Neutron stars. Macroscopic objects with quantum properties. Observatoire astronomique de Strasbourg Université de Strasbourg

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1 Neutron stars Macroscopic objects with quantum properties Jérôme Pétri Observatoire astronomique de Strasbourg Université de Strasbourg Oxford, 3rd-5th July 2017 Jérôme Pétri (Université de Strasbourg) Neutron stars 1/ 31 Oxford, 3rd-5th July / 31

2 Outline 1 Neutron stars Why to study them? Classification 2 Pulsars Brief overview Orders of magnitude Link to nebula The standard pulsar model GRQED corrections to Maxwell equations 3 Conclusions & Perspectives Jérôme Pétri (Université de Strasbourg) Neutron stars 2/ 31 Oxford, 3rd-5th July / 31

3 Outline 1 Neutron stars Why to study them? Classification 2 Pulsars Brief overview Orders of magnitude Link to nebula The standard pulsar model GRQED corrections to Maxwell equations 3 Conclusions & Perspectives Jérôme Pétri (Université de Strasbourg) Neutron stars 3/ 31 Oxford, 3rd-5th July / 31

4 Why study neutron stars? The discovery of pulsars (Hewish et al., 1968) was a revolution in astrophysics and revived the theoretical study of neutron stars. Many progresses in (astro)physics confirmation of the existence of neutron stars. Figure: Simplified structure of a neutron star. Jérôme Pétri (Université de Strasbourg) Neutron stars 4/ 31 Oxford, 3rd-5th July / 31

5 Why study neutron stars? The discovery of pulsars (Hewish et al., 1968) was a revolution in astrophysics and revived the theoretical study of neutron stars. Many progresses in (astro)physics confirmation of the existence of neutron stars. indices on their internal structure. Figure: Interior of a neutron star. Jérôme Pétri (Université de Strasbourg) Neutron stars 4/ 31 Oxford, 3rd-5th July / 31

6 Why study neutron stars? The discovery of pulsars (Hewish et al., 1968) was a revolution in astrophysics and revived the theoretical study of neutron stars. Many progresses in (astro)physics confirmation of the existence of neutron stars. indices on their internal structure. indirect detection of gravitational waves. Figure: Double neutron star system. Jérôme Pétri (Université de Strasbourg) Neutron stars 4/ 31 Oxford, 3rd-5th July / 31

7 Why study neutron stars? The discovery of pulsars (Hewish et al., 1968) was a revolution in astrophysics and revived the theoretical study of neutron stars. Many progresses in (astro)physics confirmation of the existence of neutron stars. indices on their internal structure. indirect detection of gravitational waves. detection of the first planetary system. Figure: Planets around pulsars. Jérôme Pétri (Université de Strasbourg) Neutron stars 4/ 31 Oxford, 3rd-5th July / 31

8 Why study neutron stars? The discovery of pulsars (Hewish et al., 1968) was a revolution in astrophysics and revived the theoretical study of neutron stars. Many progresses in (astro)physics confirmation of the existence of neutron stars. indices on their internal structure. indirect detection of gravitational waves. detection of the first planetary system. study of quantum processes in a strong magnetic field. Figure: Magnetic reconnection in a magnetar. Jérôme Pétri (Université de Strasbourg) Neutron stars 4/ 31 Oxford, 3rd-5th July / 31

9 Why study neutron stars? The discovery of pulsars (Hewish et al., 1968) was a revolution in astrophysics and revived the theoretical study of neutron stars. Many progresses in (astro)physics confirmation of the existence of neutron stars. indices on their internal structure. indirect detection of gravitational waves. detection of the first planetary system. study of quantum processes in a strong magnetic field. motion of matter and photons in strong gravitational fields. Figure: General-relativistic effects (Shapiro delay). Jérôme Pétri (Université de Strasbourg) Neutron stars 4/ 31 Oxford, 3rd-5th July / 31

10 Why study neutron stars? The discovery of pulsars (Hewish et al., 1968) was a revolution in astrophysics and revived the theoretical study of neutron stars. Many progresses in (astro)physics confirmation of the existence of neutron stars. indices on their internal structure. indirect detection of gravitational waves. detection of the first planetary system. study of quantum processes in a strong magnetic field. motion of matter and photons in strong gravitational fields. survey of the interstellar medium in the Milky Way. Figure: Map of the electronic density in the Milky Way. Jérôme Pétri (Université de Strasbourg) Neutron stars 4/ 31 Oxford, 3rd-5th July / 31

11 Why study neutron stars? The discovery of pulsars (Hewish et al., 1968) was a revolution in astrophysics and revived the theoretical study of neutron stars. Many progresses in (astro)physics confirmation of the existence of neutron stars. indices on their internal structure. indirect detection of gravitational waves. detection of the first planetary system. study of quantum processes in a strong magnetic field. motion of matter and photons in strong gravitational fields. survey of the interstellar medium in the Milky Way. survey of the galactic magnetic field in the Milky Way. Figure: Map of the magnetic field in the Milky Way. Jérôme Pétri (Université de Strasbourg) Neutron stars 4/ 31 Oxford, 3rd-5th July / 31

12 Why study neutron stars? Important to better understand neutron star physics and especially pulsars. Figure: Interior view of a neutron star. Figure: Larousse (french dictionary) view of a pulsar. Jérôme Pétri (Université de Strasbourg) Neutron stars 4/ 31 Oxford, 3rd-5th July / 31

13 Outline 1 Neutron stars Why to study them? Classification 2 Pulsars Brief overview Orders of magnitude Link to nebula The standard pulsar model GRQED corrections to Maxwell equations 3 Conclusions & Perspectives Jérôme Pétri (Université de Strasbourg) Neutron stars 5/ 31 Oxford, 3rd-5th July / 31

14 The hidden face of neutron stars neutron star energy source rotation accretion magnetic field heat nuclear energy process B +Ω E acceleration e ± hot matter accretion dissipation B > B qed reconnection? cooling thermonuclear reaction observations radio X,γ non thermal thermal X-rays soft gamma thermal X-rays thermal X-rays Figure: Different classes of neutron stars distinguished through their source of energy responsible for the stellar activity. Jérôme Pétri (Université de Strasbourg) Neutron stars 6/ 31 Oxford, 3rd-5th July / 31

15 Outline 1 Neutron stars Why to study them? Classification 2 Pulsars Brief overview Orders of magnitude Link to nebula The standard pulsar model GRQED corrections to Maxwell equations 3 Conclusions & Perspectives Jérôme Pétri (Université de Strasbourg) Neutron stars 7/ 31 Oxford, 3rd-5th July / 31

16 Brief overview What is a pulsar? Jérôme Pétri (Université de Strasbourg) Neutron stars 8/ 31 Oxford, 3rd-5th July / 31

17 Brief overview What is a pulsar? 1 a neutron star compact object with compactness Rs R 0.4. strong gravity effects. Jérôme Pétri (Université de Strasbourg) Neutron stars 8/ 31 Oxford, 3rd-5th July / 31

18 Brief overview What is a pulsar? 1 a neutron star compact object with compactness Rs R 0.4. strong gravity effects. 2 strongly magnetized plasmas, QED effects. (pair creation e ±, cyclotron lines). Jérôme Pétri (Université de Strasbourg) Neutron stars 8/ 31 Oxford, 3rd-5th July / 31

19 Brief overview What is a pulsar? 1 a neutron star compact object with compactness Rs R 0.4. strong gravity effects. 2 strongly magnetized plasmas, QED effects. (pair creation e ±, cyclotron lines). 3 rotating huge electric fields. violent acceleration of particles. E schw cb q V/m Jérôme Pétri (Université de Strasbourg) Neutron stars 8/ 31 Oxford, 3rd-5th July / 31

20 Brief overview What is a pulsar? 1 a neutron star compact object with compactness Rs R 0.4. strong gravity effects. 2 strongly magnetized plasmas, QED effects. (pair creation e ±, cyclotron lines). 3 rotating huge electric fields. violent acceleration of particles. E schw cb q V/m Figure: A pulsar. (Lorimer & Kramer, 2004) Jérôme Pétri (Université de Strasbourg) Neutron stars 8/ 31 Oxford, 3rd-5th July / 31

21 Brief overview What is a pulsar? 1 a neutron star compact object with compactness Rs R 0.4. strong gravity effects. 2 strongly magnetized plasmas, QED effects. (pair creation e ±, cyclotron lines). 3 rotating huge electric fields. violent acceleration of particles. E schw cb q V/m Figure: A pulsar. (Lorimer & Kramer, 2004) Some useful definitions obliquity χ: angle between magnetic moment µ and rotation axis Ω light cylinder: corotation reaches speed of light c: r L = c/ω transition from quasi-static to wave zone very different plasma regimes in both regions. Jérôme Pétri (Université de Strasbourg) Neutron stars 8/ 31 Oxford, 3rd-5th July / 31

22 The Hertzsprung-Russel diagramm of pulsars Indisputable observations rotation period P [1.5 ms,10 s]. derivative of period Ṗ [10 18,10 15 ]. slowdown by rotational braking constrained by L rot = 4π 2 I Ṗ P W I: moment of inertia. A doubtful interpretation magnetic field estimated by magnetodipole losses B sinχ = P Ṗ T = T only constrain B = B sinχ. B around B qed = T. electrodynamics requires QED. Figure: P Ṗ diagramm. (Lorimer & Kramer, 2004) Jérôme Pétri (Université de Strasbourg) Neutron stars 9/ 31 Oxford, 3rd-5th July / 31

23 Some observables related to multipolar emission But from thermal X-ray blackbody radiation from surface, inferred magnetic field strength is 100 times stronger and polar cap area 100 smaller than expections from a dipole. needs for multipolar components. For any magnetic multipole of order l, useful observables are the spindown luminosity (different from magnetodipole losses) L B 2 Ω 2l+2 R 2l+4 (1) the braking index n (a measure of the efficiency of braking) such that Ω = K Ω n (2) For a multipole of order l it becomes approximately n = 2l+1. for a dipole n = 3. for a quadrupole n = 5 (the same for gravitational radiation). Jérôme Pétri (Université de Strasbourg) Neutron stars 10/ 31 Oxford, 3rd-5th July / 31

24 Magnetic field strength estimates luminosity L, stellar radius R and period P (or Ω) being known, we cant get an estimate of the magnetic field strength at the surface. usually done for a pure dipole. but if multipoles are present, the estimate becomes inaccurate or even wrong. log(y) B dip B quad L quad/l dip log(x) log(y) B dip B quad L quad/l dip log(x) Normal pulsar L dip L quad. Millisecond pulsar x = B quad /B dip. Magneto-dipole losses useless to get drastic upper limits for multipole components. L dip L quad B dip B quad (Pétri, 2015b) Jérôme Pétri (Université de Strasbourg) Neutron stars 11/ 31 Oxford, 3rd-5th July / 31

25 Braking index: observations Pulsar Distance Period P Ṗ Braking de References (kpc) (s) (10 15 ) index n B ± Lyne et al. (1993) J ± 0.1 Middleditch et al. (2006 B ± Livingstone et al. (2005 B ± 0.20 Lyne et al. (1996) B ± Kaspi et al. (1994) J ± 0.01 Livingstone et al. ( ± 0.13 Livingstone et al. (2011 J ± 0.05 Weltevrede et al. (2011) J ± 0.2 Espinoza et al. (2011) J Roy et al. (2012) J Archibald et al. (2016) Table: Observational properties of some typical pulsars. Jérôme Pétri (Université de Strasbourg) Neutron stars 12/ 31 Oxford, 3rd-5th July / 31

26 Braking index: theory n dipole quadrupole hexapole octopole quadrupole hexapole octopole 3 1 m = 1 m = 2 n hexapole octopole octopole R = ΩR r L c Ω 1/P (3) 1 m = 3 m = R/rL R/rL Figure: Braking index of rotating magnetic multipoles.(pétri, 2015b) 1 < n < 3 topology between monopolar wind and dipolar radiation. 3 < n < 5 topology between dipolar and quadrupolar radiation. Jérôme Pétri (Université de Strasbourg) Neutron stars 13/ 31 Oxford, 3rd-5th July / 31

27 Outline 1 Neutron stars Why to study them? Classification 2 Pulsars Brief overview Orders of magnitude Link to nebula The standard pulsar model GRQED corrections to Maxwell equations 3 Conclusions & Perspectives Jérôme Pétri (Université de Strasbourg) Neutron stars 14/ 31 Oxford, 3rd-5th July / 31

28 Orders of magnitude Electromagnetic field electric field induced at the stellar crust E = ΩB R = V/m instantaneous acceleration at ultra-relativistic speeds (τ acc < s). Lorentz factor γ 1. Gravitational field negligible gravitational force! For proton with mass m p F grav G Mm p/r (4) F em eωb R and a factor m p /m e 2,000 less for electrons. Neutron star characteristics masse M 1.4M. radius R 10 km. centrale density ρ c kg/m 3. Jérôme Pétri (Université de Strasbourg) Neutron stars 15/ 31 Oxford, 3rd-5th July / 31

29 Orders of magnitude dynamic of the magnetosphere dominated by the electromagnetic field. gravitational field negligible to first approximation! Figure: View of a neutron star magnetosphere. Figure: Pulsar in a gravitational field. Jérôme Pétri (Université de Strasbourg) Neutron stars 15/ 31 Oxford, 3rd-5th July / 31

30 Outline 1 Neutron stars Why to study them? Classification 2 Pulsars Brief overview Orders of magnitude Link to nebula The standard pulsar model GRQED corrections to Maxwell equations 3 Conclusions & Perspectives Jérôme Pétri (Université de Strasbourg) Neutron stars 16/ 31 Oxford, 3rd-5th July / 31

31 Supernova remnant and nebula the pulsar and its magnetosphere, source of relativistic e ± pairs r L = 10 6 m. Figure: Link between the pulsar and its surrounding nebula. Jérôme Pétri (Université de Strasbourg) Neutron stars 17/ 31 Oxford, 3rd-5th July / 31

32 Supernova remnant and nebula the pulsar and its magnetosphere, source of relativistic e ± pairs r L = 10 6 m. the cold ultra-relativistic wind streaming to the nebula. Γ v Figure: Link between the pulsar and its surrounding nebula. Jérôme Pétri (Université de Strasbourg) Neutron stars 17/ 31 Oxford, 3rd-5th July / 31

33 Supernova remnant and nebula the pulsar and its magnetosphere, source of relativistic e ± pairs r L = 10 6 m. the cold ultra-relativistic wind streaming to the nebula. the shocked wind composed of particles heated after crossing the MHD shock, r ts = m= 0.1 pc main source of radiation observed in radio, optics, X-rays and gamma-rays. vent choqué Γ v choc terminal (MHD) Figure: Link between the pulsar and its surrounding nebula. Jérôme Pétri (Université de Strasbourg) Neutron stars 17/ 31 Oxford, 3rd-5th July / 31

34 Supernova remnant and nebula the pulsar and its magnetosphere, source of relativistic e ± pairs r L = 10 6 m. the cold ultra-relativistic wind streaming to the nebula. the shocked wind composed of particles heated after crossing the MHD shock, r ts = m= 0.1 pc main source of radiation observed in radio, optics, X-rays and gamma-rays. the supernova remnant. vent choqué Γ v choc terminal (MHD) Figure: Link between the pulsar and its surrounding nebula. Jérôme Pétri (Université de Strasbourg) Neutron stars 17/ 31 Oxford, 3rd-5th July / 31

35 Supernova remnant and nebula the pulsar and its magnetosphere, source of relativistic e ± pairs r L = 10 6 m. the cold ultra-relativistic wind streaming to the nebula. the shocked wind composed of particles heated after crossing the MHD shock, r ts = m= 0.1 pc main source of radiation observed in radio, optics, X-rays and gamma-rays. the supernova remnant. the interstellar medium. vent choqué Γ v choc terminal (MHD) Figure: Link between the pulsar and its surrounding nebula. Jérôme Pétri (Université de Strasbourg) Neutron stars 17/ 31 Oxford, 3rd-5th July / 31

36 Supernova remnant and nebula the pulsar and its magnetosphere, source of relativistic e ± pairs r L = 10 6 m. the cold ultra-relativistic wind streaming to the nebula. the shocked wind composed of particles heated after crossing the MHD shock, r ts = m= 0.1 pc main source of radiation observed in radio, optics, X-rays and gamma-rays. the supernova remnant. the interstellar medium. Figure: The Crab nebula. Jérôme Pétri (Université de Strasbourg) Neutron stars 17/ 31 Oxford, 3rd-5th July / 31

37 Outline 1 Neutron stars Why to study them? Classification 2 Pulsars Brief overview Orders of magnitude Link to nebula The standard pulsar model GRQED corrections to Maxwell equations 3 Conclusions & Perspectives Jérôme Pétri (Université de Strasbourg) Neutron stars 18/ 31 Oxford, 3rd-5th July / 31

38 Pulsar magnetosphere Radiation mechanisms and sites Figure: The standard pulsar model. thermal, synchrotron, inverse Compton, curvature. radio photons from polar caps. high-energy photons from slot/outer gaps because high magnetic opacity at small radii. Electrodynamics magnetosphere filled with a quasi-neutral (pair?) plasma. pair creation in the polar caps. source of particles for the wind and nebula. are protons/ions also present? wind radially expanding outside the light-cylinder. Jérôme Pétri (Université de Strasbourg) Neutron stars 19/ 31 Oxford, 3rd-5th July / 31

39 Do pulsars get on well with magnetic fields? Radio emission requires a intense magnetic field for the reaction: B +γ e ±. a pair cascade e ± for the reaction: 1 e ± N 1 γ N 1 N 2 e ± but too a strong magnetic field B > B qed inhibits radio emission thus pair creation efficiency. May be due to photon splitting according to B +γ γ 1 +γ 2 radio emission disappears. the theory tells us that neutron stars at B > B qed are no more radio pulsars. let us call them magnetars. Figure: Pair cascade Figure: Photon splitting. Jérôme Pétri (Université de Strasbourg) Neutron stars 20/ 31 Oxford, 3rd-5th July / 31

40 Parts of the answer leading to new questions! High B-pulsars B (> B edq ) Radio emission detected from several pulsars PSR J : T (McLaughlin et al., 2003). PSR J : T (Kaspi & McLaughlin, 2005). PSR J : T (Gotthelf et al., 2000). Figure: High-B pulsars.(ng et al., 2011) Low B-magnetars B (< B edq ) Magnetars with pulsar properties and low field exist SGR : T (Rea et al., 2010) SGR : T (Rea et al., 2012) 3XMM J : < T (Rea et al., 2014) Figure: Low-B magnetars.(rea et al., 2012) Jérôme Pétri (Université de Strasbourg) Neutron stars 21/ 31 Oxford, 3rd-5th July / 31

41 Parts of the answer leading to new questions! Is the value B qed T really discriminating? Is the B field reliably determined? What is the influence of gravitation on B-field QED processes? Figure: Pair production. Figure: Artist view of a magnetar. Figure: Photon scattering. Jérôme Pétri (Université de Strasbourg) Neutron stars 21/ 31 Oxford, 3rd-5th July / 31

42 Outline 1 Neutron stars Why to study them? Classification 2 Pulsars Brief overview Orders of magnitude Link to nebula The standard pulsar model GRQED corrections to Maxwell equations 3 Conclusions & Perspectives Jérôme Pétri (Université de Strasbourg) Neutron stars 22/ 31 Oxford, 3rd-5th July / 31

43 Corrections to Maxwell equations An accurate and quantitative analysis of phenomena at the neutron star surface must take into account an important space time curvature. a magnetic field strength of the order or larger than B qed. a relativistic pair plasma e ± (classical/quantum?). high-energy radiation processes (curvature, synchrotron, inverse Compton). QED processes. gravitational redshift. Jérôme Pétri (Université de Strasbourg) Neutron stars 23/ 31 Oxford, 3rd-5th July / 31

44 Space-time in 3+1 formalism A first approach starts with an effective theory for the electromagnetic field including quantum and gravitational corrections to Maxwell equations formulation in space and time based on general relativity (3+1). Lagrangian description of the electromagnetic field. The metric is divided in space Σ t and a time coordinate ds 2 = α 2 c 2 dt 2 γ ab (dx a +β a c dt)(dx b +β b cdt) with lapse function α. shift vector β. spatial metric γ ab. Figure: Space-time split in 3+1. Jérôme Pétri (Université de Strasbourg) Neutron stars 24/ 31 Oxford, 3rd-5th July / 31

45 Space-time in 3+1 formalism Constitutive relations for electromagnetic field in general relativity ε 0 E = αd+ε 0 c β B µ 0 H = αb β D ε 0 c Curvature of absolute space taken into account by lapse function factor α in the first term. frame dragging effect in the second term, cross-product between the shift vector β and the fields. Jérôme Pétri (Université de Strasbourg) Neutron stars 25/ 31 Oxford, 3rd-5th July / 31

46 The QED Lagrangian X classical Lagrangian of electromagnetic field. + QED corrections à la Euler-Heisenberg. I i, A i : 4-current and 4-potential. F ik : electromagnetic tensor. I 1 = F ik F ik, I 2 = F ik F ik field invariants. L QED = QED Lagrangian η 1 Euler-Heisenberg Born-Infeld α sf 180π 1 2µ 0 B 2 qed η η 1 η µ 0 b 2 with α sf the fine structure constant and b = T. Jérôme Pétri (Université de Strasbourg) Neutron stars 26/ 31 Oxford, 3rd-5th July / 31

47 The QED Lagrangian X classical Lagrangian of electromagnetic field. + QED corrections à la Euler-Heisenberg. I i, A i : 4-current and 4-potential. F ik : electromagnetic tensor. I 1 = F ik F ik, I 2 = F ik F ik field invariants. QED Lagrangian Classical terms L QED = 1 4µ 0 F ik F ik I i A i + η 1 Euler-Heisenberg Born-Infeld α sf 180π 1 2µ 0 B 2 qed η η 1 η µ 0 b 2 with α sf the fine structure constant and b = T. Jérôme Pétri (Université de Strasbourg) Neutron stars 26/ 31 Oxford, 3rd-5th July / 31

48 The QED Lagrangian X classical Lagrangian of electromagnetic field. + QED corrections à la Euler-Heisenberg. I i, A i : 4-current and 4-potential. F ik : electromagnetic tensor. I 1 = F ik F ik, I 2 = F ik F ik field invariants. QED Lagrangian Classical terms QED corrections. L QED = 1 4µ 0 F ik F ik I i A i + η 1 I 2 1 +η 2 I 2 2 η 1 Euler-Heisenberg Born-Infeld α sf 180π 1 2µ 0 B 2 qed η η 1 η µ 0 b 2 with α sf the fine structure constant and b = T. Jérôme Pétri (Université de Strasbourg) Neutron stars 26/ 31 Oxford, 3rd-5th July / 31

49 Maxwell equations in GRQED Time evolution from the variational principle L QED A i 1 g k g L QED k A i = 0 constitutive relations for QED (Pétri, 2015a) (ξ 1 = 1 K η 1 and ξ 2 η 2 ) Homogeneous Maxwell equations F = ξ 1 D+ ξ 2 c B G = ξ 1 H ξ 2 c E Inhomogeneous Maxwell equations F = ρ G = J+ 1 γ t ( γf) E = 1 γ t ( γb) B = 0 GR and QED seen as material media in standard classical Newtonian theory. (Pétri, 2015a) Jérôme Pétri (Université de Strasbourg) Neutron stars 27/ 31 Oxford, 3rd-5th July / 31

50 Simple approximation for plasma: GRFFQED For a pair plasma e ± infinite conductivity σ = +. zero temperature T = 0 then zero pressure. negligible mass m e = 0. In the force-free approximation J E = 0 ρe+j B = 0 from which we deduce the electric current J = ρ E B B 2 + B G F E B 2 B. The system of Maxwell equations is complete, the charge density ρ adapting to the field configuration. Jérôme Pétri (Université de Strasbourg) Neutron stars 28/ 31 Oxford, 3rd-5th July / 31

51 Vacuum perpendicular solutions L flat dip = 8π 3µ 0 c 3 Ω4 B 2 R 6 Vacuum orthogonal dipole y/rl Newtonian GR x/rl Luminosity (L/L vac dip ) Vacuum orthogonal dipole n=3 Newtonian GR Spin rate (R/rL) Figure: Magnetic field lines. Figure: Poynting flux L/L dip compared to the Deutsch solution. Spin parameter a = 2 5 R R r L. (Pétri, 2014) Ω-redshift and B-amplification omitted (Rezzolla & Ahmedov, 2004). Jérôme Pétri (Université de Strasbourg) Neutron stars 29/ 31 Oxford, 3rd-5th July / 31

52 Vacuum dipole field Spindown (L/L vac dip ) Vacuum orthogonal dipole (N, -3) (GR, -3) (N, 0) (GR, 0) Figure: Spindown luminosity for different rotation rates, magnetic field strengths given by log(b/b q) and gravitational field (Newtonian or GR). R/r L (Pétri, 2016) QED has no impact on spindown luminosity. Also true for FFQED. Jérôme Pétri (Université de Strasbourg) Neutron stars 30/ 31 Oxford, 3rd-5th July / 31

53 Possibles applications of QED dynamics of neutron star magnetospheres spindown luminosity, no effects. wave propagation quantum/relativistic plasmas vacuum birefringence, signature from optical? (Mignani et al., 2017) X-ray polarisation prediction (Weisskopf et al., 2016). an observable for the future IXPE mission. do photons follow curve field lines (magnetic lensing)? (Shabad & Usov, 1984), (Shaviv et al., 1999) do we need QMHD and chiral MHD? (Haas, 2005), (Boyarsky et al., 2015) as a long term task, possibility to test QED in strong magnetic AND gravitational fields. more and more detailed radio observations are NOT what is needed to help with theoretical modeling (Radhakrishnan, 1992). forget about lasers, watch the sky. Figure: The IXPE satellite. Jérôme Pétri (Université de Strasbourg) Neutron stars 31/ 31 Oxford, 3rd-5th July / 31

54 THANKS FOR YOUR ATTENTION Jérôme Pétri (Université de Strasbourg) Neutron stars 1/ 4 Oxford, 3rd-5th July / 4

55 References I Archibald R. F. et al., 2016, ApJL, 819, L16 Boyarsky A., Fröhlich J., Ruchayskiy O., 2015, Physical Review D, 92, Espinoza C. M., Lyne A. G., Kramer M., Manchester R. N., Kaspi V. M., 2011, ApJL, 741, L13 Gotthelf E. V., Vasisht G., Boylan-Kolchin M., Torii K., 2000, The Astrophysical Journal Letters, 542, L37 Haas F., 2005, Physics of Plasmas, 12, Hewish A., Bell S. J., Pilkington J. D., Scott P. F., Collins R. A., 1968, \nat, 217, 709 Kaspi V. M., Manchester R. N., Siegman B., Johnston S., Lyne A. G., 1994, ApJL, 422, L83 Kaspi V. M., McLaughlin M. A., 2005, The Astrophysical Journal Letters, 618, L41 Livingstone M. A., Kaspi V. M., Gavriil F. P., 2005, ApJ, 633, 1095 Livingstone M. A., Kaspi V. M., Gotthelf E. V., Kuiper L., 2006, ApJ, 647, 1286 Livingstone M. A., Ng C.-Y., Kaspi V. M., Gavriil F. P., Gotthelf E. V., 2011, ApJ, 730, 66 Jérôme Pétri (Université de Strasbourg) Neutron stars 2/ 4 Oxford, 3rd-5th July / 4

56 References II Lorimer D. R., Kramer M., 2004, Handbook of Pulsar Astronomy. Cambridge University Press Lyne A. G., Pritchard R. S., Graham-Smith F., 1993, MNRAS, 265, 1003 Lyne A. G., Pritchard R. S., Graham-Smith F., Camilo F., 1996, Nat, 381, 497 McLaughlin M. A. et al., 2003, \apjl, 591, L135 Middleditch J., Marshall F. E., Wang Q. D., Gotthelf E. V., Zhang W., 2006, ApJ, 652, 1531 Mignani R. P., Testa V., González Caniulef D., Taverna R., Turolla R., Zane S., Wu K., 2017, Monthly Notices of the Royal Astronomical Society, 465, 492 Ng C., Kaspi V. M., Göğüş E., Belloni T., Ertan, 2011, AIP Conference Proceedings, 1379, 60 Pétri J., 2014, Monthly Notices of the Royal Astronomical Society, 439, 1071 Pétri J., 2015a, Monthly Notices of the Royal Astronomical Society, 451, 3581 Pétri J., 2015b, Multipolar electromagnetic fields around neutron stars. EWASS-2015, La Laguna, Ténérife Pétri J., 2016, Astronomy and Astrophysics, 594, A112 Jérôme Pétri (Université de Strasbourg) Neutron stars 3/ 4 Oxford, 3rd-5th July / 4

57 References III Radhakrishnan V., 1992, in IAU Colloq. 128: Magnetospheric Structure and Emission Mechanics of Radio Pulsars, Hankins T. H., Rankin J. M., Gil J. A., eds., p. 367 Rea N. et al., 2010, Science, 330, 944 Rea N. et al., 2012, The Astrophysical Journal, 754, 27 Rea N., Viganò D., Israel G. L., Pons J. A., Torres D. F., 2014, The Astrophysical Journal Letters, 781, L17 Rezzolla L., Ahmedov B. J., 2004, Monthly Notices of the Royal Astronomical Society, 352, 1161 Roy J., Gupta Y., Lewandowski W., 2012, MNRAS, 424, 2213 Shabad A. E., Usov V. V., 1984, \apss, 102, 327 Shaviv N. J., Heyl J. S., Lithwick Y., 1999, \mnras, 306, 333 Weisskopf M. C. et al., 2016, in, pp Weltevrede P., Johnston S., Espinoza C. M., 2011, MNRAS, 411, 1917 Jérôme Pétri (Université de Strasbourg) Neutron stars 4/ 4 Oxford, 3rd-5th July / 4