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Review

A Review of Axion Lasing in Astrophysics

by
Liang Chen
1,2,† and
Thomas W. Kephart
3,*,†
1
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China
2
University of Chinese Academy of Sciences, Beijing 100190, China
3
Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Universe 2024, 10(1), 24; https://doi.org/10.3390/universe10010024
Submission received: 28 November 2023 / Revised: 3 January 2024 / Accepted: 7 January 2024 / Published: 9 January 2024
(This article belongs to the Section High Energy Nuclear and Particle Physics)

Abstract

:
Axions can be stimulated to decay into photons by ambient photons of the right frequency or by photons from the decay of neighboring axions. If the axion density is high enough, the photon intensity can be amplified, which is a type of lasing or an axion maser. Here, we review the astrophysical situations where axion lasing can appear and possibly be detected.

1. Introduction

The Peccei–Quinn mechanism [1] is of particular interest because it is still viewed as the most credible solution to the strong CP problem. The spontaneous breaking of Peccei–Quinn symmetry implies the existence of the spin-0 pseudo-Goldstone boson referred to as the axion [2], which then becomes a candidate for dark matter. Effective field theory reduces the coupling between axion and Standard Model particles to
α s 8 π f a a G μ ν a G ˜ a μ ν + α K 8 π f a a F μ ν F ˜ μ ν + 1 f a J μ μ a ,
where α and α s are fine structure coefficients of electromagnetic and strong interactions, respectively; a, F μ ν and G μ ν are fields of the axion, QED and QCD, respectively; F ˜ μ ν and G ˜ μ ν are the corresponding dual fields of QED and QCD, respectively; J μ is the Noether current of the broken symmetry, K is a model dependent coefficient, and the decay constant f a is the energy scale that suppresses the coupling of axions to Standard Model particles. Axions with f a of electroweak symmetry breaking scale v weak 250 GeV were ruled out [3,4] by experiments, which left models, namely, KSVZ [5,6] and DFSZ [7,8], predicting invisible axions with f a v weak . Also, effective field theory [9] determines the product of axion mass m a and decay constant f a via m a f a = m π f π = [ 75.5 MeV ] 2 , where m π and f π are the mass and decay constant of the pion, respectively.
The axion couples to photons via the interaction α K 8 π f a a F μ ν F ˜ μ ν , which suggests the axion lifetime is
τ a = 256 π 3 K 2 α 2 m a f a m a 2
where model dependent coefficient K could be on the order of 1 to 10 [10]. The lifetime (2) of the axion could exceed the age of the universe if m a a few eV. This coupling also gained astrophysical interest because of axion–photon conversion in external magnetic fields [11] and can become a strategy for detecting axions. Extensive reviews and references to most of the early work on axions in astrophysics and cosmology can be found in [12,13,14,15,16].
Axions can be stimulated to decay into two photons by ambient photons of the right frequency or by photons from the decay of other neighboring axions. Formation of axion miniclusters and Bose stars from axion self-interaction or gravity are discussed in [17,18,19]. If the axion density is high enough, the photon intensity can be amplified, which is a type of lasing or masing. There are several astrophysical situations where axion lasing appears possible. These include various dense dark matter axion cluster [20,21] configurations and axions produced by superradience around primordial black holes (pBHs), also known as the black hole lasers powered by axion superradiant instabilities (BLASTs) [22]. We review and summarize the current possibility of detecting these astrophysical lasers.

2. Axion Masers

2.1. Maser Luminosity

Tkachev [20] examined the possibility that the growing axion density in the center of a gravitational well gives rise to a coherent cosmic maser source through the stimulated a γ γ process during the galaxy formation era. For one model, upon collapse of the irregularities in the axion medium, a substantial luminosity develops: L m a 3 Δ p r p 2 exp ( D ) , where r p is a gravity-related distance, Δ p is the uncertainty in axion momentum, and D is the integrated amplification factor, as defined below. The luminosity L is comparable with that of the brightest quasars, provided D 10 2 , which is attainable if M < 10 8 [ ( 10 12 GeV ) / f a ] 4 M , where M is the mass of irregularities and M is the solar mass.
Assuming that cosmological strings [23] are the seeds of gravitational condensation, and considering the formation of spherically symmetric axionic configuration due to the velocity dispersion, phase space density (occupation number) f a is isotropic within the “core” region [24]. If the photon phase space density is far less than the axion phase space density ( f γ f a ) and the gravitational field is weak, then for a wide class of axion distribution f a , the photon phase space density f γ evolves according to
d f γ d t = π 2 Γ a m a 4 β ϵ ( 1 + f γ ) ,
where
ϵ = m a f a ( p , r ) d 3 p ( 2 π ) 3
is the axion energy density, and β is the axion escape velocity characterizing the depth of the gravitational well. f γ increases exponentially with time if D > 1 is satisfied, where the amplification coefficient D is introduced as
D ( r ) = 0 r d d t f γ ( r ) d r .
For a self-gravitating system, the amplification becomes [24]
D f π r c f a ,
where r c is the radius of the core region. D > 1 gives [24]
r c < 10 7 β 10 12 GeV f a cm .
If the characteristic energy scale of the symmetry breaking during phase transitions in the early Universe is μ , then the linear mass density of cosmic strings is μ , and the network of strings produces oscillating loops of size r s c t at time t. A spherical shell of radius r s and mass 2 π r s μ may approximate the gravitational effect of the string loop [25]. If axions initially were inside the loop and form the core, then they can constitute galactic halos [25] and maintain the energetics of the core. A rapidly moving string alters axion trajectories, which suggests that if r c is equal to the loop size r s , this may violate the stimulated emission condition (7). But the effect of higher multipole moments is small in distant regions [26], and axions are not disturbed by string motion; and, if the core formed by axions can reach a smaller radius, then the enhancement coefficient (6) is still a valid choice. Thus, this region can provide a luminosity of [24]
L 0 10 15 M pl 2 m s M 1 yr t c 1 3 ,
where t c is the recollapse time for the axions and M pl is the Planck mass.
Axion accretion on strings may result in a core with a very high stimulated emission rate or a quasar-like energy release. A pure axionic object produces a monochromatic spectrum with frequency centered at m a / 2 . To produce the complicated spectrum of quasars, the axionic core in a gravitational well may be surrounded by ordinary (baryonic) matter [20]. If one cannot identify certain lines in spectra with any molecular or atomic level, then the axion mass can be determined [24]. Odd-integer harmonics of the fundamental frequency can also be produced by interactions 3 a 2 γ at a much lower magnitude [27].
Tkachev [28] proposes that the properties (energy release, duration, event rate) of FRB can be matched with the explosive maser effect of axion miniclusters or the decay of axions in an external magnetic field. Related effects have been found in localized axion–photon states in a strong magnetic field, e.g., there can be a back reaction from the axion field and electromagnetic waves on the external magnetic field. Guendelman [29] takes this back reaction into account on a strongly time-independent external magnetic field and finds a localized axion–photon soliton.

2.2. Parametric Resonance

Levkov et al. [30] have developed a quasistationary formalism of parametric resonance in a finite volume for nonrelativistic axions, incorporating (in)coherence, finite-volume effects, axion velocities, binding energy, gravitational redshift, and back reaction of photons on axions. Axions with large occupation numbers are described by a classical field a ( t , x ) = f a 2 [ ψ ( t , x ) e i m a t + h . c . ] and affected by a potential
V = m a 2 2 a 2 g 4 2 m a 2 4 ! f a 2 a 4 + . . . .
If λ a is the wavelength of the axion, then the nonrelativistic approximation reads
m a λ a 1 , t ψ ψ / ( m a λ a 2 ) , x ψ / λ a .
A stationary solution of the Schrödinger–Poisson system gives a Bose–Einstein condensate of axions in the ground state of a nonrelativistic gravitational potential Φ , for ψ = e i ω s t ψ s ( r ) , where ω s < 0 is the binding energy of axions. Since the phase of ψ s is independent of spacetime, the axions are coherent [30]. Consider the electromagnetic potential A along an arbitrary z-direction,
A i = C i + e i m a ( z + t ) / 2 + C i e i m a ( z t ) / 2 + h . c .
Substituting A i into Maxwell’s equations shows that the electromagnetic field changes fast, t C C / λ , which prompts adiabatically the ansatz [30],
C i ± = e t μ ( t ) d t c i ± ( t , x ) ,
where μ and the quasistationary amplitudes and c i ± evolve on the same time scales m a λ 2 as ψ . Static homogeneous axions in an infinite volume give z c i ± = 0 and μ = g m a | ψ | , where g α K is the dimensionless axion–photon coupling. Let L be the size of an axion cloud; photons accumulate if μ L 1 .
Assuming that ψ is real, which means the axions are static and coherent, there exist localized solutions with
c i + | z + = c i | z = 0 , Re μ 0 ,
representing resonance instabilities. Defining D ( z ) as
D ( z ) = g m a z d z ψ ( z ) ,
parametric resonance along the arbitrary z-direction corresponds to D ( + ) π 2 . Resonance starts with a small exponent μ L 1 immediately after the condition (14) is met, which means initial growth is tiny. When the electromagnetic amplitude become large, the back reaction will cause the resonant flux to fall immediately, but a long-lived quasistationary electromagnetic field could appear, causing a glowing axion star to be formed [30].
Levkov et al. [30] argue that the Bose stars with D ( + ) 1 are better amplifiers (stimulated decay) than diffuse axions when an external radio wave of frequency m a / 2 travels through the axions. For a diffuse axion cloud, photon fluxes could be amplified but exponential growth is not expected. The case of collapsing axion stars is also investigated in [30]: the star initially contracts without an electromagnetic effect, and growth of the luminosity begins once the localized solution appears.
Other notable findings in [30] include: the modes with different angular harmonic number l of a spherical axion star grow at rate μ , resonance may develop when two axion stars come close to each other with negligible relative velocity even if resonance does not occur for individual Bose stars, and as expected relative velocities among axions prohibit resonance, etc.
Another important type of astrophysical axion objects are axion Bose condensates, found in the work of Sikivie et al. [31,32] and further analyzed by Hertzberg and Schiappacasse [33], focusing on axion clump resonance of photons. These objects correspond to unstable (resonant) and stable solutions of the Mathieu equation, which is the equation of motion for homogeneous small amplitude axion fields. The electromagnetic modes have a maximum exponential growth rate of [33]
μ H * α K 8 π f a m a a 0 ,
in the first resonant region, where a 0 is the amplitude of homogeneous axion oscillation a ( t ) . Note that μ H * in [33] is comparable with μ in [30].
The homogeneous axions may eventually become unstable and collapse/condensate towards an axion clump from gravity and attractive self-interactions. A spherically symmetric axion clump was found [34] to be accurately approximated by
ψ = 3 N π 3 R 3 sech r R e i μ t ,
where R is the radius of the clump, μ serves as a correction to the frequency m a / , and N = d 3 x ψ * ψ is the particle number of axions. A clump of N axions cannot resonate if N < N c , where N c is a critical value of the particle number. In the case of attractive axion self-interactions, there is a maximum particle number N max in an axion clump [33],
N max 10.12 f a | g 4 | G m a 2 .
If a clump of QCD axions has N max and attractive self-interactions and g 4 2 = 0.3 (the preferred value for conventional QCD axions) [9], there would be no resonance due to axion–photon coupling coefficient K being too small in current models (however, resonance of hidden sector photons could still occur [33]). The general criteria for clump resonance is that a pair of photons being produced has to stimulate another pair of photons before escaping the axion clump, which is succinctly expressed as
μ H * α K 8 π f a m a a 0 > c 2 R , where a 0 = 2 m a 3 N π 3 R 3 ,
i.e., the homogenous axion field growth rate must be higher than the photon escape rate [33]. A typical growth time for a spherical clump of QCD axions with m a = 10 5 eV is estimated to be 1 / μ * 2 × 10 4 s, which is similar to the duration (∼ms) of pulses calculated in [22].
A non-spherical clump profile was found to be accurately approximated by a modified Gaussian [35], which leads to a maximally allowed number N max of particles in the clump being larger than that of a spherical clump. N max of a non-spherical clump increases rapidly with angular momentum l, and thus, it is easier to achieve resonance of photons. The condition for resonance that μ H * > c 2 R carries over from spherical clumps to non-spherical axion configurations. For conventional QCD axions, resonance does not occur in non-spherical clumps unless the angular momentum is very large l O ( 10 3 ) [33].
A scenario of clump resonance in astrophysics would be: clumps formed under gravity in the past with particle number N > N c resonate into photons and lose energy individually, which inevitably results in N < N c . Clumps with N < N c merge together and become a clump with N > N c , which could still resonate today [33].

3. Lasing Axions as Particles

3.1. Spontaneous Emission

Kephart and Weiler [21] conservatively proposed that the luminosity of an axion cluster is comparable to that of an astrophysical object (star, galaxy, or galaxy cluster) of similar mass, considering solely the mechanism of spontaneous decay of the axion. Let N a 10 66 ( M / M ) [ ( 1 eV ) / m a ] be the total number of axions in a cluster of mass M, where L is the solar luminosity. The luminosity of photons L from spontaneous emission of the cluster is then
L = m a N a τ a 4 × 10 29 m a 1 eV 5 M M erg s 10 4 m a 1 eV 5 M M L .
If an axion cluster is at a distance of D = 300 h 1 ( z c / 0.1 ) from the earth, the flux observed at the earth becomes
F = L 4 π D 2 = 4.7 × 10 16 h 2 f ( z g ) r 1 pc 0.1 z c 2 m a 1 eV 5 W m 2 ,
where z c is the cosmological redshift, h is related to the present Hubble parameter H 0 by H 0 = 100 h km/s Mpc, r is the radius of the cluster, and f ( z g ) describes the surface gravitational red shift through f ( z g ) z g ( 2 + z g ) / ( 1 + z g ) 2 = 2 G M / r . Suppose that a mass fraction x a of a galactic halo is axionic; the spectral photon radiance of the Milky Way and the spectral photon irradiance of Andromeda are then found to be
d I d Ω Δ λ 10 4 x a m a 1 eV 5 ( cm 2 · s · sr · Å ) 1 and I Δ λ 20 x a m a 1 eV 5 ( cm 2 · s · Å ) 1 ,
respectively. Comparing these with the background photons of the relevant spectrum in both galaxies, one can find lower bounds on x a that allow axions to be detectable.

3.2. Stimulated Emission Rate Equations

For any species of particles with occupation number f ( p , r , t ) , the particle number density n ( r , t ) and the total particle number N in a volume V are, respectively,
n ( r , t ) = d 3 p 8 π 3 f ( p , r , t ) and N = V d 3 r n ( r , t ) .
The rate of change of the photon number density n λ of helicity λ = ± 1 due to the decay process a γ γ is given by the Boltzmann equation,
d n λ d t = d X LIPS ( 3 ) [ f a ( 1 + f 1 λ ) ( 1 + f 2 λ ) f 1 λ f 2 λ ( 1 + f a ) ] | M ( a γ γ ) | 2 ,
where f a ( p ) , f i λ = f λ ( k i ) are occupation numbers of axion and photon, respectively. M ( a γ γ ) is the decay amplitude of the coupling term α K 8 π f a a F μ ν F ˜ μ ν , and d X LIPS ( 3 ) is the Lorentz invariant three-body phase space of the axion and two photons. Assuming spherical symmetry f a ( p ) = f a ( | p | ) f a ( p ) , f λ ( k ) = f λ ( | k | ) f λ ( k ) for both the axion and photon occupation numbers, one could carry out the integration over the momentum space of one of the photons,
d n λ d t = m a Γ a 2 π 2 m a d p 0 k min k max d k { f a ( p 0 ) [ 1 + 2 f λ ( k ) ] f λ ( k ) f λ ( p 0 k ) } ,
where
k max / min = m a 2 2 ( p 0 p ) = p 0 ± ( p 0 ) 2 m a 2 2
is the maximum/minimum photon momentum from the decay of an axion of momentum p . The rate of change of the axion density is
d n a d t = 1 2 λ = ± d n λ d t ,
which, together with Equations (22) and (24), become a set of integro-differential equations for the evolution of the axion–photon system [36]. For the approximately static clusters to which the formalism has been applied, it is appropriate to treat the axions as particles [37].

3.3. A Simple Axion Cluster Model

A simple model [36] of lasing axion clusters assumes the following forms
f a ( p , r , t ) = f a Θ ( p max p ) Θ ( R r ) , f λ ( k , r , t ) = f λ Θ ( R r ) Θ ( k + k ) Θ ( k k ) ,
for axion and photon occupation numbers, respectively, where f a and f λ depend on time only, R is the radius of the cluster, p max = m a β is the maximum axion momentum, β is the maximum (escape) velocity of an axion, and k ± = m a γ 2 ( 1 ± β ) is the maximum/minimum photon momentum from the decay of an axion with the maximum momentum m a β . Integration of Equation (24) over p and k space leads to
d n λ d t = Γ a n a 1 + 16 π 2 n λ β m a 3 32 π 2 n λ 2 3 m a 3 β + 3 2 3 c n λ 2 R ,
where the last term accounts for the surface loss of the photons. The rate of change of the axion number density is half of that of the photon number density without surface losses,
d n a d t = 1 2 Γ a λ = ± n a 1 + 16 π 2 n λ β m a 3 32 π 2 n λ 2 3 m a 3 β ,
where we subtract the rate of production of axions, with velocity exceeding β from back reaction γ γ a . Since these fast axions escape from the cluster, they are labeled as “sterile”, with a production rate
d n s d t = 1 2 Γ a λ = ± 16 π 2 m a 3 n λ 2 .
If one assumes a common initial condition n + ( 0 ) = n ( 0 ) , then helicity densities n ± evolve identically, and n + ( t ) = n ( t ) = 1 2 n γ ( t ) for all time. Substituting n γ for n ± results in equations irrespective of helicity,
d n γ d t = 2 1 τ a n a + 16 π 2 β m a 3 τ a n a n γ 16 π 2 3 m a 3 τ a β + 3 2 n γ 2 3 c 2 R n γ , d n a d t = 1 τ a n a + 8 π 2 β m a 3 τ a n a n γ 8 π 2 β 3 m a 3 τ a n γ 2 , d n s d t = 4 π 2 m a 3 τ a n γ 2 .
Expressing time and volume in the units of spontaneous axion lifetime τ a and Compton volume 16 π 2 m a 3 , the set of evolution equations become dimensionless [36,37],
n ¯ ˙ γ = 2 n ¯ a + 1 β n ¯ a n ¯ γ β 3 + 1 2 n ¯ γ 2 3 c τ a 2 R n ¯ γ , n ¯ ˙ a = n ¯ a 1 2 β n ¯ a n ¯ γ + β 6 n ¯ γ 2 , n ¯ ˙ s = 1 4 n ¯ γ 2 ,
where n ¯ a , n ¯ γ , and n ¯ s are dimensionless number densities, and the dot derivative is with respect to dimensionless time t / τ a . The characteristic time for lasing is
τ ¯ lase τ lase / τ a = n ¯ a ( 0 ) β 3 c 2 R 1 .

3.4. Parameters and Conditions

The axion cluster has an escape velocity of 2 G M / R , which is set to be the β parameter in the axion lasing model. Axions with higher speed would not be confined by the cluster body of mass M,
β = 2 G M R = 1.8 × 10 3 ρ a g / cm 3 R R ,
where ρ a = m a 4 n ¯ a / ( 16 π 2 ) is the mass density of the axion cluster in units of g/cm 3 , and R is the solar radius.
An estimate of the necessary values of axion cluster parameters for lasing can be found by requiring the photon mean free path to be less than the diameter of the cluster, which gives
m a eV 2 ρ a g / cm 3 6 K 4 .
Another estimation of the values of these parameters for small t neglects the back reaction term in Equation (31) and demands the coefficients of n γ on the right-hand side of the equation be positive,
16 π 2 n a τ a m a 3 β 3 c 2 R > 0 .
These two lasing conditions reproduce each other up to a factor of 3 and provide a lower bound for the density of the lasing axion cluster. Keeping β 1 / 2 avoids the consideration of black hole effects and provides an upper bound for the density of a lasing cluster at a fixed radius. Considering both bounds places the cluster density in the range [36,37],
6 K 4 eV m a 2 ρ a g / cm 3 7.7 × 10 4 R R 2 .
The maximum radius for lasing to occur is obtained by saturating both bounds,
R 100 K 2 m a eV R ,
which also leads to the maximum mass of the cluster
M 6 × 10 6 K 2 m a eV M ,
There are no lower bounds for R and M.
The eventual lasing is inevitable, as it needs only a few photons to trigger lasing, regardless of the initial photon density n ¯ γ ( 0 ) of the cluster, which regulates the timing of the laser profile. Based on the ratio R / ( c τ a ) between the photon diffusion time R / c and the axion life time τ a , one can write the initial photon density from spontaneous emission of an axion cluster as
n ¯ γ ( 0 ) = 320 m a eV K 2 β 2 R R .
Photons cannot propagate if the frequencies are below the plasma frequency (due to high electron density in the early universe), which might inhibit axion decay. It has been shown [36] that axion decay proceeds without inhibition as long as the red shift z 10 9 ( m a / eV ) 2 / 3 .

3.5. Discussion

The flat distribution functions in the simple axion cluster model are idealizations. Deviations from a flat distribution will give regions of higher density, which will be more active for lasing. Gravitational collapse could trigger formation of a high axion density in the vicinity of an object such as a black hole, where gravitational corrections to the rate equations would have to be included. There are a wide range of collisionless, self-gravitating, spherically symmetric systems where the density and velocity distribution functions are known in closed analytic form [38]. To obtain general rate equations for realistic distributions by integration is straightforward.
If compact objects with a mass larger than 10 7 M in the cores of nearby galaxies were axion clusters, they would not be expected to lase since their mass and size fall outside the allowed parameters for lasing. However, spontaneous axion decay may still generate luminous emissions [21]. Furthermore, if these massive cluster were made of smaller dense clusters, lasing might still be possible for individual small clusters.
After the Universe became matter dominated, the energy released by detonation of a typical hadronic axion [39] cluster allowed for the evacuation of matter and formation of a void by multiphoton ionization and the subsequent plasma absorption [36]. The total energy available in cosmic axions is sufficient to power the formation of all the voids in the Universe.

3.6. Application—Superradiant Clouds

In Kerr spacetime, the Klein–Gordon equation admits hydrogenic-like solutions localized in the vicinity of a BH, characterized by integer quantum numbers ( n , l , m ) . Let M BH and J BH be the mass and angular momentum of the black hole, respectively. In the nonrelativistic regime, the spectrum of the quasibound state is [40]
ω n m a c 2 1 α μ 2 2 n 2 , where α μ G m a M BH c .
The scalar field extracts the BH’s rotational energy, and the axion cloud around the BH grows if ω R < m Ω BH , where ω R is the real part of the complex frequency ω = ω R + i ω I , and Ω BH is the horizon’s angular velocity. When α μ 1 , the occupation number of the fastest growing mode “ 2 p ( n = 2 , l = m = 1 ) grows at a rate
Γ s 4 × 10 4 a ˜ μ 10 5 eV α μ 0.03 8 s 1 ,
where a ˜ = c J BH / ( G M BH 2 ) is the BH’s dimensionless spin parameter ( 0 < a ˜ < 1 ) . In the nonrelativistic regime, the axion cloud is localized far away from the horizon; hence, the formalism developed in [36] is still applicable. Although the geometry of the “ 2 p ” state is more intricate than the flat, spherically symmetric model, the estimates made by Rosa and Kephart [22] by exploiting Equation (31) are sufficiently good in terms of the order of magnitude. They calculated the peak luminosity, total energy, and duration of the black hole lasers powered by axion superradiant instabilities (BLASTs). They are
L B 2 × 10 42 K 2 a ˜ 10 5 eV μ 2 α μ 0.03 7 ξ 100 erg / s , E B 3 × 10 39 K 2 a ˜ 10 5 eV μ 3 α μ 0.03 5 2 ξ 100 1 2 erg , τ B 1 a ˜ 10 5 eV μ α μ 0.03 9 / 2 ξ 100 1 / 2 ms , where ξ = log Γ s Γ a 107 4 log μ 10 5 eV + 8 log α μ 0.03 + log a ˜ K 2 .
Note that the duration τ B is similar to the growth time for a spherical clump of QCD axions, with m a = 10 5 eV estimated in [33]. The brightest bursts could blow away any interstellar plasma surrounding the BH if L B exceed the BH’s Eddington luminosity. However, the brightest bursts generate a e e + plasma by Schwinger pair production, which is dense enough to prohibit photon propagation and block axion decay. Lasing may stop after a single laser pulse and restart once the plasma becomes subcritical again (via e e + annihilations), causing repeating bursts. Local plasma density or temperature may also temporarily block lasing. By angular momentum conservation, one of the photons from each decay satisfies the superradiance condition ω R < m Ω BH , while the other is in a nonsuperradiant state, which may decrease the laser luminosity and modify its polarization through the spin-helicity effect [41,42,43].
The parameters (mass and spin) of an axion cloud have to be smaller than those of its associated BH. This restricts the masses of axion and BH for α μ 0.05 to be μ 10 8 eV , M BH 10 2 M . The notion that lasing can only occur in the non-relativistic regime is confirmed by α μ 0.03 K , which is obtained by requiring that quartic axion self-interactions are not significant. BLASTs can only occur for spinning pBHs [44] from the merger of two nonspinning pBHs.
The predicted peak luminosities and durations of the brightest BLASTs exhibit features similar to the fast radio bursts (FRBs) [45,46,47] observed in recent years. A particular example is the repeating FRB 121102 [48,49,50,51]. Geometrical and curved spacetime effects could prevent the observation of bursts along our line of sight and possibly explain why some FRBs do not repeat. The brightest BLASTs are expected to yield up to ∼10 5 FRBs per day across the whole sky. Lighter pBHs may become continuous laser sources (since Schwinger pair production is less likely to occur in these cases) with lower luminosities, but they should be less numerous than repeating BLASTs due to their shorter lifetime [22]. A similar comparison between the photon signature from superradiant ion clouds and the isotropic gamma-ray background (IGRB) is presented in [52]. For a review of superradiance, see [40]. For a more recent development on this topic from a field theoretic approach, see [53].

3.7. Non-Spherical Cluster and Static Spacetime Modification

The evolution Equations (24) and (31) are based on spherical symmetry f a ( p ) = f a ( | p | ) , f λ ( k ) = f λ ( | k | ) . One considers non-spherically symmetric occupation numbers by allowing dependence on the directions of momenta p and k . Let us write occupation numbers f a ( p ) = f a ( p , Ω p ) and f λ ( k ) = f a ( p , Ω k ) as spherical harmonic expansions,
f a ( p ) = l m a l m ( p , t ) Y l m ( Ω p ) , f λ ( k ) = l m b l m ( k , t ) Y l m ( Ω k ) ,
where Ω p and Ω k are the angular dependences from the directions of momenta p and k , respectively. The evolution equations for individual components b l m of photon occupation number are given by Equation (8) in [54], which is analogous to Equation (24), without imposing spherical symmetry in momentum space.
Many of the equations cited here and elsewhere in this subsection are from [54,55,56,57] and so are not reproduced here. We simply provide a guide to them and refer the reader to those works for the details.
The corresponding rate equations for individual components of particle number densities are also obtained as Equations (13)–(15) in [54]. Similarly, one relaxes spherical symmetry in coordinate/spatial space of a simple axion cluster model (27) by expanding occupation numbers f a ( p , r , Ω , t ) and f λ ( k , r , Ω , t ) in spherical harmonics [55],
f a ( p , r , Ω , t ) = l m f a l m ( t ) Y l m ( Ω ) Θ ( p m a x p ) Θ ( R r ) , f λ ( k , r , Ω , t ) = l m f λ l m ( t ) Y l m ( Ω ) Θ ( R r ) Θ ( k + k ) Θ ( k k ) ,
where Ω is the conventional spatial solid angle. The corresponding rate equations for individual components of particle number densities are then obtained as Equations (19)–(21) in [55], which are later applied to a study [56] of the superradiant growth of non-spherical axions as an update of the earlier analysis [22].
An axion cloud bounded by a host object in static spacetimes is studied, and the rate equations of axion and photon number densities are given as Equations (8.1)–(8.4) in [57]. Compared to the simple axion cluster model in Minkowski spacetime [36], an example [57] shows that the peak number density of photon is about 10% larger and slightly delayed (see Figure 4 in [57]) for a QCD axion ( m a = 10 5 eV) cluster of mass M = 6 × 10 21 kg a few meters away from the center of a Schwarzschild spacetime produced by a black hole of mass M BH = 8 × 10 23 kg. Climbing out of the Schwarzschild potential well, the associated tidal effects (gravitational redshift) initially slow the decay process, but this wanes quickly and gives a sharper peak signal strength at a delayed time.

4. Comments

We have reviewed two approaches of investigations into the phenomenon of axion lasing, i.e., the field theory methods in Section 2 and the particle perspective in Section 3. While the field theoretic approach gives the growth rate of photons (e.g., [33]), the particle perspective shows a detailed evolution of the pulses (e.g., [22]). But the results of the two methods are in general agreement in their conclusions.
There are many potential sources of astrophysical axion lasing. Depending on the axion mass and self coupling, these include clumps of axions and axion miniclusters and are limited by the objects’ angular momentum. In addition, lasing superradiant clouds of axions around primordial Kerr black holes provides an interesting possibility of discovery when identified with fast radio bursts. If verified, this would constitute the discovery of two components of dark matter, primordial black holes and axions.
More generally, axions and axion-like particles are a compelling class of particles to investigate. They provide numerous and varied possibilities for physics, astrophysics, and cosmological phenomena. They can arise in extensions of the Standard Model, grand unified theories, and string theory. Their discovery would provide considerable insight into aspects beyond standard model physics.

Author Contributions

These authors contributed equally to this work. T.W.K. was responsible for the ideation. Both L.C. and T.W.K. performed the literature search. L.C. performed analysis and drafted the work. T.W.K. revised the work. All authors have read and agreed to the published version of the manuscript.

Funding

This work is supported in part by the National Key Research and Development Program of China under Grant No. 2020YFC2201501 and the National Natural Science Foundation of China (NSFC) under Grant No. 12147103.

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
KSVZKim, Shifman, Vainshtein, Zakharov
DFSZDine, Fischler, Srednicki, Zhitnitsky
BHblack hole
BLASTsblack hole lasers powered by axion superradiant instabilities
pBHsprimordial black holes
FRBfast radio burst
IGRBisotropic gamma-ray background

References

  1. Peccei, R.D.; Quinn, H.R. CP Conservation in the Presence of Instantons. Phys. Rev. Lett. 1977, 38, 1440–1443. [Google Scholar] [CrossRef]
  2. Weinberg, S. A New Light Boson? Phys. Rev. Lett. 1978, 40, 223–226. [Google Scholar] [CrossRef]
  3. Barshay, S.; Faissner, H.; Rodenberg, R.; De Witt, H. Coherent Conversion of Very Light Pseudoscalar Bosons. Phys. Rev. Lett. 1981, 46, 1361–1364. [Google Scholar] [CrossRef]
  4. Barroso, A.; Mukhopadhyay, N.C. Axions: To be or not to be? Phys. Lett. B 1981, 106, 91–94. [Google Scholar] [CrossRef]
  5. Kim, J.E. Weak Interaction Singlet and Strong CP Invariance. Phys. Rev. Lett. 1979, 43, 103. [Google Scholar] [CrossRef]
  6. Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I. Can Confinement Ensure Natural CP Invariance of Strong Interactions? Nucl. Phys. B 1980, 166, 493–506. [Google Scholar] [CrossRef]
  7. Dine, M.; Fischler, W.; Srednicki, M. A Simple Solution to the Strong CP Problem with a Harmless Axion. Phys. Lett. B 1981, 104, 199–202. [Google Scholar] [CrossRef]
  8. Zhitnitsky, A.R. On Possible Suppression of the Axion Hadron Interactions. Sov. J. Nucl. Phys. 1980, 31, 260. (In Russian) [Google Scholar]
  9. di Cortona, G.G.; Hardy, E.; Vega, J.P.; Villadoro, G. The QCD axion, precisely. JHEP 2016, 2016, 34. [Google Scholar] [CrossRef]
  10. Cheng, S.L.; Geng, C.Q.; Ni, W.T. Axion—Photon couplings in invisible axion models. Phys. Rev. D 1995, 52, 3132–3135. [Google Scholar] [CrossRef]
  11. Sikivie, P. Experimental Tests of the Invisible Axion. Phys. Rev. Lett. 1983, 51, 1415–1417, Erratum in Phys. Rev. Lett. 1984, 52, 695. [Google Scholar] [CrossRef]
  12. Kim, J.E. Light Pseudoscalars, Particle Physics and Cosmology. Phys. Rept. 1987, 150, 1–177. [Google Scholar] [CrossRef]
  13. Raffelt, G.G. Astrophysical methods to constrain axions and other novel particle phenomena. Phys. Rept. 1990, 198, 1–113. [Google Scholar] [CrossRef]
  14. Marsh, D.J.E. Axion Cosmology. Phys. Rept. 2016, 643, 1–79. [Google Scholar] [CrossRef]
  15. Braaten, E.; Zhang, H. Colloquium: The physics of axion stars. Rev. Mod. Phys. 2019, 91, 041002. [Google Scholar] [CrossRef]
  16. Sikivie, P. Invisible Axion Search Methods. Rev. Mod. Phys. 2021, 93, 015004. [Google Scholar] [CrossRef]
  17. Kolb, E.W.; Tkachev, I.I. Axion miniclusters and Bose stars. Phys. Rev. Lett. 1993, 71, 3051–3054. [Google Scholar] [CrossRef] [PubMed]
  18. Kolb, E.W.; Tkachev, I.I. Nonlinear axion dynamics and formation of cosmological pseudosolitons. Phys. Rev. D 1994, 49, 5040–5051. [Google Scholar] [CrossRef]
  19. Braaten, E.; Mohapatra, A.; Zhang, H. Dense Axion Stars. Phys. Rev. Lett. 2016, 117, 121801. [Google Scholar] [CrossRef]
  20. Tkachev, I.I. Coherent scalar field oscillations forming compact astrophysical objects. Sov. Astron. Lett. 1986, 12, 305–308. [Google Scholar]
  21. Kephart, T.W.; Weiler, T.J. Luminous axion clusters. Phys. Rev. Lett. 1987, 58, 171. [Google Scholar] [CrossRef] [PubMed]
  22. Rosa, J.G.; Kephart, T.W. Stimulated Axion Decay in Superradiant Clouds around Primordial Black Holes. Phys. Rev. Lett. 2018, 120, 231102. [Google Scholar] [CrossRef]
  23. Kibble, T.W.B. Topology of Cosmic Domains and Strings. J. Phys. A 1976, 9, 1387–1398. [Google Scholar] [CrossRef]
  24. Tkachev, I.I. An Axionic Laser in the Center of a Galaxy? Phys. Lett. B 1987, 191, 41–45. [Google Scholar] [CrossRef]
  25. Sato, H. Cosmic Strings and Rotation Velocity of Spiral Galaxies. Mod. Phys. Lett. A 1986, 1, 9. [Google Scholar] [CrossRef]
  26. Silk, J.; Vilenkin, A. Cosmic Strings and Galaxy Formation. Phys. Rev. Lett. 1984, 53, 1700–1703. [Google Scholar] [CrossRef]
  27. Braaten, E.; Mohapatra, A.; Zhang, H. Emission of Photons and Relativistic Axions from Axion Stars. Phys. Rev. D 2017, 96, 031901. [Google Scholar] [CrossRef]
  28. Tkachev, I.I. Fast Radio Bursts and Axion Miniclusters. JETP Lett. 2015, 101, 1–6. [Google Scholar] [CrossRef]
  29. Guendelman, E.I. Localized Axion Photon States in a Strong Magnetic Field. Phys. Lett. B 2008, 662, 227–230. [Google Scholar] [CrossRef]
  30. Levkov, D.G.; Panin, A.G.; Tkachev, I.I. Radio-emission of axion stars. Phys. Rev. D 2020, 102, 023501. [Google Scholar] [CrossRef]
  31. Sikivie, P.; Yang, Q. Bose-Einstein Condensation of Dark Matter Axions. Phys. Rev. Lett. 2009, 103, 111301. [Google Scholar] [CrossRef] [PubMed]
  32. Erken, O.; Sikivie, P.; Tam, H.; Yang, Q. Cosmic axion thermalization. Phys. Rev. D 2012, 85, 063520. [Google Scholar] [CrossRef]
  33. Hertzberg, M.P.; Schiappacasse, E.D. Dark Matter Axion Clump Resonance of Photons. JCAP 2018, 11, 004. [Google Scholar] [CrossRef]
  34. Schiappacasse, E.D.; Hertzberg, M.P. Analysis of Dark Matter Axion Clumps with Spherical Symmetry. JCAP 2018, 01, 037, Erratum in JCAP 2018, 03, E01. [Google Scholar] [CrossRef]
  35. Hertzberg, M.P.; Schiappacasse, E.D. Scalar dark matter clumps with angular momentum. JCAP 2018, 08, 028. [Google Scholar] [CrossRef]
  36. Kephart, T.W.; Weiler, T.J. Stimulated radiation from axion cluster evolution. Phys. Rev. D 1995, 52, 3226–3238. [Google Scholar] [CrossRef]
  37. Kephart, T.W.; Weiler, T.J. A model of lasing axion clusters. Nucl. Phys. B Proc. Suppl. 1999, 72, 54–57. [Google Scholar] [CrossRef]
  38. Fridman, A.M.; Polyachenko, V.L. Physics of Gravitating Systems; Springer Science+Business Media: New York, NY, USA, 1984. [Google Scholar] [CrossRef]
  39. Kaplan, D.B. Opening the Axion Window. Nucl. Phys. B 1985, 260, 215–226. [Google Scholar] [CrossRef]
  40. Brito, R.; Cardoso, V.; Pani, P. Superradiance: New Frontiers in Black Hole Physics; Lecture Notes in Physics; Springer Nature: Cham, Switzerland, 2020; Volume 906, pp. 1–237. ISBN 978-3-319-18999-4/978-3-319-19000-6/978-3-030-46621-3/978-3-030-46622-0. [Google Scholar] [CrossRef]
  41. Rosa, J.G. Testing black hole superradiance with pulsar companions. Phys. Lett. B 2015, 749, 226–230. [Google Scholar] [CrossRef]
  42. Rosa, J.G. Superradiance in the sky. Phys. Rev. D 2017, 95, 064017. [Google Scholar] [CrossRef]
  43. Leite, L.C.S.; Dolan, S.R.; Crispino, L.C.B. Absorption of electromagnetic and gravitational waves by Kerr black holes. Phys. Lett. B 2017, 774, 130–134. [Google Scholar] [CrossRef]
  44. Carr, B.J.; Hawking, S.W. Black holes in the early Universe. Mon. Not. Roy. Astron. Soc. 1974, 168, 399–415. [Google Scholar] [CrossRef]
  45. Lorimer, D.R.; Bailes, M.; McLaughlin, M.A.; Narkevic, D.J.; Crawford, F. A bright millisecond radio burst of extragalactic origin. Science 2007, 318, 777. [Google Scholar] [CrossRef] [PubMed]
  46. Thornton, D.; Stappers, B.; Bailes, M.; Barsdell, B.R.; Bates, S.D.; Bhat, N.D.R.; Burgay, M.; Burke-Spolaor, S.; Champion, D.J.; Coster, P.; et al. A Population of Fast Radio Bursts at Cosmological Distances. Science 2013, 341, 53–56. [Google Scholar] [CrossRef] [PubMed]
  47. Petroff, E.; Barr, E.D.; Jameson, A.; Keane, E.F.; Bailes, M.; Kramer, M.; Morello, V.; Tabbara, D.; van Straten, W. FRBCAT: The Fast Radio Burst Catalogue. Publ. Astron. Soc. Austral. 2016, 33, e045. [Google Scholar] [CrossRef]
  48. Spitler, L.G.; Scholz, P.; Hessels, J.W.T.; Bogdanov, S.; Brazier, A.; Camilo, F.; Chatterjee, S.; Cordes, J.M.; Crawford, F.; Deneva, J.; et al. A Repeating Fast Radio Burst. Nature 2016, 531, 202. [Google Scholar] [CrossRef]
  49. Chatterjee, S.; Law, C.J.; Wharton, R.S.; Burke-Spolaor, S.; Hessels, J.W.T.; Bower, G.C.; Cordes, J.M.; Tendulkar, S.P.; Bassa, C.G.; Demorest, P.; et al. The direct localization of a fast radio burst and its host. Nature 2017, 541, 58. [Google Scholar] [CrossRef] [PubMed]
  50. Marcote, B.; Paragi, Z.; Hessels, J.W.T.; Keimpema, A.; van Langevelde, H.J.; Huang, Y.; Bassa, C.G.; Bogdanov, S.; Bower, G.C.; Burke-Spolaor, S.; et al. The Repeating Fast Radio Burst FRB 121102 as Seen on Milliarcsecond Angular Scales. Astrophys. J. Lett. 2017, 834, L8. [Google Scholar] [CrossRef]
  51. Tendulkar, S.P.; Bassa, C.; Cordes, J.M.; Bower, G.C.; Law, C.J.; Chatterjee, S.; Adams, E.A.K.; Bogdanov, S.; Burke-Spolaor, S.; Butler, B.J.; et al. The Host Galaxy and Redshift of the Repeating Fast Radio Burst FRB 121102. Astrophys. J. Lett. 2017, 834, L7. [Google Scholar] [CrossRef]
  52. Ferraz, P.B.; Kephart, T.W.; Rosa, J.G. Superradiant pion clouds around primordial black holes. JCAP 2022, 07, 026. [Google Scholar] [CrossRef]
  53. Spieksma, T.F.M.; Cannizzaro, E.; Ikeda, T.; Cardoso, V.; Chen, Y. Superradiance: Axionic couplings and plasma effects. Phys. Rev. D 2023, 108, 063013. [Google Scholar] [CrossRef]
  54. Chen, L.; Kephart, T.W. Photon directional profile from stimulated decay of axion clouds with arbitrary momentum distributions. Phys. Rev. D 2020, 101, 103033. [Google Scholar] [CrossRef]
  55. Chen, L.; Kephart, T.W. Photon directional profile from stimulated decay of axion clouds with nonspherical axion spatial distributions. Phys. Rev. D 2020, 102, 096010. [Google Scholar] [CrossRef]
  56. Chen, L.; Huang, D.; Geng, C.Q. Effects of stimulated emission and superradiant growth of non-spherical axion cluster. arXiv 2023, arXiv:2311.01819. [Google Scholar]
  57. Chen, L.; Kephart, T.W. Stimulated radiation from axion cluster evolution in static spacetimes. JCAP 2021, 09, 034. [Google Scholar] [CrossRef]
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Chen, L.; Kephart, T.W. A Review of Axion Lasing in Astrophysics. Universe 2024, 10, 24. https://doi.org/10.3390/universe10010024

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Chen L, Kephart TW. A Review of Axion Lasing in Astrophysics. Universe. 2024; 10(1):24. https://doi.org/10.3390/universe10010024

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Chen, Liang, and Thomas W. Kephart. 2024. "A Review of Axion Lasing in Astrophysics" Universe 10, no. 1: 24. https://doi.org/10.3390/universe10010024

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