Cool discs, hot flows

1
Timing of Accreting Millisecond Pulsars a Review
T. Di Salvo(1) L. Burderi (2), A. Riggio(2),
A. Papitto(3), M.T. Menna(3) (1)
 Dipartimento di Scienze Fisiche ed Astronomiche,
Università di Palermo Via Archirafi 36- 90123
Palermo Italy (2)  Università degli Studi di
Cagliari Dipartimento di Fisica SP
Monserratu-Sestu KM 0.7, 09042 Monserrato
Italy (3) I.N.A.F.- Osservatorio Astronomico di
Roma via Frascati 33, 00040 Monteporzio Catone
(Roma) Italy
Funasdalen (Sweden) 25 30 March 2008
2
Astronomer at work
3
The classical recycling scenario
Low mass X-ray Binaries B 108 109 G Low
mass companion (M 1 Msun)
Progenitors (Pspin gtgt 1ms)
Accretion of mass from the companion causes
spin-up
Millisecond radio Pulsars B 108 109 G Low
mass companion (M 0.1 Msun)
End products (Pspin 1ms)
4
The Recycling Scenario
Field Decay
Radio PSR off
Accretion
Radio PSR on
5
Confirmed by 10 (transient) LMXBs which show
X-ray millisecond coherent pulsations
Known accreting millisecond pulsars (in order of
increasing spin period) IGR J002915934
Ps1.7ms, Porb2.5hr (Galloway et al. 2005) Aql
X-1 () Ps1.8ms, Porb19hr (Casella et
al. 2007) SAX J1748.9-2021 Ps2.3ms,
Porb8.8hr (Altamirano et al. 2007) XTE
J1751-306 Ps2.3ms, Porb42m
(Markwardt et al. 2002) SAX J1808.4-3658
Ps2.5ms, Porb2hr (Wijnands van der Klis
1998) HETE J1900.1-2455 Ps2.7ms, Porb1.4hr
(Kaaret et al. 2005) XTE J1814-338
Ps3.2ms, Porb4hr (Markwardt et al.
2003) XTE J1807-294 Ps5.2ms, Porb40m
(Markwardt et al. 2003) XTE J0929-314
Ps5.4ms, Porb43.6m (Galloway et al.
2002) SWIFT J1756.9-2508 Ps5.5ms, Porb54m
(Markwardt et al. 2007)
6
Light Curves of 5 AMSPs
X-ray Outburst of 2002
All the 10 known accreting MSPs are transients,
showing X-ray outbursts lasting a few tens of
days. Typical light curves are from Wijnands
(2005)
7
Whereare they?(reconstruction of AMSPs
position in the Galaxy)?
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Disc Magnetic Field Interaction
.
Rm 10 B84/7 dotM-8-2/7 m1/7 km
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DiscMagnetic Field Interaction?
Magnetic Pressure B2
Disc Ram Pressure Mdot
Rm 10 B84/7 Mdot-8-2/7 m1/7 km
Rco 15 P32/3 m1/3 km RLC 47.7 P3 km
10
Accretion conditions
(Illarionov Sunyaev 1975)
Accretion regime R(m) lt R(cor) lt R(lc) Pulsar
spin-up

• accretion of matter onto NS (magnetic poles)
• energy release L dotM G M/R
• Accretion of angular momentum tacc dL/dt l
  dotM
• where l (G M Rm)1/2 is the specific angular
  momentum at Rm

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Propeller phase
Propeller regime R(cor) lt R(m) lt R(lc) No
spin-down can be observed while accreting onto
the NS

• 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 from the disc L e GM(dM/dt)/R,
  e R/2 Rm

12
Threaded disc model
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!
13
Threaded disc model
Magnetospheric radius
Total Torque on the NS Rappaport et al. 2004
Pos. Threading Torque Zone
Neg. Threading Torque Zone
Romanova et al. 2004
Corotation radius
14
Timing Technique

• Correct time for orbital motion delays
  
  t ? tarr x sin ?2?/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 ( -gt folding
  pulse profiles) with respect to constant
  frequency
• If a good orbital solution is available small
  delays caused by orbital uncertainties, that
  average to zero over Porb ltlt Tobs, propagated as
  further uncertainties on the phase delays.
• Main overall delays caused by spin period
  correction (linear term) and spin period
  derivative (quadratic term)
• Uncertainties on the source coordinates
  (producing a modulation of the phase delays over
  1 yr) can be considered as systematic
  uncertainties on the linear and quadratic term

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Timing Technique
Photon Arrival Times reported to the Solar System
barycenter.
Photon Arrival Times corrected for the source
orbital motion t tarr x sin(2 p / PORB (tarr
T))? where x a sini/c is the projected
semi-major axis in lt-sec and T is the ascending
node time transit.
Compute phase delays of the pulses ( -gt folding
pulse profiles) with respect to constant
frequency.
Sum in quadrature statistical errors on pulse
arrival time delays to the errors due to errors
on the orbital parameters used.
Main trends in Pulse Arrival Time delays are due
to 1) Orbital parameters residuals (sinusoidal
terms)? 2) spin frequency correction (linear
term)? 3) spin frequency derivaties (quadratic
and/or greater terms)? 4) Timing noise (e.g.
fluctuations in the accretion flow)?
The uncertanties ??pos on the source position
can not be taken into account on the same way
because are a systematic effect and will be
discussed later.
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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-?.
In standard disk accretion ? 2/7
Matter transfers to the neutron star its specific
angular momentum l (GM Rm)1/2 at Rm, causing
a torque ? 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 I dotW dotM l m2 / 9
Rco3
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Accretion Torque modelling
where d?(t)/dt must be derived by the
accretion theory (e.g. exponentially decresing
with time with the same decaying time of the
X-ray flux).
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IGR J00291 the fastest accreting MSP
 
Porb 2.5 h ns 600 Hz
0
8
dotn 8.5(1.1) x 10-13 Hz/s (c2/dof
106/77) (Burderi et al. 2007, ApJ Falanga et
al. 2005, AA)
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Spin-up in IGR J00291
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
IGR J002915934 shows a strong spin-up dotn0
1.2 x 10-12 Hz/s (at the beginning of the
outburst, assuming a linear decay of the X-ray
flux and hence of the spin-up rate), which
indicates a mass accretion rate of dotM0 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 an agreement if we place the
source at a quite large distance between 7 and 10
kpc.
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Timing of XTE J1751
The X-ray flux of XTE J1751 decreases
exponentially with time (TB 7.2 days). The
best fit of the phase delays 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 7-8.5 kpc (using
the same arguments used for IGR J00291).
(Papitto et al. 2007, MNRAS)
Porb 42 min ns 435 Hz
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Spin down in the case of XTE J0929-314
Spin down in XTE J0929, (almost) 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
Porb 44 min ns 185 Hz
(Galloway et al. 2002 Di Salvo et al.
2007, arXiv0705.0464)
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Spin down in the case of XTE J1814
Papitto et al. 2007, MNRAS
Phase Delays of The Fundamental
Phase Delays of The First Harmonic
Porb 4 hr ns 310 Hz
Spin-down dotn -6.7 10-14 Hz/s
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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
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The Strange case of XTE J1807-294
The outburst of February 2003 (Riggio et al. 2007
MNRAS, Riggio et al. 2008 ApJ)
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But There is order beyond the chaos!
The key idea Harmonic decomposition of the pulse
profile The source shows a weak spin-up at a
rate of dotn 2.1 10-14 Hz/s. In this case
using dotM(t) decreasing exponentially with time
gives an improvement of the fit with respect to a
simple parabola (dotM const).
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Back to the fundamental
From the spin frequency derivative we can
calculate the mass accretion rate to the NS, that
is 4 x 10-10 Msun/yr Corresponding to a
luminosity of 4.7 x 1036 ergs/cm2/s. Comparing
this to the observed X-ray flux of the source, we
infer a distance to the source of about 4 kpc.
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Positional Uncertainties of XTE J1807 (0.6)
Major source of error on the frequency derivative
given by the uncertainty in the source position.
From a scan of the chandra error box we find
that the frequency derivative must be in the
range (13.5) 10-14 Hz/s
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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 dotn 4.4 10-13 Hz/s
Porb 2 h n 401 Hz
Spin-down at the end of the outburst dotn -7.6
10-14 Hz/s
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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
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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.
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Discussion of the results for SAX J1808
Spin up dotn0 4.4 10-13 Hz/s corresponding to
a mass accretion rate of dotM0 1.8 10-9 Msun/yr
Spin-down dotn0 -7.6 10-14 Hz/s (see
Hartman et al. 2007 for a different
interpretation)
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 Rc3 2 p 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)
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Orbital Solutions and Variation of the Periastron
Time Passage
dot Porb (3.42 /- 0.05) 1012 s/s (Di Salvo
et al. 2007 Hartman et al. 2007 See next talk by
Luciano Burderi)
Orbital cicles
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Results for 6 of the 8 known LMXBs which show
X-ray millisecond coherent pulsations
Results for accreting millisecond pulsars (in
order of increasing spin period. See Di Salvo et
al. 2007 for a review) IGR J002915934
Ps1.7ms, Porb2.5hr SPIN UP (Burderi et al.
2007) XTE J1751-306 Ps2.3ms, Porb42m
SPIN UP (Papitto et al. 2007) SAX J1748.9-2021
Ps2.3ms, Porb8.8hr ??? (Altamirano et al.
2007) SAX J1808.4-3658 Ps2.5ms, Porb2hr
SPIN UP ( SPIN DOWN, Burderi et al. 2006,
but see also Hartman et al. 2007) XTE J1814-338
Ps3.2ms, Porb4hr SPIN DOWN (Papitto et
al. 2007) XTE J1807-294 Ps5.2ms, Porb40m
SPIN UP (Riggio et al. 2007) XTE J0929-314
Ps5.4ms, Porb43.6m SPIN DOWN
(Galloway et al. 2002)
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Thank you very much!
We conclude that spin-up dominates in sources
with relatively high mass accretion rate
(producing fast pulsars) and spin down dominates
in sources with relatively strong magnetic field
(producing slow pulsars). See a review of these
results in Di Salvo et al. 2007 (arXiv0705.0464)
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(No Transcript)
36
Timing Technique

• Correct time for orbital motion delays
  
  t ? tarr x sin ?2?/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 ( -gt folding
  pulse profiles) with respect to constant
  frequency
• If a good orbital solution is available small
  delays caused by orbital uncertainties, that
  average to zero over Porb ltlt Tobs, propagated as
  further uncertainties on the phase delays.
• Main overall delays caused by spin period
  correction (linear term) and spin period
  derivative (quadratic term)
• Uncertainties on the source coordinates
  (producing a modulation of the phase delays over
  1 yr) can be considered as systematic
  uncertainties on the linear and quadratic term

37
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-?.
In standard disk accretion ? 2/7
Matter transfers to the neutron star its specific
angular momentum l (GM Rm)1/2 at Rm, causing
a torque ? l ? dotM.
Possible threading of the accretion disk by the
pulsar magnetic field is modelled here as in
Rappaport et al. (2004, but see next talk by
Burderi) t dotM l m2 / 9 Rc3
38
Results for IGR J002915934
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-?. (? 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 Dn0 (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 dotn13 I45 m-2/3
Msun/yr
Maesured dotn13 11.7, gives a lower limit of
dotM (7/-1) 10-9 Msun/yr, corresponding to
Lbol 7 x 1037 ergs/s
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Distance to IGR J002915934
The timing-based calculation of the bolometric
luminosity is one order of magnitude higher than
the X-ray luminosity determined by the X-ray 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 timing-determined 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
40
The Strange case of XTE J1807
The outburst of February 2003 (Riggio et al.
2007, submitted)
41
The Strange case of XTE J1807
The outburst of February 2003 (Riggio et al.
2007, submitted)
42
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-?. (with ? 0 for a constant
accretion radius equal to Rc), 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 Dn0 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.
43
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 ltlt
-nspin-down 5.5 x 10-14 Hz /s Assuming that
the spin-up is at least a factor of 5 less than
the spin-down, we find a mass accretion rate at
the beginning of the outburst of dotM lt 6 x 10-11
Msun/yr, which would correspond to the quite low
X-ray luminosity of Lbol lt 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 !!)
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Conclusions Spin-up
IGR J002915934 shows a strong spin-up ndot
1.2 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.
SAX J1808.4-3658 shows a noisy fundamental and a
clear spin-up in the second harmonic ndot 4.4
10-13 Hz/s.
The spin up switches off at the end of the
outburst, as expected for a substantial decrease
of the accretion rate.
XTE J1807-294 shows a noisy fundamental and a
clear spin-up in the second harmonic ndot 2.1
10-14 Hz/s.
45
Conclusions Spin-down
XTE J1814-338 shows noisy fundamental and
harmonic phase delays, and a strong spin-down
ndot -6.7 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 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.
46
Another Strange case XTE J1807
The outburst of February 2003 (Riggio et al.
2007, in preparation)
47
Spin Frequencies of AMSPs
From Wijnands (2005)
48
But There is order beyond the chaos!
The key idea Harmonic decomposition of the pulse
profile
49
Pulsars spin up