Pulsations of the High-Amplitude δ Scuti star YZ Bootis

δ Scuti stars are pulsators with short periods, located inside the classical Cepheid instability strip crossing the main sequence on or above the Hertzsprung-Russell (HR) diagram. With masses between 1.5 and 2.5 M_⊙, the pulsation periods of these stars are in the range of 18 minutes to 7.2 hours and amplitudes range from millimag up to several tenths of a mag. High-amplitude δ Scuti (HADS) stars, as either Population I or II, are found to have one or two dominant radial modes and peak-to-peak light amplitude variations larger than 0.3 mag. According to their heavy element abundance, stars can be classified as Population I or Population II. Generally for δ Scuti stars, Population I stars, as slow rotators with v sin i ≤ 30 km s⁻¹, are young and have relatively higher metallicity. They are usually found closer to the main sequence. However, Population II (SX Phoenicis) stars are usually metal-poor, more evolved stars and are located in globular clusters (McNamara 2000).

YZ Bootis (= HIP 75373, ⟨V⟩ = 10.57 mag, P₀ = 0.1041 d, A6-F1) is an HADS star with a peak-to-peak amplitude of about 0.42 mag (Breger & Pamyatnykh 1998; Zhou 2006). Based on uvbyβ photometry, Joner & McNamara (1983) classified YZ Bootis as a Population I star because of the typical m₁ index of Population I stars. This star has a relatively long observational history, dating back to earlier studies of the star's light variations (Eggen 1955; Broglia & Masani 1957; Spinrad 1959; Heiser & Hardie 1964; Gieren et al. 1974) and the classification used to be either RR Lyrae or Population I HADS.

Regarding the period variability of YZ Boo, Broglia & Masani (1957) revealed that variations exist in the light curves from night to night and the largest variations of amplitude can be up to 0.07 mag in the blue band. They also found that the times of maximum seem to exhibit periodicity of about ± 0.0015 d (Broglia & Masani 1957; Heiser & Hardie 1964). Subsequent observations (Szeidl & Mahdy 1981; Jiang 1985; Peniche et al. 1985; Hamdy et al. 1986) appeared to indicate that YZ Boo has different continuous period increases around a value of (1/P)dP/dt = ∼3 × 10⁻⁸ yr⁻¹. Recently, Zhou (2006) presented an investigation on stability in the period of YZ Boo and claimed that the period change of YZ Boo is still inconclusive. Ward et al. (2008) gave a new value of (1/P)dP/dt = 6.3(6) × 10⁻⁹ yr⁻¹, assuming this star is increasing and changing smoothly. However, it is still not an easy task to decide whether its period is constant or varying.

The aim of this work is to report a detailed study of the period changes of YZ Boo, mainly using extensive time-series CCD photometry observations from 2008 to 2015 at both the Nanshan Station and Xinglong Station in China. The paper is organized as follows. In Section 2, we describe our new observations and present the data reduction procedure. In Section 3, analysis of the pulsations of YZ Boo is performed, hence giving the corresponding results. We construct the classical O – C diagram and show a new ephemeris in Section 4. The theoretical model and calculation of eigen-frequency and rate of frequency change are given in Section 5. Discussion and conclusions are provided in the last section.

In order to investigate the variability in period, YZ Boo was observed from 2008 Feb to 2015 May. The CCD images collected between 2008 and 2013 were mainly from the Xinglong 85-cm telescope, and the data from 2014 to 2015 were obtained with the Nanshan 1-m telescope (hereafter called NOWT). The Xinglong 85-cm is equipped with a PI MicroMax: 1024BFT CCD camera and the field of view is 16.5' × 16.5', corresponding to an image scale of 0.96'' pixel⁻¹ (Zhou et al. 2009). NOWT is equipped with a standard Johnson multi-color filter system (i.e. UBV RI filters) (e.g. Cousins 1976) and an E2V CCD203-82 (blue) camera mounted on the primary focus. The CCD camera has 4096 × 4196 pixels, corresponding to a field of view of 1.3° × 1.3° at a focal ratio of 2.159 with a full image size of 49.15 × 49.15mm² (Song et al. 2016).

Table 1 lists the journal of observations for YZ Boo.

All the time-series CCD images were reduced with the standard IRAF¹ routines. Firstly, all the CCD frames were calibrated by removing the bias level using the overscan data, and flat fielding usingmaster flat fields. For the data from NOWT, dark correction was not considered since the CCD camera was operating at about −120°C with liquid nitrogen cooling, hence the thermionic noise was less than 1 e pix⁻¹ h⁻¹ at the temperature, and at about −45°C for images from the Xinglong 85-cm telescope, so dark correction was also not considered. Then, the IRAF APPHOT package was employed to perform aperture photometry. In order to optimize the sizes of the aperture, five to ten different apertures were used for the data in each night and the apertures which exhibited minimum variance of magnitude differences for the check star relative to the comparison star were taken. The star C1 = GSC2569 − 1184 (V = 11.6 mag) was detected as a non-variable within observational error and then used as the comparison to obtain differential magnitudes for the variable. This comparison star was also used by Derekas et al. (2003). The star C2 = GSC2569–1050 (V = 11.4 mag) was used as the check star.

Figure 1 shows an image of the field of YZ Boo taken with NOWT, on which the variable, comparison and check stars are marked. The standard deviations of differential magnitudes between C2 and C1 yielded an estimate of the mean observational error of about 0.005mag. In total, we obtained 11 885 measurements in the V band during 48 nights for YZ Boo.

Zoom In Zoom Out Reset image size

Figures 2 and 3 show the light curves of YZ Boo in the Johnson V band observed with the Xinglong 85-cm telescope from 2008 to 2013 and NOWT from 2014 to 2015, respectively.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To study the pulsations of YZ Boo, we performed Fourier analysis with all the data in the V band using PERIOD04 (Lenz & Breger 2005) which applies Fourier transformations on the light curves to search for significant peaks in the amplitude spectra. The light curves are fitted with the following formula

$$\begin{eqnarray}&&m={m}_{0}+\Sigma {A}_{i}\sin [2\pi ({f}_{i}t+{\phi }_{i})].\end{eqnarray} \tag{ 1 }$$

Apart from the fundamental frequency f₀ and its harmonics 2f₀, 3f₀ and 4f₀, as mentioned in Zhou (2006), another two harmonics 5f₀ and 6f₀ are detected. Generally, it is reasonable that a frequency whose signal-to-noise ratio is larger than 4 (i.e. S/N > 4.0) is considered significant (Breger et al. 1993; Kuschnig et al. 1997).

Table 2 lists all the significant frequency solutions including f₀ and its five harmonic frequencies.

Figure 4 shows the amplitude spectra and the pre-whitening procedures for the light curves in the V band observed from 2014 to 2015. The residuals of YZ Boo after fitting all the six significant frequencies are only 0.0087 mag, which indicate the modeled curves fit the light curves well. One should note that we usually do not consider peaks in the low-frequency domain (typically in the range of 0–3 cycles d⁻¹) as significant signals of a variable star, because they originate from instability in instrument sensitivity and variations of sky transparency in the low-frequency domain (Yang et al. 2012).

Zoom In Zoom Out Reset image size

As can be seen from Figures 2 and 3, the modeled curves fit the observed light curves well, which demonstrates that the fundamental frequency and its harmonics can explain the pulsation behavior of YZ Boo. Therefore, YZ Boo is considered as a mono-period variable star since there is only one dependent frequency in the derived frequency.

To examine potential long-term period changes, the classical O – C diagram was constructed. Firstly, the new times of maximumlight for the light curveswere derived. We fitted the light curves around the light maxima using a third or fourth order polynomial. The fitting errors are within uncertainties that are estimated with Monte Carlo simulations of 200 iterations for each light maximum. The error in determination of maximum is from 6 s to 60 s, depending on the data. Thirty-nine new maximum times were obtained in the V band and listed in Table 4.

Secondly, we combined the newly determined times of maximum light with those provided by earlier studies (Eggen 1955; Broglia & Masani 1957; Spinrad 1959; Broglia 1961; Heiser & Hardie 1964; Fitch et al. 1966; Gieren et al. 1974; Langford 1976; Szeidl & Mahdy 1981; Joner & McNamara 1983; Jiang 1985; Peniche et al. 1985; Hamdy et al. 1986; Kim & Joner 1994; Agerer et al. 1999; Agerer & Hubscher 2000, 2003; Derekas et al. 2003; Jin et al. 2003; Hubscher 2005; Hubscher et al. 2006; Klingenberg et al. 2006; Zhou 2006;Ward et al. 2008).

A total of 248 times ofmaximumlight was collected. As in previous studies, we do not consider the maxima that have been derived from either photographic or visual observations. The seven photometrically determined data points omitted by Zhou (2006) and Ward et al. (2008) have also been discarded in this study.

To calculate the O − C values and their corresponding cycle numbers, we adopted the revised ephemeris (Ward et al. 2008),

$$\begin{eqnarray}&&{{\rm{HJD}}}_{\max }=2442146.3552(2)+0.104091576(3)\times E.\end{eqnarray} \tag{ 2 }$$

In this way, the period of YZ Boo is determined as 0.104091579(2), which is near that of Ward et al. (2008). The new period result is a more precise linear ephemeris of

$$\begin{eqnarray}&&{{\rm{HJD}}}_{\max }=2442146.3552(2)+0.104091579(2)\times E.\end{eqnarray} \tag{ 3 }$$

Figure 5 plots the O – C value versus the cycle number of YZ Boo. The standard deviation of the residuals in the linear fit of O – C values is 0.0013^d.

Zoom In Zoom Out Reset image size

As in previous studies, we make a parabolic fit to the 241 data points and obtain a continuously changing period. The new ephemeris is

$$\begin{eqnarray}\begin{array}{lll}{{\rm{HJD}}}_{\max } & = & 2442146.3550(2)+0.104091570(3)\times E\\ & & \ +1.00(13)\times {10}^{-13}\times {E}^{2},\end{array}\end{eqnarray} \tag{ 4 }$$

with the standard deviation of residuals for the parabolic fit to the O – C values being 0.0012^d. The rate of period change (1/P)dP/dt is derived as 6.7(9) ×10⁻⁹ yr⁻¹, which is similar to the results of Zhou (2006) of 5.0(±3) ×10⁻⁹ yr⁻¹, Ward et al. (2008) of 6.3(6) ×10⁻⁹ yr⁻¹ and Boonyarak et al. (2011) of 5.86 ×10⁻⁹ yr⁻¹. As the standard deviations for the residuals of both the linear and parabolic fits are close to each other, we compared the significance for the fits with these two methods using a two-sided F-test with a 95% confidence interval. From this test, no significant difference was found in these two fits. However, the parabolic fits were still meaningful, since we can obtain that the rate of period change for YZ Boo was positive and the order was comparable to the theoretical value. Hence, the two fits are equally acceptable.

5.1. Physical Parameters

5.2. Constraints from f₀

5.3. Constraints from the Period Variations

The rate of period change for YZ Boo shows a positive change based on a long interval of observations. From a theoretical point of view, the period changes caused by stellar evolution in and across the lower instability strip permit an observational test of stellar evolution theory, provided that other physical reasons for period changes can be neglected (Breger & Pamyatnykh 1998).

As indicated by Breger & Pamyatnykh (1998), HADS lie at the intersection of the main sequence and the classical instability strip on the H-R diagram. Consequently, we construct evolutionary models from the zero age main sequence and then evolve them to the end of the post main sequence. As mentioned above, the same values of α_MLT and f_ov were adopted, and the effect of rotation was not considered since YZ Boo is a low-speed rotator with a total velocity of 35 kms⁻¹ (cf. Joner & McNamara 1983).

The evolutionary tracks constructed with Z = 0.0075 for mass from 1.52 M_⊙ to 1.70 M_⊙ are shown in Figure 6.

Zoom In Zoom Out Reset image size

The rates of period change for individual models are also estimated by calculating the slopes of frequencies for adjacent models along the evolutionary tracks versus the corresponding ages. The frequency differences divided by the corresponding time intervals are taken as the rates of period change and marked along the evolutionary tracks on Figure 6.

By comparing both calculated frequencies of the fundamental radial modes of the models with the observed frequencies of YZ Boo, and the theoretical rate of period change and the observationally determined value of YZ Boo, one can obtain: (1) the evolutionary mass of YZ Boo is M = 1.61 ± 0.05 M_⊙, (2) the age of YZ Boo is between 1.30 × 10⁹ yr and 1.58 × 10⁹ yr, and (3) the metal abundance [Fe/H] is about −0.43.

With photometric data observed between 2008 and 2015 from both the Xinglong Station of National Astronomical Observatories, Chinese Academy of Sciences (NAOC) and Nanshan Station of Xinjiang Astronomical Observatory (XAO), we analyzed the pulsations of YZ Boo, and extracted six frequencies, including its fundamental frequency of f₀ = 9.6069 d⁻¹ and its six harmonics, two of which are newly detected. There is no additional frequency found in the residual spectrum after removing these six frequencies. The theoretical light variations of YZ Boo are produced.

The O – C diagram was constructed with 248 times of maximum light either determined from our new observations or collected from the literature, leading to determination of the updated pulsation period of 0.104091579(2)d. In addition, a new ephemeris with a quadratic solution hints at a continuously increasing period change for YZ Boo of (1/P)dP/dt = 6.7(9) × 10⁻⁹ yr⁻¹. This is consistent with the value predicted from our newly calculated stellar models with masses between 1.4 and 1.8 M_⊙. The mass of YZ Boo is then determined as M = 1.61 ± 0.05 M_⊙ and the location of this variable star on the H-R diagram is limited to post main sequence of the evolutionary tracks.

More observations, especially from multi-site campaigns, would help us to search for more potential pulsation frequencies of YZ Boo and provide clues to interpret the observed rate of period change.

Tao-Zhi Yang and Ali Esamdin acknowledge support from the National Natural Science Foundation of China (NSFC, Grant No. 11273051). This work is partially supported by the Chinese Academy of Sciences (CAS) "Light of West China" program (2015-XBQN-A-02) and supported by the Strategic Priority Research Program of CAS (Grant No. XDB23040100). JNF acknowledges support from the Joint Fund of Astronomy of NSFC and CAS (Grant U1231202 and 11673003), the National Basic Research Program of China (973 Program 2014CB845700 and 2013CB834900), and the LAMOST FELLOWSHIP supported by Special Funding for Advanced Users, budgeted and administrated by the Center for Astronomical Mega-Science, Chinese Academy of Sciences (CAMS). GJF acknowledges support from the NSFC (No. 11403088).