Measuring the power spectrum of dark matter substructure using strong gravitational lensing

Gilbert Holder; Laurence Perreault Levasseur; Michael Kuhlen; Neal Dalal; Theodore Kisner; Yashar Hezaveh

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Measuring the power spectrum of dark matter substructure using strong gravitational lensing

Yashar Hezaveh, Neal Dalal, Gilbert Holder, Theodore Kisner, Michael Kuhlen, Laurence Perreault Levasseur

Cosmology and Nongalactic Astrophysics · Submitted 11 Mar 2014

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The authors' main claim In particular, we show that the power spectrum of projected density fluctuations in galaxy halos can be measured using strong gravitational lensing.

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arXiv ID1403.2720 (version 3)

Pith IDJ34BGLWV, Pith's permanent record of this paper and its review

CitationGilbert Holder, Laurence Perreault Levasseur, Michael Kuhlen, Neal Dalal, Theodore Kisner, Yashar Hezaveh. "Measuring the power spectrum of dark matter substructure using strong gravitational lensing." arXiv:1403.2720 (2014). https://pith.science/paper/J34BGLWV

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.94 · compares with prior results 0.27 · mentions code or data availability 0.02.

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In recent years, it has become possible to detect individual dark matter subhalos near images of strongly lensed extended background galaxies. Typically, only the most massive subhalos in the strong lensing region may be detected this way. In this work, we show that strong lenses may also be used to constrain the much more numerous population of lower mass subhalos that are too small to be detected individually. In particular, we show that the power spectrum of projected density fluctuations in galaxy halos can be measured using strong gravitational lensing. We develop the mathematical framework of power spectrum estimation, and test our method on mock observations. We use our results to determine the types of observations required to measure the substructure power spectrum with high significance. We predict that deep observations ($\sim10$ hours on a single target) with current facilities can measure this power spectrum at the $3\sigma$ level, with no apparent degeneracy with unknown clumpiness in the background source structure or fluctuations from detector noise. Upcoming ALMA measurements of strong lenses are capable of placing strong constraints on the abundance of dark matter subhalos and the underlying particle nature of dark matter.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In recent years, it has become possible to detect individual dark matter subhalos near images of strongly lensed extended background galaxies.	background 1.00	0.07	0.03	asserted 0.60
s1	Typically, only the most massive subhalos in the strong lensing region may be detected this way.	background 0.90	0.08	0.02	hedged possibility 0.96
s2	In this work, we show that strong lenses may also be used to constrain the much more numerous population of lower mass subhalos that are too small to be detected individually.	contribution 0.94	0.77	0.44	asserted 0.83
s3	In particular, we show that the power spectrum of projected density fluctuations in galaxy halos can be measured using strong gravitational lensing.	contribution 0.97	0.91	0.64	asserted 1.00
s4	We develop the mathematical framework of power spectrum estimation, and test our method on mock observations.	method 0.84	0.96	0.04	asserted 0.99
s5	We use our results to determine the types of observations required to measure the substructure power spectrum with high significance.	contribution 0.61	0.90	0.12	asserted 0.98
s6	We predict that deep observations ($\sim10$ hours on a single target) with current facilities can measure this power spectrum at the $3\sigma$ level, with no apparent degeneracy with unknown clumpiness in the background source structure or fluctuations from detector noise.	result 0.92	0.82	0.40	asserted 0.57
s7	Upcoming ALMA measurements of strong lenses are capable of placing strong constraints on the abundance of dark matter subhalos and the underlying particle nature of dark matter.	interpretation 0.70	0.21	0.18	hedged possibility 0.77

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.83.

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The paper

Original abstract

In recent years, it has become possible to detect individual dark matter subhalos near images of strongly lensed extended background galaxies. Typically, only the most massive subhalos in the strong lensing region may be detected this way. In this work, we show that strong lenses may also be used to constrain the much more numerous population of lower mass subhalos that are too small to be detected individually. In particular, we show that the power spectrum of projected density fluctuations in galaxy halos can be measured using strong gravitational lensing. We develop the mathematical framework of power spectrum estimation, and test our method on mock observations. We use our results to determine the types of observations required to measure the substructure power spectrum with high significance. We predict that deep observations ($\sim10$ hours on a single target) with current facilities can measure this power spectrum at the $3\sigma$ level, with no apparent degeneracy with unknown clumpiness in the background source structure or fluctuations from detector noise. Upcoming ALMA measurements of strong lenses are capable of placing strong constraints on the abundance of dark matter subhalos and the underlying particle nature of dark matter.

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References

Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Through Ups and Downs: the Transient Lensing Behaviour of SIDM halos undergoing Core Collapse
astro-ph.CO 2026-11 conditional novelty 8.0 of 10

The lensing efficacy of a collapsing SIDM halo peaks early in core collapse and then declines below its initial NFW level, so steep central cusps are poor surrogate models.
Mapping the Information Geometry of an Unresolved Dark Matter Population using a Differentiable Strong Lensing Simulator
astro-ph.CO 2026-08 conditional novelty 7.0 of 10

Using a differentiable strong-lensing simulator and Fisher information geometry, the paper shows that flexible source models absorb most unresolved dark matter substructure signal across a broad range of scales, and t...
Mining for Dark Matter Substructure: Inferring subhalo population properties from strong lenses with machine learning
astro-ph.CO 2019-09 conditional novelty 7.0 of 10

A neural likelihood ratio estimator trained on simulated strong lensing images can infer the abundance and mass slope of dark matter subhalos from an ensemble of lenses.
Prospects for probing dark matter with filamentary 21cm emission
astro-ph.CO 2026-09 accept novelty 6.0 of 10

Direct imaging of individual cosmic filaments with 21cm emission cannot distinguish CDM from WDM using current or planned SKA-Low facilities due to beam smearing and sensitivity limits.
Not so fuzzy: excluding FDM with sizes and stellar kinematics of ultra-faint dwarf galaxies
astro-ph.CO 2022-03 conditional novelty 6.0 of 10

Stellar kinematics and sizes of Segue 1 and Segue 2 exclude fuzzy dark matter lighter than 3×10^-19 eV at 99% confidence, closing the window where FDM differs from CDM.

Show 5 more citing papers

CMB-HD: An Ultra-Deep, High-Resolution Millimeter-Wave Survey Over Half the Sky
astro-ph.CO 2019-06 conditional novelty 6.0 of 10

A white paper proposes CMB-HD, a two-telescope 30-meter millimeter survey over half the sky, with published Fisher forecasts reaching sigma(N_eff)=0.014, sigma(f_NL)=0.26, and 8-sigma discrimination of suppressed smal...
Detection of lensing substructure using ALMA observations of the dusty galaxy SDP.81
astro-ph.CO 2016-01 conditional novelty 6.0 of 10

A joint fit to ALMA band 6 and band 7 visibilities of the lensed galaxy SDP.81 reveals a dark subhalo of about 10^9 solar masses at 6.9 sigma, and sets upper limits on the abundance of smaller subhalos down to about 2...
There is No Missing Satellites Problem
astro-ph.CO 2017-11 conditional novelty 5.0 of 10

Once SDSS's incomplete sky and volume coverage are accounted for, the Milky Way's luminous satellite count matches cold dark matter predictions, and the corrected counts exclude thermal relic warm dark matter below ro...
Axion dark matter, solitons, and the cusp-core problem
astro-ph.CO 2015-02 conditional novelty 5.0 of 10

Fitting a soliton-core plus NFW-halo profile to Fornax and Sculptor stellar kinematics requires the axion mass to be below 1.1 x 10^-22 eV if ultra-light axions are to explain dwarf galaxy cores.
Snowmass2021 CMB-HD White Paper
astro-ph.CO 2022-03 unverdicted novelty 3.0 of 10

The paper proposes a 30-meter-class CMB survey and argues that its forecast sensitivity would probe dark matter, light relics, inflation, neutrino mass, and dark energy.

How later papers used it

74 later papers cite it

Evidence: substantial. 65 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

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2 later papers by other authors are listed below: 1 built on it and 1 used its method or tool.

Builds on it 1 of 2 papers with this label

Extended this paper's initial approach to include subhalo populations that are not necessarily isotropic and homogeneous and to take into account the 2-subhalo term.

On the Power Spectrum of Dark Matter Substructure in Strong Gravitational Lenses (2017) · 1.00 · paraphrased: the licence does not allow quoting

Uses its method or tool 1 of 2 papers with this label

Used this paper's expression for the surface density power spectrum as an integral over the mass function weighted by the surface density profile, assuming negligible spatial correlation between subhalos.

Analytic approach to astrometric perturbations of critical curves by substructures (2023) · 0.92 · paraphrased: the licence does not allow quoting

How the literature uses it

40 arXiv papers cite this in 67 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 50 sentences without a confident label

Builds on it 2 papers

We extend the initial approach presented in Ref. [ref] to include subhalo populations that are not necessarily isotropic and homogeneous, and also take into account the 2-subhalo term.

On the Power Spectrum of Dark Matter Substructure in Strong Gravitational Lenses · Introduction · 1.00
An analogous statistical method has been used before in weak gravitational lensing of the Cosmic Microwave Background radiation (e.g., [ref] , [ref] ), although we have further generalized it to the case of strong galaxy-galaxy lensing but without any assumptions of linear first order approximation in the formalism which goes beyond the current statistical methodology available in the literature (see 2012 BSc thesis of Sander Bus[https://www.astro.rug.nl/opleidingsinstituut/reports/bachelor/]; [ref] ).

The inner mass power spectrum of galaxies using strong gravitational lensing: beyond linear approximation · Introduction · 0.97

Uses its method or tool 1 paper

Using the halo formalism [ref] and assuming that the spatial correlation between subhalos can be negligible (i.e., subhalos are randomly distributed), we can compute the surface density power spectrum as an integral over the mass function weighted by their surface density profile as [ref] P_δκ(k)=∫^M_max_M_min d n^2D/d M|κ̃_M(k)|^2 d M, where $k=√(k_x^2+k_y^2)$, $M_min$ and $M_max$ are the minimum and maximum mass of subhalos, respectively, $d n^2D/d M$ is the surface number density of subhalos with masses of $[M, M+δM]$, and $κ̃_M(k)$ is the Fourier transform of the convergence $κ_M$ provided by a subhalo of mass $M$.

Analytic approach to astrometric perturbations of critical curves by substructures · Fluctuations of macrocritical curves · 0.92

Compares with it 1 paper

While our general approach follows a similar philosophy to that of Ref. [ref] , our computational technique differs at several levels, especially in our use of a mode function-based approach.

Beyond subhalos: Probing the collective effect of the Universe's small-scale structure with gravitational lensing · Introduction · 0.88

Cites it as background 9 papers

As for the surface density power spectrum, previous studies have proposed the expressions for the different types of substructures such as CDM subhalos [ref] and quantum clumps of FDM [ref] .

Analytic approach to astrometric perturbations of critical curves by substructures · Introduction · 0.83
$P_δ(k)$ is the observational realization of the substructure convergence power spectrum $P_κ(k)$ – the power spectrum of the projected dark matter density field – which [ref] first proposed as a lensing observable and [ref] computed analytically for galaxy-scale systems, showing sensitivity to CDM, warm dark matter, and self-interacting dark matter.

Statistical imprints of wave-like dark matter on multiply-imaged galaxies in strong cluster lenses from JWST · Physical interpretation · 0.83
The idea of using the subhalo convergence power spectrum [ref] was developed as a statistical detection method to obtain population-level constraints without having to individually resolve clumps.

Quantifying the Line-of-Sight Halo Contribution to the Dark Matter Convergence Power Spectrum from Strong Gravitational Lenses · Conclusions · 0.86

What it cites · 2 sentences without a confident label

Cites as background 2 papers

The distribution of substructure in ordinary galactic halos has been studied extensively in the literature [ref] .

The Diversity and Similarity of Simulated Cold Dark Matter Halos · The projected substructure power spectrum in dark matter halos · 1.00
The distribution of substructure in ordinary galactic halos has been studied extensively in the literature [ref] .

Formation and evolution of galaxy dark matter halos and their substructure · The projected substructure power spectrum in dark matter halos · 1.00

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