SLIDE 1 Testing the axion-photon coupling with polarization measurements of Sagittarius A*
Guan-Wen Yuan yuangw@pmo.ac.cn
aKey Laboratory of Dark Matter and Space Astronomy,
Purple Mountain Observatory, Chinese Academy of Sciences
b School of Astronomy and Space Science, University of Science and Technology
June 29, 2020
SLIDE 2
Outline
◮ Birefringence from Axion and Profile Density ◮ The Sgr A* Polarization Data and Constraint ◮ Discussion: DM Density and Wash-Out ◮ Summary
SLIDE 3 Birefringence from Axion
This ALP field can interact with the electromagnetic field and give rise to a rotation effect on the photon polarization, which is called the birefringence effect. The relevant Lagrangian terms include L = −1 4FµνF µν + 1 2
+ gaγ 4 aFµν ˜ F µν (1) Thus, the classical EoM and solution for axion field: a + m2a = gaγE · B (2) a(t, x) = a0(x)sin(mt + δ(x)) (3)
SLIDE 4 Birefringence from Axion
Additionally, the EoM and solution for photons: ¨ A − ∇2A = gaγ( ˙ a∇ × A + ˙ A × ∇a) (4) A(t, x) =
(2π)3 Ap
kep(ˆ
k)eik·x−i
(5) The dispersion relation of EoM and two polarization states propagate: w2
± − k2 ∓ gaγ( ˙
a + ˆ k · ∇a)|k| = 0 (6) w± = k
a + ˆ k · ∇a) k ≈ k ± 1 2gaγ∂0a (7)
SLIDE 5 Birefringence from Axion
The difference between the frequencies of the two polarization components is translated into the change of the polarization angle for a linearly polarized emission. ∆φ = 1 2 tobs
temit
(w+ − w−)dt = 1 2gaγ tobs
temit
∂0adt = 1 2gaγ[a(tobs, xobs) − a(temit, xemit)] (8) Where the a(tobs, xobs) and a(temit, xemit) are the ALP amplitude in observation and emission points, respectively. If we assumption ρDM = 1
2m2a2 0 in Eq.(8)
∆φ ≃5◦ sin
T + δ(x) ρDM 2 × 109GeV/cm3 1
2
×
10−12GeV−1 m 10−18eV −1 (9)
SLIDE 6 CDM Simulation
A slice of density field of ψDM simulation on various scales at z=11, which can be described by soliton+NFW dark matter profile.
1H.Schive,etc. Nature Physics, 2014, 10(7):496-499.
SLIDE 7 Soliton+NFW DM Profile
For ultralight axion DM, there can generate a cored soliton, due to the balance between gravitational interaction and quantum
- pressure. The De Broglie wavelength of axion (rc = 2π
mv ) can
describe solitonic core radius, and the axion field is coherent and homogeneous in it.Thus2, ρDM = 190 ×
10−18eV
−2
rc 1pc
−4 M⊙pc−3, for r < rc
ρ0 r/Rg(1+r/Rg)2 ,
for r > rc (10)
2H.Schive,etc. Physical review letters, 2014, 113(26):261302.
SLIDE 8
Very-Long Baseline Interferometry, VLBI
Figure 1: Some stations of the EHT, which operating at 1.3mm wavelength by VLBI technique.
SLIDE 9
Baseline
Figure 2: There are four telescopes have been used to observe Sgr A*, including CARMA, SMT,JCMT and SMT. This is the interferometric fractional polarization measurements for Sgr A*.
SLIDE 10 Polarization Data
Figure 3: Polarization Data from M.Johnson Fig.S8 3
The axion typical oscillation period:T = 2π
m ≃ 4 · 103( 10−18eV m
)sec. mup = 2.92 × 10−18eV ,rc = 0.018pc,ρDM = 7.46 × 109GeV /cm−3 mlow = 2.90×10−19eV ,rc = 0.183pc,ρDM = 7.36×107GeV /cm−3
3M.Johnson,etc, Science, 2015, 350(6265):1242-1245.
SLIDE 11 The Sgr A* Data Analysis
there will be a constant angle φ0 depending on our observation. Thus, the final polarization angle φa is φa = ∆φ + φ0 (11) The least square fitting is utilized in our work, and the χ2 function is expressed as χ2 =
N
(φobs − φpre)2 σ2
i
(12) where φobs and σi are the observed polarization angle and its dispersion of angle. The predicting polarization angles φpre of the ALP model and the background model are φa and φ0 in Eq.(11), respectively.
SLIDE 12
Results
Figure 4: Constraints for ALP DM in the plane m − gaγ at 95% CL.
SLIDE 13 Discussion I: DM Density
In the center of the galaxy, ultra-light boson can from a soliton core with large density as Eq.(10). A super-massive black hole within the soliton core can further increase the density around it. For example, a Kerr black hole with large spin leads to superradiance of the boson when its Compton wavelength matches the gravitational radius of the black hole. The pile-up of the dark matter also will happen outside Schwarzschild black hole. In this case, one could imagine a huge enhancement of the density. This makes our benchmark halo model Eq.(10) a very conservative
SLIDE 14 Discussion II: Wash-Out by Resolution
Figure 5: Strength and order of the polarization field from 1.3mm VLBI4.
1 δφ δφ/2
−δφ/2
cos(µt + mφ)dφ = sin(mδφ/2) mδφ/2 cos µt (13) In the case where the observing disk is face-on, the spatial resolution of Sgr A* in this observation is about 0.5π and the wash-out factor is 0.9, thus the washout effect is negligible.
4M.Johnson,etc, Science, 2015, 350(6265):1242-1245.
SLIDE 15
Discussion III: Wash-Out by Line of Sight
The radiation area observed, is within a disk of 10 times of the black hole Schwarzschild radii. When the axion mass is less than 9.65 × 10−18 eV, its Compton wavelength is much longer than this length scale. Assuming the source length in the line of sight direction is the same order, the average along this direction becomes again negligible.
SLIDE 16 Summary
⋆ Axions, with initial motivation to solve strong CP problem, are also an important ultra-light dark matter candidate. ⋆ Photon emitted from soliton core has birefringent effect making polarization angle oscillate. The amplitude of the
- scillation is dependent on the axion density of the emission
position. ⋆ Outside black hole, ultralight axion, which can be the most dense in universe, can generate a cored soliton. The de Broglie wavelength of axion can describe its radius. ⋆ Depending on EHT excellent spatial resolution, the polarization data of neighboring Sgr A*(∼ 6RSch) have been
- bserved, which can constraint m − gaγ in a specific window.
⋆ After quantitative estimation, wash-out by resolution and line
- f sight can be negligible.
SLIDE 17
Thank you!
