THE SECRET LIVES OF CEPHEIDS: EVOLUTIONARY CHANGES AND PULSATION-INDUCED SHOCK HEATING IN THE PROTOTYPE CLASSICAL CEPHEID δ Cep^*

Photoelectric UBVRI photometry for this program was carried out with the Four College Automatic Photoelectric Telescope (FCAPT; Adelman et al. 2001) housed at Fairborn Observatory. The full data set was split to produce two well-covered light curves, centered at epochs 2008.9 and 2011.4. Fourier analyses of the resulting light curves yielded two times the maximum light, which were added to those found in the literature (Berdnikov et al. 2000). Our analysis of the complete timings data set (Figure 2) shows the period to be decreasing over time. From a quadratic fit to the O−C data, the rate of period change is calculated to be dP/dt = −0.1006 ± 0.0002 s yr^-1, indicating that δ Cep is currently making its second crossing of the instability strip (Turner et al. 2007). According to theory, the star contracts and heats up during the second crossing, and its surface temperature rises. Thus, the average density of the star increases, resulting in a decrease in pulsation period, according to the Period–Density Relation:

$$\begin{equation*} P\propto \frac{1}{\sqrt{\overline{\rho }}}, \end{equation*}$$

where P is the pulsation period and $\overline{\rho }$ is the average stellar density. Residuals of the quadratic O−C fit show no significant, additional (cyclic or otherwise) period variability.

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B- and V-band light amplitudes of ∼1.31 ± 0.013 and 0.86 ± 0.010 mag, respectively, were also obtained from the individual FCAPT light curves and compared to archival observations. From this comparison, the light amplitude of δ Cep appears to be increasing over time. If simple linear trends are assumed, the light amplitude of δ Cep has been increasing at a rate of ∼0.011 mag in the V band and ∼0.012 mag in the B band per decade over the last ∼50 years (total changes of ∼0.05 mag in V and ∼0.06 mag in B; Figure 3). It is interesting to note that many of the early observations of δ Cep, from the discovery of its variability in the late 1700s through to the early 1900s, display still smaller visual light amplitudes of ∼0.5–0.7 mag (Hertzsprung 1919; Meyermann 1904). Known as a very capable and meticulous observer, Stebbins (1908) observed δ Cep with a polarizing photometer and reported a visual amplitude of 0.76 mag (although a Fourier analysis of the data returned an amplitude of 0.73 mag), based on observations made in 1906. These values would extend the amplitude trend observed in the past ∼50 years (Figure 3). However, these visual data sets require modern, careful calibrations before a conclusive determination of continued amplitude change can be achieved. In addition, the bottom panel of Figure 3 shows that the average brightness of δ Cep has also increased over the same time span.

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Constructing a theoretical model from spectroscopic observations, Sasselov & Lester (1994) concluded that Cepheids could produce X-ray activity via pulsation-induced shock heating of their atmospheres. However, pointed Einstein and Röntgen Satellite (ROSAT) observations failed to detect any such activity and indicated that Cepheids were not (at least significant) X-ray sources. Even with log L_X ≈ 29 erg s^-1 (as determined by Sasselov & Lester), the problem with detecting X-rays from Cepheids is that these stars (except for Polaris at ∼133 pc; van Leeuwen et al. 2007) are far away at d > 250 pc. Thus, they are expected to have relatively weak X-ray fluxes (f_X < 10^-14 erg s^-1 cm^-2). Even though Polaris was detected at the 3σ level in a ROSAT/High Resolution Imager archival image, the detection was not noticed until several years after the observation was carried out (see Evans et al. 2007). Confirmation of Polaris's X-ray activity and definitive detections of X-rays from other nearby Cepheids would not occur until the arrival of more powerful X-ray observatories such as XMM-Newton and Chandra.

We successfully obtained Chandra (PI: Evans) and XMM-Newton (PIs: Guinan & Engle) observations of five Cepheids—Polaris, δ Cep, β Dor, SU Cas, and ℓ Car have been observed so far. The Chandra data reduction for Polaris is discussed in Evans et al. (2010). XMM-Newton data were reduced in the usual fashion, making use of the Science Analysis System (SAS v13.0.0) routines. Modeling of the Chandra and XMM-Newton data were then carried out using the Sherpa modeling and fitting package (distributed as part of the Chandra Interactive Analysis of Observations, CIAO, v4.5 suite). MEKAL models (Drake et al. 1996) were used for the final two-temperature (2-T) fitting and flux calculations.

The nearest three Cepheids (and so far the only Cepheids detected)—Polaris, δ Cep, and β Dor—have X-ray luminosities of log L_X ≈ 28.6–29.2 erg s^-1. Neither the short-period Cepheid SU Cas (P = 1.95 days; d = 395 ± 30 pc) nor the long-period, luminous Cepheid ℓ Car (P = 35.5 days, d = 498 ± 55 pc; Benedict et al. 2007) were detected. Upper X-ray luminosity limits of log L_X ≲ 29.6 and 29.5 erg s^-1 were estimated for ℓ Car and SU Cas, respectively, based on exposure times, background count rates, and stellar distances. Therefore, it is still possible that SU Cas and ℓ Car are X-ray sources with similar levels of activity to the Cepheids detected thus far, but are too distant to be detected above the background of the XMM-Newton exposures. However, the failure to detect two of our targets underscores a long-standing ambiguity present in the X-ray studies of Cepheids. Since Cepheids are young stars (∼50–200 Myr), any coeval main-sequence G-K-M companions (if present) would be coronal X-ray sources with X-ray luminosities similar to that of the Cepheids (see Guinan & Engle 2009, and references therein). Therefore, caution must be exercised as to whether unresolved companions are producing the X-ray activity. However, the HST-COS results (Engle & Guinan 2012; this study) show plasmas with temperatures up to ∼10⁵ K that vary (in phase) with the Cepheids' pulsation periods. This indicates that plasmas approaching soft X-ray-emitting temperatures do exist in Cepheid atmospheres.

As part of this study, five separate XMM-Newton visits were carried out for δ Cep. To provide better pulsation phase coverage, three of the visits were split during reduction into ∼30–50 ks sub-exposures, resulting in eight individual exposures for analysis. Background-subtracted count rates were ∼0.002–0.006 counts s^-1 for all exposures. A neutral hydrogen (N_H) column density value of 3.5 × 10²⁰ (log N_H = 20.5) cm^-2 was adopted, based on distance relationships determined by Paresce (1984) and corroborated by target reddening (Ayres et al. 2005). The relevant two-temperature MEKAL model fitted parameters are given in Table 2. All X-ray energy distributions peak in the kT ≈ 0.6–0.9 keV range (∼7–10 × 10⁶ K (MK)) and have measured flux values in the range of ∼4.5–13 × 10^-15 erg s^-1 cm^-2 (X-ray luminosities of log L_X ≈ 28.6–29.1 erg s^-1). The phased X-ray fluxes are shown in Figure 4. The Cepheid's X-ray activity appears to reach a maximum near 0.5 ϕ. This is different than what is found for the UV emission lines, which peak in the phase range 0.9–1.0 ϕ (see Figure 4). The nearby A0-type companion of δ Cep—HD 213307—is also detected in the X-ray data, implying that this star may have a cooler, unresolved companion. For comparison, the X-ray flux of the companion star remains essentially constant in all exposures, while the X-ray flux of δ Cep increases by two to three times in the exposure near 0.5 ϕ. Although our analysis has ruled out a possible flare or other transient events, this observation still represents a single (37 ks) sub-exposure. A new (recently approved by Chandra) observation at similar phase will further investigate the high flux level. X-ray observations of β Dor (P = 9.84 days), the subject of a follow-up paper, show a similar flux increase at 0.5 ϕ.

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Possibly related to the X-ray variations reported here for δ Cep is the recent discovery by Oskinova et al. (2014) of small, pulsation-phased X-ray variations of the β Cep-type variable star ξ¹ CMa. The periodic X-ray variations for ξ¹ CMa (HD 46328) have the same period as the fundamental stellar pulsation of this hot, magnetic B0.5 IV star. The X-ray fluxes peak near the optical maximum brightness that occurs near the minimum stellar radius and highest temperature. The relatively strong X-ray emissions observed for β Cep-type variables as well as other hot, massive stars arise from shock-heated winds (see Feldmeier et al. 1997). Oskinova et al. (2014) suggest that the periodic X-ray variations arise from small pulsation-induced changes in the wind structure, possibly coupled with changes in the magnetic field.

Prior to the installation of HST-COS, the most thorough UV studies of Cepheids were carried out in the 1980s–1990s with IUE. Studies of particular note are the series of papers by Schmidt & Parsons (1982, 1984a, 1984b) involving IUE data (∼1200–3200 Å) for multiple Cepheids, including δ Cep and Bohm-Vitense & Love (1994), which focused on the large available IUE data set for the 35 day Cepheid ℓ Car. These studies found UV emission lines, including O i 1305 Å, C iv 1550 Å, and He ii 1640 Å, to vary with the Cepheid pulsation periods—evidence that the Cepheids (and not unseen companions) were responsible for the emissions, and pulsations may be the formation mechanism. The emissions are indicative of hot plasmas up to 100,000+ K (also, He ii can be partly formed via photoionization by coronal radiation; Pagano et al. 2000).

One of the major aims of this study is to improve upon previous IUE results since what appeared to be photospheric continuum flux introduced uncertainties in both emission line identifications and flux measures. COS, with finer spectral resolution, higher sensitivity, and lower noise, can return superior spectra, for which much more precise studies could be carried out. In addition, closely spaced emission lines that were blended together in IUE spectra could be individually resolved in COS data and perhaps even less prominent emission lines would be detected. Since the only reliable data in the ∼1200–1600 Å  region available for Cepheids (at the beginning of this project) was low-resolution (∼5–6 Å) IUE Short Wavelength Prime/Reseau Camera spectra, it was quite frankly unknown exactly what the COS observations would show. The HST-COS spectra of delta Cep used in this study, and measured fluxes, are given in Table 3

IUE was known to suffer from scattered optical light contamination (Basri et al. 1985), though it turned out to be much more of an issue than was anticipated. Figure 5 shows a comparison of representative IUE and COS spectra for δ Cep. The improvement is dramatic. The much higher resolution was expected, but as the figure shows, a great deal of what could have been continuum flux from the photosphere turned out to be scattered light. This was the reason that IUE spectra of the program Cepheids could unambiguously show only the strongest emission lines (if any). In the case of Polaris, there was uncertainty as to whether any emission lines were present in the spectra; there was only a possible detection of the strong, but blended, oxygen/sulfur lines near ∼1300 Å. The scattered light is not present in the COS spectra of Cepheids, however, which display a wealth of emission lines not detected in the archival IUE spectra. These lines define rich and complex Cepheid atmospheres and, as is well known, offer excellent atmospheric diagnostic potential (Linsky et al. 1995 and references therein) since different line species originate in plasmas of specific temperatures. Also, emission line strengths and ratios, as well as line broadening and radial velocities (RVs), when measured over the stars' pulsation cycles, offer important atmospheric diagnostics and can also help distinguish Cepheid supergiant atmospheric emissions from those of possible unresolved main-sequence companions (if present). The flux values reported here are integrated fluxes for the emission lines with the continuum flux subtracted. To determine RVs for the emission lines, Gaussian fits were made.

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Although many important emission lines are present in the COS spectra, a few of importance were selected for the current study. These lines were selected because they represent a wide range of formation temperatures and are relatively free from contamination via blending with nearby lines, offering a "pure" measurement of the emission line in question. The lines selected are as follows.

• 1.  
  O i 1358 Å—selected in favor of the well-known O i triplet at ∼1300 Å because the triplet are fluorescent lines excited by H Lyβ radiation (Koncewicz & Jordan 2007) and suffer from blending with (primarily) nearby S i lines and heavy airglow contamination. Therefore, the flux of the O triplet is not necessarily indicative of plasmas at the O i peak equilibrium formation temperature of 1–2 × 10⁴ K (Doyle et al. 1997).
• 2.  
  Si iv 1393/1403 Å—a doublet with a peak formation temperature of ∼5–8 × 10⁴ K (Linsky et al. 1995). This doublet represents an important link between the cooler, O i-emitting plasmas and the hotter plasmas responsible for the N v and O v emission lines.
• 3.  
  N v 1239/1243 Å—another doublet, but with a higher peak formation temperature of ∼1.5–2.5 × 10⁵ K (Linsky et al. 1995). This doublet is very important because the lines occur at shorter wavelengths where photospheric continuum flux is essentially negligible. The N v doublet is the best measure of higher-temperature plasma variability in the UV spectra of the Cepheids.
• 4.  
  Additional lines—although not selected for a variability study due to its location on the red wing of the Lyα geocoronal-contaminated emission line, the O v 1218 Å line is present in certain spectra and has a peak formation temperature of ∼2–4 × 10⁵ K (Linsky et al. 1995). This places it among the hottest lines observable in the UV spectra of cool stars like the Cepheids, and its detection provides an important link to higher-temperature X-ray emissions. Additionally, measures have been made of the Si iii 1206 Å and 1298 Å features, and the 1298/1206 flux ratio was used to carry out atmospheric density estimates.

Data accumulation and results in the satellite-based high-energy studies have been much slower than for the optical studies. However, δ Cep currently has the most complete phase coverage with COS. As an illustration of the results of the UV program thus far, the current COS light curves of δ Cep are given in Figure 4. In looking at these plots, the most informative features are the following.

• 1.  
  The phase at which line emissions begin to increase. The phase coverage of δ Cep has been illustrative in terms of the rise in emission flux. In comparing the emission line fluxes to the included photospheric RV plot for δ Cep, we see good correlation between the phase where UV line emissions begin to peak and a "pre-piston phase" as given by the RVs. During this pre-piston phase, the photosphere has almost reached its minimum radius, its recession is decelerating, and it is about to begin expanding again. Fokin et al. (1996) have shown that a shock should be propagating through the atmosphere of δ Cep at this phase (∼0.8–0.85 ϕ). The phasing of the flux increase is strong evidence in favor of a shock-heating mechanism.
• 2.  
  The abruptness of the increase in UV emissions from δ Cep is indicative of a sudden heating or excitation mechanism. Over a span of ∼10 hr (from ∼0.86–0.93 ϕ), the O i 1358 Å flux increases by ∼7 times (numbered points 4–7 in Figure 4) and the Si iv flux increases by ∼10 times. Such an abrupt, strong excitation also points to a shock-related mechanism. The decrease in flux is also rapid (though not as rapid as the increase), as one would expect for a sudden heating event such as a shock.
• 3.  
  The presence of an apparent quiescent level of UV emissions during 0.6–0.8 ϕ. This indicates a persistent atmospheric heating, possibly magnetic in origin, as is the case for numerous other classes of cool stars.

Another feature of note is the phase difference between the peak flux of the most energetic (highest peak formation temperature) emission feature observed—N v ∼ 1240 Å—and the peak fluxes of the two cooler emission features. Unfortunately, for δ Cep, this aspect of the program requires a number of very narrowly phase-spaced observations that we simply do not have. Thus, a strict, quantitative conclusion cannot yet be drawn. However, the lower-temperature plasma emission lines do appear to peak earlier than N v. In Figure 4, spectrum 7 is clearly the most active spectrum in terms of O i 1358 Å and Si iv 1393 Å emissions. Qualitatively speaking, spectrum 7 looks to represent the peak phase of emissions for these two features. However, for N v emissions, spectrum 7 has nearly the same flux as spectrum 8. Since the overall shapes of the emission curves for these three features are so similar, it can be concluded that N v emissions are still rising in spectrum 7, where O i and Si iv emissions have essentially peaked. Thus, N v must have a peak emission slightly later (∼0.02–0.03 ϕ) in phase than O i and Si iv. As discussed by Bohm-Vitense & Love (1994), emissions from the hottest plasmas are expected to peak first in the case of shock heating, followed by line emissions from cooling plasmas in the post-shock regions. However, it is worth noting that the similarity of the rise times in UV line fluxes may result from the plasma exciting line emissions of various temperatures as it begins ionizing through to higher ionization states, and the process continues as the shock front moves through more neutral and singly ionized plasma. This is an interesting behavior, but one that will require more in-depth modeling and analysis before firm conclusions are drawn.

In addition to what is learned from emission line fluxes about the heating mechanism(s) at work in Cepheid atmospheres, the emission line profiles and RVs can provide valuable, complementary information. Figure 6 gives the profiles of the O i 1358 Å and Si iv 1393 Å emission lines observed in several spectra of δ Cep. The most potentially informative characteristic is the asymmetry present in spectra 6–8, where the lines show a strong, additional blueshifted emission component. This component is likely caused by an expanding shock emerging from the Cepheid photosphere. On the "near" side of the Cepheid atmosphere, the shock is approaching, producing the blueshifted emission. In spectrum 8, the O i line still shows heavy asymmetry, but the Si iv line shows an extremely broad and even emission profile, indicative of a large velocity distribution but no additional blueshifted feature. At this phase (0.04 ϕ), we are likely observing Si iv emission from a very turbulent post-shock region, where the high turbulence is responsible for the velocity distribution, meaning that the shock has "passed by" the Si iv-emitting region. The difference in O i and Si iv line profiles at this phase indicates that they are likely originating from different regions (heights) within the Cepheid atmosphere. The line profiles offer up further evidence in favor of shock heating and compression being responsible for the enhanced emissions.

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The RVs of the UV emission lines can give information on the workings of the δ Cep atmosphere, although we note there are COS wavelength calibration issues affecting their absolute accuracy (Aloisi et al. 2010). As such, the velocities can show a larger than normal uncertainty, but the agreement in overall velocity trends between the three lines plotted gives confidence in the measures. In Figure 7, the RVs (from top to bottom panels) of the O i, Si iv, and N v emission lines and photosphere are plotted. As indicated in the figure, the emission line RVs have had the phase-specific photospheric RV removed. For the three emission line RV plots, the dashed gray horizontal line indicates zero velocity: when the line-emitting region and the photosphere have identical velocities. Thus, line RVs above this line indicate that the line-emitting region is compressing on to the photosphere, and line RVs below this line indicate the region is expanding away from the photosphere. In the bottom (photospheric RV) plot, the dashed gray horizontal line represents the average velocity of the star. For spectra where the Si iv and/or O i line showed asymmetry, two Gaussian profiles were fit to the line, and the RV of the broad atmospheric emission is plotted, as opposed to the blueshifted emission component discussed in the previous paragraph. The agreement between the Si iv and O i velocity behaviors and that of the N v line, which maintained a symmetric single-Gaussian profile throughout the observed phases, gives confidence in the double-Gaussian approach.

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Figure 7 shows that from ∼0.86–1.04 ϕ (spectra 4–8 in Figure 4), the atmosphere of δ Cep is compressing on top of the photosphere. This compression begins just as the Cepheid photosphere is starting to expand again (the piston phase). This compression would result in further plasma excitation at these phases, contributing to the increased emission lines fluxes (Figure 4) and line broadening (Figure 6) that are observed.

Attempts have also been made to find suitable electron density-sensitive emission line ratios to gain further physical insights into the Cepheid's atmosphere. A handful of well-studied ratios exist in the literature, making use of such emission lines as, e.g., C iii (1909 Å), Si iii (1892 Å), and O iv (∼1400 Å). Unfortunately, either the spectra available for δ Cep do not cover the wavelengths of these emission lines (C iii 1909 Å or Si iii 1892 Å), or the lines are not strong enough to allow an unambiguous measurement (O iv ∼1400 Å). Thus, none of these density measures could successfully be applied. Making use of the latest chianti atomic database⁶ available at the time of writing (v7.1.3), investigations were carried out using a ratio of Si iii line fluxes (1298/1206 Å), as mentioned previously.

Measurements of almost all spectra for δ Cep give densities below the diagnostic range of the Si iii 1298/1206 Å ratio (N_e ≲ 6 × 10⁹ cm^-3). Spectrum 6 of δ Cep (as numbered in Figures 4 and 6), where the flux is steeply rising, gives a much higher density of N_e ≈ 3.2 × 10¹⁰ cm^-3. For reference, at similar plasma temperatures to those probed by the Si iii ratio above, quiet regions of the Sun have measured densities of ∼5 × 10¹⁰ cm^-3 and active regions have densities of ∼1 × 10¹⁰ cm^-3 (Dupree et al. 1976), and other studies (e.g., Keenan et al. 1989) have also found solar densities to match that measured for spectrum 6 of δ Cep.

However, issues have been raised with using the Si iii 1206 Å line in density diagnostics. Dufton et al. (1983) calculated that for the Sun, the 1206 line would be far too optically thick to give an accurate density. Although we believe that in a supergiant such as δ Cep the line would essentially be optically thin and suitable in that regard, there is also the temperature sensitivity to take into account when using a ground state transition, such as Si iii 1206 Å, with other subordinate features from higher levels. As such, we view the result as confirmation of increased atmospheric density during the phase of rising flux, but we are still investigating the usefulness of the Si iii ratio in returning a precise, numerical density measure.

All previously mentioned features of the spectra support the conclusion that δ Cep's atmospheric plasmas are heated/excited via pulsation-driven compression and shock propagation.