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If dark matter annihilates into standard model particles with a cross-sectionwhich is velocity dependent, then Local Group dwarf galaxies will not be thebest place to search for the resulting gamma ray emission. A greater flux wouldbe produced by more distant and massive halos, with larger velocitydispersions. We construct full-sky predictions for the gamma-ray emission fromgalaxy- and cluster-mass halos within $\sim 200 \, {\mathrm{Mpc}}$ using asuite of constrained $N$-body simulations (CSiBORG) based on the BayesianOrigin Reconstruction from Galaxies algorithm. Comparing to observations fromthe Fermi Large Area Telescope and marginalising over reconstructionuncertainties and other astrophysical contributions to the flux, we obtainconstraints on the cross-section which are two (seven) orders of magnitudetighter than those obtained from dwarf spheroidals for $p$-wave ($d$-wave)annihilation. We find no evidence for either type of annihilation from darkmatter particles with masses in the range $m_\chi = 2-500 \,{\mathrm{GeV}}/c^2$, for any channel. As an example, for annihilationsproducing bottom quarks with $m_\chi = 10 \, {\mathrm{GeV}}/c^2$, we find$a_{1} < 2.4 \times 10^{-21} \, {\mathrm{cm^3 s^{-1}}}$ and $a_{2} < 3.0 \times10^{-18} \, {\mathrm{cm^3 s^{-1}}}$ at 95% confidence, where the product of thecross-section, $\sigma$, and relative particle velocity, $v$, is given by$\sigma v = a_\ell (v/c)^{2\ell}$ and $\ell=1, 2$ for $p$-, $d$-waveannihilation, respectively. Our bounds, although failing to exclude the thermalrelic cross-section for velocity-dependent annihilation channels, are among thetightest to date.

No evidence for p- or d-wave dark matter annihilation from local large-scale structure