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A dark matter annihilation cross-section limit plot shows, at each assumed particle mass, the largest annihilation rate still allowed by the observations under a specified model and analysis. Read the axes and legend first, then check the channel, confidence level, target and halo assumptions. Points above an upper-limit curve are excluded at its stated confidence level; the curve is not evidence that dark matter was detected.
Start with the axes and units
The horizontal axis is usually dark matter particle mass. The vertical axis is the velocity-weighted annihilation cross section, written ⟨σv⟩ and commonly reported in cm³/s. Both axes are often logarithmic: equal spacing represents multiplication by a factor, not addition of a fixed amount. Read the tick labels rather than estimating values from visual distance.
Check the caption and legend for the precise quantity and units. A plot may show a continuum-search limit or a spectral-line limit; these are distinct analyses and should not be treated as interchangeable.
Read the upper-limit curve
At each mass, the curve gives the upper bound on the cross section obtained by that analysis. In the H.E.S.S. Inner Galaxy Survey continuum example, for the stated W⁺W⁻ channel and Einasto density profile, cross sections above the observed 95% confidence-level curve are excluded under those assumptions. The curve is a constraint, not a measured annihilation rate.
A 95% confidence limit does not mean there is a 95% probability that a particular dark matter model is false. It is a statistical limit derived using the analysis procedure and assumptions; consult the paper or figure caption for how that procedure is defined.
Distinguish observed and expected limits
An observed limit is calculated from the actual data. An expected limit, sometimes described as sensitivity, indicates the constraint anticipated under a background-only expectation. If both curves are plotted, use the legend and caption to identify each line and any uncertainty bands: conventions can differ between figures.
Check the channel and astrophysical assumptions
Identify what annihilation produces
The final state, or annihilation channel, shapes the predicted gamma-ray signal. A continuum channel such as W⁺W⁻ produces a spectrum across energies, whereas a gamma-ray line search looks for a narrow spectral feature. Limits from different channels answer different model questions, even when their axes use the same units.
Look for the target and halo profile
The expected annihilation flux depends both on the particle annihilation rate and on the amount and distribution of dark matter along the line of sight. The annihilation J-factor captures the astrophysical contribution: it integrates the squared dark matter density over the line of sight and the observed solid angle. A different density profile changes that factor and therefore the conversion from a flux constraint to a cross-section limit.
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For the Milky Way Inner Galaxy, the H.E.S.S. 2026 overview considers profiles including Einasto, NFW, cNFW, FIRE-2 and Auriga and shows their resulting J-factors. Do not read a cross-section curve as independent of the adopted halo model.
Treat a thermal-relic line as a benchmark
A thermal-relic reference line is a theoretical comparison associated with thermal production; it is not a telescope measurement or a universal cutoff for all dark matter. A limit crossing that reference can be informative only for the model and assumptions being compared. Check whether the reference uses a compatible channel, mass range and cosmological or particle-physics scenario rather than treating it as a pass/fail test for dark matter in general.
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Worked example: the H.E.S.S. 2026 line search
The H.E.S.S. Collaboration reports a search for gamma-ray spectral lines using 546 hours of Inner Galaxy Survey observations collected from 2014 to 2020. The analysis covers 61 energy bins from 300 GeV to 64 TeV and 25 spatial regions. It found no significant line signal and reports 95% confidence-level upper limits for dark matter masses from 300 GeV to 70 TeV.
In its 1 August 2026 overview, H.E.S.S. reports a line cross-section limit of 2.3×10⁻²⁸ cm³/s at a dark matter mass of 1 TeV. The journal abstract also reports 2.4×10⁻²⁷ cm³/s at 10 TeV under an Einasto profile. Those are line-search results, not values from the separate 2022 W⁺W⁻ continuum plot.
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Repair Windows errors before they cause bigger problemsFix Now →Fix the driver behind crashes, sound loss and screen glitchesFind Drivers →The overview 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. These conclusions depend on the analysis and model assumptions; they should not be generalized to every limit plot or every dark matter model.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Compare curves only after matching their assumptions
A lower upper-limit curve generally means a tighter constraint only when the compared curves address the same quantity under comparable conditions. Before ranking them, match:
- dark matter mass and plotted quantity;
- annihilation channel, including line versus continuum;
- confidence level and observed-versus-expected convention;
- target region, instrument and data set;
- halo profile and J-factor assumptions.
If any of these differ, the curves may not be directly comparable. A plot’s caption and underlying analysis are needed to interpret what its apparent strength means.
Quick Recap
A quick reading sequence
- Read both axis labels, units and tick marks; note whether the scales are logarithmic.
- Use the legend and caption to identify the channel, target, halo profile and confidence level.
- Determine which curve is observed and which, if present, is expected.
- At the mass of interest, read the upper bound; values above it are excluded at the stated confidence level under the plotted assumptions.
- Interpret any thermal-relic reference as a model benchmark, then compare with another plot only after checking that the assumptions match.
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