LONG-TERM OPTICAL STUDIES OF THE BE/X-RAY BINARY RX J0440.9+4431/LS V+44 17

Most of our spectra of RX J0440.9+4431 were obtained with the 2.16 m telescope at Xinglong Station of National Astronomical Observatories. The optical spectroscopy with an intermediate resolution was made with a CCD grating spectrograph at the Cassegrain focus of the telescope. We took the red spectra covering from 5500 to 6700 Å. Sometimes low-resolution spectra (covering from 4300 to 6700 Å) were also obtained. In 2012 March and 2013 November, we also carried out the spectroscopic observations with the Yunnan Faint Object Spectrograph and Camera (YFOSC) instrument of the Lijiang 2.4 m telescope in the Yunnan Astronomical Observatory. The Grism #8 was used with a resolution of 1.47 Å pixel⁻¹, with a spectral range from 5050 to 9750 Å. The journal of our observations is summarized in Table 1, including observational date, exposure time, Modified Julian Date (MJD), and spectral resolution, respectively. All spectroscopic data were reduced with the IRAF³ package. They were bias-subtracted, flat-field corrected, and had cosmic rays removed. Helium-argon spectra were taken in order to obtain the pixel-wavelength relations.

The EWs of the Hα line have been measured by selecting a continuum point on each side of the line and integrating the flux relative to the straight line between the two points using the procedures available in IRAF. The measurements were repeated five times for each spectrum and the error is estimated from the distribution of these values. The typical error for the measurements is within 1%, arising due to the subjective selection of the continuum. The results of Hα EWs are listed in Table 1 and plotted in Figure 1. The published data of Hα (adopted from Reig et al. 2005), are also plotted in Figure 1 with open symbols.

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Since 2007, we performed systematic photometric observations on a sample of X-ray binaries with the 100 cm Education and Science Telescope (EST) and the 80 cm Tsinghua-NAOC Telescope (TNT) at Xinglong Station of NAOC. The EST, manufactured by EOS Technologies, is an altazimuth-mounted reflector with Nasmyth foci at a focal ratio of f/8. TNT is an equatorial-mounted Cassegrain system with a focal of f/10, made by AstroOptik, funded by Tsinghua University in 2002 and jointly operated with NAOC (Huang et al. 2012). Both telescopes are equipped with the same type of Princeton Instrument 1340 × 1300 thin back-illuminated CCD. The CCD cameras use standard Johnson-Cousins UBVRI filters made by Custom Scientific.

The photometric data reduction was performed using standard routines and aperture photometry packages in IRAF, including bias subtraction and flat-field correction. In order to study the variation of the optical brightness, we selected eight reference stars in the field of view (see Figure 2) to derive the differential magnitude of RX J0440.9+4431. We follow the algorithm of Broeg et al. (2009) to compute an artificial companion star using all the eight reference stars with different weights. The BVRI differential magnitudes and their errors are listed in Table 2 and plotted in Figure 3 together with the light curves of the reference star #8 in the right panel. In order to plot the same level with the target star, we add some offsets to the BVRI magnitudes of the reference star #8 in Figure 3.

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In order to study the long-term optical brightness variability of the source, we also make use of the public optical photometric data from the international database of the American Association of Variable Star Observers (AAVSO).⁴ Only the photometric observations made with the Johnson V-band filter are used and plotted in Figure 1 with 10 day bins. Using the secondary standard star C5 (our reference star #5 in Figure 2, with $\bar{V}$ = 14.625 mag and $\bar{B}$ = 15.665 mag) listed in Reig & Fabregat (2015), we also plot our V-band results with an offset of ∼14.05 mag in Figure 1. In addition, we also adopt the photometric data in Reig et al. (2005) and plot them in Figure 1 with open symbols. The (B − V) color of the source between our 2007 and 2014 observations is also plotted in Figure 1.

The Burst Alert Telescope (BAT) on board Swift (Barthelmy 2000) has monitored RX J0440.9+4431 in the hard X-ray energy band (15–50 keV) since 2005 February. Three consecutive X-ray outbursts were detected between 2010 March and 2011 February (Ferrigno et al. 2013). The positions of the peak time for three X-ray outbursts are marked with three dashed lines in Figure 1.

The profile of Hα lines showed a subtle change during each observational run. We select one typical Hα line from each run during our 2001–2014 observations and plot them in Figure 4, which indicates that the Hα profile of RX J0440.9+4431 usually showed an obvious double-peaked profile, except for the observations in 2010, when the Hα line displayed a strong single-peaked structure. Symmetric double-peaked Hα lines were observed during 2001 and 2002 observations. The central depression of the double-peaked Hα line during our 2001 observations was below the stellar continuum, which was also reported in Reig et al. (2005). The intensity of Hα during the 2001 observations was in the lowest level during our 15 year observations. Its intensity showed an obvious increase in the following two years. The Hα intensity showed an abrupt decrease in 2005 and it had the same level as that in 2002. After that, the intensity of the Hα line kept increasing in the following five years and reached a peak value with an averaged EW of approximately –12.9 Å during our 2010 observations. It is interesting that asymmetric profiles with a strong red peak were observed during 2008 and 2009 observations, while only a nearly symmetric single-peaked Hα line was observed during 2010. After 2010, the intensity of the Hα line showed a rapid decline and had an EW of approximately –5 Å during our 2012 October observations. The typical Hα profile during 2011 was an asymmetric structure with a strong violet peak, while the profile during 2012 October with a stronger red peak. Figure 1 indicates that the intensity of the Hα line kept decreasing before our 2013 October observations and it had a faint nearly symmetric double-peaked profile in our 2013 October 26 spectrum. The Hα intensity during our 2013 October observation was at a low emission level, which is similar to the level during our 2012 observations. One moth later, we observed a stronger Hα line during our 2013 November observations. The Hα intensity kept increasing during the following year and its emission during our 2014 observations returned to the level during 2012 observations. The asymmetric Hα lines during our 2014 observations showed rapid changes, with a stronger violet peak in the 2014 September 17 spectrum, while a stronger red peak on 2014 September 29.

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Following the method of Reig et al. (2005), we also define the V/R ratio of the Hα line as $V/R=(I(V)-{I}_{c})/(I(R)-{I}_{c})$, where I(V), I(R), and I_c are the intensities of the violet peak, red peak, and continuum, respectively. The V/R ratios of the Hα lines using logarithmic scales are listed in Table 1 and plotted in Figure 1, together with the data adopted from Reig et al. (2005) with open symbols. The V/R ratio could change rapidly within each observational run. In the long run we cannot see any periodic variation from the V/R ratio curves. In order to study the short-term variability of the Hα line, we plot the Hα lines observed in 2012 March and October at Lijiang Observatory and Xinglong Station, respectively, in Figure 5. On the right region of each spectrum, it is marked with the value of $\mathrm{log}(V/R)$. Due to the lower resolution of the spectra observed at Lijiang station, only an asymmetric profile with strong red peak was observed on 2012 March 13 and 14. A clearly double-peaked profile with a stronger red peak was observed on the spectrum of 2012 March 16. During the 2012 October observations, most of our spectra showed as an asymmetric profile with strong violet peak, except for the spectra observed on 2012 October 22 and 25 with a stronger red peak.

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The intensity of the Hα emission line can be used as an indicator of disk size around the Be star. Hanuschik (1989) found a correlation between the ratio of the Hα double peak separation (${\rm{\Delta }}{v}_{\mathrm{peak}}$) and the Be star projected rotational velocity $v{\rm{sin}}i$, and the Hα EWs with a factor of two scatter given by

$$\begin{eqnarray}&&\mathrm{log}[{\rm{\Delta }}{v}_{\mathrm{peak}}/2v{\rm{sin}}i]=-0.32\mathrm{log}({\mathrm{EW}}_{{\rm{H}}\alpha })-0.20,\end{eqnarray} \tag{ 1 }$$

where, ${\mathrm{EW}}_{{\rm{H}}\alpha }$ is in a unit of $-\mathring{\rm A}$. Assuming a Keplerian circumstellar disk around the Be star, we can estimate the disk size using Huang's formula (Huang 1972),

$$\begin{eqnarray}&&{R}_{d}/{R}_{*}={(2v{\rm{sin}}i/{\rm{\Delta }}{v}_{\mathrm{peak}})}^{2},\end{eqnarray} \tag{ 2 }$$

where R_d is the radius of the Hα emission region, and R_* is the radius of the central Be star. Following Equation (3) in Coe & Kirk (2015), we can estimate the disk size around the Be star using the Hα EWs with the following equation

$$\begin{eqnarray}&&\mathrm{log}\sqrt{{R}_{*}/{R}_{d}}\;=\;-0.32\mathrm{log}({\mathrm{EW}}_{{\rm{H}}\alpha })-0.20.\end{eqnarray} \tag{ 3 }$$

The Hα emission regions are calculated by Equation (3) in the unit of the central star radius R_* and the results are listed in Table 1 and shown in Figure 1. The maximum circumstellar disk with a radius of ∼ $12.9{R}_{*}$ corresponds to the strongest Hα emission during our 2010 observations.

Our photometric observational results of RX J0440.9+4431 with BVRI filters are plotted in Figure 3. Only BV-band data are available between the 2007 and 2009 observations. After 2010, we monitored the source with the BVRI filters. Figure 3 indicates that the V-band brightness of RX J0440.9+4431 showed a continuous decrease between our 2007 and 2013 observations and it had a minimum brightness around MJD 56595. The source faded by about 0.3 mag during the six years. After our 2013 October observations, a rapid increase was observed in the V-band photometry and the system brightened by about 0.15 mag within nearly one year. The B-band observations showed the same evolutionary way as the V-band observations, but the B-band magnitudes decreased more slowly between our 2007 and 2013 observations with an amplitude of ∼0.2 mag. The brightness of the source in RI-band observations has a more rapid variation. After the system reached a minimum brightness during our 2013 observations, the R and I brightness increased about 0.2 and 0.3 mag, respectively, within about one year.

The (B − V) color index kept declining on average between our 2007 and 2013 observations, which indicates that the spectrum of the Be star became bluer and bluer. The bluer spectrum means that the contribution of the disk emission decreased by the depletion of the inner part of the disk once the mass supply from the Be star stopped around our 2007 observations (we will discuss this in the next section). With the diffusion of the circumstellar material around the Be star out into the outer space, its spectrum became bluer and bluer. When the brightness began to increase after the 2013 October observations, a reddening of (B − V) was also observed simultaneously. This means that a new circumstellar disk was being formed around the Be star.

Due to the lack of V-band data before MJD ∼ 53250, we can only study the correlation between the Hα emission and the V-band brightness after that time. Figure 1 indicates that the V-band brightness increased continuously between MJD ∼ 53250 and ∼54400 with an amplitude of 0.2 mag on average. During this period, the intensity of the Hα line showed a complicated variability. Subtle changes were observed between our 2003 and 2004 Hα intensity, changing from approximately –6.5 Å to approximately –5.8 Å. The Hα line had a low emission level with an averaged EW of −2.9 Å during our 2005 October observations. The optical brightness had an obvious increase after our 2005 observations. The intensity of the Hα line also became stronger during our 2006 September observations with an averaged EW of approximately –7.0 Å. The Hα emission during our 2007 November observations had the same level as that during 2006, while the synchronous photometric observations indicates that the V-band brightness of the system had the highest level in the last two decades. After that, the V-band brightness showed a continuous decline between our 2007 and 2013 September observations, with an amplitude of ∼0.3 mag, which has been discussed above. Unlike the evolutionary behavior of the V-band brightness, the intensity of the Hα line showed an abrupt increase during our 2008 September observations. Its intensity kept increasing in the following two years and reached a maximum with an EW of approximately –12.9 Å during our 2010 October observations, which was the strongest Hα emission that has been reported in the literature. After 2010, the Hα intensity showed a continuously rapid decline and had a minimum EW of approximately –2.25 Å during our 2013 October observations, changing with an amplitude of ∼10.35 Å within three years of observations. After they reached their minima around our 2013 October observations, both of the V-band brightness and the intensity of the Hα line showed a rapid increase. The V-band magnitude brightened about ∼0.17 mag and the intensity of the Hα line was in a level of approximately –5.6 Å during our 2014 September observations.