An Examination of Pulsational Changes in the Classical Cepheid X Cygni

A total of 344 spectrum of X Cyg were obtained from 2010 June until 2020 October, using the 1.2 m McKellar Telescope of the Dominion Astrophysical Observatory (DAO). Along with X Cyg, spectra from a number of calibration stars from Joner & Hintz (2015) were also secured. The Coudé spectrograph with the 3231 grating was used along with the Site4 CCD. This provided coverage from about 4450–6970 Å over 4096 pixels. The combination of 40.9 Å/mm, with the pixel size of 15 μm, provides 0.614 Å/pixel. After a careful examination of the data, nine frames from 2011 December were removed from the analysis due to significantly lower S/N values than other data.

Each spectrum was processed with the DOSLIT package in IRAF, and was then wavelength calibrated with either a FeAr or ThAr comparison arc, depending on the observing season. From each spectrum we extracted the H-α and H-β values as detailed in Joner & Hintz (2015) and zeropointed these values with the stars mentioned above. We then obtained radial velocities from two methods. First a single high S/N spectrum was selected as a template and compared to all other spectra using the FXCOR function within IRAF. This provided a differential radial-velocity curve. We then performed the same process with three spectra for HR 662 serving as templates. HR 662 is a G7 III and has a published radial velocity of -12.28 km s⁻¹ in the GAIA catalog. We averaged the three values from HR 662 comparison and the shifted differential curve. This provided error per observation values of about 0.3–0.5 km s⁻¹. The H-α, H-β, and radial-velocity values are gathered in Table 1.

From a small number of sources we gathered published times of maximum light or photometric measurements from which we determined times. The majority of the early times of maximum light for X Cyg are reported in Szabados (1981) with a few additional times in Szabados (1991). Other data or times of maximum light came from Berdnikov (1992, 1993), Kiss (1998), and Turner et al. (1999).

In addition to published times of maximum light, we collected published data sets from which we could determine times of maximum light. We retrieved all observations of X Cyg from the AAVSO data archive (Kafka 2021). An occasional time was published (Speil 1985) based on AAVSO data, but we have chosen to pull the data from the archive and determine our own times of maximum light. We pulled the visual data string into Peranso (Paunzen & Vanmunster 2016) and binned the data into 0.51 days bins. Then the entire data string was examined to find individual times of maximum light with sufficient points to allow for a clean fit. We used Persano to fit each curve with a four-order polynomial and then determine the time of maximum light, with typical errors of 0.6 days. In Table 2 we gather times of maximum light from Szabados (1991) and in Table 3 all times since, including our new times of maximum. While the available AAVSO data covers a very large time period, we focused on times of maximum since the Szabados (1991) paper.

In Szabados (1981), using a period of 16.386332 days, they postulate a parabolic shape in the O-C diagram with the second-order term being on the order of 10⁻⁷ days cycle⁻². Once this shape is removed they believe there could be a sinusoidal pattern with a 55 yr cycle. However, they note that this is not supported by the published radial velocities published up to that point. It should be noted that this value includes the entire data string. These values for the period change in X Cyg persist up to Turner et al. (1999). Meyer (2005) argues that if you remove the early data, which they claim is biased, there is no evidence for a period change.

From an examination of all the times of maximum light we find that there is a clear period break at about JD2421512 (1917). Therefore two ephemerides were generated from data points before and after this date. The new ephemerides are given in Equations (1) and (2) for before and after, respectively.

$$\begin{eqnarray}&&\mathrm{HJD}=2410256.36(11)+16.38438(36)\ast E\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\mathrm{HJD}=2443830.607(18)+16.386470(28)\ast E.\end{eqnarray} \tag{ 2 }$$

Using Equation (2) we generate the O-C diagram displayed in Figure 1 and show the values in Tables 2 and 3. The figure shows the large number of visual observations starting at JD2445583 that came from the AAVSO archive. The clear period break is also seen at the point mentioned above. Performing a second-order fit yields a period change estimate of about −10⁻⁷ days cycle⁻², or −1.6 × 10⁻⁸ days days⁻¹ that is right at the 3σ level. It should be noted that this change is in the opposite direction from that in Szabados (1981) and Turner et al. (1999).

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In Figure 2 we show the O-C diagram for only the data after the date of the period break. Published times of maximum light are blue triangles and the AAVSO times are red circles. It is clear that this portion of the curve is flat over the entire time, and that the scatter is on the order of 0.3 days. Given the scatter of the AAVSO data we averaged over sets of four times of maximum light. This is again plotted with the published data in Figure 3.

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Spectral data of X Cyg were obtained from 2010 June up to 2020 October. An example spectra is given in Figure 4. The spectra were obtained in sets of 2 to 4 spectra per night over one to five consecutive nights. We clearly did not ever obtain a complete, continuous cycle, but as we phased the H-alpha data over the decade of data the curve became more complete. However, sometime after 2013 October 19, the entire H-alpha curve shifted down by about 0.01 magnitudes. All data acquired since 2013 phases at this lower value. This is all shown in Figure 5 with 2010–2013 data shown as blue triangles and 2014 to present data shown as red circles. During the time of the shift we see a drop in the O-C for a short time, as shown in Figure 3 at about JD2456923. In Figure 6 we show the O-C values around the time of the shift. The left line is the last 2013 October spectrum and the right line is the first 2014 July spectrum. During the interval there appears to be a sharp drop in the O-C value.

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We used the equation from Joner & Hintz (2015) for the relation between their H-alpha index and temperature. From this we found a curve that ranged from 5600–7100 K, which is much higher than previous estimates of 4900–6200 K (Fernley et al. 1989; Kiss & Szatmaŕy 1998). This is likely from the fact that the Joner & Hintz (2015) equation was based on luminosity class V targets and X Cyg is a Ib. Even with this consideration we estimated that the shift from before 2013 October and after 2014 July would represent a drop in surface temperature of about 200 K. This should have caused a change in the overall magnitude of the star and shape of the light curve.

To look for any change in the light curve we took approximately 350 visual observations from before 2013 October and the same number after July 2014. We determined the phase values with Equation (2) and then averaged over every 10 observations to allow for the lower accuracy visual observations. We then plotted the two curves as shown in Figure 7. There is no discernible change in the light curve leading to the conclusion that there was no temperature change.

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In addition to determining the index values, we also used cross-correlation methods to determine radial velocities. The minimum and maximum values for the radial velocities, along with overall shape, match those from Abt (1978). There is no evidence of an overall shift between our data and the Abt (1978) data to indicate an orbital motion. In addition, we compared our radial velocity values for each observing season and see no indication of shifting values. The spread is the line is from random errors. In Figure 8 we show a phased radial-velocity curve for X Cyg. This is a very detailed radial-velocity curve made up of over 300 individual observations. It is interesting to note that as the radial velocity comes down from its maximum positive value it takes a slight zig to the right. This occurs at about phase point 0.79 and is likely related to the second shock detailed in Gillet (2014).

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