Complementary Planetary Spectroscopy Probes of Dark Matter

Carlos Blanco; Joshua Tong; Marianne Moore; Rebecca K. Leane

REVIEW 4 major objections 5 minor 1 cited by

Complementary Planetary Spectroscopy Probes of Dark Matter

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Existing UV airglow measurements of Jupiter and Saturn could place the strongest current limits on sub-GeV dark matter scattering, even when annihilation goes through a heavy mediator.

desk verdict A genuinely useful framework for planetary DM energy deposition with a serious unaddressed problem in the UV airglow constraints: they count annihilation below the homopause that cannot contribute to the observed emission. read the letter →

arxiv 2508.00980 v2 pith:VEN2K7DQ submitted 2025-08-01 hep-ph astro-ph.EPastro-ph.HE

Carlos Blanco , Rebecca K. Leane , Marianne Moore , Joshua Tong This is my paper

classification hep-phastro-ph.EPastro-ph.HE PACS 95.35.+d

keywords darkmattercaptureplanetaryUVairglowsub-GeVinternalheatflowlong-livedmediatorsgasgiantatmospheresspin-dependentscattering

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that planets can act as dark matter detectors: dark matter that scatters off planetary material and is captured can annihilate, and the energy it injects shows up as ultraviolet nightglow from molecular hydrogen in the atmosphere or as excess heat flowing from the interior. The authors compare predicted annihilation power with existing UV airglow and internal heat measurements for Earth, the gas giants, the ice giants, and a hypothetical Super-Jupiter, and derive constraints on dark matter-nucleon scattering. Their headline result is that for sub-GeV dark matter annihilating through a heavy mediator, ultraviolet airglow limits from Jupiter and Saturn on both spin-independent and spin-dependent proton scattering surpass current direct detection limits, because a portion of the captured dark matter sits in the isothermal upper atmosphere and annihilates there. A sympathetic reader would care because this would mean the strongest current limits on the lightest dark matter masses come from planetary observations already in hand, not from new underground detectors.

What carries the argument

The load-bearing quantity is the atmospheric annihilation fraction $f_{\rm atm}$, the share of dark matter annihilation events that deposit energy in the atmosphere, defined through an integral over the squared normalized dark matter density profile $G_\chi(r)$. The profile itself combines a local-thermal-equilibrium interior distribution with an isothermal atmospheric extension at the planet's surface temperature (Eq. 9), truncated at a mass-dependent radius $R_{\rm max}$ (Eq. 10), with the two limiting regimes blended according to the Knudsen number, the ratio of the dark matter mean free path to its scale radius. This machinery makes the paper's central effect possible: light dark matter extends into the rarefied atmosphere, so a substantial fraction of captured particles annihilate there and produce UV airglow even when the mediator is heavy.

What would settle it

Run a full atmospheric simulation of the exobase region for Jupiter or Saturn, including vertical mixing, winds, and momentum transfer from dark matter scattering, and compare the steady-state captured dark matter density above the 1-bar surface with the isothermal extension of Eq. 9. If the atmosphere depletes the dark matter population by a factor of two or more, the headline sub-GeV airglow constraints weaken by the same factor; if the population survives, the constraints stand.

Watch

Extended reading notes

Core claim

The paper's central claim is that the energy injected by dark matter annihilation inside a planet can be separated into an atmospheric fraction and an interior fraction, computable from the dark matter radial profile, the planet's temperature and density structure, and the mediator's decay length, and that comparing these fractions with observed UV airglow and internal heat flow produces dark matter constraints. Even when annihilation goes through a heavy mediator, more than ten percent of captured sub-GeV dark matter annihilates in the atmosphere because a thermalized population resides in the upper atmosphere, which is treated as an isothermal layer at the planet's surface temperature. The resulting hydrogen Lyman and Werner band emission is bounded by Voyager and New Horizons nightglow data for the giant planets, giving Jupiter and Saturn the best current limits on spin-independent (scattering independent of nuclear spin) and spin-dependent proton (scattering on unpaired proton spin) interactions below about a GeV. For light, long-lived mediators, planets of different radii probe different decay lengths, so the ensemble of Earth, ice giants, and gas giants maps out mediator parameter space in a way that complements collider long-lived particle searches.

Load-bearing premise

The results assume captured dark matter in the atmosphere follows an isothermal distribution at the planet's surface temperature, truncated at a mass-dependent radius; if that atmospheric population is depleted by winds, incomplete thermalization, or a different boundary treatment, the airglow limits weaken in proportion to the lost annihilation fraction.

Editorial extensions

If this is right

Existing Jupiter and Saturn UV nightglow data constrain sub-GeV dark matter-nucleon scattering more strongly than current direct detection experiments, so a first test of this mass range requires no new instrumentation.
The airglow channel opens parameter space for strongly interacting dark matter subcomponents that never reach underground detectors, and for spin-dependent neutron-only scattering that cosmology cannot constrain.
Planets of different radii are sensitive to different mediator decay lengths, so the Solar System ensemble and future Super-Jupiters map out light-mediator parameter space in a way that complements long-lived particle collider searches.
A free-floating Super-Jupiter could extend the same techniques: UV airglow observations project new sub-GeV sensitivity, and internal heat observations near the Galactic Center project sensitivity to large, previously untested cross sections.
Because the constraints depend only on total energy deposited, they are insensitive to branching ratios and spectral details of the annihilation products, which makes them applicable across many dark sector models.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: if the atmospheric dark matter population is partially depleted by winds, vertical mixing, or incomplete thermalization, the sub-GeV airglow limits would weaken approximately in proportion; atmospheric modelling of the exobase, the transition to the collisionless upper atmosphere, could quantify this.
Beyond the paper: the same capture-and-deposition machinery could be applied to hydrogen-rich brown dwarfs and mini-Neptunes with measured or modelable exobase temperatures, extending the mass and decay-length reach beyond the Solar System.
Beyond the paper: the conversion from brightness to precipitating power, about 10 Rayleigh per microwatt per square meter, is the single largest observational multiplier, so an improved empirical calibration of H2 Lyman and Werner band brightness versus electron power would shift all airglow limits by a common factor.
Beyond the paper: a latitudinally or time-resolved UV dataset could separate a dark matter airglow component from auroral and dayglow backgrounds, potentially turning the constraints reported here into a positive detection channel.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two quick takeaways. First, the paper genuinely advances the planetary-DM program: the internal heat flow constraints, the radial energy-deposition framework, the displaced-mediator Monte Carlo, and the SD-neutron/subfraction results are all useful and mostly well executed. Second, the headline UV airglow constraints on sub-GeV DM have a serious potential flaw that the paper does not address.

The problem is altitude. The observed H2 Lyman-Werner nightside emission comes from above the homopause; below that, the atmosphere is optically thick and the UV photons are absorbed or quenched. But Eq. (30) assigns the full annihilation power from the 1-bar surface out to the exobase as if it all produced observable airglow. For a 0.3 GeV DM particle on Jupiter, the DM scale height in the atmosphere is ~170 km, and the homopause sits ~400 km up, so only about 1% of the annihilations counted in f_atm occur in the UV-transparent region. The 10 R per µW/m^2 conversion factor is calibrated for energy deposited in the emitting layer, not deep in the atmosphere. This is not a minor detail; it removes the factor that allows Jupiter and Saturn to beat direct detection in Fig. 4.

The internal heating constraints are on much firmer ground, since they don't care where below the surface the energy is deposited. The light-mediator deposition framework is carefully described and looks reproducible. I also appreciate the honest discussion of composition and advection uncertainties, and the self-citation to the companion paper is appropriate since that is where the UV airglow idea originates.

The model-dependent ingredients—the isothermal atmospheric density profile, the solar-fitted blending parameters, the evaporation cutoff—are secondary compared to the homopause issue, but they are worth sensitivity checks. And the plotted limits don't propagate the quoted observational uncertainties, which is a referee-level request, not a fatal flaw.

Who should read this: anyone working on DM capture in celestial bodies, and planetary spectroscopists who want to see how their data are being used. I would send it to peer review, because the framework and the heating constraints are worth publishing, but the referee must insist on a proper treatment of the UV emitting layer, or a redefinition of f_atm to only count annihilations above the homopause. If the authors can show that the escaping UV or a related observable still tracks the deep annihilation power, the paper might stand; otherwise the airglow sections need major revision.

Referee Report

4 major / 5 minor

Summary. The paper develops a general framework for interpreting dark matter energy injection in planets through two observables: UV airglow from the atmosphere and internal heat flow from the interior. It models DM capture, thermalization, annihilation, and evaporation, and computes the fraction of annihilation energy deposited in the atmosphere versus the interior for both a heavy (prompt) mediator and a light/long-lived mediator. These fractions are combined with published UV brightness and heat-flow measurements for Earth, Jupiter, Saturn, Uranus, and Neptune, as well as projections for a benchmark Super-Jupiter, to derive constraints on spin-independent and spin-dependent DM-nucleon scattering cross sections. The headline claim is that planetary UV airglow observations surpass direct detection limits for sub-GeV DM even with a heavy mediator, because a portion of the captured DM population annihilates in the atmosphere, and that planetary spectroscopy is therefore a powerful and complementary dark-sector probe.

Significance. If the central claims hold, the paper would establish a qualitatively new and competitive channel for sub-GeV DM-nucleon scattering, particularly for spin-dependent proton scattering where direct detection is weak. The framework is genuinely general: it treats radial DM profiles, mediator decay lengths, and planetary structure in a unified way, and the heavy- versus light-mediator comparison is a useful organizational principle. The authors make good use of existing public tools (Asteria) and public datasets, and they are careful to separate constraints from projections. However, the headline UV-airglow limits rest on an atmospheric emission model that is not developed in the paper, and several model-dependent ingredients (the atmospheric DM profile, the solar-calibrated transition parameters, and the evaporation cutoff) are adopted with only partial sensitivity testing. The paper is therefore valuable and likely correct in its broad architecture, but the quantitative sub-GeV limits require further support.

major comments (4)

[II.B, Eqs. (30)-(31), (34), and Fig. 4] The UV airglow constraints count all annihilation events between the 1-bar radius R and the exobase Ratm through the fraction f_atm in Eq. (34), and impose Eq. (31) using a 10 R per uW/m2 conversion factor calibrated for precipitating electrons. However, H2 Lyman and Werner band photons are collisionally quenched and absorbed below the homopause, and the observed nightside UV airglow originates mainly above the homopause. The DM atmospheric density falls with scale height H = kT(R)/(m_chi g); for Jupiter at m_chi = 0.3 GeV this is roughly 170 km, while the homopause is typically a few hundred km above the 1-bar level. Thus only a small fraction of the events counted in f_atm occur in the UV-transparent region. The manuscript contains no radiative-transfer or quenching treatment and does not distinguish the energy deposition altitude from the emission altitude. This is a load-bearing issue for the central sub-GeV UV-airglow limits in Fig. 4, which may be overestimated by orders of magnitude. I ask the authors to either perform a vertical radiative-transfer estimate, conservatively restrict f_atm to the region above the homopause, or quantify the resulting reduction of the claimed limits.
[I.B.3, Eqs. (9)-(10)] The atmospheric DM profile is assumed to be isothermal at the planetary surface temperature T(R), joined to the interior LTE profile at R and truncated at a mass-dependent radius Rmax given by Eq. (10). This assumption directly controls the atmospheric annihilation fraction and hence the 'more than 10% of captured DM annihilates in the atmosphere' claim in Sec. V. The paper notes that an alternative truncation changes results by only about 10%, but it does not quantify the sensitivity to the assumed profile shape, e.g., a depleted profile due to atmospheric winds or incomplete thermalization, or a different treatment of the exobase boundary. Because this is the key physical input that enables the sub-GeV airglow constraints, the authors should provide a sensitivity study over plausible atmospheric DM distributions and demonstrate that the headline limits are robust, or state the extent to which they weaken.
[I.B.5, Eqs. (12)-(13)] The transition between the LTE and isothermal radial profiles is interpolated using f(K) with K0 = 0.4 and sigma = 0.5, parameters fitted to solar simulations [105]. The same functional form is applied to all planets, whose atmospheric compositions, temperatures, and Knudsen-number regimes differ substantially from the Sun. Since the cross-section limits in Fig. 4 span the intermediate regime where this blending matters, the authors should show the sensitivity of the constraints to the choice of K0 and sigma, for example by comparing the pure-LTE and pure-isothermal limits with the blended result. Without this, the robustness of the limits across the full cross-section range is not established.
[I.D, Eqs. (22)-(29)] The low-mass reach of all the constraints is set by the evaporation cutoff, and the paper states that the evaporation smoothing changes results by 'a few tens of percent' and that varying the core temperature shifts the cutoff approximately linearly in DM mass. Since the headline sub-GeV sensitivity in Fig. 4 extends to masses near 0.1 GeV and below, the evaporation uncertainty directly affects the claimed region of new parameter space. I recommend displaying the evaporation mass cutoff as an uncertainty band, or explicitly quoting the range of cutoff masses for each planet under reasonable core-temperature variations, so that the reader can judge how much of the sub-GeV reach is robust.

minor comments (5)

[II.A.1, Table I] The conversion factor of 10 R per uW/m2 is stated to be model-dependent, with values ranging from 7.8 to 14.6 R depending on electron energy. Since this factor enters all airglow limits linearly, its uncertainty should be propagated into the final constraints or quoted as a systematic band.
[II.A.3 and II.C.3] The Super-Jupiter is described as 'local free-floating' for the UV airglow projection but as located at 0.1 kpc from the Galactic Center for the internal-heating projection. These are different benchmarks with different DM densities and backgrounds; the text should state this explicitly to avoid confusion.
[Fig. 2] The caption does not mention that Earth is omitted from the 0.5 GeV isothermal panel; the text explains this, but a short caption note would improve readability.
[I.B.3, Eq. (10)] The expression Rmax ~ GM m_chi / T_chi is dimensionally correct only in units where Boltzmann's constant is unity; this should be stated or written with k_B explicitly for clarity.
[I.C, Eq. (17)] The notation Cann is used both as an annihilation rate coefficient in Eq. (1) and as the coefficient in Eq. (18); the two are related but distinct, and a brief clarifying sentence would help the reader track the dimensions.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the constraints are obtained by comparing a forward DM energy-deposition calculation to externally measured UV airglow and internal heat fluxes.

full rationale

I walked the derivation chain: capture (Eq. 2, with Asteria), radial DM profiles (Eqs. 5-12), annihilation rate (Eqs. 17-18), atmospheric/interior deposition fractions (Eqs. 34-40), and the final constraints (Eqs. 31 and 33). The observed powers P_observed_atm and P_observed_int are external datasets from Voyager, New Horizons, Cassini, AMS-02, ELFIN, and boreholes, not quantities fitted from the DM model. The isothermal atmospheric extension (Eq. 9) and the solar-calibrated blending parameters K0 = 0.4 and ς = 0.5 (Eq. 13) are explicit physical inputs, not inversions of the target airglow or heat-flow signals. The self-citations to the companion paper [120] and to the Asteria package [124,125] are not load-bearing in the circular sense: [120] is a separate study comparing the same UV airglow mechanism to real observations, and Asteria is a public, code-released capture package; neither is fitted to the planetary observables used here. The statement that more than 10% of captured DM can annihilate in the atmosphere is the geometric fraction f_atm of Eq. (34) under the adopted atmospheric profile; it is model-dependent, and the homopause/radiative-transfer concern raised by the skeptic is a genuine physical uncertainty rather than a circularity, because the model is not fit to the UV data. No step reduces an output to an input by construction.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central constraints inherit uncertainty from four non-derived inputs: the transition-regime blending parameters fitted to solar simulations, the isothermal atmospheric extension of the DM profile, the evaporation model's low-mass cutoff, and the brightness-to-power conversion factor. Each is taken from prior literature or chosen as a benchmark; none is fitted to the dark matter signal itself.

free parameters (4)

Transition blending parameters K0, ς = K0 = 0.4, ς = 0.5
Used in Eq. 13 to interpolate between LTE and isothermal DM profiles; fitted to solar simulations [105] and applied to all planets without re-fitting.
UV brightness to power conversion factor = 10 R per µW/m^2
Adopted in Sec. II.A from electron precipitation literature; the text notes 7.8-14.6 R per µW/m^2 depending on electron energy, so this is a model-dependent calibration.
Advection timescales = 100 yr giant planets, 1 Myr Earth
Assumed in Sec. I.B.6 from Ref. [133]; sets the cross-section threshold above which advection may alter the DM profile.
Super-Jupiter benchmark parameters = density x10, temperature x5 vs Jupiter; heat 459 W/m^2; DM density enhancement ~1500
Benchmark choices in Sec. II.D and Appendix A for the free-floating Super-Jupiter forecast; not tied to a specific observed target.

assumptions (6)

domain assumption Capture-annihilation equilibrium is assumed for the main constraints (Eq. 21).
The annihilation signal is set by Nχ = sqrt(Ccap/Cann) after equilibrium. The authors verify in Appendix B that equilibrium holds for most s-wave parameter space and partially for p-wave; if it fails, constraints weaken.
domain assumption DM-SM interactions are contact interactions; long-range interactions are neglected.
Stated in Sec. I.D; long-range interactions would change capture and evaporation rates.
domain assumption DM annihilates entirely into visible SM particles, neglecting neutrino branching.
Stated in Sec. II; results can be rescaled by the visible branching fraction.
ad hoc to paper Atmospheric DM follows an isothermal distribution at the surface temperature T(R), with outer boundary Rmax (Eq. 9).
Introduced in Sec. I.B.3; this modeling choice produces the atmospheric annihilation fractions that drive the UV airglow limits.
ad hoc to paper The transition between LTE and isothermal regimes is interpolated with f(K) using K0=0.4 and ς=0.5, fitted to solar simulations.
Eq. 13 in Sec. I.B.5; these literature values are applied to planets without re-fitting, which affects the radial profile at intermediate cross sections.
domain assumption Evaporation is modeled with the Gould and Jeans frameworks of Refs. [129,143-147].
Eqs. 22-28 in Sec. I.D; the low-mass cutoff of all constraints is set by this model, with a smoothing function that changes results by tens of percent.

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Cite this review

Pith. "Pith review of Complementary Planetary Spectroscopy Probes of Dark Matter." pith.science (2026). https://pith.science/paper/VEN2K7DQ

@misc{pith2026250800980,
  author       = {Pith},
  title        = {Pith review of: Complementary Planetary Spectroscopy Probes of Dark Matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VEN2K7DQ}},
  note         = {Machine review of arXiv:2508.00980}
}

read the original abstract

We investigate dark matter (DM) interactions via spectroscopic signatures of energy injection in planetary environments. We develop a general framework to account for how DM energy injection signals depend on the DM spatial distribution, planetary structure, and DM energy deposition profile. We combine UV airglow data on the Solar System's gas giants from the Voyager and New Horizons flybys, and ionospheric measurements from AMS-02 and ELFIN CubeSat on Earth, with internal heat flow data from Cassini, Voyager, and terrestrial boreholes, to constrain DM-nucleon scattering across both heavy and light mediator scenarios. We show that Earth, gas giants, and ice giants probe complementary DM masses and mediator properties, and forecast the reach of a free-floating Super-Jupiter. These results establish planetary spectroscopy as a powerful and versatile probe of the dark sector, complementary to direct detection, cosmology, and collider searches.

Figures

Figures reproduced from arXiv: 2508.00980 by the authors.

**Figure 2.** DM radial number density profile in the Solar System planets and a Super-Jupiter as labeled, normalized to the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Fraction of energy deposited in the atmosphere [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: Constraints (solid, shaded) and future projections (dashed) on spin-independent (SI) nucleon scattering (left) [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: Fraction of energy deposited in Saturn’s atmosphere [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: Fraction of energy deposited in the atmosphere ( [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: Parameter space constrained by planetary UV airglow and internal heat flow for a benchmark mediator lifetime of [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

**Figure 8.** Figure 8: Spin-dependent proton cross section constraints (solid, shaded) and future projections (dashed) using UV airglow [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

**Figure 9.** Figure 9: Optimal UV airglow limits including a factor accounting for potential non-equilibration with [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]

**Figure 10.** Figure 10: Optimal internal heating limits including a factor accounting for potential non-equilibration with [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]

**Figure 11.** Figure 11: Constraints (solid, shaded) and future projections (dashed) on spin-dependent neutron scattering, assuming DM [PITH_FULL_IMAGE:figures/full_fig_p019_11.png]

**Figure 12.** Figure 12: Constraints (solid, shaded) and future projections (dashed) on spin-independent nucleon scattering (left) and [PITH_FULL_IMAGE:figures/full_fig_p019_12.png]

**Figure 13.** Figure 13: Parameter space constrained by planetary UV airglow and internal heat flow for a benchmark mediator lifetime of [PITH_FULL_IMAGE:figures/full_fig_p020_13.png]

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Reference graph

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247 extracted references · 17 canonical work pages · cited by 1 Pith paper

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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Gas and Ice Giants Space probes such as Voyager 1, Voyager 2, and New Horizons have obtained UV nightglow spectra of the gas and ice giant planets away from their polar auroral re- gions. Our analysis of the Solar System giant plan- ets focuses on the excitation of the Lyman and Werner bands of molecular hydrogen (H 2), which dominate far UV emissions and...

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Nonetheless, a UV nightglow has been observed, e.g

Earth Earth’s atmosphere differs markedly from those of the giant planets due to its much lower hydrogen content. Nonetheless, a UV nightglow has been observed, e.g. by the Universitetskii-Tatiana satellite [166]. Thanks to the wealth of experiments in the Earth’s upper at- mosphere, the precipitating electron energy flux can be directly measured, for exa...

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The main origin of UV airglow in this case is not stellar, but rather from cosmic-ray electrons precipitating in the at- mosphere

Local Free-Floating Super-Jupiter To investigate an exoplanetary scenario, we use a benchmark free-floating Super-Jupiter; free-floating tar- gets will be optimal due to their lower backgrounds. The main origin of UV airglow in this case is not stellar, but rather from cosmic-ray electrons precipitating in the at- mosphere. We calculate the expected elect...

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This is done by considering the photon power incident on the planet, and measuring the planet’s Bond albedo (the fraction of scattered light), using optical instruments

Gas and Ice Giants In the giant planets, the internal heating is estimated by evaluating the photon power absorbed by the planet. This is done by considering the photon power incident on the planet, and measuring the planet’s Bond albedo (the fraction of scattered light), using optical instruments. The effective temperature of the planet is obtained via i...

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Oceanic and continental boreholes are used to directly measure the temperature without the influ- ence of variation in the Earth’s surface temperature, from e.g

Earth On Earth, several techniques are used to measure the internal heat. Oceanic and continental boreholes are used to directly measure the temperature without the influ- ence of variation in the Earth’s surface temperature, from e.g. day-night variance [177]. We use recent results which take into account effects from the local environment, i.e., matchin...

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heavy mediator

Super-Jupiter in the Galactic Center We adopt the internal heat flux of a 10 Gyr Super- Jupiter from the ATMO model [161]. We take this bench- mark to be free-floating at 0.1 kpc from the Galactic Center, such that it is not irradiated by a star and its internal heat is a remnant from its formation. D. DM Induced Internal Heat Flow DM annihilation can inj...

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Details of the Monte Carlo method are provided in Appendix D

Deposition in the Atmosphere The atmospheric energy deposition fraction from DM annihilation into light mediators is computed as f light atm = X i Patm i /N , (37) where Patm i is the probability that a mediator decays in the atmosphere, given an annihilation at point i, and N is the total number of sampled points. Details of the Monte Carlo method are pr...