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X. Hernandez

Publications and source records attributed to X. Hernandez.

At least 19 recordsLinked to original sources
arXiv2026

A detailed MOND modelling of the Bullet Cluster

The colliding galaxy clusters system 1E 0657-56, the "Bullet Cluster", is often presented as a serious objection to modified gravity theories dispensing with dark matter in general, and in particular, to the MOND formalism. The argument centres on the fact that the baryonic matter distribution of this system is dominated by the X-ray emitting gas, while the projected surface density required under General Relativity to explain the observed lensing signal, centres on the observed galaxies. This spatial offset is interpreted as being in conflict with MOND, naively assuming that dark matter being absent, the gravitational potential should centre upon the largest mass distribution, the X-ray gas. However, as under General Relativity, under MOND, the gravitational potential of a system depends upon the volume density and not just the total mass. I here show that the surface density which QUMOND predicts will be inferred under General Relativity from the gravitational potential of the "Bullet Cluster", qualitatively matches the spatial distribution of what General Relativity inferences of lensing observations return. The close-to-point-like galaxies imply under QUMOND a relatively larger surface density signal than what is expected from the diffuse gas. As is common under MOND modeling of galaxy clusters, a mass deficit on the baryon content is obtained, in this case by a factor of 1.6. Beyond this, only small offsets on the details with respect to GR interpretations of lensing observations remain; MOND is hence shown to be no more discrepant with the "Bullet Cluster" than with any other galaxy cluster.

astro-ph.GA↗
arXiv2026

Most open clusters follow the radial acceleration relation (RAR) and the baryonic Tully-Fisher relation (BTFR)

We test whether parsec-scale stellar systems in the Milky Way follow the galactic radial acceleration relation (RAR) or the baryonic TullyFisher relation (BTFR). We analyse 5646 Gaia DR3 open clusters from the Hunt \& Reffert catalogue. Observed accelerations are derived from velocity dispersions and characteristic radii, and baryonic accelerations from stellar masses and characterisitc radii. The clusters are placed on the RAR and BTFR planes and compared with Newtonian and MOND expectations. Approximately 90 per cent of open clusters (those with $N_\star \leq 250$) lie close to the RAR, albeit with significant scatter. In a first-of-its-kind test, a smaller fiducial sample is consistent with a best-fitting acceleration scale $g_\dagger \approx 1.2 \times 10^{-10}\ \mathrm{m\,s^{-2}} \pm 0.5$ dex, compatible with canonical MOND values. More massive clusters approach the Newtonian virial expectation. No correlations are found between RAR residuals and galactocentric radii, distance to the Galactic disk midplane, age, or morphology. Tidal effects and unresolved binaries are insufficient to reproduce the observations without fine-tuning. Interpreted within a MOND framework, the alignment of most open clusters with the RAR and BTFR suggests that low-acceleration dynamics operate on parsec scales within the Milky Way. This implies that the Galactic gravitational field is not smooth on these scales and may include regions where the total gravitational acceleration falls below $a_0$, partially mitigating the external field effect, thereby motivating higher-resolution modelling of the Galactic potential and informing other small-scale gravity tests within the Galaxy.

astro-ph.GA↗
arXiv2026

Detection of Gravitational Anomaly at Low Acceleration from a Highest-quality Sample of 36 Wide Binaries with Accurate 3D Velocities

We set out to accurately measure gravity in the low-acceleration range $(10^{-11},10^{-9})$ m s$^{-2}$ from 3D motions of isolated wide binary stars. Gaia DR3 provides precise measurements of the four sky-plane components of the 3D relative displacement and velocity ($\mathbf{r}, \mathbf{v}$) for a wide binary, but not comparably precise line-of-sight (radial) separation and relative velocity $v_{r}$. Based on our new observations and the public databases/publications, we assemble a sample of 36 nearby (distance $<150$pc) wide binaries in the low-acceleration regime with accurate values of $v_{r}$ (uncertainty $< 100$ m s$^{-1}$). Kinematic contaminants such as undetected stellar companions are well under control using various observational diagnostics such as Gaia's ruwe parameter, the color-magnitude diagram, multi-epoch observations of radial velocities, Speckle interferometric follow-up observations, and requiring Hipparcos-Gaia proper motion consistency. For the parameter $\Gamma \equiv \log_{10}\sqrt{\gamma}$ with $\gamma \equiv G/G_{\rm N}$ (where $G$ is a parameter generalizing Newton's constant $G_{\rm N}$ in elliptical orbits), we find $\Gamma=0.102_{-0.021}^{+0.023}$, inconsistent with standard gravity at $4.9\sigma$, giving a gravity boost factor of $\gamma=1.600_{-0.141}^{+0.171}$. Four wide binaries have 3D relative velocities exceeding their estimated Newtonian escape velocities with $1<v_{\rm obs}/v_{\rm escN}\le1.2$. These systems are unlikely to be chance associations and are expected in a nonstandard paradigm such as Milgromian dynamics (MOND). The hypothesis that Newtonian gravity can be extrapolated to the low-acceleration limit is falsified by this independent study with accurate 3D velocities. Future radial velocity monitoring and Speckle interferometric imaging for larger samples will be useful to refine the present result.

astro-ph.GA↗
arXiv2026

Elastic overtones: an equal temperament 12 tone music system with "perfect" fifths

The impossibility of a transposable 12 semitone tuning of the octave arises from the mathematical fact that $2 \times 2^{7/12} \neq 3$ i.e., the second harmonic of the fifth can not exactly match the third harmonic of the fundamental. This in turn, stems from the whole number harmonic structure of western music, and the subsequent fundamental character of the octave interval as multiples of 2 in frequency, a property inherited by our music system from the physics of instruments with vibrating elements being to a good approximation one dimensional. In the current era of electronic music, one can relax the above assumptions to construct an analogous music system where all the structural properties of the standard music system are preserved, but where harmonics are not whole number multiples of the fundamental frequency, and the octave is no longer a factor of 2 in frequency. This now allows to construct a transposable 12 semitone music system where the second harmonic of the fifth exactly matches the third harmonic of the fundamental. The enhanced harmonic qualities of this system recover to a good approximation the musical qualities of Just Intonation, whilst retaining by construction all the versatility and modulating ability of 12TET.

physics.soc-ph↗
arXiv2025

Dynamical Friction Constraints on the Dark Matter Hypothesis Across Astronomical Scales

Dynamical friction implies a consistency check on any system where dark matter particles are hypothesised to explain orbital dynamics requiring more mass under Newtonian gravity than is directly detectable. Introducing the assumption of a dominant dark matter halo will also imply a decay timescale for the orbits in question. A self-consistency constraint hence arises, such that the resulting orbital decay timescales must be longer than the lifetimes of the systems in question. While such constraints are often trivially passed, the combined dependencies of dynamical friction timescales on the mass and orbital radius of the orbital tracer and on the density and velocity dispersion of the assumed dark matter particles leads to the existence of a number of astronomical systems where such a consistency test is failed. Here, we review cases from stars in ultrafaint dwarf galaxies, galactic bars, satellite galaxies, and, particularly, the multi-period mutual orbits of the Magellanic Clouds, as recently inferred from the star formation histories of these two galaxies, as well as the nearby M81 group of galaxies, where introducing enough dark matter to explain observed kinematics leads to dynamical friction orbital decay timescales shorter than the lifetimes of the systems in question. Taken together, these observations exclude dark matter halos made of particles as plausible explanations for the observed kinematics of these systems.

astro-ph.GA↗
arXiv2025

Thermodynamics of harmony: extending the analogy across musical systems

It is common for most people to think of science and art as disparate, or at most only vaguely related fields. In physics, one of the biggest successes of thermodynamics is its explanation of order arising from disordered phases of matter through the minimization of free energy; In 2019, Berezovsky showed that the mechanism describing emergent order from disorder in matter can be used to explain how ordered sets of pitches can arise out of disordered sound, thus bridging the gap between science and the arts in a powerful way. In this paper we analyze his method in detail, generalizing it beyond the 12 tone system of intonation of Western music by explicitly considering Gamelan instruments and clarifying some details in the hope of strengthening it and making it better known and recognized.

physics.soc-ph↗
arXiv2024

A recent confirmation of the wide binary gravitational anomaly

Concerning recent published studies exploring the presence or otherwise of a gravitational anomaly at low accelerations in wide binary stars as observed by the {\it Gaia} satellite, the paper published by Cookson on the subject last year presents an interesting case. In that study, RMS values of binned relative internal velocities in 1D for wide binaries are compared to Newtonian predictions for that quantity, with the author concluding that the data presented show no indication of any inconsistency with Newtonian expectations. However, the comparison presented is critically flawed, as the Newtonian predictions used refer to wide binaries with mean total masses of 2.0 $M_{\odot}$. This is larger than the 1.56 $M_{\odot}$ value which applies to the data used in said paper. In this short note we correct the error mentioned above and show that the data and error bars as given by Cookson are in fact inconsistent with Newtonian expectations. Contrary to the assertion in that study, the data presented there actually show a clear anomaly in the low acceleration gravitational regime, { with the overall slope of the velocity-separation scaling being inconsistent with Newtonian expectations at a 3.3$\sigma$ level.} Based on the data presented in the paper by Cookson, wide binary systems show a clear Milgromian deviation from Newtonian dynamics.

astro-ph.GA↗
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.

astro-ph.GA↗
arXiv2023

Internal kinematics of GAIA DR3 wide binaries: anomalous behaviour in the low acceleration regime

The {\it Gaia} eDR3 catalogue has recently been used to study statistically the internal kinematics of wide binary populations using relative velocities of the two component stars, $ΔV$, total binary masses, $m_{B}$, and separations, $s$. For $s \gtrsim 0.01$ pc, these binaries probe the low acceleration $a \lesssim 2a_{0}$ regime where gravitational anomalies usually attributed to dark matter are observed in the flat rotation curves of spiral galaxies, where $a_{0}\approx 1.2\times 10^{-10}$m s$^{-2}$ is the acceleration scale of MOND. Such experiments test the degree of generality of these anomalies, by exploring the same acceleration regime using independent astronomical systems of vastly smaller mass and size. A signal above Newtonian expectations has been observed when $a \lesssim 2a_{0}$, alternatively interpreted as evidence of a modification of gravity, or as due to kinematic contaminants; undetected stellar components, unbound encounters or spurious projection effects. Here I take advantage of the enhanced DR3 {\it Gaia} catalogue to perform a more rigorous study of the internal kinematics of wide binaries than what has previously been possible. Internally determined {\it Gaia} stellar masses and estimates of binary probabilities for each star using spectroscopic information, together with a larger sample of radial velocities, allow for a significant improvement in the analysis and careful exclusion of possible kinematic contaminants. Resulting $ΔV$ scalings accurately tracing Newtonian expectations for the high acceleration regime, but markedly inconsistent with these expectations in the low acceleration one, are obtained. A non-Newtonian low acceleration phenomenology is thus confirmed.

astro-ph.GA↗
arXiv2023

Formal stability analysis for the recent $γ=5/3$ power-law spherical accretion solution

Recently, an exact spherically symmetric analytic accretion solution was presented having simple $ρ\propto R^{-3/2}$ and $V \propto R^{-1/2}$ scalings in Hernandez et al. (2023). In dimensionless variables that solution forms a one-parameter family of solutions ranging from an empty free-fall solution to a hydrostatic equilibrium configuration. This power-law solution is characterised by a constant Mach number for the flow, which can vary from zero to infinity as a function of the one parameter of the solution, and has an accretion density profile which naturally goes to zero at large radii. This accretion density profile was shown in Hernandez et al. (2023) to be an accurate representation of the accretion density profiles of a sample of AGN galaxies, over hundreds of Bondi radii. The observed density profiles fall by many orders of magnitude in density beyond their Bondi radii, something which is inconsistent with classical Bondi models where the accretion density profiles rapidly converge to a constant outside of the Bondi radius. While the good agreement with observations is suggestive of a global stability for the solution mentioned, no formal stability analysis for it has previously been presented. Here we perform such stability analysis and show the solution mentioned to be globally stable for all values of the parameters governing it, both for its accretion and outflow modes. This result makes the $γ=5/3$ power-law spherical accretion model an interesting analytical addition to the study and description of accretion problems in astrophysics.

astro-ph.GA↗
arXiv2023

A new hydrodynamic spherical accretion exact solution and its quasi-spherical perturbations

We present an exact $γ=5/3$ spherical accretion solution which modifies the Bondi boundary condition of $ρ\to const.$ as $r\to \infty$ to $ρ\to 0$ as $r \to \infty$. This change allows for simple power law solutions on the density and infall velocity fields, ranging from a cold empty free-fall condition where pressure tends to zero, to a hot hydrostatic equilibrium limit with no infall velocity. As in the case of the Bondi solution, a maximum accretion rate appears. As in the $γ=5/3$ case of the Bondi solution, no sonic radius appears, this time however, because the flow is always characterised by a constant Mach number. This number equals 1 for the case of the maximum accretion rate, diverges towards the cold empty state, and becomes subsonic towards the hydrostatic equilibrium limit. It can be shown that in the limit as { $r \to 0$}, the Bondi solution tends to the new solution presented, { extending the validity of the Bondi accretion value to} cases where the accretion density profile does not remain at a fixed constant value out to infinity. We then explore small deviations from sphericity and the presence of angular momentum through an analytic perturbative analysis. Such perturbed solutions yield a rich phenomenology through density and velocity fields in terms of Legendre polynomials, which we begin to explore for simple angular velocity boundary conditions having zeros on the plane and pole. The new solution presented provides complementary physical insight into accretion problems in general.

astro-ph.HE↗
arXiv2021

Internal kinematics of GAIA eDR3 wide binaries

Using the recent GAIA eDR3 catalogue we construct a sample of solar neighbourhood isolated wide binaries satisfying a series of strict signal-to-noise data cuts, exclusion of random association criteria and detailed colour-magnitude diagram selections, to minimise the presence of any kinematic contaminating effects having been discussed in the literature to date. Our final high-purity sample consists of 423 binary pairs within 130 pc of the sun and in all cases high-quality GAIA single-stellar fits for both components of each binary (final average RUWE values of 0.99), both also restricted to the cleanest region of the main sequence. We find kinematics fully consistent with Newtonian expectations for separations, $s$, below 0.009 pc, with relative velocities scaling with $ΔV \propto s^{-1/2}$ and a total binary mass, $M_{b}$, velocity scaling consistent with $ΔV \propto M_{b}^{1/2}$. For the separation region of $s> 0.009$ pc we obtain significantly different results, with a separation independent $ΔV \approx 0.5$ km/s and a $ΔV \propto M_{b}^{0.24 \pm 0.21}$. This situation is reminiscent of the low acceleration galactic baryonic Tully-Fisher phenomenology, and indeed, the change from the two regimes we find closely corresponds to the $a \lesssim a_{0}$ transition. These results are at odds not only with Newtonian expectations, but also with MOND predictions, where the presence of an external field effect implies only small deviations from Newtonian dynamics are expected for Solar Neighbourhood wide binaries.

astro-ph.GA↗
arXiv2020

Choked accretion onto a Schwarzschild black hole: A hydrodynamical jet-launching mechanism

We present a novel, relativistic accretion model for accretion onto a Schwarzschild black hole. This consists of a purely hydrodynamical mechanism in which, by breaking spherical symmetry, a radially accreting flow transitions into an inflow-outflow configuration. The spherical symmetry is broken by considering that the accreted material is more concentrated on an equatorial belt, leaving the polar regions relatively under-dense. What we have found is a flux-limited accretion regime in which, for a sufficiently large accretion rate, the incoming material chokes at a gravitational bottleneck and the excess flux is redirected by the density gradient as a bipolar outflow. The threshold value at which the accreting material chokes is of the order of the mass accretion rate found in the spherically symmetric case studied by Bondi and Michel. We describe the choked accretion mechanism first in terms of a general relativistic, analytic toy model based on the assumption of an ultrarelativistic stiff fluid. We then relax this approximation and, by means of numerical simulations, show that this mechanism can operate also for general polytropic fluids. Interestingly, the qualitative inflow-outflow morphology obtained appears as a generic result of the proposed symmetry break, across analytic and numeric results covering both the Newtonian and relativistic regimes. The qualitative change in the resulting steady state flow configuration appears even for a very small equatorial to polar density contrast ($\sim 0.1\,\%$) in the accretion profile. Finally, we discuss the applicability of this model as a jet-launching mechanism in different astrophysical settings.

astro-ph.HE↗
arXiv2019

Asymptotic kinematics of Globular Clusters: the emergence of a Tully-Fisher relation

Using a recent homogeneous sample of 40 high quality velocity dispersion profiles for Galactic globular clusters, we study the low gravitational acceleration regime relevant to the outskirts of these systems. We find that a simple empirical profile having a central Gaussian component and a constant large radius asymptote, $σ_{\infty}$, accurately describes the variety of observed velocity dispersion profiles. We use published population synthesis models, carefully tailored to each individual cluster, to estimate mass to light ratios from which total stellar masses, $M$, are inferred. We obtain a clear scaling, reminiscent of the galactic Tully-Fisher relation of $σ_{\infty}( km s^{-1})= 0.084^{+0.075}_{-0.040} (M/M_{\odot})^{0.3 \pm 0.051} $, which is interesting to compare to the deep MOND limit of $σ_{\infty} (km s^{-1})=0.2(M/M_{\odot})^{0.25}$. Under a Newtonian interpretation, our results constitute a further restriction on models where initial conditions are crafted to yield the outer flattening observed today. Within a modified gravity scheme, as the globular clusters studied are not isolated objects in the deep MOND regime, the results obtained point towards a modified gravity where the external field effect of MOND does not appear, or is much suppressed.

astro-ph.GA↗
arXiv2019

Choked accretion: from radial infall to bipolar outflows by breaking spherical symmetry

Steady state, spherically symmetric accretion flows are well understood in terms of the Bondi solution. Spherical symmetry however, is necessarily an idealized approximation to reality. Here we explore the consequences of deviations away from spherical symmetry, first through a simple analytic model to motivate the physical processes involved, and then through hydrodynamical, numerical simulations of an ideal fluid accreting onto a Newtonian gravitating object. Specifically, we consider axisymmetric, large-scale, small amplitude deviations in the density field such that the equatorial plane is over dense as compared to the polar regions. We find that the resulting polar density gradient dramatically alters the Bondi result and gives rise to steady state solutions presenting bipolar outflows. As the density contrast increases, more and more material is ejected from the system, attaining speeds larger than the local escape velocities for even modest density contrasts. Interestingly, interior to the outflow region, the flow tends locally towards the Bondi solution, with a resulting total mass accretion rate through the inner boundary $choking$ at a value very close to the corresponding Bondi one. Thus, the numerical experiments performed suggest the appearance of a maximum achievable accretion rate, with any extra material being ejected, even for very small departures from spherical symmetry.

astro-ph.HE↗
arXiv2019

Relativistic interpretation and cosmological signature of Milgrom's acceleration

We propose in this letter a relativistic coordinate independent interpretation for Milgrom's acceleration $a_{0}=1.2 \times 10^{-8} \hbox{cm/s}^{2}$ through a geometric constraint obtained from the product of the Kretschmann invariant scalar times the surface area of 2--spheres defined through suitable characteristic length scales for local and cosmic regimes, described by Schwarzschild and Friedman--Lema\^ıtre--Robertson--Walker (FLRW) geometries, respectively. By demanding consistency between these regimes we obtain an appealing expression for the empirical (so far unexplained) relation between the accelerations $a_0$ and $c H_0$. Imposing this covariant geometric criterion upon a FLRW model, yields a dynamical equation for the Hubble scalar whose solution matches, to a very high accuracy, the cosmic expansion rate of the $Λ$CDM concordance model fit for cosmic times close to the present epoch. We believe that this geometric interpretation of $a_0$ could provide relevant information for a deeper understanding of gravity

gr-qc↗
arXiv2019

Challenging a Newtonian prediction through Gaia wide binaries

Under Newtonian dynamics, the relative motion of the components of a binary star should follow a Keplerian scaling with separation. Once orientation effects and a distribution of ellipticities are accounted for, dynamical evolution can be modelled to include the effects of Galactic tides and stellar mass perturbers, over the lifetime of the solar neighbourhood. This furnishes a prediction for the relative velocity between the components of a binary and their projected separation. Taking a carefully selected small sample of 81 solar neighbourhood wide binaries from the {\it Hipparcos} catalogue, we identify these same stars in the recent Gaia DR2, to test the prediction mentioned using the latest and most accurate astrometry available. The results are consistent with the Newtonian prediction for projected separations below 7000 AU, but inconsistent with it at larger separations, where accelerations are expected to be lower than the critical $a_{0}=1.2 \times 10^{-10} $ { m s$^{-2}$} value of MONDian gravity. This result challenges Newtonian gravity at low accelerations and shows clearly the appearance of gravitational anomalies of the type usually attributed to dark matter at galactic scales, now at much smaller stellar scales.

astro-ph.GA↗