3 Results

3.1 The spectrum of BD + 60$^{\circ }$ 2522

The blue-violet spectrum of BD  $+60^{\circ }$ 2522 is shown in Fig. 1. Besides the typical absorption lines of H  I, He  I and He  II, this spectral domain contains the complex emission blend of N  III $\lambda\lambda$ 4634-41 and C  III $\lambda\lambda$ 4647-50 as well as the double-peaked He II$\lambda$ 4686 emission. The latter emission lines are found on top of a broad emission extending from about 4610 to 4720 Å, a feature that is quite common among Of stars (Underhill et al. 1989). We also note the faint Of emission lines at 4485 and 4505 Å attributed to S  IV by Werner & Rauch (2001). We caution that the Balmer absorption lines might be contaminated by nebular emission from the Bubble Nebula.

The ratio of the equivalent widths (EWs) of the He I$\lambda$ 4471 and He II$\lambda$ 4542 lines, $\log{W'} = \log({\it EW}({\rm He I}~\lambda~4471)/$ ${\it EW}({\rm He II}~\lambda~4542))$  =   $-0.18 \pm 0.03$, as measured on our spectra (Table 2), points towards an O6.5 spectral type for BD  $+60^{\circ }$ 2522 according to the classification scheme of Conti (1973). This result is in excellent agreement with previous classifications. Doroshenko (1972) inferred an O5 spectral type, while Walborn (1973) and Conti & Leep (1974) classified BD  $+60^{\circ }$ 2522 as O6.5 (n)(f)p and O6.5 IIIef respectively.

The giant luminosity class quoted by Conti & Leep was first proposed by Conti & Alschuler (1971). Since none of the conventional luminosity criteria (mainly based on the nature and strength of He II$\lambda$ 4686) can be applied to BD  $+60^{\circ }$ 2522 in a straightforward manner, we refrain from proposing a luminosity class ourselves.

  
3.2 Radial velocities

Doroshenko (1972) noted an apparently "abnormal energy distribution'' and suggested that this could be the signature of a binary system with the secondary being of spectral type F5 Ib. Subsequent investigations revealed however that flat energy distributions are common among Of stars and can be attributed to the effect of atmospheric extension (see e.g. Kuan & Kuhi 1976).

To investigate the multiplicity of BD  $+60^{\circ }$ 2522, we have measured the radial velocities (RVs) of the two most prominent absorption lines in the 4455-4905 Å domain (i.e. He I$\lambda$ 4471 and He II$\lambda$ 4542) by fitting Gaussians. The results indicate a rather small range of variability. For the He I$\lambda$ 4471 and He II$\lambda$ 4542 lines we find standard deviations around the mean RV of respectively 9.4 and 7.1 km s^-1.

We applied a Fourier analysis to the entire RV data set of each of the two absorption lines. The most prominent peaks in the power spectra occur at frequencies below $\sim$0.03 d^-1. The amplitudes of the sine waves fitted to the data at the "highest-peak'' frequencies are 7.2 and 5.4 km s^-1 respectively for He I$\lambda$ 4471 and He II$\lambda$ 4542. These amplitudes are of the same order as the typical errors on a single RV point ($\sim$10 km s^-1 for the 33 Å mm^-1 data) and we do not regard them to be significant. Moreover, both absorption lines undergo profile variations (see Sect. 3.3.2) that may account for the small amplitude RV variations discussed here.

Since no significant short-term variability was found, we have averaged the RVs from each observing campaign (see Table 2). Most of these values overlap within the errors with the mean of the entire data set (Fig. 2).

In summary, there is no consistent and significant periodicity in the RVs of the different absorption lines and although we cannot completely rule out a long period binary system seen under a very low inclination angle, it seems more likely that BD  $+60^{\circ }$ 2522 is indeed a single star.

3.3 Line profile variability

To identify the features in the spectrum of BD  $+60^{\circ }$ 2522 that display significant variability, we have computed the time variance spectrum (TVS, Fullerton et al. 1996) of our entire data set over the spectral range 4465 to 4800 Å. The largest amplitude of the TVS is found over the He II$\lambda$ 4686 line. Significant variability occurs also in the He I$\lambda$ 4471 and He II$\lambda$ 4542 lines. On the other hand, the TVS of the entire data set yields some marginal variability in the N III $\lambda\lambda$ 4634-41 and C III $\lambda\lambda$ 4647-50 blend, but this variability disappears when we consider the TVS of individual observing campaigns. The variability in the entire data set could either result from long term changes or from small normalization discrepancies between the various data sets. Indeed, some variability is also detected over the narrow diffuse interstellar bands (DIBs) at 4502, 4726, 4763 and 4780 Å. The apparent variability in these features most probably results from small normalization discrepancies between different observing campaigns. During a single observing campaign, these normalization errors are always limited to TVS $^{1/2} \leq 0.004$.

 

 

Table 2: Properties of the He I$\lambda$ 4471 and He II$\lambda$ 4542 lines in the spectrum of BD  $+60^{\circ }$ 2522. The second column yields the mean observation date in HJD-2450000. Typical standard deviations on the mean equivalent widths are of order 0.03 Å.

Run	$\overline{T}$	He I$\lambda$ 4471		He II$\lambda$ 4542
		RV	EW	RV	EW
		(km s-1)	(Å)	(km s-1)	(Å)
[1]	312.1	$-20.9 \pm 8.7$	0.39	$1.1 \pm 6.3$	0.65
[2]	641.5	$-14.3 \pm 4.9$	0.45	$6.4 \pm 5.3$	0.61
[3]	1071.1	$-20.0 \pm 5.3$	0.42	$-2.7 \pm 8.6$	0.67
[4]	1376.5	$-22.6 \pm 10.7$	0.46	$-3.0 \pm 9.6$	0.66
[5]	1403.7	$-28.3 \pm 8.9$	0.45	$-1.1 \pm 5.7$	0.67
[6]	1815.7	$-28.9 \pm 7.7$	0.46	$-5.1 \pm 3.8$	0.70
[7]	2167.0	$-26.1 \pm 8.0$	0.46	$-3.9 \pm 4.2$	0.72
[8]	2522.4	$-28.8 \pm 8.8$	0.46	$-8.6 \pm 2.8$	0.70

Figure 2: Epoch-dependent mean RVs of the He I$\lambda$ 4471 and He II$\lambda$ 4542 lines in the spectrum of BD  $+60^{\circ }$ 2522. The dashed lines yield the average RV over the entire data set. The error bars correspond to the 1-$\sigma$ RV dispersion during a specific run.

Figure 3: Top panel: mean spectrum of BD  $+60^{\circ }$ 2522 as observed with the Aurélie spectrograph at OHP from 1996 to 2002. Bottom panel: square root of the time variance spectrum. The dotted horizontal line corresponds to the threshold for variations significant at the 99% level for a total of 104 spectra and an average S/N ratio of 350 (see Fullerton et al. 1996).

3.3.1 Profile variability of the He II$\lambda$ 4686 line

A simple inspection of the data during the observing runs suggested that the He II$\lambda$ 4686 line varies on time scales of a few days (see Fig. 4). However, when we compare the variations as observed during the various campaigns, we find significant epoch-dependent differences (see Fig. 5).

Figure 4: Variations of the He II$\lambda$ 4686 profile as observed in September 2000. During this campaign, the variations mainly resulted from changing relative intensities of the violet and red emission component.

The overall level of profile variability changes with time. Our TVS variability estimator reached its maximum in July 1999 and September 2000, whereas it was lowest in August 1996. Also the wavelength range over which the TVS^1/2 exceeds the 99% significance level varied from one observing campaign to the other and reached its largest extent in September 2000. But most of all, it is the morphology of the TVS^1/2 that varies. During observing campaigns [1], [2], [7] and [8], the variability reaches its maximum in the core of the absorption component, whereas the TVS is larger over the emission components during campaigns [5] and [6].

If the line profile variability of the He II$\lambda$ 4686 line were periodic, some of the differences discussed hereabove might actually result from the sampling of the cycle during the various observing campaigns. We have applied the 2-D Fourier techniques described by Rauw et al. (2001) to the time series of each campaign. The results are indicated in Table 3 below. Most of the time the periodograms display one dominant peak together with its one-day aliases. However, in August 1999 (campaign [5]), we find no clearly dominant peak. Most intriguing is the fact that the position of the dominant peak changes from somewhere around 0.34 d^-1 (or 0.66 d^-1 depending on which alias is the right one, if any) to somewhere between 0.40 and 0.45 d^-1. To illustrate this situation, Fig. 6 displays the 2-D power spectra of three different data sets corresponding to a dominant peak at 0.34 d^-1 (July 1997), no dominant peak (August 1999) and a dominant peak found in both emission components around 0.40 d^-1 (September 2000).

Since each observing campaign contains only a limited number of data, one may wonder about the robustness of the Fourier analyses. Therefore, we have performed some trials to evaluate the impact of specific spectra on the aspect of the TVS and the location of the highest peaks in the periodograms. To do this, we have removed the different data points one at the time from the time series and repeated the analysis of the remaining data set. These tests showed that the periodograms are usually very stable except for campaigns [3], [5], [7] and [8] that turned out to be quite sensitive to the presence or absence of individual spectra. For campaigns [3] (September 1998) and [8] (September 2002) this is indeed not unexpected given the very limited number of spectra obtained during these runs. For campaign [5], we cannot blame the number of spectra or the sampling. In this latter data set, the periodogram does not reveal a clearly dominating peak and the poor stability of the periodogram is yet another indication that the variability was most probably not periodic in August 1999. Finally, the periodogram of the September 2001 campaign ([7]) turned out to be quite sensitive to the spectra obtained during the night of September 11-12 (HJD 2452165.431 and 2452165.455). If we omit these data from our analysis, we recover peaks at 0.34 and 0.66 d^-1, pretty close to those found for campaigns [1] and [2]. However, there is no reason a priori to discard these data.

In the case of the He II$\lambda$ 4686 line profile in the spectrum of BD  $+60^{\circ }$ 2522, it seems therefore more appropriate to talk about time scales rather than periodicities. Indeed, a search for a stable coherent periodicity over the entire data set turned out to be illusory: the periodogram of the combined data set is dominated by very low frequencies and their daily aliases. The same conclusion holds for the He I$\lambda$ 4471 and He II$\lambda$ 4542 lines (see below). Also interesting to note is the fact that observations separated by only one month (July and August 1999) produce different power spectra. Finally, we note that the periodograms usually do not reveal strong peaks at frequencies higher than 1.0 d^-1, except for some daily aliases of the peaks from the [0.0, 1.0] d^-1 interval.

Figure 5: The top three panels correspond to the variability of the He II$\lambda$ 4686 line profile during campaigns [1], [2] and [4] from left to right, while the lower three panels correspond to campaigns [5], [6] and [7] (also from left to right). Each panel is divided into two subpanels. The upper subpanels yield the mean profiles as observed during a specific observing campaign (solid line) compared to the mean profile as evaluated from the entire data set (dashed line). The bottom subpanels yield the square root of the TVS while the dotted lines correspond to the thresholds for variations significant at the 99% level.

Figure 6: Grey-scale images of the two-dimensional power spectra of the time series of the He II$\lambda$ 4686 line in the frequency range [0.0, 1.0] d-1. The power spectra were computed using the Fourier technique described by Rauw et al. (2001). From left to right, the three panels correspond respectively to the data sets from July 1997 (campaign [2]), August 1999 (campaign [5]) and September 2000 (campaign [6]).

 

 

Table 3: Properties of the 2-D periodogram of the time series consisting of the He II$\lambda$ 4686 line profile as observed during various observing runs. The second column yields the maximum value of TVS^1/2 and the wavelength where this maximum occurs. The third column indicates the wavelength range over which TVS^1/2 exceeds the 99% significance level. The fourth and fifth columns yield the highest and second highest peaks in the periodogram over the [0.0, 1.0] d^-1 frequency range. The last column provides the mean equivalent width of the line as integrated between 4675 and 4700 Å. The maximum 1 - $\sigma$ dispersion of this EW during a specific run amounts to $\sim$0.1 Å.

Run	TVS $^{1/2}_{\max}$	$\lambda$ - range	$\nu _1$	$\nu_2$	$\overline{\it EW}$
		(Å)	d-1	d-1	(Å)
[1]	0.009 at 4685.1	4683-4691	0.66	0.33	-1.26
[2]	0.014 at 4686.4	4681-4693	0.34	0.66	-1.48
[4]	0.017 at 4684.3	4681-4690	0.45	0.55	-1.38
[5]	0.013 at 4684.1	4683-4690	0.35a	0.65a	-1.46
[6]	0.016 at 4683.2	4679-4692	0.40	0.60	-1.42
[7]	0.015 at 4684.6	4682-4690	0.43b	0.57b	-1.24
[8]	0.013 at 4686.9	4682-4692	0.42a, c	0.85a, c	-1.38

^a There are a number of other "peaks'' in the periodogram that have only slightly lower amplitudes than $\nu _1$ and $\nu_2$.
^b These frequencies correspond to the highest peaks over the wavelength interval 4682-4685. Over the entire range given in Col. 3, the highest peaks are found at 0.13 and 0.86 d^-1.
^c The periodogram for this run is very sensitive to the inclusion of individual spectra in the time series and the highest peak frequencies are very unstable.

Another illustration of the epoch dependence of the He II$\lambda$ 4686 profile variations can be obtained by fitting an expression

$$F(\lambda,t) = c_0(\lambda) + A(\lambda)~\sin{(2~\pi~\nu_1~[t - t_0] + \phi_0 (\lambda))}$$ (1)

to the time series of an individual campaign at every wavelength step. Here, $\nu _1$ corresponds to the dominant peak found in the Fourier analysis of the specific data set, while $c_0(\lambda)$, $A(\lambda)$ and $\phi_0(\lambda)$ are fit parameters that represent the mean profile, the amplitude of variability and the phase constant at wavelength $\lambda$ respectively (see also Rauw et al. 2001). These parameters are illustrated in Fig. 7 for observing campaigns [2] and [6]. We remind the reader that the phase constant $\phi_0$ has physical meaning only if the period is clearly detected at the specific wavelength.

Figure 7: Left: variability of the He II$\lambda$ 4686 line in July 1997 (campaign [2]) as a function of phase assuming a "period'' of 2.94 days ( $\nu _1 = 0.34$ d-1). The three panels display the mean line profile, as well as the amplitude and the phase of a sine wave of frequency $\nu _1$ fitted to our data. The reference date for the phase (t0) was arbitrarily chosen on JD 2450000.00. Right: same for the September 2000 (campaign [6]) data and assuming a "period'' of 2.50 days ( $\nu _1 = 0.40$ d-1).

This reconstruction technique reveals that the profile modulation in July 1997 is mainly concentrated in the central absorption component (4683-4689 Å). In addition the phase of the modulation $\phi_0$ remains roughly constant over this wavelength interval. Therefore, the variations of the profile in July 1997 can be described as a sinusoidal modulation of the depth of the absorption component with a "period'' of 2.94 days. Such a variation might result for instance from a periodic modulation of the optical depth along the line of sight towards the stellar core.

On the contrary, the September 2000 data reveal a completely different picture. The amplitude peaks in the emission components of the line and $\phi_0$ varies strongly across the peaks of the amplitude. In summary, the variations in September 2000 can be described as a modulation of the strengths of the two emission peaks with a "period'' of 2.50 days; the red peak reaching its maximum intensity when the violet peak is minimum and vice versa.

  
3.3.2 Profile variability of the absorption lines

We have applied the Fourier techniques to the profiles of the He I$\lambda$ 4471 and He II$\lambda$ 4542 absorption lines. It turns out that the level of variability during a specific observing run is usually rather low (TVS $^{1/2} \leq 0.007$ on average). However, visual inspection of the spectra indicates profile variability in the line cores for those nights where we have obtained spectra separated by several hours (this is essentially the case for the August 1996 campaign, see Fig. 8, and for one night of the September 2002 run).

While the Fourier analysis of the entire data set fails to reveal a stable period, we find nevertheless that the Fourier periodograms of individual campaigns suggest that the line cores are variable on rather short time scales of the order of hours. Unfortunately, our data set was designed to search for variability on time scales of days rather than hours and hence does not allow us to study these short term variations in detail. From the analysis of the best suited data set (August 1996), we tentatively propose a time scale of about 4-5 hours. A more intensive monitoring of the star with a good time resolution and a good S/N ratio is required to eventually establish the period(s) or time scale(s) of the phenomenon. Figure 8 suggests that the variations of the absorption line profiles may be due to non-radial pulsations (NRPs). This would not be surprising since NRPs have already been reported for the two brightest members of the Oef class (see Sect. 4 below). It seems very likely that the low amplitude RV changes discussed in Sect. 3.2 are in fact a result of the absorption line profile variability.

Figure 8: Top: variations of the He I$\lambda$ 4471 and Mg  II $\lambda$ 4481 line profiles during the night of 22-23 August 1996. The labels on the right yield the time of the observation in HJD-2450300. Consecutive spectra are shifted vertically by 0.02. Bottom: same but for the He II$\lambda$ 4542 line.