Read a dark matter annihilation cross-section limit plot by checking its axes and units, identifying the particle-physics and halo assumptions, and then treating the observed curve as an upper bound at each mass. For the stated confidence level and assumptions, cross sections above that curve are excluded; the curve is not evidence that dark matter has been detected.
Start with the axes, units and scale
- Horizontal axis: usually dark-matter particle mass, often in GeV or TeV.
- Vertical axis: the velocity-weighted annihilation cross section, written ⟨σv⟩ and commonly measured in cm³/s.
- Scale: both axes are often logarithmic. Read the tick labels: equal visual spacing on a logarithmic axis represents multiplicative steps, not equal additive differences.
Use the units and mass range shown on the specific figure. A plot spanning GeV to TeV can cover several orders of magnitude, so a small vertical or horizontal distance may represent a large ratio.
Identify what the plotted constraint assumes
A cross-section limit is conditional, not a result independent of the model or target. Before comparing curves, read the legend and caption for the annihilation channel, whether the search is for a continuum spectrum or a spectral line, the target region, and the assumed dark-matter density profile.
- Channel: Annihilation into W⁺W⁻ produces a continuum spectrum; a gamma-ray line search targets a narrow spectral feature. These are different signals and their limits should not be treated as the same measurement.
- Target and data: The observed region, instrument and data set affect the constraint.
- Halo profile: The assumed distribution of dark matter affects how an observed flux constraint translates into a cross-section limit.
Read the upper-limit curve correctly
At each mass, an observed upper-limit curve gives the largest cross section allowed by the data under the analysis assumptions. In the H.E.S.S. 2022 continuum example, the plotted observed 95% upper-limit curve is for the W⁺W⁻ channel and an Einasto profile; values above the curve are excluded at the stated confidence level. The curve does not mean a signal was found.
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A 95% confidence-level limit is a statistical statement about the analysis procedure and data. It does not mean there is a 95% probability that a particular dark-matter model is false. Check the figure’s caption for the exact confidence-level convention and analysis.
Distinguish observed limits from expected sensitivity
If the plot shows both observed and expected curves, the observed result comes from the actual data. An expected or sensitivity curve describes the constraint anticipated under a background-only expectation. The legend and caption define the precise convention, so do not infer it from line style or color alone.
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Understand the thermal-relic reference line
A thermal-relic line is a theoretical benchmark associated with thermal production, not a telescope measurement and not a universal cutoff for every dark-matter model. Its exact value and relevance depend on the model and assumptions used for the comparison.
If an experimental limit crosses a thermal-relic reference, that can indicate that the analysis constrains the benchmark under the stated conditions. It does not by itself establish that all thermal dark matter is excluded. Check that the channel, mass, confidence level and other assumptions match the comparison being made.
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Why the J-factor and halo profile change the result
For annihilation, the expected gamma-ray flux depends both on the particle annihilation rate and on the dark matter along the line of sight. The annihilation J-factor encodes the astrophysical contribution: it is the integral of the squared dark-matter density over the line of sight and the relevant solid angle. A different assumed density profile can change the J-factor and therefore the cross-section limit inferred from the same flux constraint.
The H.E.S.S. Collaboration’s August 2026 overview compares J-factors for Einasto, NFW, cNFW, FIRE-2 and Auriga profiles. A curve should therefore be read as a limit for its adopted halo model, not as a profile-independent constraint.
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Worked example: H.E.S.S. Inner Galaxy Survey line search
The H.E.S.S. Collaboration’s 2026 Inner Galaxy Survey search looked for gamma-ray spectral lines using 546 hours of observations collected from 2014 to 2020. The analysis covered 61 energy bins from 300 GeV to 64 TeV across 25 spatial regions. It reported no significant line signal and set 95% confidence-level upper limits over dark-matter masses from 300 GeV to 70 TeV.
The collaboration overview reports a line-cross-section limit of 2.3×10⁻²⁸ cm³/s at a dark-matter mass of 1 TeV. This is a result for that line search and its analysis assumptions; it should not be merged with a continuum-search curve. The journal abstract separately reports a value of 2.4×10⁻²⁷ cm³/s at 10 TeV assuming an Einasto profile.
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The overview also describes model-specific implications: it says the results challenge the thermal Higgsino for an Einasto profile, test it to about 10 TeV for Auriga, and exclude thermal Wino and Quintuplet models for the Milky Way profiles considered. Those conclusions apply to the analysis and models stated, not to every dark-matter limit plot.
Compare curves only when the conditions match
A lower upper-limit curve is more restrictive only when the curves constrain comparable quantities under comparable conditions. Before calling one result stronger, check:
- the dark-matter mass and mass range;
- the annihilation channel and whether it is a continuum or line search;
- the confidence level and observed-versus-expected convention;
- the target, instrument and data set;
- the adopted halo profile and J-factor assumptions.
The H.E.S.S. 2022 continuum explanation is useful for reading a W⁺W⁻, Einasto-profile curve against a thermal-relic reference. The 2026 line search is a separate analysis with a different signal target; its values and conclusions should be read in that context.
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