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A constant dark matter halo surface density in galaxies
F. Donato, G. Gentile, P. Salucci, C. Frigerio Martins, M. I. Wilkinson, G. Gilmore, E. K. Grebel, A. Koch, R. Wyse
TL;DR
The paper asks whether the central dark-matter surface density remains related to galaxy luminosity despite large variations in halo and luminous properties. Using rotation-curve mass models, URCs, weak lensing, and dwarf-spheroidal kinematics, it finds that ρ0r0 stays nearly constant across a broad galaxy range.
Problem
The paper investigates whether µ0D remains nearly constant when galaxy central densities and core radii vary by several orders of magnitude.
Method
The study combines rotation-curve mass modelling, THINGS analyses, weak-lensing measurements, and dwarf-spheroidal kinematics using cored dark-matter halo profiles.
Results
ρ0r0 remains almost constant and independent of galaxy luminosity across systems spanning fourteen magnitudes and multiple Hubble Types.
Takeaways & Limitations
The central dark-matter surface density remains constant to within less than a factor of two across at least nine and possibly fourteen galaxy magnitudes.
Takeaways & Limitations
The reliable halo sample remains limited relative to present-day cosmic variance, and distorted or strongly centrally concentrated systems remain difficult to analyse.
Abstract
from arXiv · showhide
We confirm and extend the recent finding that the central surface density r_0*rho_0 galaxy dark matter halos, where r_0 and rho_0 are the halo core radius and central density, is nearly constant and independent of galaxy luminosity. Based on the co-added rotation curves of about 1000 spiral galaxies, mass models of individual dwarf irregular and spiral galaxies of late and early types with high-quality rotation curves and, galaxy-galaxy weak lensing signals from a sample of spiral and elliptical galaxies, we find that log(r_0*rho_0) = 2.15 +- 0.2, in units of log(Msol/pc^2). We also show that the observed kinematics of Local Group dwarf spheroidal galaxies are consistent with this value. Our results are obtained for galactic systems spanning over 14 magnitudes, belonging to different Hubble Types, and whose mass profiles have been determined by several independent methods. In the same objects, the approximate constancy of rho_0*r_0 is in sharp contrast to the systematical variations, by several orders of magnitude, of galaxy properties, including rho_0 and central stellar surface density.
1 INTRODUCTION
The paper examines whether the dark-matter halo quantity µ0D ≡ ρ0r0 is nearly independent of galaxy luminosity. It extends earlier evidence using diverse galaxy samples and mass-modelling approaches, while adopting cored halo profiles.
- Prior evidence: Earlier studies found µ0D ≡ ρ0r0 nearly independent of galaxy blue magnitude, with a value near 100 M⊙pc−2.Here ρ0 is the central density and r0 the core radius of the adopted cored halo profile.
- Motivation: The paper investigates galaxies whose central densities and core radii vary by several orders of magnitude.The goal is to test the µ0D–magnitude relationship across broad galaxy properties.
- Approach: The analysis combines URC fits, individual-galaxy kinematic mass models, THINGS rotation curves, and weak-lensing measurements.The samples include spiral, elliptical, dwarf irregular, and dwarf spheroidal systems.
- Modelling framework: The study assumes cored dark-matter halos and reports that the stellar disk plus Burkert halo plus HI disk model satisfactorily fits the available kinematics.The paper states that these fits are generally superior to NFW fits, while noting that directly testing NFW is not its aim.
- Data provenance: Mass models from earlier work are reused for most systems, whereas weak-lensing and dwarf-spheroidal analyses provide additional tests.The paper redirects readers to prior publications for most previously obtained mass models.
2 THE ρ0r0 VS MAGNITUDE RELATIONSHIP
The paper tests the µ0D–magnitude relation across multiple galaxy populations and independent methods. The resulting evidence supports an approximately constant central dark-matter surface density, including in very faint systems.
- Prior spiral-galaxy evidence: The Donato et al. sample shows nearly constant µ0D while disk scale length RD varies by more than one order of magnitude.The sample contains 25 spiral and low-surface-brightness galaxies modelled from rotation curves.
- Universal Rotation Curve: The URC derives ρ0 and r0 by fitting a Burkert halo plus Freeman disk velocity model without fixing the baryonic mass.The URC is based on co-added kinematic data from a large spiral-galaxy sample.
- THINGS galaxies: THINGS mass models combine unconstrained χ2 fits with color-based stellar mass-to-light ratios to provide an independent check.The selected galaxies reproduce their rotation curves, with halo-parameter uncertainties generally no larger than 50%.
- Dwarf spirals: NGC 3741 and DDO 47 extend the relation to very faint dwarf spirals using rotation curves fitted with stellar, gaseous, and Burkert-halo components.NGC 3741 has MB = −13.1 and an HI disk traced to 42 B-band exponential scale lengths.
- Weak lensing: Weak-lensing shear measurements of roughly 10^5 spiral and elliptical galaxies provide a gravitational-potential probe distinct from rotation-curve analyses.The data span 70–560 kpc from lens centers, where the stellar contribution to shear is negligible.
- Milky Way satellites: For dwarf spheroidals, µ0D remains approximately 100 M⊙pc−2 despite large, opposing changes in central density and core radius.The result implies that the near-constant product can coexist with strong discontinuities in the separate halo parameters.
3 RESULTS
Across galaxy systems spanning nearly fourteen magnitudes and all Hubble types, independently modeled data support an approximately constant dark-matter central surface density. The relation remains consistent despite large variations in halo parameters and cannot presently be ruled out at sub-30% variation levels.
- The constant µ0D result is supported by different, independent mass-modeling techniques across dwarf disks, spheroidals, spirals, and ellipticals.
- Fourteen magnitudes and all Hubble Types are covered by the assembled galaxy systems.
- The relation ρ0r0 ≈ constant may extend to the faintest galaxy systems based on Local Group dwarf spheroidal kinematics.
- ρ0 and r0 vary over several orders of magnitude, while µ0D ≡ ρ0r0 remains almost constant.
- Systematic or object-by-object variations smaller than 30% cannot presently be excluded.
4 THE INTRIGUING RELATION BETWEEN µ0D AND THE STELLAR CENTRAL SURFACE DENSITY
The dark-matter central surface density is nearly constant even though stellar central surface density varies strongly with galaxy luminosity and Hubble type. This makes µ0D the only identified dark-matter quantity not correlated with its stellar analogue.
- Stellar central surface density Σ∗ varies strongly with galaxy luminosity and Hubble type, unlike µ0D.
- Σ∗ rises from about 50 M⊙pc−2 at MB = −17 to about 800 M⊙pc−2 at MB = −22.5 in spirals.
- The central surface density is the only dark-matter quantity identified as uncorrelated with its stellar analogue.
- The stellar component dominates galaxy centers except in dwarfs, where it is surprisingly very sub-dominant.
5 DISCUSSION AND CONCLUSIONS
The near-constancy of µ0D links dark-halo structure to spiral scaling laws despite large variations in halo and stellar properties. The result is broad but limited by uncertainties in inferring ρ0–r0 relations and by incomplete coverage of galaxy types and kinematic settings.
- Inverting the fitted ρ0–r0 trend is unreliable because propagated uncertainties make r0 uncertain by at least 2 × 10^0.2 and sometimes 2 × 10^0.5.The paper states that the relationship must instead be derived from selected data and suitable mass-modelling methods.
- For Burkert haloes, constant µ0D implies Mh0 ∝ ρ0r0^3 and Vh0 ∝ r0^0.5, connecting halo structure to established spiral scaling laws.
- The derived disk and halo velocity scalings imply a velocity-contribution fraction proportional to R0^-0.6, consistent with less luminous spirals having proportionally more dark matter.
- r0 and ρ0 correlate with luminous counterparts, whereas µ0D does not, so their separate correlations do not explain the observed halo surface-density constancy.
- ρ0r0 remains constant to within less than a factor of two across at least nine, possibly fourteen, galaxy magnitudes and several Hubble types.Early-type spirals remain comparatively poorly constrained.
- The cosmological interpretation remains open because the sample is limited relative to cosmic variance, while distorted kinematics and strongly concentrated two-component stellar systems remain difficult to analyse.
APPENDIX A:
Weak lensing measures galaxy mass distributions at projected distances beyond those reached by internal kinematics. Modeling tangential shear with a Burkert profile yields halo structural parameters, while the NFW fit is less satisfactory for the most luminous galaxies.
- Weak lensing probes galaxy mass distributions at projected source–lens distances up to 530 kpc, beyond internal kinematic measurements.
- The analysis uses azimuthally averaged tangential shear from about 10^5 isolated galaxies divided into five luminosity bins.
- A Burkert density profile provides an excellent fit to the tangential shear and yields the structural parameters rho_0 and r_0 through standard best-fitting techniques.
- For the most luminous galaxies, the NFW fit is marginally sufficient but less satisfactory than the Burkert fit, with reduced chi^2 = 2 in one reported case.
- At low luminosities, the Burkert and NFW models agree because the shear signal-to-noise is too low to discriminate between them.