178
A. Patruno and A. L. Watts
since observations usually cover only a narrow (high) energy band. If we assume that
the X-ray flux is F X ∝ F bol then we expect to see ˙
ν s ∝ F
γ
X . However this assumes
that the mass accretion rate ˙
M ∝ F X , which has been shown to be untrue in some
LMXBs [340]. There is one additional complication: AMXPs have outbursts that
are almost always too short to split data segments long enough to yield more than
one short-term “instantaneous” spin frequency derivative.
If one keeps these caveats in mind, then it is possible to test the relation between
˙
ν s and F X for some AMXPs, such as XTE J1807-294 and XTE J1814-338 which
have shown long outbursts (∼100 and ∼40 days, respectively) and high S/N ratio for
the pulsations. In XTE J1807-294, the “instantaneous” ˙
ν changes sign several times
during the outburst decay and all “instantaneous” spin frequency derivatives ˙
ν s are
insignificant and consistent with being part of the underlying timing noise process
[254]. In XTE J1814-338, the instantaneous ˙
ν are too large (up to 10 −11 Hz s −1 ) to
be physically meaningful, requiring accretion rates well above the Eddington limit
[352]. This is at odds with the fact that AMXPs are faint and rarely reach accretion
rates above 10% Eddington, suggesting that ˙
ν is different to ˙
ν s and is completely
dominated by timing noise. This does not prove that ˙
ν s does not scale with flux,
but only that measurements of “instantaneous” ˙
ν s are contaminated by timing noise,
which prevents testing of the relation between ˙
ν s and F X .
Theoretical expectations for ˙
ν s mostly exceed observed values measured by
taking into account the contamination of timing noise (Table 4.3). This means that
most AMXPs do not behave in accordance with the predictions of accretion torque
theory (Eq. (4.8)). In addition, once gas attaches to the magnetic field lines of the
AMXP, an exchange of angular momentum is inevitable unless r m = r co . But this
cannot be the case throughout an outburst: r m ∝ ˙
M −2/7 and the mass accretion rate
varies, so r m must at some point differ from r co . Larger torques, which are expected
close to the outburst peak, are clearly ruled out in some AMXPs [123, 127, 259]. The
angular momentum of the accreting plasma must however be transferred somewhere
so that the mismatch between expected and observed ˙
ν s appears problematic.
4.4.2.1 The Origin of X-ray Timing Noise
The phase wandering of pulsations in coherent timing analysis requires careful
consideration if we are to understand how a NS responds to accretion. Theoretically
the phenomenon is easy to explain if one assumes that the accretion hot spot is
not completely anchored to one location on the surface. One possibility is that the
magnetic and rotational axes of the NS are almost aligned and the hot spot wanders
around the magnetic axis by small displacements, generating large variations in
phase and amplitude [178]. In this case pulsed fractions and times of arrivals
should be anti-correlated. A moving hot spot has been observed in 3D-MHD
simulations of magnetized accreting NSs [11, 293]. In particular, it was shown that
the usual assumption of a fixed hot spot is valid only for large misalignment angles
between the magnetic and spin axes (Fig. 4.6, [11]), in good agreement with the
magnetic and rotational axis alignment model [178, 298]. This strengthens the idea
A. Patruno and A. L. Watts
since observations usually cover only a narrow (high) energy band. If we assume that
the X-ray flux is F X ∝ F bol then we expect to see ˙
ν s ∝ F
γ
X . However this assumes
that the mass accretion rate ˙
M ∝ F X , which has been shown to be untrue in some
LMXBs [340]. There is one additional complication: AMXPs have outbursts that
are almost always too short to split data segments long enough to yield more than
one short-term “instantaneous” spin frequency derivative.
If one keeps these caveats in mind, then it is possible to test the relation between
˙
ν s and F X for some AMXPs, such as XTE J1807-294 and XTE J1814-338 which
have shown long outbursts (∼100 and ∼40 days, respectively) and high S/N ratio for
the pulsations. In XTE J1807-294, the “instantaneous” ˙
ν changes sign several times
during the outburst decay and all “instantaneous” spin frequency derivatives ˙
ν s are
insignificant and consistent with being part of the underlying timing noise process
[254]. In XTE J1814-338, the instantaneous ˙
ν are too large (up to 10 −11 Hz s −1 ) to
be physically meaningful, requiring accretion rates well above the Eddington limit
[352]. This is at odds with the fact that AMXPs are faint and rarely reach accretion
rates above 10% Eddington, suggesting that ˙
ν is different to ˙
ν s and is completely
dominated by timing noise. This does not prove that ˙
ν s does not scale with flux,
but only that measurements of “instantaneous” ˙
ν s are contaminated by timing noise,
which prevents testing of the relation between ˙
ν s and F X .
Theoretical expectations for ˙
ν s mostly exceed observed values measured by
taking into account the contamination of timing noise (Table 4.3). This means that
most AMXPs do not behave in accordance with the predictions of accretion torque
theory (Eq. (4.8)). In addition, once gas attaches to the magnetic field lines of the
AMXP, an exchange of angular momentum is inevitable unless r m = r co . But this
cannot be the case throughout an outburst: r m ∝ ˙
M −2/7 and the mass accretion rate
varies, so r m must at some point differ from r co . Larger torques, which are expected
close to the outburst peak, are clearly ruled out in some AMXPs [123, 127, 259]. The
angular momentum of the accreting plasma must however be transferred somewhere
so that the mismatch between expected and observed ˙
ν s appears problematic.
4.4.2.1 The Origin of X-ray Timing Noise
The phase wandering of pulsations in coherent timing analysis requires careful
consideration if we are to understand how a NS responds to accretion. Theoretically
the phenomenon is easy to explain if one assumes that the accretion hot spot is
not completely anchored to one location on the surface. One possibility is that the
magnetic and rotational axes of the NS are almost aligned and the hot spot wanders
around the magnetic axis by small displacements, generating large variations in
phase and amplitude [178]. In this case pulsed fractions and times of arrivals
should be anti-correlated. A moving hot spot has been observed in 3D-MHD
simulations of magnetized accreting NSs [11, 293]. In particular, it was shown that
the usual assumption of a fixed hot spot is valid only for large misalignment angles
between the magnetic and spin axes (Fig. 4.6, [11]), in good agreement with the
magnetic and rotational axis alignment model [178, 298]. This strengthens the idea