Radio Ejection in Accreting Millisecond Pulsars: Evidence and Mechanisms
Is Radio−Ejection ubiquitous among
Is Radio−Ejection ubiquitous among
Accreting Millisecond Pulsar?
Accreting Millisecond Pulsar?
Luciano Burderi, University of Cagliari
Collaborators:
Tiziana di Salvo, Rosario Iaria, University of Palermo
Fabio Pintore, Alessandro Riggio, Andrea Sanna, University of Cagliari
The Radio-Ejection mechanism
The Radio-Ejection mechanism
(Burderi et al. 2001, ApJ)
accretor
radio-ejector
propeller
P
DISC
≈ dM/dt × r
−2.5
P
MAG
≈ B
2
× r
−6
P
PSR
≈ B
2
Ω
4
× r
−2
Roche-Lobe Radius
Corotation Radius
Light-cylinder Radius
dM/dt
radio-ejector
log r (from NS center)
log p
Pressure of a rotating magnetic dipole
Magnetostatic (inside light cylinder): P
MAG
≈ B
2
× r
−6
Radiative (outside light cylinder) ν
RAD
400 Hz: P
PSR
≈ B
2
Ω
4
× r
−2
Outburst:
Outburst:
a
a
ccretion episode
ccretion episode
Quiescence: radio ejection
Quiescence: radio ejection
The Radio-Ejection hypothesis
The Radio-Ejection hypothesis
(Burderi et al. 2001, ApJ, Di Salvo et al. 2008, ApJ)
Evidence of Radio-Ejection in
Evidence of Radio-Ejection in
Accreting Millisecond Pulsars
Orbital evolution:
Orbital evolution:
q = m
q = m
2
2
/m
/m
1
1
dm
dm
2
2
/dt < 0 (Secondary loses mass)
/dt < 0 (Secondary loses mass)
dm
dm
1
1
/dt = − dm
/dt = − dm
2
2
/dt (conservative case, no mass loss from the system)
/dt (conservative case, no mass loss from the system)
Secondary star equation:
Secondary star equation:
(dR
(dR
2
2
/dt)/R
/dt)/R
2
2
= n × (dm
= n × (dm
2
2
/dt)/m
/dt)/m
2
2
(stellar index n = -1/3)
(stellar index n = -1/3)
Driving mechanism GR angular momentum losses:
Driving mechanism GR angular momentum losses:
(dJ/dt)
(dJ/dt)
GR
GR
/J
/J
ORB
ORB
≈ − (32/5c
≈ − (32/5c
5
5
)(2π)
)(2π)
8/3
8/3
(Gm
(Gm
1
1
5/3
5/3
)q(1+q)
)q(1+q)
-1/3
-1/3
P
P
ORB
ORB
−8/3
−8/3
Angular momentum conservation:
Angular momentum conservation:
(dR
(dR
RL2
RL2
/dt)/R
/dt)/R
RL2
RL2
≈ 2 (dJ/dt)
≈ 2 (dJ/dt)
GR
GR
/J
/J
ORB
ORB
− 2 (dm
− 2 (dm
2
2
/dt)/m
/dt)/m
2
2
× (5/6 – q)
× (5/6 – q)
Accretion condition:
Accretion condition:
(dR
(dR
RL2
RL2
/dt)/R
/dt)/R
RL2
RL2
= (dR
= (dR
2
2
/dt)/R
/dt)/R
2
2
For q <<1
For q <<1
dm
dm
2
2
/dt ≈ 1.5 m
/dt ≈ 1.5 m
2
2
× (dJ/dt)
× (dJ/dt)
GR
GR
/J
/J
ORB
ORB
Evidence of Radio-Ejection in
Evidence of Radio-Ejection in
Accreting Millisecond Pulsars
IGR J1749.8-2921 (Papitto et al. 2011):
IGR J1749.8-2921 (Papitto et al. 2011):
P
P
SPIN
SPIN
= 2.5 ms
= 2.5 ms
P
P
ORB
ORB
= 3.8 h
= 3.8 h
m
m
2
2
≥ 0.17 M
≥ 0.17 M
SUN
SUN
(for m
(for m
1
1
= 1.4 M
= 1.4 M
SUN
SUN
)
)
or
or
q
q
3
3
≥ f(m) (1+q)
≥ f(m) (1+q)
2
2
/m
/m
1
1
(f(m) = m
(f(m) = m
1
1
sin(i)
sin(i)
3
3
q
q
3
3
/(1+q)
/(1+q)
2
2
orbital mass function)
orbital mass function)
dm
dm
2
2
/dt ≈ 1.5 m
/dt ≈ 1.5 m
2
2
× (dJ/dt)
× (dJ/dt)
GR
GR
/J
/J
ORB
ORB
L = (Gm
L = (Gm
1
1
/R
/R
1
1
) × (−dm
) × (−dm
2
2
/dt)
/dt)
L ≥ (48/5c
L ≥ (48/5c
5
5
)(Gm
)(Gm
1
1
)
)
5/3
5/3
(2π/P
(2π/P
ORB
ORB
)
)
8/3
8/3
m
m
1
1
1/3
1/3
f(m)
f(m)
2/3
2/3
(Gm
(Gm
1
1
/R
/R
1
1
) = L
) = L
MIN
MIN
L
L
AVERAGE
AVERAGE
= L
= L
OUT
OUT
× (Δt
× (Δt
OUT
OUT
/Δt
/Δt
TOT
TOT
)
)
decreases if the source is still in quiescence after the first outburst
decreases if the source is still in quiescence after the first outburst
If L
If L
AVERAGE
AVERAGE
<< L
<< L
MIN
MIN
conservative evolution is IMPOSSIBLE!
conservative evolution is IMPOSSIBLE!
Evidence of Radio-Ejection in
Evidence of Radio-Ejection in
Accreting Millisecond Pulsars
L
L
MIN
MIN
Results from timing of 5 outburst of SAXJ1808.4-
Results from timing of 5 outburst of SAXJ1808.4-
3658 (1998−2015)
3658 (1998−2015)
Delays of the time of ascending node passage of all the outbursts show a clear
Delays of the time of ascending node passage of all the outbursts show a clear
parabolic trend
parabolic trend
which implies a costant
which implies a costant
dP
ORB
/dt, more than 10 times what is
expected by conservative mass transfer from a fully convective and/or degenerate
secondary (n ≈ -1/3) driven by GR (Di Salvo, 2008; Hartman, 2008) !
1998
1998
2000
2000
2002
2002
2005
2005
2008
2008
2011
2011
2015
2015
Orbital period increases:
dP
ORB
/dt = (3.89 ± 0.15) × 10
-12
s/s
Burderi et al. 2009 using XMM and RXTE
Following Di Salvo et al. (2008):
a) J
TOT
conservation;
b) third Kepler's law;
c) AM losses by GR;
gives the orbital period derivative:
Theory of Dynamical (Orbital) evolution in SAXJ1808.4-3658
Theory of Dynamical (Orbital) evolution in SAXJ1808.4-3658
Following Di Salvo et al. (2008) we adopt:
a) J
TOT
conservation;
b) contact condition: and
c) MB and GR angular momentum losses as driving
mechanism
Predictions from Secular evolution
Predictions from Secular evolution
Highly non conservative mass-transfer is required by the
Secular evolution to drive the high mass-transfer rate
implied by the Dynamical evolution!
Hartman et al. (2008) and Patruno et al. (2011) proposed that magnetic activity in the
Hartman et al. (2008) and Patruno et al. (2011) proposed that magnetic activity in the
companion is responsible for the orbital variability of SAXJ1808 – as discussed by
companion is responsible for the orbital variability of SAXJ1808 – as discussed by
Applegate & Shaham (1994) and Arzoumanian et al. (1994) to explain the orbital
Applegate & Shaham (1994) and Arzoumanian et al. (1994) to explain the orbital
varability observed in PSR B1957+20 – and predicted that quasi-cyclic variability of
varability observed in PSR B1957+20 – and predicted that quasi-cyclic variability of
P
P
ORB
ORB
would reveal itself over the next few years, but…
would reveal itself over the next few years, but…
Arzoumanian et al. (1994)
Arzoumanian et al. (1994)
∆ t ≈ 3.8 s
∆ t ≈ 3.8 s
Sinusoid
Sinusoid
P
P
MOD
MOD
≈ 6 yr
≈ 6 yr
∆ t ≈ 70 s
∆ t ≈ 70 s
Parabola
Parabola
T
T
≈ 17 yr
≈ 17 yr
P
P
MOD
MOD
≥ 68 yr ?
≥ 68 yr ?
Explaining the large observed dP
Explaining the large observed dP
ORB
ORB
/dt
/dt
In the model of Applegate & Shaham (1994) variations of the
In the model of Applegate & Shaham (1994) variations of the
quadrupole moment, ∆ Q, of the secondary istantaneously reflect
quadrupole moment, ∆ Q, of the secondary istantaneously reflect
(through the action of gravity) in ∆ P
(through the action of gravity) in ∆ P
ORB
ORB
:
:
The Applegate & Shaham model for periodic orbital modulations
The Applegate & Shaham model for periodic orbital modulations
∆Q varies because of AM transfer between (internal) shells of
∆Q varies because of AM transfer between (internal) shells of
the secondary caused by the action of a strong (internal)
the secondary caused by the action of a strong (internal)
magnetic field.
magnetic field.
This mechanism has a cost: the internal energy flow required to
This mechanism has a cost: the internal energy flow required to
power the action of the magnetic field is (assuming a Roche
power the action of the magnetic field is (assuming a Roche
Lobe filling secondary) :
Lobe filling secondary) :
For PSR B1957+20 a sinusoidal modulation is observed with
For PSR B1957+20 a sinusoidal modulation is observed with
P
P
ORB
ORB
≈ 9.17 h, ∆P/P ≈ 1.0×10
≈ 9.17 h, ∆P/P ≈ 1.0×10
-7
-7
, P
, P
MOD
MOD
≈ 6 yr, m
≈ 6 yr, m
1
1
= 1.4,
= 1.4,
m
m
2
2
= 0.025.
= 0.025.
For SAXJ1808.4-3658 no sinusoidal modulation is observed,
For SAXJ1808.4-3658 no sinusoidal modulation is observed,
although is possible to believe that what we observe is part of a
although is possible to believe that what we observe is part of a
sinusoid with
sinusoid with
P
P
ORB
ORB
≈ 2.01 h,
≈ 2.01 h,
∆P/P ≈ 72×10
∆P/P ≈ 72×10
-7
-7
and P
and P
MOD
MOD
≈ 70 yr
≈ 70 yr
,
,
m
m
1
1
= 1.56, m
= 1.56, m
2
2
= 0.08.
= 0.08.
This gives:
This gives:
dE/dt ≈ 3 ×10
dE/dt ≈ 3 ×10
30
30
erg/s = 7.5×10
erg/s = 7.5×10
-4
-4
L
L
SUN
SUN
(
(
PSR B1957+20)
PSR B1957+20)
dE/dt ≈ 8 ×10
dE/dt ≈ 8 ×10
32
32
erg/s = 0.1
erg/s = 0.1
L
L
SUN
SUN
(SAXJ1808.4-3658
(SAXJ1808.4-3658
)
)
Energy constrains in the Applegate & Shaham
Energy constrains in the Applegate & Shaham
The tidal-dissipation Applegate & Shaham mechanism
The tidal-dissipation Applegate & Shaham mechanism
For small secondaries the internal energy flow required to power the
For small secondaries the internal energy flow required to power the
action of the magnetic field (dE/dt) cannot come from nuclear burning
action of the magnetic field (dE/dt) cannot come from nuclear burning
since L = m
since L = m
2
2
5
5
L
L
SUN
SUN
and:
and:
M
M
2
2
≈ 0.025 M
≈ 0.025 M
SUN
SUN
(
(
PSR B1957+20)
PSR B1957+20)
M
M
2
2
≈ 0.080 M
≈ 0.080 M
SUN
SUN
(
(
SAX J1808.4-3658)
SAX J1808.4-3658)
Applegate & Shaham (1994) argued that the required power is
Applegate & Shaham (1994) argued that the required power is
provided by tidal dissipation in a sligthly asynchronous secondary
provided by tidal dissipation in a sligthly asynchronous secondary
(∆Ω/Ω ≈ 10
(∆Ω/Ω ≈ 10
-3
-3
).
).
Tidal power proportional to (R
Tidal power proportional to (R
RL2
RL2
/R
/R
2
2
)
)
9
9
: drop vertically as R
: drop vertically as R
2
2
R
R
RL2
RL2
The secondary is kept out of perfect corotation by the magnetic
The secondary is kept out of perfect corotation by the magnetic
braking action of a strong stellar wind.
braking action of a strong stellar wind.
This mechanism operates in PSR B1957+20
This mechanism operates in PSR B1957+20
because the companion
because the companion
underfills (80-90%) its Roche Lobe.
underfills (80-90%) its Roche Lobe.
On the other hand, the companion of SAX
On the other hand, the companion of SAX
J1808.4-3658 fills its
J1808.4-3658 fills its
Roche Lobe, as testified by the accretion episodes, thus tidal
Roche Lobe, as testified by the accretion episodes, thus tidal
dissipation cannot wok to power the Applegate & Shaham
dissipation cannot wok to power the Applegate & Shaham
mechanism in this source.
mechanism in this source.
a) Some degree of asynchronism could drive a
a) Some degree of asynchronism could drive a
tidal-dissipation Applegate & Shaham
tidal-dissipation Applegate & Shaham
mechanism with orbital oscillations of few seconds amplitude. The power required is
mechanism with orbital oscillations of few seconds amplitude. The power required is
10
10
−3
−3
÷ 10
÷ 10
−4
−4
times less than the power required to produce the main (parabolic)
times less than the power required to produce the main (parabolic)
modulation:
modulation:
dE/dt ≈ 10
dE/dt ≈ 10
29
29
÷ 10
÷ 10
30
30
erg/s.
erg/s.
b) The mass outflow induced by Radio-ejection is highly variable up to 30÷40% in line
b) The mass outflow induced by Radio-ejection is highly variable up to 30÷40% in line
with the observed peak bolometric luminosity variations (see right panel below).
with the observed peak bolometric luminosity variations (see right panel below).
Since dP
Since dP
ORB
ORB
/dt ≈ −dm
/dt ≈ −dm
2
2
/dt these variations induce dP
/dt these variations induce dP
ORB
ORB
/dt variations of the same
/dt variations of the same
order.
order.
Arzoumanian et al. (1994)
Arzoumanian et al. (1994)
∆ t ≈ 3.8 s
∆ t ≈ 3.8 s
Sinusoid
Sinusoid
P
P
MOD
MOD
≈ 6 yr
≈ 6 yr
Explaining the 7s delay observed in the 2011 outburst
Explaining the 7s delay observed in the 2011 outburst
1998
1998
2000
2000
2002
2002
2005
2005
2008
2008
2011
2011
2015
2015
Conclusions
Radio-ejection is a necessary outcome if accretion onto a rotating magnetic
dipole drops moving the truncation radius of the disc beyond the light cylinder.
Accreting Millisecond Pulsar are Transient: the onset of radio ejection
during quiescence is likely.
Conservative orbital evolution driven by GR is excluded at least in
IGR J1749.8−2921.
IGR J1749.8−2921.
The large orbital period derivative detected in SAXJ1808.4−3658 implies a high
average mass transfer rate not compatible with a conservative scenario.
The tidal-dissipation Applegate & Shaham mechanism that produces
The tidal-dissipation Applegate & Shaham mechanism that produces
quasi-sinusoidal orbital period modulation works in
quasi-sinusoidal orbital period modulation works in
PSR B1957+20
PSR B1957+20
because the companion underfills its Roche Lobe and asinchronous
because the companion underfills its Roche Lobe and asinchronous
dissipation is possible.
dissipation is possible.
The companion of SAXJ1808.4-3658 fills its Roche Lobe, and tidal
The companion of SAXJ1808.4-3658 fills its Roche Lobe, and tidal
dissipation cannot wok to power the Applegate & Shaham mechanism
dissipation cannot wok to power the Applegate & Shaham mechanism
in this source.
in this source.
The
tidal-dissipation Applegate & Shaham mechanism could explain the small
tidal-dissipation Applegate & Shaham mechanism could explain the small
discrepancy
discrepancy
observed during the 2011 outburst (7s) that is comparable to the orbital
Fluctuations observed in
PSR B1957+20.
PSR B1957+20.
Alternatively, fluctuations of the mass outflow induced by the onset of
Alternatively, fluctuations of the mass outflow induced by the onset of
Radio-ejection are proportional to fluctuations in dP
Radio-ejection are proportional to fluctuations in dP
ORB
ORB
/dt
/dt
That’s all Folks!
That’s all Folks!
Thank you for your attention
Thank you for your attention
Investigating the phenomenon of radio ejection in accreting millisecond pulsars, this study explores the mechanisms behind this process and presents evidence from observations and theoretical models. Led by Luciano Burderi and collaborators from the University of Cagliari and University of Palermo, the research delves into the radio-ejection hypothesis, the orbital evolution of these pulsars, and specific case studies like IGR J1749.8-2921. The findings shed light on the intricate dynamics of these astrophysical systems.
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Presentation Transcript
Is RadioEjection ubiquitous among Accreting Millisecond Pulsar? Luciano Burderi, University of Cagliari Collaborators: Tiziana di Salvo, Rosario Iaria, University of Palermo Fabio Pintore, Alessandro Riggio, Andrea Sanna, University of Cagliari
The Radio-Ejection mechanism (Burderi et al. 2001, ApJ) Pressure of a rotating magnetic dipole Magnetostatic (inside light cylinder): PMAG B2 r 6 Radiative (outside light cylinder) RAD 400 Hz: PPSR B2 4 r 2 PDISC dM/dt r 2.5 accretor PMAG B2 r 6 propeller dM/dt log p radio-ejector radio-ejector PPSR B2 4 r 2 Corotation Radius Light-cylinder Radius Roche-Lobe Radius log r (from NS center)
The Radio-Ejection hypothesis (Burderi et al. 2001, ApJ, Di Salvo et al. 2008, ApJ) Outburst: accretion episode Quiescence: radio ejection
Evidence of Radio-Ejection in Accreting Millisecond Pulsars Orbital evolution: q = m2/m1 dm2/dt < 0 (Secondary loses mass) dm1/dt = dm2/dt (conservative case, no mass loss from the system) Secondary star equation: (dR2/dt)/R2 = n (dm2/dt)/m2 (stellar index n = -1/3) Driving mechanism GR angular momentum losses: (dJ/dt)GR/JORB (32/5c5)(2 )8/3(Gm15/3)q(1+q)-1/3PORB 8/3 Angular momentum conservation: (dRRL2/dt)/RRL2 2 (dJ/dt)GR/JORB 2 (dm2/dt)/m2 (5/6 q) Accretion condition: (dRRL2/dt)/RRL2 = (dR2/dt)/R2 For q <<1 dm2/dt 1.5 m2 (dJ/dt)GR/JORB
Evidence of Radio-Ejection in Accreting Millisecond Pulsars IGR J1749.8-2921 (Papitto et al. 2011): PSPIN = 2.5 ms PORB = 3.8 h m2 0.17 MSUN (for m1 = 1.4 MSUN) or q3 f(m) (1+q)2/m1 (f(m) = m1sin(i)3q3/(1+q)2 orbital mass function) dm2/dt 1.5 m2 (dJ/dt)GR/JORB L = (Gm1/R1) ( dm2/dt) L (48/5c5)(Gm1)5/3(2 /PORB)8/3m11/3 f(m)2/3 (Gm1/R1) = LMIN LAVERAGE = LOUT ( tOUT/ tTOT) decreases if the source is still in quiescence after the first outburst If LAVERAGE << LMIN conservative evolution is IMPOSSIBLE!
Evidence of Radio-Ejection in Accreting Millisecond Pulsars LMIN
Results from timing of 5 outburst of SAXJ1808.4- 3658 (1998 2015) Delays of the time of ascending node passage of all the outbursts show a clear parabolic trendwhich implies a costant dPORB/dt, more than 10 times what is expected by conservative mass transfer from a fully convective and/or degenerate secondary (n -1/3) driven by GR (Di Salvo, 2008; Hartman, 2008) ! Orbital period increases: dPORB/dt = (3.89 0.15) 10-12 s/s 2015 Burderi et al. 2009 using XMM and RXTE 2011 2008 2005 2002 19982000
Theory of Dynamical (Orbital) evolution in SAXJ1808.4-3658 Following Di Salvo et al. (2008): a) JTOT conservation; b) third Kepler's law; c) AM losses by GR; gives the orbital period derivative: 2 ( ) 2/3q1/3 For matter ejected at L1a = 1-0.462 1+q 0.7 (for m2=0.08) g(b,q,a)=1-bq-(1-b)(a +q 3) (1+q)=0.32 (for b =1)
Predictions from Secular evolution Following Di Salvo et al. (2008) we adopt: a) JTOT conservation; b) contact condition: and c) MB and GR angular momentum losses as driving mechanism Highly non conservative mass-transfer is required by the Secular evolution to drive the high mass-transfer rate implied by the Dynamical evolution!
Explaining the large observed dPORB/dt Hartman et al. (2008) and Patruno et al. (2011) proposed that magnetic activity in the companion is responsible for the orbital variability of SAXJ1808 as discussed by Applegate & Shaham (1994) and Arzoumanian et al. (1994) to explain the orbital varability observed in PSR B1957+20 and predicted that quasi-cyclic variability of PORB would reveal itself over the next few years, but t 70 s Parabola T 17 yr PMOD 68 yr ? t 3.8 s Sinusoid PMOD 6 yr Arzoumanian et al. (1994)
The Applegate & Shaham model for periodic orbital modulations In the model of Applegate & Shaham (1994) variations of the quadrupole moment, Q, of the secondary istantaneously reflect (through the action of gravity) in PORB: Q varies because of AM transfer between (internal) shells of the secondary caused by the action of a strong (internal) magnetic field. This mechanism has a cost: the internal energy flow required to power the action of the magnetic field is (assuming a Roche Lobe filling secondary) : 2/3m2 ( ) q -2/3DPORBPORB ( )-7PMODerg/s dE dt =1.6 10321+q 5/3P2h
Energy constrains in the Applegate & Shaham For PSR B1957+20 a sinusoidal modulation is observed with PORB 9.17 h, P/P 1.0 10-7, PMOD 6 yr, m1 = 1.4, m2 = 0.025. For SAXJ1808.4-3658 no sinusoidal modulation is observed, although is possible to believe that what we observe is part of a sinusoid with PORB 2.01 h, P/P 72 10-7 and PMOD 70 yr, m1 = 1.56, m2 = 0.08. This gives: dE/dt 3 1030 erg/s = 7.5 10-4 LSUN (PSR B1957+20) dE/dt 8 1032 erg/s = 0.1LSUN (SAXJ1808.4-3658)
The tidal-dissipation Applegate & Shaham mechanism For small secondaries the internal energy flow required to power the action of the magnetic field (dE/dt) cannot come from nuclear burning since L = m25 LSUN and: M2 0.025 MSUN M2 0.080 MSUN (PSR B1957+20) (SAX J1808.4-3658) Applegate & Shaham (1994) argued that the required power is provided by tidal dissipation in a sligthly asynchronous secondary ( / 10-3). Tidal power proportional to (RRL2/R2)9: drop vertically as R2 RRL2 The secondary is kept out of perfect corotation by the magnetic braking action of a strong stellar wind. This mechanism operates in PSR B1957+20 because the companion underfills (80-90%) its Roche Lobe. On the other hand, the companion of SAXJ1808.4-3658 fills its Roche Lobe, as testified by the accretion episodes, thus tidal dissipation cannot wok to power the Applegate & Shaham mechanism in this source.
Explaining the 7s delay observed in the 2011 outburst a) Some degree of asynchronism could drive a tidal-dissipation Applegate & Shaham mechanism with orbital oscillations of few seconds amplitude. The power required is 10 3 10 4 times less than the power required to produce the main (parabolic) modulation: dE/dt 1029 1030 erg/s. b) The mass outflow induced by Radio-ejection is highly variable up to 30 40% in line with the observed peak bolometric luminosity variations (see right panel below). Since dPORB/dt dm2/dt these variations induce dPORB/dt variations of the same order. 2011 2002 t 3.8 s Sinusoid PMOD 6 yr 1998 2015 2005 2008 2000 Arzoumanian et al. (1994)
Conclusions Radio-ejection is a necessary outcome if accretion onto a rotating magnetic dipole drops moving the truncation radius of the disc beyond the light cylinder. Accreting Millisecond Pulsar are Transient: the onset of radio ejection during quiescence is likely. Conservative orbital evolution driven by GR is excluded at least in IGR J1749.8 2921. The large orbital period derivative detected in SAXJ1808.4 3658 implies a high average mass transfer rate not compatible with a conservative scenario. The tidal-dissipation Applegate & Shaham mechanism that produces quasi-sinusoidal orbital period modulation works in PSR B1957+20 because the companion underfills its Roche Lobe and asinchronous dissipation is possible. The companion of SAXJ1808.4-3658 fills its Roche Lobe, and tidal dissipation cannot wok to power the Applegate & Shaham mechanism in this source. The tidal-dissipation Applegate & Shaham mechanism could explain the small discrepancy observed during the 2011 outburst (7s) that is comparable to the orbital Fluctuations observed in PSR B1957+20. Alternatively, fluctuations of the mass outflow induced by the onset of Radio-ejection are proportional to fluctuations in dPORB/dt
Thats all Folks! Thank you for your attention
