1. SAX J1808-3658 : Witnessing the Banquet of a Hidden Black Widow? Luciano Burderi (Dipartimento di Fisica, Universita’ di Cagliari) Tiziana Di Salvo (Dipartimento di Fisica, Universita’ di Palermo) Collaborators: A. Riggio (Universita’ di Cagliari) A. Papitto (Oss. Astr. Roma) M.T. Menna (Oss. Astr. Roma) Cool Discs, Hot Flows Funasdalen (Sweden) 2008, March 25-30

3. SAX J1808: the outburst of 2002 Phase Delays of The Fundamental Phase Delays of The First Harmonic Spin-down at the end of the outburst: dot = -7.6 10 -14 Hz/s (Burderi et al. 2006, ApJ Letters; see also similar results for all the outbursts in Hartman et al. 2007, but with a different interpretation) Porb = 2 h  = 401 Hz Spin-up: dot = 4.4 10 -13 Hz/s

4. SAX J1808: the outburst of 2002 Phase Delays of The First Harmonic Spin-down at the end of the outburst: dot = -7.6 10 -14 Hz/s (Burderi et al. 2006, ApJ Letters; see also similar results for all the outbursts in Hartman et al. 2007, but with a different interpretation) Porb = 2 h  = 401 Hz Spin-up: dot = 4.4 10 -13 Hz/s Spin up: dot 0 = 4.4 10 -13 Hz/s corresponding to a mass accretion rate of dotM = 1.8 10 -9 Msun/yr Spin-down: dot 0 = -7.6 10 -14 Hz/s corresponding to a NS magnetic field: B = (3.5 +/- 0.5) 10 8 Gauss

5. 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

6. 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.

7. Discussion of the results for SAX J1808 Spin up: dot 0 = 4.4 10 -13 Hz/s corresponding to a mass accretion rate of dotM = 1.8 10 -9 Msun/yr Spin-down: dot 0 = -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:  2 / 9 Rc 3 = 2  dot sd from where we evaluate the NS magnetic field: B = (3.5 +/- 0.5) 10 8 Gauss (in agrement with previous results, B = 1-5 10 8 Gauss, Di Salvo & Burderi 2003 and in agreement with the optical luminosity in quiescence, see below).

8. New results from timing of SAXJ1808.4-3658: variations of the time of ascending node passage between different outburst (Di Salvo et al. 2007, Hartman et al. 2007) Orbital period increases: dot Porb =(3.40+-0.12) 10 -12 s/s (Di Salvo et al. 2007)

9. Orbital Period Derivative From the definition of the orbital angular momentum, J orb, and the third Kepler's law, after differentiation, we obtain: dot J / J orb 0: a lower limit on the positive quantity –dot M 2 / M 2 can be derived assuming dot J / J orb = 0

10. Fully Conservative case The mass function gives q >= 4 10 -2 ~ 0 (for M 1 = 1.4 Msun).  = 1, g (1, q,  ) = 1 – q ~ 1 From the observed luminosity in quiescence and in outburst, we derive the average luminosity from the source: Lx = 3.9 10 34 ergs/s, and 3 (-dot M 2 / M 2 ) = 6.6 10 -18 s -1. From experimental data: dot P orb / P orb = 4.7 10 -16 s -1. Therefore measured dot P orb / P orb about 70 times higher than predicted from the conservative mass transfer scenario Excluded!

11. Totally non-conservative case The mass function gives q >= 4 10 -2 ~ 0 (for M 1 = 1.4 Msun).  = 0, g (0, q,  ) = (1 –  + 2/3 q) / (1 + q) ~ 1 –  dot P orb / P orb <= 3 (1 –  ) (-dot M 2 / M 2 ) Since dot P orb / P orb > 0,  < 1 For matter leaving the system with the specific angular momentum of the primary,  = q 2 ~ 0: similar to the conservative case (as expected). For matter leaving the system with the specific angular momentum of the secondary,  = 1: the orbital period evolution is frozen (as the orbital period of an Earth-orbiting satellite which does not change halving its mass). For matter leaving the system with the specific angular momentum of the inner Lagrangian point (with q = 4 10 -2 from the mass function with M 1 = 1.4 Msun ),  = [1 - 0.462 (1 + q) 2/3 q 1/3 ] 2 ~ 0.7: dot P orb / P orb <= (-dot M 2 / M 2 ) Assuming dot P orb / P orb = 4.7 10 -16 s -1 (from experimental data) we derive 8.3 10 -10 Msun/yr <= (-dot M 2 ) = dot M ejected

12. Secular Evolution - conservative Solve the angular momentum equation taking into account losses of angular momentum from the system (which drive the system evolution), and impose contact between the secondary and its Roche lobe along the evolution. dot Porb predicted by conservative mass transfer driven by GR angular momentum losses is: which gives dot Porb ~ 7 10 -14, about a factor 50 lower than the observed value. -1/2 for q ~ 0 and n = -1/3 (n= -1/3 for fully convective companion), Excluded, as expected

13. Secular evolution - non-conservative Solve the angular momentum equation taking into account losses of angular momentum from the system (which drive the system evolution), and impose contact between the secondary and its Roche lobe along the evolution. dot Porb predicted by non-conservative mass transfer driven by GR angular momentum losses is. -18 for q = 0.564 and n = -1/3

14. Fully Non Conservative mass transfer in SAXJ1808.4-3658 (Di Salvo et al. 2007)

15. Why high dotM and mass ejection? Secular evolution - non-conservative Predicted mass loss rate

16. Optical counterpart in quiescence (Homer et al. 2001) Optical modulation at 2h- orbital period, antiphase with X-ray ephemeris (incompatible with ellipsoidal modulation!) m V semiamplitude ~ 0.06 mag Folded lightcurve In quiescence [Aug 1999, Jul 2000] m V ~ 21.5 (uncompatible with intrinsic luminosity from a < 0.1 Msun companion, uncompatible with intrinsic luminosity from an accretion disk in quiescence)

17. We proposed an alternative scenario! Optical emission in quiescence interpreted as reprocessed spin-down luminosity of a magneto-dipole rotator by a companion and/or remnant disk Burderi et al. 2003, Campana et al. 2004

18. Estimated reprocessed luminosity

19. Rotating magnetic dipole phase Radio Ejection phase (Burderi et al. 2001) Rotating magnetic dipole emission overflowing matter swept away by radiation pressure pulsar pressure given by the Larmor formula: Prad = 2 /3c 4   (2  / P) 4 /(4  R 2 ) matter pressure given by the ram pressure of the infalling gas: Pram = dotM (G M 1 /2) 1/2 /(2  R 5/2 )

20. is observed during the radio-ejection phase? (Burderi et al. 2002) The first MSP in an interacting binary: J1740-5340 in the Globular Cluster NGC 6397 and in a long period system!

21. Is SAXJ1808 in quiescence a radio-ejector? Using: R = R RL2 (Roche lobe radius of the secondary) M 2 = 10 -9 Msun / yr (as derived from the non-conservative secular evolution)  = 3 - 5 10 26 Gauss / cm 3 (as derived from 2002 timing) we find: Pram = 150 dyne / cm 3 Prad = 80 - 230 dyne / cm 3 Pram ~ Prad: living at the border between accretors (outburst) and radio-ejectors (quiescence)

22. Conclusions The high orbital period derivative in SAXJ1808.4-3658 is an indirect proof that A magnetodipole rotator is active in the system The system harbors a hidden “Black Widow” eating its companion during outbursts and ablating it during quiescence

23. That’s all Folks!