Spin-up and Spin-down of Accreting Millisecond Pulsars

Alessandro Papitto Università di Roma Tor Vergata INAF-Astronomical Observatory of Rome

& my research group L.Burderi (Univ.CA) – T.Di Salvo (Univ.PA) – A.Riggio (Univ.CA) –

M.T.Menna (INAF-OAR) – G.Lavagetto (Univ.PA)

The Recycling Scenario

Low Mass X-ray Binary

B ~ 108 – 109 G

Mcomp ≤ 1 Msun

Long lived (108-109 yr)

Millisecond Radio Pulsar

B ~ 108 – 109 G

Pspin ~ few ms

Mcomp ~ 0.1 Msun

AMSP – binary system: low mass companion star (few 0.1 Msun) + NS fed by the companion ( X-rays ) & spinning at few ms

Evaluation of the accretion torque

SAX J1808.4-3658SAX J1808.4-3658 Ps=2.5ms, Porb=2hr (Wijnands & van der Klis 1998)

XTE J1751-306XTE J1751-306 Ps=2.3ms, Porb=42min (Markwardt et al. 2002)

XTE J0929-314XTE J0929-314 Ps=5.4ms, Porb=43.6min (Galloway et al. 2002)

XTE J1807-294XTE J1807-294 Ps=5.2ms, Porb=40min (Markwardt et al. 2003)

XTE J1814-338XTE J1814-338 Ps=3.2ms, Porb=4hr (Markwardt et al. 2003)

IGR J00291+5934IGR J00291+5934 Ps=1.7ms, Porb=2.5hr (Galloway et al. 2005)

HETE J1900.1-2455HETE J1900.1-2455 Ps=2.7ms, Porb=1.4hr (Kaaret et al. 2005)

…but LMXB don’t show coherent pulsations…which spin period ???

1996 – RXTE (Rossi X-ray Time Explorer) – Time res = few μs large collecting

area

All transients (outburst few weeks – trecur years) and faint (few % LEdd)

Accretion & Spin UpPulsations: channelling of the matter to the magnetic poles

magnetic field strong enough (B>108G) to disrupt the disc

Inner disc radius – balance of matter ram + thermal pressure & magnetic pressure

We see pulsations if Rm > RNS ≈ 10 km

& accretion can effectively take place if the NS-magnetosphere system is not faster than accreting matter – otherwise centrifugal inhibition

i.e. it has to be RM < RCO = 31 P32/3 km

The Timing Technique

Measure of the times of arrival (& their evolution) of X-ray photons

Fold an X-ray Light Curve around the supposed spin period

Measure the phase of the oscillation in all obs and consider their evolutionWrong folding period (linear trend)

Orbital motion of the source (Doppler effect) measure of Porb,a sini, T*,e – orbital evolution if the source recurred

Changes of the spin period (parabolic trend) torques acting on the NS – dynamical estimate of Mdot, inertia of NS

Uncertainity on position (need for few tenths of arcsec uncs)

Evaluation of the accretion torque

Disentangling of the orbital effects: after having found an orbital solution, the residual uncertainity on the orbital parameters can be treated as timing noise around the NS rotational behaviour

But timing analises performed by now led to doubtable conclusions…

AMSP: PORB << Tspinup

Const νdot case

νdot dep. on Mdot

Timing formula

Measure of ννdotdot → dynamical measure of Mdot

Accretion torques caught in action: XTE J1751-305

Pspin = 2.3 ms

dν/dt(T0)=6.8(9)x10-13 Hz/s

dM/dt > 34x10-10 Msun/yr (17% LEdd)

From the comparison with the estimate from the X-ray flux one would deduce D>10kpc

But the source is located just 2° from Galactic Centre (D<8.5kpc)

The source is accreting on both polar caps but one is not visible (sinusoidal pulse)

χ2red = 1.4Confirmation of an higher than average accreting AMSP

“The world is beautiful because it is varied”

XTE J1814-338

Pspin = 3.2 ms Porb =

15388.7229(2) s asini/c = 0.390633(9) lt-s

dν/dt = - 6.7(7)x10-14 Hz/s

Spin down while accreting !

…but as far as the disc rotates in the same sense of the compact object, this should be spun up by accretion

Papitto et al. 2007, MNRAS

The spin down of an accreting pulsar

Role of the magnetic field

Ghosh&Lamb (1979), Wang(1987): when the magnetosphere is next to the corotation radius the field lines are able to thread the disk in regions where they are faster than matter → negative torque on the NS

Rappaport, Fregeau & Spruit (2004)

Material

torque

Negative

threading

torque

B ≈ 8 x 108 γ-1/2 G – higher than average

Phase jiggle – correlation with the Mdot

Phases oscillate around the mean spin down trend

Poor fit : χ2red = 16 !!!

τosc ~ 10d (no orbital explanation)

No superorbital modulation (system too close)

Strong correlation with the oscillation of the X-ray LC (Mdot): when the flux increases the hot spot moves forward and vice versa

Correlation confirmed also for the second harmonic of the signal

Field lines twist

disc

NS

disc

footpoint

shifts

Higher disc density (Mdot)

Phase jiggle – correlation with the Mdot

When Mdot increases (hence disc matter density) threading field lines are bent by solwer rotating matter

The accretion footpoint shifts forward and vice versa when Mdot decreasesSignature of a close interaction between matter in the disc and the threading magnetic field

Variations of Mdot can change the geometry of accretion (indications in other case also, SAX J1808.4-3658, Burderi et al. 2007 – MHD sims, Romanova et al. 2004)

ConclusionsImportance of timing analyses on the coherently pulsed emission of AMPs

Physics of the accretion onto a NS in the low Mdot regime (torque models) Estimate of the magnetic field

DistanceEvolution of the binary system

Results:3 (out of 5 analyzed) spin up because of accretion ( νdot=10-12-10-13 Hz/s) low magnetic field estimate (1-2 x 108 G)

need for an hidden spot to have reasonable distance estimates

2 spin down while accreting (role of the magnetic field) νdot= - 5 x 10-14 Hz/s a popolution with higher B field ( 8-9 x 108 G ) ?

Opportunities: build a statistically significant sample to address different behaviors study of the interaction between the magnetic field & disc matter formulate & testify torque models