c Pleiades Publishing, Inc., 2014. ISSN 1063-7737, Astronomy Letters, 2014, Vol. 40, No. 7, pp. 435–448. c I.A. Usenko, A.Yu. Kniazev, L.N. Berdnikov, A.B. Fokin, V.V. Kravtsov, 2014, published in Pis’ma v Astronomicheski˘ı Zhurnal, 2014, Vol. 40, No. 7, Original Russian Text pp. 484–497.
Spectroscopic Studies of Southern-Hemisphere Cepheids: Three Cepheids in Crux (BG Cru, R Cru, and T Cru) I. A. Usenko1, 2* , A. Yu. Kniazev3, 4, 5 , L. N. Berdnikov5 , A. B. Fokin6 , and V. V. Kravtsov5, 7 1
Astronomical Observatory, Odessa National University, Shevchenko Park, Odessa, 65014 Ukraine 2 Nikolaev Astronomical Observatory, Observatornaya ul. 1, Nikolaev, 54030 Ukraine 3 South African Astronomical Observatory, 7925 Observatory, Cape Town, South Africa 4 Southern African Large Telescope Foundation, 7925 Observatory, Cape Town, South Africa 5 Sternberg Astronomical Institute, Lomonosov Moscow State University, Moscow 119991, Russia 6 Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya ul. 48, Moscow, 119017 Russia 7 ´ Universidad Cat’olica del Norte, Avenida Angamos 0610, Antofagasta, Chile Instituto de Astronomia, Received September 10, 2013
Abstract—This paper is devoted to spectroscopic studies of three bright Cepheids (BG Cru, R Cru, and T Cru) and continues the series of our works aimed at determining the atmospheric parameters and chemical composition of southern-hemisphere Cepheids. We have studied 12 high-resolution spectra taken with the 1.9-m telescope of the South African Astronomical Observatory and the 8-m VLT telescope of the European Southern Observatory in Chile. The atmospheric parameters and chemical composition have been determined for these stars. The averaged atmospheric parameters are: Teff = 6253 ± 30 K, log g = 2.15, Vt = 4.30 km s−1 for BG Cru; Teff = 5812 ± 22 K, log g = 1.65, Vt = 3.80 km s−1 for R Cru; and Teff = 5588 ± 21 K, log g = 1.70, Vt = 4.30 km s−1 for T Cru. All these Cepheids exhibit a nearly solar metallicity ([Fe/H] = +0.04 dex for BG Cru, +0.06 dex for R Cru, and +0.08 dex for T Cru); the carbon, oxygen, sodium, magnesium, and aluminum abundances suggest that the objects have already passed the first dredge-up. The abundances of other elements are nearly solar. An anomalous behavior of the absorption lines of metals (neutral atoms and ions) in the atmosphere of the small-amplitude Cepheid BG Cru is pointed out. The main components in these lines split up into additional blue and red analogs that are smaller in depth and equivalent width and vary with pulsation phase. Such splitting of the absorption lines of metals (with the hydrogen lines being invariable) is known for the classical Cepheid X Sgr. The calculated nonlinear pulsation model of BG Cru with the parameters L = 2000 L , Teff = 6180 K, and M = 4.3 M shows that this small-amplitude Cepheid pulsates in the first overtone and is close to the blue boundary of the Cepheid instability strip. According to the model, the extent of the Cepheid’s atmosphere is relatively small. Therefore, no spectroscopic manifestations of shock waves through variability are possible in this Cepheid and the observed blue and red components in metal absorption lines can be explained solely by the presence of an extended circumstellar envelope around BG Cru. DOI: 10.1134/S106377371407007X Keywords: Cepheids, spectra, atmospheric parameters, chemical composition, circumstellar envelopes.
INTRODUCTION We present our fourth work devoted to the studies of southern-hemisphere variable yellow supergiants based on observations performed at the South African Astronomical Observatory. In the first part (Berdnikov et al. 2010), we formulated the main goals and tasks of our studies and presented the first results of determining the atmospheric parameters and *
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chemical composition for six classical Cepheids. In the second part (Usenko et al. 2011), we obtained similar estimates for eight more classical Cepheids and three bright supergiants falling into the Cepheid instability strip. In the third paper (Usenko et al. 2013), we presented our results for six Cepheids, two of which are members of open star clusters and two more objects are Cepheids with extended envelopes, one of which (X Sgr) is known for the anomalous behavior of metal absorption lines. In this paper, we present the results of our spectroscopic studies 435
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Table 1. Information about the objects and observations Cepheid
α (2000.0)
δ (2000.0)
V (mag.)
Exposure time, min
Vr , km s−1
HJD 2450000+
Signal-to-noise ratio
BG Cru
12 31 40.3
–59 25 26
5.49
40
−17.73 ± 0.14
5784.2683
52
40
−13.59 ± 0.13
5785.2262
75
40
−20.23 ± 0.16
5787.2500
108
40
−19.53 ± 0.18
5789.2264
120
20
−23.32 ± 0.17
5790.2977
69
8
–
5279.9979
200
60
−24.96 ± 0.11
5785.2752
33
60
−7.32 ± 0.12
5787.2950
54
40
+2.71 ± 0.12
5788.2839
49
20
−31.32 ± 0.17
5790.2224
62
40
−5.22 ± 0.09
5787.2139
62
40
−7.54 ± 0.11
5790.2580
75
(VLT) R Cru
T Cru
12 23 37.7
12 21 21.1
–61 37 45
–62 16 54
6.77
6.57
for three Cepheids in Crux. The Cepheid BG Cru was previously suspected of the presence of nonradial pulsations owing to the bumps on the blue side of metal absorption lines (Kovtyukh et al. 2003). We have already studied the Cepheid T Cru in our first paper (the results of our abundance analysis based on a single spectrum), while the spectroscopic studies for R Cru are carried out for the first time. OBSERVATIONS AND PRIMARY REDUCTION Our observations were performed in August 2011 with the GIRAFFE (Grating Instrument for Radiation Analysis with a Fiber Fed Echelle) fiber echelle spectrograph mounted at the Coude focus of the 1.9-m telescope at the South African Astronomical Observatory (SAAO, South African Republic). We took 11 spectra for the three Cepheids: two for T Cru, four for R Cru, and five for BG Cru. To improve the quality of our spectroscopic data, two or three spectra were taken for each object in succession on
each observing night with the same exposure time, which were summed after the primary reduction. In addition, we used four of the eight spectra taken on August 7, 2001, for several minutes with the Very Large Telescope (VLT) of the European Southern Observatory (ESO), which were summed into one combined spectrum tied to the averaged time of observations. These spectra were retrieved from the ESO archive. Information about the objects and some details of our observations are presented in Table 1. Its columns from the first to the eighth give, respectively, the object name, its equatorial coordinates α and δ (epoch 2000), the period P of brightness variations from GCVS-4 (Kholopov et al. 1986), the mean V magnitude taken from the catalog by Berdnikov et al. (2000), the exposure time, the heliocentric radial velocities Vr that we determined from the spectra described in this paper together with their errors, the mid-exposure heliocentric Julian date HJD, and the summed signal-to-noise ratio. The signal-tonoise ratio for wavelength in the range 5000–6000 A˚ ASTRONOMY LETTERS
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was calculated using a robust AMD (Absolute Mean Deviation) estimate (Kniazev et al. 2004) for each of the individual spectra. The corresponding signal-tonoise ratio for each summed spectrum was calculated √ as n(S/N), where n is the number of individual spectra and (S/N) is the signal-to-noise ratio for an individual spectrum (this value was assumed to be approximately the same). The signal-to-noise ratio for each of the four spectra from the ESO archive was about 100. As has already been mentioned in our previous papers (Berdnikov et al. 2010; Usenko et al. 2011, 2013), GIRAFFE is a copy of the MUSICOS spectrograph designed at the Meudon observatory (Bau¨ drand and Bohm 1992) and allows high-resolution (R = 39 000) echelle spectra to be obtained in the ˚ For our observations, spectral range 3820–10 400 A. we used a prism optimized for the spectral range 5200–10 400 A˚ and an optical fiber with a diameter of 50 μm. The detector was a 1024 × 1024-pixel TEK6 CCD camera. The total recorded spectral ˚ contained 52 spectral orders. range (4250–7100 A) For all three objects, the spectral range used for our ˚ analysis was 4250–6750 A. The full process of taking spectra and reducing CCD images is described in detail in our previous papers (Berdnikov et al. 2010; Usenko et al. 2011, 2013). As has been said above, to increase the signalto-noise ratio and to remove cosmic-ray particle hits, we summed two (or three) spectra of the same object taken in succession followed by median filtering. We determined the radial velocities using the cross-correlation technique in the XSPEC2 software package designed for GIRAFFE echelle spectra (Balona 1999). The accuracy of determining Vr is 0.1–0.3 km s−1 . The spectra from the ESO archive were taken with the UVES echelle spectrograph (Dekker et al. ˚ and red (λ = 2000) in the blue (λ = 4780−5800 A) ˚ wavelength ranges with the resolution 5850−6800 A) R = 80 000. Each of the ranges consisted of 15 spectral orders. We reduced the spectra with the DECH 20 software package (Galazutdinov 1992). The equivalent widths of absorption lines for R Cru and Y Cru were measured either by Gaussian fitting or by direct integration. For BG Cru, we used only direct integration because of its complex absorption line profiles. ASTRONOMY LETTERS
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MODEL PARAMETERS To calculate the chemical composition of a star, it is first necessary to determine its effective temperature Teff , surface gravity log g, and microturbulent velocity Vt . The effective temperatures Teff were determined by a method based on the depth ratios of selected pairs of spectral lines most sensitive to the temperature. Several spectroscopic criteria (Kovtyukh 2007) were used in this case. This method provides an internal accuracy of ∼10–30 K for Teff (the error of the mean). The microturbulent velocity Vt was determined from the condition for the Fe II abundance derived from a set of lines being independent of their equivalent widths (Kovtyukh and Andrievsky 1999). The surface gravity log g was determined from the ionization equilibrium condition for Fe I and Fe II atoms. The derived atmospheric parameters for the summed pairs of spectra are listed in Table 2. It also provides the calculated times of maxima and pulsation periods. When estimating the atmospheric parameters and chemical composition, we used the solar oscillator strengths (Kovtyukh and Andrievsky 1999) and model atmospheres from Kurucz (1992). More detailed information about the methods of determining the atmospheric parameters of our program stars and their measurement errors is given in our previous paper (Berdnikov et al. 2010). CHEMICAL COMPOSITION We determined the chemical composition of the program stars in the LTE approximation using the WIDTH9 code and a grid of models from Kurucz (1992). Tables 3, 4, and 5 present the derived elemental abundances relative to the Sun [El/H] with their errors σ and give the number of lines NL used for each element. Complete information about the influence of uncertainties in determining the atmospheric parameters on the elemental abundance estimates was provided in our previous paper (Berdnikov et al. 2010). DISCUSSION BG Cru. This small-amplitude (DCEPS) Cepheid of spectral type F7 Ib–II is known for its asymmetric profiles of metal absorption lines (Kovtyukh et al. 2003). Based on a single spectrum taken by D. Bersier with the 74-inch telescope of the Mount Stromlo Observatory (MSO) in 1999 (HJD = 2451231.6472, the pulsation phase φ = 0.799 according to the ephemeris in Table 2, the wavelength ˚ the resolution R = 56 000, range λ = 5500−6800 A,
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Table 2. Atmospheric parameters and light elements for the program Cepheids Star
HJD 2450000+
Teff , K
log g
Vt , km s−1
Time of maximum, 2450000+
Period, day
Phase
BG Cru
5784.2683
6225 ± 35
2.10
4.00
5080.9200
3.341965
0.460
5785.2262
6140 ± 28
2.00
4.50
0.746
5787.2500
6264 ± 26
2.20
4.60
0.352
5789.2264
6416 ± 25
2.20
4.20
0.943
5790.2977
6218 ± 34
2.20
4.20
0.264
(VLT)
5279.9979
6192 ± 8
2.10
3.70
0.569
R Cru
5785.2752
6008 ± 29
1.70
3.40
5787.2950
5521 ± 17
1.50
4.00
0.530
5788.2839
5412 ± 14
1.60
4.40
0.700
5790.2224
6305 ± 28
1.80
3.50
0.032
5787.2139
5417 ± 14
1.60
4.50
5790.2580
5792 ± 17
1.70
4.50
T Cru
and the signal-to-noise ratio 50), the authors suspected this Cepheid of the presence of nonradial pulsations (see Fig. 1 in Kovtyukh et al. (2003), where the authors point to the bumps in the blue parts of the wings of two strong neutral iron absorption lines). The atmospheric parameters for this spectrum turned out to be Teff = 6101 ± 30 K, log g = 2.0, and Vt = 3.80 km s−1 (Kovtyukh et al. 2003). The chemical abundances for some of the elements were derived from a small number of absorption lines (Andrievsky et al. 2002), which are given in Table 3. In addition, according to Szabados (1989), BG Cru is a spectroscopic binary with an orbital period within the range 4050–6650 days and a companion of possible spectral type A1 V (Evans 1992). We took five spectra during a one-week set of observations (see Table 1). The radial velocities are given in the same table. For our analysis, we also used the spectrum summed from several shortexposure spectra taken in succession at VLT ESO with the UVES spectrograph on August 7, 2002. The Cepheid’s atmospheric parameters and the phases for
5172.5100
5164.9700
5.825701
6.733060
0.183
0.416 0.868
all six spectra are listed in Table 2. Figure 1 shows the radial velocity, effective temperature, surface gravity, and microturbulent velocity variations with pulsation phase for the star. Only our data are presented for the plot of radial velocity variations, while the values obtained with the 74-inch MSO telescope and VLT ESO were added for the remaining plots. As can be seen from Fig. 1, the curves of Vr , Teff , and log g variations exhibit a steep rise of the ascending branch and a gentler fall of the descending branch. This curve shape is more typical of the fundamentalmode pulsations than the overtone ones. No such picture is observed for the turbulent velocity. The mean atmospheric parameters of BG Cru are Teff = 6253 ± 30 K, log g = 2.15, and Vt = 4.30 km s−1 . Figure 2 presents the changes of the neutral iron 6055.99 A˚ line profile by analogy with what we presented for X Sgr in our previous paper (Usenko et al. 2013). As can be seen from Fig. 2a, the line profile shapes are asymmetric and change with pulsation phase. The bumps are noticeable not only on the blue side of the line but also on its red side. For comparASTRONOMY LETTERS
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Vr, km s–1
–0.5 –10
439
0
0.5
1.0
1.5
0
0.5 Phase
1.0
1.5
–15 –20 –25 6500
Teff, K
6400 6300 6200 6100 6000 2.3
log g
2.2 2.1 2.1 2.0
Vt, km s–1
1.9 5
4
3 –0.5
Fig. 1. Curves of Vr , Teff , log g, and Vt variations for BG Cru. The open five-point stars are our observations, the filled five-point stars are those from VLT ESO, and the six-point star is the observation with the 74-inch MSO telescope. The accuracies of determining Vr and Yeff for each data point are listed in Tables 1 and 2.
ison, the dashed curve in the upper part of Fig. 2a indicates a fragment of the averaged (from the five obtained ones) spectrum. The apparent differences of the spectra obtained from the averaged one are clearly seen. To make sure that the bumps actually exist, Fig. 2b presents the profile of the same line but with a resolution twice as higher obtained with VLT ESO: as a result, we clearly see that the secondary blue and red components that stand out very clearly are indeed responsible for the line asymmetry. The same can also be said about the absorption lines of ions (Fig. 3); for example, the same components are seen for Fe II ˚ To show that the 6369.46 A˚ and Si II 6371.355 A. blue and red components are actually present in our ASTRONOMY LETTERS
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spectra, Fig. 4 presents fragments of the spectrum from Fig. 3 divided by the averaged spectrum. The dashed straight lines indicate the ±σ-wide noise band at the mean value of R = 1. We see that the signal level exceeds the noise level, i.e., it is greater than σ, on both sides of the band. The maximum points of the signal exactly correspond to the appearances of the blue and red components. Consequently, our conclusions are quite trustworthy. It can be clearly seen that the line depths of both components change with phase. The fact that the smaller is the depth of the main component, the more distinct are the secondary ones is interesting. We encountered a similar situation for X Sgr, but the main
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Table 3. Elemental abundances for BG Cru SAAO
Species
VLT ESO
[El/H]
σ
NL
[El/H]
σ
CI
–0.25
0.18
36
–0.23
OI
–0.00
0.13
10
Na I
+0.28
0.12
Mg I
+0.10
Al I
Andal02 NL
[El/H]
σ
NL
0.08
6
–0.18
0.10
4
–0.01
0.08
3
+0.08
–
1
20
+0.20
0.15
4
+0.24
–
1
0.23
21
–0.13
0.06
3
–
–
–
+0.27
0.25
10
+0.19
0.06
2
+0.29
0.10
2
Si I
+0.17
0.11
60
+0.03
0.11
18
+0.07
0.11
8
Si II
–0.00
0.23
4
+0.11
0.26
2
+0.27
–
1
SI
+0.04
0.17
17
+0.15
0.10
6
–
–
–
Ca I
+0.09
0.17
52
+0.04
0.19
12
–0.01
0.16
6
Sc I
+0.61
0.24
13
+0.19
0.05
3
–
–
–
Sc II
+0.05
0.14
28
–0.08
0.13
8
–0.33
–
1
Ti I
+0.16
0.17
142
+0.13
0.16
42
+0.18
0.12
4
Ti II
+0.04
0.16
46
+0.17
0.15
6
–0.08
–
1
VI
+0.28
0.15
41
+0.14
0.16
12
+0.20
0.24
2
V II
+0.05
0.20
20
–0.00
0.22
3
+0.05
–
1
Cr I
+0.10
0.26
161
–0.02
0.22
23
+0.09
–
1
Cr II
+0.05
0.16
44
+0.10
0.19
13
–0.06
0.14
7
Mn I
–0.01
0.18
53
–0.07
0.10
11
–0.01
0.15
5
Fe I
+0.04
0.14
615
+0.04
0.15
187
–0.02
0.07
72
Fe II
+0.05
0.10
108
+0.03
0.11
33
–0.01
0.05
16
Co I
+0.13
0.19
64
+0.03
0.22
17
–0.06
–
1
Ni I
+0.02
0.18
268
–0.05
0.14
70
–0.16
0.12
10
Cu I
+0.27
0.19
18
+0.32
0.30
3
–0.68
–
1
Zn I
–0.28
0.32
14
+0.13
0.81
2
–
–
–
Sr I
+0.31
0.37
8
+1.23
0.00
1
–
–
–
Y II
+0.08
0.19
27
+0.16
0.22
8
–0.04
0.12
5
Zr II
+0.16
0.18
20
+0.20
0.18
6
–0.04
–
1
La II
+0.22
0.24
17
–0.01
0.38
3
–
–
–
Ce II
+0.02
0.18
44
+0.06
0.17
8
+0.28
0.07
2
Pr II
+0.14
0.28
10
–0.13
0.26
3
–0.44
–
1
Nd II
+0.12
0.27
61
+0.08
0.20
13
–0.14
0.24
5
Sm II
+0.12
0.20
14
+0.16
0.13
2
–
–
–
Eu II
+0.27
0.08
10
+0.05
0.14
2
–0.14
0.24
5
Gd II
+0.15
0.23
5
–0.14
0.00
1
+0.25
–
1
SAAO—the present paper; VLT ESO—from the VLT ESO spectrum; Andal02—the data from Andrievsky et al. (2002).
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Table 5. Elemental abundances for T Cru
Table 4. Elemental abundances for R Cru
Species
[El/H]
σ
NL
38
CI
–0.20
0.25
31
0.08
9
OI
–0.03
0.13
7
+0.24
0.18
25
Na I
+0.17
0.23
15
Mg I
+0.03
0.20
18
Mg I
+0.07
0.25
10
Al I
+0.11
0.13
7
Al I
+0.16
0.10
7
Si I
+0.07
0.12
82
Si I
+0.06
0.14
60
Si II
+0.22
0.24
5
Si II
+0.11
0.35
5
SI
–0.00
0.33
13
SI
–0.09
0.14
16
Ca I
+0.03
0.18
35
Ca I
+0.06
0.22
52
Sc I
+0.16
0.09
8
Sc I
–0.05
0.27
18
Sc II
–0.06
0.09
15
Sc II
–0.09
0.20
27
Ti I
+0.03
0.21
144
Ti I
+0.03
0.21
228
Ti II
+0.00
0.18
23
Ti II
–0.04
0.16
47
VI
+0.00
0.17
58
VI
+0.03
0.18
75
V II
+0.00
0.33
13
V II
–0.03
0.14
18
Cr I
+0.12
0.23
118
Cr I
+0.05
0.20
186
Cr II
+0.16
0.23
29
Cr II
+0.06
0.18
52
Mn I
–0.19
0.19
42
Mn I
–0.10
0.19
68
Fe I
+0.08
0.14
529
Fe I
+0.06
0.18
684
Fe II
+0.08
0.14
103
Fe II
+0.06
0.12
125
Co I
–0.03
0.21
77
Co I
–0.05
0.21
105
Ni I
–0.05
0.16
245
Ni I
–0.02
0.12
342
Cu I
–0.21
0.19
10
Cu I
+0.11
0.25
15
Zn I
+0.01
0.36
6
Zn I
+0.10
0.46
11
Sr I
+0.25
0.31
4
Sr I
+0.09
0.25
YI
+0.08
0.42
2
7
Y II
+0.05
0.17
16
Y II
+0.04
0.15
23
Zr II
+0.13
0.22
15
Zr II
–0.02
0.10
20
Ru I
+0.01
0.44
2
La II
+0.03
0.18
22
La II
+0.12
0.23
15
Ce II
–0.05
0.19
45
Ce II
+0.05
0.22
32
Pr II
–0.13
0.30
13
Pr II
–0.16
0.35
11
Nd II
+0.02
0.20
62
Nd II
+0.13
0.25
42
Sm II
–0.17
0.21
13
Sm II
+0.11
0.42
7
Eu II
–0.01
0.20
8
Eu II
+0.04
0.11
6
Gd II
–0.03
0.34
4
Gd II
–0.06
0.19
3
Species
[El/H]
σ
NL
CI
–0.20
0.21
OI
–0.03
Na I
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6055 1.15
6056
6057
6368 1.9
6369
6370
6371
6372
6373
Fe II
1.05
1.7
Si II
Phase = 0.943
Phase = 0.943
0.95 Phase = 0.746
1.5
Phase = 0.460
1.3
Phase = 0.746
Phase = 0.460
R
R
0.85 0.75 Phase = 0.352
1.1 Phase = 0.352
0.65 Phase = 0.264
0.9 Phase = 0.264
0.55 0.7
0.45 1.1
0.5 1.05 Phase = 0.569
1.0
Phase = 0.569
R
R
0.95
0.85
0.9
Fe II
Si II
0.8 6055
0.75 6368 6056 Wavelength, Å
6057
Fig. 2. Change of the Fe I 6055.99 absorption line profile with pulsation phase for BG Cru: (a) our observations with R = 40 000; (b) for comparison, the VLT ESO observations of the same line with R = 80 000. The averaged line profile derived from our observations is indicated by the dashed curve in Fig. 2a.
line there split up into 2–3 components more clearly (see Fig. 5 in Usenko et al. 2013). Meanwhile, just as with X Sgr, no such effect is observed for the Hβ and Hα absorption lines (see Figs. 5 и 6). By analogy with our previous work, we may suggest that such an effect is caused either by the presence of nonradial pulsations or by the propagation of shocks during the pulsation period due to the κ mechanism operating in the Cepheid’s atmosphere; both these factors can be due to the existence of its companion mentioned above. We also pointed out in our previous paper (Usenko et al. 2013) that such a strange behavior
6369
6370 6371 6372 Wavelength, Å
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Fig. 3. Change of the Fe II 6369.46 and Si II 6371.355 absorption line profiles with pulsation phase for BG Cru: (a) our observations with R = 40 000; (b) for comparison, the VLT ESO observations of the same lines with R = 80 000. The averaged line profiles derived from our observations are indicated by the dashed curve in Fig. 2a.
of metal and hydrogen absorption lines can also be caused by the presence of an extended circumstellar envelope. As a confirmation, it should be noted that the fraction of the polarized flux p for BG Cru is 0.66 ± 0.035%, comparable to p = 0.775 ± 0.016% estimated for the Cepheid W Sgr (Heiles 2000) that has such an envelope. For comparison, this estimate is even larger for X Sgr: p = 1.708 ± 0.232%. Table 3 listed the abundances of chemical elements in the atmosphere of BG Cru. We separately give the values averaged over our five spectra, over the VLT ESO spectrum, and, for comparison, the results from the spectrum taken with the 74-inch MSO teleASTRONOMY LETTERS
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Phase = 0.352
1.0 0.9 1.1
Phase = 0.264
1.0 0.9 6368
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6370 6371 Wavelength, Å
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Fig. 4. Change in the profiles of the ratios of the Fe II 6369.46 and Si II 6371.355 absorption line profiles to the averaged line profile with pulsation phase for BG Cru. The ±σ-wide noise band at R = 1 is designated by the dashes.
scope (Andrievsky et al. 2002). As can be seen from Table 3, our results obtained from spectrograms with a factor of 2 lower resolution show good agreement with those from the VLT ESO spectrum. BG Cru exhibits a nearly solar iron abundance, a carbon underabundance, nearly solar oxygen and magnesium abundances, and a slight overabundance of sodium and aluminum. The abundances of α-elements, ironpeak elements, r-process elements, heavy and light s-process elements are also nearly solar. Hence we may conclude that the Cepheid has already passed the first dredge-up.
A Nonlinear Pulsation Model for BG Cru Using the radiative hydrodynamic code (Fokin 1990), we computed a series of models for BG Cru with the same 3.34-day period but with different luminosities and effective temperatures with the goal of choosing the model that corresponded primarily to the observed brightness and radial velocity amplitudes. The problem of numerical simulations for specific pulsating stars, as, for example, BG Cru, is that ASTRONOMY LETTERS
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the pulsation computations based on the luminosity, effective temperature, and mass estimates obtained from observations occasionally do not closely correspond to the results of pulsation computations for theoretical models. Another problem related to BG Cru is that its pulsation amplitude is small compared to other Cepheids. As is well known, the Cepheid instability strip (CIS) contains regions where the stars pulsate in different modes. Cepheids with periods of about 3–4 days are believed to pulsate, as a rule, in the first overtone, with the amplitude decreasing as the blue CIS boundary is approached. Since the chemical composition for BG Cru turned out to be nearly solar, we chose one of the models with Y = 0.7 and Z = 0.02. The model is close to the blue CIS boundary; it has a small amplitude and a fairly smooth bolometric light curve. It contains 125 Lagrangian mass zones; the temperature at the lower boundary of its envelope is 1.3 × 106 K, corresponding to an envelope extent of about 80% of the stellar radius. The model has the following input parameters: L = 2000 L , Teff =
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Phase = 0.943
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Phase = 0.746
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R
1.0 0.8
Phase = 0.264
0.6 0.4 0.2 0 –0.2 4850
4855
4860 Wavelength, Å
4865
4870
Fig. 5. Change of the Hβ hydrogen line profile with pulsation phase for BG Cru.
6180 K, and M = 4.3 M . The opacities were calculated using the OPAL92 table for the corresponding chemical composition. Figure 7 presents the output parameters: the theoretical bolometric light curve (upper diagram) and the variations in the radii of the model’s mass zones (lower diagram). Analysis of the output parameters for the model under consideration confirmed that it pulsates in the first overtone. At the beginning of our computations, we specified a velocity profile corresponding to the fundamental mode with an amplitude at the outer boundary of 5 km s−1 for the model. However, after some time, the amplitudes passed into the first overtone with the period observed for BG Cru, with the oscillations having been strictly periodic. As can be seen from Fig. 7, the model shows an asymmetric bolometric light curve for the Cepheid. In the limitcycle regime, the bolometric brightness amplitude was 0m. 38, which is slightly larger than the observed visual one (about 0m. 2). However, given the bolometric correction for F5 supergiants (−0.2), this discrepancy is quite explainable. The velocity amplitude at the photospheric level was 25 km s−1 . As we see, the velocity gradient in the atmosphere is very small due to its small extent. Since the pulsational motions in
the atmosphere are essentially synchronous from the photosphere to the surface, no shock waves arise. Based on this model and several other models with similar parameters, we can reach several conclusions: (1) BG Cru pulsates in the first overtone; (2) the star is very close to the blue CIS boundary, which is responsible for its comparatively small amplitude; (3) in view of the small amplitudes and the small extent of the atmosphere, one cannot expect spectroscopic manifestations of shocks, as, for example, the emission in hydrogen lines or the splitting of metal lines; (4) since the latter phenomenon is clearly observed, its cause should be sought outside the intrinsic variability of BG Cru: as has already been mentioned above, in the presence of an extended circumstellar envelope. R Cru. This Cepheid of spectral type F7 Ib–II may be a member of the open cluster NGC 4349 (Majaess et al., 2012). Its chemical composition has not been studied in detail previously. We took four spectra during a one-week set of observations (see Table 1). This table gives the measured radial velocities. The Cepheid’s atmospheric ASTRONOMY LETTERS
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R
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Phase = 0.264
0.6 0.4 0.2 0 –0.2 6540
6550
6560 Wavelength, Å
6570
6580
Fig. 6. Change of the hydrogen Hα line profile with pulsation phase for BG Cru.
parameters, the time of its brightness maximum, and the phases of the period for all spectra are listed in Table 2. Figure 8 shows the effective temperature, surface gravity, and microturbulent velocity variations with pulsation phase for the star. As can be seen from the figure, Teff and log g clearly vary with pulsation phase, while the the turbulent velocity behaves unusually: the maximum of the Vt curve is shifted toward the minimum of the effective temperature curve. The averaged atmospheric parameters for R Cru are Teff = 5812 ± 22 K, log g = 1.65, and Vt = 3.80 km s−1 . In contrast to BG Cru, no anomalous changes in the hydrogen and metal absorption line profiles are observed for R Cru. Table 4 provides the abundances of chemical elements in the atmosphere of R Cru. Like BG Cru, this Cepheid exhibits a nearly solar iron abundance, approximately the same carbon underabundance, nearly solar oxygen, magnesium, and aluminum abundances, and a sodium overabundance. The abundances of other elements (α, iron-peak, rprocess, heavy and light s-process ones) are also nearly solar. Thus, R Cru has also passed the first dredge-up. ASTRONOMY LETTERS
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T Cru. We have already studied this Cepheid in our previous paper (Usenko et al. 2011): one spectrum was taken in 2009 at phase 0.135 according to the ephemeris from Table 2 with the atmospheric parameters Teff = 5726 ± 28 K, log g = 1.80, and Vt = 3.80 km s−1 . Despite the small difference in pulsation periods with R Cru, this variable star belongs to a later spectral type, G2 Ib, and does not exhibit any anomalies in hydrogen and metal spectral lines either. Szabados (1989) surmised that T Cru had a companion, with the lower limit of its spectral type being A2 (Evans 1992). The atmospheric parameters for T Cru are given in Table 2. We took two of the three available spectra near the Cepheid’s brightness maximum and one spectrum near its minimum. This makes it possible to adopt the following approximate mean values for the atmospheric parameters: Teff = 5588 ± 21 K, log g = 1.70, and Vt = 4.30 km s−1 . Table 5 provides the chemical composition of T Cru averaged over the three spectra. This Cepheid is very similar to R Cru in iron, carbon, oxygen, sodium, magnesium, and aluminum abundance. The same is also observed for all the remaining elements,
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mag
–1
0
1 45
R/Rsol
40
35
30
25
0
2
4 6 Time, days
8
10
Fig. 7. Results of our calculations of a nonlinear pulsation model for BG Cru: (a) theoretical bolometric light curve; (b) variations in the radii of the model’s mass zones.
which also suggests that T Cru has passed the first dredge-up. CONCLUSIONS We too 11 spectra for three classical Cepheids (BG Cru, R Cru, and T Cru) with the 1.9-m telescope of the South African Astronomical Observatory (South African Republic). In addition, we used one summed averaged spectrum from several spectra of BG Cru taken with the 8-m VLT telescope of the European Southern Observatory in Chile. The reduction of our spectra allowed us to determine for the first time (for R Cru) or to considerably refine
(for BG Cru and T Cru) the atmospheric parameters and chemical composition of the program Cepheids. Our abundance analysis for these objects revealed nearly solar abundances of α-elements, iron-peak elements, r-process and s-process elements. The carbon underabundance, the nearly solar oxygen abundance, the sodium and aluminum overabundances, and the nearly solar magnesium abundance (or slight overabundance) suggest that these supergiants have already passed the first dredge-up. The Cepheid BG Cru turned out to be the most interesting object among the program stars: the absorption lines of metals (neutral atoms and ions) in this smallamplitude Cepheid exhibit the presence of secondary ASTRONOMY LETTERS
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5300 1.9
log g
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Vt, km s–1
1.4 4.7 4.2 3.7 3.2 –0.5
Fig. 8. Curves of Vr , Teff , log g, and Vt variations for R Cru. The accuracies of determining Vr and Teff are listed for each data point in Table 1.
blue and red components, with their line depths varying with pulsation phase. At the same time, no emissions or changes of the hydrogen line profile shapes are observed for BG Cru. The Cepheid resembles in such behavior the well-known object X Sgr, a classical Cepheid with a hydrogen envelope. Our computed nonlinear pulsation model for BG Cru with the parameters L = 2000 L , Teff = 6180 K, and M = 4.3 M shows that this Cepheid pulsates in the first overtone and that its small amplitude is attributable to the closeness of the star to the blue CIS boundary. According to the model, the extent of the Cepheid’s atmosphere is relatively small and no spectroscopic manifestations of shocks through variability are possible, while the ASTRONOMY LETTERS
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observed presence of blue and red components in the absorption lines of neutral atoms and ions of metals can be explained solely by the presence of an extended circumstellar envelope around BG Cru. ACKNOWLEDGMENTS This study was financially supported by the Russian Foundation for Basic Research (project no. 1302-00203). The study was also supported by the South African National Research Foundation. I.A. Usenko is grateful to V.V. Kovtyukh for his help in preparing the reduction of spectroscopic data. We are also grateful to the European Southern Observatory for the opportunity to use their spectroscopic database.
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