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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
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
Hz/s corresponding to a mass
accretion rate of dotM = 1.8
10-9 Msun/yr
10-13
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
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
dot
J /the
Jorbdefinition
< 0 and dot
Porborbital
/ Porb >
0: a lower
limit on J ,
From
of the
angular
momentum,
orb
the
2 / Mdifferentiation,
2 can be derived
andpositive
the thirdquantity
Kepler's–dot
law,Mafter
weassuming
obtain:
dot J / Jorb = 0
P
 





P
M
J
M
orb
2
orb
2

,  :
3 3 
g
(  ,g
q,(,, q
where


PPorb
M 22 
orb
 Jorb M

 q/3
g (  , q,    1  q  (1   )
1 q
J orb 
Ga
M1  M 2
M 1M 2 ;
M 1    M 2 ;
q
m2
m1
;  
l ej
2
 orbr2
Fully Conservative case
The mass function gives q >= 4 10-2~ 0 (for M1 = 1.4 Msun).
 = 1, g (1, q, ) = 1 – q ~ 1
Porb
3
Porb
 M 2 
 

 M2 
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
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
For
matter
the system
with the
angular
of the
innerleaving
Lagrangian
point (with
q = specific
4 10-2 from
themomentum
mass
2 ~ 0: similar to the conservative case
2/3 q1/3
of
the primary,
 1==q=
(as
secondary,
1: the
orbital
evolution
the
function
with M
1.4
Msun
),  period
= [1 - 0.462
(1 + is
q)frozen
]2(as
~ 0.7:
expected).
orbital period of an
Earth-orbiting
satellite
which
does not change
dot
Porb / Porb <=
(-dot M
2 / M 2)
halving
its mass).
Assuming
dot P / P = 4.7 10-16 s-1 (from experimental
orb
orb
data) we derive
8.3 10-10 Msun/yr <= (-dot M2) = dot Mejected
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
.
13
Porb  1.4 10 m1m2,0.1m
g
 q/3
1 q
1/ 3
P2h
m2
q
m1
R2  m2
2
2 / 3 1/ 3 

  1  0.4621  q  q


n
5 / 3
 n  1 / 3 
 n  5 / 3  2g s / s


-18 for q = 0.564 and n = -1/3
Fully Non Conservative mass transfer in
SAXJ1808.4-3658 (Di Salvo et al. 2007)
Secular evolution - non-conservative
Predicted mass loss rate
1

8/ 3 2
8 / 3 
9
1/ 3

M 2  4 10 m1 q (1  q) P2h 
Msun / yr

 n  5 / 3  2g 
Why high dotM and
mass ejection?
Optical counterpart in quiescence
(Homer et al. 2001)
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)
• Optical modulation at 2horbital period, antiphase with
X-ray ephemeris (incompatible
with ellipsoidal modulation!)
• mV semiamplitude ~ 0.06 mag
Folded
lightcurve
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 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)
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)
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)
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!