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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An unexpected high concentration for the dark substructure in the gravitational lens SDSSJ0946+1006
ABSTRACT The presence of an invisible substructure has previously been detected in the gravitational lens galaxy SDSSJ0946+1006 through its perturbation of the lensed images. Using flexible models for the main halo and the subhalo perturbation, we demonstrate that the subhalo has an extraordinarily high central density and steep density slope. We robustly infer the subhalo’s projected mass within 1 kpc to be ∼2–3.7 × 109 M⊙ at >95 per cent CL for all our lens models, while the average log-slope of the subhalo’s projected density profile over the radial range 0.75–1.25 kpc is constrained to be steeper than isothermal (γ2D ≲ −1). By modeling the subhalo light, we infer a conservative upper bound on its luminosity LV < 1.2 × 108L⊙ at 95 per cent CL that shows that the perturber is dark matter dominated. We analyse lensing galaxy analogues in the Illustris TNG100-1 simulation over many lines of sight, and find hundreds of subhalos that achieve a mass within 1 kpc ≳ 2 × 109M⊙. However, less than 1 per cent of the mock observations yield a log-slope steep enough to be consistent with our lensing models, and they all have stellar masses exceeding that allowed by observations by an order of magnitude or more. We conclude that the presence of such a dark highly concentrated subhalo is unexpected in a Lambda cold dark matter universe. While it remains to be determined whether this tension can be reduced by adding more complexity to the primary lens model, it is not significantly alleviated if the perturber is assumed to be a LOS structure, rather than a subhalo.
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- NSF-PAR ID:
- 10334136
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 507
- Issue:
- 2
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- 1662 to 1683
- 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/mnras/stab2247
