1. 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)

2. The Recycling Scenario Low Mass X-ray Binary B ~ 10 8 – 10 9 G Mcomp ≤ 1 Msun Long lived (10 8 -10 9 yr) Millisecond Radio Pulsar B ~ 10 8 – 10 9 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

3. SAX J1808.4-3658 SAX J1808.4-3658Ps=2.5ms, Porb=2hr (Wijnands & van der Klis 1998) XTE J1751-306 XTE J1751-306Ps=2.3ms, Porb=42min (Markwardt et al. 2002) XTE J0929-314 XTE J0929-314 Ps=5.4ms, Porb=43.6min (Galloway et al. 2002) XTE J1807-294 XTE J1807-294 Ps=5.2ms, Porb=40min (Markwardt et al. 2003) XTE J1814-338 XTE J1814-338 Ps=3.2ms, Porb=4hr (Markwardt et al. 2003) IGR J00291+5934 IGR J00291+5934 Ps=1.7ms, Porb=2.5hr (Galloway et al. 2005) HETE J1900.1-2455 HETE 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 – t recur years) and faint (few % L Edd )

4. Accretion & Spin Up Pulsations: channelling of the matter to the magnetic poles magnetic field strong enough (B>10 8 G) 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 P 3 2/3 km

5. 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 evolution Wrong folding period (linear trend) Orbital motion of the source (Doppler effect) measure of P orb,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)

6. 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: P ORB << T spinup Const ν dot case ν dot dep. on M dot Timing formula ν dot Measure of ν dot → dynamical measure of Mdot

7. Accretion torques caught in action: XTE J1751-305 Pspin = 2.3 ms d ν /dt(T 0 )=6.8(9)x10 -13 Hz/s dM/dt > 34x10 -10 Msun/yr (17% L Edd ) 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) χ 2 red = 1.4 Confirmation of an higher than average accreting AMSP

8. “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 d ν /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

9. 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 10 8 γ -1/2 G – higher than average

10. Phase jiggle – correlation with the Mdot Phases oscillate around the mean spin down trend Poor fit : χ 2 red = 16 !!! τ osc ~ 10d (no orbital explanation) No superorbital modulation (system too close) Strong correlation with the oscillation of the X-ray LC (M dot ): when the flux increases the hot spot moves forward and vice versa Correlation confirmed also for the second harmonic of the signal

11. 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 decreases Signature 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)

12. Conclusions Importance 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 Distance Evolution of the binary system Results:3 (out of 5 analyzed) spin up because of accretion ( ν dot =10 -12 -10 -13 Hz/s) low magnetic field estimate (1-2 x 10 8 G) need for an hidden spot to have reasonable distance estimates 2 spin down while accreting (role of the magnetic field) ν dot= - 5 x 10 -14 Hz/s a popolution with higher B field ( 8-9 x 10 8 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