3 Data

   
3.1 Observations

Our observations were carried out with the Nordic Optical Telescope (NOT), La Palma, using the ALFOSC focal reducer instrument with the Loral-Lesser ( $2048\times 2048$) CCD during the two nights of September 29 and 30, 1998 (see www.not.iac.es for details). The basic instrumental data are listed in Table 1. As broad band filters we used Bessell V and Gunn i, the filter properties are listed in Table 2.

Brewer et al. (1995) observed 5 fields in M 31 with the above described method. The larger the samples of known AGB stars are, the more reliable are the derived properties of this population. As this work covered only about 2% of the whole M 31-area, we selected an additional field in M 31 for a first test of our new filter set centered on $\alpha_{2000}=0^{\rm h} 39^{\rm m} 53^{\rm s}$ and $\delta_{2000}=40^{\circ} 25^{\prime} 28^{\prime\prime}$ (also aiming for a comparison of our results with the comprehensive work of Brewer et al. 1995). This test field is located between their fields 3 and 4, about 14kpc south-west of the centre of M 31 along its major axis. Table 3 summarizes our observations of the field in M 31 and the calibration observations in the Selected Area fields #110 and #95, for which we used V and i data from Landolt (1992). Both nights were photometric, and the seeing varied between 1 $^{\prime\prime}$ and 1 $\hbox{$.\!\!^{\prime\prime}$ }$3 on the combined frames.

 

 

Table 1: Instrumental data of NOT/ALFOSC

Main mirror diameter	2.56m
CCD size	2048$\times$2048pixels
Field of view	6 $\hbox{$.\mkern-4mu^\prime$ }$5$\times$6 $\hbox{$.\mkern-4mu^\prime$ }$5
Pixel size	15$\mu$m
Pixel scale	0 $\hbox{$.\!\!^{\prime\prime}$ }$189/pixel
Readout noise	6.6e-
Gain	1.07e-/ADU

  

 

Table 2: The filters used

Filter	NOT #	$\lambda_{\rm c}$(Å)	$\Delta\lambda$(Å)	System
V	75	5300	800	Bessell
i	12	7970	1570	Gunn
TiO	-	7780	110	Wing
CN	-	8113	85	Wing

 

 

Table 3: Observing log

Field	Filter	Exp.time	Field	Filter	Exp.time
M 31	V	$3\times 400$ s	SA110	V	30 s
	i	$3\times 400$ s		i	10 s
	TiO	$4\times 1200$ s		TiO	130 s
	CN	$4\times 1200$ s		CN	250 s
			SA95	V	35 s
				i	20 s
				TiO	180 s
				CN	240 s

  
3.2 Reduction and calibration

The basic reduction of all frames was done with MIDAS (bias and dark subtraction, flat-fielding, cosmic ray removal, summing, and cropping). The narrow band filters were used in the converging beam of the telescope to avoid wavelength shifts due to the large angles of incidence in parallel beam instruments such as ALFOSC. This resulted in some vignetting and all frames were cropped to $1700\times 1600$ pix² or $5\hbox{$.\mkern-4mu^\prime$ }3\times 5^{\prime}$, in order to use only the unvignetted area. Photometry on the combined frames was done with the PSF-photometry reduction packages DAOPHOT II and ALLSTAR within MIDAS (Stetson 1987, DAOPHOT User's Manual). After a detailed analysis of the influence of DAOPHOT/ALLSTAR parameters we have chosen the following quality criteria for stars to be considered in the further analysis: sharp was allowed to range between -5 and 5; the formal magnitude error (error of PSF-fitting) was allowed to reach $\sigma < 0.1^{\rm mag}$ for i₀, (V-i)₀, and (TiO-CN)₀ (see below for further information on the selection criteria).

The standard fields SA95 and SA110 of Landolt (1992) were observed to obtain the photometric zeropoints for the V and i filters. The similarity of Landolt's Cousins i-filter ($\lambda_{\rm c}=7900$Å and $\Delta\lambda=1500$Å) and our i-filter (see Table 2) motivated this approach.

No photometric calibration was done for the two narrow band filters. As we know, that stars with "early'' spectral type lack TiO/CN-features, and therefore have (TiO-CN) $_0 \approx 0^{\rm mag}$, we can use them as a photometric calibration for this colour index. Choosing "blue'' stars [ $(V-i)_0 < 0.7^{\rm mag}$], with strict quality criteria ( $\sigma< 0.05^{\rm mag}$ for all filters and colour indices, sharp between -1.5 and 1.5) we determined an offset in (TiO-CN)₀ of $0.37^{\rm mag}$, which we applied to all stars.

For the atmospheric extinction correction the standard coefficients for KPNO of k_V=0.152, k_i=0.061, $k_{\rm TiO}=0.055$and $k_{\rm CN}=0.051$ were applied. As a check of the reliability of our photometry we tried to identify known Cepheids in our field, which lies just on the south-western border of field III in Baade & Swope (1965). It turned out, that we have variables #168, #192, and #193 in common. These are Cepheids with periods of 13.125, 4.773, and 15.524days, respectively. By using the mean PL-relationships given in Groenewegen & Oudmaijer (2000), a distance modulus for M 31 of $(m-M)=24.43^{\rm mag}$ (Freedman & Madore 1990), and applying the reddening corrections given below to our observations, we get the results listed in Table 4. The photometry of star #192 is affected by a nearby field star, and the results are therefore only listed for reference.

 

 

Table 4: Observed Cepheids in the field

#	Period	Filter	app. mag	app. mag
	[d]		calc.	obs.
168	13.125	V0	19.9	19.2
		i0	19.1	18.8
(192)	(4.773)	V0	(21.1)	(20.1)
		i0	(20.5)	(19.5)
193	15.524	V0	19.7	19.0
		i0	18.9	18.5

Keeping in mind the random Cepheid phases of our observations, the known $m_{\rm phot}$-amplitudes of the Cepheids (1.3 $^{\rm mag}$, 0.7 $^{\rm mag}$, and 1.55 $^{\rm mag}$, respectively), the low number of Cepheids found, as well as the accuracy of our photometry (typically around 0.08 $^{\rm mag}$ in V and 0.13 $^{\rm mag}$ in i), the measured and calculated values are consistent. The shift of V₀ and i₀ into the same direction suggests to be caused by pulsation, i.e. a change in luminosity. Moreover, one should note that the determination of the interstellar reddening E_B-V contributes an additional uncertainty (see below). For a more definite statement a larger sample of Cepheids is needed. The positions of the identified Cepheids in the colour-magnitude diagram (CMD) can be seen in Fig. 5.

3.3 Interstellar reddening

The correction for interstellar reddening was done following the method described by Brewer et al. (1995). A foreground reddening E_B-V of 0.23 $^{\rm mag}$ was assumed, leading to an absorption of $A_{V} =3.1 \cdot 0.23 = 0.713^{\rm mag}$ and $A_{i} =0.6 \cdot A_{V} = 0.428 ^{\rm mag}$. No correction was made for the TiO and CN data because of a negligible difference in center wavelength between the two filters and our artificial zeroing of the (TiO-CN) colour index.

A note on the reliability of this approach. Within our field (having a size of $\approx$1.1kpc at the distance of M 31) the amount of internal extinction will definitely vary (our V frame shows clear indications of dark clouds). Moreover we will find objects at different "depths'' in the disk. This will lead to an additional uncertainty in our (V-i) colour indices, acting as the temperature indicator. But it will not affect the (TiO-CN) values due to the very small difference in the center wavelengths of the Wing filters [using the calculations of Battinelli & Demers (2000) we find, that $E_{\rm TiO-CN}$ is negligible]. To get a feeling for this influence, we plotted a 1kpc-reddening-vector with rough absorption values, known from the Milky Way ( $A_{V}=1^{\rm mag}$, $A_{I}=0.43^{\rm mag}$, $E_{V-I}=0.57^{\rm mag}$), in the diagrams. This uncertainty may affect some quantitative measurements, such as the star counts in the selection areas, the mean magnitudes of the luminosity functions (LF), and hence the distance determinations derived from the C-star LF.

3.4 Astrometry

The astrometric calibration within our field was done in two steps. First, all individual filter results were paired using the DENIS-software "Cross_Color'' with the i filter as reference. A pairing-radius of 3pixel, corresponding to $\approx$0 $\hbox{$.\!\!^{\prime\prime}$ }$6, was chosen after testing a range of values. This procedure led to a total of 5448 stars having V and i measurements (sample 1) out of which 2546 stars also have the corresponding TiO and CN data (sample 2).

As a second step, an astrometric solution was produced for all stars, using the ASTROMET-package of MIDAS and four field stars included in the Guide Star Catalogue (2788_1818, 2788_1555, 2788_1453, -2_627), which were on our frames. A list of coordinates and photometric results of the C stars identified in Sects. 4.2 and 4.5 can be found in Table 1. Typical accuracies of the photometry are $\sigma_{I}=0.02^{\rm mag}$, $\sigma_{V-I}=0.06^{\rm mag}$, $\sigma_{A-B}=0.04^{\rm mag}$.

3.5 Detectability

From the total number of objects detected in each of the filters it is clear, that the combined i frame is the deepest exposure. In both, the narrow band filters (TiO and CN) and V, we have not reached a sufficient limiting magnitude for certain groups of objects. First, the V exposure is not long enough to reach all red objects, which we detect even in the narrow band filters (see Sect. 4.5). Second, many blue objects were too faint to be detected in TiO and CN. These are the main reasons for the different sizes of sample 1 and sample 2. Since we were not interested in TiO and CN data for the warmer objects, the second limitation is of no relevance for the results in this paper.