THE ARAUCARIA PROJECT: FIRST CEPHEID DISTANCE TO THE SCULPTOR GROUP GALAXY NGC 7793 FROM VARIABLES DISCOVERED IN A WIDE-FIELD IMAGING SURVEY^*

In our ongoing Araucaria Project (Gieren et al. 2005b), we are engaged in an accurate determination of the environmental dependences of several of the most important stellar methods of distance determination, with the aim of improving the current weakest link of the calibration of the extragalactic distance scale, the determination of the absolute distances to galaxies in the near field. These form the fundament for the calibration of secondary methods of distance determination reaching out into the unperturbed Hubble flow, where the Hubble constant can be reliably measured from distance and velocity data. One of the most important stellar methods to measure the distances to nearby galaxies is the period–luminosity (PL) relation obeyed by Cepheid variables. This is particularly true when the PL relation is used at near- or mid-infrared wavelengths (e.g., Persson et al. 2004; Freedman et al. 2008) where the effect of reddening on the measured distances becomes small or even negligible. In the lack of infrared photometry, an excellent alternative to derive very accurate Cepheid distances is to use the (V − I) Wesenheit function W_I. Recent evidence from our own project (Pietrzyński & Gieren 2006) and other work (Bono et al. 2010) shows that not only is the effect of reddening on the derived distances minimized, but also the effect of the (many times unknown) metallicity of the Cepheid populations in the target galaxies on the derived distances is very small. In previous papers, we have reported on the discoveries of abundant Cepheid populations in a number of irregular galaxies in the Local Group (Pietrzyński et al. 2004, 2006a, 2007), and in several spiral galaxy members of the Sculptor Group (Pietrzyński et al. 2002, 2006b; Garcia et al. 2008). These galaxies span a broad range of metallicities which is useful not only to study the dependence of the Cepheid PL relation on this parameter, but also of other tools for distance determination studied in our project, like the flux-weighted gravity–luminosity relation obeyed by blue supergiant stars (Kudritzki et al. 2008; Urbaneja et al. 2008).

In this paper, we report on the discovery of a population of Cepheids in another target galaxy in the Sculptor Group included in our project, NGC 7793. NGC 7793 is a relatively tightly wound spiral of type Sd (Sandage & Bedke 1988), similar in appearance to NGC 300 in the Sculptor Group. Unlike NGC 300, however, little work has been done in the past to determine the distance to NGC 7793. Only two distance indicators have been applied on NGC 7793: the I-band tip of the red giant branch (TRGB) method and the Tully–Fisher (TF) method. While the TF method has yielded a distance modulus of 28.06 ± 0.35 mag (Tully et al. 2009), application of the TRGB technique has resulted in distances of 27.96 ± 0.24 mag (Karachentsev et al. 2003), and more recently of 27.79 ± 0.08 mag (Jacobs et al. 2009). The Jacobs et al. determination was made from Hubble Space Telescope (HST) data obtained in an outer field of NGC 7793 which explains its higher accuracy, as compared to the result of Karachentsev et al. which was measured from HST data obtained for a field located much closer to the center of the galaxy where crowding and internal extinction may have complicated the TRGB measurement. Given that NGC 7793 contains a considerable number of blue massive stars indicating recent star formation, we expected to find a sizeable population of classical Cepheids in it which would provide an independent and accurate check on the previous distance determinations. Indeed, our survey has led to the detection of 17 long-period Cepheids. In this paper, we use these Cepheids to determine the first Cepheid-based distance to NGC 7793, which adds a valuable target to the existing Araucaria Project database with a distance from this indicator.

Our paper is organized as follows. In Section 2, we describe our observations, data reductions, and calibrations. In Section 3, we present the catalog of photometric properties of the Cepheid variables discovered in our survey in NGC 7793. In Section 4, we construct the PL relations in V, I, and the reddening-free (V − I) Wesenheit index and determine the distance and internal reddening of NGC 7793 from these data. In Section 5, we discuss our result and assess its accuracy. The main conclusions are presented in Section 6.

All the data presented in this paper were collected with the Warsaw 1.3 m telescope at Las Campanas Observatory. The telescope was equipped with a mosaic 8k × 8k detector, with a field of view of about 35 × 35 arcmin and a scale of about 0.25 arcsec pixel⁻¹. For more instrumental details on this camera, the reader is referred to the OGLE Web site ⁹ V and I band images of NGC 7793 were secured on 56 different nights. The exposure time was set to 900 s in both filters. The observations were obtained between 2003 July and 2005 December.

Preliminary reductions (i.e., debiasing and flatfielding) were done with the IRAF¹⁰ package. Then, the point-spread function photometry was obtained for all stars in the same manner as in Pietrzyński et al. (2002). Independently, the data were reduced with the OGLE III pipeline based on the image subtraction technique (Udalski 2003; Woźniak 2000).

In order to calibrate our photometry onto the standard system our target was monitored during two (non-contiguous) photometric nights together with some 25 standards from the Landolt fields spanning a wide range of colors (−0.14 < V − I < 1.43), and observed at widely different airmasses. Since in principle the transformation equations for each of the eight chips may have different color coefficients and zero points, the selected sample of standard stars was observed on each of the individual chips, and transformation coefficients were derived independently for each chip, on each night. Comparison of the photometry obtained on the different nights revealed that the internal accuracy of the zero points in both V and I bands is better than 0.03 mag. In order to demonstrate this, we show in Table 3 the zero point and color term values for the eight chips for the two calibrating photometric nights. Within the errors there are no color term variations from night to night. Slight zero point differences for individual chips from 0.02–0.04 mag are present. We note here this (OGLE) telescope and setup has been used now for 14 years for photometric surveys and is certainly one of the most stable photometric systems in the world. Never any significant color drift has been observed.

To correct the variation of the zero points in V and I over the mosaic, the "correction maps" established by Pietrzyński et al. (2004) were used. These maps were already applied to correct photometry obtained in the field of NGC 6822 (Pietrzyński et al. 2004) and NGC 3109 (Pietrzyński et al. 2006a). Comparison with other studies revealed that these maps allow us to correct the zero point variations down to a level of 0.02–0.03 mag.

Unfortunately, we were unable to find any modern photometry of NGC 7793 in the literature which could be used to check the accuracy of the zero point of our photometry. However, taking into account that the present photometric calibration was performed in an identical way as for the other nearby galaxies surveyed for Cepheids in the Araucaria project, and that in all cases a comparison of our photometry with the corresponding results published in the literature had shown very good agreement, we are very confident that our photometric data of NGC 7793 are also accurate to 0.03 mag in both V and I, and that a possible variation of the photometric zero points in both filters over the mosaic fields is indeed smaller than 0.03 mag.

All stars detected in NGC 7793 were searched for photometric variations with periods between 0.2 and 200 days, using the analysis-of-variance algorithm (Schwarzenberg-Czerny 1989). In order to distinguish Cepheids from other types of variables, we used the same criteria given in our initial paper reporting on the discovery of Cepheids in NGC 300 (Pietrzyński et al. 2002). The light curves of all Cepheid candidates were approximated by a fourth order Fourier series. We then rejected objects with amplitudes of their V light curves smaller than 0.4 mag, which is the approximate lower limit of V amplitudes for classical Cepheids. This procedure also helped us in screening our Cepheid sample from the inclusion of strongly blended variables. For the variables passing our selection criteria, the mean V and I magnitudes were derived by integrating their light curves which had been previously converted onto an intensity scale, and converting the results back to the magnitude scale.

Our final catalog contains 17 classical Cepheids with periods between 24 and 62 days. Fourteen of these variables have light curves in both V and I filters. Three additional Cepheids have only V-band light curves. Two of them are the faintest Cepheids in our sample and were too faint to measure their I-band light curves from our images. The third Cepheid with V-band data only is the longest period variable we discovered (91 days), but unfortunately it was located in a gap between the chips of our mosaic camera in the I images. There are certainly many more Cepheids in NGC 7793 with shorter pulsation periods which we were not able to discover because of the small size of the telescope we had at our disposal for this survey yet the sample of long-period and relatively bright Cepheids detected in our survey is completely adequate for our purpose of deriving an accurate distance to NGC 7793 as we will show in the next section.

The journal of the individual V and I observations of the Cepheids is presented in Table 1. Table 2 summarizes the photometric properties of the newly discovered Cepheids in NGC 7793: their periods and their intensity mean magnitudes in V, I, and in the (V − I) Wesenheit band (defined as W_I = I − 1.55(〈V〉 − 〈I〉); see Udalski et al. 1999). The periods of the Cepheids are typically accurate to 10⁻³ × P. Table 2 also reports precise equatorial coordinates for all the variables. In Figure 1, we show the locations of the Cepheids discovered in our survey in their host galaxy NGC 7793.

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In Figure 2, we show the light curves of the complete sample of NGC 7793 Cepheids which illustrates the good quality and phase coverage of our data. Figure 3 shows the locations of the Cepheids on the V, V − I color–magnitude diagram (CMD) for NGC 7793 constructed from our data. It is seen that all Cepheids lie in the expected region of the CMD which delineates the Cepheid instability strip, presenting supporting evidence that all variables in Table 2 were classified correctly as classical Cepheids. Figure 3 does not include the three Cepheids which have no I-band light curves, but the shapes and amplitudes of their V light curves, periods, and mean V brightnesses leave no doubt that they are classical Cepheids too.

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In Figures 4–6, we show the PL relations in the V, I, and W_I bands resulting from the data in Table 2. The V-band PL diagram contains the three variables which have V data only; these three variables are, however, not included in the distance determination. Fits to a straight line to our data yield the following slopes for the PL relations: −3.24 ± 0.25, −3.17 ± 0.18, and −3.07 ± 0.30 in V, I and W_I, respectively. The uncertainties on the slopes are rather large due to the relatively small number of Cepheids in the PL diagrams. The slope values, however, are consistent at a level of 2σ with the corresponding OGLE slopes of −2.775, −2.977, and −3.300 for the LMC (Udalski 2000). We therefore use, as in our previous papers, the extremely well defined OGLE PL relation slopes determined for the LMC to fit our observed PL diagrams in NGC 7793. Remarks on the validity of this approach will be given in the next section. Adopting the LMC slopes in fitting our data leads to the following equations:

$$\begin{eqnarray*} V &=& -2.775 \log P + (26.48 \pm 0.04)\\ I &=& -2.977 \log P + (25.91 \pm 0.03)\\ W_I &=& -3.300 \log P + (25.04 \pm 0.04). \end{eqnarray*}$$

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The uncertainties on the zero points have been calculated from the least-squares fitting. Adopting 18.50 mag as the true distance modulus to the LMC, as we did in our previous papers in this series, a value of E(B − V) = 0.018 mag as the Galactic foreground reddening toward NGC 7793 (Schlegel et al. 1998) and the reddening law given by the same authors (A_V = 3.24 E(B − V), A_I = 1.96 E(B − V)) we derive the following distance moduli for NGC 7793 in the three different bands:

$$\begin{eqnarray*} (m-M)_{0} (W_I) &=& 27.68 \pm 0.05\, {\rm mag}\\ (m-M)_{0} (I) &=& 27.78 \pm 0.03\, {\rm mag}\\ (m-M)_{0} (V) &=& 27.86 \pm 0.04\, {\rm mag}. \end{eqnarray*}$$

Again, the uncertainties on these values are derived from least-squares fitting. The distance moduli values indicate, not surprisingly, that there is additional reddening intrinsic to NGC 7793 affecting the Cepheids. A value of E(B − V) = 0.06 mag for the average intrinsic reddening, bringing the total mean reddening affecting the NGC 7793 in our sample to 0.08 mag, produces excellent agreement, at the 0.02 mag level, between the distance moduli for NGC 7793 derived from the PL relations in V, I, and W_I. We adopt, as our best Cepheid distance from the present optical study, the value of 27.68 mag derived from the Wesenheit index. In the next section, we discuss the various systematic uncertainties which may affect this value and estimate the total uncertainty on this first Cepheid distance determination to NGC 7793.

The current distance measurement of NGC 7793 is the first one based on Cepheid variables and subject to the different sources of systematic uncertainty inherent to this particular method. The first potential problem is with reddening because Cepheids, as relatively young stars, tend to be located in dusty regions in their host galaxies. While infrared photometry is the best way to minimize or even completely avoid this problem, our past work, and that of others, most notably the OGLE Project (Udalski et al. 1999; Soszyński et al. 2008), has shown that in Cepheid distance work reddening can be very effectively dealt with by using the (V − I) Wesenheit magnitude, as we have done in this paper. In all our previous papers in this series, the true distance moduli based on the Cepheid Wesenheit magnitudes agreed within the (small) uncertainties of the determinations with the distances coming from the near-infrared follow-up studies (e.g., Gieren et al. 2005a, 2008, 2009). While our intention is to check on the current distance determination to NGC 7793 using near-infrared data in the near future, we believe that the Cepheid distance presented in this paper is basically free of any significant error due to inadequate absorption corrections. In any case, NGC 7793 is a favorable target in this sense given that the Galactic foreground reddening toward the galaxy is practically negligible, and from our results in the previous section we know that the average reddening produced inside the galaxy on the Cepheids is quite small too.

At a distance of 3.4 Mpc, blending of Cepheids with nearby stars not resolved in the photometry is certainly a significant problem. For one of our target galaxies, NGC 300, we have made a stringent test on the effect of blending on a Cepheid-based distance, comparing the results from ground-based photometry in V and I to HST-based photometry of the same Cepheids (Bresolin et al. 2005). The result was that blending affects the ground-based distance result by less than 2% in this particular case. NGC 7793 has a very similar inclination with respect to the line of sight, with an orientation close to face-on like NGC 300; however, since its distance is a factor of 1.8 larger, the effect of blending is expected to be more serious than in the case of NGC 300. Scaling linearly with the distance, we expect that 3% is a reasonable upper limit to the systematics from this source. We tested this hypothesis by degrading the resolution of the ground-based images of NGC 300 to the one expected at the distance of NGC 7793, and redoing the photometry of the Cepheids observed with HST. The result is that indeed the effect of blending is somewhat larger now, but less than 3%, in agreement with our simple expectation from rescaling the error according to the larger distance of NGC 7793. It should also be noted in this context that the amplitudes of the light curves in Figure 1 are generally about as large as expected for the periods of the Cepheids (although there is no strict period–amplitude relation for classical Cepheids), which probably implies that none of these Cepheids is strongly blended, which depending on the color of a bright nearby star contaminating the Cepheid photometry would tend to reduce the light curve amplitude in V (blue companion) or I (red companion) (Gieren 1982). Regarding the effect of blending, it should be recalled that it acts to make Cepheids brighter, and thus to underestimate the distance to their host galaxy.

Since the PL relation method is a statistical one and requires that the PL plane is populated by a sufficient number of Cepheid variables to minimize problems due to an incomplete, selective filling of the instability strip, the relatively small number of 14 Cepheids in our present study is a potential reason of concern. However, both the filling of the instability strip on the CMD in Figure 2 by the variables in our catalog, as well as the non-systematic scatter of the residuals around the fitting lines in Figures 3–5 suggest that the Cepheid variables in this study do populate the instability strip quite homogeneously, with no clear preference toward either the blue or the red edge of the strip. Also, the current distance determination should not be affected at a significant level by a Malmquist bias which could originate when the faintest Cepheids in the sample were very close to the cutoff magnitude of the photometry. Figure 2 suggests that the faintest of the 14 Cepheids used in the distance determination is still about a full magnitude brighter than the faint star limit of our photometry. The effect of a Malmquist bias is to make the slope of the observed PL relation too shallow because at the short-period (faint) end of the sample only Cepheids are detected which are very bright, for the value of their period. Another argument giving us confidence that our distance determination is not significantly affected by a Malmquist bias, is the fact that the slopes of the free linear fits to a line in the V- and I-band PL planes are both steeper than the assumed true (LMC) slopes on these diagrams, which is the opposite to what would be expected if a significant Malmquist bias was indeed affecting the data in Figures 3 and 4.

A problem which has been very intensively discussed in the recent literature is the effect of metallicity on the Cepheid PL relation, both in optical and near-infrared photometric bands. A very nice and complete summary of the work on the metallicity effect on the PL relation, and corresponding conclusions both from observations and theoretical modeling of Cepheids, has been recently presented by Bono et al. (2010). In particular, Bono et al. found that the (V − I) Wesenheit PL relation used to determine the distance to NGC 7793 has a slope which, independently of metallicity, always agrees very well with the LMC slope we have used in our analysis. This empirical result is backed up by the predictions of their pulsation models for fundamental mode Cepheids and thus appears to be a very solid conclusion. In addition, Bono et al. conclude from their analysis that the zero point of the absolute (V − I) Wesenheit PL relation does not depend on metallicity either, a conclusion reached from the available data over a broad range of metallicities and again supported by their theoretical models. We note here that from the (preliminary) data set from the Araucaria Project alone available to us in 2006, we reached the same conclusion (Pietrzyński & Gieren 2006). Thus, any effect of the (currently unknown) mean metallicity of the Cepheids in our NGC 7793 sample on the distance we have derived in this paper should be negligible.

An issue of concern is the fact that the observed dispersion in the W_I Wesenheit PL relation in Figure 6 is slightly larger than the one shown by the I-band PL relation in Figure 5. We believe that the main reason for this is the photometric contamination of some of the Cepheid mean magnitudes in Table 2 by nearby, unresolved companion stars (discussed above). While this effect indeed tends to increase the scatter in Figure 6, it should not change the distance derived from this diagram within the uncertainties we determined in our analysis in Section 4 of this paper. An alternative explanation would be the validity of a non-standard reddening law in NGC 7793, the coefficient 1.55 not being appropriate in the definition of the Wesenheit magnitude to correct for reddening. We regard this as rather unlikely, however, in light of our earlier findings in NGC 300 (Gieren et al. 2005a), NGC 55 (Gieren et al. 2008), and NGC 247 (Gieren et al. 2009) where from combined optical and near-infrared photometry of the Cepheids we found solid evidence that the standard reddening law holds in these galaxies.

From the previous discussion, we identify the effect of unresolved bright nearby stars on the Cepheid photometry, or blending, as the dominant systematic uncertainty on the derived distance in the present study. The systematic uncertainty on the photometric zero points in our study is less important (less than 2% on the distance modulus). We estimate the total systematic uncertainty of our distance to be 4% with a likely tendency to act in the direction to increase the reported distance to NGC 7793. This would bring the Cepheid distance closer to the TRGB-based distance of Jacobs et al. (2009), which is clearly consistent within the respective uncertainties.

Recall that the current distance measurement of NGC 7793 assumes an LMC distance of 18.50 mag, in agreement with our earlier work in the Araucaria Project. While any possible future change in the adopted value of the LMC distance will obviously affect the absolute Cepheid distances of our different target galaxies reported in the Araucaria Project, it will not affect the relative distances between the target galaxies of our project.

We have carried out the first systematic wide-field search for Cepheid variables in the Sculptor Group spiral NGC 7793 and have discovered 17 long-period classical Cepheids. We provide the periods of these objects and their mean intensity magnitudes in the optical V and I bands, as well as their accurate positions. From a subsample of 14 Cepheids having both V- and I-band light curves, we have determined the PL relations in these bands as well as in the reddening-independent (V − I) Wesenheit band. The distance moduli derived from these PL relations demonstrate that apart from the very small foreground reddening there is additional reddening of magnitude E(B − V) = 0.06 mag produced in NGC 7793 itself and affecting its Cepheids. Our best adopted value for the distance modulus of NGC 7793 is 27.68 ± 0.05 mag (intrinsic) ± 0.08 mag (systematic). The dominant source of systematic uncertainty is the effect that unresolved nearby bright stars might have on the photometric magnitudes of some of the Cepheids, which would act toward a (small) underestimation of the true distance of the galaxy. According to recent studies, the way to determine the distance to NGC 7793 using the period–(V − I) Wesenheit magnitude diagram should be independent of the metallicities of the Cepheids in our sample.

The Cepheid distance agrees very well with the recent distance determination of NGC 7793 of Jacobs et al. (2009) who used HST photometry and the I-band TRGB method. This increases our confidence that the distance to NGC 7793 is now reliably measured with a total uncertainty not exceeding 5%. Nevertheless, we intend to obtain near-infrared single-phase photometry for our Cepheid sample with the ESO VLT to determine accurate mean magnitudes in the J and K bands (see Soszyński et al. 2005) and use our multiwavelength approach (Gieren et al. 2005a) to improve the accuracy of our present distance determination from optical photometry of the Cepheids.

The present study confirms the elongated structure of the Sculptor Group in the line-of-sight first suspected by de Vaucouleurs (1959), and later substantiated by Jerjen et al. (1998), with NGC 55 and NGC 300 at the near end with near-identical distances of 1.9 Mpc, and NGC 247 and NGC 7793 at the far end at about 3.5 Mpc. From the Cepheid work in the Araucaria Project, the distances to these four galaxies are now all determined to 5% or better.

We are grateful to Las Campanas Observatory, and to the CNTAC for providing the large amounts of telescope time which were necessary to complete this project. We gratefully acknowledge financial support for this work from the Chilean Center for Astrophysics FONDAP 15010003, and from the BASAL Centro de Astrofisica y Tecnologias Afines (CATA) PFB-06/2007. Support from the Polish grant N203 387337 and the FOCUS subsidy of the Foundation for Polish Science (FNP) is also acknowledged. P.F. suddenly feels old realizing that he started his astronomical work measuring the distance of NGC 7793 through the H i TF relation in 1978, finding a similar distance to the one we report in this paper. We thank the anonymous referee for his comments.

W.G. is grateful to Conicyt, to the Astronomy Department at the Universidad de Chile, and to the Sociedad Chilena de Astronomia SOCHIAS for their encouragement and financial aid which helped the Astronomy Department at the Universidad de Concepción to quickly recover from the material damages suffered from the earthquake which struck us on 2010 February 27.