THE ARAUCARIA PROJECT. A DISTANCE DETERMINATION TO THE LOCAL GROUP SPIRAL M33 FROM NEAR-INFRARED PHOTOMETRY OF CEPHEID VARIABLES^*

We have chosen the observed VLT/HAWKI field in M33 with the criteria to maximize the number of long-period Cepheids contained in the field and optimize their period distribution. We also chose the field as to be located at a medium galactocentric distance where crowding of the Cepheids and its expected systematic effect on the Cepheid photometry is reasonably small whereas at the same time the average expected metallicity of the Cepheids is close to the metallicity of LMC Cepheids, which constitutes our adopted fiducial PL relations, in order to minimize the effect of metallicity on the derived distance to M33. As can be seen in Figure 2, the Cepheid sample in M33 used in this study is quite large (26 variables), and it covers the broad period range from 6 to 74 days very homogeneously. The location of the Cepheids in the K versus J−K color–magnitude diagram shown in Figure 4 confirms their nature as classical Cepheids.

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The observed dispersion on the PL diagram in the J band is likely dominated by the random-phase nature of the observations in this band, where in a few cases Cepheids might be up to 0.25 mag brighter or fainter than their mean magnitudes if our observation happened to occur close to maximum or minimum light for these variables (the total light amplitude in J and K of a typical long-period Cepheid is about 0.5 mag; see Persson et al. 2004). Since in K we have two to five observations at different epochs for the variables, the data points in the K-band PL diagram should exhibit smaller scatter around the ridge line, which is actually observed in Figure 2.

The contribution of the random photometric errors of the magnitudes (see Table 2) on the scatter in Figure 2 are negligible whereas unusually strong dust absorption could be important in a few cases, particularly in the J-band PL relation where the effect of dust absorption is stronger than in K. Our sample, consisting of Cepheids all having periods longer than six days, should not contain any overtone pulsators which would introduce additional scatter at the short-period end of the PL diagram in Figure 2 and a bias in the distance determination. Numerous studies (e.g., Soszynski et al. 2008) have shown that at periods longer than about five days all classical Cepheids are fundamental mode pulsators. As a test on this hypothesis, we have done fits to the PL relations in Figure 2 excluding the Cepheids with period shorter than 10 days. This led to negligible changes in the zero points of the relations, and in the distance to M33 providing strong evidence that our sample does indeed not contain any overtone Cepheids.

Without a doubt, reddening is one of the most serious sources of systematic error on distances to galaxies determined with classical Cepheids or other young stars, and frequently the discrepancies between reported distance results for a given galaxy can be attributed to differences in the adopted reddenings. In the case of M33, all studies in Table 1 published later than 2001 which have used optical photometry of Cepheid variables to determine the distance have adopted a mean reddening value of 0.20 which was derived in the HST Key Project final paper of Freedman et al. (2001). The resulting M33 true distance moduli from Cepheids cluster is around 24.6. Interestingly, in their original study of M33 Cepheids, Freedman et al. (1991) had determined E(B − V) = 0.10 and a true distance modulus of 24.64; with the revised reddening of 0.20 adopted in the Key Project, they would have obtained a shorter M33 true distance modulus of 24.32. The Galactic foreground reddening to M33 from the Schlegel et al. (1998) maps is E(B − V) = 0.04 mag.

Contrasting with the 0.20 mag reddening value, two other recent studies employing young stars for a distance determination to M33 have found lower reddenings of E(B − V) = 0.09 for an O-type eclipsing binary (Bonanos et al. 2006), and 0.08 from a sample of 22 blue supergiant stars for which individual reddenings were determined spectroscopically from fits to their observed spectral energy distributions (U et al. 2009), leading in both cases to distance moduli about 0.3 mag larger than the value determined from Cepheids. In the U et al. paper, a range of E(B − V) values between 0.02 and 0.16 was measured for the different supergiants, demonstrating a considerable local variation of dust absorption in M33. This is also seen in the E(B − V) values determined for H ii regions in M33 which for a few objects exceed 0.6 mag, although the mean value is close to 0.11 mag (Rosolowsky & Simon 2008). From the data in that paper, H ii regions with reddenings close to 0.20 are no exception. We also note here that Bresolin (2011) found that for 11 H ii regions in common with Rosolowsky & Simon, the mean E(B − V) values were 0.13 mag larger, so that a value of E(B − V) in the range 0.20–0.25 for H ii regions is certainly consistent with modern data. In fact, Bresolin (2011) obtains a mean E(B − V) of 0.25 ± 0.17 from 25 H ii regions studied in his paper, suggesting that one can certainly not discard the possibility that the average E(B − V) value corresponding to H ii regions in M33 is ∼0.2.

The existence of strong local variations of the dust extinction intrinsic to M33 obviously complicates the distance analysis from Population I objects and underlines the crucial importance of deriving the reddening for a given sample of stars with the utmost care and precision. In our Araucaria Project, we have shown in a number of previous papers that our adopted approach to use combined near-infrared and optical photometry, creating a very long wavelength baseline, is capable of yielding a very robust determination of the mean reddening affecting a given Cepheid sample (Gieren et al. 2005b; Pietrzyński et al. 2006; Soszyński et al. 2006; Gieren et al. 2006; Gieren et al. 2008a, 2008b; Gieren et al. 2009). The mean reddening of 0.19 ± 0.02 mag we have obtained in this study for our Cepheid sample agrees very well with the Freedman et al. (2001) determination from Cepheids but is clearly more accurate due to the inclusion of near-infrared photometry in our analysis.

In order to check the stability of our result for the extinction-corrected distance modulus on the adopted reddening law, we have calculated the extinction-corrected distance and reddening as in Figure 3, adopting different values for R_V ranging from 2.5 to 4.5, taking into account that local variations of the reddening law of such size are not uncommon in star forming regions in spiral galaxies. The result is that the extinction-corrected distance modulus is extremely insensitive to the adopted reddening law–it varies from 24.63 for R_V = 2.5 to 24.60 for a rather extreme value of R_V = 4.5, or just by 1.5%, which is within the statistical error of our adopted distance modulus of 24.62. The reddenings vary more strongly, from 0.242 ± 0.029 to 0.134 ± 0.016, for the different R values. Therefore, an assumed high mean value for R can alleviate to some extent the discrepancy of the photometric with the low spectroscopic reddenings of the blue supergiants in M33 analyzed by U et al. (2009), but the discrepancy cannot be fully explained this way. The important conclusion of this section, however, is the strong insensitivity of our distance result for M33 to the assumed reddening and reddening law, which is mainly a consequence of having K-band photometry at our disposal, and underlines the importance of including K-band photometry in the distance determinations with Cepheid variables.

The effect of metallicity on Cepheid absolute magnitudes and the PL relation is still poorly understood, but, on the other hand, is obviously of crucial importance for a distance determination based on Cepheid variables. While most researchers will agree that the slope of the PL relation is metallicity independent, particularly in near- and mid-infrared photometric bands (e.g., Storm et al. 2011a, 2011b; Freedman et al. 2009), the effect of metallicity on the zero point of the PL relations in different photometric bands has been widely disputed in the past, with no consensus reached yet. The "classical" method of measuring the metallicity effect has been to determine, for a given spiral galaxy, the distance to a sample of Cepheids located close to the center of the galaxy (inner Cepheids), and to another sample located in the outskirts of the same galaxy (outer Cepheids). The zero point difference between the two samples is interpreted as due to the difference in the mean metallicities of the two samples, the inner Cepheids being more metal-rich than the outer Cepheids. This way, it has generally been found that metal-rich Cepheids appear to be brighter, at the same period, than their more metal-poor counterparts, however, with the reported size of the effect varying enormously from a mild effect of about −0.2 mag dex⁻¹ (e.g., Kennicutt et al. 1998) up to a very strong effect close to −0.6 mag dex⁻¹ (Gerke et al. 2011) in the reddening-free V−I Wesenheit magnitude. A fundamental problem in this approach is the choice of the metallicity gradient to be adopted for this determination of the metallicity effect (e.g., Kudritzki et al. 2012; Bresolin et al. 2009) which strongly depends on the adopted calibration of H ii region oxygen abundances. Arguments have been given which seem to exclude a strong metallicity effect on Cepheid magnitudes (Majaess et al. 2011) which are supported by the results for Cepheid distances to Milky Way and Magellanic Cloud Cepheids from the infrared surface brightness technique (Storm et al. 2011a).

On the other hand, Romaniello et al. (2008) have found even a different sign of the metallicity effect from high-resolution spectroscopic abundance determinations for Cepheids in the Milky Way and Magellanic Clouds, casting doubts on the validity of the results produced by the "classical" technique, which might be strongly affected by the crowding and blending affecting Cepheids in the central regions of spiral galaxies making these Cepheids spuriously brighter than Cepheids located further away from the center of the galaxy, through significant photometric contamination by unresolved companion stars (e.g., Majaess et al. 2012). In a recent paper, Freedman & Madore (2011) have related PL relation magnitude residuals for Magellanic Cloud Cepheids to their spectroscopic metallicities as determined by Romaniello et al., for photometric bands ranging from U through the 8.0 μm Spitzer band, yielding evidence that the metallicity effect varies sytematically with wavelength in size and sign. According to their study, the metallicity effect on Cepheid absolute magnitudes is smallest, and consistent with zero, in the near-infrared JHK bands, and particularly in K. This study has the advantage that the Cepheid magnitude residuals can be assumed to be unbiased by blending and crowding, due to the relative proximity of the clouds.

Even at HST resolution, galaxies located farther away than a few megaparsecs are very difficult to resolve in their central regions which makes photometric contamination as a significant contributor to the observed brightening of inner Cepheids, particularly in massive spiral galaxies, very likely, and a separation of the effects belonging to metallicity and crowding very difficult. In the particular case of M33, the relatively large magnitude difference between inner and outer field Cepheids found by Scowcroft et al. (2009) is almost certainly due to the low spatial resolution of their images and the resulting severe problems with crowding and blending effects discussed in the next section, and is not caused by a significant difference in the mean metallicities of these two samples. In our much higher-resolution HAWKI images, we do not see any evidence for a significant radial variation of the mean brightness of Cepheids of similar periods, although admittedly the coverage of our HAWKI image in galactocentric distance in M33, and the number of Cepheids in the field is not large enough to reach very strong conclusions in this regard.

In order to handle the metallicity problem in the most practical way in the present study, we chose our target field as to reach an optimum compromise between avoiding crowding as much as possible, and having a mean metallicity of the Cepheids in the field close to the one of LMC Cepheids (−0.35 dex; Luck et al. 1998; Romaniello et al. 2008). Indeed, using the metallicities and metallicity gradient in M33 as determined from blue supergiants and H ii regions (U et al. 2009; their Figure 14), including metallicities for beat Cepheids determined by Beaulieu et al. (2006), the expected metallicity of Cepheids at the center of our HAWKI field is about [Fe/H] = −0.3, very close to the mean metallicity of classical Cepheids in the LMC. With a reasonable expected deviation of the mean metallicity of our current M33 Cepheid sample from the mean metallicity of LMC Cepheids by ±0.1 dex, and an assumed metallicity sensitivity of the near-infrared PL relations of −0.1 ± 0.1 mag dex⁻¹ (Storm et al. 2011b), which is in line with the recent result of Freedman & Madore (2011), the expected effect of a metallicity difference between our M33 Cepheid sample and the LMC Cepheids defining the fiducial PL relations on the distance modulus of M33 is in the order of just ±0.01–0.02 mag. Metallicity effects on our present determination of the M33 true distance modulus seem therefore negligible.

At a distance of 839 kpc, corresponding to our present result for M33, the possible overbrightening of some of the observed Cepheids due to relatively bright companion stars unresolved in the photometry is clearly a potential problem, particularly in ground-based observations. A good way to estimate the expected effect is to use the investigation of Bresolin et al. (2005) of the effect of blending on Cepheid magnitudes in NGC 300, a galaxy very similar to M33 in mass, stellar density, and inclination with a distance being a factor of 2.2 larger than M33 (Gieren et al. 2005b). In NGC 300, the effect of blending of Cepheids on the distance modulus was determined to be 0.04 mag if ground-based BVI images obtained at a 2.2 m telescope (the ESO 2.2 m telescope and Wide Field Imager) are used to obtain the Cepheid photometry. In the case of the present near-infrared photometry, which strongly dominates our derived distance modulus of M33, blending should be less a problem given the larger spatial resolution obtained with the VLT/HAWKI telescope and imager. On the other hand, blending with the numerous bright, red asymptotic giant branch stars might become a more worrisome problem, but probably is only becoming a dominating source of error at mid-infrared wavelengths (Freedman et al. 2009). In the Bresolin et al. (2005) paper, Cepheids in outer fields in NGC 300 showing a similar stellar density as our present VLT/HAWKI field were used for the determination of the impact of blending on the distance modulus.

Scaling the Bresolin et al. result for NGC 300 to the shorter distance of M33, we would expect a ∼0.02 mag effect (systematic in the sense to make Cepheids brighter, thus underestimating the true distance of M33). This is in line with the results of the recent study of Chavez et al. (2012), who compared VI photometry for 149 Cepheids in M33 obtained with the WIYN 3.5 m telescope to archival HST data, and reached conclusions about the effect of blending on the Cepheid magnitudes which are very similar and consistent with those of Bresolin et al. (2005).

The effect of blending through companion stars unresolved in the photometry may be expected to affect shorter period and fainter Cepheids more strongly than the brighter, long-period Cepheids, which was a principal reason to restrict our sample and analysis to the brighter Cepheids available for study in our selected field. As metallicity effects, we conclude that blending of the Cepheids in our sample produces a minor systematic effect on the distance modulus of M33 in the order of 1%–2%.