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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 $\Gamma$ 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 $\Gamma=0$ at $s/r_{\rm{M}}\lesssim 0.15$ or $s\lesssim 1$~kilo astronomical units (kau), I get $\Gamma=0.068\pm 0.015$ (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 $\gamma_g = 10^{2\Gamma}$ is measured to be $\gamma_g = 1.37_{-0.09}^{+0.10}$ (stat) $_{-0.09}^{+0.16}$ (syst). With a reduced $\chi^2$ test of Newtonian and Milgromian nonrelativistic theories, I find that Newtonian gravity is ruled out at $5.8\sigma$ ($\chi^2_\nu=9.4$) by the new sample (and $9.2\sigma$ by the largest sample used). The Milgromian AQUAL theory is acceptable with $0.5\lesssim \chi^2_\nu\lesssim 3.1$. 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., Comment: 27 figures, 4 tables, minor revision to match the version published in ApJ

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., Comment: 16 pages, 6 figures, accepted for publication in MNRAS

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 $\gamma_g=g_{\rm{obs}}/g_{\rm{pred}}=1.49^{+0.21}_{-0.19}$ 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 $\approx 5.0\sigma$. The projected velocity boost factor for $s\gtrsim 5$ kau is measured to be $\gamma_{v_p} = 1.20\pm 0.06$ (stat) $\pm 0.05$ (sys) matching $\sqrt{\gamma_g}$. 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., Comment: 29 pages, 33 figures, accepted for publication in the Astrophysical Journal (This version includes a response to Banik et al. [arXiv:2311.03436].)

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 $\delta_{\rm{obs-newt}}$ between the observed acceleration at $g_{\rm{N}}$ and the Newtonian prediction is measured to be: $\delta_{\rm{obs-newt}}= 0.034\pm 0.007$ 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 $10\sigma$ 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 $g_{\rm{obs}}/g_{\rm{pred}}=10^{\sqrt{2}\delta_{\rm{obs-newt}}}=1.43\pm 0.06$. This systematic deviation agrees with the boost factor that the AQUAL theory predicts for kinematic accelerations in circular orbits under the Galactic external field., Comment: A revised version of the published ApJ paper (2023, 952, 128) including corrections of Figures 12, 18, 20, and Equation (4) to be published in an erratum in press: all corrections are minor and have no impact on the contents or conclusion of the paper

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., Comment: 6 pages, 2 figures, 1 table (results revised, conclusions strengthened)

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 $6.9\sigma$ 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., Comment: ApJ, in press (results revised, conclusions unchanged)

We consider a regression modeling of the quantiles of residual life, remaining lifetime at a specific time. We propose a smoothed induced version of the existing non-smooth estimating equations approaches for estimating regression parameters. The proposed estimating equations are smooth in regression parameters, so solutions can be readily obtained via standard numerical algorithms. Moreover, the smoothness in the proposed estimating equations enables one to obtain a robust sandwich-type covariance estimator of regression estimators aided by an efficient resampling method. To handle data subject to right censoring, the inverse probability of censoring weight are used as weights. The consistency and asymptotic normality of the proposed estimator are established. Extensive simulation studies are conducted to validate the proposed estimator's performance in various finite samples settings. We apply the proposed method to dental study data evaluating the longevity of dental restorations., Comment: 16 pages, 2 figures

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., Comment: Astrophysical Journal, accepted (7 figures, 1 table)

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 $>4\sigma$ 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., Comment: Astrophysical Journal, in press, 13 figures, 3 tables