Invisible ${{\mathit A}^{0}}$ (Axion) MASS LIMITS from Astrophysics and Cosmology

INSPIRE   PDGID:
S029IAA
$\mathit v_{1}$ = $\mathit v_{2}$ is usually assumed ($\mathit v_{\mathit i}$ = vacuum expectation values). For a review of these limits, see RAFFELT 1991 and TURNER 1990. In the comment lines below, D and K refer to DFSZ and KSVZ axion types, discussed in the above minireview.
VALUE (eV) CL% DOCUMENT ID TECN  COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
1
CHENG
2023
ASTR BH superradiance
$>3.2 \times 10^{-19}$ 95 2
DELLA-MONICA
2023
ASTR Ultralight DM soliton halo core
$<141$ 90 3
DERBIN
2023
CNTR K, solar axions
$<0.24$ 95 4
NOTARI
2023
COSM K, Hot dark matter
5
ROGERS
2023
COSM Ultra-light axion DM
$\text{none } 10^{-24} - 5 \times 10^{-23}$ 95 6
SMARRA
2023
EPTA Ultralight DM mass limit
7
XIA
2023
ASTR Fuzzy DM
8
LAGUE
2022
COSM Ultralight axion DM
$\text{none } 0.15 - 1.5 \times 10^{-12}$ 95 9
YUAN
2022A
 ASTR BH superradiance
$>1.4 \times 10^{-21}$ 95 10
BANIK
2021
ASTR Fuzzy DM
$<1.9 \times 10^{4}$ 11
BAUMHOLZER
2021
COSM warm dark matter
12
CROON
2021
ASTR SN 1987A, axion-muon coupling
13
FUJIKURA
2021
ASTR Microlensing
14
MARTINCAMALIC..
2021
ASTR SN 1987A, ${{\mathit \Lambda}}$ decay
$\text{none } 1.3 - 2.7 \times 10^{-13}$ 15
NG
2021
ASTR BH superradiance
$>2 \times 10^{-20}$ 95 16
ROGERS
2021
COSM Lyman-$\alpha $
$\text{none } 0.8 - 6.5 \times 10^{-13}$ 95 17
TSUKADA
2021
ASTR BH superradiance
$>2 \times 10^{-17}$ 18
IRSIC
2020
COSM Isocurvature fluctuations
19
PODDAR
2020
ASTR Compact binary systems
$>2.1 \times 10^{-21}$ 20
SCHUTZ
2020
COSM Fuzzy DM
$\text{none } 6.4 - 8.0 \times 10^{-13}$ 95 21
SUN
2020
ASTR BH superradiance
$\text{none } 2.9 - 4.6 \times 10^{-21}$ 22
DAVOUDIASL
2019
ASTR BH superradiance
$\text{none } 10^{-21} - 6 \times 10^{-20}$ 23
MARSH
2019
ASTR Fuzzy DM
$\text{none } 1.1 - 4 \times 10^{-13}$ 95 24
PALOMBA
2019
ASTR BH superradiance
$<0.06$ 25
CHANG
2018
ASTR K, SN 1987A
26
PORAYKO
2018
PPTA Fuzzy DM
$<0.67$ 95 27
ARCHIDIACONO
2013A
 COSM K, hot dark matter
$\text{none } 0.7 - 3 \times 10^{5}$ 28
CADAMURO
2011
COSM ${}^{}\mathrm {D}$ abundance
$<105$ 90 29
DERBIN
2011A
 CNTR D, solar axion
30
ANDRIAMONJE
2010
CAST K, solar axions
$<0.72$ 95 31
HANNESTAD
2010
COSM K, hot dark matter
32
ANDRIAMONJE
2009
CAST K, solar axions
$<191$ 90 33
DERBIN
2009A
 CNTR K, solar axions
$<334$ 95 34
KEKEZ
2009
HPGE K, solar axions
$<1.02$ 95 35
HANNESTAD
2008
COSM K, hot dark matter
$<1.2$ 95 36
HANNESTAD
2007
COSM K, hot dark matter
$<0.42$ 95 37
MELCHIORRI
2007A
 COSM K, hot dark matter
$<1.05$ 95 38
HANNESTAD
2005A
 COSM K, hot dark matter
$3\text{ to }20 $ 39
MOROI
1998
COSM K, hot dark matter
$<0.007$ 40
BORISOV
1997
ASTR D, neutron star
$<4$ 41
KACHELRIESS
1997
ASTR D, neutron star cooling
$<(0.5 - 6){\times }\text{ 10}$$^{-3}$ 42
KEIL
1997
ASTR SN 1987A
$<0.018$ 43
RAFFELT
1995
ASTR D, red giant
$<0.010$ 44
ALTHERR
1994
ASTR D, red giants, white dwarfs
45
CHANG
1993
ASTR K, SN 1987A
$<0.01$
WANG
1992
ASTR D, white dwarf
$<0.03$
WANG
1992C
 ASTR D, C-O burning
$\text{none 3 - 8}$ 46
BERSHADY
1991
ASTR D, K, intergalactic light
$<10$ 47
KIM
1991C
 COSM D, K, mass density of the universe, supersymmetry
48
RAFFELT
1991B
 ASTR D,K, SN 1987A
$<1 \times 10^{-3}$ 49
RESSELL
1991
ASTR K, intergalactic light
$\text{none } 10^{-3} - 3$
BURROWS
1990
ASTR D,K, SN 1987A
50
ENGEL
1990
ASTR D,K, SN 1987A
$<0.02$ 51
RAFFELT
1990D
 ASTR D, red giant
$<1 \times 10^{-3}$ 52
BURROWS
1989
ASTR D,K, SN 1987A
$<(1.4 - 10){\times }\text{ 10}$$^{-3}$ 53
ERICSON
1989
ASTR D,K, SN 1987A
$<3.6 \times 10^{-4}$ 54
MAYLE
1989
ASTR D,K, SN 1987A
$<12$
CHANDA
1988
ASTR D, Sun
$<1 \times 10^{-3}$
RAFFELT
1988
ASTR D,K, SN 1987A
55
RAFFELT
1988B
 ASTR red giant
$<0.07$
FRIEMAN
1987
ASTR D, red giant
$<0.7$ 56
RAFFELT
1987
ASTR K, red giant
$\text{< 2-5}$
TURNER
1987
COSM K, thermal production
$<0.01$ 57
DEARBORN
1986
ASTR D, red giant
$<0.06$
RAFFELT
1986
ASTR D, red giant
$<0.7$ 58
RAFFELT
1986
ASTR K, red giant
$<0.03$
RAFFELT
1986B
 ASTR D, white dwarf
$<1$ 59
KAPLAN
1985
ASTR K, red giant
$\text{<0.003 - 0.02}$
IWAMOTO
1984
ASTR D, K, neutron star
$>1 \times 10^{-5}$
ABBOTT
1983
COSM D,K, mass density of the universe
$>1 \times 10^{-5}$
DINE
1983
COSM D,K, mass density of the universe
$<0.04$
ELLIS
1983B
 ASTR D, red giant
$>1 \times 10^{-5}$
PRESKILL
1983
COSM D,K, mass density of the universe
$<0.1$
BARROSO
1982
ASTR D, red giant
$<1$ 60
FUKUGITA
1982
ASTR D, stellar cooling
$<0.07$
FUKUGITA
1982B
 ASTR D, red giant
1  CHENG 2023 employ an improved approximation of the boson cloud eigenfrequency to calculate the superradiance rate. They find that sensitivity depends on initial spin distribution and the merger timescale, and identify two preferred ranges for boson mass centered at $1.78 \times 10^{-12}$ and $7.94 \times 10^{-13}$ eV.
2  DELLA-MONICA 2023 consider the solitonic core implied by ultralight scalar dark matter in the centre of the Milky Way and the effect its presence would have on the precisely tracked orbits of the stars orbiting our galaxy's central supermassive black hole, Sagittarius A${}^{*}$.
3  DERBIN 2023 employ a thulium garnet crystal bolometer to search for the 8.4 keV solar axion line emitted from the M1 nuclear transition of thulium-169, ${}^{169}\mathrm {Tm}$. Mass bound applies to KSVZ axions, value for DFSZ is 244 eV.
4  NOTARI 2023 improved the evaluation of axion production from pion scatterings by using pion-pion scattering data and incorporating the momentum dependence of the Boltzmann equation. The limit is based on the Planck 2018, BAO, and Pantheon SN Ia data.
5  ROGERS 2023 use the CMB and BOSS galaxy-clustering data to set limits on the abundance of ultralight axion DM. They obtained $\Omega _{{{\mathit A}^{0}}}$ $<$ 0.002 for ${\mathit m}_{{{\mathit A}^{0}}}$ = $10^{-30} - 10^{-28}$ eV and set upper limits ranging from 0.002 to 0.07 for ${\mathit m}_{{{\mathit A}^{0}}}$ = $10^{-32} - 10^{-25}$ eV. See their Fig. 22 for mass-dependent limits.
6  SMARRA 2023 is the European Pulsar Timing Array's constraint on the contribution of ultralight DM to the DM density in our local galactic neighbourhood. Ultralight DM cannot saturate the known DM density of 0.3 GeV/cc for masses inside this mass interval of $10^{-24} - 5 \times 10^{-23}$ eV.
7  XIA 2023 is analogous to PORAYKO 2018 and use the Fermi-LAT pulsar timing array. They set a bound on the local density as $\rho _{{{\mathit A}^{0}}}{ {}\lesssim{} }$ 8 GeV/cm${}^{3}$ for ${\mathit m}_{{{\mathit A}^{0}}}{ {}\lesssim{} }$ $10^{-23}$ eV at 95$\%$ CL, with weaker constraints up to $10^{-22}$ eV. See their Fig. 1 for the mass-dependent limits.
8  LAGUE 2022 used the BOSS galaxy-clustering data to set limits on the abundance of ultralight axion dark matter. When combined with the CMB data, they obtained $\Omega _{{{\mathit A}^{0}}}\mathit h{}^{2}$ $<$ 0.004 for ${\mathit m}_{{{\mathit A}^{0}}}$ = $10^{-31} - 10^{-26}$ eV. See their Figs. 1 and 15 for mass-dependent limits.
9  YUAN 2022A use the data of Advanced LIGO and Advanced Virgo's first three observing runs to search for stochastic GW background produced by scalar bosonic clouds formed by the BH superradiant instability. They set the limit, taking into account all the unstable modes.
10  BANIK 2021 use the subhalo mass function inferred from the analyses of the GD-1 and Pal 5 stellar streams. The limit is strengthened to $2.2 \times 10^{-21}$ eV when adding dwarf satellite counts.
11  BAUMHOLZER 2021 study the freeze-in production of axion dark matter through couplings to photons, and set the limit using Lyman-$\alpha $ forest data and the observed number of Milky Way subhalos.
12  CROON 2021 study the supernova cooling effect of the axion-muon coupling, taking account of semi-Compton scattering and muon-proton bremsstrahlung, as well as the loop-induced axion-photon coupling, and exclude the range of $\mathit g_{{{\mathit A}} {{\mathit \mu}} {{\mathit \mu}}}$ $\simeq{}$ $7 \times 10^{-3} - 2 \times 10^{-10}$ for ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $0.5$ GeV. See their Fig. 8 for mass-dependent limits.
13  FUJIKURA 2021 use the EROS-2 survey and the Subaru HSC observation to set limits on spherically symmetric axion clumps, taking account of the finite lens and source size effects. $\mathit f_{{{\mathit A}^{0}}}{ {}\gtrsim{} }$ $10^{12}$ GeV can be constrained depending on the fraction of the axion dark matter collapsed into clumps, and the clump densities. See their Figs. $7 - 10$ for the limits.
14  MARTINCAMALICH 2021 considered axion emission from a supernova core through the ${{\mathit \Lambda}}$ hyperon decay, and set the limit on B( ${{\mathit \Lambda}}$ $\rightarrow$ ${{\mathit n}}{{\mathit A}^{0}}$) ${ {}\lesssim{} }$ $8 \times 10^{-9}$, or equivalently, $\mathit f_{{{\mathit A}^{0}}}/C_{sd}{ {}\gtrsim{} }$ $2.6 \times 10^{9}$ GeV in terms of the flavor-violating axion coupling to the down and strange quarks.
15  NG 2021 use the binary black holes reported by LIGO and Virgo to determine the black hole spin distribution at formation and the scalar boson mass simultaneously, neglecting the boson self-interaction.
16  ROGERS 2021 set the limit by using a framework involving Bayesian emulator optimization to accurately forward-model the Lyman-$\alpha $ flux power spectrum, and comparing this with small-scale data to constrain the predicted suppression of cosmic structure growth.
17  TSUKADA 2021 look for a stochastic GW background produced by extragalactic BH-hidden photon cloud systems through the superradiant instability. They assume a uniform spin distribution at birth of isolated BHs from 0 to 1.
18  IRSIC 2020 used the Lyman-$\alpha $ forest constraint on small-scale isocurvature perturbation to derive limits on the axion mass and decay constant, assuming that the axion makes up all dark matter in the post-inflationary scenario. See their Fig. 1 for other astrophysical limits as well as the limits on the case of the temperature-dependent axion mass.
19  PODDAR 2020 used the observed decay in orbital period of four compact binary systems to derive a limit on the emission of axions with ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $1 \times 10^{-19}$ eV, assuming they couple to nucleons and the strong $\mathit CP$ phase vanishes at the potential minimum. They exclude $\mathit f_{{{\mathit A}^{0}}}{ {}\lesssim{} }$ $10^{11}$ GeV for such axions.
20  SCHUTZ 2020 set a limit on fuzzy dark matter based on the existing limits for warm dark matter derived from the inferred subhalo mass function.
21  SUN 2020 look for quasimonochromatic gravitational waves emitted from boson clouds around the Cygnus X-1 black hole. The quoted limit assume the black hole age of $5 \times 10^{6}$ years. A mass range of $9.6 - 15.5 \times 10^{-13}$ eV is disfavored when repeated induction of bosenova for string axions with decay constant $\mathit f_{{{\mathit A}^{0}}}$ $\simeq{}$ $10^{15}$ GeV prevents the superradiance from being saturated.
22  DAVOUDIASL 2019 used the observed data of M87* by the Event Horizon Telescope to set the limit. A mass range of $0.85 - 4.6 \times 10^{-21}$ eV is disfavored for a spin-1 boson.
23  MARSH 2019 considered heating of star clusters due to the stochastic oscillations of the core and granular quasiparticles in the outer halo. The limit was derived by requiring the survival of the old star cluster in Eridanus II, where the lower end is set by the validity of diffusion approximation. The effect of tidal stripping is also discussed for lower masses.
24  PALOMBA 2019 used the LIGO O2 dataset to derive limits on nearly monochromatic gravitational waves emitted by boson clouds formed around a stellar-mass black hole. They exclude boson masses in a range of $1.1 \times 10^{-13}$ and $4 \times 10^{-13}$ eV for high initial black hole spin, and $1.2 \times 10^{-13}$ and $1.8 \times 10^{-13}$ eV for moderate spin. See their Figs. 2 and 3 for limits based on various values of black hole initial spin, boson cloud age, and distance.
25  CHANG 2018 update axion bremsstrahlung emission rates in nucleon-nucleon collisions, shifting the excluded mass range to higher values. They rule out the hadronic axion with mass up to a few hundred eV, closing the hadronic axion window. See their Fig. 11 for results based on several different choices of the temperature and density profile of the proto-neutron star.
26  PORAYKO 2018 look for time-dependent oscillations in the gravitational potential generated by ultralight scalar dark matter, and set a bound on its local density as $\rho _{{{\mathit A}^{0}}}{ {}\lesssim{} }$ 6 GeV/cm${}^{3}$ for ${\mathit m}_{{{\mathit A}^{0}}}{ {}\lesssim{} }$ $10^{-23}$ eV at 95$\%$ CL. See their Fig. 4 for the limits.
27  ARCHIDIACONO 2013A is analogous to HANNESTAD 2005A. The limit is based on the CMB temperature power spectrum of the Planck data, the CMB polarization from the WMAP 9-yr data, the matter power spectrum from SDSS-DR7, and the local Hubble parameter measurement by the Carnegie Hubble program.
28  CADAMURO 2011 use the deuterium abundance to show that the ${\mathit m}_{{{\mathit A}^{0}}}$ range 0.7$~$eV -- 300$~$keV is excluded for axions, complementing HANNESTAD 2010.
29  DERBIN 2011A look for solar axions produced by Compton and bremsstrahlung processes, in the resonant excitation of ${}^{169}\mathrm {Tm}$, constraining the axion-electron ${\times }$ axion nucleon couplings.
30  ANDRIAMONJE 2010 search for solar axions produced from ${}^{7}\mathrm {Li}$ (478 keV) and ${}^{}\mathrm {D}({{\mathit p}},{{\mathit \gamma}}){}^{3}\mathrm {He}$ (5.5 MeV) nuclear transitions. They show limits on the axion-photon coupling for two reference values of the axion-nucleon coupling for ${\mathit m}_{{{\mathit A}}}<$ 100 eV.
31  This is an update of HANNESTAD 2008 including 7 years of WMAP data.
32  ANDRIAMONJE 2009 look for solar axions produced from the thermally excited 14.4 keV level of ${}^{57}\mathrm {Fe}$. They show limits on the axion-nucleon ${\times }$ axion-photon coupling assuming ${\mathit m}_{{{\mathit A}}}<$ 0.03 eV.
33  DERBIN 2009A look for Primakoff-produced solar axions in the resonant excitation of ${}^{169}\mathrm {Tm}$, constraining the axion-photon ${\times }$ axion-nucleon couplings.
34  KEKEZ 2009 look at axio-electric effect of solar axions in HPGe detectors. The one-loop axion-electron coupling for hadronic axions is used.
35  This is an update of HANNESTAD 2007 including 5 years of WMAP data.
36  This is an update of HANNESTAD 2005A with new cosmological data, notably WMAP (3 years) and baryon acoustic oscillations (BAO). Lyman-$\alpha $ data are left out, in contrast to HANNESTAD 2005A and MELCHIORRI 2007A, because it is argued that systematic errors are large. It uses Bayesian statistics and marginalizes over a possible neutrino hot dark matter component.
37  MELCHIORRI 2007A is analogous to HANNESTAD 2005A, with updated cosmological data, notably WMAP (3 years). Uses Bayesian statistics and marginalizes over a possible neutrino hot dark matter component. Leaving out Lyman-$\alpha $ data, a conservative limit is 1.4 eV.
38  HANNESTAD 2005A puts an upper limit on the mass of hadronic axion because in this mass range it would have been thermalized and contribute to the hot dark matter component of the universe. The limit is based on the CMB anisotropy from WMAP, SDSS large scale structure, Lyman $\alpha $, and the prior Hubble parameter from HST Key Project. A ${{\mathit \chi}^{2}}$ statistic is used. Neutrinos are assumed not to contribute to hot dark matter.
39  MOROI 1998 points out that a KSVZ axion of this mass range (see CHANG 1993) can be a viable hot dark matter of Universe, as long as the model-dependent $\mathit g_{{{\mathit A}} {{\mathit \gamma}}}$ is accidentally small enough as originally emphasized by KAPLAN 1985; see Fig.$~$1.
40  BORISOV 1997 bound is on the axion-electron coupling $\mathit g_{\mathit ae}<1 \times 10^{-13}$ from the photo-production of axions off of magnetic fields in the outer layers of neutron stars.
41  KACHELRIESS 1997 bound is on the axion-electron coupling $\mathit g_{\mathit ae}<1 \times 10^{-10}$ from the production of axions in strongly magnetized neutron stars. The authors also quote a stronger limit, $\mathit g_{\mathit ae}<9 \times 10^{-13}$ which is strongly dependent on the strength of the magnetic field in white dwarfs.
42  KEIL 1997 uses new measurements of the axial-vector coupling strength of nucleons, as well as a reanalysis of many-body effects and pion-emission processes in the core of the neutron star, to update limits on the invisible-axion mass.
43  RAFFELT 1995 reexamined the constraints on axion emission from red giants due to the axion-electron coupling. They improve on DEARBORN 1986 by taking into proper account degeneracy effects in the bremsstrahlung rate. The limit comes from requiring the red giant core mass at helium ignition not to exceed its standard value by more than 5$\%$ ($0.025$ solar masses).
44  ALTHERR 1994 bound is on the axion-electron coupling $\mathit g_{\mathit ae}<1.5 \times 10^{-13}$, from energy loss via axion emission.
45  CHANG 1993 updates ENGEL 1990 bound with the Kaplan-Manohar ambiguity in $\mathit z={\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$ (see the Note on the Quark Masses in the Quark Particle Listings). It leaves the window $\mathit f_{\mathit A}=3 \times 10^{5}-3 \times 10^{6}$ GeV open. The constraint from Big-Bang Nucleosynthesis is satisfied in this window as well.
46  BERSHADY 1991 searched for a line at wave length from $3100 - 8300$ $Å$ expected from 2${{\mathit \gamma}}$ decays of relic thermal axions in intergalactic light of three rich clusters of galaxies.
47  KIM 1991C argues that the bound from the mass density of the universe will change drastically for the supersymmetric models due to the entropy production of saxion (scalar component in the axionic chiral multiplet) decay. Note that it is an $\mathit upperbound$ rather than a lowerbound.
48  RAFFELT 1991B argue that previous SN$~$1987A bounds must be relaxed due to corrections to nucleon bremsstrahlung processes.
49  RESSELL 1991 uses absence of any intracluster line emission to set limit.
50  ENGEL 1990 rule out $10^{-10}~{ {}\lesssim{} }$ $\mathit g_{\mathit AN}{ {}\lesssim{} }~10^{-3}$, which for a hadronic axion with EMC motivated axion-nucleon couplings corresponds to $2.5 \times 10^{-3}~$eV ${ {}\lesssim{} }{\mathit m}_{{{\mathit A}^{0}}}{ {}\lesssim{} }$ $2.5 \times 10^{4}~$eV. The constraint is loose in the middle of the range, i.e. for ${\mathit g}_{\mathit AN}$ $\sim{}~10^{-6}$.
51  RAFFELT 1990D is a re-analysis of DEARBORN 1986.
52  The region ${\mathit m}_{{{\mathit A}^{0}}}{ {}\gtrsim{} }$ 2 eV is also allowed.
53  ERICSON 1989 considered various nuclear corrections to axion emission in a supernova core, and found a reduction of the previous limit (MAYLE 1988) by a large factor.
54  MAYLE 1989 limit based on naive quark model couplings of axion to nucleons. Limit based on couplings motivated by EMC measurements is 2$-$4 times weaker. The limit from axion-electron coupling is weak: see HATSUDA 1988B.
55  RAFFELT 1988B derives a limit for the energy generation rate by exotic processes in helium-burning stars $\epsilon $ $<$ 100 erg g${}^{−1}$ s${}^{-1}$, which gives a firmer basis for the axion limits based on red giant cooling.
56  RAFFELT 1987 also gives a limit ${\mathit g}_{\mathit A{{\mathit \gamma}}}$ $<$ $1 \times 10^{-10}$ GeV${}^{-1}$.
57  DEARBORN 1986 also gives a limit ${\mathit g}_{\mathit A{{\mathit \gamma}}}$ $<$ $1.4 \times 10^{-11}$ GeV${}^{-1}$.
58  RAFFELT 1986 gives a limit ${\mathit g}_{\mathit A{{\mathit \gamma}}}$ $<$ $1.1 \times 10^{-10}$ GeV${}^{-1}$ from red giants and $<2.4 \times 10^{-9}$ GeV${}^{-1}$ from the sun.
59  KAPLAN 1985 says ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 23 eV is allowed for a special choice of model parameters.
60  FUKUGITA 1982 gives a limit ${\mathit g}_{\mathit A{{\mathit \gamma}}}$ $<$ $2.3 \times 10^{-10}$ GeV${}^{-1}$.
References