SAX%20J1808-3658%20:

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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
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SAX J1808 the outburst of 2002
(Burderi et al. 2006, ApJ Letters see also
similar results for all the outbursts in Hartman
et al. 2007, but with a different interpretation)
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 the outburst of 2002
(Burderi et al. 2006, ApJ Letters see also
similar results for all the outbursts in Hartman
et al. 2007, but with a different interpretation)
Phase Delays of The First Harmonic
Spin up dotn0 4.4 10-13 Hz/s corresponding to
a mass accretion rate of dotM 1.8 10-9
Msun/yr Spin-down dotn0 -7.6 10-14 Hz/s
corresponding to a NS magnetic field B (3.5
/- 0.5) 108 Gauss
Porb 2 h n 401 Hz
Spin-up dotn 4.4 10-13 Hz/s
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 dotM 1.8 10-9
Msun/yr Spin-down dotn0 -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 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 and in
agreement with the optical luminosity in
quiescence, see below).
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New results from timing of SAXJ1808.4-3658variat
ions 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)
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Orbital Period Derivative
dot J / Jorb lt 0 and dot Porb / Porb gt 0 a lower
limit on the positive quantity dot M2 / M2 can
be derived assuming dot J / Jorb 0

• From the definition of the orbital angular
  momentum, Jorb,
• and the third Kepler's law, after
  differentiation, we obtain

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Fully Conservative case
The mass function gives q gt 4 10-2 0 (for M1
1.4 Msun). b 1, g (1, q, a) 1 q 1
Excluded!
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
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Totally non-conservative case
The mass function gives q gt 4 10-2 0 (for M1
1.4 Msun). b 0, g (0, q, a) (1 a 2/3 q)
/ (1 q) 1 a dot Porb / Porb lt 3 (1 a)
(-dot M2 / M2) Since dot Porb / Porb gt 0, a lt
1 For matter leaving the system with the
specific angular momentum of the primary, a q2
0 similar to the conservative case (as
expected).
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), a 1 - 0.462 (1 q)2/3 q1/32
0.7 dot Porb / Porb lt (-dot M2 / M2) Assuming
dot Porb / Porb 4.7 10-16 s-1 (from
experimental data) we derive 8.3 10-10 Msun/yr lt
(-dot M2) dot Mejected
For matter leaving the system with the specific
angular momentum of the secondary, a 1 the
orbital period evolution is frozen (as the
orbital period of an Earth-orbiting satellite
which does not change halving its mass).
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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

.
Excluded, as expected
-1/2 for q 0 and n -1/3 (n -1/3 for fully
convective companion)
,
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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
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Fully Non Conservative mass transfer in
SAXJ1808.4-3658 (Di Salvo et al. 2007)
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Why high dotM and mass ejection?
Secular evolution - non-conservativePredicted
mass loss rate
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Optical counterpart in quiescence(Homer et al.
2001)
In quiescence Aug 1999, Jul 2000 mV 21.5
(uncompatible with intrinsic luminosity from a lt
0.1 Msun companion, uncompatible with intrinsic
luminosity from an accretion disk in quiescence)

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

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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
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Estimated reprocessed luminosity
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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 m2 (2 p / P)4 /(4 p R2)
• matter pressure given by the
• ram pressure of the infalling gas
• Pram dotM (G M1/2)1/2 /(2p R5/2)

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

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Thats all Folks!