Pis'ma v ZhETF, vol. 101, iss. 1, pp. 3-8 © 2015 January 10
Fast radio bursts and axion miniclusters
1.1. Tkachev1^
Institute for Nuclear Research of the RAS, 117312 Moscow, Russia Submitted 11 November 2014
Non-linear effects in the evolution of the axion field in the early Universe may lead to the formation of gravitationally bound clumps of axions, known as "miniclusters." Minicluster masses should be in the range Mmc ~ 1O-12M0, and in plausible early-Universe scenarios a significant fraction of the mass density of the Universe may be in the form of axion miniclusters. Here I argue that observed properties (total energy release, duration, high brightness temperature, event rate) of recently discovered Fast Radio Bursts can be matched in a model which assumes explosive decay of axion miniclusters.
DOI: 10.7868/S0370274X15010014
I. Introduction. The recent detection of unusual radio pulses [1-5], known as Fast Radio Bursts (FRBs), has generated strong interest in identifying their origin and nature. The bursts exhibit a frequency-dependent time delay, which obeys a quadratic form so strictly, that the only explanation remains - signal dispersion in cold cosmic plasma during propagation. The magnitude of this delay, proportional to the electron column density along the line of sight, and called dispersion measure, is so large that the cosmological distances are inferred for the sources.
Thornton et al. [3] deduce redshifts for four different FRBs observed at Parkes radio telescope to be in the range from 0.45 to 0.96. Recently detected FRB at Arecibo Observatory [4] (which has larger size antenna and therefore excludes atmospheric artefacts as possibility for FRB) has derived redshift of z = 0.26. All observers agree on a high rate of FRBs, ~ 104 events/day for the whole sky.
FRBs are also characterized by extremely high flux densities (~Jy) over very short time scales (milliseconds). Short time scales imply that the size of emitting region is small, less then 300 km. Observed fluxes imply that the total energy radiated in the band of observation was in the range 1038 —1040 ergs [3, 4], assuming isotropy and quoted redshifts. Derived redshifts, and therefore the radiated energy, can be smaller if significant part of dispersion measure accumulates in the host galaxies. With this parameters, and assuming FRBs are at Gpc distances, their brightness temperature would be Tb ~ 1036K, leading to the conclusion that radiation from FRB sources should be coherent [6-9].
-^e-mail: thachev@ms2inr.ac.ru
The source of the FRB signals is hotly debated in the literature, with suggested progenitors ranging from terrestrial interference to neutron star-neutron star mergers. Wide range of models was thoroughly discussed in Kulkarni et al. [8], and refs. therein. While all models have problems, the verdict was that several arguments [10], which relate giant flares of young magnetars with FRBs, may offer plausible physical scenario [11] based on assumption that FRBs could be attributed to synchrotron maser emission from relativistic, magnetized shocks.
FRBs are so mysterious that a new physics models were also suggested and discussed in literature [12-15]. E.g., Ref. [7] even discussed, en route, the possibility that FRBs are signals beamed at Earth by advanced civilizations.
In this paper I consider possible relation of FRBs and axions [16]. In Ref. [17] it was suggested that axion field may form gravitationally bound compact astrophysical objects, where under some conditions parametric instability occurs, resulting in a powerful coherent burst of maser radiation. Such instability has been also studied in Refs. [18, 19]. Here I reconsider this scenario and discuss several mechanisms where axion miniclusters [2023] are responsible for Fast Radio Bursts, see also [15]. I'd like to note, that a general case of axion like particles (ALP, where particle mass, self coupling, and coupling to electromagnetic field are not tightly related to each other), opens a lot of possibilities which are ruled out otherwise. I do not consider general case of ALP, staying instead with the standard QCD invisible axion model. Generalization to ALP is straightforward.
II. Dense axion objects. The invisible axion is among the best motivated candidates for cosmic dark matter [16]. The axion is the pseudo-Nambu-Goldstone
boson resulting from the spontaneous breaking of a U(l) global symmetry known as the Peccei-Quinn, or PQ, symmetry introduced to explain the apparent smallness of strong CP-violation in QCD [24].
There are stringent astrophysical, cosmological, and laboratory constraints on the properties of the ax-ion [16]. In particular, the combination of cosmological and astrophysical considerations restricts the axion mass ma to be in the window peV < ma < meV. Corresponding value of the axion decay constant fa can be found using relation fama = /^m,, where 7r referes to pion. The contribution to the mean density of the Universe from axions in this window is guaranteed to be cosmologically significant. Thus, if axions exist, they will be dynamically important in the present evolution of the Universe.
For what follows, it is important for PQ-symmetry to be restored after inflationary stage of the Universe evolution. This happens if reheating temperature is larger than the corresponding PQ-scale, but this may also happen [25] already during reheating, in a transient highly non-equilibrium state, even if resulting temperature is small. In this situation the axion field takes different values in different casually disconnected regions at temperatures well above the QCD confinement, when the axion is effectively massless. At the confinement temperature and below, QCD effects produce a potential for the axion of the form V(0) = to2/2[1—cos(6>)], where the axion field was parametrized as a dimensionless angular variable 0 = a/fa. Axion oscillations commence and field variations are transformed into density contrasts, pa, which later lead to tiny gravitationally bound "mini-clusters".
A. Axion Miniclusters. Since density variations in this circumstances are large from the very beginning, we do not refer to them as "perturbations", and let us call corresponding regions as "clumps". It is easy to understand that today those clumps, or miniclusters, will be very dense objects. Let us specify the density of a dark-matter clump prior to matter-radiation equality as 5pa/pa = In situation when $ ~ 1 (which would arise for non-interacting field V(0) = iTf.2/2^2 with random initial conditions), these clumps separate from cosmological expansion and form gravitationally bound objects already at T = Teq, where Teq is the temperature of equal matter and radiation energy densities. Density of such clump today will correspond to a matter density back then, i.e. will be 1010 times larger than the local galactic halo dark matter density.
However, at the time when axion oscillations commence, in many regions 0 ~ 1, and self-interaction is important. Numerical investigation of the dynamics of the
axion field around the QCD epoch [21-23] had shown that the non-linear effects result in regions with $ much larger than unity, possibly as large as several hundred, leading to enormous mini cluster densities. In such situation a clump separates from cosmological expansion at T ~ (1 + §)Teq which leads to a final minicluster density today given by [22]
pmc~ 140$3(l + $)pa(Te
eq )
(1)
Even a relatively small increase in $ is important because the final density depends upon for $ > 1.
The scale of minicluster masses is set by the total mass in axions within the Hubble radius at a temperature around T k, 1 GeV when axion oscillations commence, which is about 10~12M©. Masses of miniclusters are relatively insensitive to the particular value of $ associated with the minicluster. Corresponding minicluster radius clS cl function of M and
1/3
Rmr. « -^- ( TT TTTT ] km. (2)
$(1 + $)1/3a^2 V10-12Mg
Since large-"!» miniclusters are very dense, form early, and are well separated from each other, they should escape tidal disruption and merging.
According to Ref. [23], more than 13 % of all axionic dark matter are in miniclusters with $ > 10, more than about 20 % are in miniclusters with $ > 5 and 70 % are in miniclusters > 1). Since roughly half of all axions reside in miniclusters, the total number of miniclusters in the Galaxy is large, N ~ 1024.
At this point, an important relation
M„
10~12M© = 2 • 1042 ergs,
(3)
and the fact that gigahertz frequency radiation is within allowed axion mass range, v = ma/2v: « « 2.4 (ma/10/xeV) GHz, should tell us that if a fraction of axion minicluster mass is rapidly transformed into radiation, this will lead to something similar to observed FRB. Interestingly, in my notes dating back to 1997 I have found the following phrase: "Even if the tiny fraction 10-25Mg of the minicluster mass 10~12M© will go into radiation on this frequency, it can be detected from anywhere in the Galaxy halo (L. Rosenberg, private communication)". Back then this (and several un-certainness which I will describe below) actually had prevented me from submitting already prepared paper. Let us discuss farther evolution of axion miniclusters and possible mechanisms of their mass transfer into radiation.
B. Axion Bose-clusters. Miniclusters with $ > > 30 undergo the Bose-condensation later on and consequently became even denser and more compact [20].
Usually, in the related literature, an existence of a Bose-star is just postulated, without questioning of how it can be formed, for a review of Bose-stars see, e.g. [26]. However, in the case of invisible axion all couplings are so small, that mere possibility of condensate formation has to be studied [27-30]. Simple estimates has been done in Ref. [27], while Bose-condensation in the frameworks of Boltzmann equation was studied numerically in Ref. [28]. In Boltzmann approach Bose-condensate does not form ac
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