Future Probes of the Neutron Star Equation of State Using X-ray Bursts

Observations with NASA's Rossi X-ray Timing Explorer (RXTE) have resulted in the discovery of fast (200 - 600 Hz), coherent X-ray intensity oscillations (hereafter, "burst oscillations") during thermonuclear X-ray bursts from 12 low mass X-ray binaries (LMXBs). It is now beyond doubt that these oscillations result from spin modulation of the thermonuclear burst flux from the neutron star surface. Among the new timing phenomena revealed by RXTE the burst oscillations are perhaps the best understood, in the sense that many of their properties can be explained in the framework of this relatively simple model. Because of this, detailed modelling of burst oscillations can be an extremely powerful probe of neutron star structure, and thus the equation of state (EOS) of supra-nuclear density matter. The new discoveries have spurred much new theoretical work on thermonuclear burning and propagation on neutron stars, so that in the near future it is not unreasonable to think that detailed physical models of the time dependent flux from burning neutron stars will be available for comparison with the observed pulse profiles from a future, large collecting area X-ray timing observatory. In addition, recent high resolution burst spectroscopy with XMM/Newton suggests the presence of redshifted absorption lines from the neutron star surface during bursts. This leads to the possibility of using large area, high spectral resolution measurements of X-ray bursts as a precise probe of neutron star structure. In this work I will explore the precision with which constraints on neutron star structure, and hence the dense matter EOS, can be made with the implementation of such programs.Comment: 8 pages, 7 figures, AIP conference proceedings format. Contribution to "X-ray Timing 2003: Rossi and Beyond." meeting held in Cambridge, MA, November, 200

Millisecond Time Variations of X-Ray Binaries

The Rossi X-Ray Timing Explorer (RXTE) has found that the neutron stars in low-mass X-ray binaries exhibit oscillations in the range 300-1200 Hz. Persistent emission may exhibit one or both of two features. In bursts a nearly coherent pulsation is seen, which may be the rotation period of the neutron star. For some the frequency equals the difference between the two higher frequencies, suggesting a beat frequency model, but in others it is twice the difference. Similar maximum frequencies suggests that it corresponds to the Kepler orbit frequency at the minimum stable orbit or the neutron star surface, either of which would determine the neutron star masses, radii and equation of state. Theories of accretion onto black holes predict a quasi-periodic oscillation (QPO) related to the inner accretion disk. The two microquasar black hole candidates (BHCs) have exhibited candidates for this or related frequencies.Comment: 4 pages, to be published in the proceedings of IAU Symposium 188: The Hot Univers

Discovery of a 115 Day Orbital Period in the Ultraluminous X-ray Source NGC 5408 X-1

We report the detection of a 115 day periodicity in SWIFT/XRT monitoring data from the ultraluminous X-ray source (ULX) NGC 5408 X-1. Our ongoing campaign samples its X-ray flux approximately twice weekly and has now achieved a temporal baseline of ~485 days. Periodogram analysis reveals a significant periodicity with a period of 115.5 +- 4 days. The modulation is detected with a significance of 3.2 e-4. The fractional modulation amplitude decreases with increasing energy, ranging from 0.13 above 1 keV to 0.24 below 1 keV. The shape of the profile evolves as well, becoming less sharply peaked at higher energies. The periodogram analysis is consistent with a periodic process, however, continued monitoring is required to confirm the coherent nature of the modulation. Spectral analysis indicates that NGC 5408 X-1 can reach 0.3 - 10 keV luminosities of ~2 e40 ergs/s. We suggest that, like the 62 day period of the ULX in M82 (X41.4+60), the periodicity detected in NGC 5408 X-1 represents the orbital period of the black hole binary containing the ULX. If this is true then the secondary can only be a giant or supergiant star.Comment: Accepted for Publication in the Astrophysical Journal Letter

X-ray Burst Oscillations: From Flame Spreading to the Cooling Wake

Type I X-ray bursts are thermonuclear flashes observed from the surfaces of accreting neutron stars (NSs) in Low Mass X-ray Binaries. Oscillations have been observed during the rise and/or decay of some of these X-ray bursts. Those seen during the rise can be well explained by a spreading hot spot model, but large amplitude oscillations in the decay phase remain mysterious because of the absence of a clear-cut source of asymmetry. To date there have not been any quantitative studies that consistently track the oscillation amplitude both during the rise and decay (cooling tail) of bursts. Here we compute the light curves and amplitudes of oscillations in X-ray burst models that realistically account for both flame spreading and subsequent cooling. We present results for several such "cooling wake" models, a "canonical" cooling model where each patch on the NS surface heats and cools identically, or with a latitude-dependent cooling timescale set by the local effective gravity, and an "asymmetric" model where parts of the star cool at significantly different rates. We show that while the canonical cooling models can generate oscillations in the tails of bursts, they cannot easily produce the highest observed modulation amplitudes. Alternatively, a simple phenomenological model with asymmetric cooling can achieve higher amplitudes consistent with the observations.Comment: 8 pages, 7 figures, Accepted for publication in ApJ, Additional calculations and discussion compared to v

Large frequency drifts during Type I X-ray bursts

We study the spin-down of a neutron star atmosphere during the Type I X-ray burst in low mass X-ray binaries. Using polar cap acceleration models, we show that the resulting stellar ``wind'' torque on the burning shell due to the flowing charged particles (electrons, protons and ions) from the star's polar caps may change the shell's angular momentum during the burst. We conclude that the net change in the angular momentum of the star's atmosphere can account for rather large frequency drifts observed during Type I X-ray burst.Comment: 8 pages, more discussion adde

Where Are the r-modes? Chandra Observations of Millisecond Pulsars

We present the results of {\it Chandra} observations of two non-accreting millisecond pulsars, PSRs J1640$+$2224 (J1640) and J1709$+$2313 (J1709), with low inferred magnetic fields and spin-down rates in order to constrain their surface temperatures, obtain limits on the amplitude of unstable $r$-modes in them, and make comparisons with similar limits obtained for a sample of accreting low-mass X-ray binary (LMXB) neutron stars. We detect both pulsars in the X-ray band for the first time. They are faint, with inferred soft X-ray fluxes ($0.3-3$ keV) of $\approx$ $6\times10^{-15}$ and $3\times 10^{-15}$ erg cm$^{-2}$ s$^{-1}$ for J1640 and J1709, respectively. Spectral analysis assuming hydrogen atmosphere emission gives global effective temperature upper limits ($90\%$ confidence) of $3.3 - 4.3 \times 10^5$ K for J1640 and $3.6 - 4.7 \times 10^5$ K for J1709, where the low end of the range corresponds to canonical neutron stars ($M=1.4 M_{\odot}$), and the upper end corresponds to higher-mass stars ($M=2.21 M_{\odot}$). Under the assumption that $r$-mode heating provides the thermal support, we obtain dimensionless $r$-mode amplitude upper limits of $3.2 - 4.8 \times 10^{-8}$ and $1.8 - 2.8 \times 10^{-7}$ for J1640 and J1709, respectively, where again the low end of the range corresponds to lower-mass, canonical neutron stars ($M=1.4 M_{\odot}$). These limits are about an order of magnitude lower than those we derived previously for a sample of LMXBs, except for the accreting millisecond X-ray pulsar (AMXP) SAX J1808.4$-$3658, which has a comparable amplitude limit to J1640 and J1709.Comment: 9 pages, 4 figures, published in Ap