Evidence for hot clumpy accretion flow in the transitional millisecond pulsar PSR J1023+0038
T. Shahbaz Y. Dallilar A. Garner S. Eikenberry A. Veledina P. Gandhi
 

[
    Rakesh Kumar
    December 30, 2023
=====================



 
We present simultaneous optical and near-infrared (IR) photometry 
of the millisecond pulsar PSR J1023+0038 during its low-mass 
X-ray binary phase. The r'- and K_s-band light curves show 
rectangular, flat-bottomed dips, similar to the X-ray 
mode-switching (active–passive state transitions) behaviour 
observed previously. The cross-correlation function (CCF) of the 
optical and near-IR data reveals a strong, broad negative 
anti-correlation at negative lags, a broad positive correlation 
at positive lags, with a strong, positive narrow correlation 
superimposed. The shape of the CCF resembles the CCF of black 
hole X-ray binaries but the time-scales are different. The 
features can be explained by reprocessing and a hot accretion 
flow close to the neutron star's magnetospheric radius. 
The optical emission is dominated by the reprocessed 
component, whereas the near-IR emission contains the emission from plasmoids in the hot 
accretion flow and a reprocessed component. 
The rapid active–passive state transition occurs 
when the hot accretion flow material is channelled onto the neutron star and is expelled from 
its magnetosphere. 
During the transition the optical reprocessing component decreases  
resulting in the removal of a blue spectral component. 
The accretion of clumpy material through the magnetic barrier of the neutron star 
produces the observed near-IR/optical CCF and variability.
The dip at negative lags corresponds to the suppression of the near-IR 
synchrotron component in the hot flow, whereas the broad positive correlation at positive lags 
is driven by the increased synchrotron emission of the outflowing plasmoids. The narrow peak 
in the CCF is due to the delayed reprocessed component, enhanced by the increased X-ray 
emission. 




binaries: close – 
stars: fundamental parameters – 
stars: individual: PSR J1023+0038 –  
stars: neutron – 
X-rays: binaries












§ INTRODUCTION

 
Millisecond radio pulsars (MSPs) are believed to be the descendants of 
old, slowly rotating weakly magnetic field neutron stars that show radio, 
X-ray, and/or γ-ray pulsations, that are present in low-mass X-ray 
binaries (LMXBs). The theory of recycled pulsars suggests that after the 
neutron star turns off its radio pulsations, the transfer of angular 
momentum from the low-mass companion star to the neutron star via 
accretion is responsible for the spin-up of the initially slowly rotating 
neutron star <cit.>. During this accretion 
phase, X-ray pulsations at the spin frequency of the neutron star are 
detected and the system shows the typical features of an accreting 
millisecond X-ray pulsar (AMXP). The recycling scenario of MSPs discussed 
above was initially confirmed by  <cit.>, which was 
the first source that showed the transition between the rotation powered 
state to the accretion powered state. We now know of three transitional 
MSPs:  <cit.>, XSS J12270–4859 <cit.> 
and M28I (=IGR J18245–2452) <cit.>.

 transitioned from a rotation-powered to an accretion-powered LMXB 
state in 2013 June <cit.> and so far has 
remained in this state. The state transition involved the disappearance of 
the radio pulsed signal as well as an increase in the GeV flux by a factor 
∼ 5 <cit.>. In the optical, the system brightened by 
∼ 1 mag and showed the presence of several broad emission lines 
typical of an accretion disc <cit.>. In the LMXB state, the 
X-ray luminosity varied between ∼ 10^32.5-10^34.5 showing 
three distinct states: (1) high “active” state with L_X ∼ 
3×10^33 present 80 per cent of the time; (2) low “passive” 
state with L_X∼ 5 ×10^32 present 20 per cent of the 
time; (3) and the “flare” state with L_X ∼ 3× 10^34 
present for about 2 per cent of the time <cit.>. 
Coherent X-ray pulsations have been observed but appear only in the high 
state, and have been interpreted as being due to the inflowing accretion 
material heating the magnetic polar caps of rotating neutron star 
<cit.>. The transitions between the low and high states are 
very rapid with a time-scale of 10 s and results in rectangular-shaped 
dips in the X-ray light which seem to be ubiquitous in all of the 
X-ray observations. Similar variability has also been observed at 
optical wavelengths with rectangular dip ingress and egress times of 
∼20 s <cit.>.
However, given the limited simultaneous optical/X-ray 
observations, it is not clear if the X-ray and optical dips are 
direct counterparts of each other. Simultaneous XMM–Newton 
X-ray and B-band optical light curves show X-ray dips that do not 
usually have corresponding optical dips <cit.>. However, 
the uncertaintes in the B-band data are large and given that the 
dips in the blue are weak <cit.>. one cannot rule out if 
the dips are present. 

In this paper we present the results of simultaneous optical/near-IR fast 
imaging of . We deterimine the auto-correlation function (ACF) of 
the optical and near-IR light curves as well as the cross-correlation 
(CCF) function of the two light curves. We explain the observed features 
of the ACFs and CCFs as due to the hot, clumpy inner accetion flow close to the 
pulsar's magnetosphere.








§ OBSERVATIONS AND DATA REDUCTION





 §.§ High-speed optical photometry



Fast optical imaging of  was carried out on the night of 2017 
February 8 using ACAM on the 4.2 m William Herschel Telescope (WHT). The 
CCD was binned by a factor of 2 and windowed down to 200×400 
pixels, which reduced the dead time between exposures to only 1.85 s.  
The plate scale was 0.25 arcsec pixel^-1. We used the r' filter and an 
exposure time of 2.0 s which resulted in a time resolution of 3.85 s.  
Observations were obtained from 2017 February 9 01:37:21 to 05:31:29 UT 
and the seeing was typically between 1.0–2.0 arcsec.

The images were first bias-subtracted and flat-fielded.  The target counts 
were then extracted using optimal photometry with a seeing-dependent 
variable circular aperture tracking the centroid of the source on each 
image. The sky background was measured from the clipped mean in an annular 
aperture around the target.  Relative photometry of  was then 
carried out with respect to the local standard star 
SDSS J102343.30+003819.1 r' = 14.778. The mean magnitude of  
was r' = 16.48.




 §.§ High-speed near-Infrared photometry



Fast near-Infrared imaging of  was carried out on the night of 
2017 February 8 using Canarias InfraRed Camera Experiment (CIRCE; 
) on the 10.4 m Gran Telescopio Canarias (GTC). The 
plate scale of the array was 0.1 arcsec pixel^-1 and the image size was 
1855×1365 pixels. The K_s filter was used with an exposure time of 
5.0 s and a dead-time of 1 s, resulting in a time resolution of 5 s. A 
five-point dither pattern was used with 5 exposures at each 
dither position. Observations were obtained from 2017 February 9 01:12:21 
to 05:31:04 UT. Dark images were also taken with the same detector 
configuration and exposure time.

The CIRCE data reduction was carried out using the 
SuperFATBOY[SuperFATBOY is an XML-controlled 
GPU-enabled Python pipeline developed at the University of Florida] data 
reduction pipeline. We first performed the linearity correction and dark 
subtraction on all the images. A flat-field was then generated and 
applied to the science images. The sky background was determined using the 
images in each dither pattern. Finally, bad pixels and cosmic ray events 
were interpolated and the images binned by 2 pixels to improve 
signal-to-noise.

Before extractng the counts from the stars in the field the images were 
first shifted and aligned. We used optimal photometry with a 
seeing-dependent variable circular aperture tracking the centroid of the 
source on each image to determine the star counts.  The sky background was 
measured from the clipped mean in an annular aperture around the target.  
Relative photometry of  was then carried out with respect to the 
local standard star 2MASSXJ10235051+0038163 with K_s = 14.894 (the 
ACAM local standard could not be used because it occasionally fell into 
the cosmetic gap of the IR array). The mean magnitude of  was 
K_s = 15.14.

















§ LIGHT CURVES



Figure <ref> shows the observed flux r'- and K_s-band light 
curves of  and a comparison star of similar brightness, where we 
converted the magnitudes to flux density using the appropriate zero point 
for each band. The r'-band light curve clearly show the secondary star's 
heated ellipsoidal modulation with superimposed flaring activity. Flares 
and rectangular shaped dips are present similar to previous optical light 
curves <cit.>. We also show the light curves of the 
comparison stars. As one can see there is some low-level structure in the 
K_s-band comparison star light curve.

Fig. <ref> shows the de-reddened, de-trended r'- and 
K_s-band flux light curves. We used a colour excess of E(B-V) = 0.073 
<cit.> and A_ V/E(B-V) = 3.1 <cit.> to 
de-reddened the magnitudes and then converted the magnitudes to flux 
density. Finally we de-trended the light curves using a 3rd and 1st order 
polynomial for the r'- and K_s band light curves, respectively. The 
passive-, active- and flare-states are clearly seen in the r'-band light 
curve rectangular, flat-bottomed dip features are apparent, which are 
similar to the mode-switching behaviour (passive- and active-state) that 
have been observed in the X-ray and optical light curves 
<cit.>. The histogram of the 
de-reddened, de-trended r'-band flux values (see Fig. <ref>) 
clearly show a bi-modal distribution between the passive- and 
active-states. Such a distribution is not so apparent in the K_s-band 
light curve. This is because the rectangular dips in the r'-band light 
curve are deeper than the dips in the K_s-band light curve; the 
active minus passive (active-passive)  flux of the de-reddened light curves are 0.40 and 0.14 mJy 
for the r'- and K_s band light curves, respectively.









 §.§ Light curve correlations


In an attempt to understand the origin and emission mechanism of the 
optical and near-IR light curves, we calculate the ACF of the optical and 
near-IR light curves and the CCF between the observed optical and near-IR 
light curves. The analysis is a simple determination of the relative 
time-variability between the two wavelength dependent light curves and 
provides a clear, uncomplicated (average) comparison of the two signals 
with respect to time. The ACF represents a correlation of a light curve 
with itself, and gives a measure of the effective coherence time-scales in 
the data. The CCF represents the convolution of two light curve and 
reveals whether they have the same features and the time delay between 
them. To determine the ACF and CCF between two light curves (i.e. the 
cross-correlation coefficient versus time-delay between the light curves) 
we compute the discrete correlation function (DCF) using 
pydc[https://github.com/astronomerdamo/pydcf], which 
works well with unevenly sampled data <cit.>. 
Positive time-lags mean that the optical leads the near-IR, whereas 
negative time-lags means that the optical lags the near-IR. To 
calculate the ACF we use the whole light curve and the time-resolution of 
the data. To calculate the CCF between optical and near-IR light curves we 
only use data that are simultaneous (14000 s). Given that time-resolution 
of the r'-band data is better than the K_s-band data, when calculating 
the CCF we rebin the light curves to the best time resolution of the 
K_s-band data. 



  §.§.§ ACFs



In Fig. <ref> we show the ACF of entire r'- and 
K_s-band light curves of . The r'- and K_s-band ACFs have 
different widths; with a full width at half maximum (FWHM) of 130 s and 
90 s, respectively. Above ∼70 s the K_s-band ACF is broader than 
the r'-band ACF, which argues for a reprocessing origin for the 
slowly-variable component, most likely in the outer regions of the 
accretion disc. 
However, very close to the core, the r'-band ACF is broader than the 
K_s-band ACF, which argues against a simple reprocessing origin (see 
Section <ref>). The K_s-band comparison star light curve 
(see Fig. <ref>) shows some low-level correlated variability. 
Indeed, this is seen in its ACF (see Fig. <ref>), which 
has a non-zero width, with a full width at half maximum of 40 s, similar 
to the time-scale of the dither pattern (see Section <ref>). In 
contrast, the ACF of the r'-band comparison star light curve does not 
show any peaks. This suggests that there are some low-level systematics in 
the data reduction of the near-IR data possibly due to under-corrected 
cosmetic defects in the CIRCE engineering-grade detector array. Hence, the 
true width of the ACF of  is smaller.

In Fig. <ref> we show the optical and near-IR CCF using 
all the simultaneous optical and near-IR data (14000 s). The negative lag 
implies the optical band is delayed with respect to the near-IR, whereas 
an anti-correlation implies that the variability between the near-IR and 
optical fluxes is out of phase. We observe a strong, broad negative 
anti-correlation on time-scales of ∼-300 s, a broad positive 
correlation near-IR lag at ∼+300 s and a strong, positive and narrow 
correlation at ∼+5 s (see Fig. <ref>).

To see if there is a time-dependent evolution in the ACF and CCF
we compute the dynamic ACF and CCFs (see Fig. <ref>)
calculated using a windows size of 1000 s and a step size of 500 s, i.e. 
overlapping sections where every second ACF/CCF is independent. A mean CCF 
is then derived for each time series pair, which effectively acts as a 
high-pass filter, and variations with time-scales longer than ∼500 s 
do not appear. One can see, the K_s-band ACF is not always broader 
than the r'-band ACF, the width of the ACFs change with time.




  §.§.§ Light curves



In Figs. <ref> and <ref> we show the 
de-trended light curves and the r'/K_s flux ratio and the r'/K_s 
versus K_s-band flux ratio diagram. for each 2000 s block of data. 
The yellow and green points mark the passive and active-states, respectively, which 
are also shown in the r'/K_s light curve plot. During the transition 
from the active to passive-state, the r'/K_s flux ratio decreases 
because there is a larger decrease in the r'-band flux compared to the 
K_s-band flux: there is a removal of a blue spectral component.




 §.§ POWER DENSITY SPECTRUM



In Fig. <ref> we show power density spectrum (PDS) of the 
de-reddened optical and near-IR light curves of  (see 
Section <ref>). We use the Lomb-Scargle method to compute the 
periodograms <cit.> with the constraints imposed by the Nyquist 
frequency, the typical duration of each observation and use the recipe 
given in <cit.> to calculate the number of independent 
frequencies. We then bin and fit the PDS in logarithmic space 
<cit.>, where white noise level was subtracted by fitting the 
highest frequencies with a white-noise (constant) plus red-noise 
(power-law; P∝ν^β) model (only for the  light 
curves). We find that the PDS of the r'- and K_s-band light curve of 
 is dominated by a red-noise component with a power-law index of 
β=-1.34±0.04 and -1.04±0.08, respectively, typical of 
aperiodic activity in X-ray binaries and X-ray transients in outburst and 
quiescence, which have β in the range -1.0 to -2.0 <cit.>. The 
power-law index of the r'- and K_s-band comparison star PDS 
β=0.04±0.04 and -0.22±0.04, respectively. The r'-band PDS 
is consistent with zero, however, for the K_s-band, the power-law index 
is significant, suggesting that there are systematic effects in the data 
(the PDS of the light curves using of a different local standard is also 
non-zero),  possibly due to under-corrected cosmetic defects in the 
CIRCE engineering-grade detector array.

When determining the light curve of  we divided the counts of 
 into the counts of the local standard which does not vary To 
investigative the effects of using a red-noise dominated local standard 
star (which has some low level variability) when computing the 
differential light curve of  and comparison star, we perform a 
Monte Carlo simulation where we generate light curves with exactly the 
same sampling and integration times as the  data. For each Monte 
Carlo, we simulate two light curve (LC_1 and LC_2) using the method of 
<cit.>, with different PDS power-law indices, β_1 and 
β_2, respectively. We divide the two light curves (LC=LC_2/LC_1) 
and calculate the PDS. We perform 1000 simulations, bin and fit the PDS in 
logarithmic space <cit.>, and then determine the  PDS 
power-law index β. We assume that the local standard (LC_1) has 
low-level variability with β_1=0.0 to 0.50, whereas, the target of 
interest (LC_2) is dominated by red-noise, where β_2=0.5–1.5.
Our simulations show that β lies between β_1 and β_2, 
i.e. the red-noise dominated local standard light curve (LC_1) makes 
power-law index of the differential light curve (LC) less steep. In 
Fig. <ref> shows the results of a simulation where final 
light curve LC has β=-1.04. As one can see the real PDS power-law 
index (β_2) of the target light curve LC_2 is steeper than the 
power-law index of differential light curve LC, β_2<β.
Although we cannot determine the real power-law index of the PDS of the 
K_s-band light curve because we do know the PDS power-law index of 
the local standard star used in the near-IR  analysis. All we can 
say is we say is that the near-IR light curve of  has a PDS of 
<-1.04±0.08. Given that the PDS of the comparison star is
-0.22±0.04, at most we expect a similar amount of variability in the 
local standard star. Hence, we find that r'-band PDS is steeper than the 
K_s-band PDS. Both PDS have similar power at low-frequencies, however, 
the K_s-band PDS has more variability at high frequencies.











§ DISCUSSION




 §.§ The spectral energy distribution of the rectangular dips



To date there are three (PSR J1023+0038, M28I and XSS J12270–4859) 
transitional pulsars systems that transition between accretion-powered 
LMXB and rotation-powered radio pulsar states <cit.>. Of these systems  and XSS J12270–4859 show 
rapid (<10 s) transitions from a high X-ray luminosity active-state to 
a low luminosity passive-state. In  similar optical transitions 
are observed but on a slightly longer time-scale (∼20 s.
Simultaneous XMM–Newton X-ray and B-band optical light curves show X-ray 
dips that do not usually have corresponding optical dips 
<cit.>. However, given that the B-band dips are much weaker 
compared to in the r'-band <cit.>
combined with the large uncertainties in the B-band data, one cannot
cannot rule out if the dips are present and one cannot rule out that 
the X-ray and optical dips are direct counterparts of each 
other.

) therefore suggest that the optical analogue of the X-ray 
model-switching may be due to reprocessing of the X-ray signal.

During the active-state X-ray pulsations are observed, which implies that 
matter is being channelled onto the neutron star's magnetic poles. 
However, during the passive-state there is no sign of X-ray pulsations 
<cit.>. Indeed, optical 
pulsations have also been observed which are interpreted as being due to 
synchrotron emission by relativistic electrons and positrons in the pulsar 
magnetosphere <cit.>. In the proposed model, the particles residing at 
a constant fraction of the light cylinder radius have a power-law energy 
distribution and emit incoherent synchrotron radiation <cit.>. 
The synchrotron self-absorption produces a turnover in the 
spectral energy 
distribution (SED) Indeed, in the Crab there is evidence for synchrotron 
self-absorption which is observed as a turnover in the SED near the H-band <cit.>.

Simultaneous X-ray and radio observations have revealed key features 
<cit.>. Firstly, an anti-correlation between the X-ray and 
radio flux in the active- and passive-states. During the X-ray active 
state and the radio luminosity is low and X-ray pulsations are observed, 
but when the source transitions into the passive-state, the pulsations 
disappear and the radio emission increases rapidly. Secondly, during the 
X-ray passive-state, the radio spectrum evolves from a self-absorbed to 
optically thin spectrum on time-scales of several minutes, reminiscent of 
a classical evolving synchrotron spectrum. <cit.> conclude the 
radio flares are due to expanding synchrotron emitting plasma arising from 
the inner regions of the accretion disc.

In Fig. <ref> we show the SED of the 
u'-, g'- and r'-band dips observed in 2015 by <cit.> and 
the r'- and K_s-band dips observed in 2017 (see 
Section <ref>). The SED shows a 
turnover which is what one expects if the synchrotron emission arises from 
an expanding synchrotron emitting plasma <cit.> or synchrotron 
emission by relativistic electrons and positrons <cit.>. The 
synchrotron emission idea is also supported by the high K_s-band PDS 
variability at high frequencies (inner disc regions; see 
Section <ref>), which is what one expects for emission is 
non-thermal, likely from optically thin synchrotron emission.

An alternative explanation for the turnover in the SED 
of the dips is from a combination of clumpy accretion and 
irradiation. In Figs. <ref> and <ref> we show the 
r'/K_s versus K_s-band flux ratio diagram for different sections of the 
data. As one can see, during the transition from the active to 
passive-state, the r'/K_s flux ratio decreases because there is a 
larger decrease in the r'-band flux compared to the K_s-band flux, i.e there is 
a disappearance of a blue component. This is what one would expect if 
the reprocessing optical component is removed during the active–passive state transitions while 
the synchrotron component remains constant (see Section <ref>).  
In  contrast <cit.> observed the disappearance of a red spectral 
component and attributed it to the removal of an irradiated disc. 
The difference between the r'-band dip observed in 2015 and 
2017 (see Fig. <ref>) is due to the different amounts of clumpy 
material at the time of the observations. The combination of the removal 
of a red and blue component with different strengths gives rise to a 
turnover in the SED which lies somewhere between the 
r'- and K_s-band.













 §.§ Comparison with X-ray binaries



Simultaneous optical and X-ray observations of X-ray binaries have 
revealed multi-component optical variability on sub-second time-scales, 
arising from components such as a hot inner flow, accretion disc 
reprocessing and a jet. These appears to be a common feature in many X-ray 
binaries during the hard state and resuls in as narrow positive 
peak is the observed in the CCF, superimposed on an anti-correlation 
<cit.>. Intense and 
rapid sub-second flaring is also seen and in a few systems it has been 
attributed to synchrotron emission from a jet <cit.>. On time-scales of minutes Swift J1753.5−0127 has shown strong 
optical variations <cit.>. <cit.> have 
shown that the X-ray and optical variability in Swift J1753-0127 
<cit.> is well reproduced by a simple model assuming that the 
optical variability is a mixture of X-ray reprocessing plus a hot flow 
synchrotron component that is exactly anti-correlated with respect to the X-rays. 
The hot flow model has also been used to explain the anti-correlated 
optical/X-ray behaviour in BW Cir <cit.>. Near-IR variations on 
time-scales of minutes have been observed in GRS 1915+105 and have been 
associated with synchrotron-emitting plasma <cit.>.

The shape of the optical/near-IR CCF of , with the anti-correlation 
and a sharp rise at zero lag, resembles the optical/X-ray CCFs found in 
X-ray binaries, indicating an interplay of, at least, two separate 
components. This scenario was originally proposed for black hole X-ray 
binaries <cit.>, where the correlated component comes from the  
reprocessing of the incident X-ray flux, and the anti-correlated component 
originates from the hot accretion flow emitting in the optical via 
synchrotron. The time-scale of the optical and near-IR variability and 
correlations we observe in  are, however, much longer than what is 
observed in other X-ray binaries.

A hot accretion flow can, in principle, can exist close to the pulsar 
magnetosphere and can be occasionally expelled away by the rotating 
magnetic field <cit.>. Such synchrotron-emitting outflowing 
plasmoids arising from the inner regions of the accretion disc could then 
be responsible for the increased radio emission during the X-ray passive 
states <cit.>. Given the low luminosity, and hence, low 
accretion rate and electron number density in   the hot flow 
synchrotron emission is likely to be optically thin down to the near-IR. 
The entire spectrum is thus similar to those of the outer parts of the hot 
flow for higher accretion rates <cit.>. A 
combination of the red synchrotron spectrum with the blue spectrum of 
reprocessed radiation (Veledina et al., 2018, in preparation) can produce 
the observed power-law F_ν∝ν^0.9 (see Fig. <ref>).

The shape of the optical/near-IR CCF of  somewhat resembles the 
optical/X-ray CCF observed in the black hole X-ray binary 
Swift J1753.5–0127 <cit.>. However, the characteristic 
time-scales are different by an order of magnitude, and the broad positive 
peak at positive lags is missing in the CCF of Swift J1753.5–0127. The 
difference can be explained by the presence of a solid surface and neutron 
star magnetosphere in . Because the accretion disc is truncated at this 
radius, the characteristic viscous time-scales are somewhat longer than in 
black hole binaries, giving broader features in the CCF. The absence of 
the broad peak at positive lags can be due to disappearance of the 
plasmoids under the event horizon, rather than their ejection, as is the 
case of .







 §.§ Light curve correlations



Reprocessing of high energy photons to lower energies in an extended 
accretion disc is thought to dominate the observed optical and near-IR 
fluxes. The expected cross-correlation signature is delayed because of 
the light travel time and smeared response of the optical and near-IR 
light curves with respect to the X-ray light curve. The optical and near-IR 
light curve is the convolution of the X-ray light curve with a broad 
transfer function representing the response of the extended accretion 
disc. The inner regions of the accretion disc reprocess high energy X-rays 
into the soft X-rays/UV bands. Therefore we expect the near-IR ACF to be 
broader than the optical CCF and the CCF to show a single strong, positive 
peak at positive lags (near-IR arriving after optical).

At first sight the ACFs of the entire r'- and K_s-band light curves 
have different width cores and wings (see Section <ref>). Near 
the the K_s-band ACF is broader than the r'-band ACF which argues for 
a reprocessing origin for the slowly-variable component, most likely in 
the outer regions of the accretion disc. However, very close to the core, 
the r'-band ACF is broader than the K_s-band ACF, which argues against 
a simple reprocessing origin. A detailed look at the ACF for different 
segments in time reveals that on average the r'-band ACF is a factor of 
∼3–4 times broader than the K_s-band ACF (see 
Fig <ref>), which is not what one would expect from a 
reprocessing model. A broader K_s-band ACF is expected if the K_s-band 
PDS is steeper than the r'-band PDS <cit.> which implies 
that there is more aperiodic variability from the accretion disc at low 
frequencies (outer disc regions) in the K_s-band light curve compared to 
the r'-band. However, we find that the r'-band PDS is steeper than the 
K_s-band PDS (even allowing for the systematic effects, see 
Section <ref>) and that the K_s-band PDS has more variability 
at high frequencies from the inner regions of the accretion disc/pulsar 
magnetosphere (see Section <ref>). This is what one expects for 
emission from a non-thermal component such as optically thin synchrotron 
emission.

The CCF of the simultaneous optical and near-IR data reveals a strong, 
broad negative anti-correlation and negative lags and a broad positive 
correlation at positive lags, with a strong, positive and narrow 
correlation superimposed (see Fig. <ref>). The broad 
positive correlation implies that the optical leads the near-IR flux. 
However, the broad negative delay implies the optical band is delayed with 
respect to the near-IR and the anti-correlation implies that the 
variability between the near-IR and optical fluxes is out of phase.

The narrow correlation implies that optical leads the near-IR flux, 
consistent with a reprocessing origin. The ∼+5 s correlation is 
similar to the time-scale we would expect for the light travel time 
between the binary components. The light travel times of photons arise 
from the differences between the time of flight of photons that are 
observed directly and those that are re-processed and re-emitted before 
travelling back to the observer. For  with an orbital period of 
4.75 h, the corresponding binary separation of ∼1.8 R_⊙ 
(assuming a total binary mass of 2 M_⊙)  implies a light travel 
time of ∼4 light-seconds. However, given that the delay is not phase 
resolved, it is not always present in the CCFs (see 
Figs. <ref> and <ref>), suggesting that it is not 
due to the reprocessing on the secondary star, but is due to 
reprocessing in the accretion disc.



 §.§ The hot accretion flow model



The observed broad anti-correlation at negative lags implies that 
the optical flux is delayed with respect to the near-IR flux and the 
anti-correlation implies that the variability between the near-IR and 
optical fluxes is out of phase. These features are not due to reprocessing 
because a reprocessing CCF would rise quickly near zero and fall less 
quickly towards positive lags <cit.>. The broad components of 
the CCF and the sudden change near zero lag are strongly indicative of 
at least two separate processes superposed in the light curves, such as a 
hot flow for the anti-correlation and a reprocessing/jet component for the 
positively correlated optical/near-IR components. A combination of 
reprocessing and the interaction of a hot flow with the pulsar 
magnetosphere can produce the observed optical/near-IR correlations.

Given that the reprocessed emission is expected to have a blue spectrum, 
we expect it to be more prominent in the r'-band compared to in the 
K_ s-band. We propose that the r'-band emission is totally 
dominated by the reprocessed component, while the K_ s-band 
contains both synchrotron and reprocessed emission. 
In the optical the reprocessing component dominates in the 
active–state transiton and decreases during the transition. In the 
near-IR, there are two components, a reprocessing component which also 
decreases (but not as much as in the optical) during the transition, however, 
the synchrotron does not, which results in the removal of the blue spectral 
component during the dips (see Figs. <ref> and <ref>). 
If the accretion proceeds through the occasional penetration 
of the clumps/blobs of plasma through the magnetic barrier, the following 
scenario can lead to the observed near-IR/optical CCF. Consider the hot 
accretion flow with the inner radius close to the magnetospheric radius 
and emitting through the synchrotron self-Compton mechanism (similar to 
the hot flows in black hole X-ray binaries <cit.>. If there 
is a local increase in the mass transfer rate, then the accretion flow 
becomes inhomogeneous and the resulting spectrum depends on the local 
number density of electrons. For a higher electron number density the 
(near-IR) synchrotron emission is suppressed due to the increased 
self-absorption. The inhomogeneities in the hot accretion flow containing 
a higher electron number density have a higher chance to penetrate through 
the magnetic barrier, hence once there is a sufficiently dense plasmoid, 
with the near-IR synchrotron emission suppressed, the flow accretes/drifts 
towards the compact object causing an increase in the X-ray emission. The 
X-ray emission triggers the reprocessing in the disc, both in the optical 
and near-IR (likely without a significant delay between them). The 
plasmoids are then expelled by the rotating magnetic field, forming an 
outflow and giving rise to the increase of the synchrotron near-IR 
emission as the plasmoids become optically thin. At the same time, the 
X-ray luminosity drops and the source switches to the passive state. 
Indeed, these ideas are further supported by the fact that transition from 
the X-ray active to X-ray passive state are always accompanied by a radio 
brightening, which has been interpreted as being due to rapid ejections 
synchrotron emitting plasma by the pulsar <cit.>.

The near-IR/optical CCF can be explained by two components, synchrotron 
emission from plasmoids and reprocessing. The dip at negative lags 
corresponds to the suppression of the near-IR synchrotron emission of the 
plasmoids in hot accretion flow, which occurs just before the X-ray switches 
to the active-state. The narrow peak at ∼5 s corresponds to the 
delayed reprocessed component, enhanced by the increased X-ray emission 
<cit.>. The broad positive correlation at positive lags is 
driven by the increased synchrotron emission of the outflowing plasmoids, 
which become optically thin as they expand. The width of the 
anti-correlation and broad positive correlation corresponds to the 
characteristic time-scale for the penetration of the (entire) inhomogeneity 
into the magnetosphere, which is roughly comparable to the viscous time-scale at 
the magnetospheric radius. In the r'-band light curves, this corresponds 
to the average duration of the active-state.

In Fig. <ref> we show model predictions for the optical and 
near-IR ACFs and CCFs expected from the hot accretion flow model. Our aim 
is to show that the model can indeed reproduce the main features of the 
CCFs. We leave the detailed modelling to a future paper, as it involves a 
number of unknown parameters for the disc and synchrotron components. To model the 
ACFs and CCFs, we simulate the light curve as mass accretion rate 
fluctuations from a prescribed PDS shape using the <cit.> 
algorithm.  We assume that the X-ray light curve is proportional to the 
mass accretion rate light curve. We assume a zero-peak Lorentzian profile 
for the PDS accretion rate and equal contributions of the disc and 
synchrotron components. The disc to synchrotron ratio determines the 
relative importance of the dip and peak in the CCF <cit.>. 
The r'-band light-curve is obtained by convolving the X-ray light curve 
with the accretion disc transfer function. The synchrotron emission of 
the plasmoids is simulated through the mean-subtracted accretion rate light 
curve. For the radiation of the hot flow we take this light curve with a 
minus sign (similar to eq. 2 of ) and shift it in time so 
that it leads the X-rays. The synchrotron emission of expanding plasmoids 
is modelled as the accretion rate light curve, shifted in time towards 
positive lags, i.e. it comes after the X-rays. The K_ s band 
contains the synchrotron components of the plasmoids and the reprocessed 
component. The main parameters effecting the shape of the CCF are the assumed 
PDS shape of the mass accretion rate fluctuations and relative contribution of 
various synchrotron/disc components. The model predictions for the optical 
and near-IR ACFs and CCFs expected are 
shown in Fig. <ref>. As one can see there is a remarkable 
agreement in the general features predicted by the model with what is 
observed, a broad negative anti-correlation at negative lags, a broad 
positive correlation at positive lags, with a strong, positive narrow 
correlation superimposed.

If the active-state luminosity L_X ∼ 3×10^33 
<cit.> is due to accretion, i.e. 
L = G M Ṁ/R, where the neutron star mass is M=1.71M⊙ 
<cit.>, radius R=12 km <cit.> and G is the 
gravitational constant, then the accretion rate is 
Ṁ = 1.5×10^13g s^-1. With this mass inflow 
rate at the magnetospheric boundary, the active-state magnetospheric 
radius (the radius when the pressure of the neutron star magnetosphere is  able
to halt the inflowing matter) is R_ m∼150 km, assuming a  dipole
magnetic field with strength B∼10^8 G <cit.>. In
the  passive-state, the mass inflow rate is likely smaller, leading to a
higher  magnetospheric radius.  The corotation radius (at which the matter in 
Keplerian orbit co-rotates with the neutron star) is R_ co=24 km  and
the light cylinder radius (at which field lines anchored to the  neutron star
rotate at the speed of light) is R_ lc = 80 km.   Hence for such low
X-ray luminosities, the magnetospheric radius exceeds  the light cylinder radius, 
and by far exceeds the corotation radius. This implies that the hot flow has to
be truncated outside of the light cylinder, ≳100 km. The viscous
time-scale at this radius is of  the order of a few 100 s, which is roughly
consistent with the width of the  negative dip and broad peak in the CCF.  The
magnetic field inside the  flow is likely self-generated by the flow and can be
much lower than   at the neutron star surface.  We estimate the magnetic field
inside the  flow using condition that the turnover frequency is close to
K_s-band  and the requirement for the observed synchrotron luminosity is equal
to  the synchrotron luminosity at the turnover frequency. Using eq. (6) of 
<cit.> for the K_s-band flux at a radius of ∼100 km  and a
distance of 1.368 kpc <cit.>, we obtain a rough estimate  for the
magnetic field strength inside the hot flow of B∼10^4 G, 
which is comparable to the magnetic field of the pulsar at this radius.
We leave the
detailed spectral and timing modelling of the observed  characteristics to a
future paper.




§ CONCLUSION


Below we list the main results of this paper.



  * Our simultaneous r'- and K_s-band light curves  show
rectangular, flat-bottomed dips, similar to the X-ray mode-switching 
(active–passive state transitons) behaviour observed previously. During the 
active–passive state transition, the r'/K_ s flux ratio  decreases due to
the larger decrease in the r'-band flux compared to  the K_ s-band flux.  The SED
of the dips (active minus passive flux) shows a  turnover between the r'- and
K_ s-band.


  * The CCF of the optical and near-IR data reveals a strong, broad negative 
anti-correlation and negative lags, a broad positive correlation at 
positive lags, with a strong, positive narrow correlation superimposed. 
The shape of the CCF resembles the optical/X-ray CCF observed in the black 
hole X-ray binary Swift J1753.5–0127, but the time-scales are different. 
The difference can be explained by the presence of a solid surface and 
the pulsar's magnetosphere in .



The active–passive transiton and features in the CCF can be 
explained by reprocessing and a hot accretion flow close to the 
neutron star's magnetospheric radius. Since the accretion disc is 
truncated at distance comparable to the magnetospheric radius, the 
characteristic viscous time-scales are longer than in black hole 
binaries, giving broader features in the CCF. The optical emission is 
dominated by the reprocessed component, whereas the near-IR emission 
contains a component due to the emission from plasmoids in the hot 
accretion flow and a reprocessed component. 

The rapid transitions between the active and passive states are 
due to the penetration of the hot accretion flow material onto the 
neutron star and the expelling of the blobs of synchrotron emitting 
plasma fed by the hot inner flow from the magnetosphere. The 
plasmoids are expelled by the rotating magnetic field of the neutron 
star, giving rise to the increase of the synchrotron near-IR emission 
as they expand and become optically thin. During the active–passive 
transition the optical reprocessing component decreases which results 
in the removal of a blue spectral component.
The combination of the red synchrotron spectrum with the blue 
reprocessed spectrum also produces the observed SED. The dip at 
negative lags corresponds to the suppression of the near-IR 
synchrotron component in the hot flow, whereas the broad positive 
correlation at positive lags is driven by the increased synchrotron 
emission of the outflowing plasmoids. The narrow peak in the CCF is 
due to the delayed reprocessed component, enhanced by the increased 
X-ray emission. The accretion of clumpy material through the magnetic 
barrier of the neutron star produces the observed near-IR/optical CCF 
and variability.



§ ACKNOWLEDGEMENTS


TS acknowledges support from the Spanish Ministry of Economy and 
Competitiveness (MINECO) under the grant AYA2013-42627. AV acknowledges 
support from the Academy of Finland grant 309308. P.G. thanks STFC 
(ST/J003697/2) for support. The ACAM and CIRCE data are based on 
observations made with William Herschel Telescope and the Gran Telescopio 
Canarias, respectively, installed in the Spanish Observatorio del Roque de 
los Muchachos of the Instituto de Astrofísica de Canarias, in the island 
of La Palma. Development of CIRCE was supported by the University of 
Florida and the National Science Foundation (grant AST-0352664), in 
collaboration with IUCAA.



Facilities: WHT (ACAM), GTC (CIRCE)





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