4 Accreting Millisecond X-ray Pulsars
185
where P b is in hours and M NS and M 2 are the NS and donor masses. The
observed value, however, implies an expansion of the orbit on a timescale of ∼70
Myr [39, 81, 123, 125]. Further observations in 2011 provided a long enough
baseline to detect an orbital period acceleration (top panel in Fig. 4.8; [262]). SAX
J1808.4-3658 may therefore behave like the “black widow” binary millisecond
pulsars observed at radio frequencies [184] with a short-term exchange of angular
momentum between the donor star and the orbit. A similar suggestion was also
previously proposed for this AMXP [39, 81], invoking a “hidden” black widow
scenario in which the AMXP switches on as a radio pulsar during quiescence and
ablates its donor.
IGR J00291+5934 Long-term spin down has also been measured between the
2004 and 2008 outbursts of IGR J00291+5934. The AMXP rotation behaves like a
saw-tooth, spinning up during the 2004 outburst then spinning down until the 2008
outburst. The spin-down rate is ≈−3 × 10 −15 Hz s −1 [126, 245, 259], comparable
to that observed in SAX J1808.4-3658. Although spin down between outbursts
has been observed only once and it is not possible (until the next outburst) to
verify whether it is constant, the most likely explanation also involves magnetic
dipole radiation spin-down. If this saw-tooth behaviour is a good indicator of the
secular spin evolution of this AMXP, then the net spin frequency is increasing
at ≈+2.5 × 10 −15 Hz s −1 . Indeed, the spin frequency at the beginning of the
2004 outburst was less than that observed in the 2008 outburst: the 2004 spin-up
accelerated the pulsar more than it subsequently decelerated in quiescence. The
relatively small baseline did not permit any useful constraints on orbital period
evolution: this should be possible after the observation of the next outburst.
XTE J1751-305 Comparing the spin frequencies from 2002, 2005, 2007 and
2009 reveals a secular spin down of −5.5 × 10 −15 Hz s −1 [288]. This is again
consistent with magnetic dipole spin-down. If the spin-up measured during the
2005 outburst reported in [241] is not strongly affected by timing noise, then its
behaviour resembles IGR J00291+5934, with spin frequency increasing in outburst
and decreasing between outbursts in a saw-tooth. The inferred magnetic field is
∼4 × 10 8 G, in line with the other two AMXPs constrained in this way. The low
quality of the data taken in the 2002 outburst does not permit stringent constraints
on orbital evolution.
Swift J1756.9-2508 Observations during the outbursts in 2007 and 2009 give upper
limits of |˙ ν| 2 × 10 −15 Hz s −1 on the secular spin evolution of this AMXP [259].
This requires a magnetic field <9 × 10 8 G. Magnetic field estimates for all four of
these AMXPs are given in Table 4.4.
185
where P b is in hours and M NS and M 2 are the NS and donor masses. The
observed value, however, implies an expansion of the orbit on a timescale of ∼70
Myr [39, 81, 123, 125]. Further observations in 2011 provided a long enough
baseline to detect an orbital period acceleration (top panel in Fig. 4.8; [262]). SAX
J1808.4-3658 may therefore behave like the “black widow” binary millisecond
pulsars observed at radio frequencies [184] with a short-term exchange of angular
momentum between the donor star and the orbit. A similar suggestion was also
previously proposed for this AMXP [39, 81], invoking a “hidden” black widow
scenario in which the AMXP switches on as a radio pulsar during quiescence and
ablates its donor.
IGR J00291+5934 Long-term spin down has also been measured between the
2004 and 2008 outbursts of IGR J00291+5934. The AMXP rotation behaves like a
saw-tooth, spinning up during the 2004 outburst then spinning down until the 2008
outburst. The spin-down rate is ≈−3 × 10 −15 Hz s −1 [126, 245, 259], comparable
to that observed in SAX J1808.4-3658. Although spin down between outbursts
has been observed only once and it is not possible (until the next outburst) to
verify whether it is constant, the most likely explanation also involves magnetic
dipole radiation spin-down. If this saw-tooth behaviour is a good indicator of the
secular spin evolution of this AMXP, then the net spin frequency is increasing
at ≈+2.5 × 10 −15 Hz s −1 . Indeed, the spin frequency at the beginning of the
2004 outburst was less than that observed in the 2008 outburst: the 2004 spin-up
accelerated the pulsar more than it subsequently decelerated in quiescence. The
relatively small baseline did not permit any useful constraints on orbital period
evolution: this should be possible after the observation of the next outburst.
XTE J1751-305 Comparing the spin frequencies from 2002, 2005, 2007 and
2009 reveals a secular spin down of −5.5 × 10 −15 Hz s −1 [288]. This is again
consistent with magnetic dipole spin-down. If the spin-up measured during the
2005 outburst reported in [241] is not strongly affected by timing noise, then its
behaviour resembles IGR J00291+5934, with spin frequency increasing in outburst
and decreasing between outbursts in a saw-tooth. The inferred magnetic field is
∼4 × 10 8 G, in line with the other two AMXPs constrained in this way. The low
quality of the data taken in the 2002 outburst does not permit stringent constraints
on orbital evolution.
Swift J1756.9-2508 Observations during the outbursts in 2007 and 2009 give upper
limits of |˙ ν| 2 × 10 −15 Hz s −1 on the secular spin evolution of this AMXP [259].
This requires a magnetic field <9 × 10 8 G. Magnetic field estimates for all four of
these AMXPs are given in Table 4.4.