Dark Matter Halo Profile Research Articles

Searching for Sub-GeV dark matter in the galactic centre using Hyper-Kamiokande

Indirect detection of dark matter via its annihilation products is a key technique in the search for dark matter in the form of weakly interacting massive particles (WIMPs). Strong constraints exist on the annihilation of WIMPs to highly visible Standard Model final states such as photons or charged particles. In the case of s-wave annihilation, this typically eliminates thermal relic cross sections for dark matter of mass below \U0001d4aa(10) GeV . However, such limits typically neglect the possibility that dark matter may annihilate to assumed invisible or hard-to-detect final states, such as neutrinos. This is a difficult paradigm to probe due to the weak neutrino interaction cross section. Considering dark matter annihilation in the Galactic halo, we study the prospects for indirect detection using the Hyper-Kamiokande (HyperK) neutrino experiment, for dark matter of mass below 1 GeV . We undertake a dedicated simulation of the HyperK detector, which we benchmark against results from the similar Super-Kamiokande experiment and HyperK physics projections. We provide projections for the annihilation cross-sections that can be probed by HyperK for annihilation to muon or neutrino final states, and discuss uncertainties associated with the dark matter halo profile. For neutrino final states, we find that HyperK is sensitive to thermal annihilation cross-sections for dark matter with mass around 20 MeV, assuming an NFW halo profile. We also discuss the effects of neutron tagging, and prospects for improving the reach at low mass.

Strong constraints on thermal relic dark matter from Fermi-LAT observations of the Galactic Center

The extended excess toward the Galactic Center (GC) in gamma rays inferred from Fermi-LAT observations has been interpreted as being due to dark matter (DM) annihilation. Here, we perform new likelihood analyses of the GC and show that, when including templates for the stellar galactic and nuclear bulges, the GC shows no significant detection of a DM annihilation template, even after generous variations in the Galactic diffuse emission models and a wide range of DM halo profiles. We include Galactic diffuse emission models with combinations of three-dimensional inverse Compton maps, variations of interstellar gas maps, and a central source of electrons. For the DM profile, we include both spherical and ellipsoidal DM morphologies and a range of radial profiles from steep cusps to kiloparsec-sized cores, motivated in part by hydrodynamical simulations. Our derived upper limits on the dark matter annihilation flux place strong constraints on DM properties. In the case of the pure $b$-quark annihilation channel, our limits on the annihilation cross section are more stringent than those from the Milky Way dwarfs up to DM masses of approximately TeV and rule out the thermal relic cross section up to approximately 300 GeV. Better understanding of the DM profile, as well as the Fermi-LAT data at its highest energies, would further improve the sensitivity to DM properties.

The M-sigma relation of supermassive black holes from the scalar field dark matter

We show a relation between the mass of supermassive black holes in galaxies and the velocity dispersions of their bulges in the scalar field or the Bose–Einstein condensate dark matter model. The gravity of the central black holes changes boundary conditions of the scalar field at the galactic centers. Owing to the wave nature of the dark matter, this significantly changes the galactic dark matter halo profiles even though the black holes are much lighter than the bulges. As a result the heavier the black holes are, the more compact the bulges are, and hence the larger the velocity dispersions are. This tendency is verified by a numerical study showing the M-sigma relation reproduced with the dark matter particle mass [Formula: see text] eV.

The milky way total mass profile as inferred from Gaia DR2

ABSTRACT We determine the Milky Way (MW) mass profile inferred from fitting physically motivated models to the Gaia DR2 Galactic rotation curve and other data. Using various hydrodynamical simulations of MW-mass haloes, we show that the presence of baryons induces a contraction of the dark matter (DM) distribution in the inner regions, r ≲ 20 kpc. We provide an analytic expression that relates the baryonic distribution to the change in the DM halo profile. For our galaxy, the contraction increases the enclosed DM halo mass by factors of roughly 1.3, 2, and 4 at radial distances of 20, 8, and 1 kpc, respectively compared to an uncontracted halo. Ignoring this contraction results in systematic biases in the inferred halo mass and concentration. We provide a best-fitting contracted NFW halo model to the MW rotation curve that matches the data very well.1 The best-fit has a DM halo mass, $M_{200}^{\rm DM}=0.97_{-0.19}^{+0.24}\times 10^{12}\,\mathrm{M}_\odot$, and concentration before baryon contraction of $9.4_{-2.6}^{+1.9}$, which lie close to the median halo mass–concentration relation predicted in ΛCDM. The inferred total mass, $M_{200}^{\rm total}=1.08_{-0.14}^{+0.20} \times 10^{12}\,\mathrm{M}_\odot$, is in good agreement with recent measurements. The model gives an MW stellar mass of $5.04_{-0.52}^{+0.43}\times 10^{10}\,\mathrm{M}_\odot$ and infers that the DM density at the Solar position is $\rho _{\odot }^{\rm DM}=8.8_{-0.5}^{+0.5}\times 10^{-3}\,\mathrm{M}_\odot \,\mathrm{pc}^{-3}\equiv 0.33_{-0.02}^{+0.02}\,\rm {GeV}\,\rm {cm}^{-3}$. The rotation curve data can also be fitted with an uncontracted NFW halo model, but with very different DM and stellar parameters. The observations prefer the physically motivated contracted NFW halo, but the measurement uncertainties are too large to rule out the uncontracted NFW halo.

Gravitational potential from small-scale clustering in action space: application to Gaia Data Release 2

ABSTRACT Most measurements of mass in astronomy that use kinematics of stars or gas rely on assumptions of equilibrium that are often hard to verify. Instead, we develop a novel idea that uses the clustering in action space, as a probe of the underlying gravitational potential: the correct potential should maximize small-scale clustering in the action space. We provide a first-principle derivation of likelihood using the two-point correlation function in action space, and we test it against simulations of stellar streams. We then apply this method to the second data release of Gaia, and we use it to measure the radial force fraction fh and logarithmic slope α of the dark matter halo profile. We investigate stars within 9–11 kpc and 11.5–15 kpc from the Galactic Centre, and we find (fh, α) = (0.391 ± 0.009, 1.835 ± 0.092) and (0.351 ± 0.012, 1.687 ± 0.079), respectively. We also confirm that the set of parameters that maximize the likelihood function does correspond to the most clustering in the action space. The best-fitting circular velocity curve for the Milky Way potential is consistent with past measurements (although it is ∼5–10 per cent lower than previous methods that use masers or globular clusters). Our work provides a clear demonstration of the full statistical power that lies in the full phase space information, relieving the need for ad hoc assumptions such as virial equilibrium, circular motion or steam-finding algorithms.

A Comprehensive Catalog of Dark Matter Halo Models for SPARC Galaxies

Abstract We present rotation curve fits to 175 late-type galaxies from the Spitzer Photometry and Accurate Rotation Curves database using seven dark matter (DM) halo profiles: pseudo-isothermal, Burkert, Navarro–Frenk–White (NFW), Einasto, Di Cintio et al. (2014, hereafter DC14), cored-NFW, and a new semi-empirical profile named Lucky13. We marginalize over the stellar mass-to-light ratio, galaxy distance, disk inclination, halo concentration, and halo mass (and an additional shape parameter for Einasto) using a Markov Chain Monte Carlo method. We find that cored halo models, such as the DC14 and Burkert profiles, generally provide better fits to rotation curves than the cuspy NFW profile. The stellar mass-halo mass relation from abundance matching is recovered by all halo profiles once imposed as a Bayesian prior, whereas the halo mass–concentration relation is not reproduced in detail by any halo model. We provide an extensive set of figures as well as best-fit parameters in machine-readable tables to facilitate model comparison and the exploration of DM halo properties.

Mass models of gas-rich void dwarf galaxies

ABSTRACT We construct mass models of eight gas rich dwarf galaxies that lie in the Lynx–Cancer void. From NFW fits to the dark matter halo profile, we find that the concentration parameters of haloes of void dwarf galaxies are similar to those of dwarf galaxies in normal density regions. We also measure the slope of the central dark matter density profiles, obtained by converting the rotation curves derived using 3D (fat) and 2D (ROTCUR) tilted ring fitting routines, into mass densities. We find that the average slope (α = −1.39 ± 0.19), obtained from 3D fitting is consistent with that expected from an NFW profile. On the other hand, the average slope measured using the 2D approach is closer to what would be expected for an isothermal profile. This suggests that systematic effects in velocity field analysis have a significant effect on the slope of the central dark matter density profiles. Given the modest number of galaxies we use for our analysis, it is important to check these results using a larger sample.

The Influence of the Void Environment on the Ratio of Dark Matter Halo Mass to Stellar Mass in SDSS MaNGA Galaxies

Abstract We study how the void environment affects the formation and evolution of galaxies in the universe by comparing the ratio of dark matter halo mass to stellar mass of galaxies in voids with galaxies in denser regions. Using spectroscopic observations from the Sloan Digital Sky Survey MaNGA DR15, we estimate the dark matter halo mass of 641 void galaxies and 937 galaxies in denser regions. We use the relative velocities of the Hα emission line across the galaxy’s surface to measure the rotation curve of each galaxy because the kinematics of the interstellar medium is smoother than the stellar kinematics. We find that neither the stellar-to-halo-mass relation nor the relationship between the gas-phase metallicity and the ratio of dark matter halo mass to stellar mass is affected by the void environment. We also observe no difference in the distribution of the ratio of dark matter halo mass to stellar mass between void galaxies and galaxies in denser regions, implying that the shape of the dark matter halo profile is independent of a galaxy’s environment.

GHASP: an H α kinematical survey of spiral galaxies – XIII. Distribution of luminous and dark matter in spiral and irregular nearby galaxies using H α and H i rotation curves and WISE photometry

Abstract We present the mass models of 31 spiral and irregular nearby galaxies obtained using hybrid rotation curves (RCs) combining high-resolution GHASP Fabry–Perot H α RCs and extended WHISP H i ones together with 3.4 $\mu$m WISE photometry. The aim is to compare the dark matter (DM) halo properties within the optical radius using only H α RCs with the effect of including and excluding the mass contribution of the neutral gas component, and when using H i or hybrid RCs. Pseudo-isothermal (ISO) core and Navarro–Frenk–White (NFW) cuspy DM halo profiles are used with various fiducial fitting procedures. Mass models using H α RCs including or excluding the H i gas component provide compatible disc M/L. The correlations between DM halo and baryon parameters do not strongly depend on the RC. Clearly, the differences between the fitting procedures are larger than between the different data sets. Hybrid and H i RCs lead to higher M/L values for both ISO and NFW best-fitting models but lower central densities for ISO haloes and higher concentration for NFW haloes than when using H α RCs only. The agreement with the mass model parameters deduced using hybrid RCs, considered as a reference, is better for H i than for H α RCs. ISO density profiles better fit the RCs than the NFW ones, especially when using H α or hybrid RCs. Halo masses at the optical radius determined using the various data sets are compatible even if they tend to be overestimated with H α RCs. Hybrid RCs are thus ideal to study the mass distribution within the optical radius.

Energy equipartition between stellar and dark matter particles in cosmological simulations results in spurious growth of galaxy sizes

ABSTRACT The impact of 2-body scattering on the innermost density profiles of dark matter haloes is well established. We use a suite of cosmological simulations and idealized numerical experiments to show that 2-body scattering is exacerbated in situations where there are two species of unequal mass. This is a consequence of mass segregation and reflects a flow of kinetic energy from the more to less massive particles. This has important implications for the interpretation of galaxy sizes in cosmological hydrodynamic simulations, which nearly always model stars with less massive particles than are used for the dark matter. We compare idealized models as well as simulations from the eagle project that differ only in the mass resolution of the dark matter component, but keep subgrid physics, baryonic mass resolution, and gravitational force softening fixed. If the dark matter particle mass exceeds the mass of stellar particles, then galaxy sizes – quantified by their projected half-mass radii, R50 – increase systematically with time until R50 exceeds a small fraction of the redshift-dependent mean interparticle separation, l (${\rm R_{50}} \gtrsim 0.05\times l$). Our conclusions should also apply to simulations that adopt different hydrodynamic solvers, subgrid physics, or adaptive softening, but in that case may need quantitative revision. Any simulation employing a stellar-to-dark matter particle mass ratio greater than unity will escalate spurious energy transfer from dark matter to baryons on small scales.

Dark matter and H i in ultra-diffuse galaxy UGC 2162

ABSTRACT Our GMRT (Giant Metrewave Radio Telescope) H i observations of the ultra-diffuse galaxy (UDG) UGC 2162, projected ∼ 300 kpc from the centre of the M 77 group, reveal it to a have an extended H i disc ($R_{\rm H\,{\small I}}/R_{25}$ ∼ 3.3) with a moderate rotational velocity (Vrot ∼ 31 km s−1). This Vrotis in line with that of dwarf galaxies with similar H i mass. We estimate an Mdyn of ∼1.14 × 109 M⊙ within the galaxy’s $R_ \rm {H\,{\small I}}$ ∼ 5.2 kpc. Additionally, our estimates of M200 for the galaxy from NFW models are in the range of 5.0–8.8 × 1010 M⊙. Comparing UGC 2162 to samples of UDGs with H i detections show it to have amongst the smallest Re with its MH i/M* being distinctly higher and g – icolour slightly bluer than typical values in those samples. We also compared H i and dark matter (DM) halo properties of UGC 2162 with dwarf galaxies in the LITTLE THINGS sample and find its DM halo mass and profile are within the range expected for a dwarf galaxy. While we were unable to determine the origin of the galaxy’s present-day optical form from our study, its normal H i rotation velocity in relation to its H i mass, H i morphology, environment, and dwarf mass DM halo ruled out some of the proposed ultra-diffuse galaxy formation scenarios for this galaxy.

WALLABY early science – III. An H i study of the spiral galaxy NGC 1566

ABSTRACTThis paper reports on the atomic hydrogen gas (H i) observations of the spiral galaxy NGC 1566 using the newly commissioned Australian Square Kilometre Array Pathfinder radio telescope. We measure an integrated H i flux density of $180.2$ Jy km s−1 emanating from this galaxy, which translates to an H i mass of $1.94\times 10^{10}\, \mathrm{ M}_{\odot }$ at an assumed distance of $21.3$ Mpc. Our observations show that NGC 1566 has an asymmetric and mildly warped H i disc. The H i-to-stellar mass fraction (M$_{\rm{H\,{{\small I}}}}$/M∗) of NGC 1566 is 0.29, which is high in comparison with galaxies that have the same stellar mass ($10^{10.8}$ M⊙). We also derive the rotation curve of this galaxy to a radius of $50$ kpc and fit different mass models to it. The NFW, Burkert, and pseudo-isothermal dark matter halo profiles fit the observed rotation curve reasonably well and recover dark matter fractions of 0.62, 0.58, and 0.66, respectively. Down to the column density sensitivity of our observations ($N_{\rm{H\,{{\small I}}}}\, =\, 3.7\times 10^{19}$ cm−2), we detect no H i clouds connected to, or in the nearby vicinity of, the H i disc of NGC 1566 nor nearby interacting systems. We conclude that, based on a simple analytic model, ram pressure interactions with the IGM can affect the H i disc of NGC 1566 and is possibly the reason for the asymmetries seen in the H i morphology of NGC 1566.

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.

Dark matter response to galaxy assembly history

Aims. It is well known that the presence of baryons affects the dark matter host haloes. Exploring the galaxy assembly history together with the dark matter haloes properties through time can provide a way to measure these effects. Methods. We have studied the properties of four Milky Way mass dark matter haloes from the Aquarius project during their assembly history, between z = 0 − 4. In this work, we used a published SPH run and the dark matter only counterpart as case studies. To asses the robustness of our findings, we compared them with one of the haloes run using a moving-mesh technique and different sub-grid scheme. Results. Our results show that the cosmic evolution of the dark matter halo profiles depends on the assembly history of the baryons. We find that the dark matter profiles do not significantly change with time, hence they become stable, when the fraction of baryons accumulated in the central regions reaches 80 per cent of its present mass within the virial radius. Furthermore, the mass accretion history shows that the haloes that assembled earlier are those that contain a larger amount of baryonic mass aforetime, which in turn allows the dark matter halo profiles to reach a stable configuration earlier. For the SPH haloes, we find that the specific angular momentum of the dark matter particles within the five per cent of the virial radius at z = 0, remains approximately constant from the time at which 60 per cent of the stellar mass is gathered. We have explored different theoretical and empirical models for the contraction of the haloes through redshift. A model to better describe the contraction of the haloes through redshift evolution must depend on the stellar mass content in the inner regions.

A Possible Relic Star Cluster in the Sextans Dwarf Galaxy*

Abstract We report a possible discovery of a relic star cluster in the Sextans dwarf spheroidal galaxy. Using the hk index (≡(Ca − b)−(b − y)) as a photometric metallicity indicator, we discriminate the metal-poor and metal-rich stars in the galaxy and find unexpected number density excess of metal-poor stars located 7.′7 (∼190 pc in projected distance) away from the known galactic center. The V − I color−magnitude diagram (CMD) for stars around the density excess reveals that both the main sequence and the giant branch are considerably narrower and redder than the bulk of field stars in Sextans. Our stellar population models show (a) that the narrow CMD is best reproduced by a simple stellar population with an age of ∼13 Gyr and [Fe/H] of ∼−2.3 dex, and (b) that the redder V − I color of the hk-weak population is explained only if it is ∼2 Gyr older than the field stars. The results lead us to conclude that the off-centered density peak is likely associated with an old, metal-poor globular cluster. The larger spatial extent (>80 pc in radius) and the smaller number of stars (∼1000) than typical globular clusters point to a star cluster that is in the process of dissolution. The finding serves as the first detection of a surviving star cluster in Sextans, supporting previous suggestions of the presence of star cluster remnants in the galaxy. If confirmed, the survival of a relic star cluster until now implies a cored dark matter halo profile for this dwarf galaxy.

On velocity-dependent dark matter annihilations in dwarf satellites

Milky Way dwarf spheroidal satellites are a prime target for Dark Matter (DM) indirect searches. Recently the importance of possible long-range interactions has been recognized, as they can boost the expected DM gamma ray signal by orders of magnitude through an effect commonly known as the Sommerfeld enhancement. However, for such analyses precise modelling of DM phase-space distribution becomes crucial and can introduce large uncertainties in the final result. We provide a pioneering attempt towards a comprehensive investigation of these systematics. First, the DM halo profiles are constrained using Bayesian inference on the available stellar kinematic datasets with a careful treatment of observational and theoretical uncertainties. We consider both cuspy and cored parametric DM density profiles, together with the case of a non-parametric halo modelling directly connected to observable quantities along the line-of-sight. After reconsidering the study case of ergodic systems, the basic ingredient of all previous analyses, we investigate for the first time scenarios where DM particles are allowed to have anisotropic velocity distributions. Referring to a generalized J-factor, sensitive to velocity-dependent effects, an enhancement (suppression) with respect to the isotropic phase-space distributions is obtained for the case of tangentially (radially) biased DM particle orbits. We provide new estimates for J-factors for the eight brightest Milky Way dwarfs also in the limit of velocity-independent DM annihilation, in good agreement with previous results in literature, and derive data-driven lower-bounds based on the non-parametric modelling of the halo density. This work presents a state-of-the-art analysis of the aforementioned effects and falls within the interest of current and future experimental collaborations involved in DM indirect detection programs.

A constant characteristic volume density of dark matter haloes from SPARC rotation curve fits

We study the scaling relations between dark matter (DM) haloes and galaxy discs using 175 galaxies from the SPARC data base. We explore two cosmologically motivated DM halo profiles: the Einasto profile from DM-only simulations and the DC14 profile from hydrodynamic simulations. We fit the observed rotation curves using a Markov Chain Monte Carlo method and break the disc-halo degeneracy using near-infrared photometry and ΛCDM-motivated priors. We find that the characteristic volume density ρs of DM haloes is nearly constant over ∼5 decades in galaxy luminosity. The scale radius rs and the characteristic surface density ρs · rs, instead, correlate with galaxy luminosity. These scaling relations provide an empirical benchmark to cosmological simulations of galaxy formation.

A gradient based method for modeling baryons and matter in halos of fast simulations

Fast N-body PM simulations with a small number of time steps such as FastPM or COLA have been remarkably successful in modeling the galaxy statistics, but their lack of small scale force resolution and long time steps cannot give accurate halo matter profiles or matter power spectrum. High resolution N-body simulations can improve on this, but lack baryonic effects, which can only be properly included in hydro simulations. Here we present a scheme to calibrate the fast simulations to mimic the precision of the hydrodynamic simulations or high resolution N-body simulations. The scheme is based on a gradient descent of either effective gravitational potential, which mimics the short range force, or of effective enthalpy, which mimics gas hydrodynamics and feedback. The scheme is fast and differentiable, and can be incorporated as a post-processing step into any simulation. It gives very good results for the matter power spectrum for several of the baryonic feedback and dark matter simulations, and also gives improved dark matter halo profiles. The scheme is even able to find the large subhalos, and increase the correlation coefficient between the fast simulations and the high resolution N-body or hydro simulations. It can also be used to add baryonic effects to the high resolution N-body simulations. While the method has free parameters that can be calibrated on various simulations, they can also be viewed as astrophysical nuisance parameters describing baryonic effects that can be marginalized over during the data analysis. In this view these parameters can be viewed as an efficient parametrization of baryonic effects.

Lyman α forest and non-linear structure characterization in Fuzzy Dark Matter cosmologies

Fuzzy Dark Matter (FDM) represents an alternative and intriguing description of the standard Cold Dark Matter (CDM) fluid, able to explain the lack of direct detection of dark matter particles in the GeV sector and to alleviate small scales tensions in the cosmic large-scale structure formation. Cosmological simulations of FDM models in the literature were performed either with very expensive high-resolution grid-based simulations of individual haloes or through N-body simulations encompassing larger cosmic volumes but resorting on significant approximations in the FDM non-linear dynamics to reduce their computational cost. With the use of the new N-body cosmological hydrodynamical code AX-GADGET, we are now able not only to overcome such numerical problems, but also to combine a fully consistent treatment of FDM dynamics with the presence of gas particles and baryonic physical processes, in order to quantify the FDM impact on specific astrophysical observables. In particular, in this paper we perform and analyse several hydrodynamical simulations in order to constrain the FDM mass by quantifying the impact of FDM on Lyman-$\alpha$ forest observations, as obtained for the first time in the literature in a N-body setup without approximating the FDM dynamics. We also study the statistical properties of haloes, exploiting the large available sample, to extract information on how FDM affects the abundance, the shape, and density profiles of dark matter haloes.

Phenomenological consequences of superfluid dark matter with baryon-phonon coupling

Recently, a new form of dark matter has been suggested to naturally reproduce the empirically successful aspects of Milgrom's law in galaxies. The dark matter particle candidates are axion-like, with masses of order eV and strong self-interactions. They Bose-Einstein condense into a superfluid phase in the central regions of galaxy halos. The superfluid phonon excitations in turn couple to baryons and mediate an additional long-range force. For a suitable choice of the superfluid equation of state, this force can mimic Milgrom's law. In this paper we develop in detail some of the main phenomenological consequences of such a formalism, by revisiting the expected dark matter halo profile in the presence of an extended baryon distribution. In particular, we show how rotation curves of both high and low surface brightness galaxies can be reproduced, with a slightly rising rotation curve at large radii in massive high surface brightness galaxies, thus subtly different from Milgrom's law. We finally point out other expected differences with Milgrom's law, in particular in dwarf spheroidal satellite galaxies, tidal dwarf galaxies, and globular clusters, whose Milgromian or Newtonian behavior depends on the position with respect to the superfluid core of the host galaxy. We also expect ultra-diffuse galaxies within galaxy clusters to have velocities slightly above the baryonic Tully-Fisher relation. Finally, we note that, in this framework, photons and gravitons follow the same geodesics, and that galaxy-galaxy lensing, probing larger distances within galaxy halos than rotation curves, should follow predictions closer to the standard cosmological model than those of Milgrom's law.