A&A 487, 323-327 (2008)
DOI: 10.1051/0004-6361:200809935

Long-term monitoring of ${\theta^1}$ Ori C: the spectroscopic orbit and an improved rotational period
(Research Note)

O. Stahl¹ - G. Wade² - V. Petit³ - B. Stober⁴ - L. Schanne⁵

1 - ZAH, Landessternwarte Königstuhl, 69117 Heidelberg, Germany
2 - Dept. of Physics, Royal Military College of Canada, PO Box 17000, Station Forces, Kingston, ON, K7K 7B4, Canada
3 - Département de physique, génie physique et optique, Centre de recherche en astrophysique du Québec, Université Laval, Québec (QC) G1K 7P4, Canada
4 - Nelkenweg 14, 66791 Glan-Münchweiler, Germany
5 - Hohlstraße 19, 66333 Völklingen-Ludweiler, Germany

Received 9 April 2008 / Accepted 12 June 2008

Abstract
Context. The young O-type star ${\theta^1}$ Ori C, the brightest star of the Trapezium cluster in Orion, is one of only two known magnetic rotators among the O stars. However, not all spectroscopic variations of this star can be explained by the magnetic rotator model. We present results from a long-term monitoring to study these unexplained variations and to improve the stellar rotational period.
Aims. We want to study long-term trends of the radial velocity of ${\theta^1}$ Ori C, to search for unusual changes, to improve the established rotational period and to check for possible period changes.
Methods. We combine a large set of published spectroscopic data with new observations and analyze the spectra in a homogeneous way. We study the radial velocity from selected photo-spheric lines and determine the equivalent width of the H${\alpha }$ and He II  $\lambda4686$ lines.
Results. We find evidence for a secular change of the radial velocity of ${\theta^1}$ Ori C that is consistent with the published interferometric orbit. We refine the rotational period of ${\theta^1}$ Ori C and discuss the possibility of detecting period changes in the near future.

Key words: stars: individual: ${\theta^1}$ Ori C - stars: emission-line, Be - stars: variables: general - stars: circumstellar matter - stars: early-type

1 Introduction

The young O star ${\theta^1}$ Ori C, the brightest star of the Trapezium cluster in Orion, is one of the only two O-type stars with detected magnetic fields (the other is HD 191612, cf. Donati et al. 2006). Regular variations of the H${\alpha }$ line with a period of 15.4 days were discovered from equivalent width measurements by Stahl et al. (1993). Later, this same period was also detected in e.g. UV spectral lines (Walborn & Nichols 1994) and the X-ray flux (Gagné et al. 1997).

The magnetic field of ${\theta^1}$ Ori C, which also varies according to the 15.4 day period, was first detected by Donati et al. (2002) and later studied in more detail by Wade et al. (2006). For a detailed spectroscopic analysis of the star see Simón-Díaz et al. (2006).

The observations are explained conceptually by the magnetically-confined wind shock (MCWS) model, originally proposed by Babel & Montmerle (1997). In this model, a dipolar magnetic field confines the outflowing radiatively-driven stellar wind, which is channeled toward the magnetic equator where it generates a strong shock. The resulting circumstellar plasma is forced to rotate with the star, generating periodic variability of the emitted optical, UV and X-ray fluxes. This model has more recently been extended using MHD simulations by ud-Doula & Owocki (2002) and Gagné et al. (2005), who have investigated the stability and dynamics of this phenomenon.

The period of ${\theta^1}$ Ori C was determined to be 15.422 $\pm$ 0.002 days by Stahl et al. (1996) and later revised to 15.426 $\pm$ 0.002 by Stahl (1997). However, most publications (e.g. Wade et al. 2006) use the older period value of 15.422 days. The difference in both periods has now accumulated to a phase difference of about 0.1, which is quite significant. Observations obtained at the current epoch should therefore be able to distinguish between these two periods.

In addition to the strict periodicity, ${\theta^1}$ Ori C also shows additional variations, which are probably not periodic, or have unknown periods e.g. the spectral type variations reported by Walborn (1981) or the radial velocity variations found by Stahl et al. (1996). Also, ${\theta^1}$ Ori C is in fact a multiple system and interferometric measurements recently propose a long orbital period of more than ten years (Patience et al. 2008; Kraus et al. 2007).

The published radial-velocity measurements have been analyzed by Vitrichenko (2002), but more data are available.

Long-term monitoring is necessary to study these variations. We therefore collected all available published spectra of ${\theta^1}$ Ori C and obtained new observations to study long-term trends, to search for unusual variations and to improve the determination of the rotational period.

2 Observations

For the study of the long-term variations, we primarily used published echelle observations: the Heros data published by Stahl (1997), complemented by a few other observations obtained with the same instrument; the Feros observations published by Reiners et al. (2000); the MuSiCoS spectra published by Wade et al. (2006); a few ESPaDOnS spectra (Petit et al. 2008) and two spectra extracted from the Elodie archive (Moultaka et al. 2004, http://atlas.obs-hp.fr/elodie/). All of these observations cover a large spectral range with high resolving power.

In addition, we have been obtained a few spectra with amateur instruments. For these observations we used the spectrograph Lhires III, which is available from http://www.shelyak.com/, attached to Celestron 14 $^{\prime\prime}$ Schmidt-Cassegrain telescopes at private observatories. The detector for most observations was a CCD with 2184 $\times$ 1472 pixels (used with 2 $\times$ 2 binning) with a pixel size of 6.8 $\mu$m. A grating with 1200 lines/mm was used for most observations (Lhires III, 1), resulting in a spectral resolution of about 1.0 Å. A few spectra were obtained with a grating with 2400 lines/mm, resulting in a higher resolution of 0.5 Å (Lhires III, 2). One spectrum was obtained with the 2400 lines/mm grating, but with another detector with 1536 $\times$ 1024 pixels with 9 $\mu$ pixel size (Lhires III, 3). All of these spectra were reduced with ESO-Midas, using standard procedures. The wavelength calibration was performed using a Neon lamp. The spectra of ${\theta^1}$ Ori C show strong nebular lines from the Orion nebula. These lines were used to verify the wavelength solution. The Lhires observations cover a relatively small spectral range around H${\alpha }$ and were used only for the equivalent width determination of H${\alpha }$. A summary of the data used is given in Table 1.

Table 1: Summary of instrumentation used for this study. Most of the spectra (except the Lhires spectra, have been partly published. The signal-to-noise ratio for the echelle data is strongly dependent on wavelength, but above 100 in the spectral ranges used for most of the spectra.

3 Radial velocity variations

The radial velocity variations of ${\theta^1}$ Ori C have been studied by various authors (e.g., Vitrichenko 2002), but with ambiguous results. It appears likely that the variations reflect the 15.4 day rotational modulation, as well as mysterious, shorter- and longer-term variations. However, the published radial velocities show significant scatter. In light of the interferometric orbits published by Kraus et al. (2007) and Patience et al. (2008) with a period of more than ten years, a re-analysis of the radial velocities seems warranted. As most spectral lines vary significantly with the 15.4 day period, we decided to use only the C IV line doublet at $\lambda \lambda$5801.51, 5812.14 Å, the He II $\lambda$5411.424 line and the O III $\lambda$5592.37 line for radial velocity studies. These lines seem to be more weakly affected by the rotational modulation (Stahl et al. 1996) and as a group they provide consistent results. The lines were modeled by fitting Gaussians to the line profiles, which matches the lines very well. The result is reported in Table 4 and plotted for the C IV lines in Fig. 1. A closer analysis shows small, but significant systematic offsets of the order of a 2-3 km s^-1 between different lines. These offsets are probably due to blends or atmospheric stratification. All lines show the same variability pattern, however.

	Figure 1: Radial velocity of C IV  $\lambda \lambda$5801, 5812 versus Julian Date. The symbols denote different instruments. $\bullet$: Flash, $\circ$: Heros, $\Box$: Feros, $\bigtriangleup$: Elodie, +: Musicos, $\times$: Espandons.
Open with DEXTER

As can been seen in Fig. 1, a large scatter on short time scales is obvious. These variations have already been detected by Stahl et al. (1993). The scatter is partly due to variations with the rotational period, but primarily it is caused by occasional variations on other timescales (cf. Fig. 2). From Fig. 2, a period of about 60 days seems possible. However, a period analysis of the radial velocities does not show a significant peak near this period. In the period range below 100 days, only the 15.4 day period is significant in the radial-velocity data. Therefore, the rapid variations in radial velocity are probably not periodic, and we speculate that they may be due to (stellar) atmospheric effects.

The Gaussian fit to the line also measures the line width (FWHM) and depth of the lines. Both quantities are strongly variable on short timescales (by about $\pm$30%), but without any obvious long-term trend. In contrast to the radial velocities, the variations in width and depth are mostly due to rotational modulation (cf. Fig. 2). The width of the lines and their depth are clearly correlated. The lines are deeper when they are narrower, see Fig. 3. The equivalent widths are therefore less variable, by only about $\pm$10%.

	Figure 2: Average radial velocity, line depth and FWHM, together with the 1$\sigma$ error bars, of the C  IV$\lambda$5801, 5812 lines for part of the time covered. The radial velocity shows strong variations, but not with the 15.4 d period. The line depth and width are clearly variable with the 15.4 d period.
Open with DEXTER

	Figure 3: Correlation of FWHM and line depth of C  IV$\lambda$5801, 5812.
Open with DEXTER

In Fig. 1, a large increase in radial velocity between 1992 and 1999 is obvious, followed by lower velocities after 2004. If these changes are due to movement in a binary system, the data suggest a long-period orbit.

In order to improve the time coverage, we searched for older published radial velocities. A number of authors have measured the radial velocity of ${\theta^1}$ Ori C. These measurements have been summarized by Vitrichenko (2002). However, their Table 1 contains errors in the mean time of the observations and partly averages data obtained over several seasons. The data of Abt et al. (1991) have been obtained over many years and are based only on the Balmer lines (which are in strong emission, and highly variable). The same is true for the data of Frost et al. (1926). The average data reported by Vitrichenko (2002) for both data sets are averaged over many seasons and therefore not useful for our period study. Therefore, only the data in Table 2 remain. They are averages over relatively short intervals and give reliable radial velocities.

A possible orbital origin for the trend in the radial velocity was already discussed by Donati et al. (2002) and Kraus et al. (2007), but we now cover a substantially longer time interval. However, our data alone still do not allow us to determine an unambiguous period. An interferometric orbit was recently published by Kraus et al. (2007), and more recently revised with newer data by Patience et al. (2008). If we assume that the radial velocity variations result from the orbit published by Patience et al. (2008), we can fit an orbital solution.

In Fig. 4, the radial velocity (mean of all lines in Table 4 and the values from Table 2) is plotted versus Julian date. All parameters derived from the interferometric orbit of Patience et al. (2008) have been kept fixed. We derived the K value of the orbit from the relation $K = (2\pi/P) a \sin i / \sqrt{1-{e}^2}$, using the parameters of Patience et al. (2008) and a distance of 440 pc (Jeffries 2007). The only free parameter was the systemic velocity $\gamma$ (dashed line). It can be seen that the radial velocity data are compatible with the interferometric orbital parameters. If we optimize the radial-velocity solution by varying all parameters, starting with the interferometric parameters, we obtain another solution plotted in Fig. 4 (full line). Both solutions are summarized in Table 3.

Note that our solution is not unique. Within the errors given by Patience et al. (2008) several different radial velocity solutions of similar quality are possible. Good solutions are also possible with parameters which are incompatible with the interferometric orbit. Therefore it is not possibly to give a reliable error estimate for our solution. This is due to our very incomplete phase coverage and the large short-term scatter. Both effects prevent a unique solution with the available data. However, the period P and the system velocity $\gamma$ are relatively robust.

	Figure 4: Heliocentric radial velocity versus Julian date. The dashed line represents an orbital solution based on the parameters published by Patience et al. (2008), with only the systemic velocity $\gamma$ as a free parameter. The full line represents a solution which is within the errors compatible with interferometric orbit, but fits the radial velocities better.
Open with DEXTER

Table 2: Published radial velocities. ``n'' is the number of spectra used.

Table 3: Summary of orbital parameters. Note that the radial velocity solution is not unique. The given solution is close to the parameters of Patience et al. (2008).

Solutions with about half the period are also possible. In particular, a highly eccentric orbit with a period near 11 years, similar to the one proposed by Kraus et al. (2007), fits the data reasonably well, although not with the phases given by Kraus et al. (2007) and with larger deviations than the solution presented above. Such a short period seems to be excluded by the interferometric data published by Patience et al. (2008), however. Clearly, a longer time coverage is needed to derive a more reliable solution.

4 Equivalent width variations of H${\alpha }$ and He II$\lambda$4686

The equivalent width of the H${\alpha }$ line of ${\theta^1}$ Ori C shows periodic variations, corresponding to the 15.4 day rotation period of the star (Stahl et al. 1993). We measured the equivalent width after subtraction of the nebular lines, following the procedure described by Stahl et al. (1996). The line was integrated between 6545 and 6580 Å. The equivalent widths are listed in Table 5. For completeness, we also include the measured equivalent widths of He II $\lambda$4686 in the table. The subtraction of the nebular lines is subjective and introduces an error, which is difficult to quantify. The error is small for the data with the highest resolution, but increases with decreasing resolution. We combined our new results with the published results to improve the period. From the AOV method (Schwarzenberg-Czerny 1989) we derive a best period of 15.424 $\pm$0.001 days. The phase diagram obtained with this period is shown in Fig. 5. The new period is, within the error bars, in agreement with all published values, also with the value originally obtained by Stahl et al. (1996) from IUE observations.

The error in the period is smaller than that obtained from previous studies. However, because ${\theta^1}$ Ori C is a member of a binary, the times need to be corrected for light-travel effects due to orbital motion. Because of the uncertain orbit, this correction has not yet been applied.

As can be seen in Fig. 5, the new measurements fit very well in the phase diagram, although the scatter is larger than with the higher resolution echelle data. This demonstrates that the magneto-spheric emission of ${\theta^1}$ Ori C as diagnosed by the H${\alpha }$ emission has been very stable over the past 15 years.

The published data of Conti (1972) are potentially important for the period determination, because they extend the covered time substantially. Their published line profiles of He  II$\lambda$4686 (their Fig. 2), show a blue-shifted emission appearing between JD 2 441 284.91 and 2 441 287.88. According to Stahl et al. (1996) (their Fig. 7), this emission appears at a phase of about 0.7. Together with our zero-point, this constrains the period to 15.42 < P < 15.426, in agreement with the period obtained from H${\alpha }$. Quantitative equivalent width measurements on the spectra of Conti (1972) could provide stronger constraints.

	Figure 5: The phase diagram of the equivalent width of H${\alpha }$ as computed with a zero point of JD = 2 448 833.0 and a period of 15.424 days. The new measurements are shown with the larger symbols.
Open with DEXTER

5 Other variations

The spectacular spectral type variations, occuring on a time-span of a few days, reported by Walborn (1981) are similar to the variations reported by Walborn et al. (2003) for the other known magnetic O star, HD 191612. In the case of HD 191612, the spectral type variations are periodic with the rotational period. For ${\theta^1}$ Ori C, periodic equivalent variations of He I and He II lines have also been reported (Stahl et al. 1996). However, the He  I and He  II lines vary in phase and the ratio of these lines does not vary significantly with the rotational period (Stahl et al. 1996). This behavior has been explained by Simón-Díaz et al. (2006) by variable continuum emission from a disk. The variations found by Walborn (1981) are different and thus probably had a different origin. In order to check our large data set for similar variations as reported by Walborn (1981), we searched for spectral type variations of ${\theta^1}$ Ori C in our spectra. We analyzed the ratio He II $\lambda$4541/He I $\lambda$4471. No variations similar to those observed by Walborn (1981) were found. As an example, we show in Fig. 6 the result of our measurements in the same time interval as the measurements in Fig. 2. The measurements indicate a spectral type of about 07V, with little variation over time. For comparison, the ratios reported by Walborn (1981) lie between 1.25 and 2.11, i.e. they indicate a much earlier spectral type. We have to conclude that such spectral-type variations are rare events in ${\theta^1}$ Ori C.

	Figure 6: The equivalent width ratio He  II$\lambda$4541/He  I$\lambda$4471 versus time. The horizontal lines at 0.9 and 1.55 mark the approximate ratio for the spectral types O7V and O5V, respectively. The measured ratio indicates a spectral type of about O7V.
Open with DEXTER

6 Discussion and conclusions

The long-term radial velocity variations of ${\theta^1}$ Ori C are in good agreement with the orbital motion expected from the published interferometric orbit. Future radial velocity studies are very important to complete the phase coverage. Together with the interferometric data (Patience et al. 2008; Kraus et al. 2007) this should eventually provide data covering the full orbit of ${\theta^1}$ Ori C. The interferometric and the radial velocity data are complementary, since some parameters are better constrained by interferometry, while others are more sensitive to radial velocity measurements.

We derive a system velocity of about 13 km s^-1 for ${\theta^1}$ Ori C, which is close to the velocity of the nebular emission, but significantly below the radial velocity of the Orion molecular cloud and the stars of the Orion nebula cluster, which have a heliocentric radial velocity of about 30 km s^-1(O'Dell 2001). While this discrepancy was already known from previous measurements, our result indicates that the discrepancy is not due to orbital motion. A large peculiar velocity of ${\theta^1}$ Ori C would have major effects on the ionization of the Orion nebula (O'Dell 2001). However, given the peculiar spectrum of ${\theta^1}$ Ori C, atmospheric effects can not be ruled out completely. At least the occasional radial velocity deviations towards smaller values (cf. Fig. 2) are probably due to atmospheric distortions and could bias the measured systemic velocity to slightly (by about 3 km s^-1) smaller values. In any case, the good agreement of the interferometric orbit with the radial velocity variations strongly indicates that the long-term radial-velocity variations are due to orbital motion.

According to Hillenbrand (1997), ${\theta^1}$ Ori C is younger than 1 Myr. From its long period, we know that it is rotating very slowly for an O-type star. A low rotation velocity of $v \sin$ = 24 km s^-1 has been found by direct spectroscopic analysis (Simón-Díaz et al. 2006). Assuming that ${\theta^1}$ Ori C was born as a fast rotator, this suggests that strong magnetic braking must have occurred.

If it is assumed that the 538 d spectral variability period of HD 191612 (Howarth et al. 2007) is in fact the rotational period of that star (an exceptionally long period for an O star), it would appear that magnetic fields are very effective in slowing down the rotation rate. Interestingly, HD 191612 also seems to be a member of a wide binary system (Howarth et al. 2007) with an orbital period of 1542 d.

A factor of 10 decrease in rotational speed over its lifetime is plausible for ${\theta^1}$ Ori C. If we assume that $p/\dot{p}$ was constant with time, this leads to an e-folding time of of 500 000 years or less. On the other hand, a period change of 0.001 days in 20 years corresponds to a $p/\dot{p}$ of 300 000 years. It seems therefore possible to directly measure the deceleration age of ${\theta^1}$ Ori C in the foreseeable future. Equivalent width measurements, especially at phase around 0.25 and 0.75, are needed. At these phases the equivalent width changes rapidly with time, therefore observations at these phases are particularly sensitive to the exact value of the period. We have demonstrated that observations acquired using small telescopes are sufficient for this purpose.

However, in order to measure intrinsic period changes, the orbital velocity of ${\theta^1}$ Ori C (which introduces a variable Doppler shift on the observed period) has to be determined with high accuracy. An orbital velocity of only 3 km s^-1 already changes the observed period by 10^-5 P, which is close to the current accuracy of the period. It is especially important to cover the minimum of the radial velocity curve. Unpublished measurements could be very valuable to fill the phase diagram. If these measurements are not available, a few more years of radial velocity monitoring are needed.

Acknowledgements

This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. G.A.W. acknowledges Discovery Grant from the Natural Science and Engineering Research Council of Canada.

References

• Abt, H. A., Wang, R., & Cardona, O. 1991, ApJ, 367, 155 [NASA ADS] [CrossRef] (In the text)
• Babel, J., & Montmerle, T. 1997, ApJ, 485, L29 [NASA ADS] [CrossRef] (In the text)
• Conti, P. S. 1972, ApJ, 174, L79 [NASA ADS] [CrossRef] (In the text)
• Donati, J.-F., Babel, J., Harries, T. J., et al. 2002, MNRAS, 333, 55 [NASA ADS] [CrossRef] (In the text)
• Donati, J.-F., Howarth, I. D., Bouret, J.-C., et al. 2006, MNRAS, 365, L6 [NASA ADS] (In the text)
• Frost, E. B., Barrett, S. B., & Struve, O. 1926, ApJ, 64, 1 [NASA ADS] [CrossRef] (In the text)
• Gagné, M., Caillault, J.-P., Stauffer, J. R., & Linsky, J. L. 1997, ApJ, 478, L87 [NASA ADS] [CrossRef] (In the text)
• Gagné, M., Oksala, M. E., Cohen, D. H., et al. 2005, ApJ, 628, 986 [NASA ADS] [CrossRef] (In the text)
• Hillenbrand, L. A. 1997, AJ, 113, 1733 [NASA ADS] [CrossRef] (In the text)
• Howarth, I. D., Walborn, N. R., Lennon, D. J., et al. 2007, MNRAS, 381, 433 [NASA ADS] [CrossRef] (In the text)
• Jeffries, R. D. 2007, MNRAS, 376, 1109 [NASA ADS] [CrossRef] (In the text)
• Kraus, S., Balega, Y. Y., Berger, J.-P., et al. 2007, A&A, 466, 649 [NASA ADS] [CrossRef] [EDP Sciences]
• Morrell, N., & Levato, H. 1991, ApJS, 75, 965 [NASA ADS] [CrossRef]
• Moultaka, J., Ilovaisky, S. A., Prugniel, P., & Soubiran, C. 2004, PASP, 116, 693 [NASA ADS] [CrossRef] (In the text)
• O'Dell, C. R. 2001, ARA&A, 39, 99 [NASA ADS] [CrossRef]
• Patience, J., Zavala, R. T., Prato, L., et al. 2008, ApJ, 674, L97 [NASA ADS] [CrossRef]
• Petit, V., Wade, G. A., Drissen, L., Montmerle, T., & Alecian, E. 2008, MNRAS, in press (In the text)
• Reiners, A., Stahl, O., Wolf, B., Kaufer, A., & Rivinius, T. 2000, A&A, 363, 585 [NASA ADS]
• Schwarzenberg-Czerny, A. 1989, MNRAS, 241, 153 [NASA ADS] (In the text)
• Simón-Díaz, S., Herrero, A., Esteban, C., & Najarro, F. 2006, A&A, 448, 351 [NASA ADS] [CrossRef] [EDP Sciences]
• Stahl, O. 1997, in ESO Workshop on Cyclic Variability in Stellar Winds, ed. L. Kaper, & A. Fullerton, 246 (In the text)
• Stahl, O., Wolf, B., Gäng, T., et al. 1993, A&A, 274, L29 [NASA ADS]
• Stahl, O., Kaufer, A., Rivinius, T., et al. 1996, A&A, 312, 539 [NASA ADS]
• Struve, O., & Titus, J. 1944, ApJ, 99, 84 [NASA ADS] [CrossRef]
• ud-Doula, A., & Owocki, S. P. 2002, ApJ, 576, 413 [NASA ADS] [CrossRef] (In the text)
• Vitrichenko, É. A. 2002, Astron. Lett., 28, 324 [NASA ADS] [CrossRef] (In the text)
• Wade, G. A., Fullerton, A. W., Donati, J.-F., et al. 2006, A&A, 451, 195 [NASA ADS] [CrossRef] [EDP Sciences]
• Walborn, N. R. 1981, ApJ, 243, L37 [NASA ADS] [CrossRef] (In the text)
• Walborn, N. R., Howarth, I. D., Herrero, A., & Lennon, D. J. 2003, ApJ, 588, 1025 [NASA ADS] [CrossRef] (In the text)
• Walborn, N. R., & Nichols, J. S. 1994, ApJ, 425, L29 [NASA ADS] [CrossRef] (In the text)

 

  
Online Material

Table 4: Radial velocity measurements.

Table 5: Equivalent width measurements.