196
A. Patruno and A. L. Watts
The four AMXPs with twin kHz QPOs (SAX J1808.4-3658, XTE J1807-294,
IGR J17511-305 and Aql X-1; Sect. 4.3) have been used to test kHz QPO formation
models (e.g., the rejection of the beat-frequency model; Sect. 4.3.1) and have
illuminated the relation with the NS spin. Taking into account also the NXPs
with twin kHz QPOs, it is clear that the relation between kHz QPO separation
Δν = ν u − ν l and spin frequency ν s is not as simple as originally thought: Δν/ν s
is not always equal to 1 or 0.5. Δν and ν s may even be unrelated: instead we see
an average Δν ≈ 300 Hz for all sources except AMXPs [212, 366]. Only for
the AMXPs, where the magnetic field is strong enough to channel accretion, is the
ratio Δν/ν s either 1 or 0.5. Some predictions of the sonic-point spin resonance and
relativistic-resonance models [164, 175] are consistent with the AMXP results. In
sonic-point spin resonance models, the magnetic and radiation fields rotating with
the star excite a vertical motion of the disk gas at the “spin-resonance” radius r sr .
There, the vertical epicyclic frequency equals the difference between the orbital
frequency and the spin. Depending on the “clumpiness” of the flow at r rs , the Xray flux exhibits Δν equal to either ν s (smooth flow) or 0.5ν s (clumpy flow). In
relativistic resonance models, a non-linear 1:2 or 1:3 resonance between orbital and
radial epicyclic motion emerges as a consequence of the deviation of the strong
gravitational potential from the Newtonian 1/r. A third model suggests that kHz
QPOs are related to the three general relativistic epicyclic frequencies [318] or to
the precession of frame dragging (Lense-Thirring precession [317]). So far none
of these models satisfactorily accounts for all of the rich phenomenology of kHz
QPOs.
Determining the origin of QPOs, in particular kHz QPOs is of fundamental
importance as this is a phenomenon that is common in LMXBs. If a clear relation
with the NS mass and/or radius is confirmed, it has the potential to place severe
constraints on the EoS of ultra-dense matter. This field has however seen few
advancements in the past few years, at least on the theoretical side. New attempts
are now using numerical simulations to interpret the observations and test some of
the original models [11, 80, 145, 146]. Most of these simulations use black hole
accretors (but see [11]) which do not have kHz QPOs, but the results are promising
in terms of understanding the generation of variability in LMXBs as a whole.
4.9 Open Problems and Final Remarks
Since the first discovery in 1998, the AMXPs have provided an incredibly body of
observational data allowing us to understand NSs and their evolution. They have
allowed the study of extreme phenomena on the surface of the NSs, in the strong
gravity regime at relativistic rotational velocities, and have helped us to understand
how radio pulsars form and evolve within the framework of the recycling scenario.
Proposed X-ray missions like the Indian ASTROSAT, the NASA AXTAR satellite
and the ESA missions LOFT and Athena+ will guarantee huge advances in our
knowledge of these systems, building on the extraordinary results from RXTE,
A. Patruno and A. L. Watts
The four AMXPs with twin kHz QPOs (SAX J1808.4-3658, XTE J1807-294,
IGR J17511-305 and Aql X-1; Sect. 4.3) have been used to test kHz QPO formation
models (e.g., the rejection of the beat-frequency model; Sect. 4.3.1) and have
illuminated the relation with the NS spin. Taking into account also the NXPs
with twin kHz QPOs, it is clear that the relation between kHz QPO separation
Δν = ν u − ν l and spin frequency ν s is not as simple as originally thought: Δν/ν s
is not always equal to 1 or 0.5. Δν and ν s may even be unrelated: instead we see
an average Δν ≈ 300 Hz for all sources except AMXPs [212, 366]. Only for
the AMXPs, where the magnetic field is strong enough to channel accretion, is the
ratio Δν/ν s either 1 or 0.5. Some predictions of the sonic-point spin resonance and
relativistic-resonance models [164, 175] are consistent with the AMXP results. In
sonic-point spin resonance models, the magnetic and radiation fields rotating with
the star excite a vertical motion of the disk gas at the “spin-resonance” radius r sr .
There, the vertical epicyclic frequency equals the difference between the orbital
frequency and the spin. Depending on the “clumpiness” of the flow at r rs , the Xray flux exhibits Δν equal to either ν s (smooth flow) or 0.5ν s (clumpy flow). In
relativistic resonance models, a non-linear 1:2 or 1:3 resonance between orbital and
radial epicyclic motion emerges as a consequence of the deviation of the strong
gravitational potential from the Newtonian 1/r. A third model suggests that kHz
QPOs are related to the three general relativistic epicyclic frequencies [318] or to
the precession of frame dragging (Lense-Thirring precession [317]). So far none
of these models satisfactorily accounts for all of the rich phenomenology of kHz
QPOs.
Determining the origin of QPOs, in particular kHz QPOs is of fundamental
importance as this is a phenomenon that is common in LMXBs. If a clear relation
with the NS mass and/or radius is confirmed, it has the potential to place severe
constraints on the EoS of ultra-dense matter. This field has however seen few
advancements in the past few years, at least on the theoretical side. New attempts
are now using numerical simulations to interpret the observations and test some of
the original models [11, 80, 145, 146]. Most of these simulations use black hole
accretors (but see [11]) which do not have kHz QPOs, but the results are promising
in terms of understanding the generation of variability in LMXBs as a whole.
4.9 Open Problems and Final Remarks
Since the first discovery in 1998, the AMXPs have provided an incredibly body of
observational data allowing us to understand NSs and their evolution. They have
allowed the study of extreme phenomena on the surface of the NSs, in the strong
gravity regime at relativistic rotational velocities, and have helped us to understand
how radio pulsars form and evolve within the framework of the recycling scenario.
Proposed X-ray missions like the Indian ASTROSAT, the NASA AXTAR satellite
and the ESA missions LOFT and Athena+ will guarantee huge advances in our
knowledge of these systems, building on the extraordinary results from RXTE,