Limits are for the dimensionless quantity [$\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }/{\mathit m}_{{{\mathit A}^{0}}}]{}^{2}\rho _{\mathit A}$ where $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ denotes the axion two-photon coupling, $\mathit L_{{\mathrm {int}}}$ = $−$ ${\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }\over 4}{{\mathit \phi}_{{A}}}{{\mathit F}}$ $_{ {{\mathit \mu}} {{\mathit \nu}} }{{\widetilde{\mathit F}}}{}^{ {{\mathit \mu}} {{\mathit \nu}} }$ = $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }\phi _{\mathit A}\mathbf {E}\cdot{}\mathbf {B}$, and $\rho _{A}$ is the axion energy density near the earth, unless otherwise stated. Notice that for QCD axions $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }/{\mathit m}_{{{\mathit A}^{0}}}$ does not depend on ${\mathit m}_{{{\mathit A}^{0}}}$. For the reference values ${\mathit m}_{{{\mathit A}^{0}}}$ = 1 $\mu $eV, $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ = $3.9 \times 10^{-16}$ GeV${}^{-1}$ (that would apply to KSVZ axions at that mass), and ${{\mathit \rho}_{{A}}}$ = 300 MeV/cm${}^{3}$ one finds [$\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }/{\mathit m}_{{{\mathit A}^{0}}}]{}^{2}\rho _{\mathit A}$ = $3.5 \times 10^{-43}$.

VALUE CL% DOCUMENT ID TECN  COMMENT • • We do not use the following data for averages, fits, limits, etc. • • $<2.8 \times 10^{-4}$ 95 1 ADE 2021 CMB ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.16 - 4.8 \times 10^{-20}$ eV $<1.1 \times 10^{-41}$ 90 2 ALESINI 2021 QUAX ${\mathit m}_{{{\mathit A}^{0}}}$ = 43 $\mu $eV $<1 \times 10^{-44}$ 90 3 BARTRAM 2021 A ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $3.3 - 4.2$ $\mu $eV $<1.6 \times 10^{-29}$ 95 4 DEVLIN 2021 TRAP ${\mathit m}_{{{\mathit A}^{0}}}$ = $2.7906 - 2.7914$ neV $<1.4 \times 10^{-23}$ 95 5 GRAMOLIN 2021 SHFT ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.012 - 12$ neV $<7 \times 10^{-43}$ 90 6 KWON 2021 CASK ${\mathit m}_{{{\mathit A}^{0}}}$ = $10.7126 - 10.7186$ $\mu $eV $<4.6 \times 10^{-40}$ 95 7 MELCON 2021 RADE ${\mathit m}_{{{\mathit A}^{0}}}$ = $34.6738 - 34.6771$ $\mu $eV $<3.5 \times 10^{-28}$ 95 8 SALEMI 2021 ABRA ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.41 - 8.27$ neV $<3 \times 10^{-3}$ 95 9 THOMSON 2021 ${\mathit m}_{{{\mathit A}^{0}}}$ = $7.44 - 19.38$ neV $<0.01$ 95 9 THOMSON 2021 ${\mathit m}_{{{\mathit A}^{0}}}$ = $74.4 - 74.5$ $\mu $eV 10 YUAN 2021 ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $10^{-20} - 10^{-17}$ eV $<1.9 \times 10^{-44}$ 90 11 BRAINE 2020 ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $2.81 - 3.31$ $\mu $eV $<2 \times 10^{-35}$ 90 12 CRISOSTO 2020 SLIC ${\mathit m}_{{{\mathit A}^{0}}}$ = $180.07 - 180.15$ neV $<4 \times 10^{-37}$ 95 13 DARLING 2020 A ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $4.2 - 165.6$ $\mu $eV $<3.2 \times 10^{-36}$ 95 14 FOSTER 2020 ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $5 - 7$, $10 - 11\mu $eV $<5.7 \times 10^{-41}$ 90 15 JEONG 2020 CASK ${\mathit m}_{{{\mathit A}^{0}}}$ = $13.0 - 13.9$ $\mu $eV 16 KENNEDY 2020 ${\mathit m}_{{{\mathit S}^{0}}}$ = $10^{-19} - 10^{-17}$ eV $<4.8 \times 10^{-42}$ 90 17 LEE 2020 A CASK ${\mathit m}_{{{\mathit A}^{0}}}$ = $6.62 - 6.82$ $\mu $eV $<2.6 \times 10^{-39}$ 95 18 ALESINI 2019 QUAX ${\mathit m}_{{{\mathit A}^{0}}}$ = 37.5 $\mu $eV $<6 \times 10^{-5}$ 19 FUJITA 2019 ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $10^{-21}$ eV $<2 \times 10^{-27}$ 95 20 OUELLET 2019 A ABRA ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.31 - 8.3$ neV $<7.3 \times 10^{-40}$ 90 21 BOUTAN 2018 ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $17.38 - 17.57$ $\mu $eV $<1.8 \times 10^{-39}$ 90 21 BOUTAN 2018 ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $21.03 - 23.98$ $\mu $eV $<3.4 \times 10^{-39}$ 90 21 BOUTAN 2018 ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $29.67 - 29.79$ $\mu $eV $<1.4 \times 10^{-44}$ 90 22 DU 2018 ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ =$2.66 - 2.81$ $\mu $eV $<2.87 \times 10^{-42}$ 90 23 ZHONG 2018 HYST ${\mathit m}_{{{\mathit A}^{0}}}$ =$23.15 - 24$ $\mu $eV 24 BRANCA 2017 AURG ${\mathit m}_{{{\mathit S}^{0}}}$ = $3.5 - 3.9$ peV $<3 \times 10^{-42}$ 90 25 BRUBAKER 2017 HYST ${\mathit m}_{{{\mathit A}^{0}}}$ = $23.55 - 24.0$ $\mu $eV $<1.0 \times 10^{-29}$ 95 26 CHOI 2017 CASK ${\mathit m}_{{{\mathit A}^{0}}}$ = $24.7 - 29.1$ $\mu $eV $<8.6 \times 10^{-42}$ 90 27 HOSKINS 2016 ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ =$3.36 - 3.52$ or $3.55 - 3.69$ $\mu $eV 28 BECK 2013 ${\mathit m}_{{{\mathit A}^{0}}}$ = 0.11 meV $<3.5 \times 10^{-43}$ 29 HOSKINS 2011 ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $3.3 - 3.69 \times 10^{-6}$ eV $<2.9 \times 10^{-43}$ 90 30 ASZTALOS 2010 ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $3.34 - 3.53 \times 10^{-6}$ eV $<1.9 \times 10^{-43}$ 97.7 31 DUFFY 2006 ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.98 - 2.17 \times 10^{-6}$ eV $<5.5 \times 10^{-43}$ 90 32 ASZTALOS 2004 ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.9 - 3.3 \times 10^{-6}$ eV 33 KIM 1998 THEO $<2 \times 10^{-41}$ 34 HAGMANN 1990 CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = ($5.4 - 5.9){}10^{-6}$ eV $<6.3 \times 10^{-42}$ 95 35 WUENSCH 1989 CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = ($4.5 - 10.2){}10^{-6}$ eV $<5.4 \times 10^{-41}$ 95 35 WUENSCH 1989 CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = ($11.3 - 16.3){}10^{-6}$ eV 1  ADE 2021 looks for a time-variable global rotation of the CMB polarization induced by the harmonic oscillations of local axion-like dark matter and uses data from the 2012 observing season of the Keck Array, part of the BICEP program. The limits get 25$\%$ weaker for ${\mathit m}_{{{\mathit A}^{0}}}$ = $4.8 \times 10^{-20} - 5.7 \times 10^{-19}$ eV. See their Eq. (80) and Fig. 6 for mass-dependent limits. 2  ALESINI 2021 is an update of ALESINI 2019 . See their Figs. 5 and 6 for the mass-dependent limits. 3  BARTRAM 2021A is analogous to DU 2018 . See their Fig.4 for mass-dependent limits. 4  DEVLIN 2021 use the superconducting resonant detection circuit of a cryogenic Penning trap with a single antiproton. See their Fig. 3 for mass-dependent limits. 5  GRAMOLIN 2021 use two detection channels, each consisting of two stacked toroids to look for the axion-induced oscillating magnetic field. The quoted limit applies at ${\mathit m}_{{{\mathit A}^{0}}}$ = 0.02 neV. See their Fig. 4 for mass-dependent limits. 6  KWON 2021 is analogous to LEE 2020A. They also obtain weaker limits in the range of ${\mathit m}_{{{\mathit A}^{0}}}$ = $10.16 - 11.37$ $\mu $eV. See their Fig. 4 for mass-dependent limits. 7  MELCON 2021 use a radio frequency cavity consisting of 5 sub-cavities coupled by inductive irises installed inside the CAST dipole magnet to look for higher axion masses. See their Fig. 9 for mass-dependent limits. 8  SALEMI 2021 is an update of OUELLET 2019A. See their Fig. 4 for mass-dependent limits. 9  THOMSON 2021 use a resonant cavity supporting two spatially overlapping microwave modes, which is sensitive to the axion mass corresponding to the sum or difference of the two resonant frequencies. The original limit was retracted due to a sign error. See their Fig. 2 in the erratum for the corrected limits. 10  YUAN 2021 use polarimetric observations of Sgr A${}^{*}$ taken by the Event Horizon Telescope to search for periodic oscillation of the polarization induced by axion dark matter, assuming a solitonic core near the Galactic center. They obtained limits in the range of $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ = $8 \times 10^{-13} - 3 \times 10^{-11}$ GeV${}^{-1}$. 11  BRAINE 2020 is analogous to DU 2018 . See Fig. 4 for their mass-dependent limits. 12  CRISOSTO 2020 used a resonant LC circuit to look for lighter axion dark matter. They obtained a similar, slightly weaker limit for ${\mathit m}_{{{\mathit A}^{0}}}$ = $174.98 - 175.19$ and $177.34 - 177.38$ neV. See their Fig. 4 for mass-dependent limits. 13  DARLING 2020A use VLA data to look for radio-frequency radiation converted from axion dark matter in the magnetosphere of the Galactic Center magnetar PSR J1745-2900. They extended the results of DARLING 2020 , which used only data with the highest angular resolution, by adding sub-optimal data. They use ${{\mathit \rho}_{{A}}}$ = $6.5 \times 10^{4}$ GeV/cm${}^{3}$ in the vicinity of the magnetar. See their Fig. 2 for mass-dependent limits. 14  FOSTER 2020 look for radio-frequency radiation converted from axion dark matter in the magnetic field around neutron stars. They use the observed data of isolated local neutron stars and in the Galactic center. The quoted limit applies to ${\mathit m}_{{{\mathit A}^{0}}}$ $\simeq{}$ 7 $\mu $eV. See their Fig. 2 for mass-dependent limits. 15  JEONG 2020 is analogous to LEE 2020A, and they use a double-cell cavity to look for axions with mass $>$ 10 $\mu $eV. See their Fig. 5 for mass-dependent limits. 16  KENNEDY 2020 is analogous to BRANCA 2017 , and they compare the frequency ratios of the ${}^{}\mathrm {Si}$ cavity measured by a ${}^{}\mathrm {Sr}$ optical lattice clock and by a ${}^{}\mathrm {H}$ maser. Assuming the local density of moduli dark matter, $\rho _{S}$ = 0.3 GeV/cm${}^{3}$, they obtain a limit $\mathit G_{ {{\mathit S}} {{\mathit \gamma}} {{\mathit \gamma}} }$ $<$ $5.8 \times 10^{-24}$ GeV${}^{-1}$ at ${\mathit m}_{{{\mathit S}^{0}}}$ = $2 \times 10^{-19}$ eV. See their Fig. 2 for mass-dependent limits as well as limits on the modulus coupling to electrons. 17  LEE 2020A used a microwave cavity detector at the IBS/CAPP to search for dark matter axions. See Fig. 3 for the mass-dependent limits. 18  ALESINI 2019 used a superconducting resonant cavity made of ${}^{}\mathrm {NbTi}$ to increase the quality factor. The limit applies to a mass range of 0.2 neV around ${\mathit m}_{{{\mathit A}^{0}}}$ = 37.5 $\mu $eV. 19  FUJITA 2019 look for photon birefringence under the oscillating axion background using the polarimetric imaging observation of a protoplanetary disk, AB Aur. See their Fig. 2 for a more conservative limit taking account of possible systematic effects. 20  OUELLET 2019A look for the axion-induced oscillating magnetic field generated by a toroidal magnetic field. The quoted limit applies at ${\mathit m}_{{{\mathit A}^{0}}}$ = 8 neV. See their Fig. 3 for the mass-dependent limits. 21  BOUTAN 2018 use a small high frequency cavity installed above the main ADMX cavity to look for heavier axion dark matter. See their Fig. 4 for mass-dependent limits. 22  DU 2018 is analogous to DUFFY 2006 . They upgraded a dilution refrigerator to reduce the system noise. The quoted limit is around ${\mathit m}_{{{\mathit A}^{0}}}$ = 2.69 $\mu $eV for the boosted Maxwellian axion line shape. See Fig. 4 for their mass-dependent limits. 23  ZHONG 2018 is analogous to BRUBAKER 2017 . The quoted limit applies at ${\mathit m}_{{{\mathit A}^{0}}}$ = 23.76 $\mu $eV. See Fig. 4 for their mass-dependent limits. 24  BRANCA 2017 look for modulations of the fine-structure constant and the electron mass due to moduli dark matter by using the cryogenic resonant-mass AURIGA detector. The limit on the assumed dilatonic coupling implies $\mathit G_{ {{\mathit S}} {{\mathit \gamma}} {{\mathit \gamma}} }$ $<$ $1.5 \times 10^{-24}$ GeV${}^{-1}$ for the scalar to two-photon coupling. See Fig. 5 for the mass-dependent limits. 25  BRUBAKER 2017 used a microwave cavity detector at the Yale Wright Laboratory to search for dark matter axions. See Fig. 3 for the mass-dependent limits. 26  CHOI 2017 used a microwave cavity detector with toroidal geometry. See Fig. 4 for their mass-dependent limits. 27  HOSKINS 2016 is analogous to DUFFY 2006 . See Fig.$~$12 for mass-dependent limits in terms of the local dark matter density. 28  BECK 2013 argues that dark-matter axions passing through Earth may generate a small observable signal in resonant S/N/S Josephson junctions. A measurement by HOFFMANN 2004 [Physical Review B70 180503 (2004)] is interpreted in terms of subdominant dark matter axions with ${\mathit m}_{{{\mathit A}^{0}}}$ = 0.11 meV. 29  HOSKINS 2011 is analogous to DUFFY 2006 . See Fig.$~$4 for the mass-dependent limit in terms of the local density. 30  ASZTALOS 2010 used the upgraded detector of ASZTALOS 2004 to search for halo axions. See their Fig.$~$5 for the ${\mathit m}_{{{\mathit A}^{0}}}$ dependence of the limit. 31  DUFFY 2006 used the upgraded detector of ASZTALOS 2004 , while assuming a smaller velocity dispersion than the isothermal model as in Eq. (8) of their paper. See Fig. 10 of their paper on the axion mass dependence of the limit. 32  ASZTALOS 2004 looked for a conversion of halo axions to microwave photons in magnetic field. At 90$\%$ CL, the KSVZ axion cannot have a local halo density more than 0.45~GeV/cm${}^{3}$ in the quoted mass range. See Fig.~7 of their paper on the axion mass dependence of the limit. 33  KIM 1998 calculated the axion-to-photon couplings for various axion models and compared them to the HAGMANN 1990 bounds. This analysis demonstrates a strong model dependence of $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ and hence the bound from relic axion search. 34  HAGMANN 1990 experiment is based on the proposal of SIKIVIE 1983 . 35  WUENSCH 1989 looks for condensed axions near the earth that could be converted to photons in the presence of an intense electromagnetic field via the Primakoff effect, following the proposal of SIKIVIE 1983 . The theoretical prediction with [$\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }/{\mathit m}_{{{\mathit A}^{0}}}]{}^{2}$ = $2 \times 10^{-14}$ MeV${}^{-4}$ (the three generation DFSZ model) and $\rho _{\mathit A}$ = 300 MeV/cm${}^{3}$ that makes up galactic halos gives ($\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }/{\mathit m}_{{{\mathit A}^{0}}}){}^{2}$ $\rho _{\mathit A}$ = $4 \times 10^{-44}$. Note that our definition of $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ is (1/4$\pi $) smaller than that of WUENSCH 1989 .

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