The Optical Counterpart of the X-ray Transient
RX J0117.6-7330: Spectroscopy and Photometry
Roberto Soria, PASA, 16 (2), in press.

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Contents Page: Volume 16, Number 2

Observations and Data Analysis

We observed the optical counterpart of RX J0117.6-7330 from August 20 to August 23, 1998, simultaneously with the 40inch telescope (photometry) and the ANU 2.3m telescope (spectroscopy) at Siding Spring Observatory. Conditions were photometric during the first half of the first night and on the last night.

High-resolution Optical Spectroscopy

Optical spectra of the primary were obtained with the Double Beam Spectrograph on the 2.3m ANU telescope at Siding Spring Observatory, with 1200 grooves/mm gratings for both the blue (4150-5115 Å) and the red (6200-7140 Å) spectral regions (resolution 1.2 Å FWHM); the detectors used were SITe

1752 x 532 CCDs in both arms of the spectrograph.

Figure 1 and Figure 2 show the average of seven 600s spectra taken on August 20 in photometric conditions, for the blue and the red part of the spectrum respectively. Atmospheric absorption bands at

$\lambda > 6860$ Å have been removed from the red spectrum using the spectra of the calibration star LTT7379. Wavelengths are heliocentric.

**Figure 1:** Flux-calibrated blue spectrum of the optical counterpart of RX J0117.6-7330, taken on August 20, 1998 from the ANU 2.3m telescope at Siding Spring Observatory
$\begin{figure} \begin{center} \centerline{\psfig{file=fig1.eps,width=10cm}}\end{center}\end{figure}$

**Figure 2:** Flux-calibrated red spectrum of the optical counterpart of RX J0117.6-7330, taken on August 20, 1998 from the ANU 2.3m telescope at Siding Spring Observatory
$\begin{figure} \begin{center} \centerline{\psfig{file=fig2.eps,width=10cm}}\end{center}\end{figure}$

The most prominent feature in the blue spectral region is a strong H $\beta$ emission line: the equivalent width of the emission core, defined as in Dachs et al. (1981)², is

$= (-1.35 \pm 0.05)$ Å; broader photospheric absorption wings are also present. H $\gamma$ is seen in absorption with a narrower and weaker emission core [EW

$= (-0.27 \pm 0.02)$ Å]. Narrow absorption is observed from He I $\lambda 4388$ (EW = 0.4 Å), He I

$\lambda \lambda 4471, 4472$ (EW = 0.6 Å) and He I $\lambda 4922$ (EW = 0.3 Å). Figures 3, 4 and 5 show the region of the blue spectrum (average of all four nights, normalised to the continuum) around H $\gamma$ and H $\beta$ . Other weaker lines identified in the blue spectrum are listed in Table 1.

**Table 1:** Most prominent lines found in the optical spectrum of RX J0117.6-7330 (Balmer lines excluded)
Line	EW (Å)
He II $\lambda 4200$	$0.05 \pm 0.02$
O II $\lambda 4254$	$0.10 \pm 0.02$
O II $\lambda 4317$	$0.10 \pm 0.02$
O II $\lambda 4349$	$0.15 \pm 0.05$
O II $\lambda 4367$	$0.03 \pm 0.01$
He I $\lambda 4388$	$0.40 \pm 0.10$
O II $\lambda \lambda 4415, 4417$	$0.07 \pm 0.02$
He I $\lambda 4438$	$0.08 \pm 0.02$
He I $\lambda \lambda 4471, 4472$	$0.60 \pm 0.10$
S II $\lambda 4550$	$-0.07 \pm 0.02$
N II/Si III $\lambda 4553$	$0.10 \pm 0.02$
Si III $\lambda 4568$	$0.09 \pm 0.02$
O II $\lambda 4642$	$0.15 \pm 0.02$
O II $\lambda \lambda 4649, 4651$	$0.25 \pm 0.05$
O II $\lambda 4662$	$0.08 \pm 0.02$
O II $\lambda 4676$	$0.09 \pm 0.02$
He II $\lambda 4686$	$0.10 \pm 0.02$
He I $\lambda 4713$	$0.12 \pm 0.02$
He I $\lambda 4922$	$0.30 \pm 0.05$
S II $\lambda 6386$	$-0.20 \pm 0.02$
He I $\lambda 6678$	$0.20 \pm 0.02$

In the red spectral region (Figure 6) the strongest emission line is H $\alpha$ (EW

$= -16.0 \pm 1.0$ Å); weaker emission is seen from S II $\lambda 6386$ (EW

$= -0.20 \pm 0.02$ Å); He I $\lambda 6678$ is seen in absorption (EW

$= 0.20 \pm 0.02$ Å).

Based on these features, the primary star can be identified as a B0.5IIIe, consistently with the results of Charles et al. (1996), and of Clark et al. (1997).

**Figure 3:** Portion of the coadded blue spectrum normalised to the continuum; some of the absorption lines listed in the text have been identified here.
$\begin{figure} \begin{center} \centerline{\psfig{file=fig3.eps,width=10cm}}\end{center}\end{figure}$

**Figure 4:** Portion of the coadded blue spectrum normalised to the continuum, with some of the major lines identified. A blend of O II, N II and C II absorption lines is responsible for the broad absorption feature at
$\lambda \sim 4600$ Å.
$\begin{figure} \begin{center} \centerline{\psfig{file=fig4.eps,width=10cm}}\end{center}\end{figure}$

**Figure 5:** Portion of the coadded blue spectrum, normalised to the continuum. H $\beta$ and He I $\lambda 4922$ are the main features in this spectral region.
$\begin{figure} \begin{center} \centerline{\psfig{file=fig5.eps,width=10cm}}\end{center}\end{figure}$

**Figure 6:** H $\alpha$ line profile, normalised to the continuum, in the coadded red spectrum. Balmer lines always appear single-peaked, and their profile is quite different from that expected for emission from a thin disk.
$\begin{figure} \begin{center} \centerline{\psfig{file=fig6.eps,width=10cm}}\end{center}\end{figure}$

Photometry

Photometric observations of the system were conducted from the SSO 40inch telescope; the detector used was a SITe

2048 x 2048 CCD. We obtain apparent magnitudes

$B = 14.12 \pm 0.01$ ,

$V = 14.19 \pm 0.01$ ,

$R = 14.13 \pm 0.01$ and

$I = 14.10 \pm 0.01$ ; no significant variations in the brightness of the star were observed during the run. Following Clark et al. (1997) [see also van der Klis et al. (1992)], we have adopted a reddening of

$E(B-V) = 0.08 \pm 0.01$ ; adopting also a distance modulus for the SMC of d = 18.9 (Feast 1991) we get absolute magnitudes

$M_B = -5.02 \pm 0.04$ ,

$M_V = -4.87 \pm 0.03$ ,

$M_I = -4.86 \pm 0.02$ .

We expect the Be star to appear redder than a non-Be star of similar temperature (Bessell 1993) because of the radiation from the circumstellar disk (colder than the star); Paschen continuum emission usually gives a particularly significant contribution in the near IR. Assuming that the B magnitude is the least affected by this additional contribution, and using the theoretical isochrones of Bertelli et al. (1994) in the range of metallicities

Z = 0.002 - 0.004 (Bessell 1993) we can estimate a bolometric magnitude

$M_{\mbox{{\footnotesize bol}}} = -7.4 \pm 0.2$ and an effective temperature

$\log T_{\mbox{{\footnotesize eff}}} = 4.44 \pm 0.03$ . These values correspond to the giant phase of evolution for stars of mass

$M_* = (18 \pm 2) M_{\odot}$ , and are therefore consistent with the spectral identification of the optical counterpart of RX J0117.6-7330 as a B0.5IIIe star.

Using the results of Underhill et al. (1979), we can also infer a radius

$R_* \simeq 10 R_{\odot}$ , although values for the same spectral types determined by Popper (1980) are lower by $\sim 30$ %.

Projected rotational velocity and radial velocity

An interesting feature of our spectra is the small full width at half maximum (FWHM) of all the lines; the narrowest absorption lines are He I $\lambda 4388$ and He I $\lambda 4922$ , for both of which we calculate an average FWHM

$= (210 \pm 20)$ km ${\rm s}^{-1}$ . The Doppler broadening of spectral lines is a function of the projected rotational velocity $v \sin i$ . The FWHM of the He I $\lambda 4471$ absorption line was used by Slettebak et al. (1975) as a parameter for a system of standard rotational velocity stars. We determine an average FWHM

$= (4.3 \pm 0.3)$ Å for He I $\lambda 4471$ in our spectra; correcting for the instrumental broadening (resolution = 1.2 Å), we estimate a FWHM

$= (4.1 \pm 0.3)$ Å

$= (275 \pm 20)$ km ${\rm s}^{-1}$ . Comparing this value with those listed in Slettebak et al. (1975) for the same spectral type, we estimate a projected rotational velocity

$v \sin i = (145 \pm 10)$ km ${\rm s}^{-1}$ .

It is generally assumed (Hardorp & Strittmatter 1970) that all Be stars are fast rotators with approximately the same rotational velocity, the observed velocity spread being due to orientation effects. The largest values of $v \sin i$ measured from line profiles are in the neighbourhood of 400 km ${\rm s}^{-1}$ (Sletteback 1982). If we assume a true rotational velocity at the equator

$v = (400 \pm 50)$ km ${\rm s}^{-1}$ , we infer an inclination angle

$i = (21 \pm 3)\deg$ .

An empirical correlation between the full width at half maximum of the emission component from H $\alpha$ , its equivalent widths and the projected rotational velocity was derived by Dachs et al. (1986):

$\begin{displaymath} \frac{{\mbox{FWHM(H$\alpha$)}}}{2} \left[\frac{{\mbox{EW(H$\... ...60 \simeq (v \sin i \pm 30) \quad {\mbox{km ${\rm s}^{-1}$}}. \end{displaymath}$

(1)

In this case, we measure a mean FWHM

$= (6.1 \pm 0.2)$ Å

$= (280 \pm 10)$ km ${\rm s}^{-1}$ , and a mean EW

$= (-16.0 \pm 1.0)$ Å for H $\alpha$ (Figure 6). This would lead to a projected rotational velocity

$v\sin i = (150 \pm 30)$ km ${\rm s}^{-1}$ , in agreement with the more reliable value derived from the He I $\lambda 4471$ absorption line.

It is reasonable to assume (Dachs et al. 1986) that the equivalent width of the H $\alpha$ emission line is proportional to the projected area of the disk orbiting the Be star in the equatorial plane; the disk is made of gas excreted from the star, and its outer radius is expected to increase during an active phase of the system. Using the empirical relation between H $\alpha$ equivalent width and disk radius given by Dachs et al. (1986), we derive

$R_d = (3.4 \pm 0.1) R_*$ , where R_* is the radius of the Be star and R_d is the radius at which optical depth equals unity for H $\alpha$ emission. As discussed in §2.2, we can take

$R_* = (10 \pm 3) R_{\odot}$ and

$M_* = (18 \pm 2) M_{\odot}$ .

If the circumstellar disk were geometrically thin and in keplerian rotation, the emitting gas at its outer rim would have a projected rotational velocity

$\begin{displaymath} v_d \sin i = \left(\frac{GM_*}{R_d}\right)^{1/2} \sin i = (114 \pm 25) \quad {\mbox {km ${\rm s}^{-1}$}}. \end{displaymath}$

(2)

We would therefore expect to observe double-peaked line profiles for H $\alpha$ and H $\beta$ with peak-to-peak separations

$\simeq 2v_d \sin i \simeq 230$ km ${\rm s}^{-1}$ (Smak 1981). This value corresponds to a separation

$\Delta \lambda = 3.7$ Å at H $\beta$ , and

$\Delta \lambda = 5.0$ Å at H $\alpha$ , well discernible with our 1.2 Å resolution. We observe that both H $\alpha$ and H $\beta$ emission line profiles are always symmetrical and single-peaked: this suggests that the circumstellar gas is not confined to a thin disk in the equatorial plane, but may form a thick torus or an envelope which extends to the polar regions of the stellar atmosphere. Alternatively, absence of double peaks could be due to non-keplerian motion in the outer disk, where radial outflows can dominate over rotation, or to a much larger disk radius [cf. the model proposed by Poeckert & Marlborough (1979)]. As shown in Dachs et al. (1986), the H $\alpha$ emission lines from Be stars are almost always single-peaked for values of EW, FWHM and $v \sin i$ similar to those measured in this system.

**Figure 7:** Radial velocity of the optical counterpart of RX J0117.6-7330.
$\begin{figure} \begin{center} \centerline{\psfig{file=fig7.eps,width=10cm}}\end{center}\end{figure}$

The projected radial velocity of the system was determined by measuring the central position (using a Gaussian fit) of H $\alpha$ , H $\beta$ , He I $\lambda 4388$ and He I $\lambda 4922$ in each spectrum (two or three consecutive 600s spectra were averaged together to increase the S/N); the values found are plotted in Figure 7. Although the variations in the measured radial velocity may be due to the orbital motion, the data are insufficient to determine the orbital period or the radial velocity amplitude from these data, or the eccentricity of the orbit (it can be

$e \lower.5ex\hbox{$\; \buildrel > \over \sim \;$}0.3$ in Be/X-ray binary systems). All known Be/X-ray binaries have orbital periods

$P \lower.5ex\hbox{$\; \buildrel > \over \sim \;$}15$ days, with periods of hundreds of days in some cases (van den Heuvel & Rappaport 1987). The average systemic velocity over the time of our spectral observations is