arXiv subjects

Kyu-Hyun Chae

Publications and source records attributed to Kyu-Hyun Chae.

At least 19 recordsLinked to original sources

arXiv2026

On the Proper 3D Modeling of Orbits in Wide Binary Gravity Tests

A gravitationally-bound system of wide binary stars with precise 3D relative displacement $\mathbf{r}$ and velocity $\mathbf{v}$ can allow a Keplerian orbit reconstruction for an assumed gravitational parameter $G$. A sufficiently large sample of such systems can also be used to directly infer $G$ specific to the sample. A recent study argued that treating the semi-major axis ($a$) explicitly free with an empirical prior imposed on it can dramatically change the inference of $G$ in the Chae et al. sample of 36 wide binaries. Here we introduce and test a Bayesian Markov chain Monte Carlo algorithm that allows $a$ to be explicitly free (with or without a prior on $a$), and find using the $α$-Cen AB - proxima system and the Chae et al. sample that the explicit-$a$ algorithm with an observational constraint is fully equivalent to the implicit-$a$ algorithm with an internal consistency relation involving the sky-projected separation $s$. For the $α$-Cen AB - proxima system, we present orbits in Milgromian (MOND) as well as Newtonian gravity models. We show that a recent claim of Newtonian gravity from the Chae et al. sample is a consequence of a fatal error in the code or arbitrarily enlarged errors. We discuss how wide binaries can be properly analyzed and modeled to probe gravity at low acceleration and test gravity models, including the necessity of deriving individual-specific parameters, the importance of follow-up observations for anomalous systems, and the relevance of Bayesian MCMC approaches.

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arXiv2026

The Baryonic Faber-Jackson Relation and Fundamental Plane of Galaxy Groups, Elliptical Galaxies, and Dwarf Galaxies

The baryonic Faber-Jackson relation (BFJR) links the baryonic mass of pressure-supported systems to their mean velocity dispersion. For elliptical galaxies, the BFJR is thought to be a projection of the fundamental plane (FP), which includes the stellar half-mass radius as a third variable. We study the BFJR and FP across eight orders of magnitude in baryonic mass, encompassing galaxy groups, ellipticals, dwarf ellipticals, and dwarf spheroidals. We compile and homogenize data for 1400 pressure-supported systems and measure their mean internal baryonic acceleration $\langle g_\mathrm{bar}\rangle$. We find that the properties of the BFJR and FP systematically depend on the internal acceleration of the sampled systems, with a transition around the acceleration scale $a_0\simeq 1.2\times10^{10}$ m s$^{-2}$. For low-acceleration systems with $\langle g_\mathrm{bar}\rangle < 0.6\,a_0$ (dwarf galaxies and galaxy groups), the BFJR relation takes the form $\log_{10}(M_\mathrm{bar}/M_{\odot}) = (4.19 \pm 0.10) \log_{10}(σ_{\rm los}/\rm{km s}^{-1}) + (2.55^{+0.16}_{-0.16})$. The FP expected from the Newtonian virial theorem is followed by high-acceleration systems (massive ellipticals with $\langle g_\mathrm{bar}\rangle \gtrsim 6 \,a_0$), whereas low-acceleration systems deviate from the FP at both low masses (dwarf galaxies) and high masses (galaxy groups). Our results generally agree with the expectations of modified Newtonian dynamics (MOND): high-acceleration systems follow the Newtonian virial theorem in which a radial variable explicitly appears (the FP), while low-acceleration systems follow the MOND virial theorem in which the radial dependence disappears (the BFJR). On average, the MOND external field effect seems to play a secondary role in dwarf galaxies in galaxy groups and clusters.

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arXiv2026

Revisiting Data Quality Control and Multiple-star Modeling in Wide Binary Gravity Tests: Confirmation of MOND-type Gravitational Anomaly at Low Acceleration

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 $γ\approx 1.3-1.6$. 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 $\tilde v$-distribution test, and the median-$\tilde v$-profile test (where $\tilde v$ 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.

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arXiv2026

Bayesian Inference of Gravity through Realistic 3D Modeling of Wide Binary Orbits: General Algorithm and a Pilot Study with HARPS Radial Velocities

When 3D relative displacement $\mathbf{r}$ and velocity $\mathbf{v}$ between the pair in a gravitationally-bound system are precisely measured, the six measured quantities at one phase can allow elliptical orbit solutions at a given gravitational parameter $G$. Due to degeneracies between orbital-geometric parameters and $G$, individual Bayesian inferences and their statistical consolidation are needed to infer $G$ as recently suggested by a Bayesian 3D modeling algorithm. Here I present a fully general Bayesian algorithm suitable for wide binaries with two (almost) exact sky-projected relative positions (as in the Gaia data release 3) and the other four sufficiently precise quantities. Wide binaries meeting the requirements of the general algorithm to allow for its full potential are rare at present, largely because the measurement uncertainty of the line-of-sight (radial) separation is usually larger than the true separation. As a pilot study, the algorithm is applied to 32 Gaia binaries for which precise HARPS radial velocities are available. The value of $Γ\equiv \log_{10}\sqrt{G/G_{\rm N}}$ (where $G_{\rm N}$ is Newton's constant) is $-0.002_{-0.018}^{+0.012}$ supporting Newton for a combination of 24 binaries with Newtonian acceleration $g_{\rm N}>10^{-9}$m\,s$^{-2}$, while it is $Γ=0.134_{-0.036}^{+0.056}$ ($0.143_{-0.041}^{+0.068}$) for 8 (6) binaries with $g_{\rm N}<10^{-9}$ ($<10^{-9.5}$) m\,s$^{-2}$ representing $> 3.5σ$ discrepancy with Newton. However, one system (Stars HD189739 and HD189760) dominates the signal. Without it, the tension with Newton is significantly lessened with $Γ=0.063_{-0.041}^{+0.065}$. Thus, to verify the tentative signal, many such systems need to be discovered and their kinematic nature such as any possibility of hidden tertiary stars needs to be thoroughly addressed. The pilot study demonstrates the potential of the algorithm.

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arXiv2025

Probing the nature of gravity in the low-acceleration limit: wide binaries of extreme separations with perspective effects

Recent statistical analyses of wide binaries have revealed a boost in gravitational acceleration with respect to the prediction by Newtonian gravity at low internal accelerations $\lesssim 10^{-9}$ m\,s$^{-2}$. This phenomenon is important because it does not permit the dark matter interpretation, unlike galaxy rotation curves. We extend previous analyses by increasing the maximum sky-projected separation from 30 to 50 kilo astronomical units (kau). We show that the so-called ``perspective effects'' are not negligible at this extended separation and, thus, incorporate it in our analysis. With wide binaries selected with very stringent criteria, we find that the gravitational acceleration boost factor, $γ_g \equiv g_{\rm obs}/g_{\mathrm N}$, is $1.61^{+0.37}_{-0.29}$ (from $δ_{\rm obs-newt}\equiv (\log_{10}γ_g)/\sqrt{2}=0.147\pm0.062$) at Newtonian accelerations $g_{\mathrm N} = 10^{-11.0}$ m\,s$^{-2}$, corresponding to separations of tens of kau for solar-mass binaries. At Newtonian accelerations $g_{\mathrm N} = 10^{-10.3}$ m\,s$^{-2}$, we find $γ_g=1.26^{+0.12}_{-0.10}$ ($δ_{\rm obs-newt}=0.072\pm0.027$). For all binaries with $g_{\rm N}\lesssim10^{-10}$ m\,$s^{-2}$ from our sample, we find $γ_g=1.32^{+0.12}_{-0.11}$ ($δ_{\rm obs-newt}=0.085\pm0.027$). These results are consistent with the generic prediction of MOND-type modified gravity, although the current data are not sufficient to pin down the low-acceleration limiting behavior. Finally, we emphasize that the observed deviation from Newtonian gravity cannot be explained by the perspective effects or any separation-dependent eccentricity variation which we have taken into account.

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arXiv2025

Low-Acceleration Gravitational Anomaly from Bayesian 3D Modeling of Wide Binary Orbits: Methodology and Results with Gaia Data Release 3

Isolated wide binary stars provide natural laboratories to directly probe gravity for Newtonian acceleration $g_{\rm{N}}\lesssim 10^{-9}$ m s$^{-2}$. Recent statistical analyses of wide binaries have been performed only with sky-projected relative velocities $v_p$ in the pairs. A new method of Bayesian orbit modeling exploiting three relative velocity components including the radial component $v_r$ is developed to measure the gravitational anomaly parameter $Γ\equiv\log_{10}\sqrt{γ_g}\equiv\log_{10}\sqrt{G_{\rm{eff}}/G_{\rm{N}}}$ where $G_{\rm{eff}}$ is the effective gravitational constant for pseudo-Newtonian elliptical orbits, while $G_{\rm{N}}$ is Newton's constant. The method infers individual probability distributions of $Γ$ and then combines the independent distributions to obtain a consolidated distribution in a specific range of $g_{\rm{N}}$. Here the method is described and applied to a sample of 312 wide binaries in a broad dynamic range $10^{-11.0}\lesssim g_{\rm{N}}\lesssim 10^{-6.7}$ m s$^{-2}$ with $v_r$ uncertainties in the range $168<σ_{v_r}<380$ m s$^{-1}$ selected from the Gaia DR3 database. The following results are obtained: $Γ= 0.000\pm 0.011$ ($N_{\rm{binary}}=125$) for the high-acceleration regime ($10^{-7.9} \lesssim g_{\rm{N}} \lesssim 10^{-6.7}$ m s$^{-2}$) agreeing well with Newton, but $Γ= 0.085\pm 0.040$ or $γ_g=1.48_{-0.23}^{+0.33}$ (35) for a MOND regime ($10^{-11.0}\lesssim g_{\rm{N}}\lesssim 10^{-9.5}$ m s$^{-2}$) and $Γ= 0.063\pm 0.015$ or $γ_g=1.34_{-0.08}^{+0.10}$ (111) for a MOND+transition regime ($10^{-11.0}\lesssim g_{\rm{N}}\lesssim 10^{-8.5}$ m s$^{-2}$). These results show that a gravitational anomaly is evident for $g_{\rm{N}}\lesssim 10^{-9}$ m s$^{-2}$ and $Γ$ in the MOND regime ($\lesssim 10^{-9.5}$ m s$^{-2}$) agrees with the prediction ($\approx 0.07$) of MOND gravity theories.

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arXiv2024

Measurements of the Low-Acceleration Gravitational Anomaly from the Normalized Velocity Profile of Gaia Wide Binary Stars and Statistical Testing of Newtonian and Milgromian Theories

Low-acceleration gravitational anomaly is investigated with a new method of exploiting the normalized velocity profile $\tilde{v}\equiv v_p/v_c$ of wide binary stars as a function of the normalized sky-projected radius $s/r_{\rm{M}}$ where $v_p$ is the sky-projected relative velocity between the pair, $v_c$ is the Newtonian circular velocity at the sky-projected separation $s$, and $r_{\rm{M}}$ is the MOND radius. With a Monte Carlo method Gaia observed binaries and their virtual Newtonian counterparts are probabilistically distributed on the $s/r_{\rm{M}}$ versus $\tilde{v}$ plane and a logarithmic velocity ratio parameter $Γ$ is measured in the bins of $s/r_{\rm{M}}$. With three samples of binaries covering a broad range in size, data quality, and implied fraction of hierarchical systems including a new sample of 6389 binaries selected with accurate distances and radial velocities, I find a unanimous systematic variation from the Newtonian flat line. With $Γ=0$ at $s/r_{\rm{M}}\lesssim 0.15$ or $s\lesssim 1$~kilo astronomical units (kau), I get $Γ=0.068\pm 0.015$ (stat) $_{-0.015}^{+0.024}$ (syst) for $s/r_{\rm{M}} \gtrsim 0.7$ or $s\gtrsim 5$~kau. The gravitational anomaly (i.e.\ acceleration boost) factor given by $γ_g = 10^{2Γ}$ is measured to be $γ_g = 1.37_{-0.09}^{+0.10}$ (stat) $_{-0.09}^{+0.16}$ (syst). With a reduced $χ^2$ test of Newtonian and Milgromian nonrelativistic theories, I find that Newtonian gravity is ruled out at $5.8σ$ ($χ^2_ν=9.4$) by the new sample (and $9.2σ$ by the largest sample used). The Milgromian AQUAL theory is acceptable with $0.5\lesssim χ^2_ν\lesssim 3.1$. These results agree well with earlier results with the "acceleration-plane analysis" for a variety of samples and the "stacked velocity profile analysis" for a pure binary sample.

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arXiv2024

A critical review of recent GAIA wide binary gravity tests

Over the last couple of years, the appearance of the third data release from the {\it Gaia} satellite has triggered various wide binary low acceleration gravity tests. Wide binaries with typical total masses $\approx 1.0 - 1.6 M_{\odot}$ and separations above a few thousand au probe the low acceleration $a \lesssim a_{0}$ regime, where at galactic and larger scales gravitational anomalies typically attributed to the presence of an as yet undetected dark matter component appear, where $a_{0} \approx 1.2\times 10^{-10}$ m s$^{-2}$ is the acceleration scale of MOND. Thus, studies of the relative velocities and separations on the plane of the sky, $v_{2D}$ and $s_{2D}$ respectively, of wide binary stars extending to separations above a few kau, provide an independent approach on the empirical study of gravity in the interesting $a \lesssim a_{0}$ acceleration range. Two independent groups, through complementary approaches, have obtained evidence for a departure from Newtonian predictions in the low acceleration regime, in consistency with MOND expectations for wide binary orbits in the Solar Neighbourhood. Two other groups however, have instead reported results showing a clear preference for Newtonian gravity over various MOND alternatives tested, over the same low acceleration regime. We here take a critical look at the various studies in question, from sample selection to statistical treatment of the wide binary relative velocities obtained. We discover a couple of critical problems in the formal design and statistical implementation shared by the two latter groups, and show explicitly how these yield biased conclusions.

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arXiv2023

Robust Evidence for the Breakdown of Standard Gravity at Low Acceleration from Statistically Pure Binaries Free of Hidden Companions

It is found that Gaia DR3 binary stars selected with stringent requirements on astrometric measurements and radial velocities naturally satisfy Newtonian dynamics without hidden close companions when projected separation $s \lesssim 2$ kau, showing that pure binaries can be selected. It is then found that pure binaries selected with the same criteria show a systematic deviation from the Newtonian expectation when $s \gtrsim 2$ kau. When both proper motions and parallaxes are required to have precision better than 0.005 and radial velocities better than 0.2, I obtain 2,463 statistically pure binaries within a `clean' $G$-band absolute magnitude range. From this sample, I obtain an observed to Newtonian predicted kinematic acceleration ratio of $γ_g=g_{\rm{obs}}/g_{\rm{pred}}=1.49^{+0.21}_{-0.19}$ for acceleration $\lesssim 10^{-10}$ m s$^{-2}$, in excellent agreement with $1.49\pm 0.07$ for a much larger general sample with the amount of hidden close companions self-calibrated. I also investigate the radial profile of stacked sky-projected relative velocities without a deprojection to the 3D space. The observed profile matches the Newtonian predicted profile for $s \lesssim 2$ kau without any free parameters but shows a clear deviation at a larger separation with a significance of $\approx 5.0σ$. The projected velocity boost factor for $s\gtrsim 5$ kau is measured to be $γ_{v_p} = 1.20\pm 0.06$ (stat) $\pm 0.05$ (sys) matching $\sqrt{γ_g}$. Finally, for a small sample of 40 binaries with exceptionally precise radial velocities (fractional error $<0.005$) the directly measured relative velocities in the 3D space also show a boost at larger separations. These results robustly confirm the recently reported gravitational anomaly at low acceleration for a general sample.

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arXiv2023

Breakdown of the Newton-Einstein Standard Gravity at Low Acceleration in Internal Dynamics of Wide Binary Stars

A gravitational anomaly is found at weak gravitational acceleration $g_{\rm{N}} < 10^{-9}$ m s$^{-2}$ from analyses of the dynamics of wide binary stars selected from the Gaia DR3 database that have accurate distances, proper motions, and reliably inferred stellar masses. Implicit high-order multiplicities are required and the multiplicity fraction is calibrated so that binary internal motions agree statistically with Newtonian dynamics at a high enough acceleration of $10^{-8}$ m s$^{-2}$. The observed sky-projected motions and separation are deprojected to the three-dimensional relative velocity $v$ and separation $r$ through a Monte Carlo method, and a statistical relation between the Newtonian acceleration $g_{\rm{N}} \equiv GM/r^2$ (where $M$ is the total mass of the binary system) and a kinematic acceleration $g \equiv v^2/r$ is compared with the corresponding relation predicted by Newtonian dynamics. The empirical acceleration relation at $< 10^{-9}$ m s$^{-2}$ systematically deviates from the Newtonian expectation. A gravitational anomaly parameter $δ_{\rm{obs-newt}}$ between the observed acceleration at $g_{\rm{N}}$ and the Newtonian prediction is measured to be: $δ_{\rm{obs-newt}}= 0.034\pm 0.007$ and $0.109\pm 0.013$ at $g_{\rm{N}}\approx10^{-8.91}$ and $10^{-10.15}$ m s$^{-2}$, from the main sample of 26,615 wide binaries within 200 pc. These two deviations in the same direction represent a $10σ$ significance. The deviation represents a direct evidence for the breakdown of standard gravity at weak acceleration. At $g_{\rm{N}}=10^{-10.15}$ m s$^{-2}$, the observed to Newton predicted acceleration ratio is $g_{\rm{obs}}/g_{\rm{pred}}=10^{\sqrt{2}δ_{\rm{obs-newt}}}=1.43\pm 0.06$. This systematic deviation agrees with the boost factor that the AQUAL theory predicts for kinematic accelerations in circular orbits under the Galactic external field.

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arXiv2022

Testing Modified Gravity Theories with Numerical Solutions of the External Field Effect in Rotationally Supported Galaxies

The strong equivalence principle is violated by gravity theories of Milgromian dynamics (MOND) through the action of the external field effect. We test two different Lagrangian theories AQUAL and QUMOND based on their numerical solutions of the external field effect, by comparing two independent estimates of the mean external field strength of the nearby universe: a theory-deduced value from fitting the outer rotation curves of 114 galaxies and an empirical value from the large-scale distribution of cosmic baryons. The AQUAL-deduced external field strength from rotation curves agrees with that from the large-scale cosmic environment, while QUMOND-deduced value is somewhat higher. This suggests that AQUAL is likely to be preferred over QUMOND as an effective non-relativistic limit of a potential relativistic modified gravity theory.

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arXiv2022

Distinguishing Dark Matter, Modified Gravity, and Modified Inertia with the Inner and Outer Parts of Galactic Rotation Curves

The missing gravity in galaxies requires dark matter, or alternatively a modification of gravity or inertia. These theoretical possibilities of fundamental importance may be distinguished by the statistical relation between the observed centripetal acceleration of particles in orbital motion and the expected Newtonian acceleration from the observed distribution of baryons in galaxies. Here predictions of cold dark matter halos, modified gravity, and modified inertia are compared and tested by a statistical sample of galaxy rotation curves from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database. Modified gravity under an estimated mean external field correctly predicts the observed statistical relation of accelerations from both the inner and outer parts of rotation curves. Taken at face value there is a $6.9σ$ difference between the inner and outer parts on an acceleration plane which would be inconsistent with current proposals of modified inertia. Removing galaxies with possible systematic concerns such as central bulges or special inclinations does not change this trend. Cold dark matter halos predict a systematically deviating relation from the observed one. All aspects of rotation curves are most naturally explained by modified gravity.

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arXiv2022

Numerical Solutions of the External Field Effect on the Radial Acceleration in Disk Galaxies

In MOND (modified Newtonian dynamics)-based theories the strong equivalence principle is generically broken in an idiosyncratic manner, manifested in the action of an "external field effect (EFE)". The internal dynamics in a self-gravitating system is affected even by a constant external field. In disk galaxies the EFE can induce warps and modify the rotational speeds. Due to the non-linearity of MOND, it is difficult to derive analytic expressions of this important effect in a disk. Here we study numerically the EFE in two non-relativistic Lagrangian theories of MOND: the `Aquadratic-Lagrangian' theory (AQUAL) and `Quasilinear MOND' (QUMOND). For AQUAL we consider only the axisymmetric field configurations with the external field along the disk axis, or a spherical galaxy with test-particle orbits inclined to the external field. For the more manageable QUMOND we calculate also the three-dimensional field configurations, with the external field inclined to the disk axis. We investigate particularly to what degree an external field modifies the quasi-flat part of rotation curves. While our QUMOND results agree well with published numerical results in QUMOND, we find that AQUAL predicts weaker EFE than published AQUAL results. However, AQUAL still predicts stronger EFE than QUMOND, which demonstrates current theoretical uncertainties. We also illustrate how the MOND prediction on the rising part of the rotation curve, in the inner parts, depends largely on disk thickness but only weakly on a plausible external field for a fixed galaxy model. Finally, we summarize our results for the outer parts as an improved, approximate analytic expression.

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arXiv2021

Testing the Strong Equivalence Principle. II. Relating the External Field Effect in Galaxy Rotation Curves to the Large-Scale Structure of the Universe

Theories of modified gravity generically violate the strong equivalence principle, so that the internal dynamics of a self-gravitating system in free fall depends on the strength of the external gravitational field (the external field effect). We fit rotation curves (RCs) from the SPARC database with a model inspired by Milgromian dynamics (MOND), which relates the outer shape of a RC to the external Newtonian field from the large-scale baryonic matter distribution through a dimensionless parameter $e_{\rm N}$. We obtain a $>4σ$ statistical detection of the external field effect (i.e. $e_{\rm N}>0$ on average), confirming previous results. We then locate the SPARC galaxies in the cosmic web of the nearby Universe and find a striking contrast in the fitted $e_{\rm N}$ {values} for galaxies in underdense versus overdense regions. Galaxies in an underdense region between 22 and 45 Mpc from the celestial axis in the northern sky have RC fits consistent with $e_{\rm N}\simeq0$, while those in overdense regions adjacent to the CfA2 great wall and the Perseus-Pisces supercluster return $e_{\rm N}$ that are a factor of two larger than the median for SPARC galaxies. We also calculate independent estimates of $e_{\rm N}$ from galaxy survey data and find that they agree with the $e_{\rm N}$ inferred from the RCs within the uncertainties, the chief uncertainty being the spatial distribution of baryons not contained in galaxies or clusters.

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arXiv2021

Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies

The strong equivalence principle (SEP) distinguishes General Relativity from other viable theories of gravity. The SEP demands that the internal dynamics of a self-gravitating system under free-fall in an external gravitational field should not depend on the external field strength. We test the SEP by investigating the external field effect (EFE) in Milgromian dynamics (MOND), proposed as an alternative to dark matter in interpreting galactic kinematics. We report a detection of this EFE using galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog. Our detection is threefold: (1) the EFE is individually detected at $8σ$ to $11σ$ in "golden" galaxies subjected to exceptionally strong external fields, while it is not detected in exceptionally isolated galaxies, (2) the EFE is statistically detected at more than $4σ$ from a blind test of 153 SPARC rotating galaxies, giving a mean value of the external field consistent with an independent estimate from the galaxies' environments, and (3) we detect a systematic downward trend in the weak gravity part of the radial acceleration relation at the right acceleration predicted by the EFE of the MOND modified gravity. Tidal effects from neighboring galaxies in the $Λ$CDM context are not strong enough to explain these phenomena. They are not predicted by existing $Λ$CDM models of galaxy formation and evolution, adding a new small-scale challenge to the $Λ$CDM paradigm. Our results point to a breakdown of the SEP, supporting modified gravity theories beyond General Relativity.

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arXiv2021

A cautionary tale in fitting galaxy rotation curves with Bayesian techniques: does Newton's constant vary from galaxy to galaxy?

The application of Bayesian techniques to astronomical data is generally non-trivial because the fitting parameters can be strongly degenerated and the formal uncertainties are themselves uncertain. An example is provided by the contradictory claims over the presence or absence of a universal acceleration scale (g$_\dagger$) in galaxies based on Bayesian fits to rotation curves. To illustrate the situation, we present an analysis in which the Newtonian gravitational constant $G_N$ is allowed to vary from galaxy to galaxy when fitting rotation curves from the SPARC database, in analogy to $g_{\dagger}$ in the recently debated Bayesian analyses. When imposing flat priors on $G_N$, we obtain a wide distribution of $G_N$ which, taken at face value, would rule out $G_N$ as a universal constant with high statistical confidence. However, imposing an empirically motivated log-normal prior returns a virtually constant $G_N$ with no sacrifice in fit quality. This implies that the inference of a variable $G_N$ (or g$_{\dagger}$) is the result of the combined effect of parameter degeneracies and unavoidable uncertainties in the error model. When these effects are taken into account, the SPARC data are consistent with a constant $G_{\rm N}$ (and constant $g_\dagger$).

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arXiv2020

On the Presence of a Universal Acceleration Scale in Elliptical Galaxies

Dark matter phenomena in rotationally supported galaxies exhibit a characteristic acceleration scale of $g_\dagger \approx 1.2\times 10^{-10}$ m s$^{-2}$. Whether this acceleration is a manifestation of a universal scale, or merely an emergent property with an intrinsic scatter, has been debated in the literature. Here we investigate whether a universal acceleration scale exists in dispersion-supported galaxies using two uniform sets of integral field spectroscopy (IFS) data from SDSS-IV MaNGA and ATLAS$^{\rm 3D}$. We apply the spherical Jeans equation to 15 MaNGA and 4 ATLAS$^{\rm 3D}$ slow-rotator E0 (i.e., nearly spherical) galaxies. Velocity dispersion profiles for these galaxies are well determined with observational errors under control. Bayesian inference indicates that all 19 galaxies are consistent with a universal acceleration of $g_\dagger=1.5_{-0.6}^{+0.9}\times 10^{-10}$ m s$^{-2}$. Moreover, all 387 data points from the radial bins of the velocity dispersion profiles are consistent with a universal relation between the radial acceleration traced by dynamics and that predicted by the observed distribution of baryons. This universality remains if we include 12 additional non-E0 slow-rotator elliptical galaxies from ATLAS$^{\rm 3D}$. Finally, the universal acceleration from MaNGA and ATLAS$^{\rm 3D}$ is consistent with that for rotationally supported galaxies, so our results support the view that dark matter phenomenology in galaxies involves a universal acceleration scale.

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arXiv2019

Radial Acceleration Relation between Baryons and Dark or Phantom Matter in the Super-critical Acceleration Regime of Nearly Spherical Galaxies

The central regions of nearby elliptical galaxies are dominated by baryons (stars) and provide interesting laboratories for studying the radial acceleration relation (RAR). We carry out exploratory analyses and discuss the possibility of constraining the RAR in the super-critical acceleration range $(10^{-9.5},\hspace{1ex}10^{-8})$~${\rm m}~{\rm s}^{-2}$ using a sample of nearly round pure-bulge (spheroidal, dispersion-dominated) galaxies including 24 ATLAS$^{\rm 3D}$ galaxies and 4201 SDSS galaxies covering a wide range of masses, sizes and luminosity density profiles. We consider a range of current possibilities for the stellar mass-to-light ratio ($M_\star/L$), its gradient and dark or phantom matter (DM/PM) halo profiles. We obtain the probability density functions (PDFs) of the parameters of the considered models via Bayesian inference based on spherical Jeans Monte Carlo modeling of the observed velocity dispersions. We then constrain the DM/PM-to-baryon acceleration ratio $a_{\rm X}/a_{\rm B}$ from the PDFs. Unless we ignore observed radial gradients in $M_\star/L$, or assume unreasonably strong gradients, marginalization over nuisance factors suggests $a_{\rm X}/a_{\rm B} = 10^{p} (a_{\rm B}/a_{+1})^q$ with $p = -1.00 \pm 0.03$ (stat) $^{+0.11}_{-0.06}$ (sys) and $q=-1.02 \pm 0.09$ (stat) $^{+0.16}_{-0.00}$ (sys) around a super-critical acceleration $a_{+1}\equiv 1.2\times 10^{-9}~{\rm m}~{\rm s}^{-2}$. In the context of the $Λ$CDM paradigm, this RAR suggests that the NFW DM halo profile is a reasonable description of galactic halos even after the processes of galaxy formation and evolution. In the context of the MOND paradigm, this RAR favors the Simple interpolating function but is inconsistent with the vast majority of other theoretical proposals and fitting functions motivated mainly from sub-critical acceleration data.

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