1 / 82

A New Model for Bulk and Thermal Comptonization in Accretion Powered X-Ray Pulsars

A New Model for Bulk and Thermal Comptonization in Accretion Powered X-Ray Pulsars. Peter A. Becker (GMU) Michael T. Wolff (NRL) Kenneth D. Wolfram (NRL) Brent West (GMU). Bulk and Thermal Comptonization in Accretion-Powered X-Ray Pulsars. Talk Outline. Observations, standard model

francess
Download Presentation

A New Model for Bulk and Thermal Comptonization in Accretion Powered X-Ray Pulsars

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A New Model for Bulk and Thermal Comptonization inAccretion Powered X-Ray Pulsars Peter A. Becker (GMU) Michael T. Wolff (NRL) Kenneth D. Wolfram (NRL) Brent West (GMU)

  2. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Talk Outline • Observations, standard model • Categories of sources, basic physical relations • Photon sources, accretion geometry • Bulk and thermal Comptonization • Low-luminosity pulsars, bulk Comptonization model • High-luminosity pulsars, static magnetic model • Photon polarization modes, approximate dynamics • Bulk and thermal Comptonization in high-luminosity pulsars • Mathematical formalism and analytical solution • Alfvén radius and constraints on accretion geometry • Applications to Her X-1, Cen X-3, LMC X-4, X Per • Phase-averaged spectra, parameter correlations • Preliminary results for millisecond pulsar SAX J1808.4-3658 • XSPEC analysis of 4U 0115+63 • Conclusions and plans for future work

  3. Observations: Pulsating X-Ray Sources

  4. 4U 1538-522 Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Observations: Basic Model

  5. standing shock fan beam Theory: Basic Model binary companion accretion flow neutron star accretion disk

  6. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Observations: Pulsar Categories Bright Pulsars Faint Pulsars • More than 100 sources now known: New discoveries by RXTE, INTEGRAL • Wide luminosity range: Lx ~ 1034-38 ergs sec-1 • Wide range of pulsation periods: P~ 10-3-103 sec • Phase-averaged spectra: power-laws with quasi-exponential cutoffs • Ironemission lines and cyclotron absorption features often observed • Spectra usually fitted using ad hoc functions (power laws, exponentials, lines) • Static magnetic models do not reproduce the spectra very well Her X-1 X Per

  7. . * * * * * * * . * Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Observations: Extreme Physics • High-speed inflow: kinetic-gravitational energy balance free-fall velocity • Gravitational potential energy powers X-ray pulsar emission:

  8. * Eddington luminosity . Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Observations: Extreme Physics • Eddington luminosity: “levitation” condition for spherical case * • Eddington limit prorated by column area: • Critical luminosity for deceleration at stellar surface:

  9. * Eddington luminosity . Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Observations: Extreme Physics • Eddington luminosity: “levitation” condition for spherical case • Critical luminosity for deceleration at stellar surface: • Radiation pressure is important in X-ray pulsars: Lx ~ 1034-38ergs sec-1

  10. magnetic-centripetal force balance particle gyration speed cyclotron gyration frequency cyclotron energy • Thermal energy in X-ray pulsars: • Kinetic energy in X-ray pulsars: Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Observations: Extreme Physics • Cyclotron energy: • Magnetic energy is quantized in X-ray pulsars

  11. 4U 1538-522 Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Observations: Extreme Physics accretion flow • Radiation pressure dominates flow dynamics in sources with luminosity • In this case the radiation flux is locally super-Eddington • Gas decelerates to rest through a radiative, radiation-dominated shock • Spectrum is Comptonized Blackbody, Cyclotron, and Bremsstrahlung

  12. White, Swank, & Holt (1983) Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Observations: Faint Pulsars • Relatively low luminosities: Lx ~ 1034-36 ergs sec-1 • Energy indices  1, without strong cutoffs • Radiative transfer dominated bybulk Comptonization GX 304-1 X Persei

  13. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Observations: Faint Pulsars • Relatively low luminosities: Lx ~ 1034-36 ergs sec-1 • Energy indices  1, without strong cutoffs • Radiative transfer dominated bybulk Comptonization 4U 0352+30 GX 304-1

  14. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars • Static magnetic models treat magnetic effects in detail • Angular and energy dependences of cross sections are fully implemented • These models neglect the dynamics in the rapid inflow • Static magnetic models and dynamic thermal models do not reproduce the observed spectra very well • The nonthermalpower-law continuum is not well fitted F()(sec-1 cm-2 keV-1) (Mészáros & Nagle 1985) Log()(keV)

  15. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars • Static magnetic models treat magnetic effects in detail • Angular and energy dependences of cross sections are fully implemented • These models neglect the dynamics in the rapid inflow • Static magnetic models and dynamic thermal models do not reproduce the observed spectra very well • The nonthermalpower-law continuum is not well fitted F()(sec-1 cm-2 keV-1) (Mészáros & Nagle 1985) Log()(keV)

  16. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars • I had experience dealing with radiation-dominated shocks around black holes • Classical Rankine-Hugoniot shocks cannot describe stagnation on the neutron star • Following Basko & Sunyaev, I studied the effect of a radiative radiation dominated shock in the accretion column • The kinetic energy of the bulk inflow is efficiently transferred to the radiation field via electron scattering Velocity Strong, conservative (RH), radiation-dominated shock Strong, radiative, radiation-dominated shock • The kinetic energy is radiated away so that the gas can settle onto the stellar surface

  17. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Sources Accretion Geometry: • Seed photons are produced via bremsstrahlung, cyclotron, and blackbody emission cyclotron • Photons are redistributedin energy via collisions with electrons bremsstrahlung blackbody • Electrons have bulk and stochastic (thermal) motion

  18. B e e p Inflow Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Sources • Seed photons are produced via bremsstrahlung, cyclotron, and blackbody emission Bremsstrahlung Thermal Mound Polar Cap Neutron Star

  19. B e e p Inflow Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Sources • Seed photons are produced via bremsstrahlung, cyclotron, and blackbody emission n=0 Cyclotron n=1 Thermal Mound Polar Cap Neutron Star

  20. B e Inflow Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Sources • Seed photons are produced via bremsstrahlung, cyclotron, and blackbody emission Blackbody Thermal Mound Polar Cap Neutron Star

  21. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Comptonization • What is Comptonization? The equilibration of a photon distribution via electron scattering • Bulk Comptonization: The up-scattering of photons in a converging electron flow • Thermal Comptonization: The up-or down-scattering of photons in a stochastic (thermal) electron distribution • Bulk vs. Thermal Comptonization: Both processes can contribute (bulk gives power-law, thermal gives Wien bump and cutoff)

  22. . N0= monochromatic photon injection rate Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars This transport equation governs the distribution function, not the specific intensity Theory: Faint Pulsars Transport Equation Formalism (Becker & Wolff 2005): • The pure-bulk Comptonization transport equation is: time derivative escape through walls photon source bulk Compton diffusion along axis where fG= Green’sfunction v= plasma accretion velocity (v < 0) tesc= local timescale for escape through column walls ||= electron scattering cross section parallel to B field energy averaged z= height above stellar surface  = photon energy

  23. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Gravity is considered in later models “Exact” Velocity Profile (Becker, ApJ, January 1, 1998): • Following Basko & Sunyaev (1975) and Davidson (1973), we can model the variation of the inflow velocity in a cylindrical) geometry. • Gravity is neglected, so that the momentum flux is conserved. • The kinetic energy is radiated away through the column walls. • The photon diffusion (escape) timescale is comparable to the dynamical (accretion) timescale (this is an eigenvalue problem). • The resulting “exact” velocity profile is given by: “exact”

  24. . M0= mass accretion rate Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Escape Transport Equation Formalism (Becker & Wolff 2005): • The escape of photons through the column walls is modeled using an escape-probability formalism: or where r0= accretion column radius ┴= electron scattering cross section perpendicular to B field ne = electron number density

  25. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Faint Pulsars • Becker & Wolff (2005) obtained an exact solution for the Green’s function describingbulk Comptonizationin“cold” X-ray pulsars • Blackbody seed photons are produced in the dense thermal mound • Photons are upscattered due to collisions with electrons in shock • Spectra haveenergy indices1, because no cutoff is included • Bulk Comptonization model agrees with observations of faint, steep-spectrum pulsars X Persei GX 304-1

  26. White, Swank, & Holt (1983) Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Observations: Bright Pulsars • Relatively high luminosities: Lx ~ 1036-38 ergs sec-1 • Flatter spectra: energy indices <1 • Spectra show high-energy quasi-exponential cutoffs GX 304-1 X Persei

  27. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars • The bulk Comptonizationmodel cannot produce flat spectra or high-energy quasi-exponentialturnovers • This suggests thatthermal Comptonizationneeds to be included • Compton scatteringtransfers energyfrom high to low frequencies, producing the cutoffs and flattening the spectra • We have incorporatedthermalandbulk Comptonizationinto our current radiative transfer model

  28. B E e p Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Polarization • Photons have either ordinary or extraordinary polarization Ordinary Mode • Ordinary photon E-field is in the plane of photon propagation and the magnetic field • No electron excitation is possible • Cross section isnon-resonant n=0 n=1 Thermal Mound Polar Cap Neutron Star

  29. B E e p Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Polarization • Photons have either ordinary or extraordinary polarization Extraordinary Mode • Extraordinary photon E-field is perpendicular to plane of photon propagation and the magnetic field • Electron excitation is possible • Cross section is resonant n=0 n=1 Thermal Mound Polar Cap Neutron Star

  30. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Polarization Ordinary Mode • Ordinary mode photons have a continuous (non-resonant) scattering cross section: • Above the cyclotron energy, the scattering cross section is Thomson • Parallel to the field direction (φ=0), the cross section is reduced by (ε/ εc)2for photons with energy ε < εc • Perpendicular to the field (φ=90), the cross section is Thomson for all photon energies

  31. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Polarization Extraordinary Mode • Extraordinary mode photons have a resonant scattering cross section: • Above the cyclotron energy, the scattering cross section is Thomson except at the resonant energy ε < εc • Resonance is due to the change in the Landau level of the electron • For non-resonant photons, the cross section is reduced by (ε/ εc)2for energy ε < εc • The two modes can exchange photons via mode conversion • Outside the resonance, the cross section has no directional dependence

  32. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Polarization Scattering Cross Sections • Most of the photons emitted by bright X-ray pulsars have energy ε < εc • Extraordinary mode photons with ε < εc see cross section T (ε/ εc)2 • Ordinary mode photons with ε < εc andφ=0 see cross section T (ε/ εc)2 • Ordinary mode photons with φ=90 see the Thomson cross section • The two modes can exchange photons via mode conversion • Hence the cross section parallel to the field is T (ε/ εc)2and therefore <<T • The dominant cross section perpendicular to the fieldis the ordinary one • We use a simplified two-dimensional model for the scattering cross section

  33. = angle-averaged electron scattering cross section _  . N0= monochromatic photon injection rate The cylindrical geometry could be replaced with a hollow or filled cone Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • The thermal+bulk Comptonization transport equation is: Bulk Kompaneets operator Thermal where fG= Green’sfunction v= plasma accretion velocity (v < 0) tesc= local timescale for escape through column walls ||= electron scattering cross section parallel to B field energy averaged energy averaged Te= electron temperature

  34. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Sources Bremsstrahlung and Cyclotron: • In strong magnetic field, bremsstrahlung and cyclotron can be treated as a single process called magnetobremsstrahlung • Magnetobremsstrahlung photons are created in a dipole pattern, mainly as ordinaryphotons emitted perpendicular to the magnetic field (Lauer et al. 1983)

  35. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Sources Bremsstrahlung and Cyclotron: • The magnetobremsstrahlung source can be approximated as the sum of bremsstrahlung and cyclotron sources • Bremsstrahlung emission is described by the spatially distributed, continuum, ordinary-mode source term includes low-energy cutoff • The low-energy self-absorption cutoff εabsis set using electron scattering energizes photons

  36. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Photon Sources Bremsstrahlung and Cyclotron: • The magnetobremsstrahlung source can be approximated as the sum of bremsstrahlung and cyclotron sources • Bremsstrahlung emission is described by the spatially distributed, continuum, ordinary-mode source term includes low-energy cutoff • The low-energy self-absorption cutoff εabsis set using • Cyclotron emission is described by the spatially distributed, monochromatic (resonant), extraordinary-mode source term

  37. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • The transport equation can be solved analytically using the approximatevelocity profile (Lyubarski & Sunyaev 1982) where v = 0 at surface • The approximate velocity profile can be stated in terms of z using: approximate • The exact velocity profile is given by: exact • The constant α is determined by setting the two profiles equal at the sonic point :

  38. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • The exact and approximate velocity profiles agree fairly well: approximate exact stagnation at stellar surface sonic point

  39. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • Using the approximate velocity profile, the transport equation can be rewritten as: where Measures escape time relative to accretion time • This equation is separable using the functions:

  40. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • The separation functionsg and h satisfy the differential equations: where Determines relative importance of bulk and thermal Comptonization • This eigenvalues for λ are determined by imposing boundary conditions on the spatial function g

  41. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • The spatial functiong satisfies the differential equation: This BC could be replaced with a free-surface condition that would allow a pencil beam with the general solution confluent hypergeometric functions • We require that g → 0 in the limit →  because of the strong advection by the fast inflow • We also require that dg/d→ 0 in the limit → 0 because the photon flux must vanish at the stellar surface

  42. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • The eigenfunction solution for g satisfying the BC’s is given by Laguerre polynomials with associated eigenvalues • The energy functionh satisfies the differential equation with λ = λn

  43. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • The solution for h is: Whittaker functions where • The Green’s function can be evaluated using the expansion: where the expansion coefficients Cn are computed using the orthogonality of the Laguerre polynomials

  44. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • Integration of the PDE with respect to energy yields the derivative jump condition • Substituting the expansion for fG yields

  45. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • Substituting in the solution for h gives: where the Wronskian is defined by • Hence we obtain • Next we utilize the orthogonality relation

  46. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • The result obtained for the expansion coefficient Cn is: • The corresponding exact solution for the Green’s function is given by: • The Green’s function for the escaping photon spectrum is:

  47. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • The Green’s function for the escaping photon spectrum is: kTe= 0.86 keV where = 1.15  = 0.20, 0.79 0= 0.1 • In terms of the escaping Green’s function becomes:

  48. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Transport Equation Formalism (Becker & Wolff, ApJ, January 1, 2007): • We can’t resolve the vertical structure of the emission column • Hence the emission we see is the vertically integrated spectrum • The vertically-integrated Green’s function for the escaping photon spectrum is calculated using: kTe= 0.86 keV = 1.15  = 0.20, 0.79 • The exact solution is given by:

  49. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bulk vs. Thermal Comptonization Photon Energization: • The totalphoton energization rate is: total rate recoil losses thermal Compton bulk Compton • This can be rewritten as: • Total energization rate vanishes at the critical energy: Low-temperature limit

  50. Bulk and Thermal Comptonization inAccretion-Powered X-Ray Pulsars Theory: Bright Pulsars Theory Parameters: • The spectrum should approach the bulk Comptonization result in the limit Te  0 (  ) Column-integrated Green’s function for escaping photon number spectrum for different plasma electron temperatures =0.79 Becker & Wolff (2005) pure-bulk Comptonization spectrum based on exact velocity profile ε=εbulk 3.95 39.5 ∞ • The value of determines the importance of the Wien bump

More Related