# Posts Tagged rotation curves

## Recent Postings from rotation curves

### Disk galaxy scaling relations at intermediate redshifts - I. The Tully-Fisher and velocity-size relations

Galaxy scaling relations such as the Tully-Fisher relation (between maximum rotation velocity Vmax and luminosity) and the velocity-size relation (between Vmax and disk scale length) are powerful tools to quantify the evolution of disk galaxies with cosmic time. We took spatially resolved slit spectra of 261 field disk galaxies at redshifts up to z~1 using the FORS instruments of the ESO Very Large Telescope. The targets were selected from the FORS Deep Field and William Herschel Deep Field. Our spectroscopy was complemented with HST/ACS imaging in the F814W filter. We analyzed the ionized gas kinematics by extracting rotation curves from the 2-D spectra. Taking into account all geometrical, observational and instrumental effects, these rotation curves were used to derive the intrinsic Vmax. Neglecting galaxies with disturbed kinematics or insufficient spatial rotation curve extent, Vmax could be determined for 137 galaxies covering redshifts 0.05<z<0.97. This is one of the largest kinematic samples of distant disk galaxies to date. We compared this data set to the local B-band Tully-Fisher relation and the local velocity-size relation. The scatter in both scaling relations is a factor of ~2 larger at z~0.5 than at z~0. The deviations of individual distant galaxies from the local Tully-Fisher relation are systematic in the sense that the galaxies are increasingly overluminous towards higher redshifts, corresponding to an over-luminosity Delta_MB=-(1.1+-0.5) mag at z=1. This luminosity evolution at given Vmax is probably driven by younger stellar populations of distant galaxies with respect to their local counterparts. The analysis of the velocity-size relation reveals that disk galaxies of a given Vmax have grown in size by a factor of ~1.5 over the past ~8 Gyr, likely via accretion of cold gas and/or small satellites.

### Angular momentum of disc galaxies with a lognormal density distribution

Whilst most galaxy properties scale with galaxy mass, similar scaling relations for angular momentum are harder to demonstrate. A lognormal (LN) density distribution for disc mass provides a good overall fit to the observational data for disc rotation curves for a wide variety of galaxy types and luminosities. In this paper, the total angular momentum J and energy $\vert{}$E$\vert{}$ were computed for 38 disc galaxies from the published rotation curves and plotted against the derived disc masses, with best fit slopes of 1.683$\pm{}$0.018 and 1.643$\pm{}$0.038 respectively, using a theoretical model with a LN density profile. The derived mean disc spin parameter was $\lambda{}$=0.423$\pm{}$0.014. Using the rotation curve parameters V$_{max}$ and R$_{max}$ as surrogates for the virial velocity and radius, the virial mass estimator $M_{disc}\propto{}R_{max}V_{max}^2$ was also generated, with a log-log slope of 1.024$\pm{}$0.014 for the 38 galaxies, and a proportionality constant ${\lambda{}}^*=1.47\pm{}0.20\times{}{10}^5\ M_{sun\ }{kpc}^{-1}{km}^{-2}\ s^2$. This relationship was close to the theoretical slope of 1, and had less scatter than the corresponding Tully Fisher relation, $M\propto{}{\left(V_{rot}\right)}^{\alpha{}}$, suggesting that the virial mass estimator may provide an alternative method to determine disc masses.

### The Luminous Convolution Model for spiral galaxy rotation curves

The Luminous Convolution Model (LCM) is an empirical formula, based on a heuristic convolution of Relativistic transformations, which makes it possible to predict the observed rotation curves of a broad class of spiral galaxies from luminous matter alone. Since the LCM is independent of distance estimates or dark matter halo densities, it is the first model of its kind which constrains luminous matter modeling directly from the observed spectral shifts of characteristic photon emission/absorption lines. In this paper we present the LCM solution to a diverse sample of twenty-five (25) galaxies of varying morphologies and sizes. For the chosen sample, it is shown that the LCM is more accurate than either Modified Newtonian Dynamics or dark matter models and returns physically reasonable mass to light ratios and exponential scale lengths. Unlike either Modified Newtonian Dynamics or dark matter models, the LCM predicts something which is directly falsifiable through improvements in our observational capacity, the luminous mass profile. The question, while interesting, of if the LCM constrains the relation of the baryonic to dark matter is beyond the scope of the current work. The focus of this paper is to show that it is possible to describe a broad and diverse spectrum of galaxies efficiently with the LCM formula. Moreover, since the LCM free parameter predicts the ratio of the Milky Way galaxy baryonic mass density to that of the galaxy emitting the photon, if the Milky Way mass models can be trusted at face values, we then show that the LCM becomes a zero parameter model. This paper substantially expands the results in arXiv:1309.7370 and arXiv:1407:7583.

### A universal velocity dispersion profile for pressure supported systems: evidence for MONDian gravity across 12 orders of magnitude in mass

For any MONDian extended theory of gravity where the rotation curves of spiral galaxies are explained through a change in physics rather than the hypothesis of dark matter, a generic dynamical behaviour is expected for pressure supported systems: an outer flattening of the velocity dispersion profile occurring at a characteristic radius, where both the amplitude of this flat velocity dispersion and the radius at which it appears are predicted to show distinct scalings with the total mass of the system. By carefully analysing dynamics of globular clusters, elliptical galaxies and galaxy clusters, we are able to significantly extend the astronomical scales over which MONDian gravity has been tested, from those of spiral galaxies, to the much larger range covered by pressure supported systems. We show that a universal projected velocity dispersion profile accurately describes various classes of pressure supported systems, and further, that the expectations of extended gravity are met, across twelve orders of magnitude in mass. This observed scalings are not expected under dark matter cosmology, and would require particular explanations tuned at the scales of each distinct astrophysical system.

### Dissipative dark matter and the rotation curves of dwarf galaxies

There is ample evidence from rotation curves that dark matter halo’s around disk galaxies have nontrivial dynamics. Of particular significance are: a) the cored dark matter profile of disk galaxies, b) correlations of the shape of rotation curves with baryonic properties, and c) the Tully-Fisher relation. Dark matter halo’s around disk galaxies may have nontrivial dynamics if dark matter is strongly self interacting and dissipative. Multicomponent hidden sector dark matter featuring a massless dark photon’ (from an unbroken dark $U(1)$ gauge interaction) which kinetically mixes with the ordinary photon provides a concrete example of such dark matter. The kinetic mixing interaction facilitates halo heating by enabling ordinary supernovae to be a source of these dark photons’. Dark matter halo’s can expand and contract in response to the heating and cooling processes, but for a sufficiently isolated halo should have evolved to a steady state or equilibrium’ configuration where heating and cooling rates locally balance. This dynamics allows the dark matter density profile to be related to the distribution of ordinary supernovae in the disk of a given galaxy. In a previous paper a simple and predictive formula was derived encoding this relation. Here we improve on previous work by modelling the supernovae distribution via the measured UV and $H\alpha$ fluxes. The resulting dark matter halo profile is then tested against the rotation curve data of all 26 dwarf galaxies in the LITTLE THINGS sample. The dissipative dark matter concept is further developed and some conclusions drawn.

### A matter of measurement: rotation velocities and the velocity function of dwarf galaxies

The velocity function derived from large scale surveys can be compared with the predictions of LCDM cosmology, by matching the measured rotation velocities Vrot of galaxies to the maximum circular velocity of dark matter (DM) halos Vmax. For Vrot<50km/s, a major discrepancy arises between the observed and LCDM velocity functions. However, the manner in which different observational measures of Vrot are associated with Vmax is not straight forward in dwarf galaxies. We instead relate galaxies to DM halos using the empirical baryon- mass to halo-mass relation, and show that different observational measures of Vrot result in very different velocity functions. We show how the W50 velocity function, i.e. using the HI profile line width at 50% of peak HI flux to measure Vrot, can be reconciled with a LCDM cosmology. Our semi-empirical methodology allows us to determine the region of rotation curves that are probed by HI measurements (RHI), and shows that the Vrot of dwarfs are generally measured at a fraction of Rmax, explaining their tendency to have rising rotation curves. We provide fitting formulae for relating RHI and Reff (the effective radius) to the virial radius of DM halos. To continue to use velocity functions as a probe of LCDM cosmology, it is necessary to be precise about how the different measures of rotation velocity are probing the mass of the DM halos, dropping the assumption that any measure of rotational velocity can be equally used as a proxy for Vmax.

### The Variation of Rotation Curve Shapes as a Signature of the Effects of Baryons on Dark Matter Density Profiles

Rotation curves of galaxies show a wide range of shapes, which can be paramaterized as scatter in Vrot(1kpc)/Vmax i.e.the ratio of the rotation velocity measured at 1kpc and the maximum measured rotation velocity. We examine whether the observed scatter can be accounted for by combining scatters in disc scale-lengths, the concentration-halo mass relation, and the Mstar-Mhalo relation. We use these scatters to create model galaxy populations; when housed within dark matter halos that have universal, NFW density profiles, the model does not match the lowest observed values of Vrot(1kpc)/Vmax and has too little scatter in Vrot(1kpc)/Vmax compared to observations. By contrast, a model using a mass dependant dark matter profile, where the inner slope is determined by the ratio of Mstar/Mhalo, produces galaxies with low values of Vrot(1kpc)/Vmax and a much larger scatter, both in agreement with observation. We conclude that the large observed scatter in Vrot(1kpc)/Vmax favours density profiles that are significantly affected by baryonic processes. Alternative dark matter core formation models are also disfavoured by the large scatter in Vrot(1kpc)/Vmax, implying that baryonic physics would be required to affect density profiles in such models, which defeats a large part of their motivation without ruling them out.

### 3D-Barolo: a new 3D algorithm to derive rotation curves of galaxies

We present 3D-Barolo, a new code that derives rotation curves of galaxies from emission-line observations. This software fits 3D tilted-ring models to spectroscopic data-cubes and can be used with a variety of observations: from HI and molecular lines to optical/IR recombination lines. We describe the structure of the main algorithm and show that it performs much better than the standard 2D approach on velocity fields. A number of successful applications, from high to very low spatial resolution data are presented and discussed. 3D-Barolo can recover the true rotation curve and estimate the intrinsic velocity dispersion even in barely resolved galaxies (about 2 resolution elements) provided that the signal to noise of the data is larger that 2-3. It can also be run automatically thanks to its source-detection and first-estimate modules, which make it suitable for the analysis of large 3D datasets. These features make 3D-Barolo a uniquely useful tool to derive reliable kinematics for both local and high-redshift galaxies from a variety of different instruments including the new-generation IFUs, ALMA and the SKA pathfinders.

### Cosmological Galaxy Evolution with Superbubble Feedback I: Realistic Galaxies with Moderate Feedback

We present the first cosmological galaxy evolved using the modern smoothed particle hydrodynamics (SPH) code GASOLINE2 with superbubble feedback. We show that superbubble-driven galactic outflows powered by Type II supernovae alone can produce $\rm{L^*}$ galaxies with flat rotation curves with circular velocities $\sim 200\; \rm{km/s}$, low bulge-to-disc ratios, and stellar mass fractions that match observed values from high redshift to the present. These features are made possible by the high mass loadings generated by the evaporative growth of superbubbles. Outflows are driven extremely effectively at high redshift, expelling gas at early times and preventing overproduction of stars before $z=2$. Centrally concentrated gas in previous simulations has often lead to unrealistically high bulge to total ratios and strongly peaked rotation curves. We show that supernova-powered superbubbles alone can produce galaxies that agree well with observed properties without the need for additional feedback mechanisms or increased feedback energy. We present additional results arising from properly modelled hot feedback.

### Cosmological Galaxy Evolution with Superbubble Feedback I: Realistic Galaxies with Moderate Feedback [Replacement]

We present the first cosmological galaxy evolved using the modern smoothed particle hydrodynamics (SPH) code GASOLINE2 with superbubble feedback. We show that superbubble-driven galactic outflows powered by Type II supernovae alone can produce $\rm{L^*}$ galaxies with flat rotation curves with circular velocities $\sim 200\; \rm{km/s}$, low bulge-to-disc ratios, and stellar mass fractions that match observed values from high redshift to the present. These features are made possible by the high mass loadings generated by the evaporative growth of superbubbles. Outflows are driven extremely effectively at high redshift, expelling gas at early times and preventing overproduction of stars before $z=2$. Centrally concentrated gas in previous simulations has often lead to unrealistically high bulge to total ratios and strongly peaked rotation curves. We show that supernova-powered superbubbles alone can produce galaxies that agree well with observed properties without the need for additional feedback mechanisms or increased feedback energy. We present additional results arising from properly modelled hot feedback.

### Mass models of disk galaxies from the DiskMass Survey in MOND

This article explores the agreement between the predictions of Modified Newtonian Dynamics (MOND) and the rotation curves and stellar velocity dispersion profiles measured by the DiskMass Survey. A bulge-disk decomposition was made for each of the thirty published galaxies, and a MOND Poisson solver was used to simultaneously compute, from the baryonic mass distributions, model rotation curves and vertical velocity dispersion profiles, which were compared to the measured values. The two main free parameters, the stellar disk’s mass-to-light ratio ($M/L$) and its exponential scale-height ($h_z$), were estimated by Markov Chain Monte Carlo modelling. The average best-fit K-band stellar mass-to-light ratio was $M/L \simeq 0.55 \pm 0.15$. However, to match the DiskMass Survey data, the vertical scale-heights would have to be in the range $h_z=200$ to $400$ pc which is a factor of two lower than those derived from observations of edge-on galaxies with a similar scale-length. The reason is that modified gravity versions of MOND characteristically require a larger $M/L$ to fit the rotation curve in the absence of dark matter and therefore predict a stronger vertical gravitational field than Newtonian models. It was found that changing the MOND acceleration parameter, the shape of the velocity dispersion ellipsoid, the adopted vertical distribution of stars, as well as the galaxy inclination, within any realistic range, all had little impact on these results.

### Testing modified Newtonian dynamics in the Milky Way

Modified Newtonian dynamics (MoND) is an empirical theory originally proposed to explain the rotation curves of spiral galaxies by modifying the gravitational acceleration, rather than by invoking dark matter. Here, we set constraints on MoND using an up-to-date compilation of kinematic tracers of the Milky Way and a comprehensive collection of morphologies of the baryonic component in the Galaxy. In particular, we find that the so-called "standard" interpolating function cannot explain at the same time the rotation curve of the Milky Way and that of external galaxies for any of the baryonic models studied, while the so-called "simple" interpolating function remains viable for a subset of models. Upcoming astronomical observations will refine our knowledge on the morphology of baryons and will ultimately confirm or rule out the validity of MoND in the Milky Way. We also present constraints on MoND-like theories without making any assumptions on the interpolating function.

### Gravitational, lensing, and stability properties of Bose-Einstein condensate dark matter halos

The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein condensate has recently been extensively investigated. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein condensate dark matter halos that could provide clear observational signatures and help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index $n=1$. The mass and the gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. Furthermore, the lensing properties of the condensate dark matter are also investigated in detail. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halos, is obtained in the form of series expansions. This enables arbitrary-precision calculations of the surface mass density, deflection angle, deflection potential, and of the magnification factor, thus providing the possibility of comparing the predicted lensing properties of the condensate dark matter halos with observations. The stability properties of the condensate halos are also investigated by using the scalar and the tensor virial theorems, respectively, and the virial perturbation equation for condensate dark matter halos is derived.

### Gravitational, lensing, and stability properties of Bose-Einstein condensate dark matter halos [Cross-Listing]

The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein condensate has recently been extensively investigated. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein condensate dark matter halos that could provide clear observational signatures and help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index $n=1$. The mass and the gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. Furthermore, the lensing properties of the condensate dark matter are also investigated in detail. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halos, is obtained in the form of series expansions. This enables arbitrary-precision calculations of the surface mass density, deflection angle, deflection potential, and of the magnification factor, thus providing the possibility of comparing the predicted lensing properties of the condensate dark matter halos with observations. The stability properties of the condensate halos are also investigated by using the scalar and the tensor virial theorems, respectively, and the virial perturbation equation for condensate dark matter halos is derived.

### Gravitational, lensing, and stability properties of Bose-Einstein condensate dark matter halos [Replacement]

The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein condensate has recently been extensively investigated. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein condensate dark matter halos that could provide clear observational signatures and help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index $n=1$. The mass and the gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. Furthermore, the lensing properties of the condensate dark matter are also investigated in detail. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halos, is obtained in the form of series expansions. This enables arbitrary-precision calculations of the surface mass density, deflection angle, deflection potential, and of the magnification factor, thus providing the possibility of comparing the predicted lensing properties of the condensate dark matter halos with observations. The stability properties of the condensate halos are also investigated by using the scalar and the tensor virial theorems, respectively, and the virial perturbation equation for condensate dark matter halos is derived.

### Gravitational, lensing, and stability properties of Bose-Einstein condensate dark matter halos [Replacement]

The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein condensate has recently been extensively investigated. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein condensate dark matter halos that could provide clear observational signatures and help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index $n=1$. The mass and the gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. Furthermore, the lensing properties of the condensate dark matter are also investigated in detail. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halos, is obtained in the form of series expansions. This enables arbitrary-precision calculations of the surface mass density, deflection angle, deflection potential, and of the magnification factor, thus providing the possibility of comparing the predicted lensing properties of the condensate dark matter halos with observations. The stability properties of the condensate halos are also investigated by using the scalar and the tensor virial theorems, respectively, and the virial perturbation equation for condensate dark matter halos is derived.

### The link between mass distribution and starbursts in dwarf galaxies

Recent studies have shown that starburst dwarf galaxies have steeply rising rotation curves in their inner parts, pointing to a close link between the intense star formation and a centrally concentrated mass distribution (baryons and dark matter). More quiescent dwarf irregulars typically have slowly rising rotation curves, although some "compact" irregulars with steep, inner rotation curves exist. We analyze archival Hubble Space Telescope images of two nearby "compact" irregular galaxies (NGC 4190 and NGC 5204), which were selected solely on the basis of their dynamical properties and their proximity. We derive their recent star-formation histories by fitting color-magnitude diagrams of resolved stellar populations, and find that the star-formation properties of both galaxies are consistent with those of known starburst dwarfs. Despite the small sample, this strongly reinforces the notion that the starburst activity is closely related to the inner shape of the potential well.

### The unexpected diversity of dwarf galaxy rotation curves

We examine the circular velocity profiles of galaxies in {\Lambda}CDM cosmological hydrodynamical simulations from the EAGLE and LOCAL GROUPS projects and compare them with a compilation of observed rotation curves of galaxies spanning a wide range in mass. The shape of the circular velocity profiles of simulated galaxies varies systematically as a function of galaxy mass, but shows remarkably little variation at fixed maximum circular velocity. This is especially true for low-mass dark matter-dominated systems, reflecting the expected similarity of the underlying cold dark matter haloes. This is at odds with observed dwarf galaxies, which show a large diversity of rotation curve shapes, even at fixed maximum rotation speed. Some dwarfs have rotation curves that agree well with simulations, others do not. The latter are systems where the inferred mass enclosed in the inner regions is much lower than expected for cold dark matter haloes and include many galaxies where previous work claims the presence of a constant density "core". The "cusp vs core" issue is thus better characterized as an "inner mass deficit" problem than as a density slope mismatch. For several galaxies the magnitude of this inner mass deficit is well in excess of that reported in recent simulations where cores result from baryon-induced fluctuations in the gravitational potential. We conclude that one or more of the following statements must be true: (i) the dark matter is more complex than envisaged by any current model; (ii) current simulations fail to reproduce the effects of baryons on the inner regions of dwarf galaxies; and/or (iii) the mass profiles of "inner mass deficit" galaxies inferred from kinematic data are incorrect.

### The unexpected diversity of dwarf galaxy rotation curves [Replacement]

We examine the circular velocity profiles of galaxies in {\Lambda}CDM cosmological hydrodynamical simulations from the EAGLE and LOCAL GROUPS projects and compare them with a compilation of observed rotation curves of galaxies spanning a wide range in mass. The shape of the circular velocity profiles of simulated galaxies varies systematically as a function of galaxy mass, but shows remarkably little variation at fixed maximum circular velocity. This is especially true for low-mass dark matter-dominated systems, reflecting the expected similarity of the underlying cold dark matter haloes. This is at odds with observed dwarf galaxies, which show a large diversity of rotation curve shapes, even at fixed maximum rotation speed. Some dwarfs have rotation curves that agree well with simulations, others do not. The latter are systems where the inferred mass enclosed in the inner regions is much lower than expected for cold dark matter haloes and include many galaxies where previous work claims the presence of a constant density "core". The "cusp vs core" issue is thus better characterized as an "inner mass deficit" problem than as a density slope mismatch. For several galaxies the magnitude of this inner mass deficit is well in excess of that reported in recent simulations where cores result from baryon-induced fluctuations in the gravitational potential. We conclude that one or more of the following statements must be true: (i) the dark matter is more complex than envisaged by any current model; (ii) current simulations fail to reproduce the effects of baryons on the inner regions of dwarf galaxies; and/or (iii) the mass profiles of "inner mass deficit" galaxies inferred from kinematic data are incorrect.

### A systematic study of the inner rotation curves of galaxies observed as part of the GASS and COLD GASS surveys

We present a systematic analysis of the rotation curves of 187 galaxies with masses greater than 10^10 M_sol, with atomic gas masses from the GALEX Arecibo Sloan Survey (GASS), and with follow-up long-slit spectroscopy from the MMT. Our analysis focuses on stellar rotation curves derived by fitting stellar template spectra to the galaxy spectra binned along the slit. In this way, we are able to obtain accurate rotation velocity measurements for a factor of 2 more galaxies than possible with the Halpha line. Galaxies with high atomic gas mass fractions are the most dark-matter dominated galaxies in our sample and have dark matter halo density profiles that are well fit by Navarro, Frenk & White profiles with an average concentration parameter of 10. The inner slopes and of the rotation curves correlate more strongly with stellar population age than with galaxy mass or structural parameters. At fixed stellar mass, the rotation curves of more actively star-forming galaxies have steeper inner slopes than less actively star-forming galaxies. The ratio between the galaxy specific angular momentum and the total specific angular momentum of its dark matter halo, R_j, correlates strongly with galaxy mass, structure and gas content. Low mass, disk-dominated galaxies with atomic gas mass fractions greater than 20% have median values of R_j of around 1, but massive, bulge-dominated galaxies have R_j=0.2-0.3. We argue that these trends can be understood in a picture where gas inflows triggered by disk instabilities lead to the formation of passive, bulge-dominated galaxies with low specific angular momentum.

### A new look at microlensing limits on dark matter in the Galactic halo

The motivation for this paper is to review the limits set on the MACHO content of the Galactic halo by microlensing experiments in the direction of the Large Magellanic Cloud. This has been prompted by recent measurements of the Galactic rotation curve, which suggest that the limits have been biassed by the assumption of an over-massive halo. The paper first discusses the security of the detection efficiency calculations which are central to deriving the MACHO content of the Galactic halo. It then sets out to compare the rotation curves from various halo models with recent observations, with a view to establishing what limits can be put on an all-MACHO halo. The main thrust of the paper is to investigate whether lighter halo models which are consistent with microlensing by an all-MACHO halo are also consistent with recent measures of the Galactic rotation curve. In this case the population of bodies discovered by the MACHO collaboration would make up the entire dark matter content of the Galactic halo. The main result of this paper is that it is easy to find low mass halo models consistent with the observed Galactic rotation curve, which also imply an optical depth to microlensing similar to that found by the MACHO collaboration. This means that all-MACHO halos cannot be ruled out on the basis of their observations. In conclusion, limits placed on the MACHO content of the Galactic halo from microlensing surveys in the Magellanic Clouds are inconsistent and model dependent, and do not provide a secure basis for rejecting an all-MACHO halo.

### Dissipative dark matter explains rotation curves [Replacement]

Dissipative dark matter, where dark matter particles interact with a massless (or very light) boson, is studied. Such dark matter can arise in simple hidden sector gauge models, including those featuring an unbroken $U(1)’$ gauge symmetry, leading to a dark photon. Previous work has shown that such models can not only explain the LSS and CMB, but potentially also dark matter phenomena on small scales, such as the inferred cored structure of dark matter halos. In this picture, dark matter halos of disk galaxies not only cool via dissipative interactions but are also heated via ordinary supernovae (facilitated by an assumed photon – dark photon kinetic mixing interaction). This interaction between the dark matter halo and ordinary baryons, a very special feature of these types of models, plays a critical role in governing the physical properties of the dark matter halo. Here, we further study the implications of this type of dissipative dark matter for disk galaxies. Building on earlier work, we develop a simple formalism which aims to describe the effects of dissipative dark matter in a fairly model independent way. This formalism is then applied to generic disk galaxies. We also consider specific examples, including NGC 1560 and a sample of dwarf galaxies from the LITTLE THINGS survey. We find that dissipative dark matter, as developed here, does a fairly good job accounting for the rotation curves of the galaxies considered. Not only does dissipative dark matter explain the linear rise of the rotational velocity of dwarf galaxies at small radii, but it can also explain the observed wiggles in rotation curves which are known to be correlated with corresponding features in the disk gas distribution.

### Dissipative dark matter explains rotation curves [Replacement]

Dissipative dark matter, where dark matter particles interact with a massless (or very light) boson, is studied. Such dark matter can arise in simple hidden sector gauge models, including those featuring an unbroken $U(1)’$ gauge symmetry, leading to a dark photon. Previous work has shown that such models can not only explain the LSS and CMB, but potentially also dark matter phenomena on small scales, such as the inferred cored structure of dark matter halos. In this picture, dark matter halos of disk galaxies not only cool via dissipative interactions but are also heated via ordinary supernovae (facilitated by an assumed photon – dark photon kinetic mixing interaction). This interaction between the dark matter halo and ordinary baryons, a very special feature of these types of models, plays a critical role in governing the physical properties of the dark matter halo. Here, we further study the implications of this type of dissipative dark matter for disk galaxies. Building on earlier work, we develop a simple formalism which aims to describe the effects of dissipative dark matter in a fairly model independent way. This formalism is then applied to generic disk galaxies. We also consider specific examples, including NGC 1560 and a sample of dwarf galaxies from the LITTLE THINGS survey. We find that dissipative dark matter, as developed here, does a fairly good job accounting for the rotation curves of the galaxies considered. Not only does dissipative dark matter explain the linear rise of the rotational velocity of dwarf galaxies at small radii, but it can also explain the observed wiggles in rotation curves which are known to be correlated with corresponding features in the disk gas distribution.

### Dissipative dark matter explains rotation curves

Dissipative dark matter, where dark matter particles interact with a massless (or very light) boson, is studied. Such dark matter can arise in simple hidden sector gauge models, including those featuring an unbroken $U(1)’$ gauge symmetry, leading to a dark photon. Previous work has shown that such models can not only explain the LSS and CMB, but potentially also dark matter phenomena on small scales, such as the inferred cored structure of dark matter halos. In this picture, dark matter halos of disk galaxies not only cool via dissipative interactions but are also heated via ordinary supernovae (facilitated by an assumed photon – dark photon kinetic mixing interaction). This interaction between the dark matter halo and ordinary baryons, a very special feature of these types of models, plays a critical role in governing the physical properties of the dark matter halo. Here, we further study the implications of this type of dissipative dark matter for disk galaxies. Building on earlier work, we develop a simple formalism which aims to describe the effects of dissipative dark matter in a fairly model independent way. This formalism is then applied to generic disk galaxies. We also consider specific examples, including NGC 1560 and a sample of dwarf galaxies from the LITTLE THINGS survey. We find that dissipative dark matter, as developed here, does a fairly good job accounting for the rotation curves of the galaxies considered. Not only does dissipative dark matter explain the linear rise of the rotational velocity of dwarf galaxies at small radii, but it can also explain the observed wiggles in rotation curves which are known to be correlated with corresponding features in the disk gas distribution.

### Dissipative dark matter explains rotation curves [Cross-Listing]

Dissipative dark matter, where dark matter particles interact with a massless (or very light) boson, is studied. Such dark matter can arise in simple hidden sector gauge models, including those featuring an unbroken $U(1)’$ gauge symmetry, leading to a dark photon. Previous work has shown that such models can not only explain the LSS and CMB, but potentially also dark matter phenomena on small scales, such as the inferred cored structure of dark matter halos. In this picture, dark matter halos of disk galaxies not only cool via dissipative interactions but are also heated via ordinary supernovae (facilitated by an assumed photon – dark photon kinetic mixing interaction). This interaction between the dark matter halo and ordinary baryons, a very special feature of these types of models, plays a critical role in governing the physical properties of the dark matter halo. Here, we further study the implications of this type of dissipative dark matter for disk galaxies. Building on earlier work, we develop a simple formalism which aims to describe the effects of dissipative dark matter in a fairly model independent way. This formalism is then applied to generic disk galaxies. We also consider specific examples, including NGC 1560 and a sample of dwarf galaxies from the LITTLE THINGS survey. We find that dissipative dark matter, as developed here, does a fairly good job accounting for the rotation curves of the galaxies considered. Not only does dissipative dark matter explain the linear rise of the rotational velocity of dwarf galaxies at small radii, but it can also explain the observed wiggles in rotation curves which are known to be correlated with corresponding features in the disk gas distribution.

### Constraints on the dark matter sound speed from galactic scales: the cases of the Modified and Extended Chaplygin Gas

We show that the observed rotation curves of spiral galaxies constrain the sound speed of the dark matter to be $c_s < 10^{-4} c$, where $c$ is the speed of light in vacuum. Using the Modified Chaplygin Gas as a representative example of a class of unified dark energy models incorporating an effective dark matter component with a non-zero sound speed, we determine the most stringent constraint to date on the value of the constant contribution to the equation of state parameter in this class of models. Finally, we explain the reason why previous constraints using the Cosmic Microwave Background and Baryonic Acoustic Oscillations were not as competitive as the one presented in this paper and discuss the limitations of the recently proposed Extended Chaplygin Gas.

### Constraints on the dark matter sound speed from galactic scales: the cases of the Modified and Extended Chaplygin Gas [Cross-Listing]

We show that the observed rotation curves of spiral galaxies constrain the sound speed of the dark matter to be $c_s < 10^{-4} c$, where $c$ is the speed of light in vacuum. Using the Modified Chaplygin Gas as a representative example of a class of unified dark energy models incorporating an effective dark matter component with a non-zero sound speed, we determine the most stringent constraint to date on the value of the constant contribution to the equation of state parameter in this class of models. Finally, we explain the reason why previous constraints using the Cosmic Microwave Background and Baryonic Acoustic Oscillations were not as competitive as the one presented in this paper and discuss the limitations of the recently proposed Extended Chaplygin Gas.

### Constraints on the dark matter sound speed from galactic scales: the cases of the Modified and Extended Chaplygin Gas [Cross-Listing]

We show that the observed rotation curves of spiral galaxies constrain the sound speed of the dark matter to be $c_s < 10^{-4} c$, where $c$ is the speed of light in vacuum. Using the Modified Chaplygin Gas as a representative example of a class of unified dark energy models incorporating an effective dark matter component with a non-zero sound speed, we determine the most stringent constraint to date on the value of the constant contribution to the equation of state parameter in this class of models. Finally, we explain the reason why previous constraints using the Cosmic Microwave Background and Baryonic Acoustic Oscillations were not as competitive as the one presented in this paper and discuss the limitations of the recently proposed Extended Chaplygin Gas.

### Searching for IMBHs in Galactic globular clusters through radial velocities of individual stars

I present an overview of our ongoing project aimed at building a new generation of velocity dispersion profiles ad rotation curves for a representative sample of Galactic globular clusters, from the the radial velocity of hundreds individual stars distributed at different distances from the cluster center. The innermost portion of the profiles will be used to constrain the possibile presence of intermediate-mass black holes. The adopted methodology consists in combining spectroscopic observations acquired with three different instruments at the ESO-VLT: the adaptive-optics assisted, integral field unit (IFU) spectrograph SINFONI for the innermost and highly crowded cluster cores, the multi-IFU spectrograph KMOS for the intermediate regions, and the multi-fiber instrument FLAMES/GIRAFFE-MEDUSA for the outskirts. The case of NGC 6388, representing the pilot project that motivated the entire program, is described in some details.

### Galaxy rotation curves with log-normal density distribution

The log-normal distribution represents the probability of finding randomly distributed particles in a micro canonical ensemble with high entropy. To a first approximation, a modified form of this distribution with a truncated termination may represent an isolated galactic disk, and this disk density distribution model was therefore run to give the best fit to the observational rotation curves for 37 representative galaxies. The resultant curves closely matched the observational data for a wide range of velocity profiles and galaxy types with rising, flat or descending curves in agreement with Verheijen’s classification of ‘R’, ‘F’ and ‘D’ type curves, and the corresponding theoretical total disk masses could be fitted to a baryonic Tully Fisher relation (bTFR). Nine of the galaxies were matched to galaxies with previously published masses, suggesting a mean excess dynamic disk mass of dex0.61+/-0.26 over the baryonic masses. Although questionable with regard to other measurements of the shape of disk galaxy gravitational potentials, this model can accommodate a scenario in which the gravitational mass distribution, as measured via the rotation curve, is confined to a thin plane without requiring a dark-matter halo or the use of MOND.

### High-resolution mass models of dwarf galaxies from LITTLE THINGS

We present high-resolution rotation curves and mass models of 26 dwarf galaxies from LITTLE THINGS. LITTLE THINGS is a high-resolution Very Large Array HI survey for nearby dwarf galaxies in the local volume within 11 Mpc. The rotation curves of the sample galaxies derived in a homogeneous and consistent manner are combined with Spitzer archival 3.6 micron and ancillary optical U, B, and V images to construct mass models of the galaxies. We decompose the rotation curves in terms of the dynamical contributions by baryons and dark matter halos, and compare the latter with those of dwarf galaxies from THINGS as well as Lambda CDM SPH simulations in which the effect of baryonic feedback processes is included. Being generally consistent with THINGS and simulated dwarf galaxies, most of the LITTLE THINGS sample galaxies show a linear increase of the rotation curve in their inner regions, which gives shallower logarithmic inner slopes alpha of their dark matter density profiles. The mean value of the slopes of the 26 LITTLE THINGS dwarf galaxies is alpha =-0.32 +/- 0.24 which is in accordance with the previous results found for low surface brightness galaxies (alpha = -0.2 +/- 0.2) as well as the seven THINGS dwarf galaxies (alpha =-0.29 +/- 0.07). However, this significantly deviates from the cusp-like dark matter distribution predicted by dark-matter-only Lambda CDM simulations. Instead our results are more in line with the shallower slopes found in the Lambda CDM SPH simulations of dwarf galaxies in which the effect of baryonic feedback processes is included. In addition, we discuss the central dark matter distribution of DDO 210 whose stellar mass is relatively low in our sample to examine the scenario of inefficient supernova feedback in low mass dwarf galaxies predicted from recent Lambda SPH simulations of dwarf galaxies where central cusps still remain.

### Rotation curves of ultralight BEC dark matter halos with rotation [Cross-Listing]

We study the rotation curves of ultralight BEC dark matter halos. These halos are long lived solutions of initially rotating BEC fluctuations. In order to study the implications of the rotation characterizing these long-lived configurations we consider the particular case of a boson mass $m=10^{-23}\mathrm{eV/c}^2$ and no self-interaction. We find that these halos successfully fit samples of rotation curves (RCs) of LSB galaxies.

### Rotation curves of ultralight BEC dark matter halos with rotation

We study the rotation curves of ultralight BEC dark matter halos. These halos are long lived solutions of initially rotating BEC fluctuations. In order to study the implications of the rotation characterizing these long-lived configurations we consider the particular case of a boson mass $m=10^{-23}\mathrm{eV/c}^2$ and no self-interaction. We find that these halos successfully fit samples of rotation curves (RCs) of LSB galaxies.

### The distribution of dark and luminous matter inferred from extended rotation curves

A better understanding of the formation of mass structures in the universe can be obtained by determining the amount and distribution of dark and luminous matter in spiral galaxies. To investigate such matters a sample of 12 galaxies, most with accurate distances, has been composed of which the luminosities are distributed regularly over a range spanning 2.5 orders of magnitude. Of the observed high quality and extended rotation curves of these galaxies decompositions have been made, for four different schemes, each with two free parameters. For a "maximum disc fit" the rotation curves can be well matched, yet a large range of mass-to-light ratios for the individual galaxies is required. For the alternative gravitational theory of MOND the rotation curves can be explained if the fundamental parameter associated with MOND is allowed as a free parameter. Fixing that parameter leads to a disagreement between the predicted and observed rotation curves for a few galaxies. When cosmologically motivated NFW dark matter halos are assumed, the rotation curves for the least massive galaxies can, by no means, be reproduced; cores are definitively preferred over cusps. Finally, decompositions have been made for a pseudo isothermal halo combined with a universal M/L ratio. For the latter, the light of each galactic disc and bulge has been corrected for extinction and has been scaled by the effect of stellar population. This scheme can successfully explain the observed rotations and leads to sub maximum disc mass contributions. Properties of the resulting dark matter halos are described and a ratio between dark and baryonic mass of approximately 9 for the least, and of approximately 5, for the most luminous galaxies has been determined, at the outermost measured rotation.

### Smoothing Rotation Curves and Mass Profiles

We show that spiral activity can erase pronounced features in disk galaxy rotation curves. We present simulations of growing disks, in which the added material has a physically motivated distribution, as well as other examples of physically less realistic accretion. In all cases, attempts to create unrealistic rotation curves were unsuccessful because spiral activity rapidly smoothed away features in the disk mass profile. The added material was redistributed radially by the spiral activity, which was itself provoked by the density feature. In the case of a ridge-like feature in the surface density profile, we show that two unstable spiral modes develop, and the associated angular momentum changes in horseshoe orbits remove particles from the ridge and spread them both inwards and outwards. This process rapidly erases the density feature from the disk. We also find that the lack of a feature when transitioning from disk to halo dominance in the rotation curves of disk galaxies, the so called "disk-halo conspiracy", could also be accounted for by this mechanism. We do not create perfectly exponential mass profiles in the disk, but suggest that this mechanism contributes to their creation.

### Smoothing Rotation Curves and Mass Profiles [Replacement]

We show that spiral activity can erase pronounced features in disk galaxy rotation curves. We present simulations of growing disks, in which the added material has a physically motivated distribution, as well as other examples of physically less realistic accretion. In all cases, attempts to create unrealistic rotation curves were unsuccessful because spiral activity rapidly smoothed away features in the disk mass profile. The added material was redistributed radially by the spiral activity, which was itself provoked by the density feature. In the case of a ridge-like feature in the surface density profile, we show that two unstable spiral modes develop, and the associated angular momentum changes in horseshoe orbits remove particles from the ridge and spread them both inwards and outwards. This process rapidly erases the density feature from the disk. We also find that the lack of a feature when transitioning from disk to halo dominance in the rotation curves of disk galaxies, the so called "disk-halo conspiracy", could also be accounted for by this mechanism. We do not create perfectly exponential mass profiles in the disk, but suggest that this mechanism contributes to their creation.

### Revisiting galactic rotation curves given a noncommutative-geometry background

It was shown earlier by Rahaman et al. that a noncommutative-geometry background can account for galactic rotation curves without the need for dark matter. The smearing effect that characterizes noncommutative geometry is described by means of a Gaussian distribution intended to replace the Dirac delta function. The purpose of this paper is two-fold: (1) to account for the galactic rotation curves in a more transparent and intuitively more appealing way by replacing the Gaussian function by the simpler Lorentzian distribution proposed by Nozari and Mehdipour and (2) to show that the smearing effect is both a necessary and sufficient condition for meeting the stability criterion.

### Cosmological simulations of galaxy formation with cosmic rays

We investigate the dynamical impact of cosmic rays in cosmological simulations of galaxy formation using adaptive-mesh refinement simulations of a $10^{12}$ solar mass halo. In agreement with previous work, a run with only our standard thermal energy feedback model results in a massive spheroid and unrealistically peaked rotation curves. However, the addition of a simple two-fluid model for cosmic rays drastically changes the morphology of the forming disk. We include an isotropic diffusive term and a source term tied to star formation due to (unresolved) supernova-driven shocks. Over a wide range of diffusion coefficients, the CRs generate thin, extended disks with a significantly more realistic (although still not flat) rotation curve. We find that the diffusion of CRs is key to this process, as they escape dense star forming clumps and drive outflows within the more diffuse ISM.

### Relational Mechanics as a gauge theory [Replacement]

Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. In this way, the resulting equations of motion are valid in any frame. Even so, there are privileged frames where Newton’s equations are valid (Newtonian frames), but they are determined by the matter distribution of the universe (Machianization). The frame of fixed stars is not exactly Newtonian when it is employed for describing the motion of subsystems having large angular momenta; a dragging effect will be perceived in this frame, which could be detectable in the galactic rotation curves. On the other hand, the absence of an absolute time is known to be a characteristic of parametrized systems. Parametrized systems with potentials that are proportional to inverse square distances are gauge invariant under scalings too (shape-dynamics).

### Relational Mechanics as a gauge theory [Replacement]

Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. In this way, the resulting equations of motion are valid in any frame. Even so, there are privileged frames where Newton’s equations are valid (Newtonian frames), but they are determined by the matter distribution of the universe (Machianization). The frame of fixed stars is not exactly Newtonian when it is employed for describing the motion of subsystems having large angular momenta; a dragging effect will be perceived in this frame, which could be detectable in the galactic rotation curves. On the other hand, the absence of an absolute time is known to be a characteristic of parametrized systems. Parametrized systems with potentials that are proportional to inverse square distances are gauge invariant under scalings too (shape-dynamics).

### Relational Mechanics as a gauge theory: Machianization and dragging effect in galactic halos

The elimination of absolute space from the body of mechanics is achieved by gauging translations and rotations in the kinetic energy of an isolated system. As a result, the gauge invariant Lagrangian leads to equations of motion that can be used in any frame. Nevertheless, there are privileged frames where Newton’s equations are valid, but they are determined by the matter distribution of the universe (Machianization). The relational equations of motion shows that there exists a dragging effect in galactic halos that contributes to the rotation curves. On the other hand, the absence of an absolute time is characteristic of parametrized systems, which are systems possessing an internal time. Parametrized systems with potentials that are proportional to inverse square distances are as well gauge invariant under scalings (shape-dynamics).

### Relational Mechanics as a gauge theory [Replacement]

Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. In this way, the resulting equations of motion are valid in any frame. Even so, there are privileged frames where Newton’s equations are valid (Newtonian frames), but they are determined by the matter distribution of the universe (Machianization). The frame of fixed stars is not exactly Newtonian when it is employed for describing the motion of subsystems having large angular momenta; a dragging effect will be perceived in this frame, which could be detectable in the galactic rotation curves. On the other hand, the absence of an absolute time is known to be a characteristic of parametrized systems. Parametrized systems with potentials that are proportional to inverse square distances are gauge invariant under scalings too (shape-dynamics).

### Relational Mechanics as a gauge theory: Machianization and dragging effect in galactic halos [Cross-Listing]

The elimination of absolute space from the body of mechanics is achieved by gauging translations and rotations in the kinetic energy of an isolated system. As a result, the gauge invariant Lagrangian leads to equations of motion that can be used in any frame. Nevertheless, there are privileged frames where Newton’s equations are valid, but they are determined by the matter distribution of the universe (Machianization). The relational equations of motion shows that there exists a dragging effect in galactic halos that contributes to the rotation curves. On the other hand, the absence of an absolute time is characteristic of parametrized systems, which are systems possessing an internal time. Parametrized systems with potentials that are proportional to inverse square distances are as well gauge invariant under scalings (shape-dynamics).

### Modified gravity models and the central cusp of dark matter halos in galaxies

The N-body dark matter (DM) simulations point that DM density profiles, e.g. the NFW halo, should be cuspy in its center, but observations disfavour this kind of DM profile. Here we consider whether the observed rotation curves "close" to the galactic centre can favour modified gravity models in comparison to the NFW halo, and how to quantify such difference. Two explicit modified gravity models are considered, MOND and a more recent approach called RGGR (in reference to Renormalization Group effects in General Relativity). It is also the purpose of this work to significantly extend the sample on which RGGR has been tested in comparison to other approaches. By analysing 62 galaxies from five samples, we find that: i) there is a radius, given by half the disk scale length, below which RGGR and MOND can match the data about as well or better than NFW, albeit the formers have fewer free parameters; ii) considering the complete rotation curve data, RGGR could achieve fits with better agreement than MOND, and almost as good as a NFW halo with two free parameters (NFW and RGGR have respectively two and one more free parameters than MOND).

### Modified gravity models and the central cusp of dark matter halos in galaxies [Cross-Listing]

The N-body dark matter (DM) simulations point that DM density profiles, e.g. the NFW halo, should be cuspy in its center, but observations disfavour this kind of DM profile. Here we consider whether the observed rotation curves "close" to the galactic centre can favour modified gravity models in comparison to the NFW halo, and how to quantify such difference. Two explicit modified gravity models are considered, MOND and a more recent approach called RGGR (in reference to Renormalization Group effects in General Relativity). It is also the purpose of this work to significantly extend the sample on which RGGR has been tested in comparison to other approaches. By analysing 62 galaxies from five samples, we find that: i) there is a radius, given by half the disk scale length, below which RGGR and MOND can match the data about as well or better than NFW, albeit the formers have fewer free parameters; ii) considering the complete rotation curve data, RGGR could achieve fits with better agreement than MOND, and almost as good as a NFW halo with two free parameters (NFW and RGGR have respectively two and one more free parameters than MOND).

### On the core-halo distribution of dark matter in galaxies [Replacement]

We investigate the distribution of dark matter in galaxies by solving the equations of equilibrium of a self-gravitating system of massive fermions (inos’) at selected temperatures and degeneracy parameters within general relativity. Our most general solutions show, as a function of the radius, a segregation of three physical regimes: 1) an inner core of almost constant density governed by degenerate quantum statistics; 2) an intermediate region with a sharply decreasing density distribution followed by an extended plateau, implying quantum corrections; 3) an asymptotic, $\rho\propto r^{-2}$ classical Boltzmann regime fulfilling, as an eigenvalue problem, a fixed value of the flat rotation curves. This eigenvalue problem determines, for each value of the central degeneracy parameter, the mass of the ino as well as the radius and mass of the inner quantum core. Consequences of this alternative approach to the central and halo regions of galaxies, ranging from dwarf to big spirals, for SgrA*, as well as for the existing estimates of the ino mass, are outlined.

### On the core-halo distribution of dark matter in galaxies

We investigate the distribution of dark matter in galaxies by solving the equations of equilibrium of a self-gravitating system of massive fermions (inos’) at selected temperatures and degeneracy parameters within general relativity. The most general solutions present, as a function of the radius, a segregation of three physical regimes: 1) an inner core of almost constant density governed by degenerate quantum statistics; 2) an intermediate region with a sharply decreasing density distribution followed by an extended plateau, implying quantum corrections; 3) a decreasing density distribution $\rho\propto r^{-2}$ leading to flat rotation curves fulfilling the classical Boltzmann statistics. The mass of the inos is determined as an eigenfunction of the mass of the inner quantum cores. We compare and contrast this mass value with the lower limit on the particle mass by Tremaine and Gunn (1979), and show that the latter is approached for the less degenerate quantum cores in agreement with the fixed halo observables. Consequences of this alternative approach to the massive core in SgrA* and to dwarf galaxies are outlined.

### On the core-halo distribution of dark matter in galaxies [Replacement]

We investigate the distribution of dark matter in galaxies by solving the equations of equilibrium of a self-gravitating system of massive fermions (inos’) at selected temperatures and degeneracy parameters within general relativity. Our most general solutions show, as a function of the radius, a segregation of three physical regimes: 1) an inner core of almost constant density governed by degenerate quantum statistics; 2) an intermediate region with a sharply decreasing density distribution followed by an extended plateau, implying quantum corrections; 3) an asymptotic, $\rho\propto r^{-2}$ classical Boltzmann regime fulfilling, as an eigenvalue problem, a fixed value of the flat rotation curves. This eigenvalue problem determines, for each value of the central degeneracy parameter, the mass of the ino as well as the radius and mass of the inner quantum core. Consequences of this alternative approach to the central and halo regions of galaxies, ranging from dwarf to big spirals, for SgrA*, as well as for the existing estimates of the ino mass, are outlined.

### On the core-halo distribution of dark matter in galaxies [Replacement]

We investigate the distribution of dark matter in galaxies by solving the equations of equilibrium of a self-gravitating system of massive fermions (`inos’) at selected temperatures and degeneracy parameters within general relativity. Our most general solutions show, as a function of the radius, a segregation of three physical regimes: 1) an inner core of almost constant density governed by degenerate quantum statistics; 2) an intermediate region with a sharply decreasing density distribution followed by an extended plateau, implying quantum corrections; 3) an asymptotic, $\rho\propto r^{-2}$ classical Boltzmann regime fulfilling, as an eigenvalue problem, a fixed value of the flat rotation curves. This eigenvalue problem determines, for each value of the central degeneracy parameter, the mass of the ino as well as the radius and mass of the inner quantum core. Consequences of this alternative approach to the central and halo regions of galaxies, ranging from dwarf to big spirals, for SgrA*, as well as for the existing estimates of the ino mass, are outlined.

### Rotation Curves and Nonextensive Statistics

We investigate the influence of the nonextensive q-statistics and kinetic theory on galactic scales through the analysis of a devised sample of Spiral Rotation Curves. Largely supported by recent developments on the foundations of statistical mechanics and a plethora of astrophysical applications, the theory also provides an alternative interpretation to the empirical cored dark matter profiles observed in galaxies. We show that the observations could well be fitted with reasonable values for the mass model parameters, encouraging further investigation into q-statistcs on the distribution of dark matter from both observational and theoretical points of view.