QED, Neutron Stars, X-ray Polarimetry

Transcription

1 QED,, X-ray Polarimetry 20 July 2016 Ilaria Caiazzo; Yoram Lithwick, Don Lloyd, Dan Mazur, Nir Shaviv; Roberto Turolla, Roberto Taverna; Wynn Ho, Dong Lai, Rosalba Perna and others. QED,, X-ray Polarimetry

2 Birefringence Propagation through Birefringent Media Effective Action For a magnetic field the effective action is the free energy of the system (actually minus the free energy). Γ[A 0 µ] = dx 4 ( 1 4 F 0 µνf 0,µν ) i Tr ln [ ] Π/ m p/ m QED,, X-ray Polarimetry

3 Birefringence Propagation through Birefringent Media The QED Lagrangian L eff = where [ ) ) ] dζ ab 8π 2 B2 k 0 ζ e iζ Bk 2 coth (ζ abk cot (ζ bbk CT (b ia) 2 = (B ie) 2 = B 2 E 2 2iE B [ 2(b ia) 2 ] = F µν F µν + iɛ µναβ F µν F αβ I + ij and CT = 1 ζ a 2 b 2 (a 2 b 2 ) B 2 k Heisenberg-Euler, Weisskopf, Schwinger QED,, X-ray Polarimetry

4 Birefringence Propagation through Birefringent Media What do the poles mean? The poles along the real axis lie at ζ B B k = ζ ω B mc 2 = τω B = nπ QED,, X-ray Polarimetry

5 Birefringence Propagation through Birefringent Media What do the poles mean? The poles along the real axis lie at ζ B B k = ζ ω B mc 2 = τω B = nπ Take n = 1. After a proper time of τ = nπ/ω B, an electron performs half a revolution. QED,, X-ray Polarimetry

6 Birefringence Propagation through Birefringent Media What do the poles mean? The poles along the real axis lie at ζ B B k = ζ ω B mc 2 = τω B = nπ Take n = 1. After a proper time of τ = nπ/ω B, an electron performs half a revolution. In the same proper time, a positron does the same. QED,, X-ray Polarimetry

7 Birefringence Propagation through Birefringent Media Field and Photons To understand the interaction of light with the magnetized vacuum, we imagine expanding the action for a uniform field plus a small photon field, E = E 0 + δe, B = B 0 + δb, F µν = (F 0 ) µν + f µν. We have two possibilities. 1. kλ e 1: we pretend that the photon field is also uniform and expand the effective Lagrangian density. QED,, X-ray Polarimetry

8 Birefringence Propagation through Birefringent Media Field and Photons To understand the interaction of light with the magnetized vacuum, we imagine expanding the action for a uniform field plus a small photon field, E = E 0 + δe, B = B 0 + δb, F µν = (F 0 ) µν + f µν. We have two possibilities. 1. kλ e 1: we pretend that the photon field is also uniform and expand the effective Lagrangian density. 2. kλ e 1: we have to expand the action itself. QED,, X-ray Polarimetry

9 Birefringence Propagation through Birefringent Media How It Works S = S f µν f αβ δ 2 S δf µν δf αβ QED,, X-ray Polarimetry

10 Birefringence Propagation through Birefringent Media How It Works S = S f µν f αβ δ 2 S S = S δf µν δf αβ 2 f µν f αβ δ 2 S δf µν δf αβ f µν f αβ f στ δ 3 S δf µν δf αβ δf στ QED,, X-ray Polarimetry

11 Birefringence Propagation through Birefringent Media Index of Refraction n = T 2 B 2 What could be a signature of this birefringence? A time delay: t 10 3 R/c 10ns? n n Magnetic Field [Gauss] QED,, X-ray Polarimetry

12 Birefringence Propagation through Birefringent Media Index of Refraction n = T 2 B 2 What could be a signature of this birefringence? A time delay: t 10 3 R/c 10ns? Magnetic lensing? Shaviv et al G G QED,, X-ray Polarimetry

13 Birefringence Propagation through Birefringent Media Index of Refraction n = T 2 B 2 What could be a signature of this birefringence? A time delay: t 10 3 R/c 10ns? Magnetic lensing? Shaviv et al. 99 These all seemed a bit too subtle. n n Magnetic Field [Gauss] QED,, X-ray Polarimetry

14 Birefringence Propagation through Birefringent Media Index of Refraction n = T 2 B 2 What could be a signature of this birefringence? A time delay: t 10 3 R/c 10ns? Magnetic lensing? Shaviv et al. 99 These all seemed a bit too subtle. We were literally staring at the answer. n n Magnetic Field [Gauss] QED,, X-ray Polarimetry

15 Birefringence Propagation through Birefringent Media Liquid Crystal Displays Wikipedia QED,, X-ray Polarimetry

16 Birefringence Propagation through Birefringent Media Liquid Crystal Displays Wikipedia QED,, X-ray Polarimetry

17 Birefringence Propagation through Birefringent Media Propagation through a twisting magnetic field Kubo and Nagata (1983) present a concise way to characterize the evolution of the polarization of light through a medium; they simply write an equation to track the four Stokes parameters of the polarization light. s l = ˆΩ s where ˆΩ = k. The vector s = (S 1, S 2, S 3 )/S 0 or (Q, U, V )/I. QED,, X-ray Polarimetry

18 Birefringence Propagation through Birefringent Media Stokes Parameters and the Poincaré Sphere An important analytic solution. What if ˆΩ l = ˆΥ ˆΩ? 1. Move into frame that corotates with ˆΩ. 2. In this frame we have s ) = (ˆΩ ˆΥ s = ˆΩ Eff s l 3. s orbits ˆΩ Eff if ( 1 ˆΩ ˆΩ ) 1 ˆΩ l 0.5 QED,, X-ray Polarimetry

19 Polarization-Limiting Radius The radius at which the polarization stops following ˆΩ is called the polarization-limiting radius. Beyond here the modes are coupled. QED,, X-ray Polarimetry

20 Polarization-Limiting Radius The radius at which the polarization stops following ˆΩ is called the polarization-limiting radius. Beyond here the modes are coupled. It is safe to assume that this occurs in the weak-field limit where ˆΩ = α ( ) 2 B 2 c 4π 15 B QED ω sin2 θ; 1 ˆΩ ˆΩ ˆΩ l 1 = n c ω r 6 QED,, X-ray Polarimetry

21 Polarization-Limiting Radius The radius at which the polarization stops following ˆΩ is called the polarization-limiting radius. Beyond here the modes are coupled. It is safe to assume that this occurs in the weak-field limit where ˆΩ = α ( ) 2 B 2 c 4π 15 B QED ω sin2 θ; 1 ˆΩ ˆΩ ˆΩ l 1 = n c ω r 6 Therefore, the polarization-limiting radius is r r pl ( α ν ) ( 1/5 µ 45 c ( µ B QED sin β Gcm 3 ) 2/5 ) 2/5 ( ν ) 1/5 (sin β) 2/5 cm, Hz QED,, X-ray Polarimetry

22 Why does this matter? r pl /R = 0 Heyl, Shaviv, Lloyd 03 QED,, X-ray Polarimetry

23 Why does this matter? r pl /R = 0 Heyl, Shaviv, Lloyd 03 r pl /R = 1.9 (AM Her, AMSP) QED,, X-ray Polarimetry

24 Why does this matter? r pl /R = 12 (XRP) Heyl, Shaviv, Lloyd 03 QED,, X-ray Polarimetry

25 Why does this matter? Quasi-Tangential Region Wang, Lai 09 r pl /R = 12 (XRP) Heyl, Shaviv, Lloyd 03 QED,, X-ray Polarimetry

26 Why does this matter? Quasi-Tangential Region Wang, Lai 09 r pl /R = 12 (XRP) Heyl, Shaviv, Lloyd 03 r pl /R = 76 (Magnetar) QED,, X-ray Polarimetry

27 Places to Look Radius Magnetic Field µ 30 r pl at 4 kev Magnetar XRP ms XRP AM Her QED,, X-ray Polarimetry

28 This is not subtle. Let s recap. Neutron star atmospheres emit polarized light. QED,, X-ray Polarimetry

29 This is not subtle. Let s recap. Neutron star atmospheres emit polarized light. The emission varies across the surface. QED,, X-ray Polarimetry

30 This is not subtle. Let s recap. Neutron star atmospheres emit polarized light. The emission varies across the surface. The rotating magnetic field twists the polarization. QED,, X-ray Polarimetry

31 Realistic Hydrogen Atmosphere G; 60-degree inclination G; 60-degree inclination Heyl, Shaviv, Lloyd 05 QED,, X-ray Polarimetry

32 QED,, X-ray Polarimetry

33 QED,, X-ray Polarimetry

34 Magnetar Thermal Emission (4U ) Caiazzo & Heyl 2016; 100ks with QED,, X-ray Polarimetry

35 Magnetar Thermal Emission (SGR ) 350ks with ; Taverna & Turolla 2016 Fig.YYY. From left to right: light curve and polarization fraction for AXP 1RXS J1708 (upper panels) and SGR (lower panels). Thermal surface photons are assumed 100% polarized in the extraordinary mode. The data points (filled circles with error bars) were generated according to the model shown with the dashed blue line. The full line shows the simultaneous best-fit, while the dashed red lines correspond to the same models Jeremy but without Heyl QED QED, effects. Neutron The geometrical Stars, X-ray angles Polarimetry are = 90 and = 60.

36 Magnetar RICS Emission AXP 1RXS J ; 250ks with ; Taverna et al Figure 9 Light curve, degree and angle of polarization expected in case of the twisted magnetosphere model with parameters similar to those derived for the AXP 1RXS J Points are generated assuming a 250 ks observation of the source and following the blue line, which represents the model including vacuum polarization. Points are fitted with models including (red line) or not (green line) such an effect; the latter is excluded with high confidence (from Taverna et al. 2014) Matter in Extreme Gravitational Fields: GR effects Galactic Black Hole systems When black hole binaries are in high state, the dominant component in the 2-10 kev band is the thermal emission from the accretion disk. The innermost regions Jeremyof Heyl the disk are QED, very Neutron close to Stars, the black X-ray hole, Polarimetry where GR effects are

37 7 P H Y S I C A L R E V I E W L E T T E R S week end 15 AUGUST Deep in the atmosphere of the neutron star the plasma dominates, while outside the vacuum dominates. X mode O mode Vacuum Resonance O mode X mode E E ad = 2.52 (f tan θ) 2/3 H 1/3 ρ,1 kev O mode Photosphere where H ρ = 1.65 T 6 g 14 µ cm he polarization Ho, Lai 03 ellipticity of the phoof density near the vacuum resonance. nd to the two different modes. In this s are B G, E 5 kev, Y e 1, ipticity of a mode is specified by the X mode O mode E = 1 kev X mode Photosphere X mode O mode E = 5 kev FIG. 2 (color online). A schematic diagram illustrating vacuum polarization affects the polarization state of the QED,, X-ray Polarimetry

38 Lai, Ho 03 QED,, X-ray Polarimetry

39 Accreting X-ray Pulsar (Her X-1) Q/I Energy [kev] Q/I Energy [kev] Caiazzo & Heyl 2016; 100ks with ; Meszaros & Nagel 1985 QED,, X-ray Polarimetry

40 Deep in the atmosphere of the neutron star the plasma dominates, while outside the vacuum dominates. For large strengths of the magnetic field, the vacuum resonance may lie between the photospheres B B l T 1/8 6 E 1/4 1 S 1/4 G where S = 1 e E/kT. This can have a strong effect on the appearance of spectral features and the high-energy slope. Ho, Lai 04 QED,, X-ray Polarimetry

41 B = G B = G Ho, Lai 04 QED,, X-ray Polarimetry

42 Places to Look Radius Magnetic Field µ 30 r pl at 4 kev Magnetar XRP ms XRP AM Her QED,, X-ray Polarimetry

43 Future directions Observations of x-ray polarization from magnetars will verify QED. Observations of x-ray polarization from x-ray pulsars could constrain the radius of the neutron star. Soft x-ray polarization from x-ray pulsars could measure the surface gravity of the star. QED,, X-ray Polarimetry