Download Discovery of Kilohertz Quasi-periodic Oscillations from 4U 1820

THE ASTROPHYSICAL JOURNAL, 483 : L119–L122, 1997 July 10
q 1997. The American Astronomical Society. All rights reserved. Printed in U.S. A.
DISCOVERY OF KILOHERTZ QUASI-PERIODIC OSCILLATIONS FROM 4U 18202303 WITH
ROSSI X-RAY TIMING EXPLORER
ALAN P. SMALE,1 WILLIAM ZHANG,2
AND
NICHOLAS E. WHITE2
Laboratory for High Energy Astrophysics, NASAyGoddard Space Flight Center, Greenbelt, MD 20771
Received 1997 March 17; accepted 1997 April 30
ABSTRACT
We have detected high-frequency (HF) quasi-periodic oscillations (QPOs) from the low-mass X-ray binary
4U 18202303 during observations performed in 1996 October using the Rossi X-ray Timing Explorer. The QPOs
are visible when the source occupies the low-state luminosity range LX 5 2.4 –3.1 3 1037 ergs s21 (2–20 keV, at
6.4 kpc); the centroid frequency of the main QPO peak varies between 546 H 2 Hz and 796 H 6 Hz and is tightly
correlated with the source count rate. The measured QPO widths are typically 120 Hz, with mean rms amplitude
4.1% H 0.3%. At the upper end of this luminosity range a second significant QPO peak appears with frequency
1065 H 7 Hz, width 40 H 20 Hz, and rms amplitude 3.2% H 0.8%. When both QPOs are visible simultaneously,
the difference between their frequencies is 275 H 8 Hz. When the source brightens beyond LX 5 3.1 3 1037
ergs s21 (110% of the Eddington limit for a helium-rich envelope), neither QPO is detected. Neither the
magnetospheric beat frequency model nor the sonic point model of HF QPOs provides a perfect explanation of
the phenomenology we observe.
These results represent the first detection of kilohertz QPO activity in a globular cluster X-ray binary, and
provide a new method of directly comparing the properties of cluster and noncluster neutron star binaries. If the
highest QPO frequency we observe is identified with the marginally stable orbit in the accretion disk, the neutron
star mass may be 12 MJ, 35%–50% more massive than usually assumed. This may have consequences for the
current evolutionary scenarios for this source and also for the debate about the evolution of millisecond pulsars
in globular clusters.
Subject headings: accretion, accretion disks — stars: individual (4U 18202303) — stars: neutron — X-rays: stars
accurate distance estimate of 6.4 H 0.6 kpc. The small amplitude (12%–3% in the high state, even smaller in the low state)
and sinusoidal shape of its orbital modulation may imply that
the source inclination is 1708– 808, with the modulation being
caused either by occultation of the central source by azimuthal
structure in the accretion disk, or by the periodic obscuration
of a small, hot corona above the disk (Stella et al. 1987a).
However, a larger amplitude of 15%–20% is observed in the
ultraviolet, and if this is modeled in terms of X-ray heating in
the secondary, a more modest inclination of 358–558 may be
required (Anderson et al. 1997).
The large collecting area of the Rossi X-Ray Timing Explorer
(RXTE) Proportional Counter Array (PCA), combined with
the configurable onboard electronics and the relatively high
telemetry rates available (Bradt, Rothschild, & Swank 1993),
now enable us to probe the behavior of 4U 18202303 on much
shorter timescales than previous data sets have allowed. In this
paper we present our discovery of two high-frequency (HF)
QPO peaks in 4U 18202303, the strong dependence of their
visibility and behavior upon the accretion rate of the source,
and the possible implications both for the currently available
physical models for HF QPOs and for the evolution of the
source itself.
1. INTRODUCTION
The bright globular cluster binary 4U 18202303 has shown
pronounced variability on every timescale on which it has been
studied. Its high and low states alternate roughly every 176
days (Priedhorsky & Terrell 1984; Smale & Lochner 1992),
and differ in intensity by a factor of 13. The Eddington-limited
X-ray bursts that occur during the low state (Vacca, Lewin, &
van Paradijs 1986; Haberl et al. 1987) define the central
compact object as a neutron star, and the 685 s orbital period
of the system—the shortest known of any cosmic binary—
strongly suggests that the mass-donating companion star is
degenerate, probably a low-mass (0.06 – 0.08 MJ ) helium white
dwarf (Stella, Priedhorsky, & White 1987a; Rappaport et al.
1987). In frequency space a broad bump is generally observed
in power density spectra from 4U 18202303 at 15–30 Hz,
superposed upon a power-law red noise distribution (Stella,
White, & Priedhorsky 1987b; Dotani et al. 1989). Although
this bump is sometimes referred to as a quasi-periodic oscillation (QPO), current usage is to reserve this term for peaks
where the ratio of FWHM to centroid frequency is less than
0.5 (e.g., van der Klis 1995). Finally, there is some suggestion
that the orbital period of the system is varying on a timescale
of 107 yr (Sansom et al. 1989; Tan et al. 1991), although the
evidence for such a variation seems to be weakening over time
(van der Klis et al. 1993a, 1993b).
The location of 4U 18202303 within 19 of the center of the
globular cluster NGC 6624 provides us with a comparatively
2. OBSERVATIONS
We performed four separate RXTE observations of
4U 18202303 on 1996 October 15.936 –16.310, October
26.548 –26.926, October 28.616 –29.166, and October 30.478 –
31.217 UT, for a total of 100 ks of on-source observing time.
The analysis here concentrates on data from the PCA, which
1 Also Universities Space Research Association, Mail Code 660.2,
NASAyGSFC.
2 Mail Code 662, NASAyGSFC.
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SMALE, ZHANG, & WHITE
Vol. 483
consists of five identical proportional counters with a total area
of 6250 cm2. In the first observation we used several parallel
single-bit observing modes with 122 ms (2213 s) resolution and
differing energy ranges. In the three subsequent pointings,
data were obtained using both a broadband 122 ms single-bit
mode and an event-counting mode with 122 ms time resolution
and 64 channels of energy resolution. PCA data were obtained
over the nominal 1–90 keV range, with the bulk of the source
count rate falling in the 1–20 keV band. The backgroundsubtracted count rate from the source ranged from 1920 –3430
PCA counts s21 (backgrounds of 90 –110 counts s21 have been
removed from all count rates quoted here and henceforth).
These count rates correspond to a dead-time– corrected 2–20
keV luminosity range of 2.4 – 4.2 3 1037 ergs s21 at 6.4 kpc,
placing the source in its low state. The publicly available RXTE
all-sky monitor light curve confirms this.
Examination of hardness ratios and color-color diagrams
reveals that 4U 18202303 continues to follow the “banana”
curve typical of atoll sources (Hasinger & van der Klis 1989)
during these observations. In the first three pointings, where
the PCA count rate is 1920 –2670 counts s21, the data form a
clump in the lower banana branch of the color-color diagram.
In the fourth observation the source is brighter (2520 –3430
counts s21 ) and moves along the upper banana branch. No
X-ray bursts were observed.
3. ANALYSIS AND RESULTS
The power density spectra generated from data obtained
during the first observation revealed the presence of QPOs
with centroid frequencies varying from 600 –700 Hz. A full
analysis of the entire data set shows that the centroid position
of this peak varies between 546 H 2 Hz and 796 H 6 Hz and is
tightly correlated with the source count rate. Figure 1 shows a
selection of HF QPO peaks at various source count rates,
illustrating this effect. The continuum power level in these
figures is 11% below the P 5 2.0 value expected from the
normalization used (Leahy et al. 1983) because of a small
contribution from the instrument dead time. Figure 2 summarizes the results of fitting Lorentzian profiles to the QPO peaks
in the power spectra and shows how the fit parameters vary
with count rate. Within the errors, the FWHM and rms
amplitude of the QPOs are consistent with constant values of
16.8 H 2.0 Hz and 4.1% H 0.3%. The coherence of these
QPOs is high, with nyDn 5 140 –200. The rms amplitudes
increase dramatically with energy; the 8 –20 keV amplitudes
are 1.8 –2.9 times greater than those measured in the 1– 8 keV
band.
In the rather narrow source count rate range 2520 –2560
counts s21 we see a second QPO peak at an even higher
frequency. 4U 18202303 spends 13.5 ks in this regime, and the
detection of this second peak is statistically secure. In Figure 3
we present the power spectrum for these data, showing the
QPO peaks and also the previously known broad low-frequency noise component. Figure 4 shows a blowup of the QPO
profiles. The second QPO peak has a mean position of 1065 H
7 Hz, a mean width of 40 H 20 Hz, and amplitude 3.2% H
0.8%, with none of these parameters varying significantly
within the narrow count rate range. Where the two peaks
appear simultaneously, the difference frequency is consistent
with a constant 275.1 H 7.6 Hz, although it is unfortunate that
we cannot test for constancy over a wider range of count rates
and frequencies.
FIG. 1.—Examples of power density spectra for four separate 12000 –3000
s intervals during the RXTE observations in 1996 October, showing directly the
dependence of the QPO centroid position on the mean source counting rate.
At count rates above 2600 counts s21 and below 2000
counts s21, neither of the QPO peaks is observed. There is an
indication that at the high count rate end of the distribution
the peaks become broader and the rms amplitude decreases
just prior to the disappearance of the QPO, although formally
this is statistically marginal (Fig. 2). In the lower panel of
Figure 3 we show the summed power spectrum for all data
obtained above 2600 counts s21. No QPO activity is detectable,
despite an extremely good signal-to-noise ratio. For a range of
trial QPO widths and centroids of 20 – 40 Hz and 800 –1100 Hz,
respectively, formal 99% upper limits on the rms amplitude of
a QPO peak are typically 0.8%.
4. DISCUSSION
With this discovery, 4U 18202303 joins the swelling ranks of
low-mass X-ray binaries (LMXBs) displaying HF QPO activity
(Zhang, Strohmayer, & Swank 1997a, and references therein).
Several candidate models now exist for the generation of such
HF oscillations. The first is the magnetospheric beat frequency
model (BFM) (Alpar & Shaham 1985; Ghosh & Lamb 1992),
in which the higher of the two frequencies is interpreted as the
Keplerian frequency at the inner disk edge nK, while the lower
is the beat between this frequency and the neutron star spin
frequency (nb 5 nK 2 nspin ). An increase in accretion rate leads
to pressure on the magnetosphere, causing its radius to shrink
No. 2, 1997
KILOHERTZ QPOs IN 4U 18202303
FIG. 2.—QPO centroid frequencies, widths, and rms amplitudes plotted
against the total PCA count rates. Values for the higher frequency kilohertz
QPOs are marked with filled squares, the 550 – 800 Hz QPOs with plus signs.
and the disk to extend closer to the neutron star, thus leading
to a positive correlation between source brightness and QPO
frequency. However, for atoll sources where the inner disk is
dominated by gas pressure rather than radiation pressure, the
magnetospheric BFM predicts that the inner radius of the disk
will be only weakly dependent upon the mass accretion rate
(Ghosh & Lamb 1992), producing a frequencyycount rate
relationship for atoll sources shallower than observed (e.g., for
4U 18202303, d log nyd log(count rate) 5 1.69 H 0.12). This
model may also have difficulty explaining the coherence and
large rms amplitudes of the HF QPOs (Miller, Lamb, & Psaltis
1997).
In the sonic-point model for HF QPOs (Miller et al. 1997)
the higher frequency (1060 Hz) oscillation is interpreted as the
Keplerian frequency nKs of the sonic point at the inner disk
edge, and the lower frequency (500 – 800 Hz) as the beat
between nKs and the neutron star spin period (nBs 5 nKs 2
nspin ). In this scenario the pattern of “clumps” of material
formed in the inner disk is frozen into the radial flow at the
sharp transition point between subsonic and supersonic accretion flow. This material then falls to the neutron stellar surface
without appreciable dissipation, to form arc-shaped stripes of
accretion (and therefore X-ray emission) with the same frequency dependence as at the sonic point. This model can
explain the frequencyyaccretion rate relationship and the
coherence, relative and absolute amplitudes, comparable
widths, and energy-dependence of the QPOs. One important
discrepancy between theory and observation is that the model
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FIG. 3.—Two power spectra covering the 1–2000 Hz range. The top panel
contains the spectrum for the count rate interval 2520 –2560 counts s21, where
both QPO peaks are observed. The bottom panel shows the mean spectrum for
the count rate range 12600 –3400 counts s21, where no QPO peaks are
detected. The broad low-frequency noise bump at 110 Hz is clearly visible in
both spectra.
predicts that the higher frequency oscillation should be the
more reliably observed of the pair and that the lower frequency peak might be weak or absent, whereas, in
4U 18202303 and several other HF QPO sources the lower
frequency QPO is seen more consistently.
When the source count rate increases beyond 2600 PCA
counts s21, the HF QPOs disappear. This may be analogous to
the behavior of the QPO observed between 5 and 50 Hz in the
FIG. 4.—Power density spectrum from the top panel of Fig. 3, expanded to
show the twin peaks and the best-fitting model (constant 1 two Lorentzians).
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SMALE, ZHANG, & WHITE
Z sources, where at higher X-ray intensities the QPO peak
grows smaller and broader and eventually vanishes into the
noise, and the variations in the HF QPO width and rms
amplitude we observe at the limiting count rates lend some
support to this idea. At higher accretion rates the radiation
pressure from the X-ray source may cause the inner disk to
puff up into a torus. The vertical extent of this toroidal
material may block our line of sight to the very innermost
regions of the disk where the HF QPOs originate. However,
the cutoff luminosity of LX 5 3.1 3 1037 ergs s21 only represents 110% of the Eddington luminosity (2.7 3 1038 ergs s21,
assuming a He-rich envelope and canonical neutron star mass
and radius), perhaps a little low for large-scale disk bloating to
occur. It may be possible to detect the buildup of an incipient
scattering cloud by a detailed study of millisecond delays
between the hard and soft X-ray flux, an investigation we will
perform at a later date.
A consequence of both BFMs is that the measured 275 Hz
frequency difference can be interpreted as the rotation frequency of a 3.63 H 0.10 ms neutron star. Clearly we must be
cautious about applying this interpretation to 4U 18202303,
since the constancy of this frequency with accretion rate
cannot be proven in the current data set, but this value would
be consistent with the other probable determinations of neutron star spin periods in LMXBs (4U 1728234: 363 Hzy2.75
ms, Strohmayer et al. 1996b; 4U 06141091: 323 Hzy3.1 ms,
Ford et al. 1997; KS 17312260: 524 Hzy1.91 ms, Smith,
Morgan, & Bradt 1997; 4U 16362536: 581 Hzy1.72 ms, Zhang
et al. 1997b; an unidentified source near J1744228: 589
Hzy1.70 ms, Strohmayer, Lee, & Jahoda 1996a. Note that for
4U 16362536 and KS 17312260, the coherent oscillations
were seen in the bursts at twice the frequency difference
observed in the persistent emission, perhaps because of contributions from two poles). Strong supporting evidence for the
identification of the spin period would be provided by the
detection of a 275 Hz (or 550 Hz) signal during a burst from
4U 18202303; it is unfortunate indeed that no bursts were
observed during our RXTE observations.
The discovery of kilohertz QPOs and a possible neutron star
spin period in 4U 18202303 takes on additional significance
because of the location of the source within the globular
cluster NGC 6624. 4U 18202303 is the first globular cluster
LMXB to show HF QPO behavior, and this detection at first
sight increases the overall similarity of the cluster binaries to
the general binary population. However, despite this similar-
ity, substantial differences exist between 4U 18202303 and the
noncluster Galactic binaries in terms of their probable evolutionary path.
Zhang et al. (1997a) note that the highest QPO frequencies
observed from the set of kilohertz QPO sources studied to
date fall into a rather narrow range of 11060 –1170 Hz,
regardless of the source scale, luminosity, and inferred magnetic field strength. They suggest that these maximum frequencies represent the orbital frequencies at the marginally stable
orbits in each system. Assuming a Schwarzschild spacetime,
the maximum frequency is then related to the neutron star
mass by the equation MnsyMJ 5 2198ynmax (e.g., Shapiro &
Teukolsky 1983), implying that the neutron star masses in
these systems (including 4U 18202303) are 12 MJ, consistent
with a neutron star of birth mass 1.4 MJ accreting matter at a
fraction of the Eddington limit for 1108 yr. In addition, a
lifetime of 15 3 107 yr is sufficient to spin a neutron star up to
millisecond periods if the mean accretion rate is close to the
Eddington limit. The implication is that the neutron star in the
4U 18202303 system may be 35%–50% more massive than the
canonical 1.4 MJ usually assumed.
However, the extremely short 685 s orbital period of
4U 18202303 implies that the secondary is an almost completely degenerate helium white dwarf with mass 10.058 –
0.078 MJ. Models for the formation of such an ultra–shortperiod binary include the collision of a neutron star with a
giant, with subsequent “spiral-in” and ejection of the envelope
(Verbunt 1987), or with a main-sequence star (Bailyn &
Grindlay 1987); another possibility is conservative mass transfer driven by gravitational radiation (Rappaport et al. 1987).
All of these models have a higher probability of occurring
within a globular cluster. The tidal capture models require an
age for 4U 18202303 of less than 107 yr, and in the GR model,
while the secondary cooling time is 1109 yr, the mass transfer
phase is expected to last no longer than 13 3 106 yr. The short
X-ray lifetimes in these models have led to the belief that the
population of neutron stars in globular clusters may be much
greater than observed, which in turn affects on our understanding of the formation of millisecond pulsars within clusters
(Bhattacharya 1995). Thus, in addition to placing direct constraints upon the parameters of the neutron star in the
4U 18202303 system, the HF results from 4U 18202303 may
also help to constrain the evolutionary models of this unique
binary in particular and of globular cluster millisecond pulsars
in general.
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