NGC 2058-65

This chapter focuses on the field surrounding the young LMC clusters NGC 2058 and NGC 2065. These two clusters are separated by ∼5^′, and are located at the eastern end of the LMC bar. This region is extremely crowded, making it a challenging task for precision photometry. There are around 20,000 stars in the 10^′×10^′ field, down to the limiting apparent magnitude of V $\approx$ 19.5. The field also has a number of other fainter clusters in it, including NGC 2057, NGC 2059 and NGC 2066. These clusters appear to be of a similar age to NGC 2058-65. Another feature of this area is the substantial change in reddening across the field. It may be seen in Figure 4.1 that the number of stars in the upper left (north-east) corner is markedly lower than the rest of the frame. Examination of the CMD indicates that the reddening is greatest in this part of the field.

**Figure 4.1:** A finding chart for the variable stars in the NGC 2058-65 field. The three clusters with large Cepheid populations are (from the top) NGC 2059, NGC 2058 and NGC 2065. See Figure 4.2 for more detailed images of these clusters. This is a 10 $^′$×10$^′$ ıband image.
$\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc205865/finder.ps,width=\linewidth}\end{center}\end{figure}$

**Figure 4.2:** The three Cepheid-rich clusters shown in more detail. The variables (mostly Cepheids) near the clusters are marked. These charts are at the same orientation but at twice the magnification as Figure 4.1.
$\begin{figure}\begin{center} \epsfig{file=ngc205865/finderzoom.ps,width=\linewidth}\end{center}\end{figure}$

Data Reduction and Analysis

The CCD data was taken as part of the observing program described in Chapters 2 and 3. Bias removal and flat-fielding of the VI CCD data was completed using the IRAF data reduction package. Photometry for each of these frames was calculated using Version 3 of the DoPhot profile-fitting photometry package (Mateo and Schechter 1989). The photometry was initially performed in the same manner as for the previous clusters. However, due to the extremely crowded nature of this part of the LMC bar, the photometry was of a lower quality than expected. This was mainly due to changes in seeing between the frames. As the seeing gets worse, faint neighbours near a brighter star become blended with the star, and contribute a different amount of flux to the magnitude of the brighter star. The effect of this is to make the frame-to-frame zero point corrections less accurate, and to produce substantially more scatter in the light curves.

To overcome the variable seeing problem, the VI photometry was recomputed using the fixed-position warm-start option of DoPhot. A frame taken in good seeing was first reduced normally, and the X-Y positions of all the stars was determined. The X-Y positions were then transformed to match the orientation of a poorer seeing frame, and these new coordinates were used to define the positions of the stars. Because the coordinates were based on a good seeing frame, stars that would normally be blended or undetected in the poorer seeing frame could now be detected and fit, since the X-Y position was known. This technique resulted in substantially improved photometry. The photometry was then transformed onto the standard system of Landolt (1992), modified to include the corrections of Bessell (1996).

JK photometry of twelve of the larger-amplitude and more regular LPVs was obtained on the 2.3m telescope at Siding Spring Observatory on two nights. The CASPIR infrared camera was used on May 14^th 1995, and a single-channel infrared photometer on December 19^th 1994, using a 10 ^′′ aperture. Full details of the JK photometry are shown in Table 5.1 in Chapter 5.

The CASPIR data was reduced using IRAF, and JK magnitudes were derived using DoPhot. The zero point offset between using the profile-fitting photometry of DoPhot and the 10 ^′′ aperture photometry (potentially affected by neighbour stars) is very small,(<0.02 magnitudes), as these stars are very bright in J and K - certainly much brighter than most of the nearby stars in the field which are mostly blue main-sequence stars.

The identification of variable stars was achieved by using an implementation of the technique described by Welch and Stetson (1993). Given a time-series of near-simultaneous observations in two colours, a statistic (or variability index) is computed which is based on the correlation of brightness changes between the two colours, in this case the V and I bands. Stars with highly-correlated variations in V and I are likely to be variable, and have a high index, whilst those stars of constant brightness have an index close to zero. This technique was found to be extremely effective at identifying variable stars, even those without periodic variability. It also works well for stars in crowded regions, as the pairs of frames were taken close together and usually have similar seeing. This technique is relatively insensitive to contamination by spurious data points in the time-series.

The stars with the highest variability index were examined manually, using the PDM task within IRAF, and the period for those stars found to vary regularly was determined.

The relatively few stars lying to the red of V-I=2.0 were explicitly examined for variability. A high fraction of these objects are variable, but have very low amplitudes and so do not have particularly high variability indices, and would probably be missed otherwise.

**Table 4.1:** J2000.0 positions of NGC 2058-65 variables
Var.	ID	R.A.	Dec.	Var.	ID	R.A.	Dec.
35		05^h36^m47.1^s	-70^o09^′37 ^′′	324		05 36 48.9	-70 10 53
40		05 37 53.0	-70 12 37	338		05 37 42.3	-70 12 57
52	HV2706	05 36 21.7	-70 06 38	340		05 37 15.9	-70 11 20
56		05 36 56.9	-70 09 40	376	HV5975	05 37 36.4	-70 08 51
60	HV2726	05 37 39.2	-70 06 31	403		05 37 01.4	-70 09 43
66	HV1009	05 37 41.6	-70 15 37	436		05 37 47.7	-70 13 49
67	HV1008	05 37 38.4	-70 16 06	446		05 37 50.2	-70 12 19
69	HV2709	05 36 35.3	-70 15 41	459		05 36 21.2	-70 14 17
72		05 36 18.4	-70 13 25	463		05 36 24.0	-70 16 35
75		05 36 59.2	-70 16 14	504		05 36 19.7	-70 13 24
82		05 36 53.8	-70 06 24	516		05 37 16.5	-70 07 37
87		05 38 02.1	-70 10 09	523		05 36 44.4	-70 09 44
88	HV2714	05 36 54.2	-70 08 59	554		05 37 57.5	-70 11 17
89		05 36 54.7	-70 09 30	566		05 36 41.2	-70 16 22
93		05 36 30.0	-70 07 07	569		05 37 19.6	-70 11 17
95		05 37 01.0	-70 08 01	586		05 36 30.6	-70 08 38
96		05 36 56.5	-70 12 36	604		05 36 47.3	-70 11 31
106		05 36 43.3	-70 10 31	607		05 37 50.4	-70 11 52
114		05 37 03.0	-70 07 28	619		05 36 38.2	-70 11 37
137		05 37 42.0	-70 14 05	627		05 37 30.1	-70 09 47
145		05 37 39.2	-70 14 17	692		05 36 50.3	-70 07 27
147		05 36 33.9	-70 09 49	695		05 36 44.0	-70 15 28
153		05 37 48.1	-70 13 56	696		05 37 28.6	-70 08 53
155	HV2712	05 36 52.5	-70 15 22	713		05 37 22.7	-70 07 40
156		05 37 38.6	-70 14 09	741		05 38 05.7	-70 14 53
157	HV2718	05 37 22.7	-70 12 16	798		05 37 55.3	-70 13 26
168	HV2720	05 37 25.7	-70 07 59	867		05 37 36.2	-70 07 26
172		05 37 02.0	-70 07 41	905		05 37 13.4	-70 10 58
179	HV5976	05 37 49.8	-70 10 17	1068		05 37 08.7	-70 11 51
183	HV2710	05 36 39.5	-70 16 03	1076		05 37 57.7	-70 12 09
185		05 37 04.7	-70 07 56	1105		05 37 22.0	-70 10 57
187		05 36 54.9	-70 10 12	1111		05 38 00.4	-70 15 18
188	HV2707	05 36 25.8	-70 14 54	1243		05 37 29.6	-70 12 23
198	HV2717	05 37 15.7	-70 10 52	1305		05 37 43.8	-70 08 04
201		05 36 52.9	-70 09 31	1366		05 37 57.2	-70 10 45
206		05 37 23.7	-70 11 44	1402		05 37 21.1	-70 13 16
212		05 37 24.2	-70 09 43	1425		05 37 48.0	-70 15 58
223		05 37 02.9	-70 07 54	1674		05 37 21.0	-70 06 53
245		05 37 30.2	-70 13 57	2056		05 37 36.2	-70 15 43
251	HV2713	05 36 53.0	-70 12 08	2405		05 38 08.6	-70 07 51
252		05 37 38.9	-70 14 43	2728		05 37 35.0	-70 06 49
253		05 36 52.1	-70 09 44	2747		05 37 01.9	-70 11 26
267		05 36 51.2	-70 09 53	3094		05 36 50.8	-70 15 55
281		05 36 36.7	-70 09 06	3440		05 36 31.1	-70 06 21
299		05 36 36.1	-70 09 14	3818		05 37 54.7	-70 07 30
300		05 36 59.3	-70 07 41	5484		05 38 03.1	-70 06 14
302		05 37 02.5	-70 10 01	8892		05 36 46.1	-70 09 38
320		05 37 14.7	-70 06 56	9268		05 36 15.8	-70 16 49

Results

All the variable stars identified in the 10^′×10^′ field are labelled in Figure 4.1. There are 50 Cepheid variables, 15 Long-Period Variables with well-defined periods, 28 non-periodic LPVs, one eclipsing binary and two unusual variables of unknown type. The distribution of Cepheids over the field is very different from that of the red variables. The red variables are more or less uniformly distributed, showing no tendency to be located near a cluster. The Cepheids however are strongly concentrated around a number of the clusters in the field. NGC 2058 has nine Cepheids lying within a radius of 90 ^′′, NGC 2065 has seven, and the smaller cluster NGC 2059 has six (Figure 4.2). It is likely that a large proportion of these Cepheids are true cluster members. Alcock et al. (1995), briefly mention the Cepheid populations of NGC 2058 and NGC 2059. The numbers of Cepheids in each cluster and their period ranges are given. The period ranges agree exactly with those found here, and the numbers of objects reported are slightly fewer than that found here.

The Colour-Magnitude Diagram

The Colour-Magnitude Diagram for this field (Figure 4.3) shows two populations of different ages in this field. The old LMC bar population (∼3 Gyr old), characterised by the clump stars at (V,V-I)=(19.2,1.0), and the AGB extending to the upper right from the clump. The AGB then turns over due to the increasing V band bolometric correction for these cool stars. To the red of (V-I)=2.0, almost all stars on the AGB are variable.

**Figure 4.3:** The Colour-Magnitude diagram for the complete 10^′ field around NGC 2058 and NGC 2065. The variable stars are identified by the larger symbols. The LPVs tail away to the right because of the increasingly large V band bolometric correction as the stars get redder. The several Cepheids lying some distance from the instability strip are those whose photometry are believed to be contaminated by unresolved bright companions.
$\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc205865/fieldcmd.ps,width=14.6cm} \vspace{-1cm}\end{center}\end{figure}$

A second much younger population is also apparent - the main sequence extends upwards to V=17.0, and there are two clumps of stars at (V,V-I)=(16.3,1.1) and (15.9,0.8). These are the red and blue ends of core-helium-burning (CHeB) loops for intermediate mass stars. The concentration of stars at either end of the CHeB loops is due to the fact that the rate evolution is relatively fast along the loops, but much slower at either end.

Nearly all the Cepheid variables lie in the blue CHeB clump. As the mass of an intermediate mass star increases, the CHeB loops get longer and extend further towards the blue, and so the position of the blue clump gets bluer. The particular age and mass (∼5M) of the young stars in this field are such that the blue end of the loop lies within the instability strip, causing a relatively high fraction of the CHeB stars to be Cepheids. The very large numbers of Cepheids occurring in the outlying LMC cluster NGC 1866 (Welch et al. 1991) has the same underlying cause.

Another feature that can be seen in Figure 4.3 is that the CHeB red giants (to the blue of the AGB) extend continuously from the old clump stars right up to the red core-helium-burning counterparts of the Cepheids. This implies a continuous range of ages of the stars in this field, from around 3 ×10⁹ years to ∼1.2 ×10⁸ years, and in turn indicates continuous star formation in this part of the LMC. This may be contrasted with the CMD of clusters such as NGC 1850 (Figure 3.3). This cluster is of a similar age to NGC 2058-65, but the CMD is almost devoid of stars between the old AGB and the young core-helium-burning stars. In NGC 1850, there were two distinct bursts of star formation, with a period of quiescence in between. The outlying cluster NGC 1866 also shows an AGB similar to that of NGC 1850 (Brocato et al. 1989), with two distinct bursts of star formation.

The Colour-Magnitude Diagrams for each of the clusters (Figures 4.4 and 4.5), while less well-defined due to severe crowding, appear quite similar to that of the field as a whole. Although there do appear to be fewer old stars than in the field, this is simply due to the much lower completeness at fainter magnitudes caused by extreme crowding. The younger population of stars is present not just in the clusters, but also throughout the field itself. This, too, is quite different from the region around NGC 1850, where the field CMD and the cluster CMD are quite different, the young stars being confined to the cluster itself.

**Figure 4.4:** The Colour-Magnitude diagram for NGC 2058. All stars within 60 ^′′ are plotted. The Cepheid variables are marked with filled symbols.
$\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc205865/n2058cmd.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}$

**Figure 4.5:** The Colour-Magnitude diagram for NGC 2065. All stars within 60 ^′′ are plotted. The Cepheid variables are marked with filled symbols.
$\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc205865/n2065cmd.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}$

The Cepheid Variables

Approximately half of the variables identified in this field are Cepheids, a total of 50 in all. This is a much higher proportion than for the LMC bar as a whole. The MACHO collaboration has identified around 1,500 Cepheids in the LMC, and ∼20,000 red variables (Cook et al. 1995). Although a large number of these red variables are very low-amplitude and aperiodic, it is clear that the LMC as a whole contains many more LPVs than Cepheids. The survey of Hughes (1989) alone contains more than 1,000 moderate to large-amplitude (ΔI>0.5) LPVs.

The region studied here clearly has a large population of young stars, giving rise to the relatively large numbers of Cepheids. Of the 50 Cepheids observed here, 16 are previously known Harvard Variables (HV), with the remaining 34 being new discoveries.

**Table 4.2:** Cepheid Variable Photometry
Var.	ID	Period	<V >	<I >	A_V	A_I	Type	Notes
		(days)	mag.	mag.	mag.	mag.
35		4.1460	14.847	13.609	0.34	0.15	F	bright companion
52	HV 2706	4.4270	15.571	14.884	0.95	0.63	F
56		4.9771	15.353	14.602	0.78	0.44	F
60	HV 2726	4.1099	15.362	14.289	0.43	0.21	F	companion
66	HV 1009	3.260	15.470	14.753	0.34	0.19	O
67	HV 1008	3.418	15.489	14.755	0.32	0.20	O
69	HV 2709	4.4120	15.406	14.758	0.62	0.43	F
72		4.7126	15.448	14.576	0.26	0.15	F	red companion
75		4.728	15.561	14.868	0.77	0.50	F
82		4.889	15.444	14.677	0.75	0.46	F
87		3.543	15.451	14.698	0.33	0.23	O
88	HV 2714	5.345	15.559	14.747	0.72	0.42	F
89		4.677	15.429	14.695	0.76	0.49	F
93	HV 13042	3.0687	15.410	14.742	0.40	0.22	O
95		5.583	15.568	14.700	0.37	0.21	F
96		2.1603	15.673	15.097	0.24	0.15	O
106		3.7685	15.673	14.899	0.66	0.43	F	red companion
114		3.3045	15.609	14.852	0.30	0.18	O
137		2.3325	15.702	15.042	0.19	0.14	O
145		4.821	15.558	14.646	0.86	0.47	F	red companion
147		2.1205	15.796	15.126	0.46	0.29	O
153		5.7845	15.825	14.894	0.24	0.14	F
155	HV 2712	2.8814	15.874	14.852	0.84	0.43	F	red companion
156		3.645	15.616	15.055	0.61	0.48	F	blue companion
157	HV 2718	3.7370	15.858	15.107	1.01	0.63	F
168	HV 2720	4.1210	15.853	15.026	0.71	0.42	F
172		2.2160	15.822	15.174	0.43	0.27	O
179	HV 5976	5.355	15.944	14.991	0.76	0.49	F
183	HV 2710	3.195	15.920	15.240	0.82	0.50	F
185		2.2387	15.955	15.280	0.34	0.22	O
187		2.2705	15.931	15.184	0.40	0.15	O
188	HV 2707	2.1051	15.788	15.178	0.38	0.23	O
198	HV 2717	3.1553	16.065	15.340	0.76	0.47	F
201		1.9177	15.942	15.337	0.18	0.14	O
206		2.2117	15.943	15.255	0.40	0.25	O
212		1.9362	15.921	15.231	0.40	0.17	O
223		2.129	16.003	15.351	0.32	0.21	O
245		4.045	15.863	15.104	0.73	0.48	F
251	HV 2713	3.4488	15.939	15.245	0.70	0.47	F
252		1.854	15.989	15.334	0.38	0.25	O
253		2.087	15.902	15.113	0.37	0.19	O	companion
267		3.6431	15.907	15.164	0.89	0.57	F
281		2.7277	16.321	15.556	1.00	0.55	F
299		2.7046	16.175	15.507	0.85	0.59	F
300		1.8607	15.996	15.404	0.42	0.24	O
302		2.044	16.126	15.615	0.40	0.15	O	blue companion
376	HV 5975	3.1735	16.274	15.480	0.74	0.44	F
436		3.3678	16.302	15.412	0.85	0.52	F
504		2.083	16.479	15.747	0.62	0.38	F	red companion
554		2.1135	16.496	15.673	0.34	0.20	O

It is very likely that there are several other Cepheids located deep in the cores of the clusters. Such variables could not have been detected due to the extreme difficulty of performing photometry on anything but the brightest stars there. The observational data for the Cepheid variables are displayed in Table 4.2, and the V and I light curves are shown in Figure 4.6. Two complete cycles of the light curve are shown in these figures, with the epoch of zero phase being Heliocentric Julian Date JD=2,440,000.0.

The Cepheids in this field are all of short periods, ranging from 1.85 to 5.78 days, with the majority lying between 2 and 4 days. The fairly narrow range of periods implies that most of the Cepheids have similar masses. This is to be expected, since the ages of all the clusters and the young field population appear to be very similar.

A number of objects listed in Table 4.2 are noted as having companions. Examination of the best seeing frames has in most cases allowed visual confirmation that the Cepheid appears as an almost unresolved pair of stars. In a few cases, the Cepheid appears to be a single object, but the luminosity or colour are quite different to that expected for a Cepheid of the given period. Comparing the V and I band Period-Luminosity diagrams, and the Period-Luminosity-Colour diagram indicates the nature of the unresolved companion. For example, if the Cepheid lies substantially brighter than the I band P-L relation, but looks otherwise normal on the V band P-L relation, it is likely that the star has an unresolved red companion.

Contamination can also be inferred from the V and I band amplitude ratios. Red companions tend to reduce the I band amplitude more than the V band, thus increasing the V:I amplitude ratio. A number of the contaminated objects in Table 4.2 have amplitude ratios of $\raisebox{-0.6ex}{$\,\stackrel {\raisebox{-.2ex}{$\textstyle >$}}{\sim}\,$}$ 2, which is substantially higher than the normal ratio of 1.5-1.6. Conversely, the presence of a blue companion will reduce the V:I amplitude ratio.

Such contamination is not unexpected, considering both the extremely crowded field, and the fact that the Cepheids are concentrated in and around the clusters in the field.

The contamination of the photometry by unresolved companions is also often easy to detect when pulsation masses are computed for these objects. The increased luminosity and change in colour cause quite large changes to the derived masses. Red companions increase the derived masses, while blue companions reduce the derived masses. For example, when the pulsation mass of the Cepheid variable 35 is computed, an absurd result of 67M is derived.

Cepheids for which the photometry is believed to be contaminated (10 objects) have been excluded from further calculations.

Long-Period Variables

There are no classical Mira variables (defined as having V band amplitudes greater than 2.5 magnitudes), but there are a number of moderate-amplitude, periodic variables (Table 4.3). Light curves for these stars are shown in Figure 4.8. The scatter in the light curves in a number of these stars is mainly due to cycle-to-cycle variations. This effect is often seen in the classical Mira type variables of our own galaxy and the LMC (for example, see Figure 2 in Hughes 1989).

Variable 1402 has an unusual light curve, due to an apparent phase and luminosity change during a gap in the dataset. The period of pulsation is consistent with being 135 days both before and after the change (occurring at around JD=2,449,150), however when the two halves are plotted together, the phases are close to 180^o different. In Figure 4.7, observations before and after the phase change are plotted in different symbols. Substantially denser phase coverage is required to investigate the behaviour of this object.

Most of the LPVs however, are very low-amplitude objects (A_V < 0.4) with non-periodic variations in brightness - these are shown in Table 4.4. From Figure 4.3, it can be seen that almost all these objects lie on the extremely red part of the asymptotic giant branch (AGB). It is also clear that there is no separation between the non-periodic variables and those with relatively well-defined periods. Both types of variables are interspersed with no trend in luminosity or colour separating them.

**Table 4.3:** Photometry of periodic LPVs
Variable	Period	<V >	<V >- <I >	A_V	A_I	<K >	<J >- <K >
	(days)	mag.	mag.	mag.	mag.	mag.	mag.
403	47	16.34	2.27	0.30	0.30	11.44	1.27
446	131	16.38	2.54	0.54	0.30	10.86	1.68
463	158	16.54	2.38	0.56	0.32	-	-
523	410	16.91	3.36	1.80	>0.52	10.30	1.37
569	238	16.64	2.46	0.37	0.30	10.90	1.65
607	65	16.60	2.20	0.52	0.31	11.91	1.17
741	283	16.83	2.74	0.71	0.45	10.69	1.87
1111	293	17.58	2.86	1.67	0.95	11.07	1.99
1243	88	17.06	2.75	0.85	0.32	11.49	1.35
1402	135	17.32	3.37	0.94	0.42	11.02	1.27
2056	154	17.65	2.73	0.91	0.31	11.02	1.37
3094	103	17.94	3.69	1.17	0.54	11.12	1.26
459	69.3	16.39	2.44	0.39	0.16	-	-
604	520?	16.72	1.75	0.53	0.38	-	-
1305	118	17.28	2.67	0.77	0.41	-	-

Other Variables

Most of the objects listed in Table 4.4 are the non-periodic low-amplitude LPVs discussed in Section 4.3.3. With the exception of variable 40, all lie to the red of V-I=2.0, and are situated on the AGB of the old LMC population. Variable 40, however, is around one magnitude more luminous than the rest of the LPVs. Inspection of the best seeing V frames (where the variable is relatively faint) does show the star to be somewhat elongated, suggesting it has a close companion. The light curve of this star is qualitatively similar to that of the other non-periodic variables.

The three objects listed at the bottom of Table 4.4, are neither Cepheids nor LPVs. Their light curves are displayed in Figure 4.8

Variable 516 is unusual in that it remained at a constant magnitude and colour for a long period ( $\;\stackrel{{\raisebox{-.2ex}{$\textstyle >$}}}{{\sim}}\;$ 800 days), before suddenly brightening by one magnitude in V, and becoming bluer at JD∼2446500. This star lies in the old AGB, but is around 0.5 magnitudes bluer than the bluest of the LPVs. Unfortunately there is only very sparse coverage of the light curve during the brightened phase.

Variable 905 is located at an unusual position in the CMD, about 0.4 magnitudes to the red of the upper main sequence. It shows fairly periodic but very low-amplitude variations of brightness over long timescales, with a possible period of around 440 days. It is possible that the unusual position in the CMD is due to blending.

Finally, variable 338 is an upper main-sequence object, and appears to be an eclipsing binary, with a period of 2.7558 days. It should be noted that the relatively sparse sampling of this dataset means that eclipsing binaries are rather difficult to detect. A large number of eclipsing binaries with a variety of light curves have been detected in the LMC bar by the EROS project (Grison et al. 1995). However, this object lies to the east of the region surveyed by EROS.

**Table 4.4:** Non-periodic LPVs and Other Variables
Variable	Period(days)	<V >	<V >- <I >	A_V	A_I	Type
	(days)	mag.	mag.	mag.	mag.
40	93?	14.97	2.12	0.30	0.18	L
320	67?	16.23	2.57	0.33	0.25	L
324	mult	16.20	2.32	0.43	0.32	L
340		16.23	2.39	0.35	0.36	L
566	mult	16.59	2.57	0.49	0.35	L
586	56 ?	16.65	2.60	0.55	0.52	L
619	440?	16.73	2.09	0.82	0.30	L
627	60?	16.62	2.01	0.22	0.19	L
692	88 ?	16.70	2.66	0.80	0.60	L
695	48?	16.74	2.09	0.20	0.16	L
696		16.70	2.23	0.36	0.29	L
713	58	16.68	2.82	0.50	0.31	L
798		16.97	2.44	0.52	0.36	L
867	144	16.91	2.11	0.57	0.28	L
1068		17.09	3.04	0.63	0.36	L
1076	32	17.15	2.63	0.52	0.21	L
1105	46?	17.06	2.08	0.32	0.18	L
1366		17.23	2.11	0.20	0.14	L
1425		17.34	2.83	0.64	0.35	L
1674		17.94	3.15	>0.5	0.30	L
2405	83	17.66	2.99	0.43	0.32	L
2728	267?	17.79	3.01	0.77	0.36	L
2747	mult	17.94	3.25	1.51	0.78	L
3440		18.10	3.53	0.60	0.28	L
3818		18.05	2.90	0.35	0.32	L
5484	210	18.39	3.48	0.38	0.34	L
8892		17.63	3.76	0.70	0.45	L
9268	246?	18.58	4.24	1.30	0.67	L
516		16.38	1.66	1.10	0.53	?
905	440?	16.95	0.40	0.35	0.30	?
338	2.7558	16.24	-0.02	0.33	0.36	E

**Figure 4.8:** Light curves for the unusual and eclipsing variables. Variable 516 and 905 are plotted against Julian Day, whilst variable 338 is plotted against phase. The upper and lower panels show the V and I light curves respectively.
$\begin{figure}\begin{center} \vspace{-2cm} \epsfig{file=ngc205865/otherlight.ps,width=\linewidth} \vspace{-0.5cm}\end{center}\end{figure}$

Reddening

The reddening in this part of the LMC is quite variable. Examination of Figure 4.1 (taken in the I band) clearly shows a dearth of stars along the eastern edge, gradually getting more pronounced toward the north-east corner of the frame. This effect becomes even more pronounced when frames taken in V and B are examined, as the bluer wavelengths are affected more strongly by reddening. The remainder of the field, fortunately, appears to have a fairly uniform background star density.

The non-uniform reddening across the field presents a problem for deriving uniform, reddening-free photometry of the variables.

In order to minimise the effects of differential reddening, the field was divided into 25 2^′×2^′ sub-regions. The (V,V-I) diagram for each sub-region was plotted, and the colour of the main-sequence stars was compared to the colour of the Bertelli isochrones. The (V,V-I) diagram was then dereddened in order to bring the main sequence into agreement with the isochrones. This procedure yielded a mean reddening for each of the smaller sub-regions.

At this point, a low-order polynomial surface was fitted to the reddenings obtained. The resulting fit has the lowest reddening in the lower right (SW) corner, of E(B-V)=0.09 and the highest reddening in the upper left (NE) corner of E(B-V)=0.34. Thus the fit allows a mean reddening for a star to be determined based on its position. The fit had a RMS error of 0.03 magnitudes, although there are individual variations of up to 0.07 magnitudes. This must be caused by sharp variation of reddening in the field in contrast to the assumed smooth variation. This is the reason why the main sequence is rather broad.

The derived (position-based) reddening corrections for the Cepheids observed are shown in Table 4.5. Only the Cepheids which appear to be uncontaminated by unresolved companions are listed. The majority of stars have reddenings close E(B-V)=0.12.

**Table 4.5:** Cepheid Variable Reddening and Masses
#	E(B-V)	Mode	M_puls	M_ev	M_ev	#	E(B-V)	Mode	M_puls	M_ev	M_ev
				f_ov=0	f_ov=0.25					f_ov=0	f_ov=0.25
52	0.176	F	3.40	5.60	5.01	179	0.164	F	4.52	5.19	4.82
56	0.124	F	4.96	5.78	5.16	183	0.085	F	4.02	4.73	4.43
66	0.133	O	4.52	5.60	5.04	185	0.131	O	3.95	4.84	4.48
67	0.139	O	4.29	5.60	5.04	187	0.124	O	5.45	4.89	4.57
69	0.085	F	4.01	5.46	4.94	188	0.091	O	4.47	4.90	4.52
75	0.110	F	3.47	5.35	4.87	198	0.119	F	3.92	4.68	4.40
82	0.132	F	4.81	5.67	5.10	201	0.126	O	4.04	4.81	4.42
87	0.196	O	4.26	5.92	5.23	206	0.118	O	4.41	4.82	4.49
88	0.127	F	4.40	5.51	5.00	212	0.133	O	5.80	4.90	4.54
89	0.125	F	4.67	5.64	5.07	223	0.130	O	3.69	4.76	4.41
93	0.156	O	4.34	5.77	5.12	245	0.119	F	3.89	4.98	4.64
95	0.129	F	5.00	5.56	5.04	251	0.120	F	3.55	4.83	4.50
96	0.117	O	4.18	5.15	4.67	252	0.124	O	5.00	4.76	4.42
114	0.133	O	4.31	5.41	4.92	267	0.127	F	4.03	4.93	4.59
137	0.121	O	4.93	5.16	4.72	281	0.144	F	4.07	4.45	4.22
147	0.147	O	5.24	5.13	4.69	299	0.145	F	3.41	4.59	4.27
153	0.121	F	4.50	5.21	4.84	300	0.130	O	3.74	4.75	4.35
157	0.116	F	4.28	4.97	4.63	376	0.169	F	3.71	4.61	4.34
168	0.162	F	4.64	5.20	4.79	436	0.121	F	4.97	4.50	4.35
172	0.131	O	4.32	5.02	4.60	554	0.153	O	3.79	4.29	4.13

Cluster ages

Flower (1982) derives an age of 1.14×10⁸ years (10^8.06yr) for both NGC 2058 and NGC 2065, based on isochrone fitting to the (V,B-V) colour magnitude diagram. In Figure 4.9, three evolutionary models of Bertelli et al. (1994) are superimposed on the dereddened (V,V-I) CMD. The three isochrones shown correspond to ages logT = 8.0, 8.1, and 8.2 (or T = 1.0, 1.3 and 1.6×10⁸ yr). The (evolution) masses of stars at the main-sequence turn-off for these models are 5.2, 4.7 and 4.2M, respectively. These evolutionary models, which are based on the newer OPAL radiative opacities (Rogers and Iglesias 1992), also include a moderate degree of convective core overshoot (ie, Λ=0.5, or f_ov=0.25).

Figure 4.9 indicates that the age of the bulk of the young population in this field is around 1.4×10⁸, although there is clearly a range of ages present, from 1.0-1.6×10⁸ yr. There is no relation between position in the field and age. After accounting for the effects of reddening, the CMD looks very similar in all parts of the field.

**Figure 4.9:** The NGC 2058-65 field Colour-Magnitude diagram. The magnitudes and colours have been dereddened by the reddening correction outlined in section 4.4. The various type of variable stars are marked in larger symbols. The theoretical red and blue edges of the Cepheid Instability Strip (CIS) are marked, for both the fundamental (solid lines) and first overtone (dotted lines). The isochrones are the log(T)=8.0, 8.1 and 8.2 models from Bertelli (1994), which correspond to turn-off masses of 5.2, 4.7 and 4.2M, respectively.
$\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc205865/n2058iso.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}$

Cepheid Properties

The Reddening-Free relation

In order to investigate the properties of Cepheids in a completely reddening- free manner, the Wesenheit function W = V - β(V-I) can be plotted (van den Bergh 1968). This quantity is similar to that plotted in the Cepheid Period-Luminosity-Colour (PLC) relation. If the value of β is chosen in an appropriate manner, W can be made to be independent of the effects of reddening. In the case where V and I passbands are used, β = 2.37 satisfies the reddening-free condition assuming the reddening law of Lee (1970). With this value of β, the fainter apparent V magnitude is exactly compensated for by subtracting the redder apparent colour.

Figure 4.10 shows the W-P relation for nearly 100 LMC Cepheids in the regions of several different clusters, and from the general LMC field. The NGC 1850 field data is from Chapter 4, and the NGC 1866 data is from unpublished VI photometry by Sebo and Wood. The longer-period objects are from Martin et al. (1979).

**Figure 4.10:** The reddening-independent P-L diagram for NGC 1850, NGC 1866, NGC 2058-65, and the LMC field Cepheids studied by Martin *et al.* (1979). The two parallel but offset sequences clearly delineate the fundamental and overtone mode Cepheids. The few outlying points, chiefly from NGC 2058-65 are due to the Cepheids having unresolved companions.
$\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc205865/wplc.ps,width=\linewidth}\end{center}\end{figure}$

The two distinct sequences on this plot correspond to the fundamental and first overtone modes of pulsation. It can be seen that the (fundamental mode) data from all four sources are coincident, showing little or no zero point offset along the y-axis. Any vertical offsets in this diagram could only be caused by distance modulus differences between the objects, or by photometric zero point differences. The dispersion of the fundamental mode Cepheids about the line is ∼0.07 magnitudes, so that the combined effect of photometric zero point differences and distance modulus differences are likely to be smaller than this.

Relative distances between the clusters may be derived from Figure 4.10 by assuming the gradient of the WPLC relation and performing fits to determine the zero point of each of the clusters. Only the fundamental mode Cepheids were used. The results of the zero point fits for each of the clusters is shown in Table 4.6, along with distance moduli relative to NGC 1850 given by ΔDM₁. If the zero point differences are assumed to be due to true cluster distance modulus differences, it would indicate that NGC 1866 is ∼0.05 magnitudes more distant than NGC 1850 and NGC 2058-65 (which lie at essentially the same distance).

This result may be compared to the cluster distances derived using the LMC rotation solution of Caldwell and Laney (1991). Applying this solution to the positions of the three fields yields distance modulus differences (relative to the dynamical centre of the LMC) as given by ΔDM₂ in Table 4.6. The rotation solution indicates that the northern part of the LMC (where NGC 1866 is located) is in fact ∼0.03 magnitudes closer than the LMC bar. We believe that the photometric zero points between the clusters should be consistent to better than 0.02 magnitudes. Given that there is a substantial young field population in the NGC 2058-65 region, and that the apparent distance of NGC 1850 matches that of NGC 2058-65, it is highly likely that these two clusters do lie close to the LMC plane. The discrepancy between the NGC 1866 Cepheid distances and the rotation solution suggests that this cluster lies in the background of the LMC. A comparison of the radial velocity of NGC 1866 (301 kms^-1, Welch et al. 1991) with the velocity of the neutral hydrogen in this region (Figure 7, Luks and Rohlfs 1992) shows that they are very similar. This does not indicate that there is anything unusual about the position of the cluster.

**Table 4.6:** Distance Modulus offsets
Cluster	WPLC ZP	ΔDM₁	ΔDM₂
NGC 1866	16.082±0.02	+0.048	-0.034
NGC 1850	16.034±0.02	0.000	-0.014
NGC 2058-65	16.040±0.02	+0.006	+0.012

The P-L relation

The traditional Cepheid Period-Luminosity relation is plotted in Figure 4.11. Only uncontaminated stars from the NGC 2058-65 region are included. The two pulsation sequences (the fundamental and overtone modes) are clearly visible, separated by ΔlogP∼0.2. The dashed line is the Caldwell and Coulson (1986) fit to the Martin et al. (1979) (MWC) sample of LMC Cepheids with P $\raisebox{-0.6ex}{$\,\stackrel {\raisebox{-.2ex}{$\textstyle >$}}{\sim}\,$}$ 10days, using the revised reddenings of Caldwell and Coulson (1985). The solid line is the least-squares fit to all the fundamental mode Cepheids plotted, 65 objects in all. The least-squares solution is

The inclusion of very short-period Cepheids in this solution extends the range in logP substantially, and should provide a better determination of the gradient of the P-L relation than the Caldwell and Coulson fit.

**Figure 4.11:** The LMC Period-Luminosity diagram. The dotted line is the Caldwell and Coulson fit to the MWC sample of (longer period) Cepheids. The solid line is the least-squares fit to all the fundamental mode objects. The NGC 1850 data is from Chapter 3, the NGC 1866 data is from unpublished VI photometry by Sebo and Wood, and the MWC data is from Martin *et al.* (1979).
$\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc205865/n2058-plnew.ps,width=\linewidth}\end{center}\end{figure}$

The P-L-C Relation and the LMC Distance Modulus

The Period-Luminosity-Colour relation (PLC) for the Cepheids in the NGC 2058-65 field is shown in Figure 4.12. The y-axis is the quantity V₀ - β(V-I)₀. The value of β = 3.28 has been used, this being the maximum likelihood value based of individual reddenings of LMC Cepheids derived by Caldwell and Coulson (1986). The qualitative appearance of this diagram however, is not sensitive to the value of β used here.

The line plotted is the fit of Caldwell and Coulson (1986), based on fitting the PLC diagram for LMC Cepheids with P $\raisebox{-0.6ex}{$\,\stackrel {\raisebox{-.2ex}{$\textstyle >$}}{\sim}\,$}$ 10 days. The slight offset of the line from the data points may be attributed to the fact that this line is an extrapolation downward from log(P)=1, and is hence well outside the domain from which the fit was computed. All the different fits in Table 1 of Caldwell and Coulson (1986) show a similar small offset to the observed data presented here.

The LMC Distance Modulus may be calculated by comparing the observed and theoretical PLC relations. The PLC relation is of the form

**Figure 4.12:** The NGC 2058-65 Period-Luminosity-Colour diagram. The symbols have the same meaning as in Figure 4.11. The line is the Caldwell and Coulson (1986) fit to LMC Cepheids based on statistical reddenings. The open symbols are objects which are probably contaminated by unresolved companions.
$\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc205865/n2058-plc.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}$

The theoretical values of the coefficients α, β and γ are computed from Chiosi et al. (1993), using composition parameters appropriate for the LMC (Y=0.27, Z=0.008), and an overshoot parameter f_ov=0.25, corresponding to moderate overshoot. The values of the coefficients are α=-3.67, β=3.84, and γ=-3.17, for the fundamental mode, and α=-3.93, β=3.68, and γ=-3.45 for the first overtone mode. By fixing α and β, and comparing the value of γ between the observed and the theoretical PLC relations, a LMC Distance Modulus of 18.52±0.03 (fundamental mode) and 18.45±0.03 (first overtone mode) is derived. Thus the two modes produce similar distance moduli.

If there is assumed to be no overshoot ( f_ov = 0.0), and the analysis above is repeated, the distance moduli derived for the fundamental and overtone modes are 18.69±0.03 and 18.60±0.03, respectively. These values are becoming less consistent as the assumed degree of overshoot is decreased.

If the maximum plausible overshoot ( f_ov = 0.5) is assumed, one obtains distance moduli of 18.34±0.03 and 18.30±0.03 for the fundamental and overtone modes. Whilst this degree of overshoot seems to be favoured based on the comparison of evolution and pulsation masses (Section 4.7), it implies a distance modulus which is substantially less than the values normally derived from the studies of LMC Cepheids. Further work is clearly required to solve this problem.

Cepheid Evolution and Pulsation Masses

The pulsation masses, non-overshoot evolution masses, and overshoot evolution masses of the Cepheids are shown in Table 4.5. All the masses have been calculated assuming a LMC distance modulus of 18.5, a metallicity of Z=0.008, and reddening correction for each star as derived in Section 4.4, and displayed in Table 4.5. This table also lists the apparent pulsation mode of each Cepheid, and this has been used in the determination of the pulsation mass. The evolution mass does not depend upon the pulsation mode of the Cepheid.

The pulsation masses have been calculated using the results of Chiosi et al. (1993). It should be noted that these pulsation masses are independent of convective overshoot.

Figure 4.13 shows the pulsation masses plotted against evolution masses. The evolution masses are derived from the models of Bertelli et al. (1994), which incorporate a moderate degree of convective core overshoot. The line corresponds to the case where the pulsation mass and evolution mass are equal.

**Figure 4.13:** A comparison of evolution and pulsation masses for the NGC 2058-65 Cepheids. Filled symbols are fundamental mode pulsators and the open symbols are overtone pulsators. Each Cepheid is plotted assuming a distance modulus of 18.50, and moderate convective overshoot (f_ov=0.25). The arrows show the effects on the derived masses of varying the overshoot, distance modulus, reddening and the assumed Colour-Temperature relation. Δ(Col-T_eff) corresponds to an increase of V-I at a given T_eff.
$\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc205865/n2058-masses.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}$

The vast majority of Cepheids lie well to the left of the equal-mass line. A few objects however, do lie to the right of the line. All but one of these objects are overtone pulsators, and most are situated close to clusters. Again, contamination of the photometry for these objects is likely.

The sensitivity of the derived masses on various parameters is indicated by the arrows. These show the effects on a 5M star of varying (within plausible limits) the overshoot parameter (f_ov=0.25 →0.0), the LMC distance modulus (DM=18.5 →18.6), the reddening (ΔE(B-V)=-0.05), and the Colour-Temperature relation (Δ(Col-Temp)=0.05). It should be noted that changes in all these parameters produce mass changes which are proportional to the mass of the star (i.e. a constant percentage change in mass). Thus, if the arrows on the diagram were plotted for a 3M star, the length of the lines would be reduced by 40%.

Based on the stars on the left of the line, the mean difference between the (moderate overshoot) evolution mass and the pulsation mass is around 15%. Models without core overshoot are unlikely - the mass discrepancy rises to 30-40% using standard values of the other parameters. In order to equate pulsation and evolution masses, a much larger degree of convective core overshoot would need to be employed in the evolutionary models. The maximum plausible overshoot (f_ov=0.5) would be required to bring the evolution mass into agreement with the pulsation mass.

Models with such high overshoot also have substantially shorter core-helium-burning loops. For the range of masses here (4-5M), evolutionary models with f_ov=0.5 would not have CHeB loops that are long enough to penetrate into the Cepheid instability strip. The models of Bertelli also incorporate convective envelope undershoot, which tends to lengthen the CHeB loops. The length of the CHeB loops is fairly sensitive to a number of input parameters to the models, and it may be possible to produce models with both the high overshoot and loops of sufficient length.

Resolution of the mass discrepancy by changing the assumed LMC distance modulus is unlikely. The distance modulus would have to rise to at least 18.65, which would be in serious conflict with other methods of distance determination. (e.g. from SN1987a (Panagia et al. 1991; Gould 1994), and recent RR Lyrae-based measurements (Simon and Clement 1993).

Examination of Figure 8 in Chiosi et al. (1993) shows that there may be scope for improvement in the Colour-Temperature (CT) relations used in the pulsation models. This figure shows an offset between the CT relations adopted for the models, and the empirical relations as determined by Bessell (1979) and McWilliam (1990). The size of the offset is around 0.05 magnitudes in V-I. If the empirical colour-temperature relations are used to calculate the pulsation masses, the derived masses are approximately 12% lower, thus exacerbating the mass discrepancy. It would not be comforting to try to force mass equivalence by adopting a CT relation even further away from the empirical calibration.

Similar uncertainties (∼0.05 mag.) in the bolometric correction also exist. However, due to the magnitude of the various coefficients in the pulsation equations, changing the bolometric correction has only a small effect on the derived masses.

The effect of reddening on the M_ev-M_puls diagram is the shortest arrow on Figure 4.13 but it is also directed perpendicular to the M_ev=M_puls line. It is conceivable that the mass discrepancy could be resolved if the Cepheid reddenings were around E(B-V)=0.06 lower than those assumed here. This scenario has numerous problems - the mean reddening of the Cepheids would be ∼E(B-V)=0.05, which is a little less than the typical foreground reddening to the LMC. Given the large variations in reddening across this field, and in particular the clearly heavily reddened regions, it is highly likely that the field has a substantially larger reddening than just the foreground value. Also, a mean reddening of E(B-V)=0.05 would leave the main-sequence stars much too red to be fit to any isochrones.

In an ideal world, the evolution masses would be correlated monotonically with the pulsation masses, even in the presence of any systematic offsets between the masses. This would correspond to a narrow line of points in Figure 4.13, however this is certainly not the case here. There is a fairly large scatter between the two masses. There are two factors involved here. The derived pulsation masses are quite sensitive to the observed colours, so individual reddening errors will lead to significant errors in the pulsation masses. Although the mean reddening has been corrected for, there are undoubtedly variations from the mean for individual objects. There is evidence for this in the width of the PLC diagram (Figure 4.12) compared to the (reddening-free) WPLC diagram (Figure 4.10). The scatter about the fundamental mode line is ∼0.04 magnitudes in the WPLC, but is ∼0.10 magnitudes in the PLC diagram. Further evidence for this reddening effect may be found by comparing the width of the main sequence in the NGC 2058-65 field CMD (Figure 4.3), to the width of the main sequence for other LMC clusters such as NGC 2004 (Bencivenni et al. (1991), Figure 5), or even NGC 1850 (Figure 3.2). Whilst some of the width difference could possibly be explained by the differing star-formation environments in each of the clusters, or perhaps differing stellar rotation, the bulk of the difference is probably due to differential reddening.

The presence of differential reddening, whilst complicating matters, does not alter the conclusions. With such a large sample of Cepheids in the one field, the effects of reddening errors should average out. A large amount of main-sequence convective core overshoot seems the most likely solution to the problem of differing evolution and pulsation masses.

LPVs

The JK photometry (Table 4.3) has been dereddened using the relation of Lee (1970), namely E(J-K)=0.59 E(B-V), and A_K=0.38 E(B-V). The mean VI magnitudes have been calculated from Fourier fits to the observed light curves in Figure 4.7, and the mean JK magnitudes have been derived from the mean of the two measurements. The very low amplitude of these variables in the JK bands (A_K∼0.2A_V) ensures that this simple mean should not have any errors larger than that already imposed by the accuracy of the photometric transformation from the instrumental magnitudes.

Seven of the variable stars have J-K∼1.3, typical of oxygen-rich LPVs of spectral type M or MS (Wood, Bessell and Fox 1983). The other four stars have much redder colours, with J-K=1.7-2.0, indicating that they are almost certainly carbon stars.

The long-period variables with well-defined periods from Table 4.3 are plotted in a Figure 4.14. The empirical K-logP relation (Feast et al. 1989) is also plotted. The longer-period objects (P>200 days) lie quite close to the line, indicating that they are similar kinds of objects to those surveyed by Feast et al. (1989) and Hughes and Wood (1990) - i.e. normal LMC Mira-like variables, although they have substantially lower amplitudes. This is probably a selection effect - the existing surveys of LMC red variables are based on photographic plates, and this limits the completeness to variables with I band amplitudes $\;\stackrel{{\raisebox{-.2ex}{$\textstyle >$}}}{{\sim}}\;$ 0.5 magnitudes. It is for this reason that none of the NGC 2058-65 LPVs appears in the Hughes catalog.

However all the objects with periods shorter than 200 days are around 1.3 magnitudes brighter than the K-logP relation. This diagram bears a striking resemblance to the Cepheid P-L relation (Figures 4.10 and 4.11), in that there appears to be a second distinct sequence of objects lying to the left of the primary sequence. In the case of the Cepheids, the second sequence corresponds to the first-overtone mode pulsators. In the case of the LPVs, the offset in period is ΔlogP=0.4, or a factor of ∼2.5. Pulsation models of LPVs (Fox and Wood 1982) predict a period ratio between the fundamental and first-overtone modes of P₀/P₁∼2.3.

Thus it seems plausible that the anomalous stars in Figure 4.14 could correspond to stars pulsating in higher overtone modes. This possibility will be investigated in detail in Chapter 5.

**Figure 4.14:** The more regular LPVs in the NGC 2058-65 field plotted on the K-logP diagram. The line is the mean K-logP relation for LMC Mira variables from Feast (1989).
$\begin{figure}\begin{center} \vspace{-1cm} \epsfig{file=ngc205865/n2058-klogp.ps,width=\linewidth} \vspace{-1cm}\end{center}\end{figure}$

Summary

The region around the LMC clusters NGC 2058-65 has been found to contain large numbers of Cepheid variables, many of which appear to be associated with a number of young clusters in the field. The field also exhibits substantial differential reddening. Isochrone fitting to the clusters show they are all of a similar age, ∼1.4×10⁸ yr.

Comparison of evolution and pulsation masses for the Cepheids indicate that a large degree of convective core overshoot would be required in the evolutionary models in order to bring agreement with the pulsation masses. Evolutionary models with a moderate degree of overshoot yield masses that are 15-20% lower than the pulsation mass.

A number of LPVs were found in the field around the clusters. These seem to fall on two sequences that can be interpreted as corresponding to fundamental and first overtone pulsation.