4 Temporal behaviour

4.1 Time-delays in the spectral features

The upper panels of the Figs.5-9 present the various emission-line flux curves at increasing distance from the stellar core (downwards). Inspection of these measurements from individual nights suggests that the time series of the fluxes of the lines formed in the outer wind show, consistently, small time-delays with respect to the lines formed in the inner wind. For example, during 14 March 1989 the N V4944 line flux around $t~{\rm (HJD)}= 2447600.65$ has passed the minimum, N V4604/20 is about to enter the minimum, and the He II lines are still decreasing rapidly. More such cases can be observed. To determine the average value of a time-delay between two different emission lines, we perform a cross-correlation of the time series.

We apply the cross-correlation technique of Edelson & Krolik (1988), as implemented into the MIDAS Time Series Analysis context, to the emission-line flux curves in 1989, 1990, and 1991. When the correlation peak is well-defined (e.g., Fig. 12), the top of the correlation function is determined by fitting a second order polynomial. The resulting time-delays are listed in Table 3. The mean delay between two time series appears to vary from 0.007 d (10 min) to more than 0.02 d (30 min). Moreover, the delays in 1990 and 1991 are longer than in 1989, possibly related to the accompanying brightening. The largest time-delay is reached by the He II lines with respect to N V 4944, confirming the WR standard model that the latter originates deeper in the stellar wind. The cross-correlation of the helium lines amongst each other did not result in a peak significantly different from zero.

The time-delays of the radial velocity behave in the same sense as the line fluxes (outer wind lines delayed with respect to inner wind lines), but they are often much larger. An illustrative example is given by the observations in the night of 14 March 1989 (Fig.5), where the maximum radial-velocity changes from around time t(HJD) = 2447600.58 to t(HJD) = 2447600.64, thus a delay of 0 $.\!\!^{\rm d}$06. The same amount of delay is found in the night of 28 February 1990 (Fig.6). Thus, the radial-velocity time-delays can be three times larger than the line-flux time-delays, and, thereby, become a significant part of the typical time scale of variation. We did not perform the cross-correlation for the radial-velocity data, since the behaviour of the radial velocity is not as persistent as that of the line flux.

Yet another kind of time-delay is apparent on the night of 15 March 1989 (Fig.5). On that night, evidently, the inner-wind lines are standing still, and it appears that with a delay of up to 0.15 d the outer-wind lines cease to move also. Apparently, the outer-wind lines trail the behaviour of the inner-wind lines also with respect to the entry of a stand-still.

In addition to the persistent line-flux time-delays, the variable radial-velocity time-delays and the delayed entry of a stand-still, we present also a line-profile time-delay. This concerns the bisector measurements of the same line but at different heights above the continuum. The top of the line precedes the lower parts: for instance, the 17 February 1991 He II 4686 bisector at 50% (Fig.7) reaches its extreme values roughly 0.04 d later than the bisector at 85%. Figure 13 presents time-delay measurements of several emission lines from different seasons measured at different heights above the continuum, using the same cross-correlation technique as above. The observations clearly indicate that the lower parts of the emission line are trailing the peak of the line. This behaviour is not always noticeable in the available data, but, if it occurs, it is systematically in the same direction.

We conclude that all the stellar emission lines of WR46 vary in concert, albeit with sizable time-delays. Also in the data by MAB (their Fig.1, bottom panel) one can clearly notice a time-delay from O VI 3811/34 to N V 4944 out to the highest optical emission lines of WR46. Both the time-delays from line to line, and within one line depending on the height above the continuum, are indicative of the stratification of the formation regions of the emission lines. Inferences are made in Sect. 5 and Paper III.

 

 

Table 3: Time-delays between various ${EW}_{\rm cc}$ curves. Column 1 lists the two emission lines for which the EW curves are cross-correlated (*). Columns 2-4 list the resulting time-delay, measured as the peak of the cross-correlation function. Positive numbers indicate a lag of the first mentioned spectral emission line with respect to the second line. The uncertainty in the last digits (bracketed) is the uncertainty of a parabolic fit to the top of the cross-correlation peak. (N V $~4610 \equiv$ N V 4603/20).

lines	1989	1990	1991
	(d)	(d)	(d)
He II 4686*N V 4610	0.0071(08)	0.0115(23)	0.0131(34)
He II 6560*N V 4610	0.0100(30)	0.0212(44)	0.0147(31)
He II 4686*N V 4944	0.0112(75)	0.036(17)	0.025(11)
N V 4610*N V 4944	-	-	0.025(02)

 

 

Table 4: Fundamental parameters resulting from WR standard model spectral analysis. The results are based on the helium lines plus either the oxygen spectrum (CSH), as indicated in the last column, or the nitrogen spectrum (CSH and HK).

object	$T_{\star}$	$R_{\star}$	logL	log$\dot{M}$	$v_{\infty}$	model
	kK	$R_{\odot}$	$L_{\odot}$	$M_{\odot}/$yr	kms-1
WR46	91	2.4	5.5	-5.1	2450	CSH-O
WR46	80	3.0	5.6	-5.3	2450	CSH-N
WR46	89	2.2	5.4	-4.9	2300	HK-N
WR3	89	2.5	5.6	-5.1	2500	HK-N

4.2 Relation with the photometric periods

The time-coverage of the spectral monitoring is not extended enough to perform an independent frequency analysis. To investigate the consistency of the line-flux variability with the photometry we folded the data with the frequencies identified in the photometry (Paper I): the so-called single-, or double-wave periods $P_{\rm sw}^{89}=0.1412$ d, $P_{\rm sw}^{91}=0.1363$ d, $P_{\rm dw}^{89}=0.2825$ d, and $P_{\rm dw}^{91}=0.2727$ d which affect both the magnitude and the colours, and a secondary frequency, the so-called $f_{\rm x}$, with a period $P_{\rm x}=0.2304$ d which affects only the magnitude. Figure 10 shows the folded line-flux curves of N V 4604/20. It does not provide any support for $f_{\rm x}$. Yet, the line fluxes in 1989, 1990 and 1991 appear well-behaved with the corresponding single- and double-wave frequencies (compare the neighbouring panels in Fig.10). The 1995 line-flux data appear to show a single-wave, similar to the photometry in 1995. These data show only marginal preference for the 1991-period. As the 1998 data lack the N V 4604/20 line, the results of He II 5411 are presented. The line flux does not behave well with any of the frequencies, similar to the photometry. Clearly, the variability of the photometry (dominated by the continuum) and that of the line fluxes is intimately related.

We conclude that the line flux provides independent evidence for the difference of the periods in 1989 and 1991. The object varies from year to year, and from cycle to cycle, but we have only three nights per season (i.e., three cycles or parts thereof). Thus, we are affected by low number statistics. Therefore, we cannot investigate whether the double-wave provides a better description of the line-flux curve than the single-wave. In addition, we cannot search for possible differences in the amplitude between the different seasons as found for the photometry. However, the mean values of the line fluxes follow the photometric behaviour (see Sect. 4.5).

Analogous to the line flux in Fig.10, Fig.11 presents the folded radial-velocity curves using the double-wave periods identified in our photometric study (Paper I), and partly supported by the line flux (the two left columns of the panels will be discussed below). While there is no satisfying match if $P_{\rm x}$ is used, the time scale of variability is, evidently, of the order of the double-wave period. However, the radial velocity is not strictly periodic with the photometric double-wave period.

We propose that this apparent a-periodicity of the radial velocity finds its origin in the large time-delays of the radial velocities. In fact, the observations of 15 March 1989 may hold a clue. During that night some lines show a stand-still, while others are on the verge of ceasing their radial motion. Precisely that night shows the largest apparent phase-delay, if $P_{\rm dw}^{89}$ is used. Thus, it is conceivable that if a time-delay becomes much larger than half a period, the radial motion comes to a stand-still.

We assume that the same mechanism does control the light-, the colour-, the line-flux-, and the radial-velocity variations with the double-wave periods. If this assumption is a correct, the photometric shallow minimum occurs during the change from maximum positive to minimum negative velocity. Furthermore, a frequency analysis of the radial velocity may be severely affected by time-delays and stand-stills, and it may identify unreliable, mostly longer, periods than the line-flux or photometric analysis would. The idea is that the stellar wind material cannot keep up with the stellar core and lags behind more and more. When the delay has built up to, say, half a period, the radial velocity averages out and the star enters a standstill. In the course of time the atmosphere will pick up the radial motion again and for a few cycles display a radial velocity curve.

Since in our 1995 observations the radial velocity shows a coherent variability in three out of four nights (see Fig. 3), spanning the largest number of consecutive nights, we investigate its frequency spectrum. Similar as to the photometry, we apply the analysis of variance ( AOV, Paper I) to a combination of N V lines from all four nights ( $\lambda 4520$ (9-7) and $\lambda$4944 (7-6)) and to a combination of He II lines ( $\lambda 4686$ (4-3) and $\lambda5411$ (7-4)). The resulting periodograms for the radial velocity are shown in Fig.14. The highest peak appears at 2.7 cd^-1 (P=0.37 d), the same as in the photometry. This agreement between photometry and spectroscopy may indicate that the period was indeed that large in 1995. However, both data sets are short, so we do not rule out the one-day alias at 3.7 cd^-1, which coincides with the P₉₁ as indicated in the insets in Fig.14. Possibly, the variability is controlled by a period comparable to P₉₁, while the time-delay has larger significance for the longer-period aliases.

Figure 12: Cross-correlation measurements of the time series of the equivalent width of He II 4686 and N V 4603-20. The maximum is fitted using a 2nd order polynomial and the hydrogen line is delayed by 0.013 d relative to the nitrogen emission line. Note that the covariance shows another maximum, a single-wave period later, as is to be expected.

Figure 13: Time-delay between radial-velocity curves derived at different intensities above the continuum versus height as a percentage of the peak. Several lines showing a significant lead by the peak are indicated (He II 4686: dots and N V 4604/20: circles on 17 February 1991 and N V 4944 on 4 April 1995: triangles), while a time series which did not show this behaviour is also indicated (N V 4944 on 11 February 1998: stars).

Figure 14: AOV-periodograms of the radial-velocity measurements in 1995 of the N V 4944 and N V 4520 lines ( upper panel) and of the He II 4686 and He II 5411 lines ( lower panel). Evidently, one of the alias peaks is at the position of the 1991 period of 0.2727 d (=3.67 cd-1).

Other period determinations of WR46 based on radial velocity measurements have been performed by Niemela et al. (1995), who found P_93/94 = 0.31 d from observations in 1993 and 1994, and by MAB who found P₉₉ = 0.329 d from 1999 data. Marchenko et al. (2000) remarked that the observations by Niemela et al. may be hampered by an apparent halt of the radial motion on one out of three consecutive nights. They conclude that both periods are compatible, while we conclude that both are not compatible with our measurements, as evidenced in Fig.11.

These large variations of the period based on radial-velocity data (0.31 d in 1993/4, 0.27 d or 0.37 d in 1995, 0.329 d in 1999 and, probably, different from before in 1989 and 1991) support our suggestion that the radial velocity is too disturbed by time-delays and possible related stand-stills. In this interpretation the photometry, or, possibly, the line fluxes, provide a better tool to determine the period(s?) of the system than the radial velocity.

In summary: (i) the line flux follows the photometric behaviour, i.e., the photometric single/double-wave period is consistent with the line-flux variability, even to the extent that (ii) the substantial period change between 1989 and 1991 is supported; (iii) the 1995 period determined (semi-independently) from the spectra may be equal to P₉₁, also suggested by the photometry; (iv) the 1998 data confirm the time scale of variability, but the period cannot be derived with precision and may well have changed since 1995; (v) the large deviations between the periods determined by other investigators from radial-velocity measurements and our photometric determinations may either result from the large and varying time-delays, or they may indicate intrinsic large period changes.

4.3 Peculiar line-profile variability of He  II 4686

Our high-resolution spectra show that the spectral variability may involve more than only line-flux and radial-velocity variability. Each panel in Fig. 15 shows consecutive spectra on 4 April 1995. There is clear evidence for complicated line-profile variability of He II 4686 on a time scale of hours. The inner-wind lines (see Fig. 3) show simultaneously a large shift from negative to positive velocity. The time coverage is not sufficient to investigate the phenomenon any more deeply. Note that the line shows radial-velocity and line-flux variability (not shown) during the other night when observing the blue spectrum (2 April 1995).

At the risk of over-interpreting the data, we note that the profile variability can be described as a large and wide emission bump moving from the red wing to the blue wing over the peak of the He II 4686 line. That is consistent with the notion of an enhanced outflow from one side of the WR star. If this side is pointed away from the observer, the enhancement is red-shifted, and as the star rotates the enhancement is shifted over the peak to the blue wing.

Figure 15: The panels present (row-wise) consecutive observations of He II 4686 on 4 April 1995 (full lines) with the time of observation indicated as HJD-2440000. To allow easy comparison between subsequent spectra, each panel shows also the succeeding spectrum (grey). Moreover, to allow comparison over the whole night, the spectrum with minimal line flux (last panel) is repeated in each panel (dotted).

4.4 A flare-like event in He  II 5411 and 6560

In addition to the short-term brightness, line-flux, radial-velocity, and line-profile variability, we find evidence for a spectral variability on a time scale of minutes, or shorter. Figure 16 shows one of the sequences of low-resolution spectra observed on 15 March 1989 (exposure time of 180 s). Obviously, one of the spectra (7th out of 10) shows significantly enhanced localized emission (a "bump'') on the blue wings of the He II 5411 (around -1600 kms^-1) and the He II 6560 (around -1800 kms^-1) lines, without notable changes to the rest of the profile. We note that the spectra observed directly before and after do not show any sign of such a "bump''. As the time interval between the 180-s exposures is less than a minute, we derive an upper limit of the life-time of the local emission excess of 5 min. In the lower panel of Fig.16 the difference between the mean of these latter spectra and the "bumpy'' spectrum is presented. We inspected the raw data, but we do not observe any defects or cosmic ray hits. Moreover, we cannot imagine any instrumental or telluric effect which would cause such an observation in two He II lines.

This flaring event occurred at $\phi = 0.1$ using the double-wave period, but we do not know whether this is significant. We searched the rapid monitoring data sets in 1989, 1990 and 1991, which amounts to about 18 hours of observing time, but found no similar feature. Obviously, such flare-like events are rare. We note that our high resolution data can not show such an event since the integration time is about ten times larger than the time scale of this variability.

4.5 Long-term spectroscopic variability

Figure 16: Flare-like variability of two He II lines, but absent in N V 4944. Ten consecutive spectra with an exposure time of 180 s were obtained in low-resolution mode on 15 March 1989 (HJD 2446701.68 ... 1.72). The seventh spectrum in the row shows a significant sudden excess emission in the He II lines at 5411 Å (left) around -1600 kms-1 and at 6560 Å (middle) around -1800 kms-1. Other emission lines in the spectrum do not show such minute-scale variability, as evidenced by N V 4944 (right). Bottom panels: difference between seventh spectrum and the mean of the preceding and following, which were observed with a spacing of only 45 s.

As discussed in Paper I, WR46 varies also on a time scale of months to years. Figure 17 shows its accompanying long-term spectroscopic behaviour. In addition to the measurements of our spectra, we quote measurements from the literature (Smith et al. 1996, spectrum obtained in March 1988) and measurements of spectra kindly provided by others: the 1986 spectrum was obtained by Dr.W.Schmutz; the 1993 spectrum is part of the spectral atlas by Dr. W.-R. Hamann (Paper I, Fig.14); the three 1994 spectra were provided by Dr.V.Niemela, see Niemela et al. (1995). Measurements of EW are notoriously subject to the determination of the continuum, which is problematic in WR spectra. The peak-to-continuum ratio is less affected for high peaks, thus, we also use these ratios.

The long-term behaviour of the EW of all emission lines from 1989 through 1991 varies clearly in concert with the photometry (Fig.17). Therefore, we will use the terms "high state'' indicating a high brightness with strong emission lines, and "low state'' indicating the opposite. The 1993 spectrum indicates that the line fluxes declined like the photometric variation to a low state. The 1994 data are at a more intermediate level, and, therefore, more ambiguous. In 1995 the He II-lines are at a low level, in agreement with the hint of a low-state from the photometry, while the N V-lines appear to be strong. We note that the N V4604/20 line is sensitive to small variations in stellar temperature and mass-loss rate (Sect. 5.2). We assume that during the 1995 run the object was still in the low state. In 1998 the He II 5411 line indicates a high state, which fits the subsequent photometric decline a few months later. In 1999 the photometry indicates a rise, supported by the spectroscopy of MAB showing strong lines again.

As to the earlier years, both the photometric and the spectroscopic measurements in 1986 all agree to a low state, while the 1988 data are ambiguous. For the 1988 data Smith et al. (1996) list for the He II 5411 and the N V 4944 line the same EW, which is surprising. The N V 4944 line is narrower than He II 5411 as in all other spectra but it is stronger (L. Smith 2000, private communication), which is unique. Moreover, their EW of He II 4686 is very large, in contrast to their EW of He II 5411, which is in accordance with the low state evident from the photometry.

We also searched the literature for earlier observations of WR46. Massey & Conti (1983) published a spectrum, probably observed in November 1981, on which we measured the peaks of the He II 4686- and N V 4604/20 lines at a value of 3.0 and 2.36 times the continuum, respectively, indicative of a low state. An earlier paper by Massey & Conti (1981) presents parts of yet another spectrum obtained before 1980, which shows a stronger N V 4604/20 line and a He II 5411 line peaking in the range of the 1991 data. The EW of He II 6560 dating from February 1982 (Vreux et al. 1983) is at an intermediate level compared to our measurements of He II 6560 obtained in 1989 through 1991 (not shown).

Figure 17: Comparison between long-term photometric and spectroscopic variability. Top panel: long-term photometric light variation with symbols as in Fig.13 of PaperI; panels 2 to 5: individual EW measurements (+) and sequences of EW measurements (dots); bottom panel: peak to continuum ratio's of emission lines as indicated individual measurements (^ ) and full range as line-element.

Figure 18: All the short-wavelength IUE spectra of WR46 display the O V 1371 line. Because of the large noise in the high-resolution spectra (black) due to its faintness, all spectra are resampled to the same low-resolution grid. The high-resolution spectrum showing the largest P-Cygni profile is observed incidentally at the time of the maximum brightness as recorded by Hipparcos (5 June 1991; see Fig.17). The second high-resolution spectrum dates from October 1979. It is evident that the absorption trough of the 1991-spectrum is deeper, while the edge velocity is unaffected. The low-resolution specra (grey) confirm that the 1991 spectrum is in a "high state''.

Additionally, the left-hand side margin of Fig.17 shows measurements obtained by Smith (1955) in the early 1950s. Evidently, his values are the smallest ever. In addition, he noted that He II 5411 and He II 6560 are faint and broad. From other early observations (1949-1951), Henize (1976) classified the emission of the latter spectral line as weak to moderate relative to the continuum. Supposedly, this means that it was weaker than the present-day. Therefore, Fig.17 may, tentatively, be interpreted to show also a rising trend on a time scale of decades to a century. Unfortunately, the photometric observations over the last century (Paper I: Table1) cannot be used to assess this proposition due to the large uncertainties of the differences in the pass-bands and the contamination by line emission. Note that we established that WR46 did not change its spectral type over the last century (Paper I: Sect. 2). It may be worthwhile to measure the line strengths in the oldest spectra from the photographic plates around 1900 available at the Harvard Observatory (Paper I).

As a last source for studying the long-term behaviour we used the IUE data base, which contains several single short- and long-wavelength range ultraviolet spectra obtained in high- and low-resolution mode between 1979 and 1991. Because of the faintness of WR46, the exposure time in high-resolution mode equals the single-wave period. These spectra confirm the variability on time scales from days to years. However, the data are too scarce to allow a period determination. The last spectrum happens to be recorded during the high optical state on June 5th 1991 (Fig.17). And, since it shows the strongest emission lines, the high state also applies to the ultraviolet part of the spectrum. Furthermore, Fig.18 displays the O V 1371 emission line from several epochs. Evidently, the absorption trough is deepest during the high state, consistent with an increase of the mass-loss rate as argued in Sect.5 on basis of the increased emission-line fluxes.

We conclude that the line flux varies also on the long-term time scale, in harmony with the photometry, evidencing variation of the mass-loss rate. Conversely, the small and large EW measurements indicate that the object underwent similar brightenings both before and after 1991. Furthermore, there is a hint in the N V 4604/20 EW data and from other early observations, that WR46 is also varying on a time scale of several decades to a century.