# Anomalous nature of outbursts of the black hole candidate 4U 1630-472

Kaushik Chatterjee Indian Center for Space Physics, 43 Chalantika, Garia St.
Road, Kolkata 700084, India  Dipak Debnath Indian Center for Space Physics, 43
Chalantika, Garia St. Road, Kolkata 700084, India  Riya Bhowmick Indian Center
for Space Physics, 43 Chalantika, Garia St. Road, Kolkata 700084, India  Sujoy
Kumar Nath Indian Center for Space Physics, 43 Chalantika, Garia St. Road,
Kolkata 700084, India  Debjit Chatterjee Indian Institute of Astrophysics,
Koramangala, Bengaluru, Karnataka, 560034, India  Indian Center for Space
Physics, 43 Chalantika, Garia St. Road, Kolkata 700084, India

###### Abstract

The Galactic black hole candidate (BHC) 4U 1630-472 has gone through several
outbursts (13 to be particular) in the last two and a half decades starting
from the RXTE era till date. Like the outbursts of other transient BHCs, the
outbursts of this source show variations in duration, peak numbers, highest
peak flux, etc. However, unlike any other soft X-ray transients, this source
showed outbursts of two types, such as normal and super. The normal outbursts
of duration $\sim 100-200$ days are observed quasi periodically at an average
recurrence/quiescence period of $\sim 500$ days. The super outbursts of
duration $\sim 1.5-2.5$ years contain one or more normal outbursts other than
one mega outburst. We make an effort to separate flux contribution of the
normal and the mega outbursts from the super outbursts, and tried to
understand the nature of evolution of both types (normal and mega) of
outbursts, based on the quiescent period prior to the outbursts. Archival data
of RXTE/ASM from January 1996 to June 2011, and MAXI/GSC from August 2009 to
July 2020 are used for our study. A possible linear relation between the
quiescent and outburstsing periods for both types of outbursts are observed.
This makes the BHC a special source, and it may contain two companion
binaries. Two companions might be responsible for two types of outbursts.

X-ray binary stars(1811) – X-ray transient sources(1852) – Black holes(162) –
Black hole physics(159) – Accretion(14)

††journal: ApJ

##  1 Introduction

Compact objects like white dwarfs (WDs), neutron stars (NSs) and black holes
(BHs) are the end products of stars. Astrophysical black holes form from more
massive stars than those which end up their lives as WDs or NSs. Based on the
mass, BHs are divided into three classes: (a) stellar mass black holes (SBHs),
(b) intermediate mass black holes (IMBHs) and (c) super massive black holes
(SMBHs). Depending on the spin, BHs are divided into two categories: (a) non-
rotating Schwarzschild black holes and (b) rotating Kerr black holes. The most
prominent way to detect a BH is by detecting the radiation that is coming from
the accretion disk of the BH during the course of an outburst. Outbursts are
thus of very much importance in case of detection of a BH. We are interested
about the outburst of the stellar mass black holes. Depending on the outburst
nature, they are mainly of two types: transient and persistent. Transient
black holes are those which mostly stay in the quiescent phase and
occasionally become active and show outbursts when there is rise-in viscosity
of the infalling matter from the companion. Mostly we are interested in these
transient SBHs and their outbursts. The radiation from the close region of the
disk of these outbursts are in X-rays. Generally, for most of the times, two
different outbursts of the same BH are likely to be different. The nature of
the light curves of outbursts of BH transients divide themselves into various
different kinds of morphologies, of which, according to Chen et al. (1997),
the most prominent one is the fast rise exponential decay (FRED, Kocevski et
al. 2003) type. Debnath et al. (2010), classified BH sources based on their
outburst profiles into two classes: fast-rise slow-decay (FRSD) and slow-rise
slow-decay (SRSD). During an outburst of a transient black hole, we observe
transition between various spectral states. There are four defined spectral
states of a black hole candidate (BHC): hard state (HS), hard inter-mediate
state (HIMS), soft inter-mediate state (SIMS) and soft state (SS) (Remillard &
McClintock 2006). Generally, during an outburst, a transient BHC makes
spectral state transition as HS $\rightarrow$ HIMS $\rightarrow$ SIMS
$\rightarrow$ SS $\rightarrow$ SIMS $\rightarrow$ HIMS $\rightarrow$ HS. This
type of outbursts are called type-I outburst. In case of type-II outburst, we
do not see transition towards the softer states and these outbursts are also
known as ‘failed’ outbursts (Debnath et al. 2017 and the references therein).
Low frequency quasi periodic oscillations (LFQPOs) are also the common feature
in most of the BH outbursts, which are mainly observed in the HS and HIMS.
LFQPOs are also observed in SIMS, but sporadically on and off (Casella et al.
2005; van der Klis 2005). Generally, it has been observed that during the
rising phase of the outburst, the QPO frequency rises monotonically while it
decreases in the declining phase (Nandi et al. 2012; Debnath et al. 2013).
LFQPOs are generally absent in SS.

The soft X-ray transient (SXT) 4U 1630-472 (Kuulkers et al. 1997) was
discovered by the Uhuru satellite (Jones et al. 1976). Based on its spectral
and temporal behaviour, 4U 1630-472 is thought to be the repository of a black
hole (Kuulkers et al. 1997). This is a very active SXT with occurrence of
outburst at roughly every 400-550 days (Jones et al. 1976; Priedhorsky 1986).
Its first outburst was recorded back in 1969 by VELA 5B (Priedhorsky 1986) and
since then it has gone through outbursts more than 20 times. With this
recurrence time, 4U 1630-472 is known to be the shortest recurrent SXT
(Kuulkers et al. 1997). According to Seifina et al. (2014), it has a mass
$\sim 10~{}M_{\odot}$ and is at a distance of $10-11~{}kpc$. There are
presence of three pulsars, such as IGR J16358-4726, IGR J16393-4643, and IGR
J16320-4751, in very close angular separation of 4U 1630-472. These sources
are visible in the ASM and GSC field of views (FOVs) of 4U 1630-472. There
could be contamination of these sources due to this close separation during
the outbursts of 4U 1630-472. Due to the crowded region where it is situated,
no companion has been clearly detected yet (Kuulkers et al. 1997). However,
from its IR properties, Capitanio et al. (2015) suggested that it contains an
early-type secondary star with an orbital period ($P_{orb}$) of a few days.
According to Parmar et al. (1997), the outbursts of this SXT is not strictly
periodic, but vary by an $8~{}\%$ of rms.

There has always been this debate about the mechanism that triggers an
outburst. Primarily, it is due to the fact that when there is enhancement in
viscosity, matter comes closer to the compact object, triggering an outburst.
Chakrabarti et al. (2019, hereafter CDN19) tried to explain the triggering
mechanism in black holes by analysing the outburst profiles of the BHC H
1743-322. Bhowmick et al. (2021) studied relation between quiescent and
outburst phases of the well known Galactic transient BHC GX 339-4 in the post
RXTE era. These works motivated us to study outburst profiles of 4U 1630-472
as it is one of the most active transient BHCs. It shows outbursts in a
frequent interval of times. In the post RXTE era (1996-2020), it showed 13
outbursts, out of them 3 are of long duration and rest are of short duration.

This paper is organized as the following. In §2, we present the analysis
technique. In §3, we will present our results. Finally in §4, we will discuss
about the results and concluding remarks will be made.

##  2 Analysis

4U 1630-472 is a highly active recurring transient BHC, which shows outbursts
frequently. Light curve profiles from the RXTE to post-RXTE eta (1996-2020)
are used for the study in the paper. We used RXTE/ASM data (1996-2011) in the
$1.5-12~{}keV$ and MAXI/GSC data (2009-2020) in $2-10~{}keV$ energy bands for
our study. 2009–10 outburst is commonly observed by both the instruments (ASM
and GSC). So, it allowed us to normalize integrated fluxes and other measured
quantities from the data of the two instruments. We downloaded archival daily
average light curves which are in $counts/s$ and $photons~{}cm^{-2}~{}s^{-1}$
units in case of ASM and GSC data respectively. With proper conversion factor,
we have converted all the light curves into $mCrab$ unit. For ASM, $1~{}mCrab$
equals $0.075~{}counts/s$ in the $1.5-12~{}keV$ energy band while, in case of
GSC, $1~{}mCrab$ is equal to $0.00282~{}photons~{}cm^{-2}~{}s^{-1}$.

It is mentioned earlier that the most prominent morphology amongst the
outbursting light curve profiles is FRED. Here, we also can notice that all
the light curve profiles contain multiple peaks, which are FRED in nature. For
our current work, a profile fitting of the light curves are necessary. It
helped us to measure properties (peak flux, peak time, duration integral flux,
etc.) of each outburst. To do this, we make use of the FRED model (will be
discussed in later Section). Using this model, we used a code written in C++
language, which takes care of the FRED morphology of light curve profiles. We
fit all the outburst profiles (shown in Figure 1) using one or combination of
multiple FRED profiles. For fitting with this code, we make use of CERN’s data
analysis software, ROOT (version 6.13/01). We also calculated integral flux of
the outbursts using simple integration method. It helped us to verify FRED
fitted results.

We have also estimated the periodicity of the duration and gap between normal
outbursts using NASA’s Lomb Scargle Periodogram website (Peter et al. 2008;
Kovacs et al. 2002; Horne & Baliunas 1986; Scargle 1982).

To check for the contamination from nearby sources, we have also downloaded
daily average light curves of the IGR pulsar sources from Swift/BAT, RXTE/ASM
and MAXI/GSC archives and fitted each available curves with FRED profile by
converting them into mCrab unit.

##  3 Results

Figure 1: Daily averaged and mCrab converted light curve profiles of various
outbursts of the BHC 4U 1630-472. The online red curves are $1.5-12~{}keV$
RXTE/ASM data and online blue represent the $2-12~{}keV$ MAXI/GSC data. All
the light curve data are converted into $mCrab$ unit using proper conversion
factors.

Comparative study of light curves and duration of the quiescent period prior
to the outbursts, help us to understand the nature of the outbursts along with
the other underlying properties. It helps us to understand the triggering
mechanism of the outbursts along with the relation of the outbursts with their
preceding quiescent periods. To do this, we have fitted a total of 13
outbursts of 4U 1630-472 using the FRED model in ROOT. Out of those, 8
outbursts are from RXTE era and we have made use of ASM data. The rest 6 are
from post-RXTE era and we have taken MAXI/GSC data for those. The 2009–10
outburst is common for both the instruments. It helped us to normalize
integral flux of other outbursts. If Fig. 1, we have shown daily average
fluxes in $mCrab$ unit.

In the quiescent period between two outbursts, photon counts/fluxes in the
light curves stay at very low range. We define start and end of an outburst by
taking $12~{}mCrab$ flux as the threshold. This threshold was also used by
CDN19 and Bhowmick et al. (2021) in their studies for the BHCs H 1743-322 and
GX 339-4 respectively. In Fig. 2, to signify this threshold, two vertical
lines have been drawn other than one horizontal line at $12~{}mCrab$ flux for
all four shown figures. Detailed analysis results are mentioned in the
following sub-Sections.

###  3.1 Outburst Profiles

In Figure 1, we show the daily average light curve profiles (in mCrab) for the
BHC 4U 1630-472 in the RXTE and MAXI era. RXTE/ASM light curve in the
$1.5-12~{}keV$ energy band from $1996$ to $2009-10$ is shown with the red
curve, while $2-10~{}keV$ MAXI/GSC light curve from $2009-10$ to $2020$ is
shown with the blue curve. We see $8$ outbursts with the ASM data and $6$
outbursts with the GSC data. The $2009-10$ outburst was a commonly observed
outburst by the two instruments. We used integrated flux and other parameters
obtained from this outburst for the normalization to the other outbursts
observed lonely by the two instruments. In these total $13$ outbursts a large
variation in the peak flux, duration, etc are observed. If we compare these
outbursts with outbursts of other SXTs, these outbursts of 4U 1630-472 are
very much peculiar and unfamiliar in nature. In general, an SXT shows
outbursts every $2-3$ years for the duration of a few months of active
periods. But 4U 1630-472 showed two types of outbursts with differences in
duration, integrated flux, prior quiescent period, etc.

4U 1630-472 is a very interesting transient BHC as it showed outbursts in a
short gap of the recurrence period. From the RXTE era (1996-2020), 4U 1630-472
has gone through 13 outbursts. Most of its outbursts lasted for almost
$100-200$ days while some has lasted more than $500$ days. We can classify 4U
1630-472 outbursts into two types: normal and super. The normal outbursts are
recurring and observed in a gap of $\sim 400-550$ days. These outburst
duration roughly followed a quasi-periodic variations, if we looked into the
structure of the super outbursts. It seems that super outbursts contain one or
two normal-outbursts other than one mega-outburst.

The super outburst that started in early September 2002 (MJD $52521.4\pm
0.4$), and ended in December 2004 (MJD $53368.7\pm 22.0$), i.e., lasted for
$\sim 2.35$ years ($\sim 850$ days). This was in the RXTE era. In the MAXI era
too, there are two super outbursts. One of which started in late November 2011
(MJD $55889.7\pm 6.2$) and has continued till the very end of December 2013
(MJD $56651.2\pm 15.0$), lasting for $\sim 2.1$ years ($\sim 760$ days). The
other occurred in 2018–19, which started in April 2018 (MJD $58233.9\pm 1.2$)
and came below threshold in November 2019 (MJD $58789.2\pm 6.9$), lasting for
almost 1.5 years ($\sim$ 550 days). Since, there is some error in the value at
which date the $\sim 12~{}mCrab$ flux has been reached, especially in the
declining phase, we have taken the first super outburst as $2002-05$ instead
of $2002-04$ and the second one as $2011-14$ instead of $2011-13$. There is
also various reports of some super outbursts before the RXTE era, for example
the 1988 outburst, that lasted for $\sim 2.4$ years (Kuulkers et al. 1997).
Before that there were also report about the super outburst in 1977.

Although the average recurrence period for normal outbursts is close to $500$
days, the outbursts are not always exactly periodic. For example, the 1997–98
outburst occurred after a recurrence period of $\sim$ 540 days, while the next
outburst in 1999 occurred after a period of $\sim$ 400 days. The duration of
outbursts also differ from one another. In case of the super outburst also,
this duration is changing. In fact, if we notice carefully, we find that the
super outbursts are becoming smaller in duration. While the super outburst in
1988-91 lasted for almost 870 days (Kulkeers et al. 1997), we find that the
2002–05, 2011–14 and 2018–19 have duration of $\sim$ 850, 760 and 550 days
respectively.

Figure 2: FRED profile fitted (a) 1999 normal and (b) 2002–05, (c) 2011–14,
(d) 2018–19 super outbursts. A $12~{}mCrab$ line (black) is also drawn to
signify the start and end of the outburst in the rising and declining phases
respectively. Solid red lines are used to differentiate between normal and
super outbursts.

###  3.2 Calculation of Integrated Fluxes

An outburst profile contain one or multiple peaks having nature of fast-rise
and exponential decay. So, we use the FRED model to fit each peak of the
outburst. The combined FRED fit allows us to get overall nature of the
outburst profiles. The equation of the FRED model (Kocevski et al. 2003) is
defined as,

$F(t)=F_{m}\left(\frac{t}{t_{m}}\right)^{r}\left[\frac{d}{d+r}+\frac{r}{d+r}\left(\frac{t}{t_{m}}\right)^{r+1}\right]^{-\frac{r+d}{r+1}}$
$None$

where, $F_{m}$ is called the peak flux, i.e., the highest flux value in the
light curve, $t_{m}$ is the peak time, i.e., the time at which the source or
the outburst reaches its maximum flux value. $r$ and $d$ signify the rising
and decaying indices. One thing we have to keep in mind is that, here $r$ and
$d$ do not give the value of the slopes in the rising and declining phases.

We have also used numerical simple integration method (trapezoidal to be more
specific) to estimate integral flux during the outburst. This method allows us
to verify the integral flux calculated using the FRED model fitting. We have
integrated the fluxes of each outbursts from their respective daily average
light curves using this method and normalized them using the $2009-10$
outburst flux from MAXI/GSC data. We notice that all the integrated fluxes
using this method lie very close to the values integrated by FRED model method
(see, Table 1). However, the downloaded daily average light curves have some
discrepancies. Some of the data have negative values as well as for some day,
the data are missing. There is also some random variations in the data where
it shows sudden dips or ups. These are mainly due to the instrumental error.
Since there is no significant difference between the two methods, it is more
scientific to make use of the FRED model. In Bhowmick et al. (2021), we have
made use of both these methods for our analysis of the BHC GX 339-4.

As stated above, in the first method, we have fitted all the light curves
using FRED model, as shown for the $2009-10$ outburst in Figure 2. Using the
Bayesian Information Criterion (BIC) selection method, we confirmed that
$k$-number of FRED profiles that are needed to obtain best fit of the entire
lightcurve profile of an outburst (for more details see, Bhowmick et al.
2021). Same selection method is followed for all the outbursts of 4U 1630-472.
We have estimated the integral fluxes (I.F.) for all these outbursts from the
model fits using the combined FRED profiles. Assuming $12~{}mCrab$ flux as
outburst threshold (Chakrabarti et al. 2019), we first mark the start and end
of an outburst using first and last occurrence of the $12~{}mCrab$ flux points
in the rising and declining phases respectively. We show the variation of the
estimated integral fluxes in Figure 3. Here in panel (a), we show the
normalized flux per day during the outbursts and in panel (b), the normalized
flux per day in case of accumulation periods. The accumulation period of each
outburst is the time during which matter accumulate at a distance, far away
from the black hole (namely pile-up radius $X_{p}$) before the outburst
(Chakrabarti et al. 2019). The width of each bar in panel (a) signifies the
duration of that particular outburst. We have used the MAXI/GSC $2009-10$
outburst fitted I.F. value to normalize all the I.F. values as it is less
noisy than the RXTE/ASM one.

As mentioned in the previous Section, 4U 1630-472 showed two different nature
(normal and super) of outbursts. The super outbursts are long duration and
their light curve profiles show that they contain one or two normal outbursts.
Normal outbursts are roughly periodic in their outburst duration and
accumulation periods (quiescent period prior to an outburst). From these two
parameters and light curve profiles, we found that 2002–05 and 2011–14 super
outburst contained two normal and one mega outbursts, where as 2018–19 super
outburst contained one mega and one normal outbursts (see, Fig. 2). The
2002–05 super outburst started on MJD $52521.4\pm 0.4$ after a quiescent gap
of close to 460 days after the previous 2000–01 outburst. If we look closely
into this 2002–05 outburst, we can see that, after passing through rise and
decay phases within $\sim 170$ days, the flux became as low as $\sim 12$ mCrab
close to MJD $\sim$ 52680, which is close to the average duration of a normal
outburst. If this would have been a normal outburst, then the next normal
outburst would have occurred close to the time where we saw third peak of the
2002–05 super outburst. This third peak started close to MJD $\sim$ 53080\.
Near to this day, the flux became very low ($\sim 12$ mCrab) before again
starting to rise. This third peak also had a duration, close to the average
duration of normal outbursts. The 2nd peak was observed between MJD $\sim$
52680 and MJD $\sim$ 53080, which continued for a longer duration than its
other two peaks. We termed this as the ‘mega’ outburst. We recalculated the
integral fluxes for these three outbursts separately from the combined FRED
model fit and using start and end time of each outbursts as days mentioned
above. The 1st and 3rd peaks are termed as 2002–03 and 2004 normal outburst
respectively and 2nd peak is termed as 2003–04 mega outburst. A similar
procedure is followed to separate normal outbursts from mega outbursts within
the super outbursts for 2011–14 and 2018–19. Integral fluxes are also
calculated by selecting suitable inputs of start and end dates of the normal
and mega outbursts, where flux became close to $\sim 12$ mCrab within the
super outbursts.

Figure 3: Histogram plot of normalized flux per day for (a) outburst and (b)
accumulation periods. All these estimations are done using the $2009-10$
values.

Figure 4: Histogram plot of normalized flux per day for (a) outburst and (b)
accumulation periods in case of only normal outbursts. All these estimations
are done using the $2009-10$ values.

Figure 5: Histogram plot of normalized flux per day for (a) outburst and (b)
accumulation periods in case of only mega outbursts. All these estimations are
done using the $2009-10$ values.

Figure 6: Variation of duration between normal outbursts. Here, each tick
represents the number of normal outbursts.

Figure 7: Variation of gaps between normal outbursts. Here, each tick
represents the number of normal outbursts.

Figure 8: Lomb Scargle Periodogram plot for periodicity calculation of
duration between normal outbursts (Figure 6).

Figure 9: Lomb Scargle Periodogram plot for periodicity calculation of gaps
between normal outbursts (Figure 7).

###  3.3 Comparative Study of Outburst and their Fluxes

To have a comparative study of all the outbursts of 4U 1630-472, observed by
two different satellite (RXTE and MAXI) instruments (ASM and GSC), we make use
of commonly observed outburst i.e., $2009-10$ outburst fitted parameters to
normalize integral flux and other parameters of the other outbursts. In Fig.
3, a histogram is drawn, where we show variation of the normalized integral
fluxes per day of outburst or accumulation periods of all outbursts including
both the normal and super outbursts. The evolution of the same integral fluxes
for the 15 normal and 3 mega outbursts, after their separation from the super
outbursts whenever applicable are shown in Figs. 4 and 5 respectively. Average
integral fluxes for per day of accumulation i.e. quiescent periods prior to
each outburst are marked with the horizontal dashed lines in each Figures.

Figure 3(a) shows the integrated flux per day during the time of the outburst.
This is shown for all the outbursts using a histogram, where the width of each
histogram signifies the duration of every outburst. So, the area of each
histogram represents the total I.F. during that outburst. These integral
fluxes represent the total energy released during the outbursts (normalized
with respect to the $2009-10$ outburst I.F.). We notice that three outbursts
($2002-05$, $2011-14$ and $2018-19$) have higher values of I.F. during
outbursts. Figure 3(b) shows the integrated flux per day in the period of
matter accumulation prior to each outburst. The black dashed line, that is
drawn in this panel of the Figure, represents the average of all these values.
This actually tells us about the mass transfer from the pile up radius
$X_{p}$. When this value is high, i.e., for the cases of $2002-05$,
$2011-2014$ and $2018-19$, it means that more matter is coming from the
$X_{p}$. This also tells us that the more matter was accumulated prior to the
triggering of these three outbursts. That is why, the values for these
outbursts are very high and much above the average values. These are termed as
the super outbursts, in which the I.F. for both the cases of outburst and
accumulation is higher than the other short period outbursts. As we see in the
other outbursts, I.F. is much less and stays roughly close to each other. This
tells us that during these normal outbursts, the supply of matter from the
companion is not as large as the cases of those super outbursts. Except for
the presence of the super outbursts, the nature of 4U 1630-472 seems fairly
the same as of other SXTs. In those sources also, the supply of matter from
the companion also changes from time to time for different outbursts. The
presence of these super outbursts makes the SXT 4U 1630-472 an interesting
candidate to study.

In the previous Section, we have discussed the method about separation of the
super outbursts into its two constituents : normal and mega. In Figure 4(a),
we show the normalized integrated flux per day during outburst for only the
normal outbursts including the normal parts of the super outbursts, while
Figure 4(b) shows that for accumulation period. If we look in panel (b), we
can notice that during the accumulation period the normalized flux per day for
all the outbursts stay close to an average value. Figure 5(a-b) shows the same
properties for only the mega parts of the super outbursts. We see that while
the accumulation of matter were close to each other for 2003–04 and 2012–13
outbursts, it increased for the 2018–19 one. All the estimated properties are
given in Table 1, 2 and 3 for the cases of all the outbursts, only normal
outbursts and only mega outbursts respectively.

###  3.4 Estimation of Periodicity of Duration and Gap of Normal Outbursts

We have first estimated the duration and gaps between normal outbursts from
our FRED fitted light curve profiles. Duration of outbursts are the time
periods between start and end of 12 mCrab fluxes. Gaps between outbursts are
the time from the peak of the preceding outburst to the peak of the current
outburst. Here, normal outbursts also includes the normal parts from the super
outbursts. We have plotted the variations of these two properties in Figures 6
and 7 respectively. These show quasi periodic type of variations. This is why
we tried to estimate their periodicity.

We have mainly used the Lomb Scargle Periodogram (LSP) method from NASA
exoplanet archive to estimate these periodicities. The LSP is a variation of
the Discrete Fourier Transform (DFT), which is optimized to identify
sinusoidal shaped signals in time series data. If there is a sinusoidal signal
of with a frequency $\omega_{0}$, the periodogram gives a large peak value of
power at the period $T=2\pi/\omega_{0}$. When the data is not purely
sinusoidal (like in our case), the x-axis value of the largest peak in power
signifies the period of the data. The NASA exoplanet archive implemented the
periodogram power as the normalization of the total power ($P_{x}(\omega)$) by
variance ($\sigma$) or $P_{n}(\omega)=P_{x}(\omega)/\sigma^{2}$, where
$P_{n}(\omega)$ is the normalized power. We show the LSP plots for normal
outburst duration and gap in Figures 8 and 9 respectively, i.e., Figures 8 and
9 corresponds to Figures 6 and 7 respectively. For our case, we have obtained
highest power values of $\sim$ 2.31 and 2.88 for normal outburst duration and
gaps respectively. These values correspond to periods of 10.92 and 4.25
respectively. This tells us that the duration and gap of normal outbursts has
periodicities of 10.92 and 4.25 respectively.

###  3.5 Contamination of Closely Situated Pulsars

Figure 10: One day (from 2020 December 08 00:00 to 2020 December 09 00:00)
MAXI/GSC FOV image of 4U 1630-472 in different energy bands. This image is
downloaded from the MAXI website.

To check for the contamination from the nearly situated IGR pulsar (IGR
J16358-4726, IGR J16393-4643, IGR J16320-4751) sources, we have also analyzed
their light curve profiles. For IGR J16358-4726, we use Swift/BAT light curve
in 15-50 keV energy band (since ASM and GSC data are not available), for IGR
J16393-4643 we use archival 15-50 keV Swift/BAT and 1.5-12 keV RXTE/ASM light
curves (since GSC data is not available), while for IGR J16320-4751, we only
use the 1.5-12 keV RXTE/ASM (as BAT and GSC data are not available). Using all
the proper conversion factors, we have converted the light curves into mCrab
unit and fitted them with FRED model. During the outbursts of 4U 1630-472,
none of these sources were very much active and average flux was always close
to our assumed threshold value ($\sim$ 12 mCrab) for quiescent.

##  4 Discussion and Concluding Remarks

The soft X-ray transient (SXT) 4U 1630-472 was discovered by Uhuru satellite.
This SXT is a very active source and showed recurring outbursts in a gap of
400–550 days since its discovery. Nature of the outbursts of the source are
studied here in RXTE and post RXTE era. Daily average archival data of
RXTE/ASM ($1.5-12$ keV) and MAXI/GSC ($2-10$ keV) are used for our study.
Outburst profiles are fitted with the FRED model, to extract peak flux,
integral flux, duration, etc. parameters. Here, we would like to discuss about
some anomalous nature of the source and then try to draw concluding remarks.

One of the goals of this paper is to study the triggering mechanism of an
outburst. Although there is debate on it, we believe that it could be due to
the sudden rise in viscosity (Ebisawa et al. 1996) due to increase in rate of
supply of matter toward black hole via Roche lobe overflow or wind. Recently,
Chakrabarti, Debnath and Nagarkoti (2019; CDN19) and Bhowmick et al. (2021)
studied the nature of outbursts of the recurring transient BHCs H 1743-322 and
GX 339-4 during the RXTE and MAXI (present) eras. It is suggested by CDN19
that, there is a pile-up radius ($X_{p}$) which is situated at a distance, far
away from the source where matter, which comes in from the companion, at first
starts to accumulate due to low viscosity. Then when a large amount of matter
sets in at $X_{p}$, the temperature of the disk rises which increases the
instability of the disk. As a result, viscosity of the accumulated matter
starts to rise. When viscosity attains a critical value, matter rushes towards
the BH, triggering an outburst. When this distance is large, more matter
accumulates at $X_{p}$ and more time is needed to rise the viscosity to
critical value to start an outburst. When this $X_{p}$ is closer, it takes
less time to start the outburst. The outburst duration, which depends on the
amount of matter accumulated from the companion, is indirectly dependent on
the location of $X_{p}$ also. This rise in viscosity could also be due to the
rise in magnetic activity of the companion. When matter brings in magnetic
field from the companion, it can remove angular momentum by ejecting piled up
matter. As a result, matter rushes towards the compact source.

We can notice that, unlike other transient sources, the outbursts of 4U
1630-472 are different to some extent. First of all, the outbursts are not of
similar nature. There are outbursts which lasted for $100-200$ days, defined
as the normal outbursts. There are also few outbursts which lasted for 1.5–2.5
years. We term them as the super outbursts. This type of nature of outbursts
is generally not common in case of other BHCs. From our detailed analysis of
the super outbursts, we found that the super outbursts are the combination of
two types of outbursts: mega and normal outbursts. Here, we make an effort to
separate contribution of the normal and mega outbursts from each of the super
outbursts. The FRED model fitted parameters of each outbursts (normal, super
and mega) are noted in Tables 1-3. We use 2009–10 outburst, commonly observed
by both the RXTE and MAXI satellites, to normalize integral fluxes of all the
outbursts. In Fig. 3, histogram plots of estimated fluxes per day of the
outburst and per day of the accumulation period of all the 13 observed
outbursts of this source are shown. Similar histogram plots of the normal and
mega outbursts are plotted in Figs. 4 & 5.

From the detailed analysis of the duration of the outburst and quiescent
phases, we observe that the recurrence period (both accumulation and outburst)
of the outbursts has changed over the years. Although normal outbursts are
observed $\sim 500$ days of gap, their integral fluxes of the outbursts have
varied roughly in a cyclic way (Fig. 4). From Figures 6 and 7, we can also
notice the cyclic variations of outburst and accumulation duration of normal
outbursts. The Lomb Scargle Periodogram of these variations have helped us
find the periodicities for these two duration. For outburst and accumulation
duration (i.e., gap), we have found period of 10.92 and 4.25 respectively.
However, in case of mega outbursts, we observed decreasing nature in both the
outburst duration and the accumulation period between the outbursts. From the
decreasing trend of accumulation period of mega outbursts and average
recurrence period of normal outbursts, we can predict that the next super
outburst will consists of one normal and one mega outbursts.

Generally, during an outburst of a BHC, the changes of spectral states form a
hysteresis loop or in case of a failed outburst it stays mostly in harder
states (Remillard & McClintock 2006). For 4U 1630-472, most of the outbursts
show anomalies in case of hard state (HS) to high soft state (HSS) transition
(Capitanio et al. 2015). There is lack of hard state in both the rising and
declining phases (checked from hardness ratio or HR). In some outbursts, the
final detection level of HS is very close to the quiescent luminosity
(Capitanio et al. 2015). We have seen for H 1743-322 (Chakrabarti et al. 2019;
Fig. 5c) and GX 339-4 (Bhowmick et al. 2021; Fig. 3c) that there is roughly
constant matter supply from the companion. However, for this source, the
matter supply seems to be varying in a quasi periodic way (see Fig. 4(b)) for
different normal outbursts. All these together make the 4U 1630-472 source an
interesting and peculiar candidate in terms of outbursting nature. We think
that quasi periodic nature of matter supply for normal outbursts is linked
with the location of the pile up radius ($X_{p}$). The supply of matter could
be constant for all the outbursts. However, $X_{p}$ is changing its location
in a cyclic way. When it is closer to the BH, less amount of matter needs to
be accumulated to start an outburst and accumulation is higher when $X_{p}$ is
away. For example, before the 1996 outburst matter was accumulating at a
farther $X_{p}$ before triggering an outburst. This is why the average amount
of accumulated matter is high. For the next outburst in 1997–98, $X_{p}$ was
on a closer location and hence the average accumulated matter is less. We
think that this change of location of $X_{p}$ have taken place in a quasi
periodic way which reflects our results in Figure 4. For the cases of mega
outbursts also, we think that the pile-up location became closer gradually.
i.e., for the 2003–04 mega one $X_{p}$ was farther and the outburst gap as
well as the duration was higher. For 2012–13 case, the $X_{p}$ was at a closer
location and thus the accumulation gap was less as well as the duration. In
2018–19, it came more close as both the duration and gap both decreased. For
this outburst a huge amount of matter rushed towards the BH and this outburst
reached a very high peak, which is not similar with the other outbursts. This
cyclic change in $X_{p}$ location could be one of the plausible explanations
for the nature of normal outbursts of this source if the supply of matter from
the companion remains same over the years. For mega outbursts, closing of the
pile-up location is one factor which describes the duration and also the gap
between them. There could be another factor why these mega outbursts are
taking place.

Searching for contamination from nearby IGR pulsars, we checked their activity
during the active outburst phases of 4U 1630-472. We have not found any
significant contribution from these pulsars to the outbursts of this source.
Till now, there is no complete information on the companion of this source. If
we look at the MAXI/GSC field of view (FOV) of the source, we can find that
there are many sources in close region where 4U 1630-472 is situated (Figure
10). The second reason behind the occurrence of mega outbursts could be that
the source is in a three body (or trinary) system. The black hole is in a
binary configuration and there could be another source, coupled to this binary
system. Due to this configuration, there could be an extra unknown
perturbation which is working on the system against which the binary could
stay stable. However, due to this extra perturbation, there could be extra
supply of matter from the companion when the third body comes in a closer
distance. Due to this, there is an extra amount of radiation, coming in as the
mega outbursts.

##  5 Summary

We have studied the outburst profiles of the BHC 4U 1630-472 using archival
daily average light curve data from RXTE/ASM (1.5–12 keV) and MAXI/GSC (2–10
keV) satellites. There are two types of outbursts in this SXT: normal
outbursts, which lasts for 100–200 days and super outbursts, lasting for
1.5–2.5 years. We have assumed that the super ones are the combination of
normal ones and an extra part, which we term as ‘mega’ outbursts. The average
recurrence period for normal outbursts also supports this assumption of the
occurrence of normal outbursts inside super outbursts. We have separated the
contributions of these normal and mega outbursts from the super outbursts. We
have fitted those light curve profiles (converted to flux into mCrab unit)
using the fast rise exponential decay (FRED) model. Using the resultant FRED
fitted profile and also numerical (Trapezoidal rule) method, we have estimated
integral fluxes from all the outbursts. From the FRED fitted profile, we have
extracted some of the other outburst properties (peak flux, peak day,
duration, normalized flux per day for the cases of both outburst and
accumulation period etc) for this BHC. Based on these analysis, we have tried
to explain the nature of its outbursts.

If the matter transfer from the companion is not changing much then we think
that the pile-up radius ($X_{p}$) is changing in a cyclic manner. Before some
outbursts it is away from the source, while before some outbursts it is closer
to the source. This is why the average flux in the accumulation period looks
quasi periodic in nature. For mega outbursts also $X_{p}$ was closer than the
previous one and thus resulting in decrement in the outbursts duration as well
as the accumulation gap.

There could be a third body, coupled to the binary system which is causing an
extra perturbation. As a result, the mass transfer is occasionally changing on
a very large scale which is causing the mega outbursts.

## Acknowledgement

This work has made use of ASM data of NASA’s RXTE satellite and GSC data
provided by RIKEN, JAXA and the MAXI team. K.C. acknowledges support from
DST/INSPIRE (IF170233) fellowship. D.D. acknowledges support from Govt. of
West Bengal, India and ISRO sponsored RESPOND project (ISRO/RES/2/418/17-18)
fund. R.B. acknowledges support from CSIR-UGC NET qualified UGC fellowship
(June-2018, 527223). S.K.N. and D.D. acknowledge partial support from ISRO
sponsored RESPOND project (ISRO/RES/2/418/17-18) fund.

## References

  * (1) Bhowmick, R., Debnath, D., Chatterjee, K., et al., 2021, ApJ, 910, 138
  * (2) Capitanio, F., Campana, R., De Cesare, G., Ferrigno, C., 2015, MNRAS, 450, 3840
  * (3) Casella, P., Belloni, T., Stella L., 2005, ApJ, 629, 403
  * (4) Chakrabarti, S. K., Debnath, D., Nagarkoti, S., 2019, AdSpR, 63, 3749
  * (5) Chen, W., Shrader, C. R., Livio, M., 1997, ApJ, 491, 312
  * (6) Debnath, D., Chakrabarti, S. K., & Nandi, A., 2010, A&A, 520, 98
  * (7) Debnath, D., Chakrabarti, S. K., Nandi, A., 2013, AdSpR, 52, 2143
  * (8) Debnath, D., Jana, A., Chakrabarti, S. K., Chatterjee, D., Mondal, S., 2017, ApJ, 850, 52
  * (9) Ebisawa, K., Titarchuk, L., Chakrabarti, S. K., 1996, PASJ, 48, 59
  * (10) Horne, J. H., & Baliunas, S. L., 1986, ApJ, 302, 757
  * (11) Jones, C., Forman, W., Tananbaum, H., Turner, M.J.L., 1976, ApJ 210, L9
  * (12) Kocevski, D., Ryde, F., Liang, E., 2003, ApJ, 596, 389
  * (13) Kovács, G., Zucker, S., & Mazeh, T., 2002, A&A, 391, 369
  * (14) Kuulkers, E., Parmar, A. N., Kitamoto, S., Cominsky, R. L., Sood, R. K., 1997, MNRAS, 291, 81
  * (15) Nandi, A., Debnath, D., Mandal, S., Chakrabarti, S. K., 2012, A&A, 542, A56
  * (16) Parmar, A. N., Williams, O. R., E. Kuulkers, E., Angelini, L., White, N. E., 1997, A&A, 319, 855
  * (17) Plavchan, P., Jura, M., Kirkpatrick, J. D., Cutri, R. M., & Gallagher, S. C., 2008, ApJSS, 175, 191
  * (18) Priedhorsky, W.C., 1986, AsSS, 126, 89
  * (19) Remillard, R. A., McClintock, J. E., 2006, ARA&A, 44, 49
  * (20) Scargle, J. D., 1982, ApJ, 263, 835
  * (21) Seifina, E., Titarchuk, L., Shaposhnikov, N., 2014, ApJ, 789, 57
  * (22) van der Klis, M., 2005, AN, 326, 798

Table 1: FRED model fitted parameters in case of all the outbursts

Outburst | Duration | Peak Flux | Peak Day | Accumulation | Normalized Integrated | Normalized Integrated
---|---|---|---|---|---|---
Year |  |  |  | Period | Flux Per Day during | Flux Per Day during
| (Days) | (mCrab) | (MJD) | (Days)a | Outburst b | Accumulation b
RXTE/ASM |  |  |  |  |  |
$1996$ | $159.6\pm 6.5$ | $296.711\pm 11.6$ | $50253.1\pm 0.8$ | $730.1\pm 5.0$ | $0.0088\pm 0.0007$ | $0.0019\pm 0.0002$
$1997-98$ | $108.1\pm 1.1$ | $382.088\pm 16.3$ | $50865.4\pm 0.1$ | $612.3\pm 0.8$ | $0.0047\pm 0.0004$ | $0.0008\pm 0.0001$
$1999$ | $99.30\pm 13$ | $203.100\pm 12.8$ | $51354.0\pm 1.1$ | $488.6\pm 1.2$ | $0.0048\pm 0.0008$ | $0.0010\pm 0.0001$
$2000-01$ | $215.4\pm 9.8$ | $596.026\pm 35.8$ | $51878.5\pm 7.4$ | $524.5\pm 8.6$ | $0.0068\pm 0.0007$ | $0.0028\pm 0.0003$
$2002-05$ | $847.2\pm 22$ | $704.987\pm 13.4$ | $52811.6\pm 0.3$ | $933.1\pm 7.7$ | $0.0111\pm 0.0010$ | $0.0100\pm 0.0008$
$2005$ | $186.4\pm 12$ | $277.561\pm 13.3$ | $53738.0\pm 4.8$ | $926.4\pm 4.4$ | $0.0060\pm 0.0007$ | $0.0012\pm 0.0001$
$2007-08$ | $212.5\pm 2.0$ | $217.831\pm 7.80$ | $54505.1\pm 0.6$ | $767.1\pm 5.4$ | $0.0055\pm 0.0004$ | $0.0015\pm 0.0001$
MAXI/GSC |  |  |  |  |  |
$2009-10$ | $208.5\pm 0.3$ | $316.117\pm 15.4$ | $55220.5\pm 0.6$ | $715.4\pm 1.2$ | $0.0048\pm 0.0004$ | $0.0014\pm 0.0001$
$2011-14$ | $761.5\pm 22$ | $627.838\pm 13.5$ | $56061.8\pm 5.9$ | $841.3\pm 30.7$ | $0.0095\pm 0.0008$ | $0.0086\pm 0.0007$
$2014-15$ | $110.3\pm 2.5$ | $346.898\pm 9.80$ | $57088.4\pm 1.8$ | $1026.6\pm 28.6$ | $0.0071\pm 0.0006$ | $0.0008\pm 0.0001$
$2016-17$ | $162.7\pm 6.5$ | $316.027\pm 7.80$ | $57680.4\pm 1.6$ | $592.0\pm 1.9$ | $0.0085\pm 0.0008$ | $0.0023\pm 0.0002$
$2018-19$ | $555.3\pm 8.2$ | $2152.46\pm 35.3$ | $58489.1\pm 0.2$ | $808.7\pm 1.7$ | $0.0117\pm 0.0009$ | $0.0080\pm 0.0006$
$2020$ | $142.9\pm 5.2$ | $396.872\pm 21.7$ | $58966.8\pm 2.2$ | $477.7\pm 2.8$ | $0.0072\pm 0.0006$ | $0.0022\pm 0.0002$

a Accumulation period is the duration between peak days from the previous to
the current outburst.

b This normalization is done by the integrated flux value of the $2009-10$
outburst.

Table 2: FRED model fitted parameters for only normal outbursts

Outburst | Duration | Peak Flux | Peak Day | Accumulation | Normalized Integrated | Normalized Integrated
---|---|---|---|---|---|---
Year |  |  |  | Period | Flux Per Day during | Flux Per Day during
| (Days) | (mCrab) | (MJD) |  (Days)a |  Outburst b |  Accumulation b
RXTE/ASM |  |  |  |  |  |
$1996$ | $159.6\pm 6.5$ | $296.711\pm 11.6$ | $50253.1\pm 0.8$ | $730.1\pm 5.0$ | $0.0088\pm 0.0007$ | $0.0019\pm 0.0002$
$1997-98$ | $108.1\pm 1.1$ | $382.088\pm 16.3$ | $50865.4\pm 0.1$ | $612.3\pm 0.8$ | $0.0047\pm 0.0004$ | $0.0008\pm 0.0001$
$1999$ | $99.30\pm 13$ | $203.100\pm 12.8$ | $51354.0\pm 1.1$ | $488.6\pm 1.2$ | $0.0048\pm 0.0008$ | $0.0010\pm 0.0001$
$2000-01$ | $215.4\pm 9.8$ | $596.026\pm 35.8$ | $51878.5\pm 7.4$ | $524.5\pm 8.6$ | $0.0068\pm 0.0007$ | $0.0028\pm 0.0003$
$2002-03$ | $161.3\pm 8.3$ | $536.422\pm 11.9$ | $52534.7\pm 2.3$ | $656.2\pm 7.8$ | $0.0127\pm 0.0011$ | $0.0031\pm 0.0002$
$2004$ | $291.8\pm 2.8$ | $308.743\pm 8.41$ | $53205.2\pm 1.9$ | $670.5\pm 2.9$ | $0.0061\pm 0.0004$ | $0.0026\pm 0.0002$
$2005$ | $186.4\pm 12$ | $277.561\pm 13.3$ | $53738.0\pm 4.8$ | $532.8\pm 4.4$ | $0.0060\pm 0.0007$ | $0.0012\pm 0.0001$
$2007-08$ | $212.5\pm 2.0$ | $217.831\pm 7.80$ | $54505.1\pm 0.6$ | $767.1\pm 5.4$ | $0.0055\pm 0.0004$ | $0.0015\pm 0.0001$
MAXI/GSC |  |  |  |  |  |
$2009-10$ | $208.5\pm 0.3$ | $316.117\pm 15.4$ | $55220.5\pm 0.6$ | $715.4\pm 1.2$ | $0.0048\pm 0.0004$ | $0.0014\pm 0.0001$
$2011-12$ | $233.1\pm 3.4$ | $627.838\pm 7.27$ | $56061.8\pm 1.1$ | $841.3\pm 1.3$ | $0.0121\pm 0.0009$ | $0.0034\pm 0.0003$
$2013-14$ | $189.1\pm 6.3$ | $185.407\pm 2.31$ | $56518.4\pm 2.8$ | $456.6\pm 3.0$ | $0.0034\pm 0.0004$ | $0.0014\pm 0.0001$
$2014-15$ | $110.3\pm 2.5$ | $346.898\pm 9.80$ | $57088.4\pm 1.8$ | $570\pm 28.6$ | $0.0071\pm 0.0006$ | $0.0008\pm 0.0001$
$2016-17$ | $162.7\pm 6.5$ | $316.027\pm 7.80$ | $57680.4\pm 1.6$ | $592.0\pm 1.9$ | $0.0085\pm 0.0008$ | $0.0023\pm 0.0002$
$2018$ | $228.4\pm 2.7$ | $293.998\pm 4.70$ | $58346.5\pm 3.4$ | $666.1\pm 3.8$ | $0.0064\pm 0.0004$ | $0.0022\pm 0.0002$
$2020$ | $142.9\pm 5.2$ | $396.872\pm 21.7$ | $58966.8\pm 2.2$ | $620.3\pm 3.2$ | $0.0072\pm 0.0006$ | $0.0017\pm 0.0002$

a and b represent the same things as Table 1.

Table 3: FRED model fitted parameters for only mega outbursts

Outburst | Duration | Peak Flux | Peak Day | Accumulation | Normalized Integrated | Normalized Integrated
---|---|---|---|---|---|---
Year |  |  |  | Period | Flux Per Day during | Flux Per Day during
| (Days) | (mCrab) | (MJD) |  (Days)a |  Outburst b |  Accumulation b
RXTE/ASM |  |  |  |  |  |
$2003-04$ | $403.0\pm 1.2$ | $704.987\pm 13.4$ | $52811.6\pm 0.3$ | $4943.9\pm 7.72$ | $0.0138\pm 0.0012$ | $0.00112\pm 0.00009$
MAXI/GSC |  |  |  |  |  |
$2012-13$ | $320.0\pm 7.7$ | $627.838\pm 13.5$ | $56061.8\pm 5.9$ | $3378.7\pm 30.7$ | $0.0117\pm 0.0009$ | $0.00111\pm 0.00009$
$2018-19$ | $280.0\pm 5.2$ | $2152.46\pm 35.3$ | $58489.1\pm 0.2$ | $2298.8\pm 1.71$ | $0.0178\pm 0.0013$ | $0.00217\pm 0.00015$

a and b represent the same things as Table 1.