A resonant cyclotron scattering modelfor the X-ray spectra of Magnetar

CandidatesThirty years of magnetars: new frontieres

Aspen, 2-6 Feb 2009

Silvia Zane, MSSL, UCL

In collaboration with: Luciano Nobili, Roberto Turolla,Nanda Rea, Gianluca Israel, Alessandra Albano,

Lucia Pavan, Maxim Lyutikov, Diego Gotz

2000.38 / 2.03.98.0in SMCCXO J0100-72

~ transient5.3 - 2500.63 / 2.93.96.41E 1048-5937

transient/radio2.6 - 1700.52 / 2.92.22.01E 1547-5408

hard X80-1900.44 / 2.44.711RXS J1708-4009

~ transient/hard X17 - 1590.41 / 3.80.67.0CTB 1091E 2259+586

4 - 100

260

320 - 540

200 - 350

5 - 120

1-130

5 - 260

110

72

L (1033 erg/s)(0.2-10keV)

transient0.68/2.01.510.6in Wes1CXO 1647-4552

G337.0-0.1?

in LMC

OB

OB

G29.6+0.1

Kes 73

Hosts

GF/hardX0.43 / 2.05.75.2SGR 1900+14

GF/hardX/outburst0.6 / 1.47.87.5SGR 1806-20

GF/?0.53 / 3.17.48.0SGR 0526-66

outburst/ 2.9-6.4 ?SGR 1627-41

commentskT(keV)/ Γ

B(1014G)

P(s)

transient/ 4.6-7.0AX J1845-0258

transient/radio0.67 / 3.72.95.5XTE 1810-197

hard X0.44 / 2.07.111.81E 1841-045

hard X0.46 / 3.41.38.74U 0142+61

Introduction: magnetars

0.5 – 10 keV emission well represented by a blackbody plusa power law: WHY??

Correlation in spectral hardening, luminosity, spin down rate -as inSGR 1806, during the pre (andpost)-giant flare evolution (24 Dec 2007)

Evolution of “transient” AXPs

Our “immediate” goal:

RXS J1708-4009; from Rea et al, 2005, MNRAS

Our “medium term” project:Hard X-ray Emission

Gotz et al 2006INTEGRAL revealed substantial emission in the 20 -100 keV band from SGRs and AXPs

Hard power law tails with Γ ≈ 1-3, hardeningwrt soft X-ray emissionrequired in AXPs

Hard emission pulsed

May a twist in themagnetosphere explain theBB+PL spectral shapeobserved <10keV?

Thompson, Lyutikov and Kulkarni(2002):

Magnetars (AXPs and SGRs) differfrom radiopulsars since theirinternal magnetic field is twisted upto 10 times the external dipole.

At intervals, it can twist up theexternal field

Twisted magnetospheres

A key feature of twisted MSs is that they support current flows (inexcess of the Goldreich-Julian current).

Thermal seed photons (i.e. emitted from the star surface) travellingthrough the magnetosphere experience efficient resonant cyclotronscattering onto charged magnetospheric particles (e- and ions)

⇒the thermal surface spectrum get distorted !

⇒ typical PL tail. Qualitatively ok, but quantitatively?

Preliminary investigation (1D) Lyutikov & Gravriil, 2006: A simplified, 1D semi-analytical treatment of resonant cyclotron up-scattering of soft thermal photons

• Thomson scattering occurs in a thin, plane parallel slab. Photons can only propagate along theslab normal, i.e. either towards or away from the star.

• Static, non-relativistic, warm medium; ne constant. No electron recoil (hν << mec2)

• The NS surface emits seed photons (blackbody spectrum)

• Magnetospheric charges have a top-hat velocity distribution centered at zero and extending up to±βT ⇒ mimics a thermal, 1D, motion (βT ≈ mean e- energy ≈ temperature of the 1Delectron plasma). No bulk motion.The e- velocity distribution averages to zero:

⇒ a photon has the same probability to undergo up or downscattering⇒ no frequency shift due to the thermal motion of e-

• Photon boosting by particle thermal motion in Thomson limit occurs only due to the spatial variation of the magnetic field.

For a photon propagating from high to low magnetic fields, multiple resonant cyclotronscattering will, on average, up-scatter the transmitted radiation⇒ hard tail.

Preliminary investigation (1D)

Rea et al, 2006, 2008

• Implemented a grid of such models in XSPEC (3 parameters: τres, βT, T + norm.)

• systematic application to ALL magnetars spectra below 10keV

Distorsion of a seed blackbodyspectrum through resonantcyclotron scattering ontomagnetospheric electrons, for twovalues of the blackbodytemperature, 0.2 keV and 0.8 keV.

Black lines: βT = 0.2 and τres = 2,4, 8 (from bottom to top).

Grey lines: βT = 0.4 and τres = 2, 4,8 (from bottom to top).

The normalizations of the variouscurves are arbitrary. From Rea etal. 2008

Resonant Cyclotron Scattering in Magnetars

AXPs with hard X-ray emission

4U 0142+61 4U 0142+61

RXS J1708-4009 RXS J1708-4009

BB+PL+PL

BB+PL+PL

RCS+PL

RCS+PL

Rea, Zane, Turolla, Lyutikov & Gotz 2008, ApJ, arXiv:0802.192v2

Flu

x

1 - Energy (keV) - 200

Resonant Cyclotron Scattering in Magnetars

Transient AXPs

RCS

RCS

BB+PL

BB+PL

BB+PL

BB+PL

RCS

RCS

1E 1048-5937

1E 1547-5408

CXO 1647-4552

XTE 1810-197

Rea, Zane, Turolla, Lyutikov & Gotz 2008, ApJ, arXiv:0802.192v2

Flu

x

1 - Energy (keV) - 10

Resonant Cyclotron Scattering in Magnetars

SGRs with hard X-ray emission

BB+PL

RCS+PL

SGR 1900+14

SGR 1806-20

Rea, Zane, Turolla, Lyutikov & Gotz 2008, ApJ, arXiv:0802.192v2

SGR 1900+14

BB+PL

Flu

x

1 - Energy (keV) - 200

RCS+PL

SGR 1806-20

F

lux

1 - Energy (keV) - 10

http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/models/rcs.html

Rea, SZ, Turolla, Lyutikov & Gotz 2008, ApJ, arXiv:0802.192v2

Resonant cyclotron scattering reproduces all magnetarspectra

For sources with hard Integral tail we need to add a PLeven when fitting the emission below 10keV (contaminationof the hard component in the soft X-ray range?)

This model has a physical motivation, unlike BB+PL models

A Monte Carlo Approach

• Follow individually a large sample of photons, treatingprobabilistically their interactions with charged particles

• Can handle very general (3D) geometries• Quite easy to code, fast• Ideal for purely scattering media• Monte Carlo techniques work well when Nscat ≈ 1

Basic ingredients: Space and energy distribution of the scattering particles Same for the seed (primary) photons Scattering cross sections

More detailed modeling by Fernandez & Thompson (2006)New, up-to-dated code (Nobili, Turolla, Zane 2008)

Twisted Magnetospheres

• TLK02 investigated force-freemagnetic equilibria

• A sequence of models labeled bythe twist angle

)0( =×BJrr

BRBrrr),( θα=×∇

θθ

φπ

θ

φ

sin2 20

dBB

SN ∫=Δ −

Movie by R. Turolla

Magnetospheric Currents

• Charges move along the field lines• Spatial distribution

• Particle motion characterized by a bulk velocity, βbulk, and by athermal velocity spread (Tel )

• Electron contribution 1D relativistic Mawellian at Tel centred atβbulk (+ Landau levels in transverse plane)

• There may be e± in addition to e-p, but no detailed model as yet

(neglected!)

Bvrr

bulkvrcB

BB

epn

+=

θ

φ

π41

3-1

1416 cm

km 10G 1010

−

≈ NSp RB

Surface Emission

The star surface is divided intopatches by a cos θ - ϕ grid

Each patch has its own temperatureand beaming prescription toreproduce different thermal maps

Tests shown today: blackbody,isotropic emission (see work byF.Ozel and collaborators for adifferent approach)

Photons in a Magnetized Medium

• Magnetized plasma is anisotropic and birefringent,radiative processes sensitive to polarization state

• Two normal modes of photon propagation

• At the modesare almost linearly polarized

32214 gcm )keV 1/()G 10/( −≈< ερρ BV

The extraordinary (X) and ordinary (O) modes

Scattering Cross Sections

• QED cross section available (Herold 1979, Harding & Daugherty1991) but unwieldy ⇒ NEXT DEVELOPMENT, see next talk by RT

• Non-relativistic (Thompson) cross section ( hν<mc2/γ≈50 keV,B/BQED < 10)

Model Spectra

• 5 model parameters: B, T, Te, βbulk, Δ_

•After each Monte Carlo run, photons are collected in a (Θ,Φ) grid on the sky at infinity

Non-relativistic scattering cross section Thompson limit

scatteringafter and beforevelocity particle anddirection photon between angles ', ,/ ,/

'cos)(8

3'

)(8

3'

cos)(8

3'

'coscos)(8

3'

(ERF) resonanceat sections cross aldifferenti Completely

220

200

20220

θθω

θωωδπσ

ωωδπσ

θωωδπσ

θθωωδπσ

mceBmcer

crddcr

dd

crddcr

dd

c

cOX

cXX

cXO

cOO

==

−=Ω

−=Ω

−=Ω

−=Ω

−−

−−

Effects of increasing the currents bulk velocity βbulk

or their temperature Te

Computedspectrafor βbulk:0.3, 0.5,0.7, 0.9

Computedspectra forkTe: 5, 15,30, 60 and120 keV

Θ = 64˚ Θ = 116˚

βbulk βbulk

βbulk

Θ = 64˚ Θ = 116˚

Te Te

If comptonization starts to saturate, photons fill the Wien peak of theBose-Einstein distribution ⇒ spectrum is not peaked at ~kT, but at ~kTe

XSPEC implementation:

• Build up a huge archive of models

• B = 1014 G

• γbulk-1 = 2[1/( 1+Te] /Te ; then Te = Te/2(bulk kinetic energy = av. Eth for a 1D Maxwellian; Te=kTe/mec2)

• The resulting archive is a 22MB table with 4 model parameters:T, βbulk, Δϕ + a normalization constant ⇒ same number of degree of freedom as inthe BB+PL model (or in the 1D RCS one)

Note: we also built up a second archive (300 MB table) with viewing angles effectsincluded

For the viewing angle geometry we need to include two further dof, i.e. two angles whichdescribe the disalignement between magnetic, spin axis and LOS (0 ≤ χ ≤ 180 and 0 ≤ξ ≤ 90) ⇒ future application

Systematic fit of all sources with the 3D model(emission below 10 keV) Zane, Rea, Turolla and Nobili in prep

1) reproducing a single state: fit with NTZ model only

χ2= 1.21 (101) χ2= 1.16 (81)

CXOU J0100-7211 SGR 1627-41

χ2= 0.97 (197) χ2= 1.04 (152) χ2= 0.99 (135)

1RXS J1708-4009 1E 1841-045 SGR 1900+14

Systematic fit of all sources with the 3D model(emission below 10 keV) Zane, Rea, Turolla and Nobili in prep

1) reproducing a single state: fit with NTZ model only

2) Adding Integral data: fit NTZ+PL

χ2= 1.05 (205) χ2= 1.12 (158) χ2= 1.02 (140)

The model works but the details of the fitting in the soft range change: only true if theadditional PL is “instrinsically” due to an independent component

May a resonant scattering model explain the hard tails? In sources where the photonindex is the same from soft to hard X-rays we may need just one e- population to explainthe overall spectrum up to few hundreds of keV

1RXS J1708-4009 1E 1841-045 SGR 1900+14

χ2= 1.11 (164) χ2= 1.22 (515) χ2= 0.98 (288)

3) reproducing the source long-term evolution: fit with NTZ only

1E 1547.0-5408 1E 1048-5937 SGR 1806-20

What is left out? The XMM spectra of 1E2259 and 4U0142cannot be fitted by our model

• In the BB+PL representation both have a very step spectrum: photonindex ~4 (vs 2-3 in other cases)

• The PL component almost dominates the BB component (the departurefrom the BB occurs close to the BB peak)

Almost impossible to reproduce such shape with a comptonization model(whatever is thermal, resonant, or bulk motion comptonization):

If the PL almost dominates the BB peak of the seed photons, then comptonization is almost fully fledged ⇒ flat tail

If the PL tail is steep ⇒comptonization not very efficient ⇒ departures from a bb spectrum occurs at E>> BB peak

Emission from a single patch, observer almost antipodal

Thermal map effect? Surface temperature strongly anisotropic with theemitting cap almost never completely on view(these sources also have the lower PF among the sample)

Spectrum from a single emitting patch on the star surface, computed as in NTZ 2008Left: The emitting area is the strip 0 < cos θ < 0.25, 0 < ϕ < π/2. The LOS is at θs=90°and ϕs = 20° (dotted line), ϕs = 140° (dashed line) and ϕs = 220° (dash-dotted line).The solid line represents the seed blackbody.

Conclusions & Future Developments:• Twisted magnetosphere model, within magnetar scenario, in general agreement

with observations• 3D model of resonant scattering of thermal, surface photons reproduces almost all

AXPs and SGRs spectra below 10keV with no need of extra components (but1E2259 and 4U0142)

Many issues need to be investigated further:

Use the model archive to investigate what causes the variabilityd their outburstsin TAXPS (in progress, with N. Rea, G.L. Israel & Alessandra Albano)

More accurate treatment of cross section including QED effects and electronrecoil (Nobili, Turolla & SZ MNRAS, 2008- See next talk by RT)

Investigate QED effects in spectral formation and polarization pattern 10-100 kevtails: up-scattering by (ultra)relativistic (e±) particles ?

Twist of more general external fields (with L. Pavan, see next talk by RT)

Detailed models for magnetospheric currents (effects of pairs production?) (seenext talk by RT)