More On Wide Binaries

A paper claims to see MOND in a reanalysis of wide-binary star data. I'm still on the fence.

Wide binary stars provide natural laboratories for directly probing gravity in the low-acceleration regime, as dark matter inferred from any viable gravity has negligible effects on their internal dynamics. Various recent studies including Bayesian 3D analyses have shown that wide binaries with separations greater than several thousand astronomical units experience MOND-type gravity with a boost factor of γ≈1.3−1.6. However, results claiming preference for, or no deviation from, standard gravity have also been published during the same period, particularly highlighting the roles of data quality control and realistic modeling of multiple-star (i.e., triple and higher-order) systems that host hidden companion stars. 

Here we carefully reexamine the issues of data quality control and modeling multiple-star systems in statistical gravity tests based on sky-projected 2D velocities of wide binary stars. Through extensive tests including the acceleration-plane test, the ṽ -distribution test, and the median-ṽ -profile test (where ṽ is the sky-plane 2D relative velocity normalized by the Newtonian circular velocity between the two stars), we show that proper data quality control or reasonable variation in multiple-star modeling cannot remove the low-acceleration gravitational anomaly but confirms the MOND-type gravitational anomaly, particularly consistent with recent realistic MOND solutions of wide binary orbits. 

We find that studies claiming no evidence for the low-acceleration gravitational anomaly are consequences of bypassed calibration of the fraction of multiple-star systems using the Newtonian-regime data, bias-introduction in data quality control that is not taken into account in gravity tests, or insufficient statistics in the low-acceleration regime.

Kyu-Hyun Chae, Youngsub Yoon, "Revisiting Data Quality Control and Multiple-star Modeling in Wide Binary Gravity Tests: Confirmation of MOND-type Gravitational Anomaly at Low Acceleration" arXiv:2607.14450 (July 16, 2026) (submitted to the AAS journals).

The Latest Global Electroweak Fits Of Standard Model Physical Constants

A global electroweak fit combines experimentally measured values of Standard Model physical constants with the theoretical relationships between those constants in the electroweak sector of the Standard Model to determine where, within the range of uncertainties in the experimental measurements the true value of those physical constants is most likely to be. Basically, it uses theory to eke out a bit more precision in our determination of these constants than the measurements make possible in isolation.

The fact that it is possible with experimentally measured value of Standard Model physical constants without serious tensions (which it is) also provides a global test of the consistency of the Standard Model with reality.

The latest paper using up to date experimental data to make a global electroweak fit of Standard Model physical constants can be found here. The discussion of how the input values are chosen (basically, an educated best summary of the data to date) in the paper is also noteworthy.

The global fit of the Z boson mass is 91.1882 ± 0.0019 GeV and the global fit of the Z boson width is 2.4945 ± 0.0006 GeV.

The global fit of the W boson mass is 80.3584 ± 0.0048 GeV and the global fit of the W boson width is 2.090 ± 0.001 GeV.

The Higgs boson mass is 125.13 ± 0.11 GeV. The Standard Model expectation for the Higgs boson width is 4.10 ± 0.06 MeV; a complete global electroweak fit of the data produces 3.78 + 0.30 − 0.27 MeV, which is consistent with the Standard Model expectation. The couplings of the Higgs boson in an electroweak global fit are within roughly 1% ± 1% of the Standard Model expectation. 

The global fit of the charm quark pole mass (in the MS scheme) is 1.273 ± 0.003 GeV.

The global fit of the bottom quark pole mass (in the MS scheme) is 4.183 ± 0.004 GeV.

The global fit of the top quark pole mass is 172.67 ± 0.56 GeV.

The global fit of the strong force coupling constant at the Z boson squared energy scale is 0.1179 ± 0.0009.

The global fit of the effective leptonic weak mixing angle is sin^2(theta) = 0.23149 ± 0.00005.

Can We Measure The External Field Effect On Earth?

Color me skeptical. 

The External Field Effect can be understood as basically a swamping of a second order MOND effect by first order Newtonian effects, so I'm very doubtful that it could be measured experimentally in the solar system anywhere near Earth. Also, a 0.1 fm precision measurement, i.e. a fraction of the size of a proton or neutron, starts to run into definitional issues about what the object your measuring even is due to quantum mechanics and the parton makeup of hadrons. And, the uncertainty regarding the functional form of a MOND interpolating function further muddies the waters and makes any measurement model dependent.

Despite compelling evidence, the absence of a confirmed dark matter particle has sustained interest in modified gravity as an alternative explanation for the observed phenomenology. One prominent example is Modified Newtonian Dynamics (MOND), which predicts that the internal dynamics of a system depends on the external gravitational field in which it is embedded. This so-called External Field Effect violates the strong equivalence principle (SEP) and is absent in canonical mechanics, making it a promising avenue for experimental tests of modified gravity. 

Motivated by this, we investigate the dynamics of two spherical masses arranged such that their symmetry axis is either parallel or orthogonal to the local gravitational field. We derive solutions describing the internal dynamics of such systems in both strong uniform and radial external fields. In particular, for a radial external field, if the non-relativistic gravitational field is free to have non-vanishing curl, we find that the mutual attraction of the masses in the perpendicular configuration is not strictly aligned with their symmetry axis. It acquires a small transverse component, even when the external gravitational field is everywhere balanced by non-gravitational forces. 

Using these solutions, we determine the spatial and temporal sensitivities required to distinguish the two configurations and systematically assess experimentally relevant effects, including air drag, object size, and surface interactions. As an example, detecting the prediction of the simple MOND interpolating function requires a spatial sensitivity of order 0.1 fm for sub-millimeter masses evolving over approximately 30 minutes. Such times may be achievable with levitated particles or in space-based environments. Experiments operating at lower resolutions are also interesting as independent tests of SEP and place constraints on modified-gravity theories.

Ankit Kumar, et al., "Probing the Strong Equivalence Principle through the External Field Effect. How Do Two Masses Fall?" arXiv:2607.10247 (July 11, 2026).

A Central Black Hole's Rotation Direction Doesn't Determine A Galaxy's Rotation Direction

While I didn't have strong expectations one way or the other, this paper's conclusion is potentially important to understanding galaxy formation, and tends to disfavor a purely accretion hypothesis. 

In contrast, the fairly strong correlation between central black hole size and galaxy size tends to argue for a very important role of central black holes in the galaxy formation process, because black holes only make up ca. 1% of a galaxy's mass.

The paper also makes notable observations about other aspects of spiral galaxy geometry.

We compare the apparent directions of rotation in the plane of the sky of active galactic nuclei (AGNs) and their host galaxies. The direction of rotation of the galaxy was inferred from the direction of the spiral arms, while the direction of rotation of the AGN was inferred from spectropolarimetry, where the change in relative polarization position angle (PA) across broad lines is believed to be caused by equatorial scattering. The numbers of co-rotating and counter-rotating AGNs are equal. 

Studies of the relative position angles of radio jets have implied that there is a "zone of avoidance" where jets avoid being in the plane of disk galaxies. We point out that bi-conical narrow-line-region outflows also avoid the plane of the host galaxy. 

The equal numbers of co-rotating and counter-rotating AGNs exclude the hypothesis that the "zone of avoidance" is due to a lack of large tilts of the black hole rotating axis relative to the host galaxy rotation axis. Our results imply that the relative orientations of spin axes are random, at least for the black hole mass range we consider. 

We propose that changes in the broad-line polarization PA with wavelength that do not closely follow the predictions of the simple equatorial scattering model are a consequence of the scattering dust being clumpy. We note a couple of cases of possible changes in PA over several years, which, if real, could be due to motions of the dust clumps or changing anisotropy of the continuum emission.

Loren Gigi, C. Martin Gaskell, "The direction of rotation of supermassive black holes is unrelated to the direction of rotation of the host galaxy" arXiv:2607.06902 (July 8, 2026).

Red River

Red River (Japanese: 天は赤い河のほとり, Hepburn: Sora wa Akai Kawa no Hotori; lit. 'The Sky Is on the Banks of the Red River'), also known as Anatolia Story, is a Japanese manga series written and illustrated by Chie Shinohara. The series was published by Shōgakukan in their Sho-Comi magazine from January 1995 to June 2002 and was collected in 28 tankōbon volumes. It is published in English in North America by Viz Media. An anime television series adaptation produced by Tatsunoko Production is set to premiere in July 2026. 

As of March 2019, the manga had over 20 million copies in circulation, making it one of the best-selling manga series. In 2001, Red River won the Shogakukan Manga Award for the shōjo category.

From Wikipedia.

The river after which the series was named, the "Kızılırmak (Turkish pronunciation: [kɯˈzɯɫɯɾmak], Turkish for "Red River"), historically known as the Halys River (Ancient Greek: Ἅλυς), is the longest river flowing entirely within Turkey.

I read this manga series when my children were in middle school, basically in the early twenty-tens, not long after I began this blog, as one of the first really epic manga series that I'd read. American comics and graphic novels have almost no sub-genre that approximates this series. 

It is back on my radar screen because the first episode of an anime based upon this manga series was released today, and so far, so good. It is a pretty faithful and successful adaptation so far.

Why am I writing about it here?

Because this manga series was instrumental in spurring my interest in prehistory, anthropology, and historical linguistics, in a story that brought the late Bronze Age Hittite Empire to life and contributed a lot to me caring about all of these fields. Some of my own writing on the Hittites can be found here.

And honestly, while it has fictional and magical elements, much like Bronze Age legendary history works actually written at or within a few centuries of that time period, by and large, this series has stood the test of time and is broadly consistent with what archaeologists, anthropologists, ancient historians, and historical linguistics scholars still believe now.

What all of those disciplines lack, however, that historical fiction like this can provide, is synthesis, relatability, and meaning. Academic scholars tend to focus in on tiny details and cower from providing a larger narrative or connecting the dots for fear of being wrong. But doing so takes away the joy and allure of that once captivated the people who are doing the work and keeps them motivated enough to continue to do so. Historical fiction can give the dry piecemeal reconstructions life and a "vibe" allowing you to feel some sense of what life was like back then.

The fictional account does so in ways big and small. For example, while the dialog is in Japanese (and translated into English in the versions I consume), this series retains enough of the historically accurate Hittite proper names to make those names relatable and not so intimidating, when you encounter them as you study the actual history of the Hittite people, a culture the remains the source of pivotal and important open questions in the broader picture of the Bronze Age and Indo-European linguistics.

Even the magical and supernatural and religious aspects of the story, while not actually things that happened in the past, are largely consistent with the religious and metaphysical worldviews of the people who lived in that era in Anatolia.

The Age Of The Universe

The Big Bang was about 13.6 billion years ago, although the uncertainty in that estimate is considerable since it is model dependent. This is consistent with both the age of the oldest stars inferred from their metal content, and the LambdaCDM model with a constant cosmological constant determined based upon cosmic background radiation. 

But if the Hubble constant had its low redshift value (which calls for a faster expansion of the Universe), the age of the Universe would be much shorter than that of the oldest stars in the Milky Way. 

Thus, you can't solve the Hubble tension by tweaking the model dependent cosmic background radiation based estimate of its value in a way that works. Either the Hubble constant isn't really constant, or there is something wrong with the low redshift estimates of its value which affect all of the methodologies for estimating the Hubble constant at low redshift even though they are independent of each other in their methodology (e.g. the Universe is not as homogeneous as we think and we are in an atypical part of it).

We estimate the age of the Universe using the Xiang & Rix sample of 247,103 Milky Way stars with high-resolution spectroscopy from LAMOST DR7 and Gaia eDR3 parallaxes. Stellar ages were estimated using YY isochrones up to 20 Gyr. To remove stars with unusually high and precise ages, we require old stars to be metal-poor and α-enriched. We also require consistency between YY ages and those obtained with FLAME based only on Gaia data. Our final sample of 155,600 stars within 5 kpc provides consistent cosmic age estimates using several techniques of increasing rigour. Our main results use an MCMC reconstruction of the latent age distribution, though our iterative reconstruction is very similar. 

Applying an innovative approach to our MCMC reconstruction and its uncertainties, we find that the oldest star has an age of A⋆ = 13.73 +0.18 −0.15 Gyr. Varying the quality cuts can at most reduce this to A⋆ = 13.31 +0.21 −0.18 Gyr or raise it to 14.02 +0.18 −0.15 Gyr using a much lower or higher age-dependent metallicity ceiling, respectively. Our inferred A⋆ is consistent with the 13.6 Gyr expected in CMB-calibrated ΛCDM, assuming the first long-lived stars formed when the Universe was 0.2 Gyr old. 

This agreement casts doubt on solutions to the Hubble tension solely through new physics prior to recombination, which generally imply a cosmic age of 12.9 ±0.2 Gyr to match low redshift probes. It is difficult for stellar modelling uncertainties to reconcile such a low age with our result given the low metallicities of the oldest stars in our sample and independent asteroseismic constraints.

Indranil Banik, Thenujaya Kudakolawa Kaluarachchige, Stephen Cookson, Harry Desmond, "The age of the Universe from a large sample of the oldest Galactic stars" arXiv:2607.00764 (July 1 2026) (Submitted to the Monthly Notices of the Royal Astronomical Society).

Quote Of The Day

The sociology in the simulation community seems to be to assert complete success in explaining everything at all times until the next batch of simulations completes running, then point out all the improvements. Everything is explained all the time, only more so as time goes on.

- From Stacy McGaugh at Triton Station on June 18, 2026.

A Theoretically Innovative MOG Theory

Canadian physicist John Moffat's MOG modified gravity theory is a long standing tensor, vector, scalar modification of General Relativity (GR). As the link explains:

Scalar–tensor–vector gravity theory, also known as MOdified Gravity (MOG), is based on an action principle and postulates the existence of a vector field, while elevating the three constants of the theory to scalar fields. In the weak-field approximation, STVG produces a Yukawa-like modification of the gravitational force due to a point source. Intuitively, this result can be described as follows: far from a source gravity is stronger than the Newtonian prediction, but at shorter distances, it is counteracted by a repulsive fifth force due to the vector field.

STVG has been used successfully to explain galaxy rotation curves, the mass profiles of galaxy clusters, gravitational lensing in the Bullet Cluster, and cosmological observations without the need for dark matter. On a smaller scale, in the Solar System, STVG predicts no observable deviation from general relativity. The theory may also offer an explanation for the origin of inertia.

Yukawa forces are forces carried by massive mediator bosons (in contrast to the massless mediator boson of electromagnetism, the photon, which has an infinite range as a result), whose range is a function of the mediator mass. 

The most familiar example of a Yukawa force is the nuclear binding force (sometimes called the residual strong force) that holds photons and neutrons in atomic nuclei together, which is mediated by like composite mesons, especially pions (neutral pions have a mass of about 135 MeV, while charged ones have a mass of about 140 MeV) that have an effective range on the order of femtometers, which is similar to the size of an atomic nucleus.

In contrast, GR without a cosmological constant (including Deur's approach to explaining dark matter phenomena as gravitional) is a tensor theory, and GR with a cosmological constant is a tensor-scalar theory. Newtonian gravity is a scalar theory. Several of the main relativistic generalizations of MOND are also tensor, vector, scalar theories.

MOG, while not the subject of as much scholarship as MOND (Israeli physicist Mordehai Milgrom's 1983 non-relativistic toy model modification of Newtonian gravity that does a good job of replicating dark matter phenomena is almost near equilibrium systems of galaxy size or smaller), MOG is still one of the older modified gravity theories, has received considerable investigation from scientists other than its inventor, is relativistic, is more easily generalized to cosmology scale problems, and unlike MOND, models galaxy cluster phenomena often attributed to dark matter more successfully, at the cost of being somewhat less intuitive to understand.

Moffat's latest short paper formulates his MOG theory in a manner, that while essentially identical to the original, is easier to apply to cosmology scale questions.

We develop a Stueckelberg gauge-invariant formulation of modified gravity (MOG). 

The massive vector field is made gauge-invariant by introducing a compensating scalar field, without requiring a Higgs field, spontaneous symmetry breaking, or a vacuum expectation value to fix the effective Newtonian gravitational coupling. This separates the gauge-invariant origin of the vector mass from the cosmological evolution of the gravitational coupling. 

The formulation preserves the finite-range vector interaction of MOG, while allowing the effective gravitational coupling to be treated as an independent scalar or scale-dependent quantity. This distinction is important for cosmological tests, since early-universe constraints and late-time large-scale gravitational phenomena need not be tied to a symmetry-breaking vacuum. The Stueckelberg formulation provides a gauge-invariant framework for comparing MOG with nucleosynthesis, cosmic microwave background, large-scale structure, lensing, and distance data.

John W. Moffat, "Stueckelberg Gauge Invariant Formulation of MOG" arXiv:2606.26427 (June 4, 2026).

Another new MOG paper constrains the value of one of that theory's physical constants (to a value inconsistent with the range in the previous literature on the topic):

The scalar-tensor-vector-gravity (STVG), a prototype of modified gravity developed by Moffat, can correctly explain galaxy rotation curves, cluster dynamics, Bullet Cluster phenomena and cosmological data without invoking the observationally elusive general relativistic (GR) dark matter. Further, recent observations of neutron star masses are shown to defy some GR predictions, whereas STVG turns out to be more consistent with those observations. These successes indicate that STVG could be a potential candidate for a new theory of gravity. 

However, an important question concerns the possible range of values of the STVG dimensionless parameter α imposed by various physical scenarios. In the literature, the range 0.03 < α < 2.47 corresponding to different central source masses has been suggested. We show here that the α can be considerably constrained into the range 0 < α < 10^−5 assuming that the updated GPS fluctuation does not exceed the α-dependent correction to the terrestrial Sagnac delay.

R. Kh. Karimov, R. N. Izmailov, K. K. Nandi, "Terrestrial Sagnac delay in scalar-tensor-vector-gravity" arXiv:2606.27033 (June 25, 2026).

A footnote on f(R) gravity

Probably the other modified gravity theory with significant scholarship from multiple astrophysicists that is most often used to explain dark matter phenomena gravitationally is f(R) gravity (the image below is from this link), which like GR with a cosmological constant, and unlike MOG or some relativistic generalizations of MOND, is a tensor-scalar theory. The way f(R) gravity modifies GR is not with an extra vector field, but with a higher order derivative term. The standard Ricci scalar R in the Einstein-Hilbert action is replaced by a general function of R (e.g., R + (alpha)*R^2). Mathematically and dynamically, this higher-order derivative theory is exactly equivalent to standard General Relativity coupled to a single, dynamical scalar field (known as the scalaron), rather than only having the static scalar dark energy field that is equivalent to the cosmological constant.

Like MOG, f(R) gravity has a Yukawa correction to the gravitational potential, which (at least in part, it also has a time and scale dependent gravitational constant) is how it can explain some or all dark matter phenomena without dark matter particles.

The Modest Excess Higgs Boson Production Explained

The Standard Model is stochastic (i.e. probabilistic) and not deterministic. It doesn't say, if you do X then Y will happen. It says, if you do X, Y with happen Z percent of the time.

One of the many things that the Standard Model predicts is the Higgs boson production rate, as a probability distribution of the rate at which Higgs bosons are produced in given circumstances. The calculation is in the form of an infinite series of terms with leading order, next to leading order, next to next to leading order, etc. terms.

You haven't read much about the physics of Higgs boson production at this blog because its a lot less simple and intuitive than Higgs boson decays, which are much more straightforward and rely on simpler, less complicated processes and rules. This makes Higgs boson production harder to write good blog posts about than Higgs boson decays. Also, the experimental anomalies compared to Standard Model predictions for Higgs boson production have been less striking, with more uncertainty and not very striking discrepancies, even though the discrepancies in Higgs boson production rates have been quite persistent.

In practice, scientists calculate the Standard Model prediction for the Higgs production rate with as many terms as are practically feasible for them to calculate, and then they try to estimate the uncertainty arising from the omitted terms as best they can.

Usually, each slight incremental improvement in the accuracy of the calculation takes disproportionately more work to calculate than the amount of work that was necessary to make the previous improvement of that magnitude. 

But, now and then, scientists unexpectedly find a previous omitted term from their calculations that is really important, although figuring out which terms will be especially fruitful to include is still at a more art than science level right now. Research programs like the amplituhedron approach and related developments from it are trying to bring more science to that search, but we aren't quite there yet.

Experiments since 2012, when the Higgs boson was first discovered, have shown that Higgs production usually exceeds the rate calculated by the best available Standard Model prediction calculations, although either not by a statistically significant amount, or with only a mild statistical tension with the best available predicted value for the Standard Model Higgs boson production rate.

Initially, some scientists though that this could be because the Higgs boson was detected sooner than it would have been otherwise because of a statistical fluke of higher than expected Higgs production. At first, that was a plausible proposal.

But it has been 14 years now, so it probably wasn't that, because the slight bias towards higher the expected Higgs boson production rates hasn't completely gone away, as the sample size of Higgs bosons detected has surged and reduced statistical uncertainties (but not always systemic uncertainties in the measurements of the Higgs boson production rates). 

Of course, like every anomaly in high energy particle physics, some theorists have, instead, tried to explain this persistent, not very large anomaly, with beyond the Standard Model physics.

But, a new paper now explains most or all of what has been going on. It turns out that the Higgs boson that physicists have observed is behaving more like than Standard Model Higgs boson to higher precision than ever, once again.

The new paper recalculates the Standard Model predicted Higgs boson production rate and determines that some next to leading order terms contributing to the predicted Higgs boson production rate were more important than had been expected. It turns out that these omitted terms can led to up to 10% more Higgs bosons being produced than would have been predicted without them in some circumstances.

Including the omitted terms explains most or all of the excess of experimentally observed Higgs boson production over the old calculation of the SM predicted value. This also, by the way, tends to imply that the uncertainties in the old experimental measurements were probably overestimated, which is a common reality in electroweak physics (as opposed to QCD or astronomy where uncertainties are often underestimated).

This new discovery feels like a reprise of the comparisons between the experimentally measured values of muon g-2 and state of the art calculations of the Standard Model prediction. In both cases, the gap has been mostly bridged by improving the quality of the calculations of the Standard Model predictions with an immense amount of hard calculation work, rather than by improving experimental accuracy or discovery new beyond the Standard Model physics. And, like the muon g-2 discrepancies, the part of the Higgs boson production calculation that has impaired the accuracy of the Standard Model prediction has mostly been the very hard to calculate strong force/hadronic/quark based part of what is primarily an extremely precise electroweak calculation.

The new paper and its abstract are as follows:

We present the mixed QCD-electroweak corrections to Higgs boson pair production in the quark-antiquark channel. 

The virtual amplitudes are computed fully analytically using the method of differential equations. We determine the integration constants by matching our expressions to the large mass expansion limit of the canonical integrals. We implement the results in the POWHEG-BOX framework for phenomenological studies. 

The corrections are found to have a significant impact on the shapes of differential cross sections, reaching up to +10% for the invariant mass distribution of the Higgs boson pair near the production threshold. This channel has not been considered before in calculations of the next-to-leading order electroweak corrections to Higgs boson pair production.

Marco Bonetti, Gudrun Heinrich, Philipp Rendler, William J. Torres Bobadilla, "Electroweak corrections to Higgs boson pair production: The quark channel" arXiv:2606.25928 (June 24, 2026) (contribution to the proceedings of Loops and Legs in Quantum Field Theories 2026, Bayreuth, Germany).

The new paper above is a physics conference summary of a more detailed paper on the same topic released in January of this year.

Data On Galaxies

Are active galactic nuclei (AGNs) exceptions to the Tully-Fischer rule or are they just hard to measure?

Active galactic nuclei have sometimes been excluded from Tully-Fischer fits because the underlying data points have high uncertainties, due to their low inclinations relative to solar system based observers leading, in turn, to "large scatter" although the magnitude of the scatter really isn't all that high for fairly imprecise astronomy measurements of distant galaxies.

The small data set in a new paper doesn't really bely that but these may also be galaxies which are out of equilibrium or have non-gravitational forces (e.g., the massive nuclear forces involved in star formation) that are relevant and significant in their dynamics. The authors of a new paper note that:

While the samples used to calibrate the canonical TF relations did not explicitly flag AGNs for removal (Tully& Pierce 2000; Tully et al. 2008; Tully&Courtois 2012; Kourkchi et al. 2020a), the selection criteria generally exclude active galaxies. Primarily, all works above select spirals with inclinations greater than 45◦. As Type 1 AGNs have been observed to be preferentially hosted by face-on (<45◦) galaxies (Keel 1980; Maiolino & Rieke 1995; McLeod & Rieke 1995; Simcoe et al. 1997; Gkini et al. 2021), this criterion naturally excludes a significant amount of Seyfert 1 hosts. The nuclear flux from unobscured Type 1 AGNs represents the primary expected source of photometric scatter in TF relations, whereas the high levels of nuclear obscuration inherent in Type 2 systems are expected to largely mitigate such contamination.

Visually, their data set does show high AGN scatter but also shows big error bars largely consistent with the baryonic Tully-Fischer relation.

We present an investigation of the Tully-Fisher (TF) relation solely for galaxies hosting an active galactic nucleus (AGN). Using 22 galaxies with primary, z-independent distances, we find that active galaxies exhibit significantly larger scatter about all TF relations compared to each respective calibration for (largely) inactive galaxies. 

The larger scatter persists despite removal of the AGN contamination from the photometry of the Type 1 AGNs via 1) careful surface brightness decompositions or 2) employing SEDs to constrain the light contribution of the AGN. These results suggest that the influence of an AGN on its host galaxy's surface brightness may extend beyond the nucleus. 

We also calculate the percentage difference between TF and primary distances, and find that TF-based distances are biased towards overestimation of the primary distances to active galaxies by anywhere from 5-10 percent for the optical/near-infrared and approximately 15 percent for distances predicted from inverting the Baryonic TF (BTF) relation. As TF-based distances (especially the I-band) are relied on heavily for analysis and modeling of the local peculiar velocity (Vpec) field, we suggest that active galaxies be removed from future Vpec modeling samples.

Justin H. Robinson, et al., "On the Tully-Fisher Relation for Active Galaxies -- I: Evidence of Larger Scatter" arXiv:2606.22575 (June 21, 2026) (Accepted for publication in ApJ).

In one context, a new paper (which also has a small sample size) finds that inferred spherical dark matter halos aren't ruled out, although slightly flattened halos are still preferred.

Wide-field surveys like Euclid mark a new era of extragalactic stellar stream studies. With a large number of streams, it is now possible to constrain the dark matter halos of galaxies in a cosmological volume and draw comparisons to theoretical expectations for the geometry of dark matter halos. 

This study combines Euclid imaging with visual detection and segmentation annotations to analyse streams. We use projected stream morphologies to constrain the shape and centre-of-mass position (CoM) of each host galaxy's potential, jointly probing baryonic and dark matter distributions. These inferences complement weak lensing methods, with sensitivity to halo profile and geometry on sub-virial scales. The method enables both stacked, population-level constraints on halo flattening and CoM position, and constraints on these quantities for individual halos. 

We also present a novel method for transforming segmentation maps of stellar streams into smooth, curvature-preserving tracks optimised for fast and robust dynamical inference. This approach enables rapid modelling of stream morphology, supports a statistically rigorous combination of constraints across multiple streams within a single galaxy, and enables joint inference across galactic hosts. 

From our study of 13 galaxies with prominent tidal streams, we find agreement with spherical halos, albeit a mild preference for flattening with q=0.95+0.05−0.10 at 68% confidence. This is promising early agreement with ΛCDM predictions. 

With thousands more discovered streams expected across Euclid's mission, our programme will enable precise measurements of halo shapes and CoM positions across large samples and redshifts, offering constraints on the geometry of dark matter halos.

Euclid Collaboration, "Euclid Quick Data Release (Q1): The geometry of dark matter halos from extragalactic streams" arXiv:2606.21774 (June 19, 2026) (Submitted to A&A).

A Hot Hypothesis For Neptune And Uranus

Normally, I don't write much about planetary astronomy, not because there's anything wrong with the discipline, but because I'm concerned mostly with the quest to determine the fundamental laws of physics, and planetary astronomy is basically unrelated to that. But this paradigm shifting interpretation of the data regarding Uranus and Neptune deserves a mention.

Uranus and Neptune are commonly interpreted as volatile-rich "ice giants", an assumption that underpins most interior models. 

Here we show that their observed radii, bulk densities, gravitational harmonics, normalized moments of inertia, intrinsic luminosities, and key features of their atmospheric compositions are consistent with interiors comprising supercritical, hydrogen-rich magma oceans overlain by H2-rich envelopes. 

Our results, based on three fit parameters for each planet, provide a parsimonious explanation for the structures, thermal states, and atmospheric chemistries of Uranus and Neptune. We find that the Solar System's ice giants are better understood as magma-ocean giants, with origins parallel to those of sub-Neptune gas-dwarf planets. A continuum among gas dwarf planets permits Neptune and Uranus to serve as accessible, data-driven test cases for structure models and material properties used to understand sub-Neptunes.

Edward D. Young, Sarah P. Marcum, Aaron Werlen, Paula N. Wulff, "Ice Giants Revisited: Uranus and Neptune as Magma Ocean Worlds" arXiv:2606.18219 (June 16, 2026).

More Cosmology Limits On Neutrino Mass

In principle, the sum of the three neutrino masses and the number of neutrino types can be determined from astronomy observations in the context of a cosmology model. 

In practice, to a certain extent this determination is model dependent, although the estimates are consistently quite a bit less than 150 meV at the two sigma level. This is far less than the current 1410 meV lower bound (expected to be ultimately reduced to 660 meV) set by direct measurements of lightest of the three neutrino mass eigenstates in the Katrin experiment (currently 450 meV but expected to reach 200 meV once the experiment runs its course). 

Even fairly extreme tweaks to dark energy assumptions and a prior that the sum of the neutrino masses can't be less than the minimum established by neutrino oscillation experiments, in the paper below sets of cap of about 115 meV. So, the results are robust in the general vicinity of absolute neutrino masses, even if their specific limits vary by scores of meVs from each other.

Like other cosmology based absolute neutrino mass estimates, it doesn't absolutely rule out an inverted neutrino mass hierarchy, but it disfavors one in a statistically significant manner with fairly mild assumptions.

The effective number of neutrino types determined from cosmology measurements is more robust and overwhelming a fit to three types (plus an expected adjustment for radiation), ruling out additional sterile neutrinos with masses on the order of 10 eV or less (N(eff) is not sensitive to heavier neutrinos). 

This doesn't rule out seesaw neutrino mass models (which can involve very heavy sterile neutrinos) or sterile neutrino warm dark matter (which characteristically has keV scale masses), but it does seriously limit sterile neutrino explanations of anomalies in neutrino oscillation experiments (which tellingly are frequently inconsistent with each other).

We present a robust assessment of cosmological constraints on the sum of neutrino masses (∑mν) when relaxing the standard assumption of purely adiabatic primordial initial conditions. 

Allowing for a neutrino density isocurvature (NDI) component alongside the adiabatic mode, we analyse the latest CMB-SPA combination (Planck 2018, ACT DR6, and SPT-3G), DESI DR2 baryon acoustic oscillation data, and the DES Year 5 supernova sample. Within the ΛCDM model, the 95% upper limit weakens only marginally from ∑mν < 0.052 eV (purely adiabatic) to < 0.057 eV (including NDI), with the NDI amplitude consistent with zero. In the CPL dynamical dark energy model, the adiabatic limit is < 0.111 eV, shifting to < 0.115 eV with NDI, yet the isocurvature mode remains undetected. 

While these limits are robust against the inclusion of isocurvature perturbations, they are highly sensitive to both the assumed dark energy equation of state and the prior lower bound on ∑mν. Notably, the adiabatic ΛCDM limit of 0.052 eV lies below the minimum sum required by the normal neutrino mass hierarchy (0.05878 eV), indicating that this bound is an artifact of the statistical prior extending to zero. Imposing a physically motivated hierarchy-informed prior raises the limit to <0.092 eV. 

Our results demonstrate that current data show no evidence for NDI modes and that the inferred neutrino mass upper limit is robust against this extension, but a definitive, model-independent bound requires addressing prior dependencies and dark energy uncertainties. This work provides the first joint constraint on ∑mν and NDI using the full CMB-SPA+DESI DR2+DES dataset.

Hongsheng Hou, Sai Wang, Zhi-Chao Zhao, Xin Zhang, ""Constraints on the Sum of Neutrino Masses from ACT DR6 and DESI DR2 Considering Isocurvature Initial Conditions" arXiv:2606.17994 (June 16, 2026).

The Inferred Milky Way Dark Matter Distribution Isn't Spherical

Measuring matter dynamics outside the plane of spiral galaxies is critical 

Rotations curves of, and gravitational accelerations of, matter in the vicinity of spiral galaxies that is above or below the galactic plane where most of the ordinary matter in these galaxies is found, is critical to distinguishing between competing dark matter particle and gravity or fifth force based explanations of dark matter phenomena (or hybrids of the two paradigms like self-interacting dark matter).

These theories have been formulated and fine tuned to reproduce the dynamics of stars in the plane of spiral galaxies where they are much easier to observe and measure, and good data has been available for many decades. But because good data has not been available for the dynamics of stars outside the galactic plane of spiral galaxies, different models formulated to explain dark matter phenomena differ considerably in what they predict about that.

Measuring matter dynamics outside the plane of spiral galaxies is hard and has only recently become a viable possibility

But until very recently our astrophysical observations provided us with little data and limited accuracy outside the galactic plane of spiral galaxies with various kinds of "telescopes" for a variety of reasons. 

In the case of the Milky Way, the main problems have been that the density of stars to observe outside the galactic plane of the Milky Way is much lower than in or near the thin galactic disk where most of its stars are found, and the complication that as observers who are inside the Milky Way, the vantage point of our observations is obstructed by dense stars in the galactic plane or otherwise non-optimal.

In the case of other galaxies, one of the main problems have been that it is hard to determine if a particular star is in the galactic plane or above (or below) that plane unless we have a close to edge on view of the galaxy, that measuring rotation curves is hard with a true edge on view. Another problem is that the resolution of our view of a galaxy gets worse as the galaxy gets more distant which is especially a concern outside the plane of a spiral galaxy where the density of the stars we are trying to observe is low. And, when looking at another galaxy it is particularly hard to tell if a star outside the main plane of the galaxy is really part of the same gravitationally bound system, or is millions of megaparsecs away from it in the foreground of our observation of that galaxy.

Fortunately, we live in an era where we have an abundance of riches when it comes to astronomy observations, producing a torrent of data from extremely powerful telescopes like the Gaia space observatory (a telescope in orbit around Earth). The data from this space telescope is used by the Gaia collaboration's network of over 400 scientists and engineers funded by the European Space Agency (ESA) to build the most accurate 3D map of the Milky Way ever constructed.

As the paper below explains in its abstract, Gaia's measurement uncertainties are less than 5% for the vertical velocities of stars that it observes in the Milky Way, and are less than 20% for the vertical accelerations that it measures. 

These uncertainties may not seem all that great to someone unfamiliar with the details of galaxy scale astronomy observations. But in that subfield of astronomy,  uncertainties as low as 28% (i.e. 0.1 dex) are the considered good, and relative uncertainties on the order of 50%-100% are common place, so Gaia's measurements are gold standards of precision by comparison.

Comparing models

Both simple cold dark matter models (with their spherically symmetrical NFW dark matter particle halos) and MOND (even in its relativistic generalizations) predict dark matter phenomena are spherically symmetrical, which makes these theories mathematically much more tractable. 

Indeed, coming up with any kind of dark matter particle model without either (1) self-interactions more complex than a simple scalar field, or (2) interactions in excess of ordinary gravitational interactions with ordinary matter, that do not form spherical or nearly spherical dark matter halos, is extremely challenging and could very well be impossible (although I'm not aware of any analytically constructed "no go" theorem to that effect).

But not all explanations of dark matter phenomena predict spherically symmetric effects, and inferred dark matter halo shapes from prior observations have tended to favor non-spherical, rugby ball shaped inferred distributions of dark matter particles (even though theoretically, it has been challenging to come up with dark matter particle theories that reproduce these shapes).

Some gravity based explanations of dark matter phenomena, like the one described by Deur, also propose non-spherical dark matter phenomena in spiral galaxies. In Deur's approach dark matter phenomena arise from non-linear self-interactions within gravitational fields that manifest in, and only in, non-spherical matter distributions like those found in spiral disk disk galaxies. 

In Deur's analysis, in spiral galaxies, the pull of gravity towards the galactic center is stronger than the Newtonian expectation in the direction of rays from the galactic center in the galactic plane (especially at larger radii), while it is weaker than the Newtonian expectation in the vertical direction relative to the galactic plane (an effect which accounts, at least in part, for dark energy phenomena between galaxies).

Deur's analysis is also supported by another key data point that corroborates astronomy observations that infer non-spherical dark matter particle distributions in dark matter particle paradigms. He has observed that the relative proportion of matter in a galaxy that is made of luminous stars to inferred dark matter is strongly correlated in elliptical galaxies, with the extent to which the elliptical galaxy is not perfectly spherical.

New, high quality data shows that the Milky Way's inferred dark matter halo is not spherical 

Gaia has assembled new data with record breaking accuracy and sample sizes on the rotational velocities and accelerations of stars in the Milky Way based upon their polar coordinates (i.e. their distance from the Galactic center and their distance from the plane of the Milky Way spiral disk). This data, was compiled by the Gaia collaboration, and was analyzed and reported in a pre-print released today of an accepted for publication astronomy paper.

The new paper's analysis strongly favors inferred dark matter particle distributions which are not spherically symmetric. Instead, it strongly favors the inference in a dark matter particle paradigm of a flattened disk-like configuration around the ordinary matter of the Milky Way.

The Gaia data generically rules out all dark matter particle explanations of dark matter phenomena, gravity or fifth force based explanations,  and hybrid explanations (like self-interacting dark matter models), that predict spherically symmetric dark matter phenomena effects. 

This is a huge deal because most of the leading explanations of dark matter phenomena are spherically symmetric, and all of those models are now definitively ruled out.

The paper

We derive both the mid-plane and off-plane rotation curves, v(c)(R,z), and the vertical acceleration, a(z)(R,z), of the Milky Way (MW) using Gaia~DR3 data over the ranges of vertical heights z∈(−2,2) kpc and galactocentric distances R∈(8.5,14) kpc where the velocity components are determined with high precision, i.e., with an error <5%. In contrast, the vertical acceleration a(z)(R,z) is dominated by model-dependent systematics, with uncertainties of up to ∼20%. This level of accuracy allows us to place stringent constraints on the geometry of the MW's dark matter (DM) distribution, as the vertical gradients of the gravitational potential attain their maximum within this range of radial and vertical distances corresponding to the characteristic scales of the disk. 

We find that models including the observed stellar components together with a spherical DM halo fail to reproduce both the pronounced variation of v(c)(R,z) with height and the observed behavior of a(z)(R,z). 

In particular, spherical halos with a scale radius of rs∼15 kpc contribute negligibly to the off-plane rotation curve and vertical acceleration in the inner disk, leaving these features primarily determined by the stellar mass distribution. 

Conversely, models in which DM is confined to a flattened, disk-like configuration predict substantial contributions to both v(c)(R,z) and a(z)(R,z), resulting in a markedly better agreement with the data. We conclude that disk-like DM distributions are strongly favored over spherical halo models. 

Forthcoming Gaia data releases will enable even more stringent tests of the geometry and distribution of the MW's DM component.

Francesco Sylos Labini, Roberto Capuzzo-Dolcetta, "Constraining the Geometry of Galactic Dark Matter with Gaia Data Release 3" arXiv:2606.12548 (June 10, 2026) (accepted for publication in The Astrophysical Journal) (emphasis added in abstract).

The body text of the conclusion further explains that:

Our results show that the DM disk model provides a significantly better agreement with the data than the standard Navarro–Frenk–White (NFW) halo profile. 

In particular, spherical halos with characteristic scale radii of order ∼ 10 kpc contribute only marginally to the off-plane rotation curve and to the vertical acceleration within the inner disk, leaving these quantities predominantly determined by the distribution of the stellar mass. As a consequence, halo-based models systematically underestimate the measured vertical accelerations and fail to reproduce the observed decline of the rotation curve at intermediate heights. 

In contrast, models in which the DM is confined to a flattened, disk-like configuration predict substantial contributions to both the radial and vertical components of the gravitational field, leading to a markedly improved agreement with the observed trends of v(c)(R,z) and a(z)(R,z). This improvement is particularly evident at low to intermediate heights (|z| ≲ 2 kpc), where the vertical acceleration inferred from the data cannot be explained by the baryonic components alone. 

The success of the DM disk model arises from its geometry: a flattened mass distribution naturally enhances the vertical component of the gravitational potential without requiring an excessive total mass, and simultaneously reproduces the modest decline of the circular velocity with increasing z. These results strongly suggest that a significant fraction of the MW’s dark matter is distributed in a disk-like structure rather than in a quasi-spherical halo. 

Forthcoming Gaia data releases, offering improved statistics and reduced systematic uncertainties in stellar kinematics, will enable more stringent and spatially extended tests of the geometry of the Galaxy’s dark matter component, potentially allowing one to constrain its vertical and radial scale lengths with unprecedented precision. 

Standard Model Muon g-2 Calculation Closely Matches Experimental Data

The most accurate ever calculation of the Standard Model predicted value of muon g-2 matches the world average experimentally measured value to 0.7 sigma (with the prediction and the experimental measurement having a precision of 310 and 124 parts per billion, respectively).

The new theoretically calculated value for muon g-2 is: 

aμ = (116,592,052 ± 36) × 10−11.

The most precise available experimental measurement is as follows:

Fermilab (2025): (116,592,070.5 ± 14.8) × 10−11.

The difference is (18.5 ± 38.9) × 10−11

The relative experimental result has an uncertainty of 0.127 ppm. The new calculation of the Standard Model expected value has a relative uncertainty of 0.31 ppm.

The error weighted experimental world average, which has a relative uncertainty of 0.124 ppm is: 

(116,592,071.5 ± 14.5) × 10−11. 

This final result is recapped in an exhaustive final muon g-2 experimental data report at arXiv:2606.17323.

The difference between the world average and the new SM prediction calculation is 

(28.5 ± 38.8) × 10−11, which is 0.7 sigma (which is still closer than than one sigma expected by a random distribution of uncertainties if the results are identical).

This global test of the Standard Model (which implicates all three of its forces) at low energies passes with flying colors.

For 50 years, the standard model of particle physics has been very successful in describing subatomic phenomena. In the past quarter of a century, this was challenged by a mismatch between its predictions and precision measurements of the anomalous magnetic moment of the muon, a(μ). This disagreement was eventually reconciled, first through a determination in an ab initio lattice calculation of the most uncertain theoretical contribution, the leading-order hadronic vacuum polarization (LO-HVP), a(μ)^(LO-HVP) and subsequently by experimental results and updates of the reference standard-model predictions using lattice results for a(μ)^(LO-HVP).

Here we present a new calculation for this crucial quantity, obtaining 

. This reduces the uncertainty by a factor of 1.6 compared with our earlier computation. We use a hybrid approach that includes a small, long-distance contribution from experiments in a low-energy regime in which they all agree. Our approach combines the strengths of experimental and lattice data in different energy ranges, achieving better precision than with either alone. Our lattice quantum chromodynamics (QCD) simulations are performed on finer lattices . . . allowing for an even more accurate continuum extrapolation. 

Combined with the calculations of the other standard-model contributions . . . our result leads to a prediction that differs from the recent measurement of a(μ) by only 0.5 standard deviations. This provides a notable validation of the standard model to 11 digits.

A. Boccaletti, et al., "Hybrid calculation of hadronic vacuum polarization in muon g − 2 to 0.48%." 653 (8814) Nature 373 (April 22, 2026) (open access) DOI: 10.1038/s41586-026-10449-z

While the hadronic part of the calculation accounts for a fairly modest part of the total value, it is the source of almost all of the uncertainty in the calculation:

A Meta Post

Today is the 160th day of the year, and I am on track at 80 posts at this blog so far, the historically normal rate of about one post every two days. I have, however, had proportionately more physics posts and proportionately fewer non-physics posts, than usual, and my posts have had somewhat less depth than I'd ideally like them to, on average. There have been 2,981 posts at this blog over its entire duration.

The sister blog to this one, Wash Park Prophet, has 51 posts so far this year, which while far from being a dead blog, is the lowest posting rate there that I've had of all time (a bit more than 2.2 posts per week). I just can't maintain both blogs at my usual pace at my current job (and have shifted some of my output of hit and run posts to Facebook). I have made 9,696 posts at that blog since its inception.

I've made 12,677 posts at these two blogs combined since their inception.

Combined, I've made 131 posts in 160 days, a pace of about four posts every five days. Again, this is nothing to sniff at, but less than I've posted historically.