# FIRST DETECTION OF MULTI-SHOCKS IN RR LYRAE STARS FROM ANTARCTICA: A POSSIBLE EXPLANATION OF THE BLAZHKO EFFECT

M. Chadid, J. Vernin, G. Preston, C. Zalian, C. Pouzenc, L. Abe, A. Agabi, E. Aristidi, L.Y. Liu, D. Mekarnia, et al.

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► To cite this version:

M. Chadid, J. Vernin, G. Preston, C. Zalian, C. Pouzenc, et al. FIRST DETECTION OF MULTI-SHOCKS IN RR LYRAE STARS FROM ANTARCTICA: A POSSIBLE EXPLANATION OF THE BLAZHKO EFFECT. The Astronomical Journal, 2014, 148 (5), pp.88. 10.1088/0004-6256/148/5/88. hal-02453215

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Distributed under a Creative Commons Attribution 4.0 International License
FIRST DETECTION OF MULTI-SHOCKS IN RR LYRAE STARS FROM ANTARCTICA*:
A POSSIBLE EXPLANATION OF THE BLAZHKO EFFECT

M. CHADID<fnref n="1" />, J. VERNIN<fnref n="1" />, G. PRESTON<fnref n="2" />, C. ZALIAN<fnref n="1" />, C. POUZENC<fnref n="1" />, L. ABE<fnref n="1" />, A. AGABI<fnref n="1" />,
E. ARISTIDI<fnref n="1" />, L. Y. LIU<fnref n="3" />, D. MÉKARNIA<fnref n="1" />, AND H. TRINQUET<fnref n="4" />

Received 2014 April 9; accepted 2014 July 14; published 2014 October 9

ABSTRACT

We present the first detection of multi-shocks propagating through the atmosphere of the Blazhko star S Arae using uninterrupted, accurate optical photometric data collected during one polar night, 150 days from Antarctica at Dome C, with the Photometer Antarctica eXtinction (PAIX). We acquired 89,736 CCD frames during 323 pulsation cycles and 3 Blazhko cycles. We detected two new light curve properties in the PAIX light curve, *jump* and *rump*, which we associated with two new post-maximum shock waves ShPM1 and ShPM2. *jump*, *lump*, *rump*, *bump*, and *hump* are induced by five shock waves, with different amplitudes and origins, ShPM1, ShPM, ShPM2, ShPM3, and the main shock ShH+He. Correlations between the length of rise time and light amplitude and ShPM3 are monotonous during three Blazhko cycles, but the pulsation curve is double peaked. We discuss the physical mechanisms driving the modulation of these quantities. Finally, we hypothesize that the origin of the Blazhko effect is a dynamical interaction between a multi-shock structure and an outflowing wind in a coronal structure.

**Key words:** hydrodynamics – methods: observational – stars: atmospheres – stars: oscillations – stars: variables: general – techniques: photometric

*Online-only material:* animation, color figures

1. INTRODUCTION

Several types of pulsating stars show evidence of shock
waves (Anderson 2006) propagating through their atmosphere
(Wallerstein & Elgar 1992; Preston & Paczynski 1964).
Schwarzschild (1952) invoked the propagation of shock waves
across the atmosphere of W Virginis stars to explain the double
absorption lines during the rise-time phase duration of the as-
cending branch of the light curve. The first quantitative model
of shock waves was developed by Whitney (1956) in W Virgi-
nis stars, as reported by Wallerstein (1959). Iroshnikov (1962)
developed a model in which a shock wave propagates through
an exothermic gas in the atmosphere of RR Lyr. Hill (1972) in-
terpreted, using a hydrodynamic pulsation model, the existence
of the *bump* (occurring just before the minimum of the light
curve) and *hump* (occurring just before the maximum of the
light curve) as a consequence of two shocks propagating through
the atmosphere of RR Lyr. The main shock created by the κ and
γ mechanisms induces the hump. The early shock caused by the
collision between the infalling high atmosphere and the expand-
ing photosphere induces the bump (hereafter ShHill). Using ultra-
violet photometric observations, Hutchinson et al. (1977) found
that the bump in the light curve before rising light and the stand-
still in rising light are due to two separate shock waves. Chadid
et al. (2008) detected hypersonic shock evidence in the photo-
sphere of RR Lyrae stars, in particular in the Blazhko star S Arae.
A new bump in the light curve has been recently detected, the
*lump* (occurring when the radius of the star is near its maxi-
mum), by Chadid & Preston (2013). They explained the origin of
the lump as a consequence of a new post-maximum shock wave
ShPM created by a superimposition of the compression due to

the hydrogen recombination front and an accumulation of weak
compression waves.

A substantial fraction of RRab stars exhibit the Blazhko effect (Blazhko 1907): modulation of the light curve on timescales of tens to thousands of pulsation periods. The cause of the phenomenon remains enigmatic. Three main hypotheses have been advanced: (1) the resonance between the fundamental mode, the first overtone mode, and a higher mode (Buchler & Kollath 2011); (2) the oblique-dipole magnetic rotator model (Shibahashi 2000), ruled out by Chadid et al. (2004); and (3) variation of turbulent envelope convection during the Blazhko cycle (Stothers 2010, 2011). Recent extensive photometry from space (Chadid et al. 2010a; Chadid 2011) confirms the irregularities in Blazhko cycles noted previously by many ground-based observers.

We briefly describe the Antarctica photometric observations
and analysis in Section 2. Modulation of the pulsation and
dynamical parameters over the Blazhko cycle are discussed
in Section 3. The first multi-shock detection is described in
Section 4. In Section 5, we discuss the origin of the Blazhko
effect and its connection with the hydrodynamical phenomena.
Finally, some conclusions and remarks are given in Section 6.

2. ANTARCTICA OBSERVATIONS AND
FREQUENCY ANALYSIS

We present the first optical photometric data from Dome C at
a height of 3300 m and a 75°06 minutes 04 s S, 123°20 minutes
52 s E position on the Antarctica plateau. The observations
were performed under the extreme conditions that prevail
in the heart of Antarctica, using the Photometer Antarc-
tica eXtinction (PAIX; Chadid et al. 2010b) attached to a
40 cm Ritchey-Chretien f/10 telescope located at Dome C,
unsheltered, on an ice field. The setup of PAIX was improved by

<footnote n="1">¹ Université Nice Sophia-Antipolis, Observatoire de la Côte d'Azur, UMR 7293, Parc Valrose, F-06108 Nice Cedex 02, France; chadid@unice.fr</footnote>

<footnote n="2">² Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101, USA</footnote>

<footnote n="3">³ National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China</footnote>

<footnote n="4">⁴ DGA Matrise de l'Information, BP 7, F-35998 Rennes Armees, France</footnote>

<footnote>* Based on observations collected from Antarctica at Dome C, using the PAIX telescope, during the polar night 2009.</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** PAIX light curve of S Arae over 150 days—one polar night—from Dome C, Antarctica.
(A color version of this figure is available in the online journal.)</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Two-dimensional PAIX light curve of S Arae folded with the pulsation period (0.452) over three Blazhko cycles and showing a strong Blazhko strength.
(A color version of this figure is available in the online journal.)</figcaption></figure>

the use of a new camera, SBIG ST10–XME, yielding images of 728 × 490 pixels with 3 × 3 binning across a 12.4 × 8.3 field of view. The camera is cooled with a Peltier assembly with temperature regulation. The quantum efficiency of the KAF 3200 ME CCD is 60%, 65%, 85%, 75%, 55%, and 30% at 400, 500, 600, 700, 800, and 900 nm, respectively. PAIX was antarctized to run under extreme conditions at temperatures as low as –80°C. The 40 cm telescope and the photometer PAIX, installed at Dome C in 2006, were designed and built by PaixTeam at Université Nice Sophia–Antipolis.

A continuous, quasi-uninterrupted series of photometric observations was collected during one polar night—150 nights—from 2009 April 18 to September 20 (Figure 1), with Earth’s day–night duty cycle of 65%. The seeing reaches a median value of 1" (Vernin et al. 2009; Giordano et al. 2012). Figure 2 shows the PAIX light curve of S Arae. The V-magnitude varies between 10 and 11.5 mag, with an accuracy of 0.025 mag, in a period of 0.452 days and a Blazhko period of 48.544 ± 0.045 days. A

total of 89,736 CCD frames were acquired with 40–60 s integration times and a high optical photometric accuracy, allowing an average time resolution $T/P$ around 0.15% of the pulsation period, where $T$ is the exposure time and $P$ the pulsation period. We calibrated the CCD frames every 2 hr using five twilight flat fields and a series of bias frames. Flat fields were obtained using horizon pointing when the Sun was below the horizon. We estimate magnitudes using four standard stars identified in the NOMAD1 (Zacharias et al. 2005) catalog as 04050770258, 086, 296, and 04050769976.

S Arae shows a strong amplitude variation during its 48.5 day Blazhko cycle. Table 1 summarizes properties of the photometric data used herein. The data set covers 3 Blazhko cycles and 323 pulsation periods. The frequency analysis was performed using the PDM13 (Zalian et al. 2014a) and Period04 (Lenz & Breger 2005) packages. The details and strategies of the frequency analysis studies can be found in C. Zalian et al. (2014, in preparation).
<table><caption>**Table 1**
Pulsation and Blazhko Periods, Total and Modulation Amplitudes, Phase Variation, Magnitude, and Rise Time Minimum of the Blazhko Star S Arae</caption><thead><tr><th>ID</th><th>R.A.</th><th>Decl.</th><th>P</th><th>P<sub>B</sub></th><th>Atot.</th><th>Amod.</th><th>ΔP/P</th><th>Magnitude</th><th>Min. Rise</th></tr></thead><tbody><tr><td>S Arae</td><td>17:59:11</td><td>-49:26:00</td><td>0.452 days</td><td>48.544 days</td><td>1.300</td><td>0.500</td><td>0.002</td><td>10.27 mag</td><td>11%</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** PAIX light curve of S Arae folded by the pulsation period. Representative averaged light curves are shown in two extremal modulation Blazhko phases: $\psi = 0.00$ (red line) and $\psi = 0.50$ (green line).</figcaption></figure>

(An animation and a color version of this figure are available in the online journal.)

### 3. MODULATION OF THE PULSATION AND DYNAMICAL PARAMETERS OVER THE BLAZHKO CYCLE

Figure 3 shows the PAIX light curve of S Arae folded with the pulsation period. The light curve was fitted with an analytical signal using a polynomial fit of the observed data. Table 1 gives parameters related to the modulation and pulsation. The phase modulation is defined as the period variation. We define the total amplitude in the following way. We fit the maximum and minimum brightness values of each pulsation cycle using a high-order harmonic fit. The difference between these curves defines the amplitude. The maximum of the amplitude is the total amplitude, and the range of amplitude is the modulation amplitude.

S Arae shows an extremely large Blazhko strength with the largest modulation amplitude ($Amod = 0.50$) detected so far and a small phase variation ($\Delta P/P = 0.002$). As discussed by Chadid et al. (2008), we use the rise time to characterize the strength of the main shock. S Arae possesses a strong main shock (minimum rise time $= 0.11$ P) and, likewise, exhibits a large variation in its Blazhko modulation.

Figure 4 demonstrates the evolution of the period changes, the amplitude and rise changes, and amplitude of the bump over three Blazhko cycles, with an accuracy of 0.010 days, 0.0013 mag, 0.0065 phase unit, and 0.00035 mag, respectively. The variations are regular from extrema to extrema. The rise time and amplitude of the bump show a periodic variation equal to the Blazhko period. The rise time variation is in antiphase with that of the amplitude and shows an elbow at the maximum, while the period variation exhibits bimodal behavior. Two maxima are detected, the greater one (first peak) appears at the maximum of the rise time and the minimum of the amplitude. The second peak occurs at the minimum of the

rise time and the maximum of the amplitude. The evolution of the amplitude of the bump is periodically variable during the Blazhko modulation with a period equal to the Blazhko period. The amplitude of the bump varies in phase with the amplitude. The bump amplitude changes exhibit a shoulder at the minimum. The shock strength, related to the amplitude, increases from $\psi = 0.50$ to $\psi = 0.00$ as the bump grows and approaches the primary light maximum.

In Figure 4, both the amplitude-period and the rise-period Lissajous diagrams show a complex structure. The diagrams show that there are strong shape changes that repeat during three consecutive Blazhko cycles, and the width of the rise-period diagram shows a strong phase shift in the rise and period curves. Finally, the amplitude-period diagram shows a significant phase shift as well in the amplitude curve.

### 4. MULTI-SHOCK DETECTION

#### 4.1. Jump, Lump, Rump, Bump, and Hump

Figure 5 shows the light curve of S Arae, showing the lump, bump, and hump<fnref n="5" /> (as described in Chadid & Preston 2013). The most striking feature is that the descending branch of the light curve demonstrates the existence of new bumps at phases $\varphi = 0.10$ and $\varphi = 0.70$. We call them *jump* and *rump*. The jump occurs just after maximum light and the rump appears very close to the bump.

Figure 6 demonstrates the evolution of the light curve over one Blazhko cycle. The lump and rump show a systematic change with the Blazhko period. The rump is clearly observed roughly between the Blazhko phases $\psi = 0.40$ and $\psi = 0.80$ and coincides with the bump between the Blazhko phases $\psi = 0.80$ and $\psi = 0.40$. Figure 7 illustrates the first derivative of the S Arae light curve over three Blazhko cycles. The red color means a positive slope and the blue a negative one. The red to blue transition corresponds to a maximum in the light curve. The hump, rump, and bump are well detected, but the jump and the lump do not denote a local maximum since they are supported by a too steeply decreasing line. The bump is well followed between Blazhko phases $\psi = -0.10$ and $\psi = 0.20$ during one-third of each Blazhko cycle. We suggest that the jump and rump might be a consequence of two shock waves (hereafter $\text{Sh}_{\text{PM1}}^6$ and $\text{Sh}_{\text{PM2}}$, respectively) propagating in the atmosphere of S Arae.

#### 4.2. Shock Dynamics

The detection of the jump, lump, rump, bump, and hump points out that the atmosphere of the Blazhko star S Arae is crossed by several shock waves with a different amplitude and physical origin.

The $\text{Sh}_{\text{PM1}}$ associated with the jump occurs at the beginning of the atmospheric compression, at phase $\varphi = 0.10$. This infalling shock may be created by an accumulation of several weak

<footnote n="5">⁵ According to the adopted nomenclature used by Christy (1966).</footnote>

<footnote n="6">⁶ Post-maximum shock.</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Pulsation period, amplitude, bump maximum, and rise time as a function of time. The rise-period diagram and the amplitude-period diagram are shown at the first (black), second (red), and third (green) Blazhko cycles of S Arae.</figcaption></figure>

(A color version of this figure is available in the online journal.)

<figure><img src="image_7.png" /><figcaption>**Figure 5.** PAIX light curve of S Arae showing the hump, jump, lump, rump, and bump.</figcaption></figure>

(A color version of this figure is available in the online journal.)

compression waves occurring in the high part of the atmosphere of S Arae. The ShPM related to the lump, first detected by Chadid & Preston (2013), appears at phase $\varphi = 0.35$ and is interpreted as a superimposition of the compression due to the hydrogen recombination front and the ShPM1.

The ShPM2 connected to the rump is detected very close to the bump at phase $\varphi = 0.70$. ShPM2 could be a superimposition of a colliding shock and ShPM.

The bump is associated with ShPM3 as a result of the two shocks, ShHill and ShPM2. The hump, as described by Chadid &
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Evolution of the PAIX light curve of S Arae over the first Blazhko cycle. The dots are all the data in the Blazhko cycle folded with the pulsation period. The Blazhko phase $\psi = 0.00$ corresponds to the maximum amplitude.</figcaption></figure>

(A color version of this figure is available in the online journal.)

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Map of the first derivative of the PAIX light curve of S Arae over three Blazhko cycles. The red color indicates a positive derivative and the blue one a negative derivative.</figcaption></figure>

(A color version of this figure is available in the online journal.)
Preston (2013), is connected to the main shock, ShH and ShHe (hereafter ShH+He), created by the κ and γ mechanisms, respectively. The intensity of the main shock is correlated with the strength of the κ and γ mechanisms, and the latter is connected with the compression ratio, i.e., the compression pressure of the photosphere.

The ShPM1, ShPM, ShPM2, and ShPM3 are receding shocks in Eulerian rest coordinates while they are advancing shocks in the Lagrangian coordinates. The main shock ShH+He is the only shock to move outward of the center of S Arae. If we assume that the rise time characterizes the intensity of the main shock caused by the κ and γ mechanisms, then, as demonstrated in Figure 4, the maximum intensity of the main shock occurs at the maximum amplitude ($\psi$ = 0.00) and during the second peak of the pulsation period, while the minimum intensity of the main shock occurs at the minimum amplitude ($\psi$ = 0.50) during the first peak of the pulsation period. The shock induces the bump (ShPM3), showing a maximum intensity when the main shock is stronger and a minimum when the main shock is weaker. The strength variation of the shock (ShPM3) and the main shock (ShH+He) are in phase. The main shock intensity increases with the increase in the amplitude and the shock (ShPM3) intensity and decreases with the decrease in the amplitude and the shock (ShPM3) intensity. The elbow of the rise time indicates that the main shock is stationary during the descending branch of the first peak of the pulsation period. From that, we may hypothesize the following scenario on the hydrodynamical structure of the atmosphere of S Arae. The main shock plays a major role in the non-synchronization of the photosphere layers: the stronger the main shock, the more important the non-synchronization. When the amplitude is at the maximum at $\psi$ = 0.00, the main shock reaches its maximum intensity and then the photospheric motion is no longer synchronized, implying, at the next pulsation cycle, a smaller compression ratio and then a weaker strength of the κ and γ mechanisms. Thus, the main shock intensity gradually decreases down to the phase of the minimum amplitude $\psi$ = 0.50. The photosphere motion comes back to the synchronized phase when the non-synchronization phenomenon disappears with the decrease in the shock intensity. We estimate that the Blazhko phase interval [0.00, 0.50] is the synchronization phase, and the Blazhko phase interval [0.50, 0.00] is the non-synchronization phase. The pulsation period demonstrates a reversible motion at both synchronization and non-synchronization phases. The ShPM3, inducing the bump, is stronger at the non-synchronization phase and weaker at the synchronization phase.

## 5. HYDRODYNAMICAL AND BLAZHKO EFFECTS

At the Blazhko minimum phase $\psi$ = 0.50, the amplitude is at the minimum, the rise time is at the maximum, the shock intensity is smaller, the amplitude of the bump is lower, and the light curve of the star Blazhko S Arae roughly looks like an RRc light curve, whereas at the Blazhko phase maximum $\psi$ = 0.00, the amplitude is at the maximum, the rise time is at the minimum, the shock intensity is higher, the amplitude of the bump is stronger, and the light curve of S Arae is similar to an RR ab light curve (Figure 3). We hypothesize then that S Arae undergoes temporary cyclic transitions from the RR ab to RR c states during its Blazhko cycles. At $\psi$ = 0.00, S Arae is an RR ab pulsating star and at $\psi$ = 0.50, it is an RR c star.

During the non-synchronization phase at the Blazhko phase interval [0.50, 0.00], the main shock progressively increases and then the amplitude increases, in a similar vein to the ShPM3 intensity. Once the non-synchronization motion reaches the

maximum level at $\psi$ = 0.00, the shock intensity and then the strength of the κ and γ mechanisms show the maximum value. In this condition, the shocks develop a stationary coronal structure and drive an outflowing wind (Stellingwerf 2013). The latter gradually minimize the overall compression of the atmosphere, the strength of κ-γ mechanisms and the main shock progressively decrease, and the atmosphere layers gradually return to their synchronized motion at the Blazhko phase interval [0.00, 0.50]. Perhaps, the outflowing wind (Stellingwerf 2013) plays the major role of a trigger mechanism acting on the κ and γ mechanisms. We suggest that the Blazhko effect is a consequence of dynamical interaction between a multi-shock structure and the outflowing wind of a Stellingwerf corona. Further theoretical investigations are required toward a quantitative explanation of the mechanism of the Blazhko effect and its connection with the multi-shock structure in the atmosphere of RR ab stars.

## 6. CONCLUSIONS

We present the first detection of multi-shocks propagating through the atmosphere of the Blazhko star S Arae using long, quasi-uninterrupted, and highly accurate optical photometric data collected with PAIX over one polar night, 150 days, at the Dome C base. We find (1) that S Arae shows an extremely large Blazhko strength with the largest modulation amplitudes detected so far; (2) two new bumps in the PAIX light curve, jump and rump, that we associated with two new post-maximum shock waves ShPM1 and ShPM2; (3) five shock waves with different amplitudes and origins, ShPM1, ShPM, ShPM2, ShPM3, and the main shock ShH+He. The five shocks show a systematic change with the Blazhko period; (4) the variation of the main shock intensity is in phase with those of the bump, ShPM3, and the amplitude, while the curve of the period changes shows a double-peak phenomenon; and, finally, (5) the Blazhko effect in RR ab stars may be explained as a dynamical coupling interplay between a multi-shock structure and an outflowing wind in a coronal structure.

We thank the US Air Force Research Laboratory, Agence Nationale de la Recherche (ANR-05-BLAN-0033-01), and Conseil des Programmes Scientifiques et Technologiques (CPST) for their great support and the Polar Institute Paul Emile Victor (IPEV) for precious infrastructure help. M. Chadid is indebted to everyone who participated in the Antarctica expeditions within the PAIX framework.

We acknowledge Robert Stellingwerf for his reading of the manuscript and suggestions.

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