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Register a new userBreaking the Disk/Halo Degeneracy with Gravitational Lensing
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The degeneracy between the disk and the dark matter contribution to galaxy rotation curves remains an important uncertainty in our understanding of disk galaxies. Here we discuss a new method for breaking this degeneracy using gravitational lensing by spiral galaxies, and apply this method to the spiral lens B1600+434 as an example. The combined image and lens photometry constraints allow models for B1600+434 with either a nearly singular dark matter halo, or a halo with a sizable core. A maximum disk model is ruled out with high confidence. Further information, such as the circular velocity of this galaxy, will help break the degeneracies. Future studies of spiral galaxy lenses will be able to determine the relative contribution of disk, bulge, and halo to the mass in the inner parts of galaxies.
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The degeneracy among the disk, bulge and halo contributions to galaxy rotation curves prevents an understanding of the distribution of baryons and dark matter in disk galaxies. In an attempt to break this degeneracy, we present an analysis of the spiral galaxy strong gravitational lens SDSS J2141-0001, discovered as part of the SLACS survey. We present new Hubble Space Telescope multicolor imaging, gas and stellar kinematics data derived from long-slit spectroscopy, and K-band LGS adaptive optics imaging, both from the Keck telescopes. We model the galaxy as a sum of concentric axisymmetric bulge, disk and halo components and infer the contribution of each component, using information from gravitational lensing and gas kinematics. This analysis yields a best-fitting total (disk plus bulge) stellar mass of log_{10}(Mstar/Msun) = 10.99(+0.11,-0.25). The photometric data combined with stellar population synthesis models yield log_{10}(Mstar/Msun) = 10.97pm0.07, and 11.21pm0.07 for the Chabrier and Salpeter IMFs, respectively. Accounting for the expected gas fraction of simeq 20% reduces the lensing plus kinematics stellar mass by 0.10pm0.05 dex, resulting in a Bayes factor of 11.9 in favor of a Chabrier IMF. The dark matter halo is roughly spherical, with minor to major axis ratio q_{halo}=0.91(+0.15,-0.13). The dark matter halo has a maximum circular velocity of V_{max}=276(+17,-18) km/s, and a central density parameter of log_{10}Delta_{V/2}=5.9(+0.9,-0.5). This is higher than predicted for uncontracted dark matter haloes in LCDM cosmologies, log_{10}Delta_{V/2}=5.2, suggesting that either the halo has contracted in response to galaxy formation, or that the halo has a higher than average concentration. At 2.2 disk scale lengths the dark matter fraction is f_{DM}=0.55(+0.20,-0.15), suggesting that SDSS J2141-0001 is sub-maximal.
The mass-sheet degeneracy is a well-known problem in gravitational lensing which limits our capability to infer astrophysical lens properties or cosmological parameters from observations. As the number of gravitational wave observations grows, detecting lensed events will become more likely, and to assess how the mass-sheet degeneracy may affect them is crucial. Here we study both analytically and numerically how the lensed waveforms are affected by the mass-sheet degeneracy computing the amplification factor from the diffraction integral. In particular, we differentiate between the geometrical optics, wave optics and interference regimes, focusing on ground-based gravitational waves detectors. In agreement with expectations of gravitational lensing of electromagnetic radiation, we confirm how, in the geometrical optics scenario, the mass-sheet degeneracy cannot be broken with only one lensed image. However, we find that in the interference regime, and in part in the wave-optics regime, the mass-sheet degeneracy can be broken with only one lensed waveform thanks to the characteristic interference patterns of the signal. Finally, we quantify, through template matching, how well the mass-sheet degeneracy can be broken. We find that, within present GW detector sensitivities and considering signals as strong as those which have been detected so far, the mass-sheet degeneracy can lead to a $1sigma$ uncertainty on the lens mass of $sim 12%$. With these values the MSD might still be a problematic issue. But in case of signals with higher signal-to-noise ratio, the uncertainty can drop to $sim 2%$, which is less than the current indeterminacy achieved by dynamical mass measurements.
In this review, I discuss the use of galaxy-galaxy weak lensing measurements to study the masses of dark matter halos in which galaxies reside. After summarizing how weak gravitational lensing measurements can be interpreted in terms of halo mass, I review measurements that were used to derive the relationship between optical galaxy mass tracers, such as stellar mass or luminosity, and dark matter halo mass. Measurements of galaxy-galaxy lensing from the past decade have led to increasingly tight constraints on the connection between dark matter halo mass and optical mass tracers, including both the mean relationships between these quantities and the intrinsic scatter between them. I also review some of the factors that can complicate analysis, such as the choice of modeling procedure, and choices made when dividing up samples of lens galaxies.
We use the relations between aperture stellar velocity dispersion (sigma_ap), stellar mass (M_sps), and galaxy size (R_e) for a sample of sim 150,000 early-type galaxies from SDSS/DR7 to place constraints on the stellar initial mass function (IMF) and dark halo response to galaxy formation. We build LCDM based mass models that reproduce, by construction, the relations between galaxy size, light concentration and stellar mass, and use the spherical Jeans equations to predict sigma_ap. Given our model assumptions (including those in the stellar population synthesis models), we find that reproducing the median sigma_ap vs M_sps relation is not possible with {it both} a universal IMF and a universal dark halo response. Significant departures from a universal IMF and/or dark halo response are required, but there is a degeneracy between these two solutions. We show that this degeneracy can be broken using the strength of the correlation between residuals of the velocity-mass (Delta log sigma_ap) and size-mass (Delta log R_e) relations. The slope of this correlation, d_vr equiv Delta log sigma_ap/Delta log R_e, varies systematically with galaxy mass from d_vr simeq -0.45 at M_sps sim 10^{10}M_sun, to d_vr simeq -0.15 at M_sps sim 10^{11.6} M_sun. The virial fundamental plane (FP) has d_vr=-1/2, and thus we find the tilt of the observed FP is mass dependent. Reproducing this tilt requires {it both} a non-universal IMF and a non-universal halo response. Our best model has mass-follows-light at low masses (Msps < 10^{11.2}M_sun) and unmodified NFW haloes at M_sps sim 10^{11.5} M_sun. The stellar masses imply a mass dependent IMF which is lighter than Salpeter at low masses and heavier than Salpeter at high masses.
(abridged) We have measured line-of-sight velocity profiles (VPs) in the E0 galaxy NGC 6703 out to 2.6 R_e. From these data we constrain the mass distribution and the anisotropy of the stellar orbits in this galaxy. We have developed a non-parametric technique to determine the DF f(E,L^2) directly from the kinematic data. From Monte Carlo tests using the spatial extent, sampling, and error bars of the NGC 6703 data we find that smooth underlying DFs can be recovered to an rms accuracy of 12%, and the anisotropy parameter beta(r) to an accuracy of 0.1, in a given potential. An asymptotically constant halo circular velocity v_0 can be determined with an accuracy of +- lta 50km/s. For NGC 6703 we determine the true circular velocity at 2.6 R_e to be 250 +- 40km/s at 95% c.l., corresponding to a total mass in NGC 6703 inside 78 (13.5 h_50^-1 kpc), of 1.6-2.6 x 10^11 h_50^-1 Msun. No model without dark matter will fit the data; however, a maximum stellar mass model in which the luminous component provides nearly all the mass in the centre does. In such a model, the total luminous mass inside 78 is 9 x 10^10 Msun and the integrated M/L_B=5.3-10, corresponding to a rise from the center by at least a factor of 1.6. The anisotropy of the stellar distribution function in NGC 6703 changes from near-isotropic at the centre to slightly radially anisotropic (beta=0.3-0.4 at 30, beta=0.2-0.4 at 60) and is not well-constrained at the outer edge of the data. Our results suggest that also elliptical galaxies begin to be dominated by dark matter at radii of sim 10kpc.
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