Radial Acceleration Relation Research Articles

The Extremely High Dark Matter Halo Concentration of the Relic Compact Elliptical Galaxy Mrk 1216

Abstract Spatially compact stellar profiles and old stellar populations have established compact elliptical galaxies (CEGs) as local analogs of the high-redshift “red nuggets” thought to represent the progenitors of today’s early-type galaxies (ETGs). To address whether the structure of the dark matter (DM) halo in a CEG also reflects the extremely quiescent and isolated evolution of its stars, we use a new ≈122 ks Chandra observation together with a shallow ≈13 ks archival observation of the CEG Mrk 1216 to perform a hydrostatic equilibrium analysis of the luminous and relaxed X-ray plasma emission extending out to a radius 0.85r 2500. We examine several DM model profiles and in every case obtain a halo concentration (c 200) that is a large positive outlier in the theoretical ΛCDMc 200–M 200 relation; i.e., ranging from 3.4σ to 6.3σ above the median ΛCDM relation in terms of the intrinsic scatter. The high value of c 200 we measure implies an unusually early formation time that firmly establishes the relic nature of the DM halo in Mrk 1216. The highly concentrated DM halo leads to a higher DM fraction and smaller total mass slope at 1 R e compared to nearby normal ETGs. In addition, the highly concentrated total mass profile of Mrk 1216 cannot be described by modified Newtonian dynamics without adding DM, and it deviates substantially from the radial acceleration relation. Our analysis of the hot plasma indicates that the halo of Mrk 1216 contains ≈80% of the cosmic baryon fraction within r 200. The radial profile of the ratio of cooling time to freefall time varies within a narrow range (t c/t ff ≈ 14–19) over a large central region (r ≤ 10 kpc), suggesting “precipitation-regulated active galactic nucleus feedback” for a multiphase plasma, although there is little evidence at present for cool gas in Mrk 1216. Finally, other than its compact stellar size, the stellar, gas, and DM properties of Mrk 1216 are remarkably similar to those of the nearby fossil group NGC 6482.

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

Abstract 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 supercritical acceleration range (10−9.5, 10−8) m s−2 by using a sample of nearly round pure-bulge (spheroidal, dispersion-dominated) galaxies. This sample includes 24 ATLAS3D galaxies and 4201 SDSS galaxies, and covers 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 ⋆/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 X/a B from the PDFs. Unless we ignore observed radial gradients in M ⋆/L, or assume unreasonably strong gradients, marginalization over nuisance factors suggests with p = −1.00 ± 0.03 (stat) (sys) and q = −1.02 ± 0.09 (stat) (sys) around a supercritical acceleration a +1 ≡ 1.2 × 10−9 m s−2. In the context of the ΛCDM 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 by subcritical acceleration data.

Modified Gravity (MOG) fits to observed radial acceleration of SPARC galaxies

The equation of motion in the generally covariant modified gravity (MOG) theory leads, for weak gravitational fields and non-relativistic motion, to a modification of Newton's gravitational acceleration law. In addition to the metric $g_{\mu\nu}$, MOG has a vector field $\phi_\mu$ that couples with gravitational strength to all baryonic matter. The gravitational coupling strength is determined by the MOG parameter $\alpha$, while parameter $\mu$ is the small effective mass of $\phi_\mu$. The MOG acceleration law has been demonstrated to fit a wide range of galaxies, galaxy clusters and the Bullet Cluster and Train Wreck Cluster mergers. For the SPARC sample of rotationally supported spiral and irregular galaxies, McGaugh et al. [24] (MLS) have found a radial acceleration relation (RAR) that relates accelerations derived from galaxy rotation curves to Newtonian accelerations derived from galaxy mass models. Using the same SPARC galaxy data, mass models independently derived from that data, and MOG parameters $\alpha$ and $\mu$ that run with galaxy mass, we demonstrate that adjusting galaxy parameters within $\pm 1$-sigma bounds can yield MOG predictions consistent with the given rotational velocity data. Moreover, the same adjusted parameters yield a good fit to the RAR of MLS, with the RAR parameter $a_0=(5.4\pm .3)\times 10^{-11}\,{\rm m/s^2}$.

The radial acceleration relation and dark baryons in MOND

Recent observations of rotationally supported galaxies show a tight correlation between the observed radial acceleration at every radius and the Newtonian acceleration generated by the baryonic mass distribution, the so-called radial acceleration relation (RAR). The rotation curves (RCs) of the SPARC sample of disk galaxies with different morphologies, masses, sizes and gas fractions are investigated in the context of modified Newtonian dynamics (MOND). We include the effect of cold dark baryons by scaling the measured mass in the atomic form by a factor of $c$ in the mass budget of galaxies. In addition to the standard interpolating function, we also fit the RCs and the RAR with the empirical RAR-inspired interpolating function. Slightly better fits for about $47\%$ of galaxies in our sample are achieved in the presence of dark baryons ($c>1$) with the mean value of $c = 2.4\pm 1.3$. Although the MOND fits are not significantly improved by including dark baryons, it results in a decrease in the characteristic acceleration $g_\dag$ by $40\%$. We find no correlation between the MOND critical acceleration $a_0$ and the central surface brightness of the stellar disk, $\mu_{3.6}$. This supports $a_0$ being a universal constant for all galaxies.

Radial Acceleration and Tully-Fisher Relations in Conformal Gravity

In 2016 McGaugh, Lelli and Schombert established a universal Radial Acceleration Relation for centripetal accelerations in spiral galaxies. Their work showed a strong correlation between observed centripetal accelerations and those predicted by luminous Newtonian matter alone. Through the use of the fitting function that they introduced, mass discrepancies in spiral galaxies can be constrained in a uniform manner that is completely determined by the baryons in the galaxies. Here we present a new empirical plot of the observed centripetal accelerations and the luminous Newtonian expectations, which more than doubles the number of observed data points considered by McGaugh et al. while retaining the Radial Acceleration Relation. If this relation is not to be due to dark matter, it would then have to be due to an alternate gravitational theory that departs from Newtonian gravity in some way. In this paper we show how the candidate alternate conformal gravity theory can provide a natural description of the Radial Acceleration Relation, without any need for dark matter or its free halo parameters. We discuss how the empirical Tully-Fisher relation follows as a consequence of conformal gravity.

Study of gravitational fields and globular cluster systems of early-type galaxies

Context.Gravitational fields at the outskirts of early-type galaxies (ETGs) are difficult to constrain observationally. It thus remains poorly explored how well the ΛCDM and MOND hypotheses agree with ETGs.Aims.The dearth of studies on this topic motivated us to gather a large sample of ETGs and examine homogeneously which dark matter halos they occupy, whether the halos follow the theoretically predicted stellar-to-halo mass relation (SHMR) and the halo mass-concentration relation (HMCR), whether ETGs obey MOND and the radial acceleration relation (RAR) observed for late-type galaxies (LTGs), and finally whether ΛCDM or MOND perform better in ETGs.Methods.We employed Jeans analysis of radial velocities of globular clusters (GCs). We analysed nearly all ETGs having more than about 100 archival GC radial velocity measurements available. The GC systems of our 17 ETGs extend mostly over ten effective radii. A ΛCDM simulation of GC formation helped us to interpret the results.Results.Successful ΛCDM fits are found for all galaxies, but compared to the theoretical HMCR and SHMR, the best-fit halos usually have concentrations that are too low and stellar masses that are too high for their masses. This might be because of tidal stripping of the halos or because ETGs and LTGs occupy different halos. Most galaxies can be fitted by the MOND models successfully as well, but for some of the galaxies, especially those in centers of galaxy clusters, the observed GC velocity dispersions are too high. This might be a manifestation of the additional dark matter that MOND requires in galaxy clusters. Additionally, we find many signs that the GC systems were perturbed by galaxy interactions. Formal statistical criteria prefer the best-fit ΛCDM models over the MOND models, but this might be due to the higher flexibility of the ΛCDM models. The MOND approach can predict the GC velocity dispersion profiles better.

The Radial Acceleration Relation (RAR): Crucial Cases of Dwarf Disks and Low-surface-brightness Galaxies

Abstract McGaugh et al. have found, in a large sample of disk systems, a tight nonlinear relationship between the total radial accelerations g and their components g b that have arisen from the distribution of the baryonic matter. Here, we investigate the existence of such a relation in Dwarf Disk Spirals and Low Surface Brightness (LSB) galaxies on the basis of Karukes & Salucci and Di Paolo & Salucci. We have accurate mass profiles for 36 Dwarf Disk Spirals and 72 LSB galaxies. These galaxies have accelerations that cover the McGaugh range but also reach out to one order of magnitude below the smallest accelerations present in McGaugh et al. and span different Hubble Types. We found, in our samples, that the g versus g b relation has a very different profile and also other intrinsic novel properties, among those, the dependence on a second variable: the galactic radius, normalized to the optical radius R opt, at which the two accelerations are measured. We show that the new far from trivial g versus relationship is a direct consequence of the complex coordinated mass distributions of the baryons and the dark matter (DM) in disk systems. Our analysis shows that the McGaugh et al. relation is a limiting case of a new universal relation that can be very well framed in the standard “DM halo in the Newtonian Gravity” paradigm.

The radial acceleration relation and its emergent nature

AbstractWe review some of our recent results about the Radial Acceleration Relation (RAR) and its interpretation as either a fundamental or an emergent law. The former interpretation is in agreement with a class of modified gravity theories that dismiss the need for dark matter in galaxies (MOND in particular). Our most recent analysis, which includes refinements on the priors and the Bayesian test for compatibility between the posteriors, confirms that the hypothesis of a fundamental RAR is rejected at more than 5σ from the very same data that was used to infer the RAR.

Dark matter–baryon scaling relations from Einasto halo fits to SPARC galaxy rotation curves

Dark matter–baryon scaling relations in galaxies are important in order to constrain galaxy formation models. Here, we provide a modern quantitative assessment of these relations by modelling the rotation curves of galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database with the Einasto dark halo model. We focus in particular on the comparison between the original SPARC parameters, with constant mass-to-light ratios for bulges and discs, and the parameters for which galaxies follow the tightest radial acceleration relation. We show that fits are improved in the second case, and that the pure halo scaling relations also become tighter. We report that the density at the radius where the slope is −2 is strongly anti-correlated to this radius and to the Einasto index. The latter is close to unity for a large number of galaxies, indicative of large cores. In terms of dark matter–baryon scalings, we focus on relations between the core properties and the extent of the baryonic component, which are relevant to the cusp-core transformation process. We report a positive correlation between the core size of halos with small Einasto index and the stellar disc scale-length, and between the averaged dark matter density within 2 kpc and the baryon-induced rotational velocity at that radius. This finding is related to the consequence of the radial acceleration relation on the diversity of rotation curve shapes, quantified by the rotational velocity at 2 kpc. While a tight radial acceleration relation slightly decreases the observed diversity compared to the original SPARC parameters, the diversity of baryon-induced accelerations at 2 kpc is sufficient to induce a large diversity, incompatible with current hydrodynamical simulations of galaxy formation, while maintaining a tight radial acceleration relation.

NIHAO – XVIII. Origin of the MOND phenomenology of galactic rotation curves in a ΛCDM universe

The phenomenological basis for Modified Newtonian Dynamics (MOND) is the radial-acceleration-relation (RAR) between the observed acceleration, $a=V^2_{rot}(r)/r$, and the acceleration accounted for by the observed baryons (stars and cold gas), $a_{bar}=V_{bar}^2(r)/r$. We show that the RAR arises naturally in the NIHAO sample of 89 high-resolution LCDM cosmological galaxy formation simulations. The overall scatter from NIHAO is just 0.079 dex, consistent with observational constraints. However, we show that the scatter depends on stellar mass. At high masses ($10^9 <M_{star} <10^{11}$ Msun) the simulated scatter is just $\simeq 0.04$ dex, increasing to $\simeq 0.11$ dex at low masses ($10^7 < M_{star} <10^{9}$Msun). Observations show a similar dependence for the intrinsic scatter. At high masses the intrinsic scatter is consistent with the zero scatter assumed by MOND, but at low masses the intrinsic scatter is non-zero, strongly disfavoring MOND. Applying MOND to our simulations yields remarkably good fits to most of the circular velocity profiles. In cases of mild disagreement the stellar mass-to-light ratio and/or "distance" can be tuned to yield acceptable fits, as is often done in observational mass models. In dwarf galaxies with $M_{star}\sim10^6$Msun MOND breaks down, predicting lower accelerations than observed and in our LCDM simulations. The assumptions that MOND is based on (e.g., asymptotically flat rotation curves, zero intrinsic scatter in the RAR), are approximately, but not exactly, true in LCDM. Thus if one wishes to go beyond Newtonian dynamics there is more freedom in the RAR than assumed by MOND.

Conformal gravity and the radial acceleration relation

During the 2016 International Workshop on Astronomy and Relativistic Astrophysics (IWARA), the question was raised as to whether conformal gravity (CG) could explain the timely result which showed a universal nature found in the centripetal accelerations of spiral galaxies. At the time of the conference, the McGaugh result was only published for 2 weeks. Since then, the result has become known as the radial acceleration relation (RAR) and has been considered tantamount to a natural law. In this paper, we summarize how CG can explain the RAR in a manner consistent with the findings of the original authors without the need for dark matter.

The tight empirical relation between dark matter halo mass and flat rotation velocity for late-type galaxies

ABSTRACT We present a new empirical relation between galaxy dark matter halo mass (Mhalo) and the velocity along the flat portion of the rotation curve (Vflat), derived from 120 late-type galaxies from the SPARC data base. The orthogonal scatter in this relation is comparable to the observed scatter in the baryonic Tully–Fisher relation (BTFR), indicating a tight coupling between total halo mass and galaxy kinematics at r ≪ Rvir. The small vertical scatter in the relation makes it an extremely competitive estimator of total halo mass. We demonstrate that this conclusion holds true for different priors on M*/L[3.6$\mu$] that give a tight BTFR, but requires that the halo density profile follow DC14 rather than NFW. We provide additional relations between Mhalo and other velocity definitions at smaller galactic radii (i.e. V2.2, Veff, and Vmax) which can be useful for estimating halo masses from kinematic surveys, providing an alternative to abundance matching. Furthermore, we constrain the dark matter analogue of the radial acceleration relation and also find its scatter to be small, demonstrating the fine balance between baryons and dark matter in their contribution to galaxy kinematics.

Searching for a possible dipole anisotropy in acceleration scale with 147 rotationally supported galaxies**Supported by National Natural Science Foundation of China (11675182, 11690022, 11603005)

We report a possible dipole anisotropy in acceleration scale g† with 147 rotationally supported galaxies in the local Universe. It is found that a monopole and dipole correction for the radial acceleration relation can better describe the SPARC data set. The monopole term is negligible but the dipole magnitude is significant. It is also found that the dipole correction is mostly induced by anisotropy in the acceleration scale. The magnitude of the -dipole reaches 0.25 ± 0.04, and its direction is aligned to (l,b) = (171.30° ± 7.18°, −15.41° ± 4.87°), which is very close to the maximum anisotropy direction from the hemisphere comparison method. Furthermore, a robust check shows that the dipole anisotropy could not be reproduced by an isotropic mock data set. However, it is still premature to claim that the Universe is anisotropic, due to the small data samples and uncertainty in the current observations.

Fitting the radial acceleration relation to individual SPARC galaxies

Galaxies follow a tight radial acceleration relation (RAR): the acceleration observed at every radius correlates with that expected from the distribution of baryons. We use the Markov chain Monte Carlo method to fit the mean RAR to 175 individual galaxies in the SPARC database, marginalizing over stellar mass-to-light ratio (ϒ⋆), galaxy distance, and disk inclination. Acceptable fits with astrophysically reasonable parameters are found for the vast majority of galaxies. The residuals around these fits have an rms scatter of only 0.057 dex (~13%). This is in agreement with the predictions of modified Newtonian dynamics (MOND). We further consider a generalized version of the RAR that, unlike MOND, permits galaxy-to-galaxy variation in the critical acceleration scale. The fits are not improved with this additional freedom: there is no credible indication of variation in the critical acceleration scale. The data are consistent with the action of a single effective force law. The apparent universality of the acceleration scale and the small residual scatter are key to understanding galaxies.

Radial Acceleration Relation of ΛCDM Satellite Galaxies.

The radial acceleration measured in bright galaxies tightly correlates with that generated by the observed distribution of baryons, a phenomenon known as the radial acceleration relation (RAR). Dwarf spheroidal satellite galaxies have been recently found to depart from the extrapolation of the RAR measured for more massive objects but with a substantially larger scatter. If confirmed by new data, this result provides apowerful test of the theory of gravity at low accelerations that requires robust theoretical predictions. Byusing high-resolution hydrodynamical simulations, we show that, within the standard model of cosmology (ΛCDM), satellite galaxies are expected to follow the same RAR as brighter systems but with a much larger scatter which does not correlate with the physical properties of the galaxies. In the simulations, the RAR evolves mildly with redshift. Moreover, the acceleration due to the gravitational field of the host has no effect on the RAR. This is in contrast with the external field effect in modified Newtonian dynamics (MOND) which causes galaxies in strong external fields to deviate from the RAR. This difference between ΛCDM and MOND offers a possible way to discriminate between them.

Absence of a fundamental acceleration scale in galaxies

The Radial Acceleration Relation confirms that a nontrivial acceleration scale can be found in the average internal dynamics of galaxies. The existence of such a scale is not obvious as far as the standard cosmological model is concerned, and it has been interpreted as a possible sign of modified gravity. The implications could be profound: it could in principle explain galactic dynamics without large amounts of yet-undetected dark matter and address issues that the standard cosmological model faces at galactic scales. Here, we consider 193 disk galaxies from the SPARC and THINGS databases and, using Bayesian inference, we show that the probability of existence of a fundamental acceleration that is common to all the galaxies is essentially zero: the $p$-value is smaller than $10^{-20}$ or, equivalently, the null hypothesis is rejected at more than 10$\sigma$. We conclude that the acceleration scale unveiled by the Radial Acceleration Relation is of emergent nature, possibly caused by a complex interplay between baryons and dark matter. In particular, the MOND theory, or any other theory that behaves like it at galactic scales, is ruled out as a fundamental theory for galaxies at more than 10$\sigma$.

The radial acceleration relation and a magnetostatic analogy in quasilinear MOND

Recently a remarkable relation has been demonstrated between the observed radial acceleration in disk galaxies and the acceleration predicted on the basis of baryonic matter alone. Here we study this relation within the framework of the modified gravity model MOND. The field equations of MOND automatically imply the radial acceleration relation (RAR) for spherically symmetric galaxies, but for disk galaxies deviations from the relation are expected. Here we investigate whether these deviations are of sufficient magnitude to bring MOND into conflict with the observed relation. In the quasilinear formulation of MOND, to calculate the gravitational field of a given distribution of matter, an intermediate step is to calculate the ‘pristine field’, which is a simple nonlinear function of the Newtonian field corresponding to the same distribution of matter. Hence, to the extent that the quasilinear gravitational field is approximately equal to the pristine field, the RAR will be satisfied. We show that the difference between the quasilinear and pristine fields obeys the equations of magnetostatics; the curl of the pristine field serves as the source for the difference in the two fields, much as currents serve as sources for the magnetic field. Using the magnetostatic analogy we numerically study the difference between the pristine and quasilinear fields for simple model galaxies with a Gaussian profile. Our principal finding is that the difference between the fields is small compared to the observational uncertainties and that quasilinear MOND is therefore compatible with the observed RAR.

SDSS-IV MaNGA: a distinct mass distribution explored in slow-rotating early-type galaxies

Abstract We study the radial acceleration relation (RAR) for early-type galaxies (ETGs) in the SDSS MaNGA MPL5 data set. The complete ETG sample show a slightly offset RAR from the relation reported by McGaugh et al. (2016) at the low-acceleration end; we find that the deviation is due to the fact that the slow rotators show a systematically higher acceleration relation than the McGaugh's RAR, while the fast rotators show a consistent acceleration relation to McGaugh's RAR. There is a 1σ significant difference between the acceleration relations of the fast and slow rotators, suggesting that the acceleration relation correlates with the galactic spins, and that the slow rotators may have a different mass distribution compared with fast rotators and late-type galaxies. We suspect that the acceleration relation deviation of slow rotators may be attributed to more galaxy merger events, which would disrupt the original spins and correlated distributions of baryons and dark matter orbits in galaxies.

Theoretical implications of the galactic radial acceleration relation of McGaugh, Lelli, and Schombert

Abstract Velocities in stable circular orbits about galaxies, a measure of centripetal gravitation, exceed the expected Kepler/Newton velocity as orbital radius increases. Standard Λ cold dark matter (ΛCDM) attributes this anomaly to galactic dark matter. McGaugh et al. have recently shown for 153 disc galaxies that observed radial acceleration is an apparently universal function of classical acceleration computed for observed galactic baryonic mass density. This is consistent with the empirical modified Newtonian dynamics (MOND) model, not requiring dark matter. It is shown here that suitably constrained ΛCDM and conformal gravity (CG) also produce such a universal correlation function. ΛCDM requires a very specific dark matter distribution, while the implied CG non-classical acceleration must be independent of galactic mass. All three constrained radial acceleration functions agree with the empirical baryonic v4 Tully–Fisher relation. Accurate rotation data in the nominally flat velocity range could distinguish between MOND, ΛCDM, and CG.

The radial acceleration relation in disc galaxies in the MassiveBlack-II simulation

A strong correlation has been measured between the observed centripetal accelerations in galaxies and the accelerations implied by the baryonic components of galaxies. This empirical radial acceleration relation must be accounted for in any viable model of galaxy formation. We measure and compare the radial accelerations contributed by baryons and by dark matter in disk galaxies in the MassiveBlack-II hydrodynamic galaxy formation simulation. The sample of 1594 galaxies spans three orders of magnitude in luminosity and four in surface brightness, comparable to the observed sample from the Spitzer Photometry & Accurate Rotation Curves (SPARC) dataset used by McGaugh et al. (2016). We find that radial accelerations contributed by baryonic matter only and by total matter are highly correlated, with only small scatter around their mean or median relation, despite the wide ranges of galaxy luminosity and surface brightness. We further find that the radial acceleration relation in this simulation differs from that of the SPARC sample, and can be described by a simple power law in the acceleration range we are probing.