2 Observations, data reduction and calibration

B (ESO # 450 filter) and V (ESO # 451 filter) images were collected by one of us (E. B.) during five nights, from Nov. 28 to Dec. 2 1997 (we shall refer to the nights as N1 to N5, where N1 = Nov. 28 night), with the ESO 1.54-m Danish Telescope (La Silla, Chile). The instrument installed at the telescope was the DFOSC, equipped with a LORAL/LESSER C1W7 CCD (2052 $\times$ 2052 pixels). The scale was 0.39 arcsec/pixel. The log of observations is reported in Table 1.

The original images were pre-reduced following the usual procedures, i.e. bias subtraction and flat-fielding. However, the edges of the frames have been trimmed to remove the overscan columns and the regions of the CCD where flat-fielding showed dramatic differences with respect to the central part of the CCD image. The resulting frame dimensions were 1911 $\times$ 1811 pixels, for a total field of view of $\sim$ $12\farcm 4 \times 11\farcm 8$.

Figure 1: CCD frame region (Region 2) affected by optical aberrations. The center of the dividing circumference is (500, 905) and its radius is 1120 pixels.

Figure 2: Instrumental errors in magnitude ( $\sigma _{V}$) and colour ( $\sigma _{B-V}$) as a function of the calibrated magnitudes (V) for the stars in the frames of NGC 458.

 

 

Table 2: Standard stars used for calibration.

Night	Reference field	Standard stars	No. of B, V observations
			per field
N1	Selected Area 95 (Landolt 1992)	42, 101, 105, 107	1, 2
	E3 Region (Graham 1982)	R	1, 1
N3	Selected Area 95 (Landolt 1992)	42, 101, 105	1, 1
	E2 Region (Graham 1982)	I, m, o, s, t	3, 3
	E3 Region (Graham 1982)	T, k, v	1, 1
N4 $^{{\rm a}}$	T Phe (Landolt 1992)	A, C, D, E, F	6, 6
	E2 Region (Graham 1982)	I, m, o, s, t	3, 3
N5 $^{{\rm a}}$	T Phe (Landolt 1992)	A, C, D, E, F	4, 4
	E2 Region (Graham 1982)	I, m, o, s, t	2, 2

$^{{\rm a}}$

Photometric night.

Photometry was performed using the point-spread function (PSF) technique with the DAOPHOT II package (Stetson 1994). Raw instrumental magnitudes and errors were obtained by fitting the PSF to all identified objects using the routine ALLSTAR (Stetson 1994). A detailed test of the resulting photometry revealed a region of the frames where stellar images appeared elongated because of optical aberrations. ALLSTAR deconvolved these objects into more stars than really present, providing a bad fit with high residuals. We eliminated from our star lists all the objects identified in this region, named as "Region 2'' in Fig. 1. The field of view of the resulting "good'' field (Region 1) is $\sim$113.4 arcmin².

For a given stellar field, each frame was reduced independently; then the frame with the best seeing was chosen in each filter as a reference for coordinate and magnitude transformations. Subsequently, all the frames where transformed into the reference system to perform suitable average operations in order to obtain a set of mean instrumental magnitudes (weighted according to the photometric quality of the frames). Finally, B and V photometry for each field were matched in order to obtain the instrumental magnitudes (v), colours (b-v) and errors (see Fig. 2).

To transform instrumental magnitude into the Johnson system, several standard stars from the E-regions (Graham 1982) and from equatorial fields (Landolt 1992) were observed every night, except N2 (see Table 2 for a detailed list of standards used); however, the best photometric night turned out to be N4.

Figure 3: Panels a), c): calibrating relations for N4 night, found by a weighted least squares fit. Panels b), d): difference between standard and calculated magnitudes and colours for the calibration stars; the result appears satisfactory.

 

 

Table 3: Colour and extinction coefficients and zero points (see Fig. 3) adopted to calibrate instrumental results; ${\rm rms}_{V}$, ${\rm rms}_{B-V}$ are the root mean squares from the fitting procedures; $\epsilon _{B}$ and $\epsilon _{V}$ are the adopted extinction coefficients in B and V bands, respectively.

Night	$\alpha$	$\beta$	${\rm rms}_{V}$	$\gamma$	$\delta$	${\rm rms}_{B-V}$	$\epsilon _{B}$	$\epsilon _{V}$
N1	0.026	23.912	0.014	1.120	-0.485	0.021	0.20 $\pm$ 0.01	0.10 $\pm$ 0.01
N3	0.026	23.913	0.013	1.120	-0.487	0.010	0.20 $\pm$ 0.01	0.10 $\pm$ 0.01
N4	0.026	23.899	0.008	1.120	-0.498	0.006	0.198 $\pm$ 0.007	0.095 $\pm$ 0.006
N5	0.026	23.902	0.006	1.120	-0.486	0.009	0.20 $\pm$ 0.01	0.095 $\pm$ 0.006

Figure 4: Left panel: superposition of HST and Danish CM diagrams for the cluster NGC 1777; note that the present diagram does not include stars with R < 25 arcsec. Right panel: the same for the cluster NGC 2155; note that our diagram does not include stars with R < 16 arcsec.

Figure 5: Panels a) and c): comparison between present and HST photometry for NGC 1777. Panels b) and d): the same for NGC 2155.

Figure 6: Left panel: apparent spatial distribution of the investigated LMC clusters. Open circles indicate objects studied by Brocato et al. (2001), whereas dashed lines roughly delimitate LMC Bar ($\delta$ and RA units are degree and hour, respectively). Right panel: the integrated properties of 4 LMC clusters investigated in this work are compared to a sample representative of the global cluster population of LMC; no data are available in literature for KMHK264 and KMHK265.

We used calibrating relations of the form:

$$V-v_{{\rm a}} = \alpha (b-v)_{{\rm a}} +\beta$$ (1)

$$(B-V) = \gamma (b-v)_{{\rm a}} + \delta$$ (2)

where V, (B-V) indicate Johnson magnitude and colour, respectively, whereas $v_{{\rm a}}$ and $(b-v)_{{\rm a}}$ are instrumental results corrected for atmospheric extinction and normalised to an exposure time of 1 second, as given by the following relations:

$$b_{{\rm a}} = b + 2.5\log t - \epsilon_{B}X$$ (3)

$$v_{{\rm a}} = v + 2.5\log t - \epsilon_{V}X$$ (4)

where $\epsilon _{B}$ and $\epsilon _{V}$ are the adopted extinction coefficients and X the airmass. Coefficients $\alpha$, $\beta$, $\gamma$, $\delta$ were found by a weighted least squares fit through the data on the N4 night, where the weights take into account both the errors on Landolt's and Graham's magnitudes and the errors in the aperture photometry. Figure 3 reports the calibration for the N4 night.

To obtain internal consistence among our data from different nights, we used the SMC cluster NGC458, which was observed during each night. We adopted the $\alpha$ and $\gamma$ colour coefficients of N4 also for N1, N3, and N5 and determined new zero points, reaching a good level of consistence (residual discrepancies from one night to the other resulted less than 0.01 mag). In Table 3 we summarise the adopted relations for calibration.

2.1 Comparison with previous HST photometry

LMC clusters NGC 1777 and NGC 2155 were already observed in the previous investigation, thus one can perform a comparison between HST and the present photometry. Left panel of Fig. 4 shows that the Danish CM diagram appears not worse than in the previous investigation, even though NGC 1777 with respect to the other clusters was observed in relatively bad seeing condition and with a shorter time exposure for deep frames. The obvious improvement of the HST diagram is to provide photometric measurements of stars located in the central region of the clusters and to reach a larger limiting V magnitude, though by less than 1 mag. The CM diagrams of NGC 2155 presented in right panel of the same figure support quite similar considerations.

For the 436 stars of NGC 1777 in common (Figs. 5a, 5c), one finds a discrepancy of the order of <$\Delta V$> = < $V_{{\rm Danish}} - V_{{\rm HST}}$> $\sim$ -0.04 mag, while colours appear in better agreement, with < $\Delta (B-V)$> = < $(B-V)_{{\rm Danish}} - (B-V)_{{\rm HST}}$> $\sim$ 0.02 mag. Note that rather large number of stars with <$\Delta V$> < -0.4 (i.e. stars of present photometry brighter than in the HST measurement) can be understood in terms of a blending effect in our photometry due to the worse seeing. In the case of NGC 2155, the same kind of comparison for 274 stars in common (Figs. 5b, 5d), discloses a small difference in V, of the order <$\Delta V$> $\sim$ 0.03-0.04 mag and a good agreement in colour (< $\Delta (B-V)$> $~\sim -0.01$ mag).

We conclude that Danish and HST investigations appear consistent within 0.1 mag.