DISCOVERY OF MIRA VARIABLE STARS IN THE METAL-POOR SEXTANS DWARF SPHEROIDAL GALAXY

In order to explore Miras in the Sextans dSph, we selected two target stars from the photometric catalogs presently available. These are listed in Table 1. The first target, target 1, SDSS J101525.93−020431.8, was selected using the color criteria, J − H > 0.7, H − K_s > 0.3 on the Two Micron All Sky Survey (2MASS) catalog (Skrutskie et al. 2006) and g − r > 0.8, r − i > 0.3 on the Sloan Digital Sky Survey (SDSS) catalog (Adelman-McCarthy et al. 2008). These criteria are also used for our monitoring survey of Miras in the Galactic halo (T. Sakamoto et al., in preparation). Target 1 is carbon-rich, showing a spectrum with the strong CN absorption band at 7900 Å (Mauron et al. 2004; Cruz et al. 2007). The second target, target 2, SDSS J101234.29−013440.8, was later added because of its variation detected in QUEST1 (QUasar Equatorial Survey Team, Phase 1) variability survey (Rengstorf et al. 2009). The R-band light curve of target 2 over 2 years in the QUEST1 showed a variation with a large amplitude (ΔR ⩾ 1.2 mag) and a long period (over 100 days), although their time sampling was not good enough to estimate the period. Target 2 is oxygen-rich, showing a spectrum with clear TiO molecular absorption lines (Suntzeff et al. 1993).

We conducted photometric monitoring observations of the two selected targets in the direction of the Sextans using the 2KCCD camera attached to the 105 cm f/3.0 Schmidt telescope at Kiso Observatory (Itoh et al. 2001).

The observations started in 2008 December and 2010 February for targets 1 and 2, respectively, and were repeated until 2012 February. Time-series I_c-band images were obtained. The data were reduced following standard procedures with IRAF, including bias subtraction (both the level of the overscan region in each image and the bias pattern taken on each night) and the flat-field correction with I_c-band dome-flat images. Instrumental magnitudes of the targets and comparison stars were measured with aperture photometry using the IRAF/APPHOT package. The comparison stars were selected from the SDSS database (Adelman-McCarthy et al. 2008) and their I_c magnitudes were calculated by using the transformation of Jordi et al. (2006),

$$\begin{equation} I_c=i^{\prime }+(-0.386\pm 0.004)(i^{\prime }-z^{\prime })-(0.397\pm 0.001). \end{equation} \tag{ 1 }$$

Using these I_c magnitudes for calibrating the magnitude scale, we obtained the magnitudes of our target stars as listed in Tables 2 and 3.

Table 2. Time-series Photometric Results for Our Target 1

Target 1 (SDSS J101525.93−020431.8)
MJD	Ic (mag)	$e_{I_c}$ (mag)	MJD	Ic (mag)	$e_{I_c}$ (mag)
54836.77	17.30	0.08	55646.49	15.53	0.01
54875.69	17.20	0.06	55662.53	15.59	0.02
54904.57	17.04	0.06	55663.49	15.64	0.03
55174.78	18.50	0.13	55694.50	16.08	0.06
55221.64	17.99	0.09	55694.50	16.03	0.06
55249.61	17.24	0.05	55718.48	16.10	0.06
55288.48	16.81	0.03	55879.84	15.03	0.02
55314.58	16.87	0.09	55880.82	15.10	0.02
55342.49	17.31	0.10	55899.85	14.78	0.01
55580.79	15.66	0.07	55899.85	14.78	0.02
55580.79	15.65	0.08	55942.73	14.79	0.03
55611.56	15.38	0.03	55970.55	14.84	0.03

Note. Modified Julian Date (MJD), the I_c-band magnitude, and the photometric error are listed for each image we took.

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Table 3. Same as Table 2, but for Target 2

Target 2 (SDSS J101234.29−013440.8)
MJD	Ic (mag)	$e_{I_c}$ (mag)	MJD	Ic (mag)	$e_{I_c}$ (mag)	MJD	Ic (mag)	$e_{I_c}$ (mag)
55249.60	15.54	0.01	55663.49	15.57	0.03	55898.73	15.24	0.04
55289.42	15.27	0.03	55694.50	16.11	0.07	55898.73	15.30	0.03
55316.47	15.71	0.02	55718.47	15.95	0.08	55939.77	15.81	0.12
55344.47	15.87	0.03	55876.77	15.24	0.02	55940.76	15.98	0.05
55580.78	15.68	0.08	55877.78	15.18	0.03	55942.72	15.82	0.03
55580.78	15.78	0.09	55879.83	15.17	0.05	55967.70	15.70	0.12
55611.55	15.55	0.03	55879.84	15.23	0.03	55967.70	15.76	0.10
55611.55	15.51	0.05	55880.81	15.24	0.05	55967.70	15.70	0.06
55646.65	15.33	0.01	55880.81	15.27	0.04
55662.53	15.52	0.03	55898.72	15.28	0.04

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Figure 1 plots the I_c variations against the Modified Julian Date (MJD). Both stars show the long-period and large-amplitude variation characteristic of either Miras or semi-regular variables. The peak-to-valley amplitudes (ΔI_c) are 3.72 mag for target 1 and 0.94 mag for target 2. Miras are generally considered to have the I_c amplitude greater than 0.9–1.0 mag (Ita et al. 2004a; Matsunaga et al. 2005). Target 1 is clearly a Mira, whereas target 2 falls between Miras and semi-regulars.

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The light curve of target 1 shows a clear modulation over the entire observation run indicating a long-term variation which is often observed for carbon-rich Miras (Whitelock et al. 2003). We subtract this long-term trend which is fitted by a sine curve with a period of 1500 days. The residual light curve shows a regular periodic variation as expected. Then, we applied the phase dispersion minimization (PDM; Stellingwerf 1978) to the residual curve to obtain a period of 326 days as the best estimate. It should be noted that due to the insufficient coverage of the light curve, especially around the expected minima, we cannot exclude the possibility of the star having a period roughly half of the 326 days based only on our I_c-band data. Nevertheless, the shorter period is unlikely, considering that the star is so red, (H − K_s) ≳ 1.0, and all of such red LMC Miras in Ita et al. (2004b) have periods of 300–500 days. We examined various assumptions on the long-term trend (e.g., sine curves with different periods and/or amplitudes), and the estimated period stays within 15 days from the above value. Thus, the period of target 1 is estimated to be 326 ± 15 days. In contrast, the light curve of target 2 appears to show no long-term trend, and the period of 122 days is obtained with the PDM. Sine curves with periods of 117–127 days seem consistent with the photometric data. Thus, the periods of target 2 are estimated to be 122 ± 5 days.

For target 1, we obtained near-infrared images in the J, H, and K_s bands using the IRSF 1.4 m telescope at South African Astronomical Observatory (Nagayama et al. 2003). Our near-infrared observations were carried out on 2011 June 14 and 2012 April 28, and the magnitudes of the target were calibrated based on 2MASS magnitudes of the neighboring stars. In addition, the near-infrared magnitudes for our targets were collected from a few large-scale catalogs (2MASS, Skrutskie et al. 2006; UKIRT DR6, Lawrence et al. 2007; and DENIS, Epchtein et al. 1994). Table 4 lists the magnitudes available from these sources, where the magnitudes were transformed into those in the IRSF photometric system (Kato et al. 2007). The magnitudes in the DENIS and UKIRT DR6 photometric systems were transformed into the 2MASS system by using the equations in Carpenter (2001) and Hewett et al. (2006), respectively, and then further transformed into the IRSF system by using Kato et al. (2007). The J, H, and K_s magnitudes are listed in Table 4 and show significant variations. The mean magnitudes are obtained by taking averages of four or three independent data in Table 4.

Here we check the uncertainty in the transformation between the different catalogs by comparing the magnitudes of stars around our Miras after the transformation into the IRSF magnitude. The infrared magnitudes well match between the 2MASS, UKIRT, and IRSF photometry measurements within their uncertainties, whereas the K_s magnitudes obtained from the DENIS are different from those in the others by ∼0.3. We added a shift to the above DENIS magnitudes to fit them onto the 2MASS magnitude scale (the magnitudes in Table 4 are on this corrected scale).

We estimate the uncertainties in the random-phased mean magnitudes in the K_s band as follows. Carbon-rich Miras with periods of 300–350 days in the solar neighborhood and nearby dwarf galaxies appear to have K_s-band amplitudes of 0.5–1.0 mag (Whitelock et al. 2003). O-rich Miras with periods of 100–150 days have the K_s-band amplitude of 0.14–0.88 mag in the sample of Whitelock et al. (2000). The amplitudes of targets 1 and 2 are assumed to be 0.75 mag and 0.51 mag in the K_s band, respectively, suggesting that the observed mean magnitudes are located within ±0.38 mag and ±0.26 mag around their true mean magnitudes, respectively. Our infrared data sets consist of four and three independent data for targets 1 and 2, and thus the uncertainties in the mean magnitudes are approximately 0.19 mag and 0.15 mag.

To discuss whether or not our target stars are associated with the Sextans dSph, we estimate the distances on the basis of the period–luminosity (PL) relation of Miras. Miras, as well as semi-regulars with a relatively regular variation and an amplitude close to 1 mag, like target 2, are generally found to lie on the Mira PL relation. Thus, we can apply this relation to both of our targets (Ita et al. 2004a).

Adopting the distance modulus of the LMC to be 18.50 ± 0.02 (Alves 2004), the PL relation for the Miras (Ita & Matsunaga 2011) is expressed as

$$\begin{equation} M_K=(-3.675\pm 0.076)\log P+(1.456\pm 0.173). \end{equation} \tag{ 2 }$$

Ita & Matsunaga (2011) also found that the redder Miras tend to show large offsets from the PL relation. They suggested that such offsets are caused by the dust shells around red Miras (J − K_s ≳ 2), and we discuss the implication for our Miras in Section 3. For target 1, the offset in the K_s band is estimated to be 0.12 ± 0.09 mag (Ita & Matsunaga 2011). In contrast, target 2 is so blue that such an offset is negligible, if any. The interstellar extinctions in the Galaxy in the K_s band are calculated to be 0.02 mag from the map in Schlegel et al. (1998).

After correcting the above offset and the interstellar extinction, we obtain distances of 75.3^+12.8 _{− 10.9} kpc and 79.8^+11.5 _{− 9.9} kpc for targets 1 and 2, respectively. The uncertainties in the distances include those in periods, PL relation, and mean K_s-band magnitudes. The estimated distances are consistent with that of the Sextans dSph, 90.0 ± 10.0 kpc (Lee et al. 2003, 2009).

Here we discuss the effect of the long-term trend on the distance estimate for target 1. Long-term trends have been detected from optical and infrared wavelengths, however, the relationship among different wavelengths has not been established, in particular when our data points are poor. In addition, the observation dates for the 2MASS and the UKIRT were MJD 51174 and 53726, respectively, whereas our I_c observations started on MJD = 54836. The long interval between the infrared and the I_c observations makes the estimation of the long-term trend difficult. However, the long-term trend is suggested to be partly related with absorption by the circumstellar dust (Winters et al. 1994). The circumstellar extinction is also suggested to be correlated with the deviation from the PL relation (Ita & Matsunaga 2011) and its deviation is corrected using the (H − K_s) color in this work. Thus, the above correction considering the (H − K_s) color works, at least partly, as the correction of the long-term trend. In fact, the UKIRT photometry indicates that target 1 was both fainter and redder at its epoch than at the epochs of other photometry. Even if we exclude the UKIRT magnitudes from our calculation, with the proper correction applied, we get the same result within the uncertainty.

We check the reliability of the distance for target 2. The I_c-band PL relation in Ita & Matsunaga (2011) is relatively tight near the period of our Mira target 2 (P = 122 days), although it has a higher dispersion than the K_s-band PL relation. The distance based on the I_c-band PL relation is estimated to be 86.6^+23.1 _{− 18.2} kpc, consistent with the distance by the K_s-band PL relation (79.8^+11.5 _{− 9.9} kpc).

The systematic radial velocity of the Sextans dSph is 226.0 km s⁻¹ with a dispersion of 8.4 km s⁻¹ (Battaglia et al. 2011). For targets 1 and 2, the radial velocities at a single epoch are 202 ± 12 km s⁻¹ (Mauron et al. 2004) and 228.2 ± 2 km s⁻¹ (Suntzeff et al. 1993). The radial velocity of a Mira measured with the optical spectra shows a time variation due to the pulsation by 10–25 km s⁻¹ (Alvarez et al. 2001). The radial velocities of foreground stars in the direction of the Sextans dSph show a peak around 0–50 km s⁻¹ and a weak tail toward a large velocity. Probabilities of foreground stars with the velocities of our targets are low, and this clearly supports the memberships to the Sextans dSph.

Another possible system that the targets might be associated with is a stellar stream in the Galactic halo. The SDSS reveals the presence of a 60° long stream extending from the Ursa Major to the Sextans (e.g., Grillmair 2006). However, its heliocentric distance is about 20 kpc, much smaller than those of our targets. The model of Law et al. (2005) predicts the presence of the Sagittarius stream at a heliocentric distance of 20–60 kpc toward the Sextans dSph in the oblate dark matter halo of the Galaxy, although the stream has not been identified in its direction. Furthermore, the predicted radial velocities are 250–290 km s⁻¹, which are larger than the measured values of the targets. Thus, both of our targets are most likely associated with the Sextans dSph.