A&A 464, 1069-1074 (2007)
DOI: 10.1051/0004-6361:20066457
M. Falanga1,2 - J. Poutanen3 - E. W. Bonning4 - L. Kuiper5 - J. M. Bonnet-Bidaud1 - A. Goldwurm1,2 - W. Hermsen5,6 - L. Stella7
1 - CEA Saclay, DSM/DAPNIA/Service d'Astrophysique (CNRS FRE
2591), 91191 Gif-sur-Yvette, France
2 - Unité mixte de recherche Astroparticule et
Cosmologie, 11 place Berthelot, 75005 Paris, France
3 - Astronomy Division, PO Box 3000, 90014 University of
Oulu, Finland
4 - Laboratoire de l'Univers et de ses Théories, Observatoire de
Paris, 92195 Meudon Cedex, France
5 - SRON Netherlands Institute for Space Research, Sorbonnelaan 2,
3584 CA Utrecht, The Netherlands
6 - Astronomical Institute "Anton Pannekoek'', University of
Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands
7 - INAF-Osservatorio Astronomico di Roma, via Frascati 33, 00040
Monteporzio Catone (Roma), Italy
Received 27 September 2006 / Accepted 2 January 2007
Abstract
Aims. HETE J1900.1-2455 is the seventh known X-ray transient accreting millisecond pulsar and has been in outburst for more than one year. We compared the data on HETE J1900.1-2455 with other similar objects and made an attempt at deriving constraints on the physical processes responsible for a spectral formation.
Methods. The broad-band spectrum of the persistent emission in the 2-300 keV energy band and the timing properties were studied using simultaneous INTEGRAL and publicly available RXTE data obtained in October 2005. The properties of the X-ray bursts observed from HETE J1900.1-2455 were also investigated.
Results. The spectrum is well described by a two-component model consisting of a blackbody-like soft X-ray emission at 0.8 keV temperature and a thermal Comptonized spectrum with electron temperature of 30 keV and Thomson optical depth
for the slab geometry. The source is detected by INTEGRAL up to 200 keV at a luminosity of
erg s-1 (assuming a distance of 5 kpc) in the 0.1-200 keV energy band. We have also detected one type I X-ray burst which shows photospheric radius expansion. The burst occurred at an inferred persistent emission level of
3-4% of the Eddington luminosity. Using data for all X-ray bursts observed to date from HETE J1900.1-2455, the burst recurrence time is estimated to be about 2 days. No pulsations have been detected either in the RXTE or in the INTEGRAL data which puts interesting constraints on theories of magnetic field evolution in neutron star low-mass X-ray binaries.
Key words: stars: pulsars: individual: HETE J1900.1-2455 - stars: neutron - X-rays: binaries - X-rays: bursts
The detection of X-ray millisecond pulsation in persistent emission
from low-mass X-ray binaries (LMXBs)
remained elusive for many years until the discovery of the first
accreting millisecond pulsar (MSP) by Wijnands & van der Klis (1998). Since that time, a
total of seven accreting MSP transients have been detected. They are weakly
magnetized (
108-109 G) neutron stars (NS) with spin
frequencies in the 180-600 Hz range and
orbital periods between 40 min and 5 h (see reviews by Wijnands 2006; Poutanen 2006).
Their companion stars have been found to be either highly evolved white
or brown dwarfs. For the first time, the predicted
decrease of the NS spin period during accretion was measured in the
accreting MSP IGR J00291+5934 (Falanga et al. 2005b). This provided a strong
confirmation of the theory of "recycled'' pulsars in which old
neutron stars in LMXBs become millisecond radio pulsars through
spin-up by transfer of angular momentum by the accreting material.
MSP energy spectra can be well described by a two-component model consisting of a soft black body (or multi-color blackbody) and a hard power-law like tail. The soft thermal component could be associated with radiation from the accretion disc and/or the heated NS surface around the shock (see e.g. Gierlinski & Poutanen 2005; Poutanen 2006). The hard emission is likely to be produced by thermal Comptonization in the hot accretion shock on the NS surface (Poutanen & Gierlinski 2003; Gierlinski et al. 2002) with seed photons coming from the stellar surface. The observed hard spectra are similar to the spectra observed from atoll sources in their hard, low-luminosity state (Barret et al. 2000).
HETE J1900.1-2455 was discovered during a bright X-ray burst by the High Energy
Transient Explorer 2 (HETE-2) on 14 June 2005 (Vanderspek et al. 2005).
Followup observations with the Rossi X-ray Timing Explorer (RXTE)
identified the source as the seventh X-ray accreting millisecond
pulsar, with a pulse frequency of 377.3 Hz, an orbital period
of 83 min, and most likely a 0.016-0.07
brown dwarf companion
(Kaaret et al. 2006). The detected burst was consistent with a type I
X-ray burst with photospheric radius expansion.
Assuming that the bolometric burst peak luminosity
during photospheric radius expansion saturated at the Eddington
limit, Kawai & Suzuki (2005) estimated the distance to the source to be
5 kpc assuming helium burst burning and canonical NS values.
An optical counterpart candidate had an R-band
magnitude of 18.02 and a broad HeII emission line spectrum
(Steeghs et al. 2005a; Fox 2005). A similar line was previously
observed in IGR J00291+5934 (Filippenko et al. 2004; Roelofs et al. 2004).
The optical counterpart of the X-ray source is located at
coordinates
and
with an
uncertainty of
.
Near-infrared observations detected the optical
candidate at a constant magnitude of J=17.6. No radio
counterpart consistent with the HETE J1900.1-2455 coordinates was detected by
the VLA (Rupen et al. 2005; Steeghs et al. 2005b).
One year after the discovery, HETE J1900.1-2455 is still active (see Fig. 1).
Compared to other accreting MSPs with outburst periods of a few
days to a month, HETE J1900.1-2455 shows evidence of being a "quasi-persistent''
X-ray source. This source also has other properties atypical for accreting
MSPs. During the first 30 days after the discovery, HETE J1900.1-2455 showed
significant flux emission variability in the fractional rms amplitude
(Galloway et al. 2006).
On July 8, 2005 (MJD 53559) during the flux
brightening, the observed pulse frequency decreased by
,
and in the subsequent observations,
the pulsations were suppressed (Kaaret et al. 2006).
In this paper we report the INTEGRAL observations of HETE J1900.1-2455 obtained simultaneously with RXTE. We study the broad-band spectral and timing properties of the source. The X-ray burst properties are also investigated.
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Figure 1: RXTE/ASM light curve for HETE J1900.1-2455 averaged over 1-day intervals from May 5, 2005 (53500 MJD). The count rate has been converted into flux using 1 Crab Unit for 75 cts s-1 (Levine et al. 1996). The arrows indicate the times of the detected X-ray bursts (Vanderspek et al. 2005; Barbier et al. 2005; Galloway et al. 2005; and this work). |
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The present data were obtained during the
INTEGRAL (Winkler et al. 2003) Target of Opportunity (ToO) observation during
satellite revolution 371, starting on October 27 and ending on October 29, 2005,
with a total exposure time of 210 ks.
The observation, aimed at HETE J1900.1-2455, consists of 64 stable
pointings with a source position offset <
.
We analyzed data from the IBIS/ISGRI coded mask telescope (Ubertini et al. 2003; Lebrun et al. 2003)
at energies between 18 and 300 keV and from the JEM-X monitor, module 1
(Lund et al. 2003) between 3 and 20 keV.
The data reduction was performed using the standard Offline Science
Analysis (OSA) version 5.1 distributed by the INTEGRAL Science
Data Center (Courvoisier et al. 2003). The algorithms used for the spatial and
spectral analysis are described in Goldwurm et al. (2003). The ISGRI light
curves are based on events selected according to the detector
illumination pattern for HETE J1900.1-2455. For ISGRI we used an illumination
factor threshold of 0.25 for the energy range 18-40 keV; for JEM-X we
used the event list of the whole detector in the 3-6 keV, 6-12 keV
and 12-20 keV energy band.
We first deconvolved and analyzed separately the 64 single pointings and
then combined them into a total mosaic image in the 20-40 keV and
40-200 keV energy band, respectively. In the mosaic, HETE J1900.1-2455 is
clearly detected at a significance level of
(20-40 keV) and
at higher energy (40-200 keV).
The source position in the 20-40 keV band is
and
(error of
at the
90 per cent confidence level, Gros et al. 2003), which
is offset with respect to the optical position by
(Fox 2005).
The background-subtracted 20-40 and 40-200 keV light curves were
extracted from the images using all available pointings, each with
3.3 ks exposure. The source mean count rate was almost constant
at
4.0 cts s-1 (
erg cm-2 s-1) in the 20-40 keV band and
2.8 cts s-1 (
erg cm-2 s-1) in the 40-200 keV energy band.
The count rates were converted to un-absorbed flux using
the Comptonization model described in Sect. 3.1.1.
We used two RXTE ToO observations performed simultaneously with
INTEGRAL between October 28 and 29, 2005 (observation
id. 91432), for which the data were publicly available. The total
net exposure times were 6.2 and 3.2 ks, respectively.
We analyzed data from the Proportional Counter Array
(PCA; 2-60 keV) (Jahoda et al. 1996) and the High Energy X-ray Timing
Experiment (HEXTE; 15-250 keV) (Rothschild et al. 1998) on board the RXTE
satellite. For the spectral analysis, we extracted the PCA (modules 0,
2 and 3) energy spectrum using the standard software package FTOOLS
version 6.0.2.
For HEXTE, we used the ON-source data, using default screening criteria for
Cluster 0.
For the timing analysis we used all PCU data, which were on
during the entire observation. The PCA data were collected in the E_125us_64M_0_1s event mode, recording event arrival times with
125 s time resolution, and sorting events in 64 PHA
channels. Default selection criteria were applied.
Broad-band spectral analysis was done using XSPEC version 11.3 (Arnaud 1996), combining the 3-22 keV RXTE/PCA data with the 3-22 keV INTEGRAL/JEM-X and 16-90 keV RXTE/HEXTE data with 20-300 keV INTEGRAL/ISGRI data. A multiplicative factor for each instrument was included in the fit to take into account the uncertainty in the cross-calibration of the instruments. The factor was fixed at 1 for the PCA data. A systematic error of 1% was applied to PCA/HEXTE and 2% to JEM-X/ISGRI spectra, which corresponds to the current uncertainties in the response matrix. All uncertainties in the spectral parameters are given at a 90% confidence level for single parameters. We use a source distance of 5 kpc throughout the paper.
We analyzed the JEM-X/ISGRI spectra independently both
before and after the X-ray burst, and no significant spectral variation was
found. The burst occurred around the middle of the INTEGRAL observation.
The RXTE observations were also performed before and after the
X-ray burst, and the PCA/HEXTE spectral parameters were consistent with those
determined from the INTEGRAL spectra.
Therefore, we studied in
detail the broad-band 3-300 keV spectrum of HETE J1900.1-2455 using the joint
INTEGRAL and RXTE data. For the INTEGRAL data we
removed the time interval corresponding to the burst. The energy range
covered by JEM-X/PCA does not allow us to constrain the
interstellar hydrogen column density, ,
well.
Therefore, in all our spectral fits we fixed
at
cm-2, the value found from Swift observations
at lower energies (Campana et al. 2005). This value is close to
the Galactic value reported in the radio maps of Dickey & Lockman (1990).
We first fit the joint JEM-X/ISGRI/PCA/HEXTE (3-300 keV) spectrum
using a simple photoelectrically-absorbed power-law, PL, model which
was found inadequate with a
.
A better fit was found by adding a blackbody, BB, model for the soft thermal
emission and by replacing the PL with a cutoff PL model.
This gave a
.
The best-fit parameters
are: blackbody temperature
keV, a power-law photon index
,
and the cutoff energy
59-2+3 keV. The PCA data show
residuals in the
6-10 keV range that can be fit by a broad Gaussian
emission line. Correspondingly, the fit improved with a
.
Confining the centroid of the line in the 6.3-6.8 keV range gave a line width of
(equivalent width
102 eV); fixing the line width at 0.5 keV constrains its
position at
6.41 keV.
Table 1: Best-fit spectral parameters with G AUSSIAN + COMPPS (or cutoff PL) + BB (or DISKBB) model.
In order to compare the HETE J1900.1-2455 spectrum with previously observed spectra
of the same source class (Gierlinski et al. 2002; Falanga et al. 2005a,b; Gierlinski & Poutanen 2005), we replaced the
simple cutoff PL model with the thermal Comptonization model
COMPPS in the slab geometry
(Poutanen & Svensson 1996). The main model parameters are the Thomson optical depth
across the slab, the electron temperature
,
the soft seed photon temperature
,
and
the inclination angle
between the slab normal and the line of sight.
The seed photons are assumed to be injected from the bottom of the
slab. The soft thermal emission is fit by a simple blackbody BB or a
multi-temperature disc blackbody DISKBB model (Mitsuda et al. 1984).
The best fit parameters for the different models are reported in Table 1. In Fig. 2, we show the unfolded spectrum
and the residuals of the data to the BB plus COMPPS model.
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Figure 2: The unfolded spectrum of HETE J1900.1-2455 fit with a COMPPS model plus a BB and a Gaussian line. The data points correspond to the PCA (3-22 keV), JEM-X (3-22 keV), HEXTE (16-90 keV) and the ISGRI (20-300 keV) spectra, respectively. The blackbody model is shown by a dot-dashed curve, the dotted curve gives the COMPPS model, the dashed curve is the Gaussian line, and the total spectrum is shown by the solid curve. The lower panel shows the residuals between the data and the model. |
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The temperature of the soft thermal emission was found
to be a factor 2 higher than in other accreting millisecond pulsars
(e.g., Falanga et al. 2005a; Gierlinski & Poutanen 2005). Since its discovery, this source has
shown a rather high blackbody temperature (Kaaret et al. 2006).
It was suggested for the millisecond pulsar XTE J1751-305 that the
observed soft component could also be the source of the seed photons
(Gierlinski & Poutanen 2005), therefore, we repeated the fit with
and obtained only a marginally worse
.
As discussed by
Gierlinski & Poutanen (2005) and Kaaret et al. (2006), the true spectrum may consist of
two black-bodies (disk and the heated surface of the NS).
In adding another black-body component, we found that the new model
does not improve the fit much.
As the PCA/JEM-X energy range begins at 3 keV, it is
impossible to search for additional soft emission in these data.
We carried out a Z12-statistic (Buccheri et al. 1983) period search of HETE J1900.1-2455 using barycentered (JPL DE200 solar system ephemeris) and orbital
motion (Kaaret et al. 2006) corrected arrival times registered
by the PCA instrument during the two short pointings of the ToO observation
in the 2-10 keV and 10-20 keV energy bands.
We centered our periodicity search around the last measured frequency
value 377.2959 Hz, i.e. after the frequency shift observed on 53559 MJD
(see Kaaret et al. 2006), with a rather wide frequency range of
0.007 Hz. Within the scanned frequency range we did not find
any indication of significant pulsations in either of the two energy bands.
Thus, unless there was another
frequency shift between 53567 and 53670 MJD such that the frequency
range of our search was too small, there is no
evidence for a pulsed signal from HETE J1900.1-2455 in the two short RXTE
observations falling within the INTEGRAL observation.
Thinking that the pulsed fraction might increase above 20-30 keV, as was found for IGR J00291-5934 (Falanga et al. 2005b), we also searched the high-energy INTEGRAL data for the 2.65 ms period. No coherent pulsed signal was found in the 18-150 keV IBIS/ISGRI band near the expected pulse frequency of HETE J1900.1-2455, confirming the suppression of the pulsed signal. Galloway et al. (2006) studied the pulsed fraction in detail and find an upper limit of about 1% rms during our observation.
In Fig. 3 we show the JEM-X and ISGRI burst light
curve (28 October 2005, 10:25:12 UTC) in different energy bands. The
burst rise time was
s. The double peak profile is
clearly evident at
high energy (lower panel) within the first 12 s, while
during this time the intensity at lower energy (upper panel) remains
constant. This can be interpreted as a consequence of a photospheric
radius expansion (PRE) episode during the first part of the outburst
(see e.g., Verbunt & van den Heuvel 1995). When a burst undergoes a PRE episode,
the luminosity remains nearly constant at
the Eddington value, the atmosphere expands, and its temperature
decreases, resulting in a double-peak profile observed at high
energies. The tail of the burst at high energy can be seen for about
5 s after the PRE episode.
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Figure 3: A bright X-ray burst detected from HETE J1900.1-2455. The JEM-X (3-20 keV, upper panel) and IBIS/ISGRI (18-40 keV; lower panel) net light curves are shown (background subtracted). The time bin is 0.5 s for both IBIS/ISGRI and JEM-X light curve. At high energy the burst shows strong evidence of photospheric radius expansion. |
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We performed time-resolved analysis of the burst spectrum based on the
JEM-X/ISGRI 3-50 keV energy band data. We verified that during the burst
pointing the count rate was stable; we then used the JEM-X/ISGRI
persistent emission spectrum as background. The burst is divided into time
intervals as shown in Fig. 4, the shortest intervals being
3 s during the two spikes observed at high energy (see Fig. 4). The burst net spectrum was well fit by a
photoelectrically absorbed blackbody (
). The
inferred blackbody temperature,
,
and apparent blackbody
radius,
,
are shown in the middle and lower panels,
respectively. During the first 12 s, the un-absorbed
bolometric flux was almost constant at
erg cm-2 s-1, while the blackbody temperature dropped in the middle,
simultaneous with an increase by a factor of
1.5 in blackbody
radius. The observed temperature reached a peak at
2.5 keV, and then
gradually decreased. The softening of the emission towards the end of the
decay phase is also indicated by the e-folding decay times
of
s in the 3-6 keV to
s in the 12-20 keV
energy band. This behavior is typically observed during PRE X-ray bursts
(e.g., Kuulkers et al. 2003).
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Figure 4: Result of the X-ray burst time-resolved spectral analysis. The apparent blackbody radius was estimated assuming a source distance of 5 kpc. |
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The burst fluence,
erg cm-2, is
calculated by integrating the measured
over the burst
duration of
50 s. The effective burst duration is
s, and the ratio of the observed persistent flux to
the net peak flux is
.
The burst has the same spectral parameters as previous
bursts observed for this source with HETE-2 (Kawai & Suzuki 2005) and
RXTE (Galloway et al. 2006,2005).
Assuming a helium-burst at the Eddington limit (Lewin et al. 1992) and canonical
NS parameters (1.4 solar mass and radius of 10 km), we
estimate the source distance to be
5 kpc.
We analyzed the INTEGRAL and RXTE data of the
accretion-powered millisecond pulsar HETE J1900.1-2455. We observed the
source remaining in a bright state 136 days after its discovery with
a bolometric luminosity during our observation of 3-4 per cent
of
(Frank et al. 2002)
(see Fig. 1 for the RXTE/ASM 1.5-12 keV light
curve).
The outburst light curve of HETE J1900.1-2455 is
completely different from that of the other six observed MSPs
which have shown exponential decays
during the outburst: declining from peak luminosities of 3-30 per cent
with a decay time-scale of several days up to
120 days.
Only HETE J1900.1-2455 has shown a fairly steady behavior at a low
mass accretion rate (between 1 and 4 per cent of Eddington) with no
sign of a transition toward quiescence. The most peculiar behavior of HETE J1900.1-2455
is the suppression of the pulsation at the NS spin period
about a month from the beginning of the outburst (Kaaret et al. 2006);
all other MSPs have had detectable
pulsations throughout the duration of their outburst. The missing
pulsations and the persistent X-ray emission at low mass
accretion rate shows HETE J1900.1-2455 to be similar to the most commonly
observed persistant, non-pulsating LMXB systems. It seems that the
price to pay for being active over a long time is that pulsations are
suppressed, i.e. there is an evident link between the long period of
mass accretion and the missing pulsations.
The best spectral fit to the data required a two-component model, a cutoff PL or a thermal Comptonization model together with a soft component (see
Table 1). The soft thermal emission detected at low energies
could come either from the accretion disk or from a hot spot on the NS surface.
As for the hard component, it most likely originates from the Comptonization
of soft seed photons,
keV in a hot
keV plasma of moderate optical thickness
.
The hard spectral component up to 200 keV contributes most
of the observed flux (70%), even though a soft blackbody component is
needed to fit the data. For the source distance of 5 kpc, the
unabsorbed 0.1-300 keV luminosity was
erg s-1
(for different models).
We could not distinguish between the multi-temperature blackbody and
single blackbody models, as both gave comparable parameters and .
However, for a distance of 5 kpc, our fit for a disk blackbody gives
an inner disk radius,
km,
smaller than the expected NS radius.
For blackbody emission, the fit implies an apparent area of the
emission region
km2, which could be consistent with a
heated NS surface around the accretion shock (Poutanen & Gierlinski 2003; Gierlinski et al. 2002; Gierlinski & Poutanen 2005).
On the other hand, the observed spectra before MJD 53558 are
similar to those observed by us when pulsations are absent (Kaaret et al. 2006).
They are also very similar to those of the atoll sources at low
luminosities (Barret et al. 2000), where the X-rays are probably
produced in the boundary/spreading
layer near the NS equator (Kluzniak & Wilson 1991; Suleimanov & Poutanen 2006; Inogamov & Sunyaev 1999).
Spectral similarities can be explained if in both types of sources
(accreting MSPs and non-pulsating atoll sources), the energy dissipation
happens in the optically thin medium (i.e. accretion shock and
boundary/spreading layer) and the spectral properties
are determined solely by energy balance and feedback
from the NS surface which provides cooling in the form of soft photons
(see e.g. Stern et al. 1995; Haardt & Maraschi 1993; Poutanen & Svensson 1996; Malzac et al. 2001).
In these two-phase models (cool neutron star with a hot dissipation
region above), the product of electron temperature and optical depth
is approximately constant.
In HETE J1900.1-2455 we observe
keV
(see Table 1) which is consistent with the values determined for other MSPs
(Poutanen & Gierlinski 2003; Falanga et al. 2005a,b; Gierlinski & Poutanen 2005; Poutanen 2006) as well as with the theoretical models.
Since we found a fairly high blackbody temperature
compared to other MSP sources, we attempted to fit a blackbody model
with the soft emission being the source of the seed photons, i.e.
.
The obtained parameters are consistent with the
other models, with similar optical depth, plasma temperature, and
slightly lower soft thermal emission temperature.
However, this fit implies a much larger apparent area of the seed photons,
km2, inconsistent with the whole NS
surface.
Several X-ray bursts have been observed for this source by various
observatories. These bursts are indicated with arrows in Fig. 1. The burst described in this work is similar in its
properties to the other observed bursts as reported by
Barbier et al. (2005); Vanderspek et al. (2005); Galloway et al. (2006,2005).
From the observed INTEGRAL burst properties and mass
accretion rates inferred from
the persistent luminosity, the present theory predicts that all these
bursts are pure helium burning (e.g. Strohmayer & Bildsten 2006). For helium
flashes, the fuel burns rapidly, since there are no slow weak
interactions, and the local Eddington limit is often exceeded. These
conditions lead to PRE bursts with a duration, set mostly by the time
it takes the heat to escape, of the order of 5-10 s, as
observed. In the framework of the
thermonuclear-flash models (e.g., Lewin et al. 1995) the burst
duration, s, and the ratio of
observed persistent flux to net peak flux
indicate
a hydrogen-poor burst.
Because there were no other bursts observed during the INTEGRAL
observation, the burst recurrence time,
,
must be at
least one day. We can compute the ratio of the total energy
emitted in the persistent flux to that emitted in the burst
We have found that the source spectrum is similar to other accreting
X-ray millisecond pulsars having a high plasma temperature around 30 keV and a Thomson optical depth 2.
This source differs from other MSP in requiring thermal
soft X-ray emission with nearly double the temperature.
From our spectral fits we infer that this emission is not
likely be produced in a multi-temperature accretion
disk but more likely arises from thermal emission at the NS
surface. One might expect that the
lack of pulsations could be due to a particularly high optical depth,
but our spectral fits rule out this possibility.
The reason for the lack of coherent pulsations in the persistent emission from LMXBs is still an open question. Different explanations have been put forward to explain this phenomenon, including models which invoke gravitational lensing, electron scattering, or weak surface magnetic fields due to magnetic screening (Wood et al. 1988; Titarchuk et al. 2000; Cumming et al. 2001; Brainerd & Lamb 1987, and references therein). The high accretion rate inferred for HETE J1900.1-2455 relative to the other known MSP transients suggests that we may be observing the evolution of the NS's magnetic field due to magnetic screening in this source (Cumming et al. 2001). The transition of HETE J1900.1-2455 from an X-ray millisecond pulsar to a persistent LMXB could indicate that there is a population of suppressed X-ray millisecond pulsars among the non-pulsating LMXBs. Detailed observations of this source at the epoch of pulsation suppression can help to solving the long-standing issue of missing pulsations in persistent LMXB emission.
Acknowledgements
M.F. acknowledges the French Space Agency (CNES) for financial support. J.P. acknowledges the Academy of Finland grants 102181 and 110792. E.W.B. is supported by Marie Curie Incoming European Fellowship contract MIF1-CT-2005-008762 within the 6th European Community Framework Programme.