Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary
Probing Axions with Event Horizon Telescope Polarimetric Measurements
Yifan Chen
ITP-CAS
based on arXiv:1905.02213, by: Y. C., Jing Shu, Xiao Xue, Qiang Yuan, Yue Zhao.
New physics beyond the Standard Model 12 September 2019, Fragrant Hill Hotel Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Probing Axions with EHT Polarimetric Measurements
1 1 1 L = − F F µν − g aF F˜µν + ∇µa∇ a − V (a), 4 µν 2 aγ µν 2 µ
Axion-induced birefringence:
∆Θγ = gaγ [a(tobs, xobs) − a(temit, xemit)],
Near Kerr black hole, a/f can reach O(1). EHT polarimetric measurement can test axions!
-10 -10 )] )]
-1 -12 -1 -12 c=1 c=1/8 (GeV (GeV gaγ a [r ] =8° gaγ a [r ] =1° aγ -14 0 ring aγ -14 0 ring [g [g 10 10 -16 -16 Log Log
-18 -18 -22 -20 -18 -16 -14 -22 -20 -18 -16 -14
Log10[ma(eV)] Log10[ma(eV)] CAST SN1987A M87* SgrA * BH spin CAST SN1987A M87* SgrA * BH spin Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Outlines
1 Introduction
2 Event Horizon Telescope and M87?
3 Axion
4 Axion-induced Superradiance
5 Summary Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary
Event Horizon Telescope and M87? Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Event Horizon Telescope: an Earth-sized Telescope
For single telescope with diameter D, the angular resolution for photon of λ wavelength λ is around D ; VLBI: for multiple radio telescopes, the effective D becomes the maximum separation between the telescopes.
As good as being able to see on the moon from the Earth. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Supermassive Black Hole (SMBH) M87?
To see the shadow and the ring, an excellent spatial resolution is necessary. 9 One of the most massive black hole ever known: 6.5 × 10 M ;
Nearly extreme Kerr black hole: aJ > 0.8; Almost face-on disk with a 17◦ inclination angle; Rich astrophysical information under extremal condition; What else can we learn? Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary
Axion Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Axion/Axion-like Particle
A hypothetical pseudoscalar originally motivated by the strong CP problem: Neutron electric dipole |θ¯|10−16e.cm is smaller than 10−26e.cm. Why is θ¯ so small? Solution: introducing an dynamical field with effective potential
4 ¯ a V ∼ −ΛQCD cos(θ + ). fa
String theory predicts a wide range of axion mass. Compactified extra dimension is parameterized by complex scalars: moduli fields. e.g. A5(5D) → a(4D).
Cold dark matter candidate. Coherent wave dark matter, very different from WIMP. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Birefringence from Axion
1 1 1 L = − F F µν − g aF F˜µν + ∂µa∂ a − V (a), 4 µν 2 aγ µν 2 µ
Equation of motion for photon:
2 2 µ µ [∂t − ∇ ]AL,R = −2gaγ n ∂µa∇ × AL,R = ∓ 2gaγ n ∂µakAL,R .
Birefringent effect with different dispersion relations:
µ ωL,R ∼ k∓gaγ n ∂µa.
For linearly polarized photons, the polarization angle is shifted by
Z obs µ ∆Θγ = gaγ n ∂µa dl emit = gaγ [a(tobs, xobs) − a(temit, xemit)],
This only depends on the initial and final background axion field values. How large? Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Search Strategies
A region with: a concentration of axion field Outside black hole, the density of axion can be large. source for linearly polarized photon The polarization angle, at emission point, should be stable.
Search for: polarization angle oscillates with time; Axion field is an oscillating background field. oscillation amplitude change as a function of spatial distribution. Extended light source
Scenarios: EHT-SMBH Later we will see to a radiation ring instead of a point is necessary for polarimetric probing of axion. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary
Axion-induced Superradiance Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Penrose Process
For Kerr black hole, there exists a region near the event horizon called Ergosphere where gtt is different sign from the outside. For a particle scattering into this region, the outgoing one carries more energy since there is another particle with negative energy falling into the black hole. The net energy increase comes from rotation energy. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Black hole Superradiance: wave analogue of the Penrose Process
For ω < m Ω where m is the the azimuthal number and Ω is the black hole angular velocity, reflected waves are amplified. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Gravitational Atom
For a ultralight boson whose λC ' rg , i.e., µM ∼ O(1) in Planck unit, the wave-function is exponentially amplified from extracting rotation energy. A gravitational bound state between BH and axion cloud, very similar to the hydrogen solution with fine structure constant αG = µM:
KG equation under Kerr background has general solution
µ −iωt imφ a(x ) = e e Slm(θ)Rlm(r),
with Slm(θ) a deformed version of Ylm(θ) with zenith angle θ. Axion cloud populates more efficiently at lower l-mode. m=l mode is more efficient than other m-levels. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Radial Distribution
e.g., R11(r) is:
1.0
0.8
] 0.6 max
0.4 R/[r
0.2
r+ rring rmax 0.0 5 10 15 20
r/r g
The ring from EHT has a radius comparable to the peaking radius of the axion cloud. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Bosenova
When the peak field value is large enough ϕ = a0/f ∼ 1, one should take into account the non-perturbative axion potential: a µ2a2 µ2a4 V = µ2f 2 1 − cos = − + ...; f 2 24f 2 The eom is Sine Gordon equation under Kerr background. The leading order is the mass term, while the subleading order is the quadratic self-interaction that makes the axion cloud collapse. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Axion Density
We focus on the photon emitted from the ring where a0 is near the peak value of axion cloud.
During periodic bosenova/superradiance phase, a0/f ∼ 1.
c The main model dependent parameter is c in gaγ = 2πf . Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Axion cloud induced position angle change:
∆Θγ is dominated by the emission point density:
∆Θγ ' −gaγ a(temit, xemit)
= −gaγ a0(xemit) cos [ωtemit + β(xemit)].
where β(xemit) ' mφ. For a face-on disk (17◦ for M87?):
ΔΘ (°) [t=0,θ= π , r,ϕ] 2 10
5
0
-5
-10
Temporal dependence for a fixed position; Spatial dependence for a fixed time. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Detectability of EHT
Average effect due to the limited resolution and angular dependent phase:
Z ∆φ sin (m∆φ/2) cos(µt + mφ)dφ = cos (µt + m∆φ/2). 0 m∆φ/2
In the past, we only saw a point instead of a ring, ∆φ = 2π, no birefringent effect.
EHT hasn’t published results of polarimetric measurement. However, a subset of the EHT configuration measures the position angle at precision of ∼ 3◦. It’s reasonable to expect better precision. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Prospect of Constraints on Axions
-10 -10 )] )]
-1 -12 -1 -12 c=1 c=1/8 (GeV (GeV gaγ a [r ] =8° gaγ a [r ] =1° aγ -14 0 ring aγ -14 0 ring [g [g 10 10 -16 -16 Log Log
-18 -18 -22 -20 -18 -16 -14 -22 -20 -18 -16 -14
Log10[ma(eV)] Log10[ma(eV)] CAST SN1987A M87* SgrA * BH spin CAST SN1987A M87* SgrA * BH spin
Figure: Here we show the parameter space testable by polarimetric observations of M87? and Sgr A? with two different choices of c. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Summary
Depending on its excellent spatial resolution, EHT has seen clearly the ring and the shadow of SMBH M87?, which is the most direct evidence of black hole.
Outside Kerr black hole, ultralight bosons with Compton wavelength close to horizon radius can build up a bound state with large energy density.
Axions, with initial motivation to solve strong CP problem, are also generic prediction of string theory/extra dimension.
Photon emitted from a dense axion cloud has birefringent effect making polarization angle oscillate. The amplitude of the oscillation is dependent on the axion density of the emission position.
Axion cloud collapses once the self-interaction becomes dominant over gravitational force and builds up again.
Near Kerr black hole, axions can be most dense in the universe, thus making EHT polarimetric measurement an optimal way to look for axions. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary
Thank you! Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary
Appendix Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary
Gravitational waves from spin-3/2 fields Hunting SUSY in the sky Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Motivation for Spin 3/2
We have observed particles with spin: 0, 1/2, 1, 2.
Where is spin 3/2 ?
Well-known candidate for fundamental spin 3/2: Gravitino This is the superpartner of the graviton, smoking gun of Supergravity (SUSY as ultraviolet symmetry).
Signatures of this new particle in gravitational waves ?
16πG Z t h (k, t) = dt0 sin [k(t − t0)]a(t0)ΠTT (k, t0). ij a(t)k ij tI Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Gravitational Waves: linear perturbations
Linear perturbation of the metric in the transverse-traceless (TT) gauge:
2 2 2 i j ds = a (τ)[−dτ + (δij + hij )dx dx ].
Einstein equation: Background: Friedman-Robertson-Walker (FRW) equation; Equation of motion for GW: ¨ ˙ TT hij + 2Hhij − ∇hij = 16πGΠij ,
Solution in the momentum space: convolution between the Green function from free propagation and the source term:
16πG Z t h (k, t) = dt0sin [k(t − t0)]a(t0)ΠTT (k, t0). ij a(t)k ij tI Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Linear k dependence of source terms
Sources: kinetic terms, e.g. R 3 l m 0 Scalar : d p Λij,lm(kˆ)[∂ σ(p, t)∂ σ(p , t)], R 3 l m 0 Fermion : d p Λij,lm(kˆ)[ψ¯(p, t)γ ∂ ψ(p , t)], R 3 l µ m 0 µ l m 0 Vector : d p Λij,lm(kˆ)[∂ A (p,t)∂ Aµ(p ,t)+∂ A (p,t)∂µA (p ,t) +...]
Homogeneous: p0 = p + k. The linear dependence on k is projected out for spin-0 and spin-1/2:
l m 0 Λij,lm(kˆ) ∂ σ(p, t)∂ σ(p , t) l m m 0 = Λij,lm(kˆ) p σ(p, t)(p + k )σ(p , t) l m 0 = Λij,lm(kˆ) p σ(p, t)p σ(p , t). The linear dependence on k is preserved for spin-1:
µ l m 0 Λij,lm(kˆ) ∂ A (p, t)∂µA (p , t) µ l m 0 = Λij,lm(kˆ) p (pµ + kµ)A (p, t)A (p , t). Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Sources with adiabatic evolution
If the wave-functions of the matter fields vary adiabatically:
σ(p, t) ∼ eiωt .
The kinetic factor will force the four momentum conservation:
R 0 0 TT 0 R 3 4 µ µ 0µ dt cos (kt )Πij (k, t ) ∼ d p δ (p ± k − p )... which implies
Massless: mσ = 0 Helicity conservation: e.g., for spin-0
l p//k, Λij,lm(kˆ)p = 0.
Only massless spin-1 fields could emit GW in the adiabatic limit! Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Sources with non-adiabatic evolution
Non-adiabatic (NA) condition: ω˙ | | 1 ω2 E.g., preheating, scalar field background: 1 V = m2φ2, φ ∼ Φ sin (mτ). 2 I Matter coupling: 2 2 2 ¯ 2 2 2 2 g φ σ , gφψψ, ωφ/ψ = k + g φ .
2 2 2 2 For ωφ/ψ = k + g φ , NA condition leads to the inequality:
∗ 1 0 ≤ k ≤ k ' (gmΦI ) 2 , in such range the matter fields are excited. For bosons, one gets large occupation number in these modes. For fermions, the excited modes fulfill a Fermi sphere with radius ∗ kF = k . One gets a model-independent spectrum parameterized by kF . Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Spin-3/2 Fields as Sources for GW Emission
Wave-functions:
˜µ X 1 s 3 µ (|λ|) ψp,λ(t) = h1, , l, | , λip,l up, s (t), 2 2 2 2 s=±1,l=±1,0
Fermionic field: Fermi sphere from non-adiabatic production (i.e., preheating);
¯ µ The linear dependence on k in ψµγ(α∂ ψβ) ∈ Tαβ is preserved under projection: ˆ µ l m Λij,lm(k)p (pµ + kµ)γ p0 .
The equivalence theorem: in the relativistic limit p m3/2, q µ m µ 1 2 2 p 3/2 p,0 = (p, p + m3/2pˆ) = + O( ). m3/2 m3/2 p Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Result: GW from Fermions
dρGW The spectrum density per logarithm of frequency dlogk (k, t) is given by:
Gk 3 Z × dpdθ K(p, k, θ, m ){|I (k, p, θ, t)|2 + |I (k, p, θ, t)|2} π3a4(t) 3/2 c s
The blue part contains wave-functions, which are universal for fermions with the same Fermi-radius. Scaling factor K:
Spin-1/2 : p4 sin3 θ, 2 2 0 Helicity-3/2 : p k f3/2(θ, θ ), 4 2 Helicity-1/2 : p k f (θ, θ0). m2 1/2 3/2
3 For spin-1/2, spectrum scales k and decreases exponentially after kF . For spin-3/2, spectrum scales k5 near the peak and the amplitude gets 2 enhanced by kF . m2 3/2 Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Example: Polonyi Model
|z|4 K = |z|2 − , Λ2 2 W = µ z + W0,
We use a Polony-Like model with spontaneous SUSY breaking with positive cosmological constant.
Near the minimum, m3/2 H. We can use the quantization of gravitino in the flat limit. √ Equivalence theorem can be used for m3/2 p Fz . Effective Yukawa coupling between scalar and helicity-1/2 gravitino:
m2 m2 g˜ = √ z = z 1. 2 3m3/2MPl 2F
Peak frequency now: 10 1 fp ' 6 · 10 g˜ 2 Hz. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Corresponding GW spectrum
2 h ΩGW
zI -9 10 mz 1014 10-14 1011 10-19 108 105 10-24 102 10-29 fp (Hz) 1×10 8 5×10 8 1×10 9 5×10 9 1×10 10
Current spectrum: h2Ω (f ) ' 3 · 10−10( fp )12( zI )2. GW p 6·1010Hz mz Typically at ultra-high frequency, needs new design of GW detectors in the future. Introduction Event Horizon Telescope and M87? Axion Axion-induced Superradiance Summary Summary
Spin-3/2 is the only missing piece in the nature with spin from 0 to 2. Its existence could also be the smoking gun of SUSY.
Fields with non-adiabatically varying wave-functions can emit gravitational waves.
Non-adiabatic production of fermions fulfills a Fermi-sphere whose radius depends on the preheating/oscillating scalar model.
The helicity-1/2 component dominates the GW production. Near the peak, the scaling goes k5 instead of k3 like spin-1/2 fermions.
In the simplest model describing SUSY breaking in de-Sitter space, the corresponding peak frequency is too high, which calls for the future design of ultra-high frequency GW detectors.