Download Radio Broadcasts from Superconducting strings

Radio Broadcasts from
Superconducting strings
µ
Danièle Steer (APC)
I
Yi-Fu Cai (McGill)
Eray Sabancilar, Tanmay Vachaspati (Arizona State U.)
PRD 86 043521
PRD 85 (2012) 023530
Tuesday, February 4, 2014
[D.Thornton et al, 1307.1628, Science; D.Lorimer et al, 0709.4301, Science]
A population of fast radio bursts at cosmological distances
1Jy = 10
−26
W
m2 Hz
Brightest astronomical radio sources:
1 ∼ 100Jy
Redshifts z~ 0.5-1. Comoving distances ≤1 Gpc. Isolated bursts, rate < 0.025/hour.
Tuesday, February 4, 2014
[D.Thornton et al, 1307.1628, Science; D.Lorimer et al, 0709.4301, Science]
A population of fast radio bursts at cosmological distances
1Jy = 10
−26
W
m2 Hz
Brightest astronomical radio sources:
1 ∼ 100Jy
Radio frequency interference
from a mobile phone 1km away
transmitting 0.5W at 1800MHz
∼ 109 Jy
Redshifts z~ 0.5-1. Comoving distances ≤1 Gpc. Isolated bursts, rate < 0.025/hour.
Tuesday, February 4, 2014
[D.Thornton et al, 1307.1628, Science; D.Lorimer et al, 0709.4301, Science]
A population of fast radio bursts at cosmological distances
Characteristic dispersion in
frequency due to scattering
of radio waves as propagate
through ionized turbulent
galactic medium
∆ts ∼ ν −4
[Lee and Jokipii 1976,...]
SOURCE?
Redshifts z~ 0.5-1. Comoving distances ≤1 Gpc. Isolated bursts, rate < 0.025/hour.
Tuesday, February 4, 2014
[D.Thornton et al, 1307.1628, Science; D.Lorimer et al, 0709.4301, Science]
A population of fast radio bursts at cosmological distances
Characteristic dispersion in
frequency due to scattering
of radio waves as propagate
through ionized turbulent
galactic medium
1230 MHz
∆ts ∼ ν −4
[Lee and Jokipii 1976,...]
SOURCE?
Redshifts z~ 0.5-1. Comoving distances ≤1 Gpc. Isolated bursts, rate < 0.025/hour.
Tuesday, February 4, 2014
• Oscillating loops of superconducting cosmic strings?
γ, g
µ
I
• Act as antennas. Emit EM radiation in wide range of frequencies ω , from radio to gamma
• Also emit GWs [Vachaspati&Vilenkin, Damour&Vilenkin,....]
[Vilenkin&Vachaspati,
Blanco-Pillado&Olum,
Berezinsky et al, Cheng et al,
Cai et al....]
– Power emitted from a loop of length L decays exponentially with ω for ωL � 1
– exception: from cusps and kinks and kink-kink collisions,
which emit short bursts of radiation in certain special directions
– If an observer/experiment lies in one of those directions : stronger signal
• How many radio bursts of observed duration ∆ and flux S can be expected from
a cosmological network of loops of superconducting strings of tension µ, carrying current I?
Tuesday, February 4, 2014
Event rate of radio bursts from superconducting string loops
• fixed observed frequency ν0 = 1230 MHz
• integrated over duration of bursts
• chosen values of parameters: Gµ = 10−10 , I = 105 GeV
cusps
kinks
An experiment sensitive
to mJy fluxes would observe
~100 radio bursts from
kinks/day
kink collisions
Tuesday, February 4, 2014
~1/day from cusps
1) Dynamics of superconducting strings: assumptions
two free parameters µ, I
2) Power emitted in photons
L(t) = Li − ΓGµ(t − ti )
Γγ + Γg
3) Event rate from from cusps/kinks/kink-kink
collisions as a function of : S = observed flux
∆ = observed burst duration
Tuesday, February 4, 2014
1) Dynamics of superconducting strings: assumptions
• Models with extra fields can often support currents in the string core
[Witten ’85, P. Peter ’92, ’93,
B.Carter, C.Ringeval,
Davis&Shellard, Hindmarsh,
Baboul&Piran&Spergel...]
• Microphysics complicated, backreaction generally non-negligible;
determining effective action hard
• eg:
U(1) x U(1)
σ
condensate
|Φ|
w
Σ = σ(r)eiφ(t,z)
Aµ
string
(Φ, Bµ )
radius
0.15
w = (∂z φ)2 − (∂t φ)2
C
0.1
µ
• space-like currents (w>0)
T
0.05
Imax
0
-0.1
Tuesday, February 4, 2014
0
i
0.1
I
• Important point: maximum current Imax
w
[P. Peter]
c2L
dT
=−
dµ
• Assumptions:
1) string dynamics given by NG action.
µ=T
√
2) Strings all carry same constant current I with Imax ∼ q µ
Corresponding current density
�
µ (3)
� σ))
J µ (t, �x) = I dσ X,σ
δ (�x − X(t,
• Typical values we shall take
Gµ = 10−10
Tuesday, February 4, 2014
I = 105 GeV
Imax ∼ 1012 GeV
I
2) Power emitted in photons
• Power emitted per unit frequency, per unit solid angle
d 2 Pγ
ω2 L µ 2
=
|Jω | .
dωdΩ
2π 4π
∝I ,
µ �
M±
(k)
=
�
L
0
�µ
dσ± eik·X± /2 X±
,
• (Nearly) standard saddle-point/discontinuity analysis in ωL � 1 limit
dPγc
– cusp
∼ I 2L
dωdΩ
emitted in a cone of opening angle θω = (ωL)−2/3
dPγk
I 2 Lψ
– kink
∼
dωdΩ
(ωL)2/3
emitted in a fan-shape of solid angle Ω ∼ 2πθω
– kink-kink
dPγk
2
Pγc
√
burst of duration ∼ 1/ω
2
I Lψ emitted in all directions
∼
dωdΩ
(ωL)2
• Integrating Pγ ∼
= Γγ I µ
∼ 10
Tuesday, February 4, 2014
burst of duration δt ∼ L2/3 ω −1/3
0 ≤ ψ = sin2 (θ/2) ≤ 1
• Power emitted in GW: Pg = Γg Gµ
I∗ ∼ 105 GeV
θ
3) Estimated event rate of radio bursts
from cusps/kinks/kink-kink collisions
as a function of S, ∆
• Number/unit time/unit spatial volume of cusp, kink, and kink-kink bursts of OBSERVED
frequency νo from loops of length L at redshift z
Loop distribution
in matter era
physical volume
element in matter era
• Leading to
dṄ (L, z) = . . .
−m̃/3
ν0
...
CL1(z)
[L + ΓGµt0 (1 +
z)−3/2]2
• Event rate higher the lower the frequency (radio).
Tuesday, February 4, 2014
dL dz
“standard” [Vilenkin+
Shellard] loops distribution
3) Estimated event rate of radio bursts
from cusps/kinks/kink-kink collisions
as a function of S, ∆
• Number/unit time/unit spatial volume of cusp, kink, and kink-kink bursts of OBSERVED
frequency νo from loops of length L at redshift z
Loop distribution
in matter era
physical volume
element in matter era
S, ∆
• Leading to
dṄ (L, z) = . . .
−m̃/3
ν0
...
CL1(z)
[L + ΓGµt0 (1 +
z)−3/2]2
• Event rate higher the lower the frequency (radio).
Tuesday, February 4, 2014
dL dz
“standard” [Vilenkin+
Shellard] loops distribution
• Observed duration of burst
∆=
�
• Observed intrinsic duration 1/ν0
∆t2 + ∆t2s
• time delays generated by scattering
of radio waves in intergalactic medium
(z, ν0 )
• Observed energy flux per frequency interval from cusp/kink/kink-kink bursts on a loop
of length L at a distance r(z) from loop
1 L d2 P
S≈
r(z)2 2∆ dνo dΩ
• giving finally
dṄ (S, ∆)
So..................
Range of observable parameters for the Parkes survey:
Tuesday, February 4, 2014
Event rate of radio bursts from superconducting string loops
• fixed observed frequency ν0 = 1230 MHz
• integrated over duration of bursts
• chosen values of parameters: Gµ = 10−10 , I = 105 GeV
cusps
kinks
An experiment sensitive
to mJy fluxes would observe
~100 radio bursts from
kinks/day
kink collisions
Tuesday, February 4, 2014
~1/day from cusps
Integrating out over duration and flux
kinks
cusps
kinks
cusps
kink-kink
Tuesday, February 4, 2014
Conclusion
• 3 kinds of transient EM bursts from superconducting strings:
– bursts from cusps are strong and highly beamed
– bursts from kinks are weaker and less beamed
– bursts from kink-kink collisions are the weakest and not beamed
• Bursts occur in all frequency bands, but are wide in radio, thin in gamma rays
• So event rate is largest for radio => radio transients most likely to find superconducting strings
• For canonical parameters, event rates are high ~ several a day a 1 Jy flux for chosen I, µ
• If none are observed => constraints on I, µ
• Radiation is linearly polarised, which may be used to distinguish it from other astrophysical sources
Might expect bursts at other frequencies, GW bursts, and perhaps an accompanying burst of
neutrinos....
Tuesday, February 4, 2014
Tuesday, February 4, 2014