PHYSICAL REVIEW D 104, 055038 (2021) - Axion production in pulsar magnetosphere gaps
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PHYSICAL REVIEW D 104, 055038 (2021) Axion production in pulsar magnetosphere gaps * Anirudh Prabhu Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA (Received 20 May 2021; accepted 6 September 2021; published 27 September 2021) Pulsar magnetospheres admit nonstationary vacuum gaps that are characterized by nonvanishing E · B. The vacuum gaps play an important role in plasma production and electromagnetic wave emission. We show that these gaps generate axions whose energy is set by the gap oscillation frequency. The density of axions produced in a gap can be several orders of magnitude greater than the ambient dark matter density. In the strong pulsar magnetic field, a fraction of these axions may convert to photons, giving rise to broadband radio signals. We show that dedicated observations of nearby pulsars with radio telescopes (FAST) and interferometers (SKA) can probe axion-photon couplings that are a few orders of magnitude lower than current astrophysical bounds. DOI: 10.1103/PhysRevD.104.055038 I. INTRODUCTION toroidal magnets [18], and dielectric haloscopes [19,20]. In the aforementioned experiments, axions are assumed to be Despite the many successes of the Standard Model (SM), produced in the early Universe and make up a significant a number of observations point to the need for new physics. portion of dark matter. Other experiments do not rely on Limits on the neutron electric dipole moment (EDM) [1] axions being dark matter. For example, axions may be suggest a finely tuned cancellation of the topological θ produced by the Primakoff process in the Sun [21,22] or by parameter in QCD and the overall phase of the quark mass an oscillating background E · B field in the laboratory [23– matrix, a fine-tuning constraint known as the strong CP 29]. When produced in the laboratory by photons with problem. In addition, a number of cosmological observa- incident E parallel to an externally applied B, axions may tions point to an abundance of dark matter that does not penetrate optical barriers and convert back to photons appear to consist of SM particles. One of the best-motivated giving the appearance of light shining through walls solutions to both of these problems is the QCD axion, (LSW). LSW experiments are not currently competitive which is the pseudo Nambu-Goldstone boson of the with astrophysical bounds on axions, due in large part to spontaneously broken Peccei-Quinn symmetry [2–5]. their reliance on two low-probability events, photon-to- Nonperturbative effects generate a potential for the QCD axion conversion and axion-to-photon conversion. Signal axion that dynamically relaxes the θ parameter to its CP- power is additionally suppressed by the limitations on the conserving value, explaining the smallness of the neutron strength of magnetic fields that can be produced in the (EDM). In addition, QCD axions may be produced in the laboratory. correct abundance to account for dark matter [6–8]. Axions Beyond the laboratory, astrophysical settings are often also appear more broadly in string theory in the compacti- ideal test beds for theories of physics beyond the SM. fication of antisymmetric tensor fields on Calabi-Yau Neutron stars (NS), in particular, provide excellent labo- manifolds [9,10]. The experimental discovery of axions ratories for axion detection due to their enormous magnetic would be an important step towards understanding physics fields and dense plasma magnetospheres. Infalling axion beyond the SM. dark matter may resonantly convert to photons in neutron A number of direct detection experiments have been star magnetospheres to produce thin lines that may be proposed to detect axions by exploiting their coupling to detectable with current and planned radio missions [30– photons, L ⊃ −gaγγ aðxÞE · B. Some of these experiments 36]. Another interesting possibility is that neutron stars and make use of high-Q microwave cavities [11–17], gapped white dwarfs may be factories for axions. In particular, axions may be thermally produced in the cores of extreme * aniprabhu@stanford.edu astrophysical objects and converted to photons in their magnetospheres [37–42]. In this paper we discuss a new Published by the American Physical Society under the terms of mechanism for axion production by pulsars. Pulsars, the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to young, rapidly rotating neutron stars, are surrounded by the author(s) and the published article’s title, journal citation, a dense plasma of electrons, positrons, and ions which are and DOI. Funded by SCOAP3. thought to be responsible for gamma ray, x-ray, and radio 2470-0010=2021=104(5)=055038(10) 055038-1 Published by the American Physical Society
ANIRUDH PRABHU PHYS. REV. D 104, 055038 (2021) emission. In response to plasma outflow along open formation of gaps and their subsequent discharge has been magnetic field lines, the magnetosphere forms nonsta- demonstrated in numerical simulations [50]. tionary vacuum gaps in which E · B ≠ 0 [43,44]. The A pulsar is described by its angular velocity Ω and oscillating E · B in a gap acts as a source for axions, similar magnetic moment μ. We limit our discussion to aligned to axion generation in LSW experiments. The energy rotators (μkΩ). While aligned rotators cannot describe the density of axions produced by a gap can be several orders observed pulsation characteristic of pulsars, they capture of magnitude higher than the corresponding dark matter the important details of pulsar dynamics. The surface of a energy density and hence can give rise to very bright radio NS is an excellent electric conductor. Therefore the surface signals. electric field measured in the corotating frame of a NS is The paper is organized as follows. In Sec. II, we review zero. In the laboratory frame, electrons redistribute them- some basics of pulsar magnetospheres, including the selves to counteract the Lorentz force due to the internal formation of nonstationary vacuum gaps for plasma regen- magnetic field yielding the following (equivalent) surface eration. In Sec. III, we present a concrete model for a gap, condition: based on which we compute the spectrum of the axions produced in that gap. In Sec. IV we discuss the conversion Eint þ v × Bint ¼ 0; ð1Þ of axions to radio photons in the strong magnetic fields surrounding the pulsar. In Sec. V we discuss an observation where v ¼ Ω × r. For a vacuum magnetosphere (1) may be scheme using existing and planned radio telescopes, with a used to find the external electrostatic potential, discussion of instrumental and astrophysical backgrounds. We conclude this section with an estimate of the reach of B0 ΩR5 our scheme. We end with some concluding remarks Φðr; θÞ ¼ − P2 ðcos θÞ; ð2Þ in Sec. VI. 3r3 where B0 is the magnitude of the surface magnetic field, R II. THEORY OF PULSAR MAGNETOSPHERES is the NS radius, and Pn ðxÞ are Legendre polynomials. An important consequence of (2) is that there exists an external Pulsars are highly magnetized compact stars that emit electric field component, Ek , parallel to the dipolar mag- electromagnetic radiation over a wide range of frequencies. Many pulsars have been observed due to their coherent, netic field. It was shown by Goldreich and Julian [49] that pulsed emission of radio waves. While the mechanism for the vacuum magnetosphere solution is unstable. The coherent radio emission remains a mystery, it is widely electric force on charges due to Ek dominates gravity believed that the dense electron-positron plasma that fills and strips charges from the NS surface, accelerating them the magnetosphere plays an important role. Early explan- along magnetic field lines and populating the magneto- ations include coherent radio emission by dense, charged sphere. Eventually, the plasma surrounding the NS screens bunches [44] and maserlike two-stream plasma instabilities Ek and corotates with the pulsar. The corotating plasma [45]. The explanation based on emission by charged charge density is given by [49] bunches has fallen out of favor on theoretical grounds as a result of the difficulty in explaining the origin and 2Ω · B ρc ¼ : ð3Þ longevity of these bunches [46] as well as on observational 1 − Ω2 r2 sin2 θ grounds [47]. A more recent proposal claims that nonuni- form plasma generation in the magnetosphere, to be Corotation cannot be sustained at a radial distance discussed subsequently, gives rise to electromagnetic radi- (defined in cylindrical coordinates) r > RLC ¼ c=Ω where ation whose power and spectrum are in agreement with RLC is the radius of the light cylinder. The light cylinder observations [48]. We show that the processes responsible defines two categories of magnetic field lines: closed and for plasma generation are also very efficient axion factories. open, with the former being entirely contained within the The presence of plasma is essential not only to the light cylinder and the latter exiting it. Particles moving emission of coherent radio waves but also to the stability of along open field lines may escape freely to infinity. As a the magnetosphere [49]. Generation of electron-positron result, the region containing the open field lines lacks the pairs relies on the formation of charge-starved “gaps” in the charges necessary to screen Ek , leading to the formation of magnetosphere, which arise as a result of plasma outflow, gaps. While the existence of pulsar gaps has been well- along open field lines, through the light cylinder. The gap established, there is some uncertainty about the mechanism possesses a large component Ek , parallel to the magnetic for generating Ek and the location of gaps. Various gap field, that accelerates charged particles to high energy. models have been proposed including the polar-cap Once sufficient charge generation has taken place, Ek is [43,44], slot gap [51,52], and outer gap models [53]. In screened, and the gap is fully discharged. As a result, large this article we focus on the observable signatures of polar- amplitude fluctuations of E · B occur in the gap. The cap gap models. 055038-2
AXION PRODUCTION IN PULSAR MAGNETOSPHERE GAPS PHYS. REV. D 104, 055038 (2021) A. Polar cap production E · Bðx; tÞ 8 Along open field lines corotation cannot be sustained. As > > t=h 0 ≤ z ≤ t; 0≤t≤h a result, the electric potential deviates from that given by (2) < and the plasma that lies on open field lines decelerates ¼ 2ΩB2s h 1 0 ≤ z ≤ h; h > relative to the NS. Additionally, plasma can leave the light : T−t z ≤ 0 ≤ T − t; T −h 2me , at which frequencies are point the gap breaks down into a series of sparks. This 4=7 3=7 −1 condition occurs when [44] ω1 Bs Ω cT ¼ 42 MHz 14 : ð7Þ 2π 10 G Hz 2h 2=7 −3=7 −4=7 ρ Ω Bs The timescale of oscillation here is set by the crossing h ≈ 360 cm ; ð4Þ time of the gap at maximum thickness. Another time-scale 10 km Hz 1014 G which may contribute to axion production is the plasma frequency near the pulsar surface. where ρ is the radius of curvature of field lines exiting the polar cap and Bs is the magnitude of the surface magnetic III. AXION PRODUCTION IN GAPS field. The potential drop across the gap vanishes once eþ e− Axions couple to EM fields through the effective density coincides with (3) and Ek can be effectively Lagrangian, screened. To capture these broad features, we assume E · B is periodic in time (with period T) with 1 1 1 gaγγ LEMþa ¼ − Fμν Fμν þ ð∂ μ aÞ2 − m2a a2 − aFμν F̃μν ; 4 2 2 4 1 The RS model is restricted to antialigned pulsars where ð8Þ Ω · B < 0 and the plasma above the polar cap is positively charged. The mechanism has been extended to aligned pulsars in, where a is the axion field, ma is the axion mass, gaγγ is the for example, [55]. axion-photon coupling, and F̃μν ¼ εμναβ Fαβ =2 is the dual 055038-3
ANIRUDH PRABHU PHYS. REV. D 104, 055038 (2021) field tensor. The dynamics of axion-photon coupling are governed by the following equations: ρ ∇·E¼ − gaγγ ∇a · B; ð9Þ ϵ0 ∂E ∇×B¼ _ − ∇a × EÞ þ μ0 J þ gaγγ ðaB ð10Þ ∂t ð□ þ m2a Þa ¼ −gaγγ E · B; ð11Þ where ρ and J are the charge and current densities. The source-free Maxwell equations remain unaltered by the presence of an axion. According to (11), a region where E · B ≠ 0, such as a pulsar gap, can source axions. The production of axions using a background E · B component is employed in light shining through walls (LSW) and FIG. 2. Comparison of the axion density produced by the gap to related experiments [23–27], Any light particle search the dark matter density as a function of position in the magneto- sphere. Axion emission is beamed in the direction normal to the (ALPS) [56–58], and the CERN resonant weakly interact- polar cap (z-direction). The parameters are taken to be ma ¼ ing sub-eV particle search (CROWS) [28]. In experiments 10−7 eV, gaγγ ¼ 10−11 GeV−1 , B0 ¼ 1014 Gauss, P ¼ 1 sec. such as CROWS, axions are produced in a cavity in which E · B ≠ 0 where E comes from an excited cavity mode and B is an externally applied, static magnetic field. A single discharge of the gap induced by pair production. The mode of frequency ω sources an axion field, axion density computed using (11) and (5) is shown in Z Fig. 1 at two different magnetosphere locations in pulsar 0 gaγγ iωt eika jx−x j J1856–3754. The appearance of resonance peaks at ma ¼ aω ðx; tÞ ¼ − e d 3 x0 ðE · BÞω ðx0 Þ; ð12Þ ωn is a result of the assumption of gap oscillation 4π jx − x0 j periodicity, which is likely not realized in realistic models. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where ka ¼ ω2 − m2a is the axion momentum and In calculations of the signal power that follow we do not ðE · BÞω is the component of E · B with frequency ω. consider the effects of the resonance peaks shown in Fig. 1. For our purposes the integral is performed over the pulsar The total energy released in gap discharge is predominantly gap. In pulsar gaps E · B is time-dependent due to the in the form of ultrarelativistic eþ e− pairs. The fraction of outflow of plasma through the light cylinder and the the gap energy that is released in the form of axions is f ∼ ðgaγγ ΩBs h2 Þ2 ≪ 1, and hence the production of axions does not affect standard pulsar processes. Axions produced in the vacuum gap are also highly beamed in the direction normal to the polar cap, as demonstrated in Fig. 2. IV. AXION-PHOTON CONVERSION Once produced, axions can penetrate the dense plasma until they reach a distance at which photon conversion becomes kinematically allowed. In the presence of a strongly magnetized plasma, axion electrodynamics (9)– (11) must be supplemented by strong QED terms, α2 μν 2 7 μν 2 LQED ⊃ ðF μν F Þ þ ðF F̃ Þ ; ð13Þ FIG. 1. Comparison of axion density produced by gap oscil- 90m4e 4 μν lation to that of infalling axion dark matter at a distance of 100 km from the NS surface. The comparison is made for pulsar J1856– 3754 at angles θ ¼ 0° (blue) and θ ¼ 90° (red) with respect to the where α is the electromagnetic fine-structure constant and rotation axis. The axion dark matter density infalling onto the NS me is the electron mass. Axion-photon conversion results (black) is larger than the local DM density as a result of from mixing of the axion with the (parity-odd) state of the Liouville’s theorem. The axion-photon coupling is taken to be photon, Ak , whose polarization is parallel to the external gaγγ ¼ 10−11 GeV−1 . magnetic field, as shown below, 055038-4
AXION PRODUCTION IN PULSAR MAGNETOSPHERE GAPS PHYS. REV. D 104, 055038 (2021) Δk ðzÞ ΔB ðzÞ Ak ultrarelativistic, both the photon and axion momenta are ∂ 2z þ ω2 þ 2ω2 ¼0 well-approximated by ka;γ ≈ ω. This approximation breaks ΔB ðzÞ Δa a down when ma becomes comparable to the fundamental ω2p ðzÞsin2 θ 14α2 BðzÞ2 sin2 θ oscillation frequency of the gap. However at this mass the Δk ¼ − 2 2 2 þ 2ðω − ωp ðzÞ cos θÞ 45 m4e conversion occurs resonantly, and hence ka ¼ kγ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gaγγ ωBðzÞ sin θ m2a ω2 − m2a . In both regimes, we may reduce (14) to a system ΔB ¼ ; Δa ¼ − ; ð14Þ 2ðω2 − ωp ðzÞ2 cos2 θÞ 2ω2 of coupled first-order differential equations [59]. For ultra- relativistic axions the simplified equation is where B is the magnitude of the magnetic field, θ is the angle it makes with the z direction, ωp ðzÞ is the spatially Δk ðzÞ ΔB ðzÞ Ak i∂ z þ ω þ ω ¼ 0: ð16Þ varying plasma frequency, ω is the frequency of the axion/ ΔB ðzÞ Δa a photon fields. The refractive index in the direction parallel to the transverse magnetic field, nk (Δk þ 1) receives a In the weak-mixing limit (ΔB ≪ Δk − Δa ), (16) may be contribution from strong-field QED. This term may be solved to first-order using time-dependent perturbation neglected for nonrelativistic axions as it does not modify theory, giving a conversion probability, the resonance condition even for the highest magnetic Z R z0 fields observed in magnetars [30]; however it must be 2 ∞ 0 0 iωðΔa z0 − dz00 Δk ðz00 ÞÞ 2 Pa→γ ¼ ω dz ΔB ðz Þe zmin ; ð17Þ restored when considering possibly ultrarelativistic axions zmin converting close to the pulsar surface. We have ignored the Faraday effect, which can mix the two transverse EM where zmin is the radius at which the axion energy is equal to modes [59]. the photon mass, making photon conversion kinematically The conversion probability between axions and photons possible. In the limit of maximal mixing, conversion occurs depends critically on the relationship between the axion in a narrow region surrounding a critical radius, zc defined by mass and various pulsar parameters [60]. When the ωp ðzc Þ ¼ ma . In this limit the dispersion relations of the maximal mixing condition, axion and photon coincide, allowing us to make the follow- ing ansatz Ak ðz;tÞ ¼ Āk ðzÞe−iωtþikz ;aðz;tÞ ¼ āðzÞe−iωtþikz . ω2p sin2 θ 28α2 B2 sin2 θ 2 This ansatz, along with the WKB approximation lead to the − ω ¼ m2a ; ð15Þ 1− ω2p cos2 θ 45 m4e following first-order equation [30], ω2 is satisfied, conversion between axions and photons is ω2 Δk ðzÞ − Δa ΔB ðzÞ Ak i∂ z þ ¼ 0; ð18Þ resonantly enhanced. Strong QED effects prevent maximal k ΔB ðzÞ 0 a mixing from being achieved for axions with frequency ω > pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð360π 2 Ω2 m2e =7e2 Þ1=4 ≈ 1.6 × 10−4 eV ðΩ=HzÞ1=2 such as where k ¼ ω2 − k2a . We emphasize that (18) is only valid those produced thermally in the cores of NSs [37–39,41,42] in a narrow region around the conversion radius, zc . The and white dwarfs [40]. At lesser frequencies, strong QED amplitude of the photon field once it has left the conversion effects do not contribute significantly to conversion. region is modulated byp the varying plasma density and ffiffiffiffiffiffiffiffi ffi The fundamental Fourier mode of gap oscillations is asymptotically Ak ð∞Þ ≈ k=ωAk ðrc Þ. The final conversion ω1 ∼ 10−7 eV, which means axions produced by such probability, which includes the modulation of outgoing oscillations can convert to photons resonantly even if they photons is are ultrarelativistic. We restrict our analysis to ma ≲ 10−5 eV Z R z0 since for heavier axions the axion dark matter density ω3 ∞ 0 0 2 iωk ðΔa z0 − dz00 Δk ðz00 ÞÞ 2 dominates that of the axions produced by gap oscillations. Pa→γ;res ¼ dz ΔB ðz Þe zmin : ð19Þ k For light axions [ma < ωp ðRLC Þ] resonant conversion does zmin not occur in the magnetosphere. Intermediate mass axions Although Eqs. (16) and (18) were derived in different [ωp ðRLC Þ < ma ≪ ω1 ] require some care, as resonant con- limits, they are almost identical. The total radio flux seen on version occurs in the outer magnetosphere where magnetic Earth is related to the conversion probability as fields are considerably weaker than near the NS surface. The length scale over which the magnetic field and plasma 2 properties change is generally much larger than the de S¼ ρa ðzc ÞPa→γ vc z2c ; ð20Þ D2 Broglie wavelength of the axions and photons generated by the gap. Therefore we may approximate ω2 þ ∂ 2z ≈ where ρa ðzÞ is the axion density at distance z from the NS ðω þ kÞðω − i∂ z Þ. As mentioned above, for light axions surface, zc is the radius at which conversion takes place, vc the axion and photon dispersion relations do not coincide is the axion velocity at the conversion radius, and D is the within the light cylinder. However, since light axions are distance to the pulsar. We note that axion-photon 055038-5
ANIRUDH PRABHU PHYS. REV. D 104, 055038 (2021) conversion may also take place in the galactic magnetic conventional noise sources. It may be expressed as field; however for the nearby isolated pulsars and galactic SEFD ¼ 2T noise =Aeff where T noise is the noise temperature, magnetars discussed in this paper (see Sec. V), it is which receives contributions from instrumental as well as subdominant to conversion near the star. astrophysical sources, and Aeff is the effective area of the telescope or array. For a single-dish telescope the effective V. OBSERVATION AND BACKGROUNDS area is related to the physical area by an Oð1Þ aperature efficiency term and for an array with N ≥ 2 elements, the Periodicity of gap formation and discharge would lead to effective area is greater than that of a single telescope by a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a series of narrow axion-induced radio emission lines at integer multiples of ω1 ¼ 2π=T. In reality, the gap break- factor of NðN − 1Þ. In the following subsection we down is both inhomogeneous within the gap and likely not estimate the instrumental and astrophysical backgrounds perfectly periodic, as suggested by the complex sub-burst that contribute to SEFD. structure of pulsar emissions. While the assumption of periodicity, and hence the calculation above provides a A. Backgrounds good approximation for the axion flux produced by gap Conventional noise sources in radio astronomy include oscillations, the breakdown of this assumption necessarily radiometer losses, galactic and extragalactic radio sources, changes the signal search strategy. We therefore adopt a the CMB, atmospheric emission, and spillover radiation broadband strategy for signal detection. Most radio tele- from terrestrial sources. The total noise temperature at scopes employ a spectrometer that divides the passband frequency ν is then approximately T noise ðνÞ ¼ T R ðνÞ þ into subbands of width δν ¼ Δν=N ν to gather spectral T astro ðνÞ where T R is the receiver noise, T astro is the noise information about the source. Radio data will consist of a coming from astrophysical sources unrelated to the NS. series power measurements in the N ν frequency bins and N t The receiver noise depends on the particular radio telescope time bins each of width δt ¼ T int =N t . The power of the (s) being used and is discussed below. Astrophysical noise axion-induced signal in frequency bin i and time bin j is is dominated by anisotropic galactic synchrotron emission denoted by Sax ði; jÞ. Under the null hypothesis the power as demonstrated by Haslam et al. [61–63]. The radio sky measurement will receive contributions from astrophysical also receives contributions from an isotropic extragalactic and receiver noise sources to be discussed below. To test the component. While these sources differ in their spatial and hypothesis of an axion-induced signal we construct a χ 2 test spectral properties, the distinction is not important for our statistic, purposes. A recent measurement of the absolute sky temperature by the ARCADE 2 Collaboration [64] shows X Nν X Nt Sax ði; jÞ2 a spectrum, χ2 ¼ 2 ; ð21Þ i¼1 j¼1 σ S ðiÞ2 −2.5990.036 ν T astro ¼ ð24.1 2.1Þ K : ð23Þ where σ S is the flux density error in each bin, which is 310 MHz related to the familiar system equivalent flux density (SEFD) by σ S ðνÞ ¼ SEFD. The factor of 2 comes from the number of linear polarization states being measured. 1. Pulsar and nebula radio emission The relevant quantity to calculate the sensitivity of Ideal targets for observing the effects of axion conversion various radio telescopes to broadband signals from are nearby pulsars with high magnetic fields and minimal axion-photon conversion is the flux density Φ ¼ pulsed radio emission. The absence of coherent radio 1=ðD2 Δνsig ÞdP=dΩ where dP=dΩ is the signal power emission is often associated with inefficient plasma gener- emitted in the direction of Earth, D is the distance of ation in the polar cap and hence inefficient axion production the pulsar from Earth, and Δνsig is the bandwidth of the therein. However, there are simple explanations, consistent signal. For a given radio telescope or array the minimum with polar cap pair and axion production, for the lack of detectable flux density at unit signal-to-noise is observed radio emission from certain pulsars. For example, radio-quiet pulsars may be beamed away from Earth, but are SEFD still detectable through quasi-isotropic thermal surface Smin ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; ð22Þ npol Δνrec T int emission of soft x-rays [65]. Additionally, while axion emission is strongly beamed in the direction normal to the where SEFD is the system equivalent flux density, npol is polar cap, coherent radio emission can be generated at a the number of polarization states present in the image, Δνrec considerable distance and angle from the polar axis [48]. is the telescope bandwidth, and T int is the total integra- Other classes of targets include soft gamma repeaters (SGRs) tion time. and anomalous x-ray pulsars (AXPs), which are highly The SEFD is defined as the flux density of a source that magnetic pulsars that are widely believed to be magnetars. would deliver the same amount of power to the receiver as While few SGRs and AXPs have been observed to emit 055038-6
AXION PRODUCTION IN PULSAR MAGNETOSPHERE GAPS PHYS. REV. D 104, 055038 (2021) pulsed radio waves [66], many of them are characterized by SGRs listed in the table do not suffer from the same issue as their x-ray and gamma-ray emissions, with no observed radio ν1;1900þ14 ∼ 60 MHz, ν1;1806−20 ∼ 100 MHz. For axion counterpart. For the strong magnetic fields in SGRs and mass ma , the highest signal flux comes from the nth AXPs, the lack of radio emission may not be incompatible harmonic where n ¼ ⌈maxðma =2π; νmin Þ=ν1 ⌉ and νmin is with efficient charge generation near the polar cap. Once the lowest frequency observed by the telescope or inter- primary pairs are produced in the gaps of SGRs and AXPs, ferometer. We propose detecting the axion-induced signal the third-order QED process γ → γγ may quench further pair over an observing bandwidth equal to the fundamental gap production from curvature radiation and hence coherent oscillation frequency of the pulsar being observed, that is radio emission [67]. One potential pitfall of SGRs and δν ¼ ν1 . Thus, in contrast with axion dark matter searches AXPs is that they possess magnetic fields large enough to that look for thin radio lines, we assume the signal produce eþ e− pairs without the need for gaps. While the generated at frequency νn (n corresponding to the gap exact plasma generation mechanism in magnetars remains an oscillation harmonic generating the signal) is spread out open problem, it is possible that they possess vacuum gaps over the separation between lines. The sensitivity of this [68]. In the table below we include the relevant properties of proposal, shown in Fig. 3, corresponds to 100 hours of three candidate stars with ultrastrong magnetic fields and no observation of RX J1856.5–3754 and SGR 1806–20 with observed radio emission, perhaps due to one of the reasons the Five-hundred-meter Aperture Spherical Telescope mentioned in the preceding discussion. SGR properties are (FAST) [73]. taken from [69]. For the selected pulsars we assume radio emission from these sources is dominated by standard VI. CONCLUSIONS astrophysical noise and receiver noise of the antennas. In this work we presented a new mechanism for axion Name, Ref. Bs ðGaussÞ P0 ðsecÞ Dist. (kpc) production in pulsar magnetospheres. As shown, oscillating RX J1856.5–3754 [70] 1.5 × 1013 7.1 0.16 gap regions, where E · B ≠ 0, can source axions (as in light SGR 1900 þ 14 [71] 7.0 × 1014 5.2 12.5 shining through walls experiments) with energies corre- SGR 1806–20 [72] 2.1 × 1015 7.6 13 sponding to those of the gap oscillation modes and whose abundance greatly exceeds that of axion dark matter near The fundamental gap oscillation frequency of RX the neutron star. The conversion of the created axions to J1856–3754 is ν1 ¼ 6 MHz, which is undetectable by photons gives rise to enhanced radio emission at the Fourier terrestrial radio telescopes. Thus any detectable signal is frequencies of the gap oscillations. We found that 100 hours generated by higher order gap oscillation harmonics. The of observation of various Galactic pulsars with minimal radio emission could display an indirect signal of axion- photon conversion events. We found that radio missions operating at frequencies above 50 MHz, such as FAST and SKA, can probe axion-photon couplings that are orders of magnitude lower than astrophysical bounds over a wide range of masses. At high axion-photon couplings that are still not excluded by current bounds, axion-photon con- version events may be bright enough to explain the enigmatic fast radio bursts (FRBs) observed by a number of collaborations [74–85]. The mechanism we have pro- posed is consistent with claims that FRBs have a magnetar origin [86–88]. A more detailed analysis of the connection between gap oscillation-sourced axions and FRBs is the subject of ongoing investigation. The projected reach of this proposal also motivates the study of more sophisticated models of gap dynamics, such as those found in recent FIG. 3. Projected reach of 100 hours of observation of magnetar particle-in-cell simulations [48]. SGR 1806–20 (Blue) and pulsar J1856–3754 (Red) with the Five- hundred-meter Aperture Spherical Telescope (FAST) (for ma < 2π × 3 GHz ≈ 12 μeV) and SKA-mid (for 12 μeV < ma < ACKNOWLEDGMENTS 2π × 14 GHz ≈ 58 μeV), assuming the line-of-sight is 0° (solid) The author thanks Savas Dimopoulos for helpful con- and 90° (dashed) from the rotation axis (here assumed to coincide with the direction of the pulsar magnetic dipole moment). The versations and Robert Lasenby for useful comments on search is broadband with bandwidth set by the fundamental gap signal detection and on the manuscript. The author also oscillation frequency Δν ≈ 100 MHz (SGR 1806–20), 6 MHz thanks Anatoly Spitkovsky and Roger Blandford for (J1856–3754). Relevant parameters describing the pulsars are detailed discussion of vacuum gaps and radio emission listed in the table. properties of pulsars and magnetars. This work was 055038-7
ANIRUDH PRABHU PHYS. REV. D 104, 055038 (2021) supported by the National Science Foundation under Grant acknowledges the support of the Fletcher Jones No. PHYS- 1720397 and the Gordon and Betty Moore Foundation and the National Science Foundation (NSF) Foundation Grant No. GBMF7946. The author Graduate Research Fellowship Program. [1] C. A. Baker et al., Improved Experimental Limit on the [20] M. Baryakhtar, J. Huang, and R. Lasenby, Axion and hidden Electric Dipole Moment of the Neutron, Phys. Rev. Lett. 97, photon dark matter detection with multilayer optical halo- 131801 (2006). scopes, Phys. Rev. D 98, 035006 (2018). [2] R. D. Peccei and H. R. Quinn, CP Conservation in the [21] E. Arik et al., Probing ev-scale axions with cast, J. Cosmol. Presence of Pseudoparticles, Phys. Rev. Lett. 38, 1440 Astropart. Phys. 02 (2009) 008. (1977). [22] M. Arik et al. (CAST Collaboration), New solar axion [3] R. D. Peccei and H. R. Quinn, Constraints imposed by CP search using the cern axion solar telescope with 4He filling, conservation in the presence of pseudoparticles, Phys. Rev. Phys. Rev. D 92, 021101 (2015). D 16, 1791 (1977). [23] K. Van Bibber et al., Proposed Experiment to Produce and [4] S. Weinberg, A New Light Boson? Phys. Rev. Lett. 40, 223 Detect Light Pseudoscalars, Phys. Rev. Lett. 59, 759 (1987). (1978). [24] F. Hoogeveen, Terrestrial axion production and detection [5] F. Wilczek, Problem of Strong P and T Invariance in the using RF cavities, Phys. Lett. B 288, 195 (1992). Presence of Instantons, Phys. Rev. Lett. 40, 279 (1978). [25] P. Sikivie, D. B. Tanner, and K. van Bibber, Resonantly [6] L. Abbott and P. Sikivie, A cosmological bound on the Enhanced Axion-Photon Regeneration, Phys. Rev. Lett. 98, invisible axion, Phys. Lett. 120B, 133 (1983). 172002 (2007). [7] M. Dine and W. Fischler, The not so harmless axion, Phys. [26] J. Jaeckel and A. Ringwald, A cavity experiment to search Lett. 120B, 137 (1983). for hidden sector photons, Phys. Lett. B 659, 509 (2008). [8] J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the [27] F. Caspers, J. Jaeckel, and A. Ringwald, Feasibility, en- invisible axion, Phys. Lett. 120B, 127 (1983). gineering aspects and physics reach of microwave cavity [9] P. Svrcek and E. Witten, Axions in string theory, J. High experiments searching for hidden photons and axions, J. Energy Phys. 06 (2006) 051. Instrum. 4, P11013 (2009). [10] A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, [28] M. Betz, F. Caspers, M. Gasior, M. Thumm, and S. W. and J. March-Russell, String axiverse, Phys. Rev. D 81, Rieger, First results of the cern resonant weakly interacting 123530 (2010). sub-ev particle search (crows), Phys. Rev. D 88, 075014 [11] P. Sikivie, Experimental Tests of the “Invisible" Axion, (2013). Phys. Rev. Lett. 51, 1415 (1983). [29] R. Ballou et al. (OSQAR Collaboration), New exclusion [12] R. Bradley et al., Microwave cavity searches for dark-matter limits on scalar and pseudoscalar axionlike particles from axions, Rev. Mod. Phys. 75, 777 (2003). light shining through a wall, Phys. Rev. D 92, 092002 [13] S. J. Asztalos et al., Improved rf cavity search for halo (2015). axions, Phys. Rev. D 69, 011101 (2004). [30] A. Hook, Y. Kahn, B. R. Safdi, and Z. Sun, Radio Signals [14] S. J. Asztalos et al., Squid-Based Microwave Cavity Search from Axion Dark Matter Conversion in Neutron Star for Dark-Matter Axions, Phys. Rev. Lett. 104, 041301 Magnetospheres, Phys. Rev. Lett. 121, 241102 (2018). (2010). [31] B. R. Safdi, Z. Sun, and A. Y. Chen, Detecting axion dark [15] N. Du et al. (ADMX Collaboration), Search for Invisible matter with radio lines from neutron star populations, Phys. Axion Dark Matter with the Axion Dark Matter Experiment, Rev. D 99, 123021 (2019). Phys. Rev. Lett. 120, 151301 (2018). [32] M. Leroy, M. Chianese, T. D. P. Edwards, and C. Weniger, [16] B. M. Brubaker et al., First Results from a Microwave Radio signal of axion-photon conversion in neutron stars: A Cavity Axion Search at 24 μeV, Phys. Rev. Lett. 118, ray tracing analysis, Phys. Rev. D 101, 123003 (2020). 061302 (2017). [33] R. A. Battye et al., Dark matter axion detection in the radio/ [17] B. T. McAllister, G. Flower, J. Kruger, E. N. Ivanov, M. mm waveband, Phys. Rev. D 102, 023504 (2020). Goryachev, J. Bourhill, and M. E. Tobar, The organ experi- [34] J. Foster et al., Green Bank and Effelsberg Radio Telescope ment: An axion haloscope above 15 GHz, Phys. Dark Searches for Axion Dark Matter Conversion in Neutron Star Universe 18, 67 (2017). Magnetospheres, Phys. Rev. Lett. 125, 171301 (2020). [18] Y. Kahn, B. R. Safdi, and J. Thaler, Broadband and [35] J. H. Buckley, P. S. B. Dev, F. Ferrer, and F. P. Huang, Fast Resonant Approaches to Axion Dark Matter Detection, radio bursts from axion stars moving through pulsar Phys. Rev. Lett. 117, 141801 (2016). magnetospheres, Phys. Rev. D 103, 043015 (2021). [19] A. Caldwell et al. (MADMAX Working Group), Dielectric [36] A. Prabhu and N. M. Rapidis, Resonant conversion of dark Haloscopes: A New Way to Detect Axion Dark Matter, matter oscillons in pulsar magnetospheres, J. Cosmol. Phys. Rev. Lett. 118, 091801 (2017). Astropart. Phys. 10 (2020) 054. 055038-8
AXION PRODUCTION IN PULSAR MAGNETOSPHERE GAPS PHYS. REV. D 104, 055038 (2021) [37] J.-F. Fortin and K. Sinha, Constraining axion-like-particles ment, Nucl. Instrum. Methods Phys. Res., Sect. A 612, 83 with hard x-ray emission from magnetars, J. High Energy (2009). Phys. 06 (2018) 048. [57] K. Ehret et al., New ALPS results on hidden-sector light- [38] J.-F. Fortin and K. Sinha, X-ray polarization signals from weights, Phys. Lett. B 689, 149 (2010). magnetars with axion-like-particles, J. High Energy Phys. [58] R. Bähre et al., Any light particle search II—Technical 01 (2019) 163. Design Report, J. Instrum. 8, T09001 (2013). [39] M. Buschmann, R. T. Co, C. Dessert, and B. R. Safdi, [59] G. Raffelt and L. Stodolsky, Mixing of the photon with low- X-Ray Search for Axions from Nearby Isolated Neutron mass particles, Phys. Rev. D 37, 1237 (1988). Stars, Phys. Rev. Lett. 126, 021102 (2021). [60] S. J. Witte, D. Noordhuis, T. D. P. Edwards, and C. Weniger, [40] C. Dessert, A. J. Long, and B. R. Safdi, X-Ray Signatures of Axion-photon conversion in neutron star magnetospheres: Axion Conversion in Magnetic White Dwarf Stars, Phys. The role of the plasma in the goldreich-julian model, Rev. Lett. 123, 061104 (2019). arXiv:2104.07670. [41] S. J. Lloyd, P. M. Chadwick, A. M. Brown, H.-k. Guo, and [61] C. G. T. Haslam, A 408 MHz all-sky continuum survey. K. Sinha, Axion constraints from quiescent soft gamma- I—Observations at southern declinations and for the north ray emission from magnetars, Phys. Rev. D 103, 023010 polar region, Astron. Astrophys. 100, 209 (1981). (2021). [62] C. G. T. Haslam, M. J. S. Quigley, and C. J. Salter, A [42] J.-F. Fortin, H.-K. Guo, S. P. Harris, E. Sheridan, and K. 408 MHz survey of the galactic anticentre region, Mon. Sinha, Magnetars and axion-like particles: Probes with the Not. R. Astron. Soc. 147, 405 (1970). hard x-ray spectrum, J. Cosmol. Astropart. Phys. 06 (2021) [63] C. G. T. Haslam, C. J. Salter, H. Stoffel, and W. E. Wilson, A 036. 408 MHz all-sky continuum survey. II. The atlas of contour [43] P. A. Sturrock, A model of pulsars, Astrophys. J. 164, 529 maps., Astron. Astrophys. 47, 1 (1982). (1971). [64] D. J. Fixsen et al., Arcade 2 measurement of the absolute [44] M. A. Ruderman and P. G. Sutherland, Theory of pulsars: sky brightness at 3–90 GHz, Astrophys. J. 734, 5 (2011). Polar gaps, sparks, and coherent microwave radiation, [65] K. T. S. Brazier and S. Johnston, The implications of radio- Astrophys. J. 196, 51 (1975). quiet neutron stars, Mon. Not. R. Astron. Soc. 305, 671 [45] M. Lyutikov, R. D. Blandford, and G. Machabeli, On the (1999). nature of pulsar radio emission, Mon. Not. R. Astron. Soc. [66] F. Camilo et al., Transient pulsed radio emission from a 305, 338 (1999). magnetar, Nature (London) 442, 892 (2006). [46] D. B. Melrose, The models for radio emission from pulsars [67] M. G. Baring and A. K. Harding, Radio-quiet pulsars with —The outstanding issues., J. Astrophys. Astron. 16, 137 ultrastrong magnetic fields, Astrophys. J. 507, L55 (1998). (1995). [68] C. Thompson, Electrodynamics of magnetars. IV. Self? [47] H. Lesch, A. Jessner, M. Kramer, and T. Kunzl, On the consistent model of the inner accelerator with implications possibility of curvature radiation from radio pulsars, Astron. for pulsed radio emission, Astrophys. J. 688, 499 (2008). Astrophys. 332, L21 (1998). [69] S. A. Olausen and V. M. Kaspi, The McGill magnetar [48] A. Philippov, A. Timokhin, and A. Spitkovsky, Origin of catalog, Astrophys. J. Suppl. Ser. 212, 6 (2014). Pulsar Radio Emission, Phys. Rev. Lett. 124, 245101 [70] M. H. van Kerkwijk and D. L. Kaplan, Timing the nearby (2020). isolated neutron star RX J1856.5-3754, Astrophys. J. 673, [49] P. Goldreich and W. H. Julian, Pulsar electrodynamics, L163 (2008). Astrophys. J. 157, 869 (1969). [71] S. Mereghetti et al., The FirstXMM-Newton Observations [50] A. N. Timokhin and J. Arons, Current flow and pair creation of the soft gamma-ray repeater SGR 1900 þ 14, Astrophys. at low altitude in rotation powered pulsars’ force-free J. 653, 1423 (2006). magnetospheres: Space-charge limited flow, Mon. Not. R. [72] P. Woods et al., The prelude to and aftermath of the giant Astron. Soc. 429, 20 (2013). flare of 2004 December 27: Persistent and pulsed x-ray [51] J. Arons, Pair creation above pulsar polar caps: Geometrical properties of SGR 1806-20 from 1993 to 2005, Astrophys. structure and energetics of slot gaps, Astrophys. J. 266, 215 J. 654, 470 (2007). (1983). [73] D. Li and Z. Pan, The five-hundred-meter aperture spherical [52] A. G. Muslimov and A. K. Harding, High-altitude particle radio telescope project, Radio Sci. 51, 1060 (2016). acceleration and radiation in pulsar slot gaps, Astrophys. J. [74] D. R. Lorimer, M. Bailes, M. A. McLaughlin, D. J. 606, 1143 (2004). Narkevic, and F. Crawford, A bright millisecond radio [53] K. S. Cheng, C. Ho, and M. Ruderman, Energetic radiation burst of extragalactic origin, Science 318, 777 (2007). from rapidly spinning pulsars. I. Outer magnetosphere gaps, [75] D. Thornton et al., A population of fast radio bursts at Astrophys. J. 300, 500 (1986). cosmological distances, Science 341, 53 (2013). [54] V. S. Beskin, A. V. Gurevich, and Y. N. Istomin, Physics of [76] S. Burke-Spolaor and K. W. Bannister, The galactic position the Pulsar Magnetosphere (Cambridge University Press, dependence of fast radio bursts and the discovery of Cambridge, 1993). FRB011025, Astrophys. J. 792, 19 (2014). [55] J. Gil, G. I. Melikidze, and U. Geppert, Drifting subpulses [77] L. G. Spitler et al., Fast radio burst discovered in the arecibo and inner acceleration regions in radio pulsars*, Astron. pulsar alfa survey, Astrophys. J. 790, 101 (2014). Astrophys. 407, 315 (2003). [78] V. Ravi, R. M. Shannon, and A. Jameson, A fast radio burst [56] K. Ehret et al. (ALPS Collaboration), Resonant laser power in the direction of the carina dwarf spheroidal galaxy, build-up in ALPS: A ’Light-shining-through-walls’ experi- Astrophys. J. 799, L5 (2015). 055038-9
ANIRUDH PRABHU PHYS. REV. D 104, 055038 (2021) [79] K. Masui et al., Dense magnetized plasma associated with a [84] M. Amiri et al. (CHIME/FRB Collaboration), The chime fast radio burst, Nature (London) 528, 523 (2015). fast radio burst project: System overview, Astrophys. J. 863, [80] D. J. Champion, Five new fast radio bursts from the htru 48 (2018). high-latitude survey at parkes: First evidence for two- [85] M. Amiri et al. (CHIME/FRB Collaboration), Observations component bursts, Mon. Not. R. Astron. Soc.: Lett. 460, of fast radio bursts at frequencies down to 400 megahertz, L30 (2016). Nature (London) 566, 230 (2019). [81] M. Caleb et al., Fast radio transient searches with utmost at [86] C. D. Bochenek, A fast radio burst associated with a galactic 843 MHz, Mon. Not. R. Astron. Soc. 458, 718 (2016). magnetar, Nature (London) 587, 59 (2020). [82] K. W. Bannister et al., The detection of an extremely bright [87] S. Bhandari et al., The host galaxies and progenitors of fast fast radio burst in a phased array feed survey, Astrophys. J. radio bursts localized with the australian square kilometre 841, L12 (2017). array pathfinder, Astrophys. J. 895, L37 (2020). [83] R. Shannon et al., The dispersion-brightness relation for fast [88] B. Zhang, The physical mechanisms of fast radio bursts, radio bursts from a wide-field survey, Nature (London) 562, Nature (London) 587, 45 (2020). 386 (2018). 055038-10
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