\section{INTRODUCTION}

X-ray binaries (XRBs), consisting of a compact object and a companion star, can be
divided into low mass X$-$ray binaries (LMXBs) and high mass X$-$ray binaries (HMXBs)
according to the mass of the companion star. The compact object is either a
neutron star (NS) or a black hole (BH). Based on their spectral and timing properties,
NS-LMXBs could be classified as Z sources and atoll sources \citep{Hasinger1989}.
The Z sources, with high luminosity close to the Eddington limit, trace out a Z-shape
track on their hardness-intensity diagrams (HIDs), which are divided into three
branches, called horizontal branch (HB), normal branch (NB), and flaring branch (FB),
respectively. Among the six confirmed Z sources, Cyg X-2, GX 5-1, and GX 340+0 are
called Cyg-like Z sources, and the other three Z sources, i.e. Sco X-1, GX 17+2, and
GX 349+2, are referred to as Sco-like Z sources. On the HIDs of atoll sources with
luminosity below $\sim$$10^{38}\ {\rm ergs\ s^{-1}}$, two main segments are seen,
which are called banana state (BS) and island state (IS), respectively; in the BS,
the variation of hardness is relatively small, while their luminosity spans a wide
range; however, in the IS, the variation of hardness is obvious, while the change
of luminosity is relatively small and they are with the lowest luminosity
\citep{Church2014}. Furthermore, the segment of BS is split into two subsections,
i.e. the lower banana (LB) with lower luminosities and the upper banana (UB) with
higher luminosities. In general, atoll sources are either in IS or in BS depending
on their luminosities. Generally, a Z source cannot become an atoll source and vice
versa. However, two peculiar NS-LMXBs, i.e. Cir X-1 and XTE J1701-462, show Z source
behaviors at relatively high luminosities, while they display atoll source behaviors
at low luminosities \citep{Oosterbroek1995,Shirey1999,Homan2007,Homan2010,Lin2009}.

The spectral and timing analysis are two main methods for studying XRBs. Among
the timing analyses, the cross$-$correlation analysis can be used to study the
relation of light curves in two different energy bands. By analyzing the
cross$-$correlation function (CCF) of light curves in two different energy bands,
the correlation and time lag between soft and hard X$-$ray light curves can be
obtained, which are useful and important to investigate the structures of accretion
disk and the mechanisms for producing X-rays. According to the behaviors of CCFs,
the correlations can be classified as anti$-$correlations, positive and ambiguous
correlations, respectively. Anti$-$correlations correspond to negative
cross$-$correlation coefficients (CCCs), while positive correlations correspond to
positive CCCs. If no obvious correlations are presented in the CCFs, such
correlations are called ambiguous correlations. Soft time lags mean that the lower
energy photons reach behind, while hard time lags imply that the lower energy
photons lead the higher energy photons. The cross$-$correlation analysis technique
has been used to analyze the correlations of X-rays and long-term time lags from
tens of seconds to over one thousand seconds in two energy bands of XRBs (e.g.
Choudhury \& Rao 2004; Lei et al. 2008, 2013; Wang, et al. 2014). In addition to
the CCF method, the cross-spectral analysis is another important method for
analyzing time lags \citep{Nowak1999a}, which has been widely used to investigate
the short-term time lags in the order of milliseconds in XRBs (e.g. van der Klis
et al. 1987; Miyamoto et al. 1988; Cui 1999; Qu, Yu \& Li 2001; Qu et al. 2010a).
In the past several decades, various time lags have been detected in XRBs through
analyzing the data from X-ray satellites, of which {\it RXTE} has contributed
greatly (see review: Poutanen 2001).

GX 349+2, also known as Sco X-2, is a Sco-like Z source. Using the observations
from {\it EXOSAT}, \cite{Ponman1988} detected quasi-periodic oscillations (QPOs)
at $\sim$6 Hz in this source. Using observations from {\it Rossi X-ray Timing
Explorer (RXTE)}, \cite{ONeill2002} investigated the evolution of QPOs along a
Z track on its HID and found QPOs at 3.3-5.8 Hz on the FB and at 11-54 Hz
on the NB. Also through analyzing data from {\it RXTE}, \cite{Zhang1998} detected
a twin kilohertz (kHz) QPOs with lower and upper frequencies of 712 Hz and 978 Hz,
respectively. In particular, the kHz QPOs were only found at the top of the NB.
Using the {\it RXTE} data for this source, \cite{Agrawal2003} carried out the
spectral evolution on its Z track. They fitted the spectra in 2.5-25 keV using a
two-component model consisting of a disk blackbody and a Comptonized component
representing Comptonization in the central hot corona or the boundary layer,
which could act as the Eastern model \citep{Mitsuda1984,Mitsuda1989}. However,
\cite{Church2012} used another two-component model consisting of a blackbody and
a cut-off power law representing Comptonization in an extended corona above the disk
to fit the spectra of the Sco-like Z sources, including GX 349+2. Using the data
from {\it BeppoSAX}, \cite{DiSalvo2001} studied its broadband spectra (0.1$-$200 keV)
and a hard tail was detected in this source. Moreover, they detected an absorption
edge at $\sim$9 keV in the spectra. Using the observation from XMM,
\cite{Iaria2009} performed spectral analysis of GX 349+2. They fitted the
continuum in the 0.7-10 keV energy range with the Eastern model
\citep{Mitsuda1984}. Significantly, \cite{Iaria2009} found several broad
emission features below 4 keV and a broader emission feature in the
Fe-${\rm K_{\alpha}}$ region in the spectra and proposed that these relativistic
lines are formed due to the reflection in the inner disk region that is
illuminated by the emission around the NS. The relativistic Fe-K emission line of
GX 349+2 was also detected in its {\it Suzaku} spectra \citep{Cackett2008}.

In this work, using all the data from the proportional counter array (PCA) on
board {\it RXTE} for GX 349+2, we systematically investigate the cross-correlation
correlations between soft and hard light curves of this source. We describe our
data analyses in section 2, present our results in section 3, discuss our results
in section 4, and, finally, give our conclusions in section 5.

\section{DATA ANALYSIS}

{\it RXTE} made 138 observations from 1996 to 2011 for Z source GX 349+2,
including 23 observations from January 9 to January 29, 1998, during which the
source evolved on the most extensive NB+FB tracks ever reported on its HID
\citep{ONeill2002}. With HEASOFT 6.11 and all the {\it RXTE} observations for
GX 349+2, we systematically perform cross-correlation analysis for this source.
In our analysis, only PCA data are needed. The PCA consists of five identical
proportional counter units (PCUs) in energy range 2$-$60 keV \citep{Jahoda2006}.
We use the data during the intervals when all five PCUs were working. The PCA
Standard 2 mode data with bin size of 16 s are used to produce light curves with
{\it RXTE} FTOOLS SAEXTRCT. Then, with RUNPCABACKEST, a {\it RXTE} script, we
produce the background files from the bright background model
(pca$_{-}$bkgd$_{-}$cmbrightvle$_{-}$eMv20051128.mdl) provided by {\it RXTE}
team and thus produce the background light curves. Finally, applying LCMATH, a
XRONOS tool, we generate the background-subtracted light curves with various
energy bands. When extracting light curves, good time intervals (GTIs) are
restricted through inputting GTI files, which are created with the FTOOLS
MAKETIME obeying criteria: the earth elevation angle greater than $10^{\circ}$
and the pointing offset less than $0.02^{\circ}$.

To build the HID on which the source traced out the most extensive Z track,
following \cite{ONeill2002}, we define the hardness as the count rate ratio
between 8.7$-$19.7 keV and 6.2$-$8.7 keV energy bands, and the intensity as the
count rate in the 2.0$-$19.7 keV energy band. The produced HID is shown by
Figure~\ref{fig:HID}. In order to investigate the evolution of cross-correlation
correlations along the Z track, we divide the track into 23 regions. For minimizing
the variation of count rate and meanwhile having enough observation time in each
region, these regions are produced obeying the criteria: the count rate variation
in each region is less than 1500 count $s^{-1}$ except the region No. 23; the
hardness variation in each of the regions in the NB and in the first half FB is
less than 0.025, while it is less than 0.5 for each region in the second half FB,
because, here, the points are scattered. Then, we study the evolution of
cross-correlation correlations between hard and soft X-ray light curves
along the Z track. Firstly, based on the values of hardness and count rate in
each region, we determine the relative and absolute time intervals of each region
with FTOOLS MAKETIME and TIMETRANS, respectively. Secondly, inputting the absolute
time intervals of each region when light curves are extracted, we produce the
soft and hard X-ray background-subtracted light curves of each region in 2-5 keV
and 16-30 kev energy bands, respectively. Thirdly, with XRONOS TOOL CROSSCOR,
we generate the CCF between the soft and hard background-subtracted light curves
of each region. To get the CCCs and time lags, we fit the CCFs with an inverted
Gaussian function at a 90\% confidence level. The results of the 23 regions are
listed in Table~\ref{table1}. The total relative time length of each of the 23
regions spans from 1072 s to 8606 s and the absolute time intervals of each region
spread within 2 days.

As shown in Figure~\ref{fig:HID}, the track consists of an extensive NB and an
elongated FB, respectively. Regions 1-10 constitute the NB, while regions 11-23
make up the FB. In order to describe the positions of the 23 regions on the
NB+FB tracks, the segment of regions 1-3 is called upper NB (UNB), the segment
of regions 4-6 is called middle NB (MNB), and the segment of regions 7-10 is
called lower FB (LFB); similarly, the segment of regions 11-15 is named lower
FB (LFB), the segment of regions 16-18 is named middle FB (MFB), and the segment
of regions 19-23 is named upper FB (UFB). The intensity as a function of time
during the HID is shown in Figure~\ref{fig:lightcurve}, in which the positions
of various time intervals on the HID are marked. As shown in
Figure~\ref{fig:lightcurve}, the two panels of the first row dominate the FB
positions, while the two panels of the second row and the left panel of the
third row are occupied by the NB positions, showing that the source
evolves from the FB to the NB on the NB+FB tracks; the right panel of the third
row and the left panel of the fourth row show the next evolutionary cycle from
the FB to the NB; the right panel of the fourth row shows the beginning of the
third evolutionary cycle. Therefore, the source regularly evolved on the HID
during each evolutionary cycle, which leads to that the data of each region
spread within two days. For Fourier analysis, unbroken sections of data are
needed. Certainly, for cross-correlation analysis continuous observations should
be better than broken observations. Here, although the observations within the
HID span 21 days, yet the data within each region do not spread across very
different observations, which ensures the validity of our results.

In addition, we perform cross-correlation analysis between soft and hard X-ray
light curves for all the observations outside the period during which the
source traced out the most extensive NB+FB tracks on its HID. Similarly, we
produce the soft and hard X-ray background-subtracted light curves of each
observation and then get its CCF, CCC, and time lag. It is noted that if
there are several segments in the light curves of an observation, we
produce the CCF of each segment.

\section{RESULTS}

In this work, using all the 138 {\it RXTE} observations from 1996 to 2011
for Z source GX 349+2, we systematically perform cross-correlation analysis
between 2-5 kev and 16-30 keV light curves with the CCF method. The source
traced out the most extensive Z track on the HID during the 23 observations
from January 1 to January 29, 1998. Among the 23 regions on the HID, positive
correlations and ambiguous correlations are detected in 18 and 5 regions,
respectively, while anti-correlations are not found throughout the Z track.
The HID positions of the 18 regions, the derived CCCs and time lags, and
hardness values are listed in Table~\ref{table1}. Figure~\ref{fig:positive}
and Figure~\ref{fig:ambiguous} show two detected positive correlations and
one ambiguous correlation, respectively. Eight regions of the 18 regions with
detected positive correlations are assigned to the NB and other ten regions
are belonged to the FB. Among the five regions with ambiguous correlations,
the NB and FB host two and three regions, respectively. Fortunately, among
the observations outside the period during which the source traced out the
most extensive Z track on its HID, the anti-correlations are detected in ten
observations. The analysis results of these anti-correlations are listed in
Table~\ref{table2} and two representative anti-correlations are shown in
Figure~\ref{fig:anti-correlation}. The derived anti-correlated time lags vary
between tens of seconds and thousands of seconds. Among the ten observations
with anti-correlations, hard and soft X-ray time lags are detected in four and
six observations, respectively. In one hundred observations outside the HID
period, positive correlations are detected, which are listed in Table~\ref{table3},
while ambiguous correlations are found in five observations outside the HID
episode. The anti-correlations, positive correlations, and ambiguous correlations
are detected in 8.7\%, 87\%, and 4.3\% of the total observations outside the HID
period, respectively. Comparing the time lags listed in
Tables~\ref{table1}-\ref{table3}, one can see that the positively correlated
time lags vary from several seconds to tens of seconds, whereas the
anti-correlated time lags span a wide range from tens of seconds to thousands of
seconds, so the anti-correlated time lags of GX 349+2 are much larger than its
positively correlated time lags, which is consistent with what was found in
atoll source 4U 1735-44 and 4U 1608-52, as well as peculiar source XTE J1701-462
\citep{Lei2013,Lei2014,Wang2014}. It should be informed that a small number of
short-term time lags less than one second are obtained in the positive
correlations of GX 349+2, as listed in Tables~\ref{table1} and \ref{table3}.

\section{DISCUSSION}

\subsection{The short-term time lags in XRBs}

Through cross-spectral analysis, the short-term time lags ($<$1 s) between the
emissions of two adjacent X-ray energy bands have been detected in a few Galactic
black hole X-ray binaries (BHXBs) and NS-LMXBs. Among the BHXBs in which short-term
time lags were studied, the short-term time lag behaviors of Cyg X-1 were investigated
most deeply \citep{Miyamoto1988,Miyamoto1992,Crary1998,Nowak1999a,Pottschmidt2000,Negoro2001}.
The short-term time lags were also detected in microquasar GRS 1915+105
\citep{Cui1999,Reig2000,Pahari2013}, in GX 339-4 \citep{Miyamoto1992,Nowak1999b}, as well
as in black hole candidate GS 2013+338 and GRO J0422+32 \citep{Miyamoto1992,vanderHooft1999}.
The short-term time lags with values of several milliseconds were also found in NS-LMXBs,
such as in Cyg X-2 and GX 5-1 \citep{vanderKlis1987,Vaughan1994} as well as in Cir X-1
\citep{Qu2001,Qu2010b}. Generally, the hard X-ray short-term time lags were detected in the
hard states of BHXBs, while both hard and soft X-ray short-term time lags were detected in
NS-LMXBs \citep{vanderKlis1987,Qu2001}.

Some models have been proposed to explain short-term time lags, but the observed various
short-term time lags cannot be explained by any single model. The cross-spectral analysis
technique is based on the Fourier transform, so the time lag spectrum, i.e. the correlation
between the short-term time lag and the frequency of Fourier transform can be obtained.
Usually, the short-term time lag is anti-correlated with Fourier frequency \citep{vanderKlis1987,vanderHooft1999,Nowak1999a,Nowak1999b,Pottschmidt2000,Qu2010a}. Among the
Fourier frequencies, some are the frequencies of QPOs, sequentially leading to that the
short-term time lag is also anti-correlated with QPO frequency. Since the short-term time
lag is in connection with the QPO parameter, it could be feasible to invoke the models
responsible for QPOs to account for the short-term time lags, such as the shot model
\citep{Terrell1972}. In the shot model, it is assumed that the gravitation energy of
accreting matter is transformed to thermal energy emitted as successive bursts, which
are called ``shots'' and responsible for QPOs; the different shot profiles or shot
distribution in different energy bands results in the time delays between the hard and
soft X-ray emissions \citep{Miyamoto1989,Nowak19994,Nowak1999b,Poutanen2001}. Although
the shot model provided an explanation for the strong aperiodic variability of the flux
of accreting XRBs immediately after such variability was discovered and it was very
early applied to account for the short-term lags, yet this model inevitably encountered
difficulty when it was used to explain the large X-ray variability timescale
range \citep{Uttley2001,Churazov2001,Revnivtsev2009} and the linear rms-flux relation
\citep{Uttley2001,Ingram2013}. Since the shot model, various models have been proposed to
explain the QPOs in XRBs, such as the beat-frequency
models \citep{Strohmayer1996,Ford1997,Miller1998}, which were refuted by the fact that the
observed QPO peak separation is not a constant \citep{vanderKlis2000}, the Lense-Thirring
precession model \citep{Stella1998}, and the propagating fluctuation model \citep{Ingram2011},
etc. Using their propagating fluctuation model, \cite{Ingram2013} explained the
anti-correlation between the short-term time lag and the Fourier frequency well. There
may be a prospect of interpreting the short-term time lags observed in XRBs with the
help of these QPO models, whereas it is out of the scope of this paper.

Certainly, Comptonization is a common physical process for producing X-rays in XRBs, so
it is widely invoked to interpret the observed time lags in the order of milliseconds in
these sources \citep{vanderKlis1987,Ford1999,Nobili2000,Lee2001,Poutanen2001}. In the
Comptonization model, the low-energy seed photons, emitted from a relatively cool region
such as the accretion disk, are inversely Comptonized by the energetic electrons from a
hot source such as a hot corona or the hot plasma near the compact objects, in which the
low-energy photons gain energy, while the high-energy electrons lose part of their energy,
leading to that high-energy photons undergo more inverse Compton scatterings and,
therefore, they escape later than the low-energy photons, resulting in hard
X-ray time lags \citep{Ford1999}. Obviously, soft X-ray time lags cannot be explained by
this model. \cite{vanderKlis1987} proposed that the softening of shots could account for
soft time lags. In order to explain the time lags of GRS 1915+105, \cite{Nobili2000}
proposed a scenario in which a standard thin disk \citep{Shakura1973} coexists with a
central corona with two parts, an inner part with relatively high temperature and an outer
part with relatively low temperature. In the inner part, the inverse Compton scattering is
taken place, resulting in hard X-ray time lags. However, in the outer part, the disk seed
photons are Comptonized by the relatively cool electrons, in which the electrons gain energy,
while the seed photons lose energy, so the low-energy photons undergo more Compton
scatterings and escape later than high-energy photons, leading to soft X-ray time lags.
\cite{Qu2001} invoked this scenario to explain the detected soft and hard X-ray time lags
less than ten milliseconds in Cir X-1. In addition to the two models, there are some other
models for explaining the short-term time lags of XRBs, such as the magnetic flare model
\citep{Poutanen1999}. In this model, it is assumed that the X-rays are produced in compact
magnetic flares and the movement for magnetic loops to inflate and detach from the
accretion disk induces spectral evolution, which results in time lags corresponding to
the evolution timescales of the flares.

\subsection{The long-term time lags in XRBs}

Through CCF technique, the long-term time lags ranging from hundreds of seconds to
over one thousand seconds between hard and soft X-rays have been detected in a few
Galactic BH X-ray binaries (BHXBs). Anti-correlated long-term hard X-ray time lags
were first detected in the low/hard state of the high-mass BHXB Cyg X-3
\citep{Choudhury2004}, then this kind of hard X-ray time lags were found in
microquasar GRS 1915+105 during its $\chi$ states \citep{Choudhury2005}. It is noted
that the $\chi$ states of this microquasar are the closest analog to the low/hard
states of BHXBs. In addition, the similar long-term anti-correlated hard X-ray time
lags were also detected in another microquasar XTE J1550-564, but in its very high
state or steep power law state \citep{Sriram2007}. Interestingly, the long-term soft
X-ray time lags of microquasar GX 339-4 were found in its hard and soft intermediate
states \citep{Sriram2010}. It is noted that the spectral pivoting was shown during
the episodes when this kind of time lags were detected in these BHXBs
\citep{Choudhury2004,Choudhury2005,Sriram2007}. \cite{Choudhury2004} proposed a
truncated accretion disk model to explain the detected anti-correlated long-term
hard X-ray time lags in BHXBs. In the scenario of this model, the optically thick
accretion disk, where the soft X-rays are emitted, is truncated far away from the
BH, while the truncated area, i.e. the high-temperature region between the inner
disk edge and the location near the BH, is full of Compton cloud which is
responsible for the hard X-ray emission. Any change in the disk will trigger
corresponding anti-correlated change in the Compton cloud in a viscous timescale,
during which the accreting matter flows from the optically thick accretion disk to
the truncated area, resulting in that the hard X-rays emitted in the Compton cloud
lag behind the soft X-rays emitted in the disk.

Through the CCF method, the anti-correlated long-term hard time lags from tens of
seconds to hundreds of seconds were also detected in a few NS-LMXBs. \cite{Lei2008}
first detected anti-correlated long-term hard X-ray time lags in Z source Cyg X-2
and, meanwhile, anti-correlated long-term soft X-ray time lags were also found in
this source. \cite{Sriram2012} reported the similar anti-correlated long-term hard
and soft X-ray time lags detected in another Z source GX 5-1. Moreover, in atoll
source 4U 1735-44 and 4U 1608-52, \cite{Lei2013,Lei2014} detected four types of
long-term X-ray time lags, i.e. anti-correlated long-term hard and soft X-ray time
lags and positively correlated long-term hard and soft X-ray time lags. \cite{Wang2014}
systematically investigated the cross-correlation evolution of XTE J1701-462 on its
HIDs, detected the four types of long-term X-ray time lags, and found that its
cross-correlation behavior evolves with luminosity. The model of truncated accretion
disk was invoked to explain the detected long-term time lags in NS-LMXBs
\citep{Lei2008,Sriram2012,Wang2014}. However, we argue that the model of truncated
accretion disk cannot account for the detected long-term time lags in NS-LMXBs. Firstly,
this model can only account for the anti-correlated long-term hard X-ray time lags,
while anti-correlated long-term soft X-ray time lags are usually detected in NS-LMXBs.
Secondly, the truncated accretion disk model requires that an optically thick
accretion disk is far away from the compact object, while the accretion disk of
NS-LMXBs touches the NS \citep{Inogamov1999,Inogamov2010}. Here, we argue that in
NS-LMXBs, the accretion disk touches the NS because of the absence of a magnetoshpere
around the NS in these systems. In the XRBs hosting a strongly magnetized NS with
surface magnetic field strength ${\rm B_0\sim10^{12}\ G}$, e.g. accretion-powered
X-ray binary pulsars, most of which are NS-HMXBs, a magnetosphere will be formed
around the NS \citep{Lamb1973}. In these XRBs, when the accreting matters approach the
magnetosphere, they will be channeled onto the polar caps of the NS along the magnetic
field lines, producing X-ray pulsations, which could be an evidence for a magnetosphere
in XRBs. Additionally, cyclotron lines are usually observed in the X-ray spectra of
accretion X-ray pulsars \citep{Coburn2002,Caballero2012}, showing sufficient ${\rm B_0}$
to form a magnetosphere. Sequentially, in NS-HMXBs, the magnetic pressure from the
magnetosphere pushes the accretion disk outwards, leading to that the disk might be far
away from the NS. However, ${\rm B_0}$ of NS-LMXBs, including Z sources and atoll
sources, spans a range of ${\rm \sim10^{7}-10^{9}\ G}$ \citep{Focke1996,Campana2000,
Ding2006,Ding2011}, which is much smaller than that of strongly magnetized NSs, so that
it is unlikely for a magnetosphere to be formed in NS-LMXBs. Actually, the X-ray
pulsations have never been observed in Z sources and atoll sources except Aql X-1
\citep{Casella2008} and cyclotron lines have never been observed in these sources too,
any of which conforms the absence of a magnetosphere in NS-LMXBs. In the case of the
absence of a magnetosphere, the accretion disk will reach the NS. Therefore, the
accretion disk of NS-LMXBs touches the NS.

\subsection{The long-term time lags in GX 349+2}

In this work, using all the 138 {\it RXTE} observations from 1996 to 2011 for Z
source GX 349+2, we systematically perform cross-correlation analysis between 2-5
kev and 16-30 keV light curves with CCF method. The results are listed in
Tables~\ref{table1}-\ref{table3} and selectively shown by
Figures~\ref{fig:positive}-\ref{fig:anti-correlation}.

As reviewed and pointed out above, the long-term hard X-ray time lags of BHXBs can
be explained by the truncated accretion disk model
\citep{Choudhury2004,Choudhury2005,Sriram2007}, but this model cannot account for
the long-term time lags of NS-LMXBs, because the accretion disk in NS-LMXBs actually
contacts with the NS \citep{Church2004,Inogamov1999,Inogamov2010}. Moreover, the
long-term time lags detected in XRBs, including the results that we obtain in this
work, are larger than dozens of seconds, even over one thousand seconds, while the
short-term time lags in XRBs spans in the range of milliseconds, so it is a feasible
assumption that the mechanisms responsible for the long-term X-ray time lags could
be very different from those models accounting for the short-term time lags in XRBs,
such as the shot model reviewed above. Besides, in general, the short-term time lags
are derived from two light curves in two adjacent energy bands, e.g. 2-5 keV vs. 5-13
keV for GRS 1915+105 \citep{Reig2000} and 1.8-5.1 keV vs. 5.1-13.1 keV for Cir X-1
\citep{Qu2001}, while the long-term time lags are usually derived from two light
curves with distant energy bands, e.g. 2-7 keV vs. 20-50 keV for Cyg X-3
\citep{Choudhury2004} and 2-5 keV vs. 16-30 keV for GX 5-1 \citep{Sriram2012}, which
indicates that the X-rays responsible for the short-term time lags come from two
adjacent emission regions, even from the same area, while the the X-rays producing
long-term time lags might come from two regions which are far away each other.

Here, we invoke an extend accretion disk corona (ADC) model to explain the
long-term time lags detected in NS-LMXBs, including the long-term time lags of
GX 349+2 that we derive in this work. Analyzing the dip and non-dip spectra of
NS-LMXBs, \cite{Church1993,Church1995} proposed a Birmingham model which consists
of a blackbody component interpreted as the emission from a point source, i.e. the
NS, and a power law component that might be resulted from the Comptonization of
thermal emission in an ADC above the accretion disk. Through dip ingress time
technique, \cite{Church2004} measured the radius of the ADC and developed the
Birmingham model into an extended ADC model. The measured radius of a thin, hot
corona above the accretion disk varies in the range of $\sim$(2--70)$\times10^4$~km.
Therefore, the corona is very extended and the disk is substantially covered by the
corona. In the extended ADC model, almost all soft X-ray photons from the accretion
disk are inversely Comptonized by the energetic electrons from the extended ADC, which
produces the observed hard X-rays, while the observed soft X-rays are interpreted
as the emission from the NS; the accretion disk is illuminated by the emission of
the NS, leading to the production of the extended ADC above the disk. This model
was successfully applied to Cyg-like Z sources \citep{abc2006,Jackson2009,Balucinska2010}
and Sco-like Z sources (including GX 349+2) \citep{Church2012}, as well as atoll
sources \citep{Church2014}, so it could be a universal model for NS-LMXBs. Since
the extended ADC model is a unified model for NS-LMXBs, we try to interpret the
long-term time lags in NS-LMXBs with the help of this model. The extended ADC and
the NS are two independent emitting regions, which satisfies the request that the
hard and soft X-rays for long-term time lags are emitted from two distant regions,
as discussed above. In order to explain the long-term time lags detected in NS-LMXBs
in terms of the extended ADC model, we introduce two timescales. One is the
Comptonization timescale during which the disk seed photons are inversely Comptonized
by the high-energy electrons in the extended ADC, and another is the viscous timescale
in the order of hundreds of seconds \citep{Lei2008}, during which the accreting matter
flows from the disk onto the NS. The hard X-ray time lags will be produced if the
Comptonization timescale is less than the viscous timescale, and, contrarily, the
soft X-ray time lags will be observed if the Comptonization timescale is larger than
the viscous timescale. It is noted that a minority of positively correlated short-term
time lags ($<$1 s) are listed in Tables~\ref{table1} and \ref{table3}, which are derived
with the CCF method in our work. These short-term time lags cannot be explained by the
models reviewed in section 4.1, because those models are used to interpret the
short-term time lags produced in two adjacent energy intervals, while these short-term
time lags obtained in this work are derived from two distant energy intervals, i.e.
2-5 kev and 16-30 keV energy intervals. In the frame of the extended ADC model, we
propose that these short-term time lags will be observed under the circumstance that
the Comptonization timescale is comparable with the viscous timescale.

\section{CONCLUSION}

In this work, using all the {\it RXTE} observations for Z source GX 349+2, we
systematically perform cross-correlation analysis between soft and hard X-rays with
CCF method. Positive correlations and corresponding hard and soft X-ray long-term
time lags are detected throughout an extensive Z track on its HID. Anti-correlated
correlations and anti-correlated soft and hard X-ray long-term time lags are found
outside the HID. It is noted that in most observations outside the HID, positive
correlations and positively correlated hard and soft long-term X-ray time lags are
also obtained. We review the short-term time lags obtained with the Fourier
cross-spectral analysis in XRBs and some models responsible for the short-term time
lags. We also review the long-term hard X-ray time lags found in BHXBs, which can
be explained by the truncated accretion disk model. We argue that the long-term
X-ray time lags in NS-LMXBs cannot be interpreted by those models responsible for
the short-term time lags or the truncated accretion disk model. We invoke the
extended ADC model to explain the long-term X-ray time lags in NS-LMXBs, including
GX 349+2.

\section*{Acknowledgements}

We thank the anonymous referee for her or his constructive comments and suggestions,
which helped us carry out this research and improve the presentation of this paper.
This research has made use of the data obtained through the High Energy Astrophysics
Science Archive Research Center (HEASARC) On-line Service, provided by NASA/Goddard
Space Flight Center (GSFC). This work is partially supported by the 2014 Project of
Xinjiang Uygur Autonomous Region of China for Flexibly Fetching in Upscale Talents,
National Key Basic Research Program of China (973 Program 2015CB857100), the Natural
Science Foundation of China under grant nos. 11173024 and 11203064, and the Program
of the Light in Chinese Western Region (LCWR) under grant no. XBBS 201121 provided
by Chinese Academy of Sciences (CAS).

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