Concerning the Reported Phase‐modulated Changes in the Spectrum of 41 Sextantis

The star 41 Sextantis (HR 4237 = HD 93903 = SAO 137823, α(J2000) = 10^h50^m18^s, δ(J2000) = −08°538) belongs to an important group of chemically peculiar stars known as metallic‐line (Am) stars. According to The Bright Star Catalogue (Hoffleit & Jaschek 1982), m_v = 5.79,B - V = 0.16, and U - B = 0.13 for this star. Abt & Morrell (1995) classify its spectrum as Am(K/H/M = A3/A7 V/A9) and measure the rotational velocity to be Vsin i = 18 km s^-1. 41 Sex is a short‐period, single‐line spectroscopic binary (Worek et al. 1978) and also a visual binary, ADS 7942, with two distant, faint companions.

Metallic‐line stars were first recognized as being a distinct, chemically peculiar class by Titus & Morgan (1940). Characteristically, their spectral types based on Ca ii K and Sc ii λ4246 are too early, while for metals they are too late compared with the hydrogen lines. These stars are slow rotators, usually single‐line spectroscopic binaries, and have either weak or no measurable magnetic fields. They are main‐sequence dwarfs that range in spectral type from A0 to F4 with effective temperatures of 7000–10,000 K (Smith 1996). Michaud (1970) has proposed that the radiative diffusion of heavy elements in a stable atmosphere is the likely reason for the Am phenomenon.

In a series of papers, Sreedhar Rao and coworkers (Sreedhar Rao, Abhyankar, & Praveen Nagar 1990; Sreedhar Rao & Abhyankar 1991, 1992) have announced the discovery of phase‐modulated changes in the spectrum of 41 Sex. Using 33 and 66 Å mm⁻¹ photographic spectra, they find that absorption lines attributable to calcium, hydrogen, and various metals are noticeably stronger at the phases 0.25, 0.50, 0.75, and 1.0 relative to the time of maximum positive radial velocity in the star's orbital motion. They suggest that 41 Sex is an evolutionary link between Am and Ap stars. The Ap stars are noteworthy for their enhanced strontium, chromium, and europium absorption lines. The observed periodic changes in the strengths of these lines are explained by the oblique rotator model, where the star's magnetic axis is offset to the rotation axis and certain elements accumulate in localized regions on the stellar surface in the presence of strong magnetic fields (Babcock 1960).

Although they acknowledge that magnetic fields for Am stars are as a rule either weak or nonexistent and that no reports of such measurements appear in the literature for 41 Sex, Sreedhar Rao et al. propose an analogous explanation. Namely, elements concentrate in patches rather than disperse evenly over the surface because of a presumably undetectable "fossil" magnetic field, and the line strengths for these elements vary as the star rotates. According to Sreedhar Rao et al., the rotation of 41 Sex is synchronous since the changes in the line depths that they observe modulate in step with the orbital motion.

As recommended by Sreedhar Rao & Abhyankar (1992), their discovery of changes in the spectrum of 41 Sex should be verified with high‐dispersion CCD observations. In this paper, the results of such an effort are reported. As an aside, an updated solution for the spectroscopic orbit is presented.

Six spectra of 41 Sex were obtained with the 0.9 m feed telescope and coudé spectrograph at the Kitt Peak National Observatory between 1991 May 10 and May 14 with the observatory's TI3 CCD camera, whose pixel size is 15 μm. These spectra have a reciprocal dispersion of 9.9 Å mm⁻¹, a resolution of 0.26 Å, and a wavelength range of 117 Å centered at or near 3889 Å. The projected slit width of the spectrograph was 27 μm (20 km s⁻¹) and S/N ratio per pixel and average exposure time were 80 and 12.5 minutes, respectively. IRAF software was used to debias, flatten, extract, and linearize the dispersion.

For comparison, the projected slit width and resolution for the highest dispersion (33 Å mm⁻¹) photographic spectra used by Sreedhar Rao et al. were 20 μm and 0.66 Å, while the S/N ratio was 80 after smoothing.

Since the first orbital solution of this single‐line spectroscopic binary appeared (Worek, Beardsley, & King 1978), five others have been published. Because the radial velocity curve for the most recent orbital solution (Sreedhar Rao & Abhyankar 1992) showed much scatter, the spectroscopic orbit was reexamined for possible changes. The data for this particular analysis (Table 1), which covers a period from 1969 to 1991, include nine photographic prism spectra at 33 Å mm⁻¹ from the Allegheny Observatory, 20 photographic grating spectra at 14 Å mm⁻¹ from KPNO, and the six CCD spectra discussed in § 2. The first two sets represent previously published observations (Worek et al. 1978, 1986). As for the last set, software developed by the author was used to fit a parabola to the line cores to measure the radial velocity. Eleven lines representing ions such as H₈, Si ii, Fe i, and Ti ii, whose rest wavelengths were taken from Moore et al. (1966), were measured. The velocities derived from these lines have mean errors of ±0.7 km s⁻¹. They were corrected to the General Catalogue of Stellar Radial Velocities (Wilson 1963) with the help of standard star observations.

Sterne's method (Sterne 1941) was used to compute the orbital elements, where the following weighting scheme was adopted: 1.0 for Allegheny, 2.0 for KPNO photographic, and 3.0 for KPNO CCD. These newest elements are listed in the fourth column of Table 2, while the residuals for all of the measured radial velocities appear in the fourth column of Table 1. Figure 1 shows the theoretical radial velocity curve and the observations.

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Table 2 also includes the orbital solutions of Worek et al. and Sreedhar Rao & Abhyankar. Except for the eccentricity and the time and longitude of periastron, elements that are difficult to establish unambiguously when the orbit is nearly circular, there is satisfactory agreement. In fact, the same can be said when one compares all of the published solutions.

Table 3 lists the absorption lines in the six CCD spectra whose central depths and equivalent widths were measured for this study. Every effort was made to select those lines in the available spectral range, λλ3831–3948, which showed no obvious blending or where the blending was minimal. To normalize the spectrum near a particular line, a third‐degree polynomial was fitted to segments of the continuum free of any absorption features within an approximately 10 Å range on either side of the line except for H₈, where this range was expanded to 30 Å.

For the line depths, a parabola was fitted to the core of each normalized line. The residual intensity at the minimum (the zero slope of the parabola) was then determined. These line depths (one minus the residual intensity) are presented in Table 4 and are plotted in Figures 2 and 3. The orbital phases included with these values and those in Table 5 are for the period and time of maximum radial velocity, T₀, derived in the updated orbital solution presented in § 3.

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A pixel‐by‐pixel numerical integration using Simpson's rule was done to obtain the equivalent widths, W. These widths are reported in Table 5 and are plotted in Figure 4. One will note that fewer lines were measured for their equivalent widths than for their line depths. If the line showed any hint of blending or if the continuum could not be satisfactorily normalized in the neighborhood of the line, it was rejected.

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The line depths and the equivalent widths that were measured for various strong, intermediate, and weak lines in the high‐dispersion CCD spectra of 41 Sex (Tables 4 and 5) do not support the claim by Sreedhar Rao et al. that these quantities change during the orbital motion of the star. No measure deviates more than 2 σ (2 standard deviations) from its corresponding mean line depth or mean equivalent width. Furthermore, the value of σ for a given line is on average only 1.7% of the mean line depth and 4.4% of the mean equivalent width. These values indicate that there is not much scatter among the individual measures.

In contrast, Sreedhar Rao et al. report fluctuations in line depths having a range of 10%–20% for the ions: Fe i, Ca i, Mn i, Sr ii, Cr i, Ti i, and V ii (Sreedhar Rao & Abhyankar 1991). Since they did not publish individual line‐depth measures, standard deviations were not available to make a direct comparison with the above statistics. With regard to equivalent widths, they cite results for just one line, Sr ii λ4077 (Sreedhar Rao & Abhyankar 1992). Based on their eight measures,〈W〉 = 0.66 ± 0.08 Å. The greatest deviation for an individual measure from this mean is 1.6 σ, where σ is 0.20 Å or 31% of the mean.

Figure 8 in Sreedhar Rao et al. (1990) dramatically shows that the mean of all their measured line depths vary 70% from a maximum at phase 0.21 to a minimum at phase 0.38. The phases 0.0963 and 0.2591 in this paper, calculated with the revised period and T₀ (Table 2), are equivalent to these values. Although four of the five line depths for 0.2591 are slightly greater than are those for 0.0963 (Table 4), they are consistent (except for H₈) in that the difference between any two corresponding depths is less than the sum of their errors. Similarly, Figures 2, 3, and 4, which plot the line depths and equivalent widths listed in Tables 4 and 5, do not suggest that there is any variation with phase. It should be noted, however, that the equivalent widths for 0.9313 are a little less than their phase‐average widths, but the measured line depths for this same phase do not entirely support this trend.

Last, Sreedhar Rao et al. mention that line changes can be easily seen in the spectrum scans and that the hydrogen lines vary because of changes in the metallic lines that blend with them (Fig. 5; Sreedhar Rao et al. 1990). Figure 5 presents a portion of the spectrum of 41 Sex for five different orbital phases in the region of λ3865. The depths of the two strongest features in this region are relatively constant. As for the variation in the hydrogen lines, although the depth at 0.2591 for H₈ (Fig. 3 and Table 4) is large compared with the other depths measured for this line, it is still within 1 σ of the mean.

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The dilemma that must now be addressed is how the results of this paper can be reconciled with the findings of Sreedhar Rao et al. Their phase‐modulated changes in the spectrum of 41 Sex could be spurious. Even though statistical smoothing was done to maximize the S/N of their 33 and 66 Å mm⁻¹ photographic spectra as they detail in their papers, there are instrumental effects and data reduction biases that could corrupt the measures they acquired between 1978 and 1988. For example, changes during this period in the camera focus and the amount of scattered light in the spectrograph and the choice of the continuum points for the normalization of the spectra are just a few of the factors that would affect the line depths. Figure 6, a plot of the line depth for Si i λ3905 in the spectrum of β Vir, demonstrates that the KPNO coudé spectrograph was reasonably stable when the 41 Sex observations were made in 1991. Only the line depth for phase 0.2550 departs from the trend defined by the other measures. The line depths for 41 Sex also do not conform at phase 0.2591 as mentioned above. On the night corresponding to these particular phases, the central wavelength of the spectrograph had to be shifted from λ3889 to λ3863 in order to accommodate another observing program. This readjustment of the instrument might be responsible for these minor discrepancies.

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A second plausible explanation for the absence of phase‐modulated changes in the spectrum of 41 Sex might be that the 1991 observations analyzed here represent an epoch when 41 Sex was in a magnetically inactive, quiescent state. The spectrum changes might therefore be a transient phenomenon. If this is true, one must then question the proposed link between 41 Sex and the Ap stars, since the latter are recognized to have stable magnetic fields whose only variation is one of perspective as explained by the oblique rotator model. There would also be a need to describe how the undetectable, "fossil" magnetic field, which Sreedhar Rao et al. suggest for 41 Sex, suddenly becomes inactive.

Third, it must again be emphasized that the 1991 data cover just one orbital revolution, while that of Sreedhar Rao et al. span a 10 yr period. Could it be that the spectrum of 41 Sex varies gradually over an extended period of time rather than in a repetitious way every orbital cycle? Böhm‐Vitense & Johnson (1978) found changes in the spectrum scans of 15 Vul, τ UMa, and 60 Leo that suggested to them that Am stars just might do this over decades. They speculate that this could be caused by changes in the temperatures and radii of these stars or in their Paschen continuum absorptions.

In closing, Kitchin (1995, p. 214) notes that equivalent widths obtained with CCD spectra can be as accurate as 1%. Although the equivalent widths (and line depths) presented in this paper do not achieve this degree of accuracy, they should still be more reliable than photographic ones. Accepting this fact, one must conclude that the measures in Tables 4 and 5 simply do not verify the phase‐modulated changes in the spectrum of 41 Sex reported by Sreedhar Rao et al. Nevertheless, it should also be understood that this does not necessarily disprove their theory that Am stars might somehow be evolutionarily related to Ap stars.