DarkBit: A GAMBIT module for computing dark matter observables and likelihoods

1 Introduction

• Combining accelerator, direct, indirect, and astrophysical searches statistically is important for extracting information about dark matter candidates as experimental data grows.The paper notes that astrophysical probes are particularly relevant to scenarios beyond the standard WIMP case.Source: §1 · p. 2
• DarkBit provides flexible dark matter observables and likelihoods, including first-release limits for gamma rays, neutrinos, spin-independent and spin-dependent scattering, and relic density.Its Process Catalogue stores relevant particles and interaction rates to support calculations across particle models.Source: §1 · p. 2
• Users can combine external backends such as DarkSUSY, micrOMEGAs, DDCalc, gamLike, and nulike, switch between equivalent backends, or use DarkBit’s internal cascade-decay spectrum generator.The paper identifies modularity as a key design feature and describes dynamic C++ function objects in daFunk for exchanging real-valued functions.Source: §1 · p. 3
• Standalone use computes observables and likelihoods at chosen model points, while GAMBIT scans can combine likelihoods and treat astrophysical or nuclear uncertainties as nuisance parameters.Examples of such uncertainties include nuclear form factors and halo-model uncertainties.Source: §1 · p. 3

2 Module overview

• GAMBIT module functions each calculate one capability, and their dependencies are resolved at runtime according to the selected model and requested observables.Capabilities can include model parameters, particle spectra, experimental data, and likelihood values.Source: §2 · p. 4
• DarkBit builds central structures from scan-point parameters, including the Process Catalogue, annihilation rate, and WIMP-nucleon couplings, for relic-density, direct-detection, and indirect-yield calculations.Figure 1 sketches these relations; the complete dependency tree is more complex.Source: §2 · p. 4
• External codes such as DarkSUSY and micrOMEGAs provide reusable backend functionality, exposed to GAMBIT through frontends that specify the accessible functions.Backends are compiled as shared libraries and loaded at runtime.Source: §2 · p. 4
• Most DarkBit functionality can be used standalone to calculate observables and likelihoods for chosen parameter values, without running a GAMBIT scan.The paper also notes that it could be incorporated into a command-line tool.Source: §2 · p. 4

3.1 Background

• Dark matter density and velocity distributions affect direct-detection rates, solar capture, and signals from annihilations in astrophysical sources.GAMBIT halo models provide a consistent description of these properties across calculations.Source: §3.1 · p. 4

3.1.1 Density profiles

• DarkBit includes generalized NFW profiles, with inner, outer, and transition-shape parameters, and an Einasto profile whose logarithmic slope varies with radius.These parameterizations describe the halo’s radial density profile.Source: §3.1.1 · p. 5

3.1.2 Velocity distribution

• The velocity model uses a Maxwell-Boltzmann distribution truncated at the escape speed and transforms particle velocities to Earth’s frame using Galactic, solar, and orbital motion.The changing direction of Earth’s orbital velocity is expected to produce annual modulation in direct-detection scattering rates.Source: §3.1.2 · p. 5

3.2.1 Halo models and associated capabilities

• Halo_gNFW and Halo_Einasto describe Galactic density and local velocity parameters, while separate GalacticHalo and LocalHalo capabilities pass source-profile and local properties to calculations.The density profile can be decoupled from the local density or linked to it through child models; this capability structure allows new halo models to be added.Source: §3.2.1 · pp. 5–6

3.2.2 Likelihoods

• DarkBit supplies a log-normal likelihood for local density and Gaussian likelihoods for v0, vrot, and vesc, with default central values and uncertainties for the velocity parameters.The default local-density central value is approximately 0.4 GeV/cm3 with a 0.15 GeV/cm3 uncertainty; vrot is 235 ± 20 km s−1 and vesc is 550 ± 35 km s−1.Source: §3.2.2 · p. 6
• No specific likelihoods constrain Galactic halo-profile parameters; users can instead set parameter ranges and priors in the GAMBIT initialization file.The central values and errors of the implemented parameter likelihoods can be adjusted through YAML options.Source: §3.2.2 · p. 6

4.1 Background

• The Boltzmann calculation uses the temperature-independent invariant rate Weff and an ordered spectrum of coannihilating particles.DarkSUSY integrates in x = mχ/T and Y = n/s, using adaptive Gaussian thermal averaging and an implicit trapezoidal solver with adaptive stepsize.Source: §4.1 · p. 7, §4.3 · p. 9

4.2 Interfaces to DarkSUSY and micrOMEGAs

• DarkSUSY exposes relic-density calculation as separate functions, whereas micrOMEGAs performs the calculation through a single, coarser-grained call.Both backends can provide relic density, WIMP-nucleon effective couplings, and gamma-ray spectra; DarkSUSY is also used for Weff, solar capture, and other quantities.Source: §4.2 · p. 8
• The micrOMEGAs interface requires model-specific CalcHEP files and libraries, with separate libraries needed for each particle-physics model.GAMBIT supplies frontends for the MSSM and scalar-singlet dark matter; the MSSM frontend uses SLHA1 input, which is not compatible with SLHA2.Source: §4.2 · p. 8

4.3 Relic density implementation in DarkBit

• DarkBit represents the effective rate and ordered coannihilator spectrum as replaceable capabilities, supplied by DarkSUSY or, without important coannihilations, the Process Catalogue.DarkSUSY coannihilations can be disabled for speed at the expense of accuracy; the current implementation does not include gluino coannihilations.Source: §4.3 · pp. 8–9, Figure 2 · p. 9
• Three RD_fraction functions determine whether detection routines use the observed density or rescale by the calculated-to-reference density ratio.RD_fraction_one returns 1; RD_fraction_leq_one caps the ratio at 1, while RD_fraction_rescale uses the ratio even when it exceeds 1.Source: §4.3 · p. 9
• The modular solver calculates relic density independently of the particle model, while backend routines allow systematic comparison of DarkSUSY and micrOMEGAs.The solver relies on DarkSUSY subroutines but does not require DarkSUSY-specific particle-parameter initialisation.Source: §4.3 · p. 9
• DarkBit offers a Gaussian relic-density likelihood that includes theoretical uncertainty and a one-sided upper-limit option for candidates making up only part of the observed abundance.The Gaussian likelihood defaults to a theoretical error of 5%; its systematic treatment can be profiled or marginalised, with marginalisation as the default.Source: §4.3 · pp. 9–10

5.1 Background

• Direct-detection rates depend on the WIMP velocity distribution, differential scattering cross-section, and detector response; the section distinguishes spin-independent from spin-dependent scattering and their respective nuclear inputs.The detector response can encode analysis selections and be reused across WIMP models because it is independent of the interaction type.Source: §5.1 · pp. 10–11

5.2 DDCalc

• DDCalc addresses the limitations of single-confidence-level exclusion curves by evaluating how arbitrary proton and neutron SI and SD couplings agree with data, including systematic uncertainties from halo, nuclear, and form-factor assumptions.Its first release does not support generalized momentum- or velocity-dependent couplings out of the box, though its structure is designed to accommodate them.Source: §5.2 · p. 12

5.2.1 Methods

• DDCalc predicts signal yields from WIMP and halo inputs, computes Poisson likelihoods by analysis region, and combines them across experiments; Feldman–Cousins and maximum-gap methods provide alternative constraints.The maximum-gap method uses observed-event intervals to exploit spectral information when background shape and magnitude are unknown; Feldman–Cousins uses total signal and background yields and does not incorporate spectral information.Source: §5.2.1 · pp. 12–13

5.2.2 Experiments

• Version 1.0.0 includes eight experimental analyses: LUX, PandaX, XENON100, and SuperCDMS target SI and neutron SD sensitivity, while PICO-2L, PICO-60, and SIMPLE target proton SD sensitivity.For SIMPLE, DDCalc predicts 12.7 events against 8 observed.Source: §5.2.2 · pp. 13–14
• DDCalc uses a TPC Monte Carlo based on NEST to model XENON100 detector response and provide full gap information for analyses using spectral recoil data.The simulated detector response enables use of recoil-energy information that the supplied XENON100 efficiency curves alone do not provide.Source: §5.2.2 · p. 16
• For LUX’s second run, DDCalc approximates the published analysis with a reduced S1-S2 search window, predicting 2.3 background events versus one observed; the authors report reproducing the bound accurately despite crude background estimates and an arbitrary window.The method excludes regions likely to contain background events and estimates leakage backgrounds as uniform in S1, with other backgrounds shaped like neutron-recoil calibration data.Source: §5.2.2 · p. 16
• Xenon1T [81] provides the world-leading limits on spin-independent and neutron spin-dependent scattering, while PICO-60’s 2017 analysis [82] gives the strongest proton spin-dependent constraints.Xenon1T observed no events in its signal region against an expected background of 0.36; PICO-60 observed no events and used no background subtraction.Source: §5.2.2 · p. 17
• Likelihoods for WIMP masses below 10 GeV are difficult to implement accurately because sensitivity depends strongly on upward fluctuations and astrophysical uncertainties.The text says precision studies will likely require additional experimental information to refine the likelihoods.Source: §5.2.2 · pp. 17–18

5.2.3 Command-line usage

• DDCalc_run offers command-line and interactive modes, accepts WIMP mass and cross-section inputs, and exposes general, halo-distribution, and advanced detector options.The advanced options include detector isotopic composition and efficiency functions; the included experiment flags set their defaults for general users.Source: §5.2.3 · p. 18

5.2.4 Library interface (API)

• The DDCalc library centers calculations on WIMPStruct, HaloStruct, and DetectorStruct objects, holding the WIMP model, halo parameters, and detector analysis information, respectively.DetectorStruct includes efficiencies, background model, energy threshold, exposure, and observed events.Source: §5.2.4 · p. 18

• DDCalc_InitWIMP creates a WIMPStruct with a default mass of 100 GeV and couplings of 1 pb.Source: WIMP model · p. 18
• DDCalc_SetWIMP routines set WIMP mass and SI and SD couplings in coupling or cross-section parameterizations.Negative cross-sections indicate negative couplings; p and n denote proton and neutron.Source: WIMP model · p. 18
• DDCalc_GetWIMP routines retrieve the stored parameters, with returned cross-sections always positive regardless of coupling sign.Source: WIMP model · p. 18

• DDCalc_InitHalo initializes a HaloStruct to the Standard Halo Model, including ρχ = 0.4 GeV cm−3 and vesc = 550 km s−1.The defaults for vrot and v0 are each 235 km s−1.Source: Halo model · p. 19
• DDCalc_SetSHM sets the halo density and the vrot, v0, and vesc velocity parameters.Source: Halo model · p. 19
• DDCalc also provides routines to set and retrieve HaloStruct objects.Source: Halo model · p. 19

Experiments and analysis

• The DDCalc detector constructor defaults to the LUX 2013 analysis, while named constructors provide other analyses and an intervals flag enables maximum-gap calculations.A nonzero minimum recoil threshold can be set to obtain more conservative exclusion limits or study low-energy cutoffs.Source: Experiments and analysis · p. 19
• DDCalc_CalcRates computes rates for a specified detector, WIMP, and halo, with results available through routines for signal, background, events, and likelihoods.The log-p-value routine uses the maximum-gap method when interval information is available; otherwise it uses a zero-background Poisson calculation.Source: Experiments and analysis · p. 19

5.3.1 WIMP-nucleon couplings

• DarkSUSY and micrOMEGAs calculate MSSM WIMP-nucleon couplings, while DarkSUSY and an internal routine also support the scalar singlet model.The internal scalar-singlet calculation has SI scattering only; GAMBIT selects the appropriate micrOMEGAs backend version for the scanned model.Source: §5.3.1 · p. 20
• For MSSM couplings, loop corrections can be enabled in DarkSUSY, and micrOMEGAs includes selected corrections such as SUSY QCD Higgs-exchange corrections and gluon box diagrams.DarkSUSY's loop option defaults to true in GAMBIT 1.1.0; the micrOMEGAs box option defaults to true.Source: §5.3.1 · p. 20

5.3.2 Nuclear uncertainties

• SI and SD nuclear-parameter uncertainties are represented by Gaussian likelihoods, with default σs = 43 ± 8 MeV, σl = 58 ± 9 MeV, a3 = 1.2723 ± 0.0023, a8 = 0.585 ± 0.023, and ∆(p)s = −0.09 ± 0.03.The central values and widths can be adjusted through YAML options.Source: §5.3.2 · p. 21

5.3.3 Event rates and likelihoods

• GAMBIT 1.1.0 adds Xenon1T and the 2017 PICO-60 analysis to the direct-detection experiments supported in GAMBIT 1.0.0.PICO-60's fluorine and iodine targets are implemented as independent experiments but should be used together.Source: §5.3.3 · p. 21
• During scans, GAMBIT updates WIMP and halo objects and obtains predicted event counts, background and signal rates, and Poissonian log-likelihoods for each supported analysis.Source: §5.3.3 · p. 21

6.1 Background

• Charged cosmic rays constrain hadronic channels through antiprotons and leptonic channels through positrons, but their propagation and likelihoods are not included in this DarkBit release.The paper identifies both as high-priority planned extensions.Source: §6.1 · p. 22

6.1.1 Gamma rays

• Prompt gamma-ray features near the dark-matter mass, including line-like photons, are easier to distinguish from astrophysical backgrounds and central to indirect searches.Continuous emission from hadronisation peaks at energies about an order of magnitude below the dark-matter mass; Galactic-centre searches face diffuse-background uncertainties, while dwarf spheroidals are simpler, nearly background-free targets.Source: §6.1.1 · p. 22

6.1.2 Neutrinos

• Solar neutrinos probe dark-matter nuclear scattering because captured particles can accumulate and annihilate in the Sun, producing neutrinos that escape to Earth.DarkBit focuses on solar searches: current neutrino-telescope limits on total annihilation are weaker than gamma-ray limits, and the implemented focus is on GeV-scale neutrinos; lower energies are difficult to distinguish from solar fusion neutrinos, while TeV energies face solar opacity.Source: §6.1.2 · p. 23
• DarkBit solves for the Sun’s captured dark-matter population model by model instead of assuming capture–annihilation equilibrium.When equilibrium is reached, annihilation is capture-limited; the annihilation cross-section no longer affects the solar neutrino count. DarkBit uses DarkSUSY capture and annihilation rates and WimpSim yield tables for neutrino fluxes at Earth.Source: §6.1.2 · pp. 23–24

6.2.1 Overview

• gamLike unifies gamma-ray likelihoods to make results from different targets and experiments usable in scans of models with complex annihilation final states.Its likelihoods support profiling or marginalising over J-factor uncertainties; for the combined dwarf limits, it profiles the J-factors of all 15 dwarfs separately.Source: §6.2.1 · p. 24

6.2.2 gamLike targets

• Six years of Fermi-LAT Pass 8 dwarf-galaxy data disfavor s-wave annihilation to hadronic final states at the thermal rate below around 100 GeV.DarkBit implements the 15-dwarf composite profile likelihood, profiling each dwarf’s J-factor; it also includes older Pass 7 results. H.E.S.S. observations provide current best limits above several hundred GeV.Source: §6.2.2 · pp. 24–26
• DarkBit implements Fermi-LAT likelihoods for dwarf spheroidals and the Galactic-centre excess, alongside H.E.S.S. Galactic-centre likelihoods and a future CTA projection.The Galactic-centre excess likelihood covers 300 MeV to 500 GeV and offers alternative J-factor treatments, including a contracted NFW profile and a marginalised lognormal distribution.Source: Table 7 · p. 25, §6.2.2 · p. 26
• The treatment rescales only the overall flux in the specified region and does not account for variations in signal morphology.The region is |ℓ| < 20° and 2° < |b| < 20°.Source: §6.2.2 · p. 26
• gamLike reproduces Ref. [137]’s 265 GeV–30 TeV single-bin limits and implements its 35-bin 230 GeV–30 TeV spectral analysis, improving accuracy for structured spectra.The default halo profile is the one used in the corresponding scan; alternatively, the NFW profile from Ref. [137] uses a local density of 0.39 GeV cm−3 at 8.5 kpc. Energy dispersion is not included, so results require care, and gamma-ray lines should be constrained with a dedicated line search.Source: §6.2.2 · p. 26

Projected Galactic centre searches with CTA

• CTA projections use a morphological analysis of FoV segments and assume Galactic diffuse emission is modelled up to an unconstrained normalisation; the likelihood fixes an Einasto halo with ρχ = 0.4 GeV cm−3 over 25 GeV–10 TeV.The analysis is systematics-limited by differential detector acceptance and diffuse-emission modelling, and the projected limits cannot use the more general halo model adopted in the scan.Source: Projected Galactic centre searches… · p. 26

6.2.3 Library Interface (API)

• gamLike exposes functions to set data paths, initialise experiments, evaluate log-likelihoods from tabulated spectra, and initialise halo models; energy bins use trapezoidal integration, with no energy dispersion.Input spectra must span the activated experiments’ energy ranges and are treated as zero outside the tabulation range.Source: §6.2.3 · p. 27

6.3.1 The Process Catalogue

• The Process Catalogue records decay and annihilation channels and their rates, with genRate representing widths, velocity-dependent cross-sections, or differential three-body rates; genRateMisc adds invisible contributions relevant to relic density.Three-body rates can be positive or negative corrections to tree-level results and require care to avoid double counting; particle masses support kinematics.Source: §6.3.1 · pp. 27–28

6.3.2 Gamma rays

• SimYieldTable provides flexible access to gamma-ray spectra from DarkSUSY and micrOMEGAs, enabling backend selection and comparison where their tabulated yields can differ substantially.The yield wrapper can be combined with analytic three-body contributions or Fast Cascade Monte Carlo results in GA_AnnYield.Source: §6.3.2 · pp. 28–29
• GA_AnnYield combines backend functions and integrations into gamma-ray spectra; failed integrations return zero, making derived upper limits conservative, and Fig. 3 illustrates example spectra including line-like and Z0γ cases.The Z0γ spectrum combines a monochromatic photon with an approximate Z0-decay yield.Source: §6.3.2 · p. 29, Figure 3 · p. 29

6.3.3 Neutrinos

• DarkBit calculates solar capture, equilibration and annihilation rates before generating neutrino yields for nulike, which provides individual IceCube 79-string event-selection likelihoods and combined 79-string and 22-string likelihoods.The combined-search effective log-likelihood is capped at zero to prevent exclusion of the background hypothesis; micrOMEGAs neutrino-yield routines are not currently interfaced.Source: §6.3.3 · pp. 29–30

6.3.4 Fast Cascade Monte Carlo (FCMC)

• DarkBit’s Fast Cascade Monte Carlo generates decay chains using relative branching fractions and analyses their spectra for use in annihilation yields, with generation and analysis parallelised across CPU cores.The implementation assumes on-shell particles, two-body decays at each step, and neglects spin correlations.Source: §6.3.4 · p. 31
• To build cascade spectra, the FCMC samples photon energies from tabulated spectra, boosts them to the lab frame, and adds the resulting box spectra to histograms.The current default and only supported final state is gamma.Source: §6.3.4 · p. 31
• The FCMC spectra reproduce the box-feature endpoints and normalization expected analytically for photons from scalar decays.The example assumes χχ → φ1φ2, with φ1 decaying to photons and φ2 to bb̄; the figure varies mφ1 while fixing mχ = mφ2 = 100 GeV.Source: §6.3.4 · p. 32, Figure 5 · p. 32
• Compared with direct χχ → bb̄ annihilation, the cascade continuum peak shifts down by about a factor of 2 in energy, while its high-energy cutoff depends on mφ1.The shift reflects each quark having, on average, half the kinetic energy; the cutoff agrees with the kinematically available maximum photon energy.Source: §6.3.4 · p. 32, Figure 5 · p. 32
• The implementation neglects off-shell decays and finite particle widths, and may stop before convergence if the maximum event count is reached.The event limit can terminate the Monte Carlo before any histogram convergence criterion is met.Source: §6.3.4 · p. 32

7.1 CMSSM, MSSM and Singlet DM

• The CMSSM, MSSM7, and singlet-DM scans vary two dark-matter-relevant parameters one at a time and calculate four observables with corresponding likelihoods.The observables are relic density, spin-independent and spin-dependent DM-proton scattering, and late-time annihilation cross-section.Source: §7.1 · pp. 32–33
• Across CMSSM, MSSM7, and singlet-DM scans, DarkBit likelihoods agree with the corresponding experimental analyses.The comparisons cover relic density, spin-independent and spin-dependent scattering, and annihilation observables.Source: Figure 6 · p. 33, §7.1 · p. 33

7.2 Effective WIMPs

• The standalone WIMP example calculates likelihood tables versus dark matter mass and annihilation or scattering cross-section for indirect and direct-detection experiments.The indirect-detection examples include Fermi-LAT, HESS, and projected CTA limits.Source: §7.2 · pp. 34–35
• DarkBit’s standalone WIMP limits agree with official results for indirect and direct detection.The examples show 95% CL indirect limits and 90% CL direct-detection limits.Source: Figure 7 · p. 34, Figure 8 · p. 34, Figure 9 · p. 35

7.3 Comparing DarkSUSY and micrOMEGAs

• For resonant benchmark 14, DarkSUSY gives substantially higher Ωh2 than micrOMEGAs, whose freeze-out ⟨σveff⟩ is consistently larger.The fractional differences are largest on resonance; shifting mA0 or mh away from 2mχ0 improves agreement.Source: §7.3 · p. 35
• Small nuclear scattering cross-sections can differ substantially between codes, likely because diagram cancellations are sensitive to input parameters and calculation choices.The passage links discrepancies to spectrum-generator choices, running parameters, and loop-correction treatments.Source: §7.3 · p. 36

Development direction

• DarkBit’s modularity is intended to make extensions straightforward, with future development steered largely by community needs and contributions.The authors also expect to add new experimental likelihoods to gamLike, DDCalc, and nulike.Source: §8 · p. 36

Relic density

• Coannihilations, semiannihilating and asymmetric dark matter, Sommerfeld enhancement, non-standard cosmologies, and kinetic freeze-out are planned relic-density extensions.The current process catalogue and DarkSUSY Boltzmann solver calculate relic densities for simple arbitrary DM models; kinetic freeze-out would add a matter-power-spectrum cutoff observable.Source: §8 · p. 36

Direct detection

• DDCalc is planned to gain velocity- and momentum-dependent cross sections for studying the full set of available non-relativistic operators.Helio- and astroseismological probes of DM-nucleon couplings are also expected extensions.Source: §8 · p. 36

Indirect detection

• Charged cosmic rays are the most important planned indirect-search extension, alongside fully supporting velocity-dependent annihilation cross sections.The authors identify positron data as already imposing stringent limits on leptophilic DM models and expect antiproton constraints to improve considerably.Source: §8 · p. 36

Conclusions

• DarkBit combines reusable, self-consistent calculations with modular interfaces to existing tools, including DarkSUSY and micrOMEGAs.Internal particle and astrophysical properties are used consistently and passed to external codes when needed; calculations are split into elemental building blocks where possible.Source: §9 · pp. 36–37
• Its relic-density routines can solve the Boltzmann equation independently of the DM particle model, or call model-specific backend routines for comparison.The paper gives systematic comparison between DarkSUSY and micrOMEGAs as an example.Source: §9 · p. 37
• DDCalc supplies detailed likelihoods for major direct-detection experiments and supports self-consistent use of spin-dependent and spin-independent signals.For liquid noble gas detectors, its sensitivities are based on the TPCMC detector Monte Carlo simulation.Source: §9 · pp. 37–38
• gamLike implements gamma-ray likelihoods for Fermi-LAT and HESS observations of dwarf spheroidal galaxies and the Galactic centre, plus future CTA projections.The likelihoods are pre-tabulated for fast evaluation and use event-level mock data where possible; DarkBit also provides fast cascade-spectrum simulation and interfaces to nulike for neutrino likelihoods.Source: §9 · p. 38
• Planned extensions include charged cosmic rays, velocity-dependent annihilation and direct-detection cross sections, and additional experimental likelihoods.Future likelihood classes are also expected for helio- and astroseismological probes and radio and CMB observations.Source: §9 · p. 38

Appendix A: Getting started

• The appendix describes the contents of the DarkBit standalone download.It also outlines installation as either a standalone tool or a GAMBIT module.Source: Appendix A · p. 38
• The appendix covers installation of DarkBit in standalone mode and as a GAMBIT module.The passage directs readers to the following material for the installation details.Source: Appendix A · p. 38
• The appendix also introduces an example program for running DarkBit.The passage identifies the example as part of the getting-started material.Source: Appendix A · p. 38

A.1: Content of DarkBit download & installation

• A standalone module needs the shared GAMBIT folders as well as the DarkBit folder; using DarkBit with other GAMBIT modules requires only its module folder.The build instructions recommend an out-of-source CMake build to keep the source directory unchanged and allow multiple builds.Source: §A.1 · p. 38

A.2: Running the example program

• Two annotated YAML scan examples show how to specify a model, parameter priors, scanner, output device, and DarkBit likelihoods.The examples cover relic-density, gamma-ray, neutrino, and direct-search likelihoods, and allow selection of halo-model and nuclear parameters.Source: §A.2 · p. 39

B.1: Design goals and philosophy

• The library targets portability challenges involved in wrapping functions from different languages and returning them to backend codes.Manipulated functions may need to be wrapped back into plain C functions for use by backends such as the DarkSUSY Boltzmann solver.Source: §B.1 · p. 39
• daFunk is a lightweight, header-only C++ library for manipulating functions shared among different backends.The library is presented to facilitate operations required when functions are adapted for subsequent codes.Source: §B.1 · p. 39
• Its features include interpolation, multidimensional integration, singularity handling, parameter substitution, and function wrapping across Fortran, C, and C++.It also supports arithmetic and trigonometric operations.Source: §B.1 · p. 39

B.2: Selected examples

• daFunk::Funk provides a unified interface, while derived classes implement the actual calculations.Funk objects also expose variable names and can be combined using arithmetic and common mathematical operations.Source: §B.2 · pp. 39–40
• Binding variable positions produces a FunkBound object for evaluation, separating construction overhead from potentially many evaluations.The construction step can include string matching and consistency checks, which need to be done only once.Source: §B.2 · p. 40
• A wrapped function can fix velocity, substitute dark matter mass with centre-of-mass energy, and be wrapped back for evaluation or backend use.The example wraps dNdE, fixes v = 10^-4, substitutes m = Ecm/2, and passes the resulting function through a plain C interface.Source: §B.2 · p. 40
• A one-dimensional integral with a variable upper boundary can be constructed and bound for evaluation; failed integration prints a warning and returns zero.The example integrates x^2 from 0 to a, then evaluates the bound result at a = 2.5.Source: §B.2 · p. 40

Appendix C: Glossary

• A backend is an external code whose functions or variables may be accessed by a module function; its frontend specifies backend function capabilities and call signatures.Backend requirements declare when module functions need access to backend functions or variables.Source: Appendix C · p. 40
• A capability names the quantity calculated by a module or backend function, while a dependency declares access to another module function’s result.Dependency resolution produces a directed acyclic graph of module functions connected by resolved dependencies.Source: Appendix C · p. 41

Appendix D: Capability overview

• The capability overview covers process and coupling, halo, relic-density, direct-detection, gamma-ray, neutrino, cascade-decay, and miscellaneous capabilities.The overview references Tables A1–A13, with cascade-decay capabilities in Tables A11 and A12.Source: Appendix D · p. 41