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 FlowsFunasdalen (Sweden)2008, March 25-30

SAX J1808: the outburst of 2002

Phase Delays ofThe 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 HzSpin-up:dot = 4.4 10-13 Hz/s

Spin up: dot0 = 4.4 10-13 Hz/s corresponding to a mass accretion rate of dotM = 1.8 10-9 Msun/yr

Spin-down: dot0 = -7.6 10-14 Hz/s corresponding to a NS magnetic field: B = (3.5 +/- 0.5) 108 Gauss

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)

Orbital Period Derivative From the definition of the orbital angular momentum, Jorb,

and the third Kepler's law, after differentiation, we obtain:

22

;1

2;21;2121

13/)1(1,,(

: where,,,(32

2

rorb

ejl

m

mqMMMM

MM

GaorbJ

qqqqg

qgMM

JJ

PP

orborb

orb

dot J / Jorb < 0 and dot Porb / Porb > 0: a lower limit on

the positive quantity –dot M2 / M2 can be derived assuming

dot J / Jorb = 0

,,(3

2

2 qgMM

PP

orb

orb

Fully Conservative case The mass function gives q >= 4 10-2~ 0 (for M1 = 1.4 Msun).

= 1, g (1, q, ) = 1 – q ~ 1

2

23MM

PP

orb

orb

From the observed luminosity in quiescence and in outburst, we derive the average luminosity from the source:Lx = 3.9 1034 ergs/s, and 3 (-dot M2 / M2) = 6.6 10-18 s-1.

From experimental data: dot Porb / Porb = 4.7 10-16 s-1.

Therefore measured dot Porb / Porb about 70 times higher than

predicted from the conservative mass transfer scenario

Exclud

ed!

Exclud

ed!

Totally non-conservative case

The mass function gives q >= 4 10-2 ~ 0 (for M1 = 1.4 Msun).

= 0, g (0, q, ) = (1 – + 2/3 q) / (1 + q) ~ 1 –

dot Porb / Porb <= 3 (1 – ) (-dot M2 / M2)

Since dot Porb / Porb > 0, < 1

For matter leaving the system with the specific angular momentum of the primary, = q2 ~ 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 M1 = 1.4 Msun), = [1 - 0.462 (1 + q)2/3 q1/3]2 ~ 0.7:

dot Porb / Porb <= (-dot M2 / M2)

Assuming dot Porb / Porb = 4.7 10-16 s-1 (from experimental data) we derive

8.3 10-10 Msun/yr <= (-dot M2) = dot Mejected

Secular evolution - non-conservativeSolve 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

ssPmmmPgn

nhorb /104.1

23/5

3/13/52

3/11.0,21

13

23/13/21462.01

13/

qq

qqg

..

-18 for q = 0.564 and n = -1/3nmR

mmq

22

1

2

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

Why high dotM and mass ejection?

Secular evolution - non-conservativePredicted mass loss rate

yrMsunPqqmMgnh /1)1(104

23/53/8

23/123/8

19

2

Optical counterpart in quiescence(Homer et al. 2001)

• Optical modulation at 2h-orbital period, antiphase with X-ray ephemeris (incompatible with ellipsoidal modulation!)• mV semiamplitude ~ 0.06 mag

Folded lightcurve

In quiescence [Aug 1999, Jul 2000]mV ~ 21.5 (uncompatible with intrinsic luminosity from a < 0.1 Msun companion, uncompatible with intrinsic luminosity from an accretion disk in quiescence)

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

Estimated reprocessed luminosity

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 /3c4 (2 / P)4 /(4 R2)•matter pressure given by the ram pressure of the infalling gas: Pram = dotM (G M1/2)1/2 /(2R5/2)

is observed during the radio-ejection phase?(Burderi et al. 2002)

The first MSP in an interacting binary: J1740-5340in the Globular Cluster NGC 6397

and in a long period system!

Is SAXJ1808 in quiescence a radio-ejector?

Using: R = RRL2 (Roche lobe radius of the secondary)

M2 = 10-9 Msun / yr (as derived from the non-conservative secular evolution)

= 3 - 5 1026 Gauss / cm3 (as derived from 2002 timing)

we find:

Pram = 150 dyne / cm3

Prad = 80 - 230 dyne / cm3

Pram ~ Prad: living at the border between accretors (outburst) and radio-ejectors (quiescence)

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

That’s all Folks!