1 kpc (99% confidence).  Radial velocity measurements reveal that the satellites in this structure have the same sense of rotation about their host.”  Section Results, page 4:  Preprint page.  “a coherent planar structure of 13 satellites with a root-mean-square (rms) thickness of 12.6 ± 0.6 kpc… The extent of the structure is gigantic, over 400 kpc along the line of sight and nearly 300 kpc North-South.” ↩ ↩

2. 10b.

   Section Results, page 3:  Preprint page.  “The probability that 13 or more out of 15 objects should share the same sense of rotation is 1.4% (allowing for right-handed or left-handed rotation)… The total significance of the planar structure is approximately 99.998%.” ↩

3. 10c.

   Section Discussion, pages 5–6:  Preprint pages.  “In either type of model, the small scatter of the satellites out of the plane is a challenge to explain, even though the orbital timescales for the satellites are long (∼ 5 Gyr for satellites at 150 kpc)… In an accretion scenario, the dynamical coherence points to an origin in a single accretion of a group of dwarf galaxies.  However, the spatial extent of the progenitor group would have to be broadly equal to or smaller than the current plane thickness (< 14.1 kpc), yet no such groups are known.” ↩

Sales, Laura V., and Julio F. Navarro.  “Planes of satellites, no longer in tension with ΛCDM?”  Nature Astronomy 7:376–377.  2023.  A commentary on the paper by Sawala et al.  Its title asks whether the planes of satellites are no longer in tension with ΛCDM.  The article uses it for the commentators' acceptance of the Sawala et al. result, and for their warning that the evidence for planes around Andromeda and Centaurus A is much weaker.  Mirror:  arXiv

1. 11a.

   Page 1:  Summary paragraph of the arXiv preprint.  “The tension is unwarranted:  the thinness of the Milky Way plane is transitory and boosted by the chance alignment of its two most distant satellites, and the probability of finding such configurations in ΛCDM simulations has been severely underestimated in earlier work because of improper accounting of the radial distribution of simulated satellites.” ↩

2. 11b.

   Pages 1–2:  Sales and Navarro describing Sawala et al.  Page of the arXiv preprint.  “report that the likelihood of having a satellite system as planar as that of the Milky Way is about 50 times larger than previously thought, reaching ∼ 2% of all simulated Milky-Way like objects, a conclusion also reached by a recent independent study.  Our Galactic plane of satellites might not be extremely common, but it seems eminently possible.” ↩ ↩

3. 11c.

   Page 1:  Page of the arXiv preprint.  “Although the presence of rotating satellite planes around other galaxies, like M31 (Andromeda) and NGC 5128 (Centaurus A), has also been argued for, the evidence in those cases is much weaker and inconclusive due mainly to lack of detailed kinematic data (only line-of-sight velocities are available for external galaxies).” ↩ ↩

4. 11d.

   Page 1:  Page of the arXiv preprint.  “Thin, co-rotating planar structures are not uncommon in astrophysics, but thoroughly unexpected when it comes to galactic satellites.  Astrophysical disks form as a result of energy dissipation and angular momentum conservation, a process that takes many orbital times to complete.  None of these conditions apply to the Milky Way satellite plane:  there is no known mechanism for satellites to dissipate their orbital energy, and many Milky Way satellites have completed at most a few orbits around their host.  A rotating thin plane of satellites is therefore completely unexpected, not only in ΛCDM, but also in most, if not all, potentially viable models of galaxy formation.” ↩

Kim, Stacy Y. et al.  “Missing Satellites Problem: Completeness Corrections to the Number of Satellite Galaxies in the Milky Way are Consistent with Cold Dark Matter Predictions.”  Physical Review Letters 121:211302.  2018.  A physics paper by Stacy Kim, Annika Peter and Jonathan Hargis, of Ohio State University and the Space Telescope Science Institute, first posted on arXiv under the title 'There is No Missing Satellites Problem.'  It corrects the observed count of Milky Way satellite galaxies for the part of the sky the Sloan Digital Sky Survey could not see, and finds a match with cold dark matter predictions, assuming an empirical relation between stellar mass and halo mass.  The article uses it to show that the missing-satellites objection has been answered, while the paper itself warns that the count could now be too high.  Mirror:  arXiv

1. 12a.

   Section Abstract:  “We show that there is a match between the observed satellite counts corrected by the detection efficiency of the Sloan Digital Sky Survey (for luminosities L ≳ 340 L☉) and the number of luminous satellites predicted by CDM, assuming an empirical relation between stellar mass and halo mass.  The 'missing satellites problem', cast in terms of number counts, is thus solved.”  The abstract also warns that the counts depend on the assumed spatial distribution,  “possibly leading to a 'too many satellites' problem.” ↩ ↩ ↩

Zwicky, Fritz.  “Die Rotverschiebung von extragalaktischen Nebeln.”  Helvetica Physica Acta 6:110–127.  Translated by Heinz Andernach.  1933 (edition of 2017).  Zwicky's 1933 paper, written in German, on the redshifts of extragalactic nebulae, as astronomers then called distant galaxies.  The article uses it for the Coma cluster velocities Zwicky reported, and for his conclusion that the cluster's density would have to be at least 400 times that of its luminous matter.

1. 13a.

   Section 3:  The eight measured Coma velocities are 8500, 7900, 7600, 7000, 6700, 6600, 6000 and 5100(?) km/s, the last flagged as possibly a projected field nebula.  Section 5, Comments on the velocity dispersion in the Coma cluster of nebulae:  “As we have seen in sect. 3, there exist in the Coma cluster apparent differences in velocity of at least 1500 to 2000 km/s.”  His model cluster had a radius of.  “approximately one million light years (equal to 10²⁴ cm)”.  and contained.  “800 individual nebulae each of a mass of 10⁹ solar masses.” ↩

2. 13b.

   Section 5, item 1:  “In order to obtain, as observed, a medium-sized Doppler effect of 1000 km/s or more, the average density in the Coma system would have to be at least 400 times greater than that derived on the basis of observations of luminous matter… If this should be verified, it would lead to the surprising result that dark matter exists in much greater density than luminous matter.”  He closes the section:  “These considerations indicate that the large velocity dispersion in the Coma system (and other dense clusters of nebulae) holds an unsolved problem.” ↩

3. 13c.

   Section 4, Speculations concerning the redshift, requirement 2:  “The apparent Doppler velocity is proportional to the distance r and amounts to 558 km per second per million parsecs.”  Against the modern value near 67-73 this is about eight times too large, which is the main reason his mass-to-light ratio came out so high. ↩

Zwicky, Fritz.  “On the Masses of Nebulae and of Clusters of Nebulae.”  The Astrophysical Journal 86:217–246.  1937.  A 1937 paper by Fritz Zwicky, written in English, that argues the two usual ways of weighing nebulae, from their light and from their internal rotation, are unreliable.  It proposes three new methods, and it applies the virial theorem, the classical rule that links a system's motion to its gravity, to the Coma cluster.  The article uses it for Zwicky's mass-to-light estimate for Coma, for his use of "dark matter" to mean unseen ordinary matter, and for his proposal to weigh nebulae by gravitational lens effects.

1. 14a.

   Page 232:  Equation (36):  “M̄ > 9 × 10⁴³ gr = 4.5 × 10¹⁰ M☉,”.  derived after noting that.  “The Coma cluster contains about one thousand nebulae.”  The paper then says:  “This result is somewhat unexpected, in view of the fact that the luminosity of an average nebula is equal to that of about 8.5 × 10⁷ suns.  According to (36), the conversion factor γ from luminosity to mass for nebulae in the Coma cluster would be of the order,”.  equation (37):  “γ = 500, as compared with about γ' = 3 for the local Kapteyn stellar system.  This discrepancy is so great that a further analysis of the problem is in order.” ↩

2. 14b.

   Page 218, section I, Masses from luminosities of nebulae:  The second of three things that must be known to convert luminosity to mass:  “We must know how much dark matter is incorporated in nebulae in the form of cool and cold stars, macroscopic and microscopic solid bodies, and gases.”  Zwicky's "dark matter" here is unseen ordinary matter, not a new particle. ↩

3. 14c.

   Section Abstract, page 217:  “Method iv calls for the observation among nebulae of certain gravitational lens effects.” ↩

Gonzalez, Anthony H. et al.  “Galaxy Cluster Baryon Fractions Revisited.”  ApJ 778:14.  2013.  A measurement paper that weighs the ordinary matter (baryons, the protons and neutrons of stars and gas) in twelve galaxy clusters and groups, using XMM-Newton X-ray data, and reports what share of each system's mass that matter makes up.  The systems are nearby, at a redshift of about 0.1 and masses of 1 to 5 times 10¹⁴ solar masses, so the numbers describe nearby clusters only.  The article uses it to show how much of a cluster's mass is ordinary matter, and that hot gas is the largest part of it.  Mirror:  arXiv

1. 15a.

   Table 2, page 6:  The table is titled Derived Mass Fractions (r < r₅₀₀).  It covers twelve clusters and groups at z ~ 0.1 with M = 1-5 × 10¹⁴ M☉.  Gas fractions run 0.067 to 0.133;  stellar fractions 0.013 to 0.041;  total baryon fractions 0.095 to 0.155.  The gas therefore outweighs the stars by roughly three to eight times in every system, and everything baryonic (ordinary matter) together never exceeds 16 percent of the total mass. ↩ ↩ ↩

Rubin, Vera C. et al.  “Rotational Properties of 21 Sc Galaxies with a Large Range of Luminosities and Radii, from NGC 4605 (R = 4 kpc) to UGC 2885 (R = 122 kpc).”  ApJ 238:471–487.  1980.  A 1980 paper by Vera Rubin, W. Kent Ford Jr. and Norbert Thonnard of the Carnegie Institution of Washington.  It uses spectra taken along the long axis of 21 spiral galaxies of type Sc to measure how fast each galaxy turns at each distance from its centre, out to 122 kpc.  The article uses it for its finding that most of these rotation curves are still rising slowly at the farthest point measured, so the galaxies must hold significant mass beyond their optical image.

1. 16a.

   Section Abstract, page 471:  “Their radii range from 4 to 122 kpc (H = 50 km s⁻¹ Mpc⁻¹)… Most rotation curves are rising slowly even at the farthest measured point.  Neither high nor low luminosity Sc galaxies have falling rotation curves.  Sc galaxies of all luminosities must have significant mass located beyond the optical image.” ↩

van Albada, T. S. et al.  “Distribution of dark matter in the spiral galaxy NGC 3198.”  The Astrophysical Journal 295:305–313.  1985.  A 1985 paper by four astronomers that measures the rotation curve of the spiral galaxy NGC 3198 out to 11 disk scale lengths, and fits it with a disk and a spherical halo.  The article uses it for the measurement that the dark matter inside the last measured point is at least four times the visible matter.

1. 17a.

   Section Abstract, page 305:  “Two-component mass models, consisting of an exponential disk and a spherical halo, are constructed to fit a newly determined rotation curve of NGC 3198 that extends to 11 disk scale lengths.  The amount of dark matter inside the last point of the rotation curve, at 30 kpc, is at least 4 times larger than the amount of visible matter, with (M/L_B)_tot = 18 M☉/L_B☉.” ↩

Ostriker, Jeremiah P. et al.  “The Size and Mass of Galaxies, and the Mass of the Universe.”  ApJ Letters 193:L1–L4.  1974.  A 1974 letter by three astronomers arguing that galaxies are far more massive than their visible light suggests.  It estimates the mass of spiral galaxies from their rotation and from pairs of galaxies, and concludes that a giant spiral holds about 10¹² solar masses, roughly 200 times its light, which gives a mean cosmic density of about a fifth of the amount needed to close the universe.  The article uses it as an early estimate that galaxies carry far more mass than their light shows.

1. 18a.

   Section I. The Argument, page L1:  “There are reasons, increasing in number and quality, to believe that the masses of ordinary galaxies may have been underestimated by a factor of 10 or more.” ↩

2. 18b.

   Section Abstract, page L1:  “Currently available observations strongly indicate that the mass of spiral galaxies increases almost linearly with radius to nearly 1 Mpc.  This means that the total mass per giant spiral is of the order of 10¹² M☉, and that the ratio of this mass to the photographic light within the Holberg radius, f, is _critM/L)☉.”  The abstract prints "Holberg"; the body of the paper spells it Holmberg.  The same abstract gives a local mean mass density of ≈ 2 × 10⁻³⁰ g cm⁻³,  “corresponding to Ω ≡ ρ/ρ_crit ≈ 0.2.  The uncertainty in this result is not less than a factor of 3.”  The companion result is Einasto, Jaan, Ants Kaasik, and Enn Saar, "Dynamic evidence on massive coronas of galaxies," Nature 250 (1974): 309-310, doi:10.1038/250309a0. ↩ ↩

Hu, Wayne, and Scott Dodelson.  “Cosmic Microwave Background Anisotropies.”  Annual Review of Astronomy and Astrophysics 40:171–216.  2002.  A review by Wayne Hu and Scott Dodelson of the cosmic microwave background, the nearly uniform radiation left from the early universe, and of the small temperature differences within it.  It explains the acoustic peaks in the pattern of those differences, which established a working model of a flat universe made mostly of dark matter and dark energy.  The article uses it for the physics of why ordinary matter (baryons) and dark matter change the heights of the peaks.  Mirror:  arXiv

1. 19a.

   Section 3.4 Baryon Loading, page 18:  Preprint page.  “Since it is still the effective temperature Θ+Ψ that is the observed temperature, the zero point shift breaks the symmetry of the oscillations.  The baryons enhance only the compressional phase, i.e. every other peak.  For the working cosmological model these are the first, third, fifth… Physically, the extra gravity provided by the baryons enhance compression into potential wells.” ↩

2. 19b.

   Section 3.5 Radiation Driving, page 19:  Preprint page.  “When the Universe becomes matter dominated the gravitational potential is no longer determined by photon-baryon density perturbations but by the pressureless cold dark matter.  Therefore, the amplitudes of the acoustic peaks increase as the cold dark matter-to-radiation ratio decreases… By eliminating gravitational potentials, photon-baryon acoustic oscillations eliminate the alternating peak heights from baryon loading.  The observed high third peak (Halverson et al 2001) is a good indication that cold dark matter both exists and dominates the energy density at recombination.” ↩

Dodelson, Scott.  “The Real Problem with MOND.”  International Journal of Modern Physics D 20:2749–2753.  2011.  A short argument by Scott Dodelson, of Fermi National Accelerator Laboratory and the University of Chicago, against MOND (Modified Newtonian Dynamics, a theory that changes the law of gravity instead of adding dark matter).  It calls the shape of the matter power spectrum (the measured pattern of how clumpy matter is at each size) the biggest challenge facing MOND today, and it won an honorable mention in the Gravity Research Foundation's 2011 awards.  The article uses it for its concession that the case for dark matter rests on gravitational effects alone, and for its point that MOND faces serious problems with galaxy clusters and with matter clumping.  Mirror:  arXiv

1. 20a.

   Page 1:  Preprint page.  “the map of the cosmic microwave background (CMB) shows that inhomogeneities in the photon-baryon plasma peaked at about one part in 10,000 when the Universe was 380,000 years old.  General relativity makes a firm prediction that the amplitude of these inhomogeneities has grown by a factor of one thousand since then, a prediction that is embarrassingly wrong coming from a species that owes its existence to nonlinear structures.  The seemingly unavoidable conclusion is that the early CMB maps do not trace all the matter – only the baryonic component – and, in fact, the hidden matter is much more inhomogeneous than the visible component.” ↩

2. 20b.

   Page 4:  Preprint page.  “The biggest challenge facing MOND today is the shape of the matter power spectrum.”  Figure 1:  The caption, describing a model with no dark matter, says:  “the spectrum has pronounced Baryon Acoustic Oscillations, in violent disagreement with the data.”  Page 4:  On the peaks, the page also says:  “The problem is that the third peak should be very small in a baryon-dominated model that lacks the extra gravitational forcing usually supplied by dark matter.  The observed third peak is therefore very difficult to accommodate in the framework of MOND.” ↩ ↩

3. 20c.

   Page 2:  Preprint page.  “The only evidence to date for dark matter comes from its gravitational effects.  Until that situation changes, modified gravity will remain a viable alternative to dark matter.”  Page 3:  On clusters:  “MOND does not explain well the dynamics of galaxy clusters, and that tension was increased by the detailed study of the Bullet Cluster, which seems to require collisionless dark matter.” ↩

Massey, Richard et al.  “The dark matter of gravitational lensing.”  Reports on Progress in Physics 73:086901.  2010.  A review article by three astronomers, two at Edinburgh and one at Durham, on how gravitational lensing measures dark matter.  It covers lensing measurements of how much dark matter there is and what it is like, and its Bullet Cluster figures repeat Clowe et al. 2006 and Randall et al. 2008, which the article cites directly.  The article uses it for background on the merging-cluster method, and for the point that in an undisturbed galaxy cluster the galaxies, the gas and the dark matter all sit in the same place, so the cluster cannot tell them apart.  Mirror:  arXiv

1. 21a.

   Section 5.2, page 29:  The page is the arXiv preprint's, not the journal's.  “Galaxy clusters contain three basic ingredients:  galaxies, intra-cluster gas, and dark matter.  Inconveniently for those trying to interpret the total mass distribution, these ordinarily come to rest in approximately the same place.  However, this is not always the case.”  Also, on the Bullet Cluster:  “A great deal of extra mass (∼ 30 − 40× than that seen in the galaxies' stars) is located near the galaxies, and 8σ away from the gas peaks.” ↩

Angus, Garry W. et al.  “Can MOND take a bullet?  Analytical comparisons of three versions of MOND beyond spherical symmetry.”  MNRAS 371:138–146.  2006.  An analytical comparison of three versions of MOND, modified Newtonian dynamics, a theory that changes gravity instead of adding dark matter, for systems that are not spherically symmetric.  The article uses it only to identify the modified-gravity model that Clowe et al. 2006 answer in their section 4, and it treats the claims of this paper in its MOND article.  Mirror:  arXiv ↩

Bradač, Maruša et al.  “Revealing the Properties of Dark Matter in the Merging Cluster MACS J0025.4−1222.”  ApJ 687:959–970.  2008.  A 2008 study of the merging galaxy cluster MACS J0025.4−1222, which finds two merging subclusters of similar richness at redshift 0.586.  The article uses it as a second case of this kind, found after the Bullet Cluster, in which the mass is offset from the hot gas.  Mirror:  arXiv

1. 23a.

   Section Abstract:  “MACS J0025.4−1222 consists of two merging subclusters of similar richness at z = 0.586… The total mass distribution in each of the subclusters is clearly offset (at > 4σ significance) from the peak of the hot X-ray emitting gas (the main baryonic component), but aligned with the distribution of galaxies.”  The paper's own figures: gas fraction 0.09^+0.07_−0.03 and stellar fraction 0.010^+0.007_−0.004; self-interaction cross-section σ/m < 4 cm² g⁻¹ as an order-of-magnitude estimate. ↩

Jee, M. J. et al.  “Hubble Space Telescope/Advanced Camera for Surveys Confirmation of the Dark Substructure in A520.”  ApJ 783:78.  2014.  A Hubble Space Telescope study of the Abell 520 cluster with the Advanced Camera for Surveys, which confirms an earlier claim of a large amount of dark mass between two luminous clumps of galaxies, where the team sees very little light.  The article uses it as the counter-example to the Bullet Cluster, and sets Clowe's 2012 reanalysis of the same cluster against it.  Mirror:  arXiv

1. 24a.

   Section Abstract:  “This new ACS analysis confirms the previous claims that a substantial amount of dark mass is present between two luminous subclusters.  We examine the distribution of cluster galaxies and observe very little light at this location… the mass-to-light ratio estimated with this centroid is much higher (813 ± 78 M☉/L_R☉) than the previous value.” ↩

Clowe, Douglas et al.  “On Dark Peaks and Missing Mass: A Weak Lensing Mass Reconstruction of the Merging Cluster System Abell 520.”  ApJ 758:128.  2012.  A weak-lensing mass map of Abell 520, a merging cluster of galaxies, built from the faint bending of distant galaxies' light by the cluster's mass.  Its abstract reports that the 'dark core' earlier claimed for the cluster is not detected, and concludes that the cluster shows no evidence against collisionless dark matter (dark matter whose particles pass through one another without colliding).  The article sets it against Jee's claim of that dark core.  Mirror:  arXiv

1. 25a.

   Section Abstract:  “There is however one significant difference – we do not detect the previously claimed 'dark core' that contains excess mass with no significant galaxy overdensity at the location of the X-ray plasma… We find no such indication and instead find that the mass distribution of A520, after subtraction of the X-ray plasma mass, is in good agreement with the luminosity distribution of the cluster galaxies.  We conclude that A520 shows no evidence to contradict the collisionless dark matter scenario.” ↩

Peel, Austin et al.  “Sparse reconstruction of the merging A520 cluster system.”  ApJ 847:23.  2017.  A 2017 paper that re-analyses the merging cluster Abell 520 using sparse reconstruction, applied to two data sets.  The article cites it in the dispute over whether the cluster's dark core is real.  Mirror:  arXiv

1. 26a.

   Section Abstract:  “In particular, although we are able to identify the dark core at a certain level in both data sets, it is at much lower significance than has been reported before using the same data.” ↩

Randall, Scott W. et al.  “Constraints on the Self-Interaction Cross Section of Dark Matter from Numerical Simulations of the Merging Galaxy Cluster 1E 0657−56.”  ApJ 679:1173–1180.  2008.  A 2008 paper by five astronomers that runs full computer simulations of the merging galaxy cluster 1E 0657-56, whose gas looks like a bullet in X-ray images.  The simulations include dark matter that collides with itself, and they are compared with X-ray, lensing and optical observations.  The article uses it for the upper limit it sets on how often dark matter particles collide with one another.  Mirror:  arXiv

1. 27a.

   Section Abstract:  “This new method places an upper limit (68% confidence) of σ/m < 1.25 cm² g⁻¹.  If we make the assumption that the subcluster and the main cluster had equal mass-to-light ratios prior to the merger, we derive our most stringent constraint of σ/m < 0.7 cm² g⁻¹.” ↩

Bertone, Gianfranco, and Tim M. P. Tait.  “A new era in the search for dark matter.”  Nature 562:51–56.  2018.  A 2018 perspective by two physicists, one at the University of Amsterdam and one at the University of California, Irvine, that reviews what past experiments have taught about the nature of dark matter.  It argues that the search should spread across more kinds of experiment, including astronomical surveys and gravitational-wave observations, because the leading candidates, weakly interacting massive particles (WIMPs), axions and sterile neutrinos, have not turned up.  The article uses it for the field's sense of crisis and for the authors' admission that natural WIMPs may be a red herring.  Mirror:  arXiv

1. 28a.

   Section Abstract:  “There is a growing sense of 'crisis' in the dark matter community, due to the absence of evidence for the most popular candidates such as weakly interacting massive particles, axions, and sterile neutrinos, despite the enormous effort that has gone into searching for these particles.” ↩

2. 28b.

   Section The Fall of Natural WIMPs (preprint p. 1):  “Despite much effort, no particle other than a Standard Model-like Higgs boson has been convincingly detected at the weak scale so far, a circumstance that, as long anticipated, now raises the possibility that natural WIMPs may have been nothing more than an attractive red herring.” ↩

Cirelli, Marco et al.  “Dark Matter.”  arXiv.  Oct 31, 2025.  A 524-page review of dark matter, version 3 of the arXiv preprint, with a summary table of the properties known so far.  The article uses that table, with every entry still a question mark, to show how little is settled about the particle.

1. 29a.

   Page 9, table 1:  “DARK MATTER — • • • Needs confirmation • • •”.  “Summary of currently known Dark Matter properties.”  Every field is a question mark:  I(J^PC).  “?(???)”  mass.  “?±?”  width.  “?±?”  decay modes.  “STABLE ?”  production.  “σ(?? → ??) = ?” ↩

Goodman, Mark W., and Edward Witten.  “Detectability of certain dark-matter candidates.”  Physical Review D 31:3059.  1985.  A 1985 paper by Mark Goodman and Edward Witten, whose title says it concerns the detectability of certain dark matter candidates.  The article cites it only to date the idea of searching for dark matter in a laboratory to 1985. ↩

Aprile, E. et al.  WIMP Dark Matter Search using a 3.1 Tonne-Year Exposure of the XENONnT Experiment.  2025.  A 2025 search for WIMPs (weakly interacting massive particles, a hypothetical kind of dark matter particle) by the XENON Collaboration, using the XENONnT experiment.  It reports no significant excess of events above background, and sets upper limits on how strongly WIMPs would interact with ordinary matter.  The article uses it, with PandaX-4T, to show that two detectors using the same technology have found nothing.

1. 31a.

   Section Abstract:  “In a blind analysis of nuclear recoil events with energies above 3.8 keV_NR, we find no significant excess above background.  We set new upper limits on the spin-independent WIMP-nucleon scattering cross section for WIMP masses above 10 GeV/c² with a minimum of 1.7 × 10⁻⁴⁷ cm² at 90 % confidence level for a WIMP mass of 30 GeV/c².” ↩

Bo, Zihao et al.  Dark Matter Search Results from 1.54 Tonne·Year Exposure of PandaX-4T.  2024.  A 2024 preprint by the PandaX Collaboration reporting a search for dark matter particles with the PandaX-4T detector, after 1.54 tonne-years of exposure.  The article uses it for the lowest limit on how strongly dark matter could interact with an atomic nucleus, which it compares with the limit from XENONnT.  Mirror:  arXiv

1. 32a.

   Section Abstract:  “the lowest 90% confidence level exclusion on the spin-independent cross section is 1.6 × 10⁻⁴⁷ cm² at 40 GeV/c² DM mass.” ↩

O'Hare, Ciaran A. J.  “Fog on the horizon: a new definition of the neutrino floor for direct dark matter searches.”  Physical Review Letters 127:251802.  2021.  A 2021 letter by Ciaran O'Hare of the University of Sydney.  It defines the neutrino floor as the point where a detector's sensitivity to dark matter stops improving at the usual rate, because background neutrinos begin to swamp the signal, and it calculates that point without fixing the exposure or energy threshold in advance.  The article uses it for the point that the floor is not a hard wall: more exposure still buys sensitivity, only more slowly.  Mirror:  arXiv

1. 33a.

   Section Abstract:  “The neutrino floor is a theoretical lower limit on WIMP-like dark matter models that are detectable by direct detection experiments.  It is commonly interpreted as the point at which dark matter signals are hidden underneath a remarkably similar-looking background from neutrinos.  However, it has been known for some time that the neutrino floor is not a hard limit, but can be pushed past with sufficient exposure.  As a consequence, some have recently advocated for calling it the 'neutrino fog' instead.” ↩

Ackermann, M., and et al. (Fermi-LAT Collaboration).  “Searching for Dark Matter Annihilation from Milky Way Dwarf Spheroidal Galaxies with Six Years of Fermi Large Area Telescope Data.”  Physical Review Letters 115:231301.  2015.  A 2015 analysis of six years of Fermi gamma-ray telescope data from 15 dwarf spheroidal galaxies that orbit the Milky Way, searching for the gamma rays that dark matter particles would give off when they annihilate.  It found no significant signal, so it set upper limits on the annihilation cross section, the measure of how often annihilation happens.  The article uses it because these limits are among the strongest and most robust to date and lie below the canonical thermal relic cross section, the rate expected for a particle left over from the hot early universe, for masses ≲ 100 GeV.  Mirror:  arXiv

1. 34a.

   Section Abstract:  “None of the dSphs are significantly detected in gamma rays, and we present upper limits on the DM annihilation cross section from a combined analysis of 15 dSphs.  These constraints are among the strongest and most robust to date and lie below the canonical thermal relic cross section for DM of mass ≲ 100 GeV annihilating via quark and τ-lepton channels.” ↩

Bullock, James S., and Michael Boylan-Kolchin.  “Small-Scale Challenges to the ΛCDM Paradigm.”  Annual Review of Astronomy and Astrophysics 55:343–387.  2017.  A review article on the problems that the standard model of cosmology, ΛCDM (cold dark matter plus a cosmological constant), has at the scale of individual galaxies.  The article uses it because it names the three best-documented problems, and critics still quote it.  Mirror:  arXiv

1. 35a.

   Section Abstract:  “These issues underlie the most well-documented problems with ΛCDM:  Cusp/Core, Missing Satellites, and Too-Big-to-Fail.”  The same abstract flags the two problems this article treats as live:  “Other anomalies, including the observed planar and orbital configurations of Local Group satellites and the tight baryonic/dark matter scaling relations obeyed by the galaxy population, have been less thoroughly explored in the context of ΛCDM theory.” ↩

Oman, Kyle A. et al.  “The unexpected diversity of dwarf galaxy rotation curves.”  MNRAS 452:3650–3665.  2015.  A 2015 paper by twelve authors that compares the rotation curves of galaxies in the EAGLE and Local Group computer simulations with a compilation of observed rotation curves across a wide range of masses.  It finds that simulated galaxies with the same maximum rotation speed have very similar rotation curves, while real dwarf galaxies do not.  The article uses it for the authors' reframing of the cusp-core problem as an "inner mass deficit" problem, and for the three explanations the authors list.  Mirror:  arXiv

1. 36a.

   Section Abstract:  “The shape of the circular velocity profiles of simulated galaxies varies systematically as a function of galaxy mass, but shows remarkably little variation at fixed maximum circular velocity.  This is especially true for low-mass dark matter-dominated systems, reflecting the expected similarity of the underlying cold dark matter haloes.  This is at odds with observed dwarf galaxies, which show a large diversity of rotation curve shapes, even at fixed maximum rotation speed.” ↩

2. 36b.

   Section Abstract:  “The 'cusp vs core' issue is thus better characterized as an 'inner mass deficit' problem than as a density slope mismatch.  For several galaxies the magnitude of this inner mass deficit is well in excess of that reported in recent simulations where cores result from baryon-induced fluctuations in the gravitational potential.” ↩

3. 36c.

   Section Abstract:  “We conclude that one or more of the following statements must be true:  (i) the dark matter is more complex than envisaged by any current model;  (ii) current simulations fail to reproduce the diversity in the effects of baryons on the inner regions of dwarf galaxies;  and/or (iii) the mass profiles of 'inner mass deficit' galaxies inferred from kinematic data are incorrect.” ↩

Pawlowski, Marcel S.  “The planes of satellite galaxies problem, suggested solutions, and open questions.”  Modern Physics Letters A 33:1830004.  2018.  A 2018 review by Marcel Pawlowski of the University of California, Irvine.  It summarises the evidence that satellite galaxies of the Milky Way and Andromeda lie in flattened planes, and compares them with simulations of the standard cosmological model, ΛCDM.  It finds that similar planes are exceedingly rare in those simulations, and that the explanations proposed so far do not yet resolve the problem.  The article uses it for the satellite-plane problem in the Milky Way, and for the claim that ordinary-matter (baryonic) processes do not strongly change it.  Mirror:  arXiv

1. 37a.

   Section Abstract:  “Detailed comparisons show that similarly anisotropic phase-space distributions of sub-halos are exceedingly rare in cosmological simulations based on the ΛCDM paradigm.  Analogs to the observed systems have frequencies of ≤ 0.5 per cent in such simulations.”  Section 2.1, page 3:  The page is the arXiv preprint's, not the journal's.  On the Milky Way satellites, the paper says their.  “distribution is fit by a plane with rms height r⊥ = 20 to 30 kpc.” ↩

2. 37b.

   Section Abstract:  “In contrast to other small-scale problems, the satellite planes issue is not strongly affected by baryonic processes because the distribution of sub-halos on scales of hundreds of kpc is dominated by gravitational effects.  This makes the satellite planes one of the most serious small-scale problem for ΛCDM.”  Section 4.3, page 18:  The page is the arXiv preprint's, not the journal's.  “In summary, there is currently neither evidence that baryonic physics enhances the frequency of analogs of the observed planes of satellite galaxies in cosmological simulations, nor is it obvious what baryonic physics process would increase the coherence in the phase-space distribution of dark-mater-dominated satellite galaxy systems.” ↩

Barnes, Luke A., and Geraint F. Lewis.  The Cosmic Revolutionary's Handbook (Or: How to Beat the Big Bang).  Cambridge University Press.  2020.  A popular handbook on the observations behind the big bang and its rivals, written for general readers by two cosmologists, with ISBN 978-1-108-48670-5.  Barnes is a postdoctoral researcher at Western Sydney University; Lewis is Professor of Astrophysics at the Sydney Institute for Astronomy and was a co-author on the Andromeda satellite-plane measurement.  The article uses it for the two authors' own words on the satellite planes and on whether cosmologists would give up dark matter.

1. 38a.

   Page 226:  “We find it amusing when critics of the big bang point to the dark sector as if it were some kind of conspiracy, because cosmologists would dump the dark components in a moment.  If someone convinced us that the universe could be explained convincingly – without raising even bigger problems – using only ordinary matter, we would gleefully throw all our dark matter and dark energy models in the garbage bin.” ↩

2. 38b.

   Pages 239–240:  On the satellite planes:  “This was not predicted by any galaxy formation simulation before it was discovered… Placing dwarf galaxies on fine planar orbits is akin to a gorilla repairing a watch; not impossible, but difficult to imagine.”  The Andromeda plane is.  “36,000 light years thick, but 1,200,000 light years in extent”.  with the northern dwarfs approaching and the southern receding. ↩

Sawala, Till et al.  “The Milky Way's plane of satellites is consistent with ΛCDM.”  Nature Astronomy 7:481–491.  2023.  A study of whether the Milky Way's 11 brightest satellite galaxies really lie in an unusually thin plane.  It uses Gaia measurements of how the satellites move across the sky (proper motions) and new simulations of standard ΛCDM, and it finds the plane is transient, not a rotating disk, and compatible with standard expectations.  The article uses it as the main recent case for a short-lived alignment, and it says the question is genuinely contested.  Mirror:  arXiv

1. 39a.

   Section Abstract:  “we show that the reported exceptional anisotropy of the satellite system is strongly contingent on a lopsided radial distribution, which earlier simulations have failed to reproduce, combined with the close but fleeting conjunction of the two most distant satellites, Leo I and Leo II.  Using Gaia proper motions, we show that the orbital pole alignment is much more common than previously reported, and reveal the plane of satellites to be transient rather than rotationally supported.  Comparing to new simulations, where such short-lived planes are common, we find the Milky Way satellites to be compatible with standard model expectations.” ↩

Sawala, Till.  “Planes of satellites, at once transient and persistent.”  The Open Journal of Astrophysics 9.  2026.  A 2026 paper by Till Sawala, the first author of the 2022 Milky Way study.  It uses the TNG-50 simulation, which models Milky Way analogues (galaxies like ours), and finds that the planes of satellites around each host last no more than a few hundred million years, yet the same satellites traced back in time can stay in a plane for several billion years.  The article uses it to show that the two conflicting findings can both be true.  Mirror:  arXiv

1. 40a.

   Section Abstract:  “We show that, as the satellite populations of individual hosts rapidly change, the observed spatial anisotropies of their satellite systems are invariably short-lived, with lifetimes of no more than a few hundred million years.  However, when the progenitors of the same satellites are traced backwards, we find examples where those identified to form a plane at the present day have retained spatial coherence over several billion years.  The two ostensibly conflicting predictions for the lifetimes of satellite planes can be reconciled as two perspectives on the same phenomenon.” ↩

Pawlowski, Marcel S. et al.  “Testing a proposed 'planarity' tool for studying satellite systems: On the alleged consistency of Milky Way satellite galaxy planes with ΛCDM.”  A&A 694:L4.  2025.  A 2025 letter in Astronomy & Astrophysics by four astronomers at Potsdam and Lausanne.  It tests a "planarity" metric that Uzeirbegovic and colleagues proposed in 2024 and used to claim that the Milky Way's satellite plane is consistent with ΛCDM, by running the metric on artificial satellite systems with features unrelated to planes.  The article uses it for the authors' objection that the metric cannot show that consistency.  Mirror:  arXiv

1. 41a.

   Section Abstract, Conclusions:  “Our results demonstrate that the new proposed metric is unsuitable to measure overall 'planarity' in satellite systems… Consequently, no consistency of the observed Milky Way satellite plane with ΛCDM can be inferred using this metric.” ↩

Milgrom, Mordehai.  “A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis.”  ApJ 270:365–370.  1983.  A 1983 paper by Mordehai Milgrom that proposes changing the Newtonian law of motion for very small accelerations, as an alternative to adding hidden mass to galaxies.  The change it proposes is the basis of modified Newtonian dynamics.  The article uses it as the origin of that idea, which it covers in its own article on MOND.

1. 42a.

   Section Abstract, page 365:  “I consider the possibility that there is not, in fact, much hidden mass in galaxies and galaxy systems.  If a certain modified version of the Newtonian dynamics is used to describe the motion of bodies in a gravitational field (of a galaxy, say), the observational results are reproduced with no need to assume hidden mass in appreciable quantities… In the basis of the modification is the assumption that in the limit of small acceleration a ≪ a₀ the acceleration of a particle at distance r from a mass M satisfies approximately a²/a_{0 0}G/r², where a₀ is a constant of the dimensions of an acceleration.” ↩

McGaugh, Stacy S. et al.  “The Radial Acceleration Relation in Rotationally Supported Galaxies.”  Physical Review Letters 117:201101.  2016.  A 2016 letter by three astronomers, from Case Western Reserve University and the University of Oregon.  It compares the acceleration that rotation curves show in 153 spiral and irregular galaxies, taken from the 175-galaxy SPARC database after quality cuts, with the acceleration that their visible stars and gas alone would produce, and finds one relation between the two across 2693 measured points.  The article uses it for that tight relation, which the paper says fully specifies the dark matter contribution from the ordinary matter, and for the measured value of the acceleration scale that modified Newtonian dynamics uses.  Mirror:  arXiv

1. 43a.

   Section Abstract:  “We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons.  The same relation is followed by 2693 points in 153 galaxies with very different morphologies, masses, sizes, and gas fractions.  The correlation persists even when dark matter dominates.  Consequently, the dark matter contribution is fully specified by that of the baryons.  The observed scatter is small and largely dominated by observational uncertainties.  This radial acceleration relation is tantamount to a natural law for rotating galaxies.” ↩

2. 43b.

   Page 4:  The page is the arXiv preprint's, not the journal's.  “Residuals from the fit are well described by a Gaussian of width 0.11 dex (Fig. 3).  The rms scatter is 0.13 dex owing to the inevitable outliers.  These are tiny numbers by the standards of extragalactic astronomy.”  The error budget table gives a total expected observational scatter of 0.12 dex (0.05 inclination, 0.08 distance, 0.06 mass-to-light, 0.01 HI calibration). ↩

3. 43c.

   Page 3:  The page is the arXiv preprint's, not the journal's.  “For our adopted Υ⋆, we find g† = 1.20 ± 0.02 (random) ± 0.24 (systematic) × 10⁻¹⁰ m s⁻².” ↩

Hartnett, John G.  “Stars just don't form naturally — 'dark matter' the 'god of the gaps' is needed.”  Creation Ministries International.  Jul 28, 2015.  A young-earth article by John G. Hartnett on the website of Creation Ministries International, a group that promotes biblical creation.  It argues that known physics cannot form stars from primordial gas, so unseen dark matter must be added to make them form, and it calls that an unknown 'god of the gaps'.  The article quotes its conclusion as the clearest young-earth form of the charge that dark matter is a 'god of the gaps', and it also quotes a 2014 interview with Mordehai Milgrom.

1. 44a.

   Section Conclusion:  “One must invent unknown stuff—dark matter—with the right properties—the unknown 'god of the gaps'—to get stars to form naturalistically.  Without it, it just can't happen!” ↩

2. 44b.

   Hartnett quotes Mordehai Milgrom, interviewed by Marcus Chown in New Scientist 222 (2967): 26-27, 3 May 2014:  “A host of experiments searching for dark matter, including the Large Hadron Collider, many underground experiments and several space missions, have failed to see anything convincing. This comes on top of increasing realisation that the leading dark matter model has its failings. Among other things, it predicts that we should see many more dwarf galaxies orbiting our Milky Way than we actually see.”  The first sentence still holds.  The dwarf-galaxy claim in the last sentence was closed by Kim, Peter and Hargis in 2018. ↩