Probing dark matter structure down to 107 solar masses: flux ratio statistics in gravitational lenses with line-of-sight haloes

Abstract Strong lensing provides a powerful means of investigating the nature of dark matter as it probes dark matter structure on sub-galactic scales. We present an extension of a forward modelling framework that uses flux ratios from quadruply imaged quasars (quads) to measure the shape and amplitude of the halo mass function, including line-of-sight (LOS) haloes and main deflector subhaloes. We apply this machinery to 50 mock lenses – roughly the number of known quads – with warm dark matter (WDM) mass functions exhibiting free-streaming cut-offs parametrized by the half-mode mass mhm. Assuming cold dark matter (CDM), we forecast bounds on mhm and the corresponding thermal relic particle masses over a range of tidal destruction severity, assuming a particular WDM mass function and mass–concentration relation. With significant tidal destruction, at 2σ we constrain $m_{\rm {hm}}\lt 10^{7.9} \left(10^{8.4}\right) \, \mathrm{M}_{\odot }$, or a 4.4 (3.1) keV thermal relic, with image flux uncertainties from measurements and lens modelling of $2{{\ \rm per\ cent}} \left(6{{\ \rm per\ cent}}\right)$. With less severe tidal destruction we constrain $m_{\rm {hm}}\lt 10^{7} \left(10^{7.4}\right) \, \mathrm{M}_{\odot }$, or an 8.2 (6.2) keV thermal relic. If dark matter is warm, with $m_{\rm {hm}} = 10^{7.7} \, \mathrm{M}_{\odot }$ (5.1 keV), we would favour WDM with $m_{\rm {hm}} \gt 10^{7.7} \, \mathrm{M}_{\odot }$ over CDM with relative likelihoods of 22:1 and 8:1 with flux uncertainties of $2{{\ \rm per\ cent}}$ and $6{{\ \rm per\ cent}}$, respectively. These bounds improve over those obtained by modelling only main deflector subhaloes because LOS objects produce additional flux perturbations, especially for high-redshift systems. These results indicate that ∼50 quads can conclusively differentiate between WDM and CDM.

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Warm dark matter chills out: constraints on the halo mass function and the free-streaming length of dark matter with eight quadruple-image strong gravitational lenses

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz3480 ◽

2019 ◽

Vol 491 (4) ◽

pp. 6077-6101 ◽

Cited By ~ 24

Author(s):

Daniel Gilman ◽

Simon Birrer ◽

Anna Nierenberg ◽

Tommaso Treu ◽

Xiaolong Du ◽

...

Keyword(s):

Dark Matter ◽

Mass Fraction ◽

Mass Concentration ◽

Cold Dark Matter ◽

Finite Size ◽

Mass Function ◽

Line Of Sight ◽

Gravitational Lenses ◽

Likelihood Ratios ◽

Mass Profile

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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Clues to the nature of dark matter from first galaxies

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1924 ◽

2019 ◽

Vol 489 (1) ◽

pp. 487-496 ◽

Cited By ~ 1

Author(s):

Boyan K Stoychev ◽

Keri L Dixon ◽

Andrea V Macciò ◽

Marvin Blank ◽

Aaron A Dutton

Keyword(s):

Dark Matter ◽

Star Formation ◽

Galaxy Formation ◽

Cold Dark Matter ◽

High Redshift ◽

Formation Rate ◽

Neutral Hydrogen ◽

Mass Function ◽

Stellar Mass ◽

The Impact

ABSTRACT We use 38 high-resolution simulations of galaxy formation between redshift 10 and 5 to study the impact of a 3 keV warm dark matter (WDM) candidate on the high-redshift Universe. We focus our attention on the stellar mass function and the global star formation rate and consider the consequences for reionization, namely the neutral hydrogen fraction evolution and the electron scattering optical depth. We find that three different effects contribute to differentiate warm and cold dark matter (CDM) predictions: WDM suppresses the number of haloes with mass less than few 109 M⊙; at a fixed halo mass, WDM produces fewer stars than CDM, and finally at halo masses below 109 M⊙, WDM has a larger fraction of dark haloes than CDM post-reionization. These three effects combine to produce a lower stellar mass function in WDM for galaxies with stellar masses at and below 107 M⊙. For z > 7, the global star formation density is lower by a factor of two in the WDM scenario, and for a fixed escape fraction, the fraction of neutral hydrogen is higher by 0.3 at z ∼ 6. This latter quantity can be partially reconciled with CDM and observations only by increasing the escape fraction from 23 per cent to 34 per cent. Overall, our study shows that galaxy formation simulations at high redshift are a key tool to differentiate between dark matter candidates given a model for baryonic physics.

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The normalization and slope of the dark matter (sub-)halo mass function on sub-galactic scales

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa341 ◽

2020 ◽

Vol 493 (1) ◽

pp. 1268-1276

Author(s):

Andrew J Benson

Keyword(s):

Dark Matter ◽

Gravitational Lensing ◽

Cold Dark Matter ◽

Mass Range ◽

Mass Function ◽

Matter Content ◽

Dark Matter Halo ◽

Halo Masses ◽

Near Future ◽

Mass Functions

ABSTRACT Simulations of cold dark matter make robust predictions about the slope and normalization of the dark matter halo and subhalo mass functions on small scales. Recent observational advances utilizing strong gravitational lensing have demonstrated the ability of this technique to place constraints on these quantities on subgalactic scales corresponding to dark matter halo masses of 106–$10^9\, \mathrm{M}_\odot$. On these scales the physics of baryons, which make up around 17 per cent of the matter content of the Universe but which are not included in pure dark matter N-body simulations, are expected to affect the growth of structure and the collapse of dark matter haloes. In this work, we develop a semi-analytic model to predict the amplitude and slope of the dark matter halo and subhalo mass functions on subgalactic scales in the presence of baryons. We find that the halo mass function is suppressed by up to 25 per cent, and the slope is modified, ranging from −1.916 to −1.868 in this mass range. These results are consistent with current measurements, but differ sufficiently from the expectations for a dark matter only universe that it may be testable in the near future.

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Low-mass halo perturbations in strong gravitational lenses at redshift z ∼ 0.5 are consistent with CDM

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz464 ◽

2019 ◽

Vol 485 (2) ◽

pp. 2179-2193 ◽

Cited By ~ 19

Author(s):

E Ritondale ◽

S Vegetti ◽

G Despali ◽

M W Auger ◽

L V E Koopmans ◽

...

Keyword(s):

Dark Matter ◽

Cold Dark Matter ◽

Detection Threshold ◽

Current Data ◽

Gravitational Lens ◽

Detection Sensitivity ◽

Line Of Sight ◽

Gravitational Lenses ◽

Lepton Asymmetry ◽

Low Mass

ABSTRACT We use a sample of 17 strong gravitational lens systems from the BELLS GALLERY survey to quantify the amount of low-mass dark matter haloes within the lensing galaxies and along their lines of sight, and to constrain the properties of dark matter. Based on a detection criterion of 10σ, we report no significant detection in any of the lenses. Using the sensitivity function at the 10σ level, we have calculated the predicted number of detectable cold dark matter (CDM) line-of-sight haloes to be μl = 1.17 ± 1.08, in agreement with our null detection. Assuming a detection sensitivity that improved to the level implied by a 5σ threshold, the expected number of detectable line-of-sight haloes rises to μl = 9.0 ± 3.0. Whilst the current data find zero detections at this sensitivity level (which has a probability of P$^{{\rm 5}\sigma }_{{\rm CDM}}(n_{\rm det}=0)$ = 0.0001 and would be in strong tension with the CDM framework), we find that such a low-detection threshold leads to many spurious detections and non-detections and therefore the current lack of detections is unreliable and requires data with improved sensitivity. Combining this sample with a subsample of 11 SLACS lenses, we constrain the half-mode mass to be log (Mhm) < 12.26 at the 2σ level. The latter is consistent with resonantly produced sterile neutrino masses ms < 0.8 keV at any value of the lepton asymmetry at the 2σ level.

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Inference of the cold dark matter substructure mass function at z = 0.2 using strong gravitational lenses

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stu943 ◽

2014 ◽

Vol 442 (3) ◽

pp. 2017-2035 ◽

Cited By ~ 83

Author(s):

S. Vegetti ◽

L. V. E. Koopmans ◽

M. W. Auger ◽

T. Treu ◽

A. S. Bolton

Keyword(s):

Dark Matter ◽

Cold Dark Matter ◽

Mass Function ◽

Gravitational Lenses

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Halo concentration strengthens dark matter constraints in galaxy-galaxy strong lensing analyses

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab3527 ◽

2021 ◽

Author(s):

Nicola C Amorisco ◽

James Nightingale ◽

Qiuhan He ◽

Aristeidis Amvrosiadis ◽

Xiaoyue Cao ◽

...

Keyword(s):

Dark Matter ◽

Cold Dark Matter ◽

Large Population ◽

Dark Matter Particle ◽

Mass Function ◽

Gravitational Lenses ◽

High Concentration ◽

Expected Number ◽

Order Of Magnitude ◽

Low Mass

Abstract A defining prediction of the cold dark matter (CDM) cosmological model is the existence of a very large population of low-mass haloes. This population is absent in models in which the dark matter particle is warm (WDM). These alternatives can, in principle, be distinguished observationally because halos along the line-of-sight can perturb galaxy-galaxy strong gravitational lenses. Furthermore, the WDM particle mass could be deduced because the cut-off in their halo mass function depends on the mass of the particle. We systematically explore the detectability of low-mass haloes in WDM models by simulating and fitting mock lensed images. Contrary to previous studies, we find that halos are harder to detect when they are either behind or in front of the lens. Furthermore, we find that the perturbing effect of haloes increases with their concentration: detectable haloes are systematically high-concentration haloes, and accounting for the scatter in the mass-concentration relation boosts the expected number of detections by as much as an order of magnitude. Haloes have lower concentration for lower particle masses and this further suppresses the number of detectable haloes beyond the reduction arising from the lower halo abundances alone. Taking these effects into account can make lensing constraints on the value of the mass function cut-off at least an order of magnitude more stringent than previously appreciated.

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Out of sight, out of mind? The impact of correlated clustering in substructure lensing

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab448 ◽

2021 ◽

Author(s):

Alexandres Lazar ◽

James S Bullock ◽

Michael Boylan-Kolchin ◽

Robert Feldmann ◽

Onur Çatmabacak ◽

...

Keyword(s):

Dark Matter ◽

Principal Axis ◽

Major Axis ◽

Line Of Sight ◽

Gravitational Lenses ◽

Local Clustering ◽

Analytic Expression ◽

Halo Masses ◽

The Impact

Abstract A promising route for revealing the existence of dark matter structures on mass scales smaller than the faintest galaxies is through their effect on strong gravitational lenses. We examine the role of local, lens-proximate clustering in boosting the lensing probability relative to contributions from substructure and unclustered line-of-sight (LOS) haloes. Using two cosmological simulations that can resolve halo masses of Mhalo ≃ 109 M⊙ (in a simulation box of length Lbox ∼ 100 Mpc) and 107 M⊙ (Lbox ∼ 20 Mpc), we demonstrate that clustering in the vicinity of the lens host produces a clear enhancement relative to an assumption of unclustered haloes that persists to >20 Rvir. This enhancement exceeds estimates that use a two-halo term to account for clustering, particularly within 2 − 5 Rvir. We provide an analytic expression for this excess, clustered contribution. We find that local clustering boosts the expected count of 109 M⊙ perturbing haloes by ${\sim }35{{\ \rm per\ cent}}$ compared to substructure alone, a result that will significantly enhance expected signals for low-redshift (zl ≃ 0.2) lenses, where substructure contributes substantially compared to LOS haloes. We also find that the orientation of the lens with respect to the line of sight (e.g. whether the line of sight passes through the major axis of the lens) can also have a significant effect on the lensing signal, boosting counts by an additional $\sim 50{{\ \rm per\ cent}}$ compared to a random orientations. This could be important if discovered lenses are biased to be oriented along their principal axis.

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Probing non-spherical dark halos in the Galactic dwarf satellites

Proceedings of the International Astronomical Union ◽

10.1017/s1743921313006789 ◽

2013 ◽

Vol 9 (S298) ◽

pp. 411-411

Author(s):

Kohei Hayashi ◽

Masashi Chiba

Keyword(s):

Dark Matter ◽

Cold Dark Matter ◽

Milky Way ◽

Velocity Dispersion ◽

Line Of Sight ◽

Spherical Structure ◽

Spherical Models ◽

Galactic Satellites ◽

Best Fitting

AbstractWe construct axisymmetric mass models for dwarf spheroidal (dSph) galaxies in the Milky Way to obtain realistic limits on the non-spherical structure of their dark halos. This is motivated by the fact that the observed luminous parts of the dSphs are actually non-spherical and cold dark matter models predict non-spherical virialized dark halos on sub-galactic scales. Applying these models to line-of-sight velocity dispersion profiles along three position angles in six Galactic satellites, we find that the best fitting cases for most of the dSphs yield not spherical but oblate and flattened dark halos. We also find that the mass of the dSphs enclosed within inner 300 pc varies depending on their total luminosities, contrary to the conclusion of previous spherical models. This suggests the importance of considering non-spherical shapes of dark halos in dSph mass models.

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