Isolated Neutron Stars
XDINSs, AXPs, SGRs,
RRATs
R Turolla
Department of Physics
University of Padova, Italy
Artist impression of a magnetar
Proper motion of RX J1856.5-3754 with HST (F. Walter)
A detected RRAT
Cagliari 25-26 maggio 2007
Basics
Compact objects are born in the core
collapse following a type II supernova
explosion
 Present rate of SN events in the Galaxy:
≈ 0.01/yr (possibly higher in the past)
 Galactic population of compact objects:
≈ 108 – 109 (≈ 1% of stars)

Cagliari 25-26 maggio 2007

Nature of compact remnant depends on progenitor mass
8 < M/M < 20-25
M/M > 20-25


If N(>M) ~ M-1.3 only ~ 20% of stars with M > 8 M are
more massive than 25 M
Very massive stars may form “magnetars” (Muno et al 2006),
black holes about 10% of the total
Cagliari 25-26 maggio 2007
Pulsars and…
 Most neutron stars are known through their pulsed
radio-emission
 Galactic pulsar population ≈ 105 (≈ 1800 detected)
 The majority of neutron stars are old, dead objects
 Observations in the X- and γ-rays revealed the
existence of different populations of neutron stars
 X-ray binaries
 Geminga, CCOs in SNR
 X-ray dim isolated neutron stars (XDINSs)
 Soft γ-repeaters (SGRs)
ISOLATED
 Anomalous X-ray pulsars (AXPs)
 Rotating Radio Transients (RRATs)
Cagliari 25-26 maggio 2007
Neutron Stars in a Nutshell




Vast majority (~ 80-90%) of Galactic compact objects
are compact stars (no horizon)
Electron capture e-+p → n+ν energetically favorable at ρ
> 107 g/cm3, or R < 104 km for M ~ 1 M
Typical radius ≈ 10 km, masses in the range
0.1 < M/M < 3 (theoretical estimates)
Highly relativistic objects
 M/R ~ 0.15 (M/M)(R/10 km)-1
 J/M ~ 0.25 (1 ms/P) (M/M)(R/10 km)2 (the Kerr solution does not
describe spacetime outside a rotating star though)
Cagliari 25-26 maggio 2007
ds 2   exp( 2)dt 2  exp( 2)dr 2  r 2 (d 2  sin 2 d 2 )
Spherically symmetric space-time
d
1 dp

dr
p   dr
Einstein
equation
dp
m
p  4r
   2 1  1 
dr
r   
m
3
dm
 4r 2 
dr
exp    g 00
p  2m 
1 

r 

Gravitational mass
Cagliari 25-26 maggio 2007
1
2M
 1
r
Hydrostatic
equilibrium
(TOV)
 (0)   c
m(0)  0

R, p ( R )  0
M  m( R )
or
R, p ( R )  0
m(0)  0
 M  m( R )
Compute sequence of equilibrium models:
the Mass-radius relation
P = P(ρ) ?
Cagliari 25-26 maggio 2007
Nuclear Matter EOS: The Holy Grail
“Neutron” stars: a
misnomer
 Inner core may
contain

– Hyperons (Σ, Ξ, Λ)
– Meson (K-,π-)
condensates
– Deconfined quarks (u,
d, s) – Hybrid Stars

Strange quark stars
Page & Reddy (2006)
Cagliari 25-26 maggio 2007
R=2GM/c2
P=ρ
R~3GM/c2
Page & Reddy (2006)
R∞=R(1-2GM/Rc2)-1/2
Lattimer & Prakash (2004)
Cagliari 25-26 maggio 2007
ω=ωK
NS Masses
Stellar masses directly measured only~ Initial
in Mass
binary systems
 Accurate NS mass determination for PSRs
in relativistic systems by measuring PK
> Initial Mass
corrections
 Gravitational redshift may provide M/R in
NSs by detecting a known
spectral line,
BHs ?
E∞ = E(1-2GM/Rc2)1/2
 Fe and O lines in EXO 0748-676,
M/R ~ 0.22 (Cottam et al 2002)

Page & Reddy (2006)
Cagliari 25-26 maggio 2007
NS Cooling
NSs are born very hot, T > 1010 K
 At early stages neutrino cooling dominates
 The core is isothermal

dEth
dT
 CV
  L  L
dt
dt
Photon luminosity
Neutrino luminosity
L  4 R 2 Ts4 , Ts  T 1/ 2 (   1)
Cagliari 25-26 maggio 2007
Fast Cooling
(URCA cycle)
n  p  e   e
p  e  n  e

Slow Cooling
(modified URCA cycle)
n  n  n  p  e   e
n  p  e  n  n  e

p  n  p  p  e  e

p  p  e   p  n  e
 Fast cooling possible only if np > nn/8
 Nucleon Cooper pairing important
 Minimal cooling scenario (Page et al 2004):
 no exotica
 no fast processes
 pairing included
Cagliari 25-26 maggio 2007
“Minimal” Cooling Curves
Geppert
& Weber (2006)
Page &Page,
Reddy
(2006)
Cagliari 25-26 maggio 2007
NS Radii

A NS with homogeneous surface
temperature and local blackbody emission
L  4 R  T
L
2
4
F
 R / D   T
2
4 D
2
4
From X-ray
spectroscopy
Cagliari 25-26 maggio 2007
From dispersion
measure
NS Radii - II

Real life is a trifle more complicated…

Because of the strong B field
 Photon propagation different
 Surface temperature is not homogeneous
 Local emission may be not exactly planckian

Gravity effects are important
Cagliari 25-26 maggio 2007
Photons in a Magnetized Medium
Magnetized plasma is anisotropic and
birefringent, radiative processes sensitive
to polarization state
 Two normal, elliptically polarized modes in
the magnetized “vacuum+cold plasma”

The extraordinary (X) and ordinary (O) modes
Cagliari 25-26 maggio 2007
NS Thermal Maps
Electrons move much more easily along B
than across B
 Thermal conduction is highly anisotropic
inside a NS: Kpar >> Kperp until EF >> hνB
or ρ >> 104(B/1012 G)3/2 g/cm3
 Envelope scaleheight L ≈ 10 m << R, B ~
const and heat transport locally 1D

Greenstein & Hartke (1983)
Cagliari 25-26 maggio 2007

TS  cos   K perp / K par sin 
2
2

1/ 4
Tpole
K perp / K par  1
TS  cos 
1/ 2
Tpole
Core centered dipole
Core centered quadrupole
Cagliari 25-26 maggio 2007
Local Surface Emission
Much like normal stars NSs are covered by
an atmosphere
 Because of enormous surface gravity, g ≈
1014 cm/s2, Hatm ≈ 1-10 cm
 Spectra depend on g, chemical
composition and magnetic field
 Plane-parallel approximation (locally)

Cagliari 25-26 maggio 2007

Free-free absorption dominates
   3 , h  kT

High energy photons decouple deeper in the atmosphere
where T is higher
Zavlin & Pavlov (2002)
Cagliari 25-26 maggio 2007
Gravity Effects
 Redshift
 Ray bending
L  4 R  T
2

4

2
2
1
0
0
0
4 T   d  d  du
4

2

E , 2
E ,1
dE I ( E, B, cos , Ts ,  )
Cagliari 25-26 maggio 2007
STEP 1
Specify viewing geometry
and B-field topology;
compute the surface
temperature distribution
STEP 2
Compute emission from
every surface patch
STEP 4
Predict lightcurve and
phase-resolved spectrum
Compare with observations
Cagliari 25-26 maggio 2007
STEP 3
GR ray-tracing to obtain
the spectrum at infinity
Further Readings






Page, D., Reddy, S. 2006, Ann. Rev. Nucl. Part. Sci., 56, 327
(astro-ph/0608360)
Page, D. Geppert, U., Weber, F. 2006, Nucl. Phys. A, 777,
497 (astro-ph/0508056)
Weber, F. 2005, Progr. Part. Nucl. Phys., 54, 193 (astroph/0407155)
Lattimer, J.M., Prakash, M. 2004, Science, 304, 536 (astroph/0405262)
Yakovlev, D.G., Pethick, C.J. 2004, Ann. Rev. Astron.
Astrophys., 42, 169 (astro-ph/0402143)
Zavlin, V.E., Pavlov, G.G. 2002, Proceedings of the 270 WEHeraeus Seminar on Neutron Stars, Pulsars, and Supernova
Remnants. MPE Report 278, p.26 (astro-ph/0206025)
Cagliari 25-26 maggio 2007
The Seven X-ray Dim Isolated
Neutron stars (XDINSs)
Soft thermal spectrum (kT  50-100 eV)
 No hard, non-thermal tail
 Radio-quiet, no association with SNRs
 Low column density (NH  1020 cm-2)
 X-ray pulsations in 6 sources (P  3-10 s)
 Very faint optical counterparts

Cagliari 25-26 maggio 2007
The Magnificent Seven
Source
kT (eV)
P (s)
Amplitude/2
Optical
RX J1856.5-3754
60
7.06
1.5%
V = 25.6
RX J0720.4-3125 (*)
85
8.39
11%
B = 26.6
RX J0806.4-4123
96
11.37
6%
-
RX J0420.0-5022
45
3.45
13%
B = 26.6 ?
RX J1308.6+2127
(RBS 1223)
86
10.31
18%
m50CCD = 28.6
RX J1605.3+3249
(RBS 1556)
96
-
-
m50CCD = 26.8
1RXS J214303.7+065419
(RBS 1774)
104
9.43
4%
-
(*) variable source
Cagliari 25-26 maggio 2007
Featureless ? No Thanks !

RX J1865.5-3754 is convincingly featureless
RX J0720.4-3125 (Haberl et al 2004)
(Chandra 500 ks DDT; Drake et al 2002; Burwitz et al 2003)

A broad absorption feature detected in all
other XDINSs (Haberl et al 2003, 2004, 2004a; Van Kerkwijk
et al 2004; Zane et al 2005)
Eline ~ 300-700 eV; evidence for two lines with
E1 ~ 2E2 in RBS 1223 (Schwope et al 2006)
 Proton cyclotron lines ? H/He transitions at
high B ?

Cagliari 25-26 maggio 2007
Period Evolution
.
RX J0720.4-3125: bounds on P derived by Zane
et al. (2002) and Kaplan et al (2002)
 Timing solution by Cropper et al (2004), further
improved
by Kaplan & Van Kerkwijk (2005):
.
P = 7x10-14B s/s,
B =13
2x1013 14
G
~ 10 -10 G
 RX J1308.6+2127: timing
. solution by Kaplan &
Van Kerkwijk (2005a), P = 10-13 s/s, B = 3x1013 G
 Spin-down values of B in agreement with
absorption features being proton cyclotron lines

Cagliari 25-26 maggio 2007
Source
Energy
(eV)
EW
(eV)
Bline
(Bsd)
(1013 G)
Notes
RX J1856.5-3754
no
no
?
-
RX J0720.4-3125
270
40
5 (2)
Variable line
RX J0806.4-4123
460
33
9
-
RX J0420.0-5022
330
43
7
-
RX J1308.6+2127
300
150
6 (3)
-
RX J1605.3+3249
450
36
9
-
1RXS J214303.7+065419
700
50
14
-
Cagliari 25-26 maggio 2007
XDINSs: The Perfect Neutron Stars
XDINSs are key in neutron star astrophysics:
these are the only sources for which we have
a “clean view” of the star surface
Information on the thermal and
magnetic surface distributions
 Estimate of the star radius (and mass ?)
 Direct constraints on the EOS

Cagliari 25-26 maggio 2007
XDINSs: What Are They ?
XDINSs are neutron stars
 Powered by ISM accretion, ṀBondi ~ nISM/v3
if v < 40 km/s and D < 500 pc (e.g. Treves et

al 2000)
Measured proper motions imply v > 100
km/s
 Just cooling NSs

Cagliari 25-26 maggio 2007
Simple Thermal Emitters ?
Recent detailed observations of XDINSs allow direct
testing of surface emission models
“STANDARD MODEL” thermal emission from the
surface of a neutron star with a dipolar magnetic
field and covered by an atmosphere
The optical excess
XDINS lightcurves
The puzzle of RX J1856.5-3754
Spectral evolution of RX J0720.4-3125
Cagliari 25-26 maggio 2007
The Optical Excess
In the four sources with a
confirmed optical counterpart
Fopt  5-10 x B(TBB,X)
 Fopt  2 ?
 Deviations from a RayleighJeans continuum in RX J0720
(Kaplan et al 2003) and RX J1605
(Motch et al 2005). A non-thermal
power law ?

RX J1605 multiwavelength SED (Motch et al 2005)
Cagliari 25-26 maggio 2007
Pulsating XDINSs - I
Quite large pulsed
fractions
 Skewed lightcurves
 Harder spectrum at pulse
minimum
 Phase-dependent
absorption features

RX J0420.0-5022 (Haberl et al 2004)
Cagliari 25-26 maggio 2007
Pulsating XDINSs - II
Too
Too small
small
pulsed
pulsed fractions
fractions
Core-centred
Core-centred
Atmosphere
Blackbody ==
++
Symmetrical
Symmetrical
dipole
dipole field
field
emission
emission
pulse
pulse profiles
profiles
(Page
(Zane1995)
& Turolla 2006)
+
=
Cagliari 25-26 maggio 2007
Pulsating XDINSs - III
Pure dipole-induced
thermal maps do not
match XDINS pulse
profiles
Observed
Synthetic
Principal component representation of dipolar lightcurves
More complex thermal
and/or magnetic
surface distributions
Cagliari 25-26 maggio 2007
Beyond the Dipole
Addition of quadrupolar components (even assuming
BB emission) results in larger pulsed fractions and
non-symmetric pulse shapes (Page & Sarmiento 1996)
Star-centred
dipolar+quadrupolar
fields can reproduce
observed lightcurves
(Zane & Turolla 2006)
Cagliari 25-26 maggio 2007
Crustal Magnetic Fields

Star centred dipole +
poloidal/toroidal field
in the envelope
(Geppert, Küker & Page 2005;
2006)
Purely poloidal crustal
fields produce a
steeper meridional
temperature gradient
 Addition of a toroidal
component introduces
a N-S asymmetry

Geppert, Küker & Page 2006
Gepper, Küker & Page 2006
Cagliari 25-26 maggio 2007
Schwope et al. 2005
RBS 1223 (Zane & Turolla 2006)
Indications for non-antipodal
caps (Schwope et al 2005)
Need for a non-axsymmetric
treatment of heat transport
Cagliari 25-26 maggio 2007
RX J1856.5-3754 - I
Blackbody featureless
spectrum in the 0.1-2 keV
band (Chandra 500 ks DDT, Drake et al
2002); possible broadband
deviations in the XMM 60 ks
observation (Burwitz et al 2003)
RX J1856 multiwavelength SED (Braje & Romani 2002)
Thermal emission from NSs is not expected to be a featureless
BB ! H, He spectra are featureless but only blackbody-like
(harder). Heavy elements spectra are closer to BB but with a
variety of features
Cagliari 25-26 maggio 2007
RX J1856.5-3754 - II
 A quark star (Drake et al 2002; Xu 2002;
2003) What spectrum ?
A
The optical
excess
? and cooler
NS with
hotter
caps
equatorial region (Pons et al 2002; Braje
& Romani 2002; Trűmper et al 2005)
 A bare NS
(Burwitz
A perfect
BB ? et al 2003; Turolla, Zane
& Drake 2004; Van Adelsberg et al 2005;
Perez-Azorin, Miralles & Pons 2005)
Cagliari 25-26 maggio 2007
Bare Neutron Stars
At B >> B0 ~ 2.35 x 109 G atoms
attain a cylindrical shape
Turolla, Zane & Drake 2004
 Formation of molecular chains by
covalent bonding along the field
direction
RX J0720.4-3125
 Interactions between molecular
chains can RX
lead
to the formation
J1856.5-3754
of a 3D condensate
Fe condensation
H temperature
 Critical
depends on B and chemical
composition (Lai & Salpeter 1997; Lai 2001)

Cagliari 25-26 maggio 2007
Spectra from Bare NSs - I
The cold electron gas approximation. Reduced
emissivity expected below p (Lenzen & Trümper
1978; Brinkmann 1980)
Spectra are very close
to BB in shape in the
0.1 - 2 keV range, but
depressed wrt the BB at
Teff. Reduction factor
~ 2 - 3.
Turolla, Zane & Drake (2004)
Cagliari 25-26 maggio 2007
Spectra from Bare NS - II
Proper account for damping of free electrons
by lattice interactions (e-phonon scattering; Yakovlev
& Urpin 1980; Potekhin 1999)
Spectra deviate more
from BB. Fit in the
0.1 – 2 keV band still
acceptable. Features
may be present.
Reduction factors
higher.
Cagliari 25-26 maggio 2007
Turolla, Zane & Drake (2004)
Is RX J1856.5-3754 Bare ?



Fit of X-ray data in the 0.152 keV band acceptable
Radiation radius problem
eased
Optical excess may be
produced by reprocessing of
surface radiation in a very
rarefied atmosphere (Motch,
Does the atmosphere
keep the star surface
temperature ?
Zavlin & Haberl 2003; Zane, Turolla &
Drake 2004; Ho et al. 2006)

Details of spectral shape
(features, low-energy
behaviour) still uncertain
Cagliari 25-26 maggio 2007
What is the ion
contribution to the
dielectric tensor ?
(Van Adelsberg et al.
2005; Perez-Azorin,
Miralles & Pons 2005)
Long Term Variations in
RX J0720.4-3125

A gradual, long term
change in the shape of
the X-ray spectrum AND
the pulse profile (De Vries
et al 2004; Vink et al 2004)


Steady increase of TBB
and of the absorption
feature EW (faster
during 2003)
Evidence for a reversal
of the evolution in 2005
De Vries et al. 2004
Obs. Date
kTBB (eV)
EW (eV)
13-05-2000
86.6±0.4
-5.0
21/22-11-2001
86.5±0.5
+8.7
06/09-11-2002
88.3±0.3
-21.5
27/28-10-2003
91.3±0.6
-73.7
22/23-05-2004
93.8±0.4
-72.4
28-04-2005
93.5±0.4
-68.3
23-09-2005
93.2±0.4
-67.4
12/13-11-2005
92.6±0.4
-67.5
(Vink et al 2005)
Cagliari 25-26 maggio 2007
Cagliari 25-26 maggio 2007
A Precessing Neutron Star ?
Evidence for a periodic modulation in the spectral
parameters (Tbb, Rbb) but no complete cycle yet
 Phase residuals (coherent timing solution by Kaplan & Van Kerkwijk
2005) show periodic
behavior over a much longer
Haberl et al. 2006
timescale (> 10 yrs)
 Periods consistent within the errors, Pprec ~ 7.1-7.7 yr

(Haberl et al. 2006)
Cagliari 25-26 maggio 2007
A Simple Model
Precessing neutron star
 Blackbody emission from two “hot spots”
of different size and temperature
 A nearly aligned rotator seen almost
equator-on
 Non-antipodal spots, rather large
precession angle (~ 10o)

Haberl et al. 2006
A bare NS with a crustal field ?
Cagliari 25-26 maggio 2007
(Perez-Azorin et al 2006)
RRATs - I
11 sources detected in the Parkes
Multibeam survey (McLaughlin et al 2006)
 Burst duration 2-30 ms, interval 4 min-3 hr
 Periods in the range 0.4-7 s
 Period derivative measured in 3 sources:
B ~ 1012-1014 G, age ~ 0.1-3 Myr
 RRAT J1819-1458 detected in the X-rays,
spectrum soft and thermal, kT ~ 120 eV

(Reynolds et al 2006)
Cagliari 25-26 maggio 2007
RRATs - II
P, B, ages and X-ray properties of RRATs
very similar to those of XDINSs
 Estimated number of RRATs ~ 3-5 times
that of PSRs
 If τRRAT ≈ τPSR, βRRAT ≈ 3-5 βPSR
 βXDINS > 3 βPSR (Popov et al 2006)
 Are RRATs far away XDINSs ?

Cagliari 25-26 maggio 2007
Conclusions
Rather complex thermal maps required to explain XDINS
observations
 Progresses on the theoretical side but no self-consistent
model yet

– crustal fields (outside axial symmetry)
– phase transition and emission properties of condensed surface
– radiative transfer in the B > BQED regime

Find more sources
– is RX J1856.5-3754 unique ?
– Relationship with other NS populations:
 Pulsating XDINSs are quite likely strongly magnetized objects, B >
1013 G. A XDINS-magnetar connection ?
 XDINSs = RRATs ? Search for RRAT-like radio-emission from XDINSs
under way
Cagliari 25-26 maggio 2007
X-ray Spectra from
Magnetar Candidates
A Twist in the Field
Cagliari 25-26 maggio 2007
Soft Gamma Repeaters - I
Rare class of sources, 4 confirmed (+ 1): SGR
1900+14, SGR 1806-20, SGR 1627-41 in the
Galaxy and SGR 0526-66 in the LMC
 Strong bursts of soft γ-/hard X-rays: L ~ 1041
erg/s, duration < 1 s

Bursts from SGR 1806-20 (INTEGRAL/IBIS,,Gőtz et al 2004)
Cagliari 25-26 maggio 2007
Soft Gamma Repeaters - II





Much more energetic “Giant Flares” (GFs, L ≈
1045-1047 erg/s) detected from 3 sources
No evidence for a binary companion, association
with a SNR in one case
Persistent X-ray emitters, L ≈ 1035 erg/s
Pulsations discovered both in GFs tails and
persistent emission, P ≈ 5 -10 s
Huge spindown rates, Ṗ/P ≈ 10-10 ss-1 (Kouveliotou et
al. 1998; 1999)
Cagliari 25-26 maggio 2007
Anomalous X-ray Pulsars - I





Eight sources known (+ 1 transient):
1E 1048.1-5937, 1E 2259+586, 4U 0142+614,
1 RXS J170849-4009, 1E 1841-045, CXOU
010043-721134, AX J1845-0258, CXOU
J164710-455216 (+ XTE J1810-197)
Persistent X-ray emitters, L ≈ 1034 -1035 erg/s
Pulsations with P ≈ 5 -10 s
Large spindown rates, Ṗ/P ≈ 10-11 ss-1
No evidence for a binary companion,
association with a SNR in three cases
Cagliari 25-26 maggio 2007
Anomalous X-ray Pulsars - II

Bursts of soft γ-/hard X-rays
quite similar to those of
SGRs (AXPs much less active
though, bursts from two
sources only)
Woods &
Thompson
(2005)
Time (sec)
Cagliari 25-26 maggio 2007
A Tale of Two Populations ?
SGRs: bursting
X/γ-ray sources
AXPs: peculiar class
A Magnetar
of steady X-ray
sources
Single class of
objects
R < ctrise ≈ 300 km: a compact object
Pulsed X-ray emission: a neutron star
Cagliari 25-26 maggio 2007
Magnetars
Strong convection in a rapidly rotating (P
~ 1 ms) newborn neutron star generates a
very strong magnetic field via dynamo
action
 Magnetars: neutron stars with surface
field B > 10 BQED ~ 4 x1014 G (Duncan &
Thomson 1992; Thomson & Duncan 1993)
 Rapid spin-down due to magneto-dipolar
losses, P  1011 ( B / 1014 G) 2 P 1 ss 1

Cagliari 25-26 maggio 2007
Why magnetars ?

.LX  E rot  I
SGRs+AXPs
SGRs + AXPs
 No evidence for a companion star
High-field PSRs
 Spin down to present periods in ≈ 104
yrs requires B > 1014 G
PSRs
 Large measured spin-down rates
SPIN - DOWN ENERGY LOSS
 Quite natural explanation for the bursts
X-RAY LUMINOSITY

Cagliari 25-26 maggio 2007
SGRs and AXPs X-ray Spectra - I

0.5 – 10 keV emission well represented by
a blackbody plus a power law
AXP 1048-5937 (Lyutikov & Gavriil 2005)
SGR 1806-20 (Mereghetti et al 2005)
Cagliari 25-26 maggio 2007
SGRs and AXPs X-ray Spectra - II
kTBB ~ 0.5 keV, does not change much in
different sources
 Photon index Г ≈ 1 – 4, AXPs tend to be
softer
 SGRs and AXPs persistent emission is
variable (months/years)
 Variability mostly associated with the nonthermal component

Cagliari 25-26 maggio 2007
Hard X-ray Emission
INTEGRAL revealed
substantial emission in
the 20 -100 keV band
from SGRs and APXs
Mereghetti et al 2006
Hard power law tails
with Г ≈ 1-3, hardening
wrt soft X-ray emission
required in AXPs
Hard emission pulsed
Cagliari 25-26 maggio 2007
Hardness vs Spin-down Rate
Correlation between
spectral hardness
and spin-down rate
in SGRs and AXPs
(Marsden & White 2001)
Correlation holds
also for different
states within a
single source (SGR
1806-20, Mereghetti et al
2005; 1 RXS J1708494009, Rea et al 2005)
Harder X-ray
spectrum
Larger Spin-down rate
Cagliari 25-26 maggio 2007
SGR 1806-20 - I
SGR 1806-20 displayed a gradual
increase in the level of activity during
2003-2004 (Woods et al 2004; Mereghetti et al
2005)
Bursts / day
(IPN)
 enhanced burst rate
 increased persistent luminosity
20-60 keV flux (INTEGRAL IBIS)
The 2004 December 27 Event
Spring
2003
Autumn
2003
Spring
2004
Autumn
2004
Mereghetti et al 2005
Cagliari 25-26 maggio 2007
SGR 1806-20 - II






Four XMM-Newton observations (last on
October 5 2004, Mereghetti et al 2005)
Pulsations clearly detected in all observations
Ṗ ~ 5.5x10-10 s/s, higher than the “historical”
value
Blackbody component in addition to an
absorbed power law (kT ~ 0.79 keV)
Harder spectra: Γ ~ 1.5 vs. Γ ~ 2
The 2-10 keV luminosity almost doubled (LX ~
1036 erg/s)
Cagliari 25-26 maggio 2007
Twisted Magnetospheres – I
The magnetic field inside a magnetar is
“wound up”
 The presence of a toroidal component
induces a rotation of the surface layers
 The crust tensile strength resists
 A gradual (quasi-plastic ?) deformation of
the crust
 The external field twists up (Thompson,

Lyutikov & Kulkarni 2002)
Cagliari 25-26 maggio 2007
Thompson & Duncan 2001
Twisted Magnetospheres - II

TLK02 investigated
force-free magnetic
 
equilibria ( J  B  0)
 

   B   ( R,  ) B

A sequence of models
labeled by the twist
angle

 N  S  2 2
0
B d
B sin 
Cagliari 25-26 maggio 2007
Twisted Magnetospheres - III





Twisted magnetospheres are threaded by
currents
Charged particles provide large optical depth  rs
to resonant cyclotron scattering
Because c  c ( R, ) and Rcurrent  RNS , a powerlaw tail expected instead of an absorption line
Btwist  R  ( 2 p ,) Bdip  R 3 and Ptwist  Pdip
Both  rs and Ptwist increase with the twist
angle
Cagliari 25-26 maggio 2007
A Growing Twist in SGR 1806-20 ?
Evidence for spectral
hardening AND
enhanced spin-down
 and   L
 P
correlations
 Growth of bursting
activity
 Possible presence of
proton cyclotron line
only during bursts

All these features are
consistent with an
increasingly twisted
magnetosphere
Cagliari 25-26 maggio 2007
A Monte Carlo Approach
Follow individually a large sample of
photons, treating probabilistically their
Preliminary
investigation
(1D)
by Lyutikov
interactions
with
charged
particles
Basic ingredients:
&
Gavriil
(2005)
 Can
handle
general
(3D) geometries
 Space
andvery
energy
distribution
of the
More detailed modeling by Fernandez &
scattering
 Quite
easy toparticles
code, fast
Thompson (2006)

Same
for
the
seed
(primary)
photons
New,
Ideal up-to-dated
for purely scattering
media
code (Nobili,
Turolla,
 Scattering cross sections
Zane
Monte
Carlo techniques work well when
2007)
Nscat ≈ 1

Cagliari 25-26 maggio 2007
Generate a uniform
deviate 0<R<1
No
Select seed photon
(energy and direction)
No
Select particle from distribution
Transform photon
energyphoton,
and direction to ERF
Advance
   ln R ? 2
Escape Compute
?
photoncompute
energy after
depthscattering  '   /[1   (1  cos )]
Compute new photon direction
 
 
Yes
2
cos '
R '   d '
0
1
d ' d ( , k , k ' ) / d' /  d' d ( , k , k ' ) / d'
Transform back to LAB
Compute scattering
Yes
Store data
Cagliari 25-26 maggio 2007
4
Magnetospheric Currents
 
 Charges move along the field lines v B

Spatial distribution
1
p  1  B

n
4e  B
-3
 B p  RNS 
 14  only cm
 10 contribution
Electron
G  10 km 
 10 Mawellian
1D relativistic
at
 Particle motion characterized
Te centred at vbulk
16
 cB

 r vbulk
by a bulk
velocity, vbulk, and by a velocity spread Δv
(Beloborodov & Thompson 2006)

There may be e± in addition to e-p, but no
detailed model as yet
Cagliari 25-26 maggio 2007
Surface Emission
The star surface is
divided into patches
by a cos θ – φ grid
Each patch has its
own temperature to
reproduce different
thermal maps
Blackbody (isotropic)
emission
Cagliari 25-26 maggio 2007
Scattering Cross Sections - I
QED cross section available (Herold 1979, Harding &
Daugherty 1991) but unwieldy
 Non-relativistic (Thompson) cross section
(ε<mc2/γ ≈ 50 keV, B/BQED < 1)

Completely differenti al cross sections at resonance (ERF)
3r0 c
d

 (  c ) cos 2  cos 2  '
d' O O
8
3r0 c
d

 (  c )
d' X  X
8
3r0 c
d

 (  c ) cos 2 
d' O  X
8
3r0c
d

 (  c ) cos 2  '
d' X O
8
r0  e 2 / mc2 , c  eB / mc,  , ' angles between photon direction and particle
velocity before and after scattering
Cagliari 25-26 maggio 2007
Scattering Cross Sections - II

Because of charge motion resonance at
res

c

 (1   cos  )
For a given photon (energy ω, direction k)
  (c /  ) (c /  )    1
  res  1, 2 
(c /  ) 2   2
2
(1   i )
1
 (  res ) 
 (  i )

c i 1, 2  i    i
2
Cagliari 25-26 maggio 2007
2
Model Spectra
Model parameters: ΔΦN-S, Bpole, Te, vbulk
Surface emission geometry, viewing angle
hardness increases
Emission from entire star surface at Tγ=0.5 keV
1014 G
B  1014 G
B
 10
B G
10 G

N -S  0.7
14


14
B 
100.G
N -S
N -S7
 N -S  0.7
14
0.7
1015 G
twist
B  1015 G
increases
 N -S  1B.210
15
G
 N -S  1.2
Cagliari 25-26 maggio 2007
Conclusions & Future
Developments
Twisted magnetosphere model, within magnetar
scenario, in general agreement with observations
 Resonant scattering of thermal, surface photons
produces spectra with right properties
 Many issues need to be investigated further

– Twist of more general external fields
– Detailed models for magnetospheric currents
– More accurate treatment of cross section including QED
effects and electron recoil (in progress)
– 10-100 keV tails: up-scattering by (ultra)relativistic (e±)
particles ?
– Create an archive to fit model spectra to observations
(in progress)
Cagliari 25-26 maggio 2007