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Subsections


NGC 330

Introduction

NGC 330 is the brightest and most massive of the young SMC clusters, and is located slightly to the north of the densest region of the SMC. Robertson (1974) searched for variables in the cluster using photographic plate data but did not detect any. It has been studied in the B and V bands by Balona (1992), and a number of very short-period and low-amplitude variables were found. The time span of the Balona data was only a few days, which is insufficient to determine periods for objects varying on timescales longer than this (i.e. Cepheids and LPVs). The Balona data was also restricted to the central 2′ around the cluster: it could be possible to find variables associated with the cluster lying further away than this (e.g. NGC 1866: Welch et al. 1991). This chapter describes the results of V and Ic band imaging of NGC 330 taken over a period of more than 4 years, aiming to find Cepheids and LPVs in the cluster and the surrounding field. The field searched was approximately 10′×10′ in size.

Observations

Observations of NGC 330 were made using a number of different CCD detectors on the 1.0m and 2.3m telescopes at Siding Spring Observatory. Frames were taken in the V and Cousins' I bands. Exposure times were typically 300 seconds in V and 150 seconds in I, which yielded a limiting magnitude of about V=20.5. Approximately 100 frames in each colour were analysed in this study, spanning a time period of about 1600 days. This long timespan enabled accurate period determination for the short period variables, and allowed multiple cycles of the LPVs to be monitored.

There are several reasons why the V and I passbands were chosen, rather than the more traditional B and V bands. The CCD detectors used are more efficient in I than in B. Also, the LPVs and red giants in the cluster are bright in I, when compared to the equally luminous but bluer stars near the main-sequence turn-off. Thus, photometry of the red giants near the cluster core is easier. A second benefit is the much smaller reddening in I than in B. Finally, model atmosphere calculations for V-I colours are expected to be much more reliable than those for B-V colours, due to large metal line blanketing effects in the B band.

Reductions

The CCD frames were bias-subtracted and flat-fielded using standard routines in the IRAF data reduction package2.1. Relative photometry of each frame was obtained using the DoPhot photometry package (Mateo and Schechter 1989). Much of the data was obtained in non-photometric conditions, so a reference frame in each colour was chosen and all the other frames had empirically determined zero point corrections applied to the photometry. Absolute calibration of the photometry was carried out using photometric data obtained on three different nights. The standard fields of Landolt (1992) were used to calibrate the photometry. It should be noted there are significant zero point differences in the existing published photometry of this cluster at a level of several hundredths of a magnitude (for example, Alcaino and Alvarado 1988, Balona 1992). It is perhaps not surprising that these differences exist, given the location of NGC 330 in the central region of the SMC. The field around NGC 330 is very crowded (∼15,000 stars brighter than V=20.5 were identified in our 10′×10′ field). It is in regions such as this where the difficulties associated with crowded field photometry are most likely to arise. The zero point accuracy of the photometry reported here should be better than 0.01 magnitudes, based on the comparison of the zero points obtained from the three nights of photometry.

Candidate Selection and Period Determination

The selection of variable star candidates was done in several ways. An 'image' was produced by registering a pair of CCD frames and dividing them by each other. The resulting appearance of each star consists of the residual pattern left by dividing the two slightly different point spread functions of the two frames. Stars which have changed brightness are very obvious since they appear as dark or bright spots, in comparison to the almost uniform appearance of all the other non-variable stars in the field. Changes as small as 0.1 magnitudes could be detected with this technique. This procedure is very simple to carry out given digital CCD data, certainly far simpler to do than if one has photographic plate data. A large number of the variables were identified during this step.

Other candidates were selected from stars with larger than normal photometric scatter for their magnitude. Stars that appeared to lie in the region of the Cepheid instability strip, and stars in the red giant and supergiant regions of the HR diagram were also investigated closely. The positions of the variable stars have been determined using the PPM astrometric catalog (Roeser et al. 1991; Roeser et al. 1994), and are listed in Table 2.5. The positions should be accurate to better than 0 .′′5.

The level of completeness of this study may be judged by the fact that no RR-Lyrae type variables were found. They are known to exist in great numbers in the Magellanic Clouds, but at the distance of the SMC, they would have mean magnitudes around V = 19.8. This is close enough to the limiting magnitude of most of the frames that the large photometric errors would mask the variability of these stars. They also have very short periods, typically much shorter than one day. With the sparsely sampled data here (around one frame per night), the period finding algorithms suffer from contamination by aliasing at short periods. This makes the determination of periods for such stars very difficult. Although the aliasing hinders period determination, it does not affect detection rates, as the techniques used to identify variability are insensitive to the actual period of variation, but sensitive to the degree of variability of the star. It is estimated that perhaps >90% of the variables exceeding 0.15 magnitudes in amplitude, and brighter than V=19.0, have been detected.

Determination of possible periods was done using the Phase Dispersion Minimisation technique of Stellingwerf (1978). The periods were refined using the interactive pdm task within IRAF. Finally, magnitude means in V and I were determined by fitting a low order Fourier series to the V and I light curves of each variable. Magnitude means for the colours have been used, as they produce better fits to the various Cepheid relations, such as the P-L and P-L-C relations (Fernie 1990). Magnitude means were also used for the flux measurements.

Results

In a ∼10′×10′ region centred on NGC 330, 22 Cepheid variables have been found and have had periods determined. Eight of these were previously known, of which five had previously determined periods. Four of the Cepheids were near the edge of the CCD field and have V light curves only. Twenty LPVs were found and definite periods were determined for eight while uncertain periods were determined for another five. Balona (1992) suspected three of these stars to be variable, while none of the others were previously known. Nine other variables were also found, including two eclipsing variables, two close binaries on the main sequence, one binary emission-line star and one variable Be star. A finding chart for all variables is given in Figure 2.1.

Figure 2.1: A finding chart for the variable stars in the NGC 330 field. North is to the right and East is up. This V band frame is 8′x10′ in size.
\begin{figure}\begin{center} \epsfig{file=ngc330/finderchartc.ps,width=14cm}\end{center}\end{figure}

Balona identified numerous very short period variables in this cluster, mostly λ-Eri stars. None of these stars could be identified as variable in our data - probably due to their relative faintness and very low amplitude (<0.1 mag).

Four other stars suspected by Balona to be Cepheids were examined. B215 (the designations are those given by Balona), for which Balona determined an approximate period of 1.190 days, was confirmed to be a normal SMC Cepheid with a period of 1.18483 days. B224 is confirmed to be variable with amplitude around 0.4 magnitudes but no period could be determined. B877 cannot be located. No star can be seen in this position on any of our frames in either colour. Close examination of Balona's finding chart of the cluster reveals several objects near other bright stars which cannot be seen in our data, and which are probably fictitious. Finally, B1202 does not appear to be variable; there is no correlation in the variations in the two colours, and the scatter in the light curve is similar to other non-variable objects of similar brightness.

Figure 2.2 shows the colour-magnitude diagram for stars brighter than V = 19 in the complete survey region of 10′×10′ surrounding NGC 330. Figure 2.3 shows a similar diagram, but is restricted to the region with radius 1′ centred on NGC 330 in order to show the evolved stellar population associated with the cluster. The cluster main-sequence turn-off occurs at V ∼14, there is a group of blue helium-burning stars at V ∼13, V-I ∼0.2, and a group of red helium-burning supergiants at V ∼14, V-I ∼1.5. The few faint stars which appear to be considerably bluer than the main sequence are probably mostly due to errors when cross-referencing stars between the two colours.

Figure 2.2: The (V, V-I) diagram for all stars brighter than V=19 in the 10′×10′ field centred on NGC 330. The variable stars are marked in large symbols. The magnitudes are the average of all frames.
\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc330/cmallc.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}

Figure 2.3: The (V, V-I) diagram for stars within a 1′ radius of the NGC 330 cluster center.
\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc330/cmclus.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}

The main sequence in Figure 2.2 is dominated by stars with V-I∼-0.2. However, for V < 14, there are large numbers of stars up to 0.6 magnitudes redder than V-I=-0.2. These stars are Be stars (Bessell and Wood, 1993). The redder V-I colour is due to Paschen continuum emission from a circumstellar disk contributing to the I-band luminosity. Such emission does not contribute in the B and V bands, thus the Be stars are not separated from the other main-sequence stars in a (V, B-V) diagram.

The variable stars found in this survey are marked on a V frame in Figure 2.1, and on a colour-magnitude diagram in Figure 2.2. Tables 2.1, 2.2 and 2.3 list the observed photometric parameters for the Cepheids, LPVs and eclipsing variables, respectively. For the Cepheids and LPVs, the mean magnitudes and colours listed are magnitude means, and AV and AI are the full amplitudes in V and I, respectively. For the eclipsing variables, the mean magnitude is the uneclipsed magnitude. Light curves in both colours are given in Figures 2.4, 2.5 and 2.7. In all plots, the epoch of zero phase is Heliocentric Julian Date HJD=2,440,000.0.



Table 2.1: Cepheids in the field of NGC 330.
Name P(days) Type <V > <V >- <I > AV AI M0 M5 ID
  (days)   mag. mag. mag. mag. M$\scriptstyle \odot$ M$\scriptstyle \odot$  
170V 6.84407 F 15.01 0.70 0.86 0.56 6.48 3.85 HV1689
627V 3.48523 F 16.81 - 0.58 - - -  
1458V 2.50951 F 16.92 0.73 1.27 0.84 3.60 2.18 HV1711
389V 2.38435 F 16.54 0.60 0.45 0.30 3.61 2.18  
637V 2.31369 F 16.92 - 0.88 - - -  
1280V 1.93597 F 17.09 0.65 1.14 0.82 3.21 1.95 HV11358
818V 1.72187 F 17.25 0.61 1.21 0.90 2.84 1.73  
1440V 1.70652 F 17.90 0.81 0.70 0.46 2.88 1.76  
771V 1.50353 F 17.86 - 0.79 - - -  
1046V 1.49885 F 17.40 0.67 0.45 0.34 3.55 2.17  
952V 1.42347 F 17.19 0.60 1.34 0.84 3.75 2.28 HV12123
904V 1.37956 F 17.82 0.66 0.77 0.47 2.47 1.51  
1141V 1.19346 F 17.91 0.66 0.77 0.43 2.77 1.70  
222V 3.17400 O 16.35 - 0.18 - - -  
123V 2.77961 O 15.60 0.57 0.47 0.30 5.91 3.55 ArpIII-1
321V 2.57246 O 16.26 0.63 0.43 0.33 2.54 2.12 HV11364
248V 2.12012 O 16.25 0.61 0.35 0.22 4.78 2.86  
673V 1.43235 O 16.72 0.61 0.59 0.38 5.13 3.06 HV13014
617V 1.27827 O 17.27 0.62 0.52 0.42 3.13 1.87  
1129V 1.18483 O 17.10 0.56 0.61 0.39 3.47 2.07 B215
1457V 0.97478 O 17.20 0.50 0.58 0.42 3.36 2.00  
1063V 0.64866 O 17.72 0.46 0.60 0.45 3.01 1.79  
Notes: The variables types are given as `F' for fundamental-mode Cepheids, `O' for Cepheids pulsating in the first-overtone mode. M0 is the mass assuming no overshoot while M5 is the mass assuming an overshoot parameter of 0.5. The distance moduli in Table 2.4 were used in the derivation of the masses. All masses are in M$\scriptstyle \odot$. Other identifications are from Payne-Gaposchkin and Gaposchkin 1966 (HV), Arp 1959 (Arp), and Balona 1992 (B).




Table 2.2: Long-Period Variables.
Name P(days) <V > <V >- <I > AV AI ID
  (days) mag. mag. mag. mag.  
211V 482 16.19 1.86 0.40 0.20  
8192V 400 19.8 2.9 >0.9 >1.7  
231I  365 19.2 2.8 >0.5 >1.5  
2380V 280 18.55 2.30 2.1 1.4  
225V 260 16.28 2.06 0.48 0.27  
550V 186 17.40 3.06 0.93 0.60 B555
711V 140 16.94 1.74 0.27 0.17  
297V 129.6 16.56 - 0.20 -  
347V ∼670 15.89 1.88 0.26 0.18  
337V ∼600 15.98 1.66 0.27 0.14  
220V ∼580 16.20 1.96 0.28 0.25  
379V ∼350 16.91 2.06 0.41 0.28  
242V ∼62 15.97 - 0.16 -  
317V ? 15.75 - 0.34 -  
658V ? 16.67 - 0.31 -  
520V ? 17.01 - 0.65 -  
3180V ? 18.3 3.4 >1.4 0.8  
285V ? 16.19 1.65 0.19 0.19  
93I  ? 14.2(I) - - 1.06  




Table 2.3: Other variables in the NGC 330 field.
Name Period <V > <V >- <I > AV AI Type ID    
  (days) mag. mag. mag. mag.        
69V 3.18868 14.91 -0.17 0.73 0.93 Eclipsing HV 1669    
2414V 0.79876 18.46 -0.11 0.98 0.93 Eclipsing      
114V 1.545448 15.54 0.16 0.15 0.10 Binary      
504V 1.17130 17.09 -0.05 0.19 0.19 Binary B178    
66V 27.11 or 54.22 14.69 0.23 0.35 0.33 Binary HV 11348    
77V 227 14.48 1.27 0.26 0.27 Binary B317    
95V ? 14.61 0.01 0.22 0.32 ?      
303V ? 16.15 -0.09 0.17 0.33 ?      
515V ? 17.10 0.78 0.45 0.37 ? B224    

Figure 2.4: Light curves for the Cepheid variables. The fundamental-mode pulsators are plotted above, and the overtone pulsators below. The lower curves in each panel (filled symbols) are the V magnitude light curves, and the upper curves (open symbols) are the lower-amplitude I light curves. The error bars on the photometry are typically 0.01 mags at V=14.5, I=14.0, rising to 0.02 mags at V=17.0, I=15.7.
\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc330/cephlight.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}

Figure 2.5: Light curves for the LPVs in the NGC 330 field. The filled symbols and open symbols are the V and I light curves, respectively.
\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc330/lpvlight.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}

Figure 2.6: Light curves for the semiregular and irregular variables in the NGC 330 field. The filled symbols and open symbols are the V and I light curves, respectively.
\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc330/semireg.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}

Figure 2.7: Light curves for the eclipsing and binary variables. The V and I light curves are plotted for each variable. The star 66V is plotted twice, assuming a different period in each case.
\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc330/otherlight.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}

The Cepheid Variables

A comparison of Figures 2.2 and 2.3 shows that the most luminous Cepheid lies well below the luminosity of the helium-burning stars in the NGC 330 cluster. This implies that none of the Cepheids are members of NGC 330. In fact, the short periods of most of the Cepheids found here indicate that these stars come from a relatively low-mass population.

An examination of Figure 2.2 indicates that a number of non-variable stars appear to lie on, or just to the red of the Cepheid instability strip, going from (V,V-I) of (16,0.8) to (13,0.8). Thus, there would appear to be many non-variable stars in the instability strip. However, these stars are probably foreground objects in the galactic halo. Reid, Mould and Thompson (1987) have modelled the effects of foreground contamination on LMC colour-magnitude diagrams and found that almost all the brighter galactic halo stars lie in a colour range of 0.5 <V-I< 1.0, and form a sequence similar to that noted above in Figure 2.2. The SMC has a similar galactic latitude to the LMC, so the properties of the foreground halo stars should be very similar.

In order to derive Cepheid masses and a distance modulus to the SMC from theory in a consistent manner, the results of Chiosi, Wood and Capitanio (1993) are applied. This work used the Los Alamos opacities. From pulsation theory alone, Chiosi et al. give a P-M-MV-(V-I) relation. Addition of the (overshoot-dependent) M-L relation from stellar evolution theory is then used to eliminate M and produce a P-MV-(V-I) relation that can be used to determine the distance to the SMC. Chiosi et al. adopted the standard power law form L = aMb for the evolutionary M-L relation. Such a relation is accurate for M$ \raisebox{-0.6ex}{$\,\stackrel {\raisebox{-.2ex}{$\textstyle >$}}{\sim}\,$}$5M$\scriptstyle \odot$ and P$ \raisebox{-0.6ex}{$\,\stackrel {\raisebox{-.2ex}{$\textstyle >$}}{\sim}\,$}$3 days but begins to fail for the shorter period, lower mass Cepheids of low metallicity where the helium burning loops just penetrate the Cepheid instability strip. This is shown in Figure 2.8, where evolutionary tracks for M = 2.5, 3.5 and 5M$\scriptstyle \odot$ from Vassiliadis and Wood (1993) are plotted. Note that the lower, blueward leg of the helium burning loop (second-crossing) is where the stars spend the most time in the instability strip. The short horizontal lines indicate the luminosity the helium burning loops should have according to the M-L relation of Chiosi et al. (1993). It is clear that the power law fit is not adequate for the lower mass tracks.

Figure 2.8: Evolutionary tracks for masses M = 2.5, 3.5 and 5M$\scriptstyle \odot$, Y = 0.25 and Z = 0.004 from Vassiliadis and Wood (1993). Also shown are the fundamental (dashed lines) and first-overtone (dotted lines) instability strips for this composition from Chiosi et al. (1993). The fundamental-mode Cepheids found in this study are shown as open circles and the first-overtone mode Cepheids are shown as triangles.
\begin{figure}\begin{center} \epsfig{file=ngc330/evtracks.ps,width=\linewidth}\end{center}\end{figure}

In the present calculations, the tracks shown in Figure 2.8 are used to estimate a M-L relation appropriate for low-mass Cepheids with Y = 0.25 and Z = 0.004 appropriate for the present application. This relation is

log($ {\frac{L}{L}}$$\scriptstyle \odot$) = 2.970  log($ {\frac{M}{M}}$$\scriptstyle \odot$) + 1.114 + fov

Note that the factor fov introduced by Chiosi et al. (1993) is used to account for the unknown amount of overshoot, and has values of 0.0 for no overshoot and 0.5 for the largest plausible amount of overshoot. As noted by Chiosi et al. (1993), fov $ \approx$ dover/Hp $ \approx$ $ {\frac{{1}}{{2}}}$λ, where dover is defined by Maeder and Meynet (1989), and λ is defined by Bertelli et al. (1985). Using the M-L relation above with the PLMC relation for low mass Cepheid models of Chiosi et al. (1993), yields theoretical PLC relations for the fundamental, first and second overtone pulsation modes for overshoot parameter values fov of 0 and 0.5.

Our next task is to identify the pulsation mode of the Cepheids. The Cepheid light curves can be characterised into two types, the first as an asymmetric curve with a sharp rising phase and a slower decline, and the second as a symmetric, approximately sinusoidal light curve. Traditionally, the asymmetric light curve has been assumed to indicate a Cepheid oscillating in its fundamental mode. The classification of Cepheids with symmetric light curves is more difficult. Whilst almost all Cepheids pulsating in the first-overtone mode have symmetric lightcurves, the degree of asymmetry of the fundamental-mode pulsators if often less for short-period objects. It is possible for the mode of the fainter, low-amplitude and shorter-period fundamental-mode pulsators to be incorrectly identified, especially in the presence of noise.

The pulsation modes adopted here were arrived at by plotting the theoretical instability strip edges for the fundamental, first and second-overtone modes, on the PL diagram (figure 2.9) using the results of Chiosi et al. (1993) with no overshoot. A distance modulus of 18.9 was assumed (this value is actually our distance modulus derived below). The red (lower) edges of the instability strips are not well known theoretically, whereas the blue (upper) edges are relatively well defined. Cepheids bluer than the blue edge of the fundamental mode are uniquely classified as first overtone pulsators. The light curves of the three Cepheids close to the blue edge of the fundamental-mode instability strip were examined, since these stars could possibly belong to either mode. One star has a large-amplitude asymmetric light curve and is almost certainly a fundamental-mode pulsator. The other two were low-amplitude symmetric light curves, and were assumed to be overtone pulsators. All other variables, which are well to the red of the first-overtone strip, were assumed to be fundamental-mode pulsators. We also note that the shortest period Cepheid, 1063V, appears to have substantial scatter on its light curve, somewhat more than would be expected from the individual photometric errors of the data. It is possible that this object is a beat Cepheid, however there is insufficient data to be able to confirm this.

Figure 2.9: The SMC PL relation (upper panel) and VI band PLC relation (lower panel). Filled symbols are fundamental-mode Cepheids, and open symbols are overtone Cepheids. The solid, dashed, and dotted lines are the theoretical Cepheid instability strip edges for the fundamental, first-overtone and second-overtone modes respectively, with fov=0 and distance modulus 18.9. The thick dotted line is the observational PL fit of Caldwell and Coulson (1986). The widths of the three instability strips collapse to zero in the lower panel due to the subtraction of the colour term.
\begin{figure}\begin{center} \epsfig{file=ngc330/plcfit.ps,width=\linewidth}\end{center}\end{figure}

Distance moduli were derived by fitting the 10 fundamental-mode Cepheids with V-I colours to the fundamental-mode P-MV-(V-I) relation and the 8 first-overtone Cepheids with V-I colours to the first-overtone relation. A reddening of E(B-V)= 0.06 was adopted for all stars (Caldwell and Laney 1991; Caloi et al. 1993), and Y = 0.25 and Z = 0.004 was assumed. The results are given in Table 2.4.



Table 2.4: SMC Distance modulus estimates.
Mode fov DM  
F 0.0 18.88  
F 0.5 18.43  
O 0.0 18.96  
O 0.5 18.59  

From Table 2.4, it can be seen that there is good consistency between the distance moduli derived for the two pulsation modes for each adopted value of the overshoot parameter. If there is no overshoot, a mean distance modulus for the two modes of 18.92 (61 kpc) is derived, while for large amounts of overshoot ( fov = 0.5) a mean distance modulus of 18.51 (50 kpc) is derived. These results can be compared with those given by Caldwell and Laney (1991) for longer period Cepheids ( P$ \raisebox{-0.6ex}{$\,\stackrel {\raisebox{-.2ex}{$\textstyle >$}}{\sim}\,$}$10 days). The longer period Cepheids yield a distance modulus of 18.9, although it is known that the SMC has a significant (but somewhat uncertain) depth. Caldwell and Laney (1991) claim a depth in the central region of ∼8kpc or 0.25 magnitudes (see also Mathewson et al. 1988). Welch et al. (1987) derive a depth of ∼4kpc based on JHK photometry of a sample of SMC Cepheids. In any case, it is clear that there are depth effects at a level of tenths of magnitudes.

Given a distance modulus to the SMC, the P-M-MV-(V-I) relation can be used to derive masses for the Cepheids. The results of such calculations are given in Table 2.1 for the two cases of fov= 0 and 0.5 (using the distance moduli in Table 2.4). If the non-overshoot distance modulus of ∼18.9 is adopted, then all Cepheids are more massive than 2.47M$\scriptstyle \odot$, with most having masses in the 3-5M$\scriptstyle \odot$ range (or ages of 1 - 4×108 years). The minimum Cepheid mass derived here corresponds quite well to the mass below which the standard loops do not pass through the instability strip at the adopted abundance of Z = Z$\scriptstyle \odot$/4 (see Figure 2.8). Note that the most massive Cepheid studied here has a mass of ∼7M$\scriptstyle \odot$ (adopting the non-overshoot distance). This is considerably smaller than the cluster turn-off mass of ∼13M$\scriptstyle \odot$ (Caloi et al. 1993) and confirms the earlier suggestion that none of the Cepheids belong to the cluster.

If a large amount of convective overshoot ( fov∼0.5) is assumed, then Cepheid masses down to 1.51M$\scriptstyle \odot$ are derived, with a strong concentration around 2M$\scriptstyle \odot$. These masses are too small for the stars to enter the instability strip during core helium burning. Thus, current stellar models seem to indicate that large amounts of convective core overshoot ( fov∼0.5) during the main-sequence phase for stars of initial mass 2-3M$\scriptstyle \odot$ is ruled out. In fact, the required masses are so low that some of the stars would barely have convective cores during main-sequence evolution. Finally, it should be noted that the adoption of large amounts of convective core overshoot leads to an uncomfortably small distance modulus of ∼18.5. A value of fov up to 0.25 could not be ruled out.

The top panel of Figure 2.9 shows the PL relation for the Cepheids observed in this study. As noted above, the theoretical instability strips for the first three modes are shown. Also plotted is the observational PL relation derived by Caldwell and Coulson (1986). This relation was calculated using fundamental-mode Cepheids with periods greater than about 10 days. The longest period Cepheid in this study has a period of only 6.8 days. In spite of this, extrapolation of the Caldwell and Coulson relation yields a good fit to these short period Cepheids.

The bottom panel of Figure 2.9 shows the observational PLC relation together with the theoretical PLC relations for the first three pulsation modes from Chiosi et al. (1993). The theoretical relations are plotted assuming a distance modulus of 18.9, consistent with fov = 0, and the β values for each mode are those appropriate for fov = 0. These β values ( β = 4.50 for the fundamental mode and β = 3.96 for the first-overtone mode) were also used for the observational points. Clearly, the PLC relations are much tighter than the PL relations, and there are only two modes present.

It should be noted that the Cepheid P-L-C relation (given approximately by mV $ \approx$ - 4logP + 4(V-I)) is rather sensitive to errors in colour, or equivalently, to the photometric zero point. An error of only 0.05 in (V-I) would result in an error in distance modulus of ∼0.2 magnitudes. It is clear that particular attention should be paid to the correct determination of photometric zero points.

In the above discussion, it is assumed the Cepheids are either fundamental or first-overtone pulsators. However, Böhm-Vitense (1994) studied the PL diagram of a large sample of SMC Cepheids using photographic B photometry, and concluded that in the SMC, there were three distinct sequences of Cepheids on the PL diagram, corresponding to fundamental mode, first overtone and second overtone pulsators. The possibility that there were only two distinct sequences (fundamental and first overtone) was also discussed, but the required low gradient of the PL gradient did not favour this interpretation. In the three mode scenario, fundamental-mode pulsators appear to be restricted to log P >1. Most of the Cepheids discussed here have periods less than two days, and several have periods less than one day, and if the three mode PL relation were to be adopted then all these Cepheids must be first and second-overtone pulsators.

At first sight, it would seem possible to have all the Cepheids observed here as first and second-overtone pulsators if various parameters are pushed to plausible limits. If fov = 0.5 is adopted, then the Cepheids can be made to fit the first and second-overtone PLC relations for the acceptable distance modulus of 19.05, as shown in Figure 2.10. Note that for fov = 0.0, the unacceptably large distance moduli of 19.44 and 19.35, respectively, are derived from the PLC relation for the first and second overtones.

Figure 2.10: The same as Figure 2.9, but assuming
\begin{figure}\begin{center} \epsfig{file=ngc330/plcfit-bohm.ps,width=\linewidth}\end{center}\end{figure}

Although fov = 0.5 gives a plausible distance modulus to the SMC, there are other problems with this fit. As shown in the top panel of Figure 2.10, most of the second overtone pulsators lie to the blue side of even the theoretical second-overtone instability strip. Since we believe the theoretical blue edge to be reasonably well defined, this seems to be a problem for the second overtone assumption. Another problem is that the derived masses, 1.7 to 4.8M$\scriptstyle \odot$ for the first overtone, and 2.1 to 3.9M$\scriptstyle \odot$ for the fundamental mode, are mostly smaller than required for the loops to pass through the instability strips (and note that the theoretical loops are shorter for increased overshoot fov). The favoured interpretation is that the shortest period Cepheids are fundamental and first-overtone pulsators only. A similar conclusion was reached by Alcock et al.(1995), in their study of LMC Cepheids.

Other Variables

The stars cooler than the Cepheid instability strip in Figure 2.2 fall into two distinct sequences. Those near the tip of the bluer sequence (V ∼ 13.5, V-I∼ 1.5) are clearly red, core-helium-burning supergiants (see Figure 2.3) while the less luminous members of this sequence represent a sequence of decreasing mass down through AGB stars, probably to the low mass limit M∼2.3M$\scriptstyle \odot$. The second sequence with a tip at V ∼ 16, V-I∼ 1.8 consists of low mass field stars on both the first giant branch and the AGB. Note that for AGB stars redder than V-I ∼2, bolometric corrections can become very large and the AGB becomes fainter in V as V-I increases.

Many variables belong to the old giant sequence in Figure 2.2: these stars are LPVs. Those for which periods have been determined (Table 2.2) have periods from ∼130 to 482 days, typical of this variable class. Infrared JHK photometry is required to obtain accurate bolometric magnitudes for the LPVs.

One red variable, 77V, lies on the red supergiant/massive AGB sequence in Figure 2.2. It is just luminous enough to belong to the group of cluster supergiants shown in Figure 2.3, and it is only ∼50 ′′ from the center of the cluster. Photometric parameters are given in Table 2.3. Assuming the observed period of 227 days represents a normal LPV pulsation period, a pulsation mass of this star can be derived to see if it is consistent with the evolution mass for stars of its luminosity. The bolometric magnitude for 77V was derived by adopting the relation between bolometric correction and V-I of Bessell and Wood (1984), a distance modulus of 18.9, E(B-V)=0.06, and the (V-I, Teff) relation given in Figure 8 of Chiosi et al. (1993). The radius was derived from the definition L = 4πσR2T eff4 and the pulsation mass was then derived from the period-mass-radius relation given for supergiant LPVs by Fox and Wood (1982). The resulting pulsation mass is 0.82M$\scriptstyle \odot$, much less than possible for a star on the red supergiant/massive AGB sequence of Figure 2.2. It therefore seems that 77V is not a normal LPV in the SMC.

Another possibility is that 77V is a foreground LPV. If it is assumed that the variable belongs to the Galactic halo, then the P-M-R relation of Fox and Wood (1982) for Population II stars may be used to derive a distance to this star, if we assume it has a typical halo giant mass of ∼0.8M$\scriptstyle \odot$. The distance derived is 57 kpc, very close to the distance of the SMC. Furthermore, the luminosity required to give the observed period (M bol∼ -5.1) is much higher than the luminosity of Galactic LPVs in old globular clusters. The reason for the large luminosity and distance computed for 77V is the relatively blue colour of this star ( <V-I >= 1.27) compared to halo Miras such as those in 47 Tuc which have < V-I >  $ \raisebox{-0.6ex}{$\,\stackrel {\raisebox{-.2ex}{$\textstyle >$}}{\sim}\,$}$ 3 (Eggen 1972).

The arguments above lead us to believe that the period of 77V does not arise from a normal LPV pulsation. A clue to the nature of this star comes from a comparison of 77V with the list of emission line stars found in and near NGC 330 by Bessell and Wood (1993). This comparison shows that 77V is a star with strong Hα emission. A spectrum was obtained using the 2.3m telescope and the Double Beam Spectrograph at a resolution of 1.0Å  (Figure 2.11). The spectrum shows broad Hα emission with a FWHM of 310 km s-1 The radial velocity of this star is +180 km s-1, making it an almost certain SMC member. In general, the asymmetric twin-peaked Hα profile suggests the presence of both a rotating circumstellar disk and an expanding wind giving rise to the absorption to the blue of emission line center (e.g. Dachs 1987).

Figure 2.11: The Hα emission profiles of the binaries 66V and 77V. The
\begin{figure}\begin{center} \epsfig{file=ngc330/bespec.ps,width=\linewidth}\end{center}\end{figure}

It is unlikely that the circumstellar material causing the emission is in a disk or stellar wind surrounding a single star. Assuming the V and <V >- <I >given in Table 2.3 represent the stellar photosphere of a red supergiant or relatively massive AGB star and not circumstellar material, then the stellar radius is ∼171R$\scriptstyle \odot$. If the NGC 330 turn-off mass is taken as (an upper limit to) the stellar mass, then the escape velocity from the photosphere is 170 km s-1 and the equatorial rotational breakup velocity is 120  km s-1. Given the observed line width (FWHM) of 310 km s-1, ∼2.6 times the rotational breakup velocity, it is unlikely that the Hα emission is coming from a rotating disk. Similarly, stellar wind velocities have values typically 1/3 the escape velocity from the photosphere so that the observed velocity is ∼2.7 times larger than expected.

Thus, the favoured interpretation for 77V is that it is a binary system with an orbital period of 227 days which consists of a red supergiant or upper AGB star and a compact star surrounded by a disk from which the Hα emission arises. The disk could arise from either accretion from the red supergiant, or excretion as in normal Be stars. Many emission-line stars in binaries are known in the galaxy, with orbital periods from ∼1 day to ∼10000 days (Harmanec 1987). In the case of 77V, the light curve periodicity probably represents the orbital period in a close binary system with variable obscuration around the orbit.

A subset of the emission-line binaries, the symbiotic stars, mostly have orbital periods in the 100-1000 day range (Webbink 1988). However, the blue spectrum of 77V does not show emission lines of He II which are characteristic of symbiotic stars (Allen 1984), indicating that the surface gravity of the compact star is not as high as that of the subdwarfs typically found in symbiotic systems. Indeed, this is expected given that subdwarfs are low mass stars whereas the red star in this system is of relatively high mass and could not have had a companion capable of evolving to the subdwarf stage. The compact star is probably a normal main-sequence star in the present case. If the main-sequence companion has a mass of ∼1M$\scriptstyle \odot$ and the red star a mass of ∼13M$\scriptstyle \odot$, then the companion will be orbiting the red star at ∼2.2 stellar radii.

The variable 66V in Table 2.3 appears to be another binary system. The magnitude and colour of 66V put it near the main-sequence turn-off of NGC 330. It was found by Bessell and Wood (1993) to have strong Hα emission, making it a Be star. A spectrum was obtained with the 2.3m telescope (Figure 2.11), showing a symmetric Hα emission line with a FWHM of ∼300km s-1. The radial velocity is +170 km s-1, consistent with SMC membership. The period found here for this variable star is 27.11 or 54.22 days, much larger than the typical period of <1 day found for other variable Be stars (λ Eri variables) in NGC 330 by Balona (1992). The variability amplitude of 0.35 magnitude in V is also much greater than normal for λ Eri variables. If the longer period of 54.22 days is adopted, then the light curve shows a well-defined and relatively narrow minimum, suggesting that this star is an eclipsing variable. Much of the light curve out of the dip to minimum is poorly defined and shows a large scatter from cycle to cycle. This phase may correspond to the interval when the circumstellar disk giving rise to the Hα emission is the dominant light source. The irregularity during this phase of the light curve suggests that the circumstellar material is not in a steady state of excretion or accretion. If the 27.11 day period is adopted, then the light curve resembles that of an eclipsing contact system with two similar components, while the Hα emission requires the presence of a circumstellar disk.

The two variable stars HV1669 and 2414V in Table 2.3 are clear examples of eclipsing variables on or near the main-sequence. The bright variable HV1669 is a previously known eclipsing system (Hodge and Wright 1977). Its magnitude and colour put it near the main-sequence turn-off of NGC 330. The variable 2414V, with <V > ∼18.4 is among the faintest optically-discovered eclipsing variables presently known to us in the Magellanic Clouds. The magnitude of this system suggests that the more massive component star has a mass of ∼4M$\scriptstyle \odot$. The two variables 114V and 504V lie on the main-sequence. They have reasonably sinusoidal light curves and are probably contact binary systems of the W Ursa Majoris type. Periods for the remaining three variables in Table 2.3 were not able to be derived, although light curves are given in Figure 2.6. The blue main-sequence colours of two of these objects suggest binary status, while the position of 515V in Figure 2.2 suggests that it is a Cepheid. It is possible that this star may be a beat Cepheid, though a much denser phase coverage would be required to confirm this.

Summary

Comparison of the photometry of 18 short-period Cepheid variables around NGC 330 with theoretical models have yielded a distance modulus to the SMC of ∼18.9, for zero to moderate convective core overshoot during main-sequence evolution. Large amounts of main-sequence convective core overshoot in stars of mass ∼2M$\scriptstyle \odot$ appear to be ruled out. The short-period Cepheids appear to follow linear extensions of the PL and PLC relations for longer period Cepheids, and all appear to be fundamental or first-overtone pulsators.

None of the LPVs found near NGC 330 are cluster members: all appear to belong to the old field population of the SMC. Six eclipsing binary variables were found: two contain Hα emitting circumstellar disks, two are detached eclipsing systems and two are probably contact W Ursa Majoris systems.

The photometric data upon which this chapter is based is available on the ApJ/AJ CD-ROM Series, Volume III, December 1994.



Table 2.5: J2000.0 positions of NGC 330 variables.
Var R.A. Dec. Var R.A. Dec.
66 00h55m49.6s -72o25′27 ′′ 520 00 56 03.8 -72 31 39
69 00 55 54.5 -72 28 09 550 00 56 17.6 -72 27 04
77 00 56 09.4 -72 28 09 617 00 56 29.9 -72 30 28
95 00 56 44.3 -72 29 06 627 00 56 34.4 -72 31 16
114 00 55 30.8 -72 25 20 637 00 56 38.7 -72 31 58
123 00 55 40.8 -72 28 30 658 00 56 47.2 -72 31 06
170 00 56 28.2 -72 26 29 673 00 56 57.5 -72 24 00
211 00 55 27.2 -72 26 42 711 00 57 06.9 -72 29 17
220 00 55 33.3 -72 24 20 771 00 55 35.6 -72 24 14
222 00 55 35.6 -72 23 57 818 00 55 12.8 -72 31 29
225 00 55 31.2 -72 30 01 904 00 55 27.7 -72 29 41
242 00 55 52.0 -72 23 58 952 00 55 38.1 -72 26 56
248 00 55 52.9 -72 30 10 1046 00 55 48.3 -72 31 28
285 00 56 13.7 -72 31 07 1063 00 55 50.2 -72 31 19
297 00 56 18.7 -72 32 10 1129 00 56 06.4 -72 27 12
303 00 56 26.6 -72 26 23 1141 00 56 09.2 -72 26 16
317 00 56 40.2 -72 32 13 1280 00 56 28.9 -72 26 18
321 00 56 47.9 -72 27 51 1440 00 57 02.3 -72 24 18
337 00 57 09.0 -72 25 38 1457 00 57 02.2 -72 27 54
347 00 57 17.4 -72 28 07 1458 00 57 05.1 -72 24 52
379 00 55 17.0 -72 27 39 2380 00 56 10.1 -72 28 42
389 00 55 19.2 -72 29 05 2414 00 56 12.1 -72 29 39
504 00 56 04.4 -72 27 59 3180 00 57 26.2 -72 29 17
515 00 56 06.5 -72 28 28 8192 00 55 59.9 -72 30 25

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Kim Sebo 2008-06-20