Proprietà Osservative delle Binarie X
Contenenti Stelle di Neutroni
Tiziana Di Salvo
Dipartimento di Scienze Fisiche ed Astronomiche, Università di Palermo
Via Archirafi 36- 90123 Palermo Italy
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
X-ray Binaries Classification
• High Mass X-ray Binaries: Young objects with a high
mass companion star (> 10 Msun) and (usually) High
magnetic field (about 1012 Gauss) neutron stars
Cyclotron lines
Ec
12
 11.6B12 (unit of 10 Gauss)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
X-ray Binaries Classification
• High magnetic field neutron stars in X-ray binaries
• Black Hole Candidates in X-ray binaries
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
X-ray Binaries Classification
• High magnetic field neutron stars in X-ray binaries
• Black Hole Candidates in X-ray binaries
• Low magnetic field neutron
stars in X-ray binaries:
temporal and spectral
analysis
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Caratteristiche generali
dell’accrescimento
• Energia liberata:
• Luminosità:
– Valore massimo dato dalla
luminosità di Eddington
• Efficienza:
– Valore tipico per una NS:
– Valore tipico per la
fusione nucleare:
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Caratteristiche generali
Range tipico di emissione
Emissione X e γ
• Modalità di
accrescimento:
– Accrescimento
tramite venti
stellari.(Binarie X di
alta massa)
– Accrescimento
tramite tracimazione
dal lobo di
Roche.(Binarie X di
bassa massa)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Mass Transfer in LMXBs: Roche
Lobe Overflow
Potenziale di Roche
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
X-ray pulsars
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
PL a~1
BB
Ecyc
Fe Lines
Wien Hump
DalNazionale
Fiume et
al. 1998
Scuola
di Dottorato
Cagliari, May 25 2007
Cyclotron lines
ωc 
eB
; ωn  nωc ;
γmc
ωn  mc
2
mc 2  2 nωc sin2 θ  1
sin2 θ
E c  11.6B12
12
(unit of 10 Gauss)
Meszaros, 1992
d  c
8 ln 2kT
cos

2
mc
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Coburn et al. 2002
Meszaros 1992
d  c
8 ln 2kT
cos
2
mc
Orlandini & Dal Fiume 2001
Santangelo et al. 2003
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Multiple Harmonics?
BeppoSAX has discovered or has evidence of
multiple harmonics in some of the sources, therefore
establishing the presence of second harmonic as a
rather common feature!
CEN X-3
4U1907
4U1626-67 (?)
There are however some
“extraordinary” observations….
VELA X-1 (?)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
The case of X0115+63
The EW of harmonics were
found to be larger than the
fundamental
Deep 2nd
harmonic
E1cyc @ 12.74 E2cyc @ 24.16 keV
E3cyc @ 35.74 E4cyc @ 49.5 keV
E5cyc @ 60. keV
Santangelo et al. 1999
Similar asymmetric variations
of the cyclotron line energy
(up to 8 keV) were observed
in Cen X-3 (Burderi et al.
2000). These variations of the
cyclotron line energy could be
explained by assuming an
offset (~ 0.1 RNS) of the
dipolar magnetic field with
respect to the neutron star
center. Offsets are also
suggested by an analysis of
pulse profiles (Leahy 1991).
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Low Mass X-ray Binaries
Close X-ray binaries:
Compact object:
NS with B < 1010 G
Companion star:
M < 1 MSUN
Accretion
disk
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Low Mass X-ray Binaries
Close X-ray binaries:
• Rich time variability, such as
twin QPOs at kHz frequencies
(from 400 to 1300 Hz, increasing
with increasing mass accretion
rate); kHz QPOs are thought to
reflect Keplerian frequencies at
the inner accretion disk.
Compact object:
NS with B < 1010 G
Companion star:
M < 1 MSUN
Accretion
disk
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
kHz QPOs
Possibly related to
Keplerian frequencies at
the inner edge of the
disk.
Two peaks are usually
present, whose
frequency increses when
the mass accretion rate
increases, with almost
constant separation.
Sco X-1
4U 1608
The peak separation is
almost equal to the NS
spin frequency (if known
from pulsations or burst
oscillations)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Low Mass X-ray Binaries
Close X-ray binaries:
• Rich time variability, such as
twin QPOs at kHz frequencies
(from 400 to 1300 Hz, increasing
with increasing mass accretion
rate); kHz QPOs are thought to
reflect Keplerian frequencies at
the inner accretion disk.
• Type-I X-ray bursts, with
nearly coherent oscillations in
the range 300-600 Hz (probably
the NS spin frequency).
• Some are transient, with
quiescent luminosities of 10321033 erg/s and outburst
luminosities of 1036-1038 erg/s.
Compact object:
NS with B < 1010 G
Companion star:
M < 1 MSUN
Accretion
disk
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Radio Pulsars
The energy lost in
electromagnetic radiation and
relativistic particle beam
comes from the rotational
energy of the pulsar, which
slows down.
.
.
Measuring P and P allows to derive m:
B ~ 108 Gauss for MSPs
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
The “classical” recycling scenario
Low mass X-ray
Binaries
8
Progenitors (Pspin >> 1ms)
9
B ~ 10 – 10 G
Low mass companion
(M ~ 1 Msun)
Millisecondofradio
End
products (Pspin
~ 1ms)
Accretion
mass from the
companion
causes
spin-up
Pulsars
8
9
B ~ 10 – 10 G
Low mass companion
(M ~ 0.1 Msun)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Confirmed by 7 (transient) LMXBs which
show X-ray millisecond coherent pulsations
Known accreting millisecond pulsars (in order of increasing
spin period):
IGR J00291+5934: Ps=1.7ms, Porb=2.5hr (Galloway et al. 2005)
XTE J1751-306:
Ps=2.3ms, Porb=42m (Markwardt et al. 2002)
SAX J1808.4-3658: Ps=2.5ms, Porb=2hr (Wijnands & van der Klis 1998)
HETE J1900.1-2455: Ps=2.7ms, Porb=1.4hr (Kaaret et al. 2005)
XTE J1814-338:
Ps=3.2ms, Porb=4hr (Markwardt et al. 2003)
XTE J1807-294:
Ps=5.2ms, Porb=40m (Markwardt et al. 2003)
XTE J0929-314:
Ps=5.4ms, Porb=43.6m (Galloway et al. 2002)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Rossi X-ray Timing Explorer
RXTE carries 5 Proportional Counter Units, which constitues the
Proportional Counter Array (PCA), with a large effective area of
about 6000 cm2 and very good time resolution (up to 1 msec),
working in the X-ray range (2-60 keV)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Spin Frequencies of AMSPs
All the spin
frequencies
are in the
rather
narrow range
between 200
and 600 Hz.
(From
Wijnands,
2005)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Light Curves of AMSPs
(X-ray Outburst of 2002)
All the 7 known
accreting MSPs
are transients,
showing X-ray
outbursts lasting
a few tens of
days.
Typical light
curves are from
Wijnands (2005)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Disc – Magnetic Field Interaction
Disc Pressure
.
proportional to M
Magnetic Pressure
Proportional to B2
Rm = 10 B84/7 dotM-8-2/7 m1/7 km
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Accretion conditions
(Illarionov & Sunyaev 1975)
Rco = 15 P–32/3 m1/3 km
RLC = 47.7 P–3 km
Accretion regime
R(m) < R(cor) < R(lc)
Pulsar spin-up
• accretion of matter onto NS (magnetic poles)
• energy release L = dotM G M/R*
• Accretion of angular momentum dL/dt = l dotM
where l = (G M Rm)1/2 is the specific angular momentum at Rm
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Pulsars
spin up
The accreting matter transfers its
specific angular momentum (the
Keplerian AM at the accretion
radius) to the neutron star:
L=(GMRacc)1/2
2
The process goes on until the
pulsar reaches the keplerian
velocity at Racc (equilibrium
period); Pmin when Racc = Rns
Pmin << 1 ms
for most EoS
The conservation of AM tells us how much mass is
necessary to reach Pmin starting from a non-rotating
NS. Simulations give ~0.3Msun (e.g. Lavagetto et al. 2004)
During the LMXB phase ~1 Msun is lost by the companion
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Propeller phase
.
M
Propeller regime
R(cor) < R(m) < R(lc)
•
•
•
•
centrifugal barrier closes (B-field drag stronger than gravity)
matter accumulates or is ejected from Rm
accretion onto Rm: lower gravitational energy released
energy release L = e GM(dM/dt)/R*, e = R*/2 Rm
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Rotating magnetic dipole phase
.
M
Radio Pulsar regime
Rm > RLC
• no accretion, radio pulsar
emission
• disk matter swept away
by pulsar wind and pressure
• Energy release given by the
Larmor formula:
L = 2 R6/3c3 B2 (2 p / P)4
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Timing Technique
• Correct time for orbital motion delays:
t @ tarr – x sin 2p/PORB (tarr –T*)
where x = a sini/c is the projected semimajor axis in light-s and
T* is the time of ascending node passage.
• Compute phase delays of the pulses ( -> folding pulse profiles)
with respect to constant frequency
• Main overall delays caused by spin period correction (linear term)
and spin period derivative (quadratic term)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Accretion Torque modelling
Bolometric luminosity L is observed to vary with time during an
outburst. Assume it to be a good tracer of dotM: L= (GM/R)dotM
with 1, G gravitational constant, M and R neutron star mass and
radius
Matter accretes through a Keplerian disk truncated at magnetospheric
radius Rm  dotM-a. In standard disk accretion a =2/7
Matter transfers to the neutron star its specific angular momentum
l = (GM Rm)1/2 at Rm, causing a torque t = l  dotM.
Possible threading of the accretion disk by the pulsar magnetic field
is modelled here as in Rappaport et al. (2004), which gives the total
accretion torque:
t = dotM l – m2 / 9 Rco3
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
IGR J00291: the fastest accreting MSP
Porb = 2.5 h
ns = 600 Hz
8
0
dotn = 8.5(1.1) x 10-13 Hz/s (c2/dof = 106/77)
(Burderi et al. 2007, ApJ; Falanga et al. 2005, A&A)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Conclusions: Spin-up in IGR J00291
IGR J00291+5934 shows a strong spin-up: ndot = 1.2 x 10-12
Hz/s, which indicates a mass accretion rate of dotM = 7  10-9
M yr-1.
Comparing the bolometric luminosity of the source as derived from
the X-ray spectrum with the mass accretion rate of the source
as derived from the timing, we find a good agreement if we place
the source at a quite large distance between 7 and 10 kpc.
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Spin down in the case of XTE J0929-314
Porb = 44 min
ns = 185 Hz
Spin down in XTE
J0929, the slowest
among accreting MSPs.
During the only outburst
of this source observed
by RXTE.
Measured spin-down
rate:
dotn = -5.5 10-14 Hz/s
Estimated magnetic
field: B = 5 x 108 Gauss
(Di Salvo et al.
2007)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Results for 6 of the 7 known LMXBs which
show X-ray millisecond coherent pulsations
Results for accreting millisecond pulsars (in order of
increasing spin period):
IGR J00291+5934: Ps=1.7ms, Porb=2.5hr SPIN UP
XTE J1751-306:
Ps=2.3ms, Porb=42m SPIN UP
SAX J1808.4-3658: Ps=2.5ms, Porb=2hr
SPIN UP (SPIN DOWN)
HETE J1900.1-2455: Ps=2.7ms, Porb=1.4hr ??
XTE J1814-338:
Ps=3.2ms, Porb=4hr
SPIN DOWN
XTE J1807-294:
Ps=5.2ms, Porb=40m SPIN UP
XTE J0929-314:
Ps=5.4ms, Porb=43.6m SPIN DOWN
These exclude GR as a limiting spin period mechanism
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Spettri dei Black Holes Candidates
in X-ray Binaries
Stati hard o low
•Sono fittati da:
•Legge di potenza
G = 1.4 – 1.9
•alle alte energie, con cutoff
a circa 100 KeV.
•Corpo nero alle basse
energie (circa 0.1 keV)
•Luminosità < 0.1 LEDD.
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Spettri dei BHXB
Stati soft o high
•Sono fittati da:
•Corpo nero alle basse
energie (temp. kT circa 0.51KeV) dominante rispetto alla
legge di potenza.
•Legge di potenza:
G = 2 – 3
alle alte energie senza
evidenza di cutoff fino a
energie dell’ordine di circa
511KeV
•Luminosità > 0.2-0.3LEDD.
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Spettri dei BHXB
Stati molto alti
Stati high o soft
Stati intermedi
Stati low o hard
Stati di quiescenza
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Fe K-shell Line and Reflection
Cygnus X-1: BeppoSAX Broad Band (0.1 – 200 keV) Spectrum
Di Salvo et al. (2001)
MECS
MECS
Schema della regione di emissione
HPGSPC
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Spettri dei BHXB: Componente di
riflessione Compton
• Componente di riflessione è dovuta all’incidenza
della componente hard di Comptonizzazione sul
disco di accrescimento.
– Energia dei fotoni incidenti inferiore a circa 15 KeV:
predomina il fotoassorbimento
righe di
emissione e bordi di assorbimento (sprattutto relativi
al Fe).
– Energia dei fotoni incidenti maggiore di 15KeV:
predomina la riflessione Compton
larga
“gobba” tra circa 10 e 50 KeV.
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Fe K-shell Line and Reflection
Important information can
be obtained from the iron
line profile.
Doppler and relativistic
effects due to the
keplerian motion in the
disk modify the profile
(double peak, Doppler
boositng, Gravitational
redshift).
From high resolution
spectra we can obtain info
on the inner disk radius
and inclination of the disk.
HPGSPC
Iron line
profile
E0
E
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Self consistent models of Compton
reflection and associated iron line
narrow
Reflection from
ionized matter
Reflection from
Neutral matter
smeared
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
High resolution spectroscopy of
massive BHs: MCG-6-30-15
XMM observation
of the iron line
region in MCG-630-15 taken in
2001. The red wing
extends to less
than 4 keV,
indicating an inner
radius of less than
6 G M / C2.
Spinning black
hole? (a > 0.93)
Fabian et al. 2002)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Spettri di LMXB contenenti NS
• Forti analogie con gli spettri di BHXBs:presenza
di stati hard e soft.
• Differenza nella temperatura della nube
comptonizzante.
Raffreddamento extra dovuto alla superficie
della NS.
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Neutron star low mass x-ray
binaries classification
sources:
- Late Atoll
type mass
donor (usually K-M star) or white dwarf
Lx NS
~ 0.01-0.1
- Accreting
primary: L(Edd)
fast spinning (2-3 ms), weakly magnetic
type I X-ray
burststype I X-ray bursts,
- Characteristic
phenomena:
transients
fast (> some
100 Hz)
quasi periodic oscillations in the X-ray flux
- Useful classification: Z-sources, Atoll sources
Z-sources:
Lx ~ 0.1-1.0 L(Edd)
all persistent
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Atoll sources: energy spectra
- Soft component (few keV)
(blackbody or disk-blackbody model)
- Power law with exponential
cutoff (5-20 keV): Thermal
Comptonization.
- Soft and hard states:
in the hard state the cutoff shifts
to higher energies (up to > 200 keV)
- Iron emission (fluorescence) line
at ~6.4 keV
- Evidence for a reflection component
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
X-ray
energy
spectra
of Z sources
X-ray
energy
spectra
up to up
to
~20keV
keV
~20
Two components needed (at least):
- Eastern model (Mitsuda et al. 1984):
multitemperature-blackbody + blackbody spectra
(disk emission with kT = a R-3/4, and NS surface
comptonized emission)
- Western model (White et al. 1986):
blackbody + Comptonized blackbody spectra
(NS or disk emission, and disk emission modified by
Comptonization in a hotter region).
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Fe K-shell Line in Neutron Star Low
Mass X-ray binaries
Chandra observation of the LMXB/atoll source 4U 170544 (Di Salvo et al. 2005, ApJ Letters)
CC Mode 5 ks
TE Mode 25 ks
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Fe K-shell Line in NS LMXBs
TE Mode 25 ks
Soft Comptonization model for the
X-ray continuum plus 3 narrow lines
and a broad Fe line:
• E1 = 1.476 keV, s1 = 17 eV
(ID: Mg XII Ly-a, 1.473 keV)
• E2 = 2.03 keV, s2 = 28 eV
(ID: Si XIV Ly-a, 2.006 keV)
• E3 = 2.64 keV, s3 = 40 eV
(ID: S XVI Ly-a, 2.6223 keV)
• E_Fe = 6.54 keV, sFe = 0.51 keV
EW = 170 eV
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Fe K-shell Line in Neutron Star Low
Mass X-ray binaries
Fitting the iron line profile
with a disk (relativistic) line
we find:
TE Mode 25 ks
Hints of a
doublepeaked line
profile
• E_Fe = 6.40 keV
• Rin = 7-11 Rg (15-23 km)
• Inclination = 55 – 84 deg
Alternatively, Compton
broadening in the external
parts of the Comptonizing
corona (s = 0.5 implies
t = 1.4 for kT = 2 keV)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Hard X-ray Emission in LMXBs:
INTEGRAL/RXTE Observations of Sco X-1
Soft Comptonization:
kT (seed) = 1.3 keV (fixed)
kTe = 4.7 keV
t = 2.4
ISGRI
SPI
Hard Power law:
PI = 2.3
kT > 200 keV
Flux
10-9
Flux
10-9
(20 – 40 keV) = 5.9
ergs/cm2/s
(40 – 200 keV) = 0.33
ergs/cm2/s
Di Salvo et al. (2005, ApJL)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
INTEGRAL/RXTE Observations of
Sco X-1
Lowest dotM
Hard power law
Soft Comptonization
PI = 2.7
kT > 290 keV
Flux (40 – 200 keV) =
0.48 10-9 ergs/cm2/s
Di Salvo et al. (2005, ApJL)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
INTEGRAL/RXTE Observations
of Sco X-1
Highest dotM
PI = 2.7 (fixed)
Flux (40 – 200 keV) =
0.06 10-9 ergs/cm2/s
Di Salvo et al. (2005, ApJL)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
NS hard tails: analogy with BHCs
- BHCs in low state: extended
power law with high energy
cutoff (plus faint very soft and
reflection components seen
occasionally)
Similar to hard state Atolls
(Grove et al. 1998)
- BHCs in IS/VHS: very soft
thermal component plus power
law without high energy cutoff
up to 1 MeV
Similar to Z-sources in HB-NB
- BHCs in HS: very soft
thermal component.
Similar to Z-sources in NB-FB.
Scuola Nazionale di Dottorato
Hard X-ray NS/BHC indicators are uncertain
at least
Cagliari, May
25 2007!
Geometry and Models for hard tails in
NS binaries
Origine della legge di potenza negli stati soft di
BHXB e LMXBs:
Ipotesi I: comptonizzazione
termica
Ipotesi II: (comptonizzazione
non termica) caduta radiale
della materia in corrispondenza
di LSO.
Ipotesi III:
(comptonizzazione non
termica) Jet relativistici
Temperature
altissime
Non può spiegare
l’hard tail nelle NS
LMXB
•Distribuzione a legge di
potenza.
•Evidenze radio in BH e NS.
•Intensità radio maggiore più
è intensa la componente
hard.
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Geometry and Models for hard
tails in NS binaries
Jet: hard tail ?
Disk: soft X-rays
Comptonising
corona: hard tail ?
- Bulk motion Comptonisation converging
radial or disk inflow (Titarchuk & Zannias
1998; Luarent & Titarchuk 1999;
Psaltis 2001)
Inflow in Z-sources is strongly affected by
radiation from the NS
- Comptonisation by thermal e- in a corona
predicts high energy cutoff
- Comptonisation (or synchrotron
radiation) by non-thermal e- in a
(non-confined) corona or relativistic jets
(Zdziarski 2000; Vadawale et al. 2001;
Markoff et al. 2001)
power law spectra can extend up to very
high energies
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
The radio connection: other NS
binaries
- Radio jets: likely a common phenomenon also in X-ray binaries
Class
Persistent BHCs
Transient BHCs
NS Z-sources
NS Atoll sources
Fraction as radio sources
4/4
~15/35
6/6
~5/100
(Fender 2001)
- In Z sources (e.g. GX 17+2) radio flaring in the HB (i.e. low accretion
rates)
- Fewer searches (and detections) in Atoll sources
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
The radio jets and states of NS
X-ray binaries
- Radio emission
(probably due to
jets) is anticorrelated with
the mass
accretion rate
(Fender 2001)
-Similarity with
the hard X-ray
tails!
More simultaneous hard X-ray /
radio observations are needed
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
The end
Thank you very much!
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Threaded disc model
Dragging of the field line: a Bf
component is generated
Bz
Bf
W
Bz = h m2 / R3 ,
h<= 1 screening factor
Bf is amplificated by
differential rotation up to:
Bf = g / a [(W - WK)/WK]/Bz
(a = SS viscosity, g >= 1)
Where the amplification is limited by turbulent diffusion
(Wang 1995)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Threaded disc model
Yet, we do not have a self-consistent disc solution for this
case of disk - magnetic field interaction.
Possible threading of the accretion disk by the pulsar
magnetic field gives a negative torque which is modelled
here as in Rappaport et al. (2004):
tmag = m2 / 9 Rco3
A self consistent solution of the Threaded Disc is
required!
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Results for IGR J00291+5934
In a good approximation the X-ray flux is observed to linearly
decrease with time during the outburst:
dotM(t) = dotM0 [1-(t – T0)/TB], where TB = 8.4 days
Assuming Rm  dotM-a. (a = 2/7 for standard accretion disks; a = 0
for a constant accretion radius equal to Rc; a = 2 for a simple
parabolic function), we calculate the expected phase delays vs. time:
f = - f0 – n0 (t-T0) – ½ dotn0 (t – T0)2 [1 – (2-a) (t-T0)/6TB]
We have calculated a lower limit to the mass accretion rate (obtained
for the case a = 0 and no negative threading (m = 1.4, I45 = 1.29)
dotM = 5.9 10-10 dotn–13 I45 m-2/3 Msun/yr
Measured dotn–13= 11.7, gives a lower limit of dotM = (7+/-1) 10-9
Msun/yr, corresponding to Lbol = 7 x 1037 ergs/s
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Distance to IGR J00291+5934
The timing-based calculation of the bolometric luminosity is one order
of magnitude higher than the X-ray luminosity determined by the Xray flux and assuming a distance of 5 kpc !
The X-ray luminosity is not a good tracer of dotM, or the distance to
the source is quite large (15 kpc, beyond the Galaxy edge in the
direction of IGR J00291 !)
We argue that, since the pulse profile is very sinusoidal, probaly we
just see only one of the two polar caps, and possibly we are missing
part of the X-ray flux..
In this way we can reduce the discrepancy between the timingdetermined mass accretion rate and observed X-ray flux by about a
factor of 2, and we can put the source at a more reliable distance of
7.4 – 10.7 kpc
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
The Strange case of XTE J1807
The outburst of February 2003
(Riggio et al. 2007, in preparation)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
But… There is order beyond the chaos!
The key idea:
Harmonic decomposition of the pulse profile
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Timing of the second harmonic
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Back to the fundamental
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Positional Uncertainties of
XTE J1807 (0.6’’)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
SAX J1808: the outburst of 2002
(Burderi et al. 2006, ApJ Letters)
Phase Delays of
The First Harmonic
Phase Delays of
The Fundamental
Spin-up:
Porb = 2 h
n = 401 Hz
dotn = 4.4 10-13 Hz/s
Spin-down at the end of the outburst:
dotn = -7.6 10-14 Hz/s
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
SAX J1808.4-3658: Pulse Profiles
Folded light curves
obtained from the 2002
outburst, on Oct 20
(before the phase shift
of the fundamental) and
on Nov 1-2 (after the
phase shift), respectively
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
SAX J1808.4-3658: phase shift and
X-ray flux
Phase shifts of
the fundamental
probably caused
by a variation of
the pulse shape
in response to
flux variations.
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Discussion of the results for SAX J1808
In a good approximation the X-ray flux is observed to decrease
exponentially with time during the outburst:
dotM(t) = dotM0 exp[(t – T0)/TB], where TB = 9.3 days
derived from a fit of the first 14 days of the light curve.
Assuming Rm  dotM-a. (with a = 0 for a constant accretion radius
equal to Rco), we calculate the expected phase delays vs. time:
f = - f0 – B (t-T0) – C exp[(t-T0)/TB] + ½ dotn0 (t – T0)2
where B = n0 + C/TB and C = 1.067 10-4 I45-1 P-31/3 m2/3 TB2 dotM-10
(the last term takes into account a possible spin-down term at the
end of the outburst).
We find that the best fit is constituted by a spin up at the beginning
of the outburst plus a (barely significant) spin down term at the end
of the outburst.
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Discussion of the results for SAX J1808
Spin up: dotn0 = 4.4 10-13 Hz/s corresponding to a mass accretion
rate of dotM = 1.8 10-9 Msun/yr
Spin-down: dotn0 = -7.6 10-14 Hz/s
In the case of SAX J1808 the distance of 3.5 kpc (Galloway &
Cumming 2006) is known with good accuracy; in this case the mass
accretion rate inferred from timing is barely consistent with the
measured X-ray luminosity (the discrepancy is only about a factor 2),
Using the formula of Rappaport et al. (2004) for the spin-down at
the end of the outburst, interpreted as a threading of the accretion
disc, we find: m2 / 9 Rco3 = 2 p I dotnsd from where we evaluate the
NS magnetic field: B = (3.5 +/- 0.5) 108 Gauss: (in agrement with
previous results, B = 1-5 108 Gauss, Di Salvo & Burderi 2003)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Timing of XTE J1751
As in the case of SAX J1808,
the X-ray flux of XTE J1751
decreases exponentially with
time (TB = 7.2 days).
The best fit of the phase
delays corresponds to Rm 
dotM-a.wth a = 2/7, and gives
dotn0 = 6.3 10-13 Hz/s and
dotM0 = (3.4 – 8.7) 10-9
Msun/yr.
Comparing this with the X-ray
flux from the source, we
obtain a distance of 9.7–15.8
kpc (or 7-8.5 kpc using the
same arguments used for IGR
J00291).
(Papitto et al. 2007, in preparation)
Porb = 42 min
ns = 435 Hz
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Spin down in the case of XTE J1814
Papitto et al. 2007, MNRAS
Phase Delays of
The Fundamental
Phase Delays of
The First Harmonic
Spin-down:
dotn = -6.7 10-14 Hz/s
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Phase residuals anticorrelated to
flux changes in XTE J1814-338
Modulations of the phase
residuals, anticorrelated
with the X-ray flux, and
possibly caused by
movements of the
footpoints of the magnetic
field lines in response to
flux changes
Post fit residuals of the
Fundamental
Post fit residuals of the
harmonic
Estimated magnetic field:
B = 8 x 108 Gauss
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
XTE J0929-314: the most puzzling AMSP
The mass accretion rate is varying with time, while instead the phase
delays clearly indicate a constant (or at most decreasing) spin-down
rate of the source. We therefore assume
nspin-up << -nspin-down = 5.5 x 10-14 Hz /s
Assuming that the spin-up is at least a factor of 5 less than the spindown, we find a mass accretion rate at the beginning of the outburst
of dotM < 6 x 10-11 Msun/yr, which would correspond to the quite low
X-ray luminosity of Lbol < 6 x 1035 ergs/s.
Comparing this with the X-ray flux of the source we find an upper
limit to the source distance of about 1.2 kpc (too small !! Although this
is a high latitude source)
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Conclusions: Spin-up
XTE J1807-294 shows a noisy fundamental and a clear spin-up in
the second harmonic: ndot = (1 – 3.5) 10-14 Hz/s. No clear
diagnostic is possible, spin-up and spin-down may be both present.
XTE J1751-306 shows a strong spin-up: ndot = 6.3 x 10-13 Hz/s,
which indicates a mass accretion rate of dotM = (3.4 – 8.7)  10-9
M yr-1.
Comparing the bolometric luminosity of the source as derived from
the X-ray spectrum with the mass accretion rate of the source
as derived from the timing, we find a good agreement if we place
the source at a quite large distance between 7 and 8.5 kpc.
Scuola Nazionale di Dottorato
Cagliari, May 25 2007
Conclusions: Spin-down
XTE J1814-338 shows noisy fundamental and harmonic phase
delays, and a strong spin-down: ndot = -6.7 x 10-14 Hz/s, which
indicates a quite large magnetic field of B = 8  108 Gauss.
XTE J0929-314 shows a clear spin-down of ndot = -5.5 x 10-14
Hz/s, which indicates a magnetic field of B = 4-5  108 Gauss.
Imposing that the spin-up contribution due to the mass accretion
is negligible, we find however that the source is at the very close
distance of about 1 kpc. Independent measures of the distance to
this source will give important information on the torque acting on
the NS and its response.
Scuola Nazionale di Dottorato
Cagliari, May 25 2007