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ABSTRACT The free-streaming length of dark matter depends on fundamental dark matter physics, and determines the abundance and concentration of dark matter haloes on sub-galactic scales. Using the image positions and flux ratios from eight quadruply imaged quasars, we constrain the free-streaming length of dark matter and the amplitude of the subhalo mass function (SHMF). We model both main deflector subhaloes and haloes along the line of sight, and account for warm dark matter free-streaming effects on the mass function and mass–concentration relation. By calibrating the scaling of the SHMF with host halo mass and redshift using a suite of simulated haloes, we infer a global normalization for the SHMF. We account for finite-size background sources, and marginalize over the mass profile of the main deflector. Parametrizing dark matter free-streaming through the half-mode mass mhm, we constrain the thermal relic particle mass mDM corresponding to mhm. At $$95 \, {\rm per\, cent}$$ CI: mhm < 107.8 M⊙ ($$m_{\rm {DM}} \gt 5.2 \ \rm {keV}$$). We disfavour $$m_{\rm {DM}} = 4.0 \,\rm {keV}$$ and $$m_{\rm {DM}} = 3.0 \,\rm {keV}$$ with likelihood ratios of 7:1 and 30:1, respectively, relative to the peak of the posterior distribution. Assuming cold dark matter, we constrain the projected mass in substructure between 106 and 109 M⊙ near lensed images. At $$68 \, {\rm per\, cent}$$ CI, we infer $$2.0{-}6.1 \times 10^{7}\, {{\rm M}_{\odot }}\,\rm {kpc^{-2}}$$, corresponding to mean projected mass fraction $$\bar{f}_{\rm {sub}} = 0.035_{-0.017}^{+0.021}$$. At $$95 \, {\rm per\, cent}$$ CI, we obtain a lower bound on the projected mass of $$0.6 \times 10^{7} \,{{\rm M}_{\odot }}\,\rm {kpc^{-2}}$$, corresponding to $$\bar{f}_{\rm {sub}} \gt 0.005$$. These results agree with the predictions of cold dark matter.
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Constraints on the mass-concentration relation of cold dark matter halos with 11 strong gravitational lenses
Abstract The mass-concentration relation of dark matter halos reflects the assembly history of objects in hierarchical structure formation scenarios, and depends on fundamental quantities in cosmology such as the slope of the primordial matter power-spectrum. This relation is unconstrained by observations on sub-galactic scales. We derive the first measurement of the mass-concentration relation using the image positions and flux ratios from eleven quadruple-image strong gravitational lenses (quads) in the mass range 106 − 1010M⊙, assuming cold dark matter. We model both subhalos and line of sight halos, finite-size background sources, and marginalize over nuisance parameters describing the lens macromodel. We also marginalize over the the logarithmic slope and redshift evolution of the mass-concentration relation, using flat priors that encompass the range of theoretical uncertainty in the literature. At z = 0, we constrain the concentration of 108M⊙ halos $$c=12_{-5}^{+6}$$ at $$68 \%$$ CI, and $$c=12_{-9}^{+15}$$ at $$95 \%$$ CI. For a 107M⊙ halo, we obtain $$68 \%$$ ($$95 \%$$) constraints $$c=15_{-8}^{+9}$$ ($$c=15_{-11}^{+18}$$), while for 109M⊙ halos $$c=10_{-4}^{+7}$$ ($$c=10_{-7}^{+14}$$). These results are consistent with the theoretical predictions from mass-concentration relations in the literature, and establish strong lensing by galaxies as a powerful probe of halo concentrations on sub-galactic scales across cosmological distance.
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- Award ID(s):
- 1714953
- PAR ID:
- 10175650
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society: Letters
- ISSN:
- 1745-3925
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/mnrasl/slz173
