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Register a new userCDM Substructure in Gravitational Lenses: Tests and Results
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C.S. Kochanek
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We use a simple statistical test to show that the anomalous flux ratios observed in gravitational lenses are created by gravitational perturbations from substructure rather than propagation effects in the interstellar medium or incomplete models for the gravitational potential of the lens galaxy. We review current estimates that the substructure represents between 0.6% and 7% (90% confidence) of the lens galaxy mass, and outline future observational programs which can improve the results.
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The flux anomalies in four-image gravitational lenses can be interpreted as evidence for the dark matter substructure predicted by cold dark matter (CDM) halo models. In principle, these flux anomalies could arise from alternate sources such as absorption, scattering or scintillation by the interstellar medium (ISM) of the lens galaxy, problems in the ellipsoidal macro models used to fit lens systems, or stellar microlensing. We apply several tests to the data that appear to rule out these alternate explanations. First, the radio flux anomalies show no significant dependence on wavelength, as would be expected for almost any propagation effect in the ISM or microlensing by the stars. Second, the flux anomaly distributions show the characteristic demagnifications of the brightest saddle point relative to the other images expected for low optical depth substructure, which cannot be mimicked by either the ISM or problems in the macro models. Microlensing by stars also cannot reproduce the suppression of the bright saddle points if the radio source sizes are consistent with the Compton limit for their angular sizes. Third, while it is possible to change the smooth lens models to fit the flux anomalies in some systems, we can rule out the necessary changes in all systems where we have additional lens constraints to check the models. Moreover, the parameters of these models are inconsistent with our present observations and expectations for the structure of galaxies. We conclude that low-mass halos remain the best explanation of the phenomenon.
The properties of multiple image gravitational lenses require a fractional surface mass density in satellites of f=0.02 (0.006 < f < 0.07 at 90% confidence) that is consistent with the expectations for CDM. The characteristic satellite mass scale, 10^6-10^9 Msun, is also consistent with the expectations for CDM. The agreement between the observed and expected density of CDM substructure shows that most low mass galactic satellites fail to form stars, and this absence of star formation explains the discrepancy between the number of observed Galactic satellites and CDM predictions rather than any modification to the CDM theory such as self-interacting dark matter or a warm dark matter component.
We devise a method to measure the abundance of satellite halos in gravitational lens galaxies, and apply our method to a sample of 7 lens systems. After using Monte Carlo simulations to verify the method, we find that substructure comprises fraction f=0.02 (median, 0.006<f<0.07 at 90% confidence) of the mass of typical lens galaxies, in excellent agreement with predictions of CDM simulations. We estimate a characteristic critical radius for the satellites of 0.0001<b/arcsec<0.006 (90% confidence). For a satellite mass function of dn/dM M^x with x=-1.8 and M_l<M<M_h, the critical radius provides an estimate that the upper mass limit is 10^6Msun < M_h < 10^9Msun. Our measurement confirms a generic prediction of CDM models, and may obviate the need to invoke alternatives to CDM like warm dark matter or self-interacting dark matter.
We show that most gravitational lenses lie on the passively evolving fundamental plane for early-type galaxies. For burst star formation models (1 Gyr of star formation, then quiescence) in low Omega_0 cosmologies, the stellar populations of the lens galaxies must have formed at z_f > 2. Typical lens galaxies contain modest amounts of patchy extinction, with a median differential extinction for the optical (radio) selected lenses of E(B-V) = 0.04 (0.07) mag. The dust can be used to determine both extinction laws and lens redshifts. For example, the z_l=0.96 elliptical lens in MG0414+0534 has an R_V=1.7 +/- 0.1 mean extinction law. Arc and ring images of the quasar and AGN source host galaxies are commonly seen in NICMOS H band observations. The hosts are typically blue, L < L_* galaxies.
We map the lensing-inferred substructure in the first three clusters observed by the Hubble Space Telescope Frontier Fields Initiative (HSTFF): Abell 2744 (z = 0.308), MACSJ0416, (z = 0.396) and MACSJ1149 (z = 0.543). Statistically resolving dark-matter subhaloes down to ~10^{9.5} solar masses, we compare the derived subhalo mass functions (SHMFs) to theoretical predictions from analytical models and with numerical simulations in a Lambda Cold Dark Matter (LCDM) cosmology. Mimicking our observational cluster member selection criteria in the HSTFF, we report excellent agreement in both amplitude and shape of the SHMF over four decades in subhalo mass (10^{9-13} solar masses). Projection effects do not appear to introduce significant errors in the determination of SHMFs from simulations. We do not find evidence for a substructure crisis, analogous to the missing satellite problem in the Local Group, on cluster scales, but rather excellent agreement of the count-matched HSTFF SHMF down to M_{sub halo}/M_{halo} ~ 10^{-5}. However, we do find discrepancies in the radial distribution of sub haloes inferred from HSTFF cluster lenses compared to determinations from simulated clusters. This suggests that although the selected simulated clusters match the HSTFF sample in mass, they do not adequately capture the dynamical properties and complex merging morphologies of these observed cluster lenses. Therefore, HSTFF clusters are likely observed in a transient evolutionary stage that is presently insufficiently sampled in cosmological simulations. The abundance and mass function of dark matter substructure in cluster lenses continues to offer an important test of the LCDM paradigm, and at present we find no tension between model predictions and observations.
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