Axion and Fast Radio Bursts( a model for generation mechanism of fast radio bursts )Aiichi Iwazaki
Nishogakusha University
Phys. Rev. D91(2015);
arXiv:1412.7825; arXiv:1512.06245;
arXiv: 1707.04827

Fast Radio Bursts( FRBs )Mysterious radio bursts from extragalactic universe( originally reported in 2007 and then there are morethan 30 FRBs observed until now)

Duration ~ millisecond ( intrinsic one < millisecond )Large dispersion measure ~ >500pc/cm^(-3)( indicates z>0.1 and so large emission energies ~10^(43)GeV/s )FRBs are coherent radiations because of extremely large flux

Only observed at radio frequencies ~ (700MHz~8GHz)
No visible light, X ray, and gamma ray ( no afterglow)
coherent radiations at radio frequency just like maser
Event rate (10^3~10^4)/dayFast Radio Bursts( FRBs )All of FRBs are non-repeating except
only one ( FRB121102) is repeating
Bursts from an identical source are repeated many times even now.
( detail observations have been performed )Non-repeating FRBs were observed only once at only narrowfrequency band 700MHz~1.6GHz .
Celestial objects causing the FRBs are not identified.
( no observations at low frequencies 100MHz~400MHz)
Karastergiou, et al. 2015

The repeating FRB was observed with multiple( interferometric ) observations at wide frequency band
1.2GHz~8GHz and a host galaxy was identified as a dwarf
galaxy z=0.19. Tendulkar, et al. 2017

Almost of all non-repeating FRBs wereobserved in the frequency range
1.2GHz~1.6GHz

1.5GHzfrequency

millisecond

Parkes observatory（Australia）

1.3GHzarrival time
Arrival time depending on frequency( dispersion measure ) Photons acquire a mass, i.e. plasma frequency
owing to plasma in intergalactic spacefrequency
2.3GHzbandwidthδνcenter frequency

νc1.7GHzRepeating FRB121102
Astrophys.J. 833 (2016) no.2, 177

The figure shows that theburst is narrowband.
All of the FRBs including
non-repeating ones
might benarrowband
Repeating FRBs wereobserved in the frequency range
1.2GHz~8GHz with multiple telescopes

range of observed spectra

1.2GHz ~ 1.5GHz
1.5GHz1.2GHz

1.7GHz ~ 2.3GHz
2.3GHz

1.7GHzOrigin of the FRBs is unknown
Astrophysical models have been proposed simply for accommodating
burst energy and duration, but have no explicit emission mechanism

Black hole-neutron star merger

Massive neutron star collapsing into black hole
Asteroid collisions with neutron star
Neutron star-neutron star merger“and more”

Observation of the Repeating FRB

Giant flare of magnetars

A remaining astrophysical candidate

Giant radio pulsars ( e.g. Crab pulsar )observed only at radio frequencies
similar to FRBs although they are broadband

No explanation why there are noemissions of visible light, X ray, etc.

No association with gamma raybursts,
No explanation why there are noemissions of visible light, X ray, etc.
No observation associated withSGR1806-20
Too small fluence compared withFRBs,Broadband, not narrowband

Repeating Fast Radio Burst (FRB121102)( It is important to see the features of the FRB because detailobservations have been performed )Specific features

1) Bursts are clustered in a short period and after the bursts
there is a long or short period with no bursts( any regularity in the period has not been observed )2) Spectra of bursts are narrowband, not broadband.
( it appears that bandwidths δν are proportional to centerfrequencies ν c ) 1.5GHz < ν c < 7GHz , 200 MHz < δν < 1GHz
3) no bursts observed with low frequencies <100MHz andhigh frequencies >10GHz

Repeating Fast Radio Burst (FRB121102)
Bursts are clustered in a short period, but no regularity
Bursts arise in an interval of several 10 seconds to several hours
burstclustered

There are periods with no bursts which are several
hours to several days or months
several days
clustereda few monthclusteredclusteredRepeating Fast Radio Burst (FRB121102)
The repeating FRB121102 has been observed
simultaneously in various radio frequencies.
Remarkable features
There are bursts with various
center frequencies(narrowband, not broadband )Law et al.

1.5GHz < ν c < 7GHz

arXiv:1705.07553

 (ν − ν c ) 2  center frequency ν cGaussian spectrum ∝ exp −
2  bandwidthδν 2(δν ) It seems that widths δν are proportional to the center frequency ν cδν ~ 500 MHz
δν ~ 300MHzδν ~ 200MHz

for ν c = 3GHz,for ν c = 2GHz,for ν c = 1.3GHzδν ∝ ν cRepeating Fast Radio Burst (FRB121102)
Very remarkable observation reported at Aug. 2017( not yet published in a paper; V. Gajjar, et.al. ATel
No.10675. )15 bursts were observed by Green Bank Telescope
covering frequencies 4GHz~8GHz.
The frequencies are higher frequencies than ones ofany other bursts.
All of the bursts are shown to be narrowband.

We wish to note; the feature may indicate the origin of the bursts.

Intervals between neighboring bursts aregradually becoming shorter !!
21s 11s
38s
38s, 21s, 11s, or 94s, 51s, 27s

Axion model of FRBs

We assume the presence of coherent axion states called asaxion stars and assume axion mass, (0.6~1)×10^(-5)eV to explain
observed radio frequencies~1.4GHz.

Non-repeating FRBs are caused by the collision between the axion
stars and neutron stars.

The repeating FRBs are caused by the collision between the axion starorbiting galactic black hole and magnetized accretion disk . Axion stars
condense in galactic center as dark matter. The collisions repeatedly
take place.
The point is that strongly magnetized electron gases emit
coherent radiations ( FRBs) when they touch the axion stars

Axion model of FRBs
Axion stars are coherent axion states formed by gravitational
attraction, which are described by solutions of the axion field
equation coupled with gravity.
Note the star is oscillatinga (r , t ) = a0 f a exp(− r / Ra ) cos(ma t )2A.I, 2015

M a mass of axion star

 700km  0.6 × 10 eVa0 ≅ 3 × 10 ma Ra −5−8Ra Radius2

 0.6 × 10 −5 eV   10 −12 M sun  ≅ 720km Ra = 2ma M ama  Ma m 2pl

ma Axion mass

m pl Planck mass

The spherical solutions are not important for the explanation of various
properties of FRBs. The point is the oscillation as cos(ma t ) and the value of−8a/f
≅
a~
3×10
amplitude
0aAxion model of FRBs
11−12M=(10~10) M sun) are estimated byMasses of axion stars ( acomparing the event rate (10^3~10^4/day )of FRBs and the rate of
the collision between axion star and neutron star

Axion stars are formed by gravitational cooling of axion miniclusters. It is well known that the axion miniclusters are formed
after QCD phase transition owing to the misalignment of thephases θ = a / f a in causally disconnected regions.
Φ PQ =| Φ PQ | exp(iθ ) , θ ; Nambu-Goldstone boson (axion)

after QCD phase transition

θ1

θ3

minicluster
Kolb and Tkachev, 1993

θ2
θ4
θ5 θAxion number density of theminicluster grows in the matter
dominated period

6

Gravitational coolingGuzman and Lopez, 2006

Axion (Nambu-Goldstone mode) becomes massive
after QCD phase transition;
There are different phases θ i coherently oscillatingin causally disconnected regions.

The density
moreincreases

axion starAxion model of FRBs
Generation of electric fields by axion stars in background magnetic fielda (t , r ) E ⋅ B
1
L = kα, k = O(1), α ≅f aπ137
B magnetic field of neutron star or accretion disk− αa (t , r ) B∝ cos(ma t )E=−f aπThe electric field uniformly oscillates over the starElectrons in neutron star or accretion disk coherently oscillate andemit coherent radiations , when they are hit by the axion starma
Dipole radiation with frequency =2π

E

Oscillation of electrons


B

Energy emitted by a single electron
422e (eE )B −12 GeV  7 × 10 km   0.6 × 10 eV     10 
≅ 1.0 × 10
w=23mes Rama   10 G 
222−52Coherent radiations from electron gas in the volume λ3 = (2π / ma ) 348

  7 × 10 km   0.6 × 10 eV   B  ne   10 w N = w ( ne λ ) ≅ 10 GeV / s 18 −3  Rama 10 cm     10 G 
223

2

2−532

 0.6 × 10 −5 eV  Sufficiently large energies ~ 10 40 erg / s2π
≅ 20cm
λ=mama are emitted to beconsistent with observations

2

production of repeating FRBCollision between axion star and accretion disk of black holeaxion star hits the disk

velocity of disk V
Vaccretion disk

We assumegeometrical thin accretion disk
with strong magnetic fieldA model of accretion disk
Begelman and Silk (2017)Black hole
Vaxion star

horizontal view

10 5 cm

production of repeating FRB
RaRaλa = 2π / maEmissions arise from the surfaceof the disk

volume~ Ra2 λa
The axion star can pass through the disk
without evaporationenergy of the burst
from the location of the collision48  7 × 10 km   0.6 × 10 eV   B  ne22242   10 
W = w N = w ( ne Ra λa ) ≅ 10 erg / s 18 −3  Rama 10 cm     10 G 
22We need strong magnetic fieldand high electron density−5B ≥ 1010 G

ne ≥ 1018 / cm 32

termination of coherent radiations
 B 
2
2
2
5pm
eE
mm
eV/
2~()/~
10Oscillation energy of an electron 11 eea
 10 G 

2is larger than initial temperature of the electron gas.

The temperature increases and reaches a criticaltemperature
2B 
5given by the oscillation energy Tc ~ 10 eV  11  within a millisecond 10 G 

Thermal fluctuations terminate the coherent oscillation.
The increase of the temperature is caused bythermalization of the oscillation energies

Line spectrum is thermally broaden (ν − ν c ) 2 Tc
 , δν = ν c
S (ν ) ∝ exp −2 me 2(δν ) ; width proportional to center frequency

νcBandwidths δν are proportional to the center frequencies ν cModel prediction of bandwidth, e.g.
Tc
B
ν
=3GHzforδν = 3GHz
≅ 430 MHzc
3.3 × 1010 G
meobservationsδν ≈ 1GHz for 6GHz
δν ≈ 500MHz for 3GHzδν ≈ 300MHz for 2GHzδν ≈ 200MHz for 1.2GHz

We should note that the strengths ~ 1010 G of magnetic fields
are almost identical to the strengths needed for large
emission energies ~ 10 40 erg / s

Presence of various center frequencies in repeating FRB
Doppler shifts owing to the velocities V of the accretion disk

There are various center frequencies observed

Doppler shiftedone
νintrinsic frequency

ν c = 1.2GHz ~ 7GHz= ν int 1 − V /(1 − V cos(θ ))V ; velocity of the disk
mline of sight

2cmaa= 1.4GHz
ν int =2π
0.6 × 10 −5 eVaxion star
VAxion stars hit various points
in the disk.

θBlack hole
VDifferent point hit in the disk has different velocity, which leads to a burst with a different frequency

No observations of repeating bursts with low frequencies <100MHz . For the emission of bursts with low frequencies
ν c < 100MHz , the velocity of the disk must be large such asV > 0.99 and the angle θ must be such as θ ≅ πSuch bursts are very rare.
Our model predicts no non-repeating FRBs with high frequencies>3GHz because of no large Doppler shift.
They arise from collisions with neutron stars
No observations of non-repeating bursts with low frequencies
100MHz~400MHz
We need large redshift z>3( ν int /(1 + z ) )of the intrinsic frequencymamaSuch FRBs are very faint.
ν int == 1.4GHz−52π

0.6 × 10 eV

A regularity in intervals between bursts has been observedIntervals between neighboring bursts become shorter
V. Gajjar, et.al. ATel No.10675

Time interval(second)
A group
Another groupof bursts
of bursts

180.5s
37.9s
21.4s
11.3s

94.2s
51.2s
26.8s

Axion star is orbiting andfalling into black hole,accelerating its speed

accretion disk

The fact strongly indicates the evidenceof axion star orbiting black hole

Conclusions
We have presented a model of fast radio bursts;
Axion stars hitting neutron stars or accretion disks produce
the fast radio bursts

Energies of FRBs ( ~ 10 erg / s )Duration ( ~millisecond )40

The following features can not be explain by any astrophysical models

Narrowband (bandwidths proportional to center frequencies)( line spectra are thermally broaden )e.g. 500WHz for ν c = 3GHz
Presence of various center frequencies of repeating FRB
ν c = 1.2GHz ~ 7GHz from Doppler shifts of intrinsic frequency
Presence of irregular bursts in repeating FRBs
( axion stars hit accretion disk, orbing black hole )Although we haveassumed the sphericalsolutions,deformationa (r , t ) ∝ exp(−r / Ra ) cos(ma t )the estimation ofemission energies e.t.cdoes notdepend on the solutions.
We simply use theamplitude a(r , t ) ∝ cos(m t )for the derivation

split
Amplitude of ‘a’ does not change
so much even if the axion star isdeformed or split because themass M a does not change so mucha

M a ~ (ma a ) × volume2

Coherence of the axion star is very rigid
Number of axions in the volume (1/ma)^3
is huge ~10^(40), although the amplitude θ = a / f a ≈ 10 −8
is very small.
Thus, the coherence is not lost when the star isdeformed by tidal forces of neutron stars or black holes.
It means that the classical treatment of the axion stars
is valid for the estimation of emission energies, etc.