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The Araucaria Project: The distance to the Fornax Dwarf Galaxy from near-infrared photometry of RR Lyrae stars

We have obtained single-phase near-infrared (NIR) magnitudes in the J- and K-bands for 77 RR Lyrae (RRL) stars in the Fornax Dwarf Spheroidal Galaxy. We have used different theoretical and empirical NIR period-luminosity-metallicity calibrations for RRL stars to derive their absolute magnitudes, and found a true, reddening-corrected distance modulus of 20.818 +/- 0.015 (statistical) +/- 0.116 (systematic) mag. This value is in excellent agreement with the results obtained within the Araucaria Project from the NIR photometry of red clump stars (20.858 +/- 0.013 mag), the tip of the red giant branch (20.84 +/- 0.04 +/- 0.14 mag), as well as with other independent distance determinations to this galaxy. The effect of metallicity and reddening is substantially reduced in the NIR domain, making this method a robust tool for accurate distance determination at the 5 percent level. This precision is expected to reach the level of 3 percent once the zero points of distance calibrations are refined thanks to the Gaia mission. NIR period-luminosity-metallicity relations of RRL stars are particularly useful for distance determinations to galaxies and globular clusters up to 300 kpc, that lack young standard candles, like Cepheids.


INTRODUCTION
The main focus of the Araucaria Project is to improve the calibrations of the distance scale, with the use of major distance indicators in several nearby galaxies (e.g. Gieren et al. 2005;Pietrzyński et al. 2013a). Such a study is capable of revealing the impact of metallicity or/and age on various standard candles. Understanding and minimizing the uncertainties of distance determinations in the local scale improves the precision and accuracy of secondary distance indicators, ultimately leading to better determination of the Hubble parameter. Over the past 15 years of the Araucaria Project, distances to nearby galaxies were determined with the use of the red clump stars (Pietrzyński & Gieren 2002), the tip of the red giant branch Górski et al. 2011), late-type eclipsing binaries (Pietrzyński et al. 2013b;Graczyk et al. 2014), blue supergiants (Urbaneja et al. 2008), classical Cepheids (e.g. Gieren et al. 2013;Nardetto et al. 2014), type II Cepheids (Ciechanowska et al. 2010), and RR Lyrae stars (Pietrzyński et al. 2008;Szewczyk et al. 2008Szewczyk et al. , 2009Karczmarek et al. 2015).
Distance determinations can be significantly improved in the near-infrared (NIR) spectral range, which has been long known to be markedly less affected by interstellar extinction and metallicity (McGonegal et al. 1983). This is especially useful in the case of RR Lyrae (RRL) stars, which throughout the years of theoretical and empirical studies have proven to be excellent standard candles in the NIR domain, providing distance results which are superior to optical studies (e.g. Longmore et al. 1986;Bono et al. 2003). The NIR amplitudes of RRLs are a factor of 2-3 smaller than in the optical bands, giving the NIR full-amplitude of only 0.4 mag (e.g. Storm et al. 1992;Marconi et al. 2003). Therefore, mean NIR magnitudes can be approximated by random-phase magnitudes obtained in a modest number of observations, as long as a significant RRL sample is concerned. Yet the biggest advantage of the NIR observations of RRL stars is that they follow the periodluminosity relation (PL, Longmore et al. 1986;Fernley et al. 1987). This feature was studied extensively by Bono et al. (2001), who put the first theoretical constrains on K-band PL relation of RRLs based on nonlinear convective pulsation models. The continuation of theoretical studies of RRL stars in NIR wavebands, carried out by Bono et al. (2003) and Catelan et al. (2004), yielded the period-luminosity-metallicity (PLZ) relation in the NIR domain, showing that the effect of metallicity on the luminosity of RRLs in the NIR domain is noticeably smaller as compared to the visual one. Indeed, the metallicity term enters the PLZ relation with the coefficient of at most 0.23 mag dex −1 in K-band (Bono et al. 2003), while in the V -band the metallicity coefficient reaches 0.3 mag dex −1 (Di Criscienzo et al. 2004). Empirical PLZ relations followed the theoretical studies and showed the metallicity coefficient to be even smaller (0.08 mag dex −1 , Sollima et al. 2008), but no general consensus has been reached yet on the value of the coefficient of the metallicity term.
Within the Araucaria Project, we repeatedly showed that the NIR PLZ relation of RRL stars is a superior and reliable tool, by determining distance moduli to a number of galaxies in the Local Group: the Sculptor dwarf galaxy (Pietrzyński et al. 2008), the Magellanic Clouds (Szewczyk et al. 2008(Szewczyk et al. , 2009, and the Carina dwarf galaxy (Karczmarek et al. 2015), with precision at the 5% level or better. In this paper, we use J-and Kband PLZ relations for RRL stars to deliver the distance modulus to the Fornax galaxy.
The Fornax dSph Galaxy is an extraordinary stellar system, not only because it is one of the most massive satellites of the Milky Way, but also due to five distinctive globular clusters that reside in its body. Numerous studies of Fornax continuously add new findings to its complex picture: large internal metallicity spread −2.5 ≤ [Fe/H] ≤ 0.0 (Tolstoy et al. 2001;Pont et al. 2004;Battaglia et al. 2006), the presence of three stellar populations (Battaglia et al. 2006), the off-center overdense structure of debatable origin (Coleman et al. 2004;de Boer et al. 2013), the mean period of sub-type RRab stars falling in between average periods for Oosterhoff classes I and II (Bersier & Wood 2002). These diverse and inconclusive results amplify further interest in the Fornax galaxy. Precise and accurate determination of Fornax distance is therefore crucial in numerous distance-based studies, like the analysis of the colormagnitude diagram (CMD), as it reconciles the model with the observed CMD, and therefore allows for biasfree determination of the metallicity and age of stellar populations (de Boer & Fraser 2016).
The Fornax galaxy has been a target for many distance determination techniques in the optical and infrared domains. Distances were calculated based on the field stars as well as on the stars in each of its five globular clusters. Studies that involved field stars of the horizontal branch (Irwin & Hatzidimitriou 1995;Saviane et al. 2000;Rizzi et al. 2007), the tip of the red giant branch (Saviane et al. 2000;Bersier 2000;Gullieuszik et al. 2007;Pietrzyński et al. 2009), red clump stars (Bersier 2000;Pietrzyński et al. 2003;Rizzi et al. 2007), the CMD fitting (Weisz et al. 2014), and RRL stars (Greco et al. 2005;McNamara 2011) in the visual and infrared domains are summarized in Table 1. In this paper we complement existing distance determinations to the Fornax galaxy with a distance modulus derived from PLZ relations of field RRL stars in the J-and Kband. Taking advantage of the NIR magnitudes, which are only slightly affected by the metallicity and reddening, we achieve a precision at the 5% level.

OBSERVATIONS, DATA CALIBRATION AND REDUCTION
NIR observations were conducted between 2008 October 7 and 2008 October 23 with the High Acuity Widefield K-band Imager (HAWK-I) mounted in the Nasmyth focus of UT4/VLT ESO 8 m telescope at Paranal, Chile. The dates and coordinates of target fields are given in Table 2. The locations of four target fields in the Fornax galaxy ( Fig. 1) were purposely chosen to overlap fields from the previous visual observations of Bersier & Wood (2002). The HAWK-I field of view of four 2048 × 2048 pixels detectors was about 7.5 × 7.5 with a scale of 0.106 pixel −1 . Detailed description of HAWK-I instrument can be found in Kissler-Patig et al. (2008), and on the ESO website 1 . The fields were observed in J and K s (further denoted as K) wavebands, under photometric conditions (seeing range 0.4-0.7 ). Our objects, having minimal brightness higher than 20.8 mag (J) and 20.6 mag (K), were well above the limiting HAWK-I magnitudes, i.e. 23.9 mag and 22.3 mag in Jand K-band, respectively (Kissler-Patig et al. 2008). In order to account for frequent sky-level variations, which are especially strong in the NIR domain, the observations were carried out in the jitter mode, meaning that the consecutive exposures of a given field were randomly shifted within the radius of 20 with respect to the initial position. Exposure times of 60 seconds per jitter were fixed for the J-and K-band, resulting in total integration times of 18 and 26 minutes per field, respectively.

HAWK-I calibration pipeline
The HAWK-I pipeline, a module of ESO Recipe Execution Tool (EsoRex), was utilized to execute complete reduction of our data. After basic calibration routines (dark correction, flat fielding and bad pixel correction), the subtraction of sky level was applied in a two-step process which included the masking of stars. Next, a refinement procedure minimized the effect of any distortions caused by atmospheric refraction or non-planar surface of detectors, and abolished the shifts in the images caused by the jittering. Lastly, frames were stacked into the final image. The procedure for standard stars was analogous, only consisted of fewer steps: basic cali-1 http://www.eso.org/sci/facilities/paranal/instruments/hawki.html bration (dark correction, flat fielding), one-step sky subtraction, and distortion correction.

Photometry
Instrumental magnitudes were calculated with the pipeline developed in the course of the Araucaria Project. The point-spread function (PSF) photometry and aperture corrections were applied using DAOPHOT and ALLSTAR programs (Stetson 1987) in a way described by Pietrzyński & Gieren (2002). In order to calibrate our photometric data to the standard photometric system, standard stars from the United Kingdom Infrared Telescope list (UKIRT, Hawarden et al. 2001) were observed at different air masses and spanning a broad range in color, bracketing the colors of RRL stars in the Fornax galaxy. The accuracy of the zero point of our photometry is about 0.02 mag.
Due to insufficient number of standard stars observed 23 Oct 2008, an alternative approach was used in order to calibrate the magnitudes of stars in one field, For-II. We carried out follow-up observations of the same four HAWK-I fields with SOFI/NTT at ESO La Silla, Chile, executed reduction routine analogous to the routine described above for HAWK-I data, and performed the PSF photometry with aperture corrections in the exact same way as for HAWK-I data. The calibration of magnitudes of SOFI stars onto UKIRT photometric system was based on 10 standard stars, observed together with the target fields under photometric conditions and at different air masses. The matching algorithm paired stars from SOFI fields with remaining three HAWK-I fields: For-I, For-III, and For-IV, and found 184 common stars, which had already calibrated magnitudes from both instruments. Comparison of these magnitudes showed the consistency of the zero points at the level of 0.02 mag, and justified using SOFI calibrated magnitudes as a point of reference in order to calculate the systematical shift between the two data sets, and calibrate magnitudes of one remaining field For-II from HAWK-I data.
Additionally, we performed an independent brightness comparisons using data from Two Micron All Sky Survey (2MASS), in order to make a double check of our photometric zero point (Table 3). We paired 99 brightest stars from HAWK-I dataset and 2MASS database, transformed the photometric system to 2MASS, and  Table 3. Difference of zero point calibration between 2MASS and SOFI, and our data obtained with HAWK-I.
compared the magnitudes. The averaged zero-point differences from 2MASS and SOFI comparisons are also presented in Table 3. These results firmly support the accuracy of the absolute calibration of HAWK-I data.

Identification of variables
We used a list of RRL variables from Bersier & Wood (2002) as a reference to cross-identify RRLs in our four HAWK-I fields. Other studies of RRLs in the Fornax galaxy (Greco et al. 2007(Greco et al. , 2009) focus on globular clusters, and as such are unconnected to our study of field RRL stars. Although Greco et al. (2005) examined field RRLs in Fornax, they did not provide a list of observed targets, and therefore we could not include it in our study. Bersier & Wood field of study overlaps ours in about 11%, and this coverage was enough to pair 77 RRL stars (15% of Bersier & Wood sample), among which are 66 RRab and 11 RRc stars. The position of our RRLs on the K, J − K color-magnitude diagram (CMD) is shown in Fig. 2. The scatter is caused by the single-phase nature of our measurements. The J-and K-band randomphase magnitudes of the final RRL sample together with timestamps of observations, formal photometry errors from DAOPHOT, and pulsational periods from the reference list of Bersier & Wood (2002) Table 4. In case of 25 RRL stars, which were observed more than once or found in overlapping fields, we present individual observations in separate rows. For the purpose of the analysis described in the next section, these multiple measurements were averaged, which is expected to lead to a better approximation of the mean magnitude.

DISTANCE DETERMINATION
We used the following NIR PLZ relations to determine absolute magnitudes of RRL stars in the Fornax galaxy: (1) (Catelan et al. 2004) (3) (8)  (2002), (2) locus of the star in our HAWK-I fields, (3) right ascension, (4) declination, (5) pulsational periods, (6) type of RRL star, (7) random-phase J magnitudes with (8) their uncertainties, (9) random-phase K magnitudes with (10) their uncertainties, and the Julian Date of observations in (11) J and (12) K band. Note-Table is published in its entirety in the machine-readable format. A portion is shown here for guidance regarding its form and content.
We recall that the calibration of Sollima et al. (2008) was constructed for the 2MASS photometric system 2 , while the calibrations of Bono et al. (2003) and Catelan et al. (2004) are valid for the Bessel, Brett and Glass system (BBG). We therefore transformed our measurements (calibrated onto UKIRT photometric system) to BBG and 2MASS systems using the transformations of Carpenter (2001). The Eqs. (1)-(4) are valid for RRL fundamental periods, so in order to include firstovertone pulsators their periods were "fundamentalized" by adding a value of 0.127 to their logarithmic periods. Apparent magnitudes from our dataset of 77 RRLs were individually corrected for the foreground reddening and plotted against their logarithmic periods (Fig.  3). Both periods and reddening values were extracted from Bersier & Wood (2002). The average reddening of our sample is E(B − V ) = 0.021 mag, which translates to average extinction values A J = 0.019 mag and A K = 0.008 mag, by applying the Cardelli et al. (1989) reddening law R V = 3.1. Following McNamara (2011), we treated internal reddening in Fornax as insignificant due to the fact that old and low-mass objects, such as RRL stars, are very unlikely to be significantly obscured by the interstellar gas from dynamic evolution or mass outflow.
The linear least-square fit performed on our sample yielded the slopes of −1.63±0.39 and −2.05±0.34 for the J-and K-band, respectively. These values agree within errors with the literature slopes from Eqs. (1)−(4), as can be seen in Fig. 3. In order to reduce the uncertainty of the free parameter-the zero point of the calibration-we took advantage of this consistency and performed another least-square fit, this time with the slopes intentionally fixed on their literature values. Lastly, the metallicity of Fornax [Fe/H] = −1.6±0.2 dex (Bersier & Wood 2002) was applied to Eqs. (3) and (4), while for Eqs. (1) and (2) the metallicity term was transformed into log Z using Eq. (9) of Catelan et al. (2004).
True distance moduli calculated from Eqs. (1)−(4), together with associated uncertainties, are summarized in Table 5. As the final distance modulus to the Fornax galaxy we adopt the average of these values, coupled with the largest of statistical errors. This yields a distance modulus of 20.818 ± 0.015 mag. Systematic errors are discussed in the following section. . Period-luminosity relations for J-and K-bands defined by combined sample of 77 RRL stars (66 RRab + 11 "fundamentalized" RRc) observed in the Fornax galaxy, plotted along with the best fitted lines. The slopes of the fits were adopted from chosen theoretical and empirical calibrations, and the zero points were determined from our data. Filled and open circles denote RRab and RRc stars, respectively. The observed scatter is related mostly to the singlephase nature of our photometry. Magnitude error bars are within the size of circles.

DISCUSSION
The results in Table 5 demonstrate that the true distance moduli obtained from theoretical and empirical NIR PLZ relations for RRL stars are consistent to within their quoted errors. Among them, results from three theoretical calibrations (Bono et al. 2003;Catelan et al. 2004) are virtually identical, while the calibration of Sollima et al. (2008) diverges by as much as 0.06 mag. The same remark was made before by e.g Karczmarek et al. (2015) and Szewczyk et al. (2009) in the context of distance determinations to the Carina galaxy and the SMC, together with the conclusion that this difference is not significant, taking into account all the uncertainties, which affect the entire process of calculating distance moduli.
However, the reappearance of this particular discrepancy between empirical and theoretical distance moduli may reveal some calibration difficulties that are still to overcome in order to achieve a full consistency of results. One of possible issues is the underestimation of the effect of metallicity in Eq. (4). Muraveva et al. (2015) reported a similarly low value of metallicity coefficient based on RRL stars in the LMC, and explained that the dependence on the metallicity can be decreased if it is derived from a stellar sample characterized by narrow metallicity range. Since both metallicity and distance vary from cluster to cluster, the empirical calibration suffers from degeneracy between the metallicity coefficient and the zero point, as no constraints can be assessed for metallicity without the prior knowledge of the distance and reddening. The metallicity coefficient in Eq. (4) was derived by Sollima et al. (2006) based on a sample of 5 datapoints-globular clusters and RR Lyrae variable itself-with known metallicities and distances, but also large uncertainties associated with them, which could have hampered the result. The uncertainty of the zero point of Sollima's calibration was based on the prototype of this class of variable stars, RR Lyrae itself, whose distance modulus was measured via trigonometric parallax with Hubble Space Telescope (Benedict et al. 2002), and equals 0.11 mag. Thanks to the first Gaia data release (Gaia Collaboration et al. 2017) this value has already been reduced to 0.09 mag and by the end of the mission is expected to reach 0.02 mag, which translates to unprecedented 0.1% precision in distance determination (Gould & Kollmeier 2017). Equipped with such a precise tool, we will be able to determine distance moduli from NIR PLZ relations of RRLs at the precision level of 3%.
More subtle effects, like helium abundances or bolometric corrections (Catelan et al. 2004), can also slightly affect distance calibrations by altering the absolute magnitudes of RRL stars. This was the case of Sollima et al. (2008), who recalculated the zero point of their earlier PLZ relation (Sollima et al. 2006) incorporating a new bolometric correction for the K-band, and resulted in 0.03 mag shift towards better coherence with theoretical calibrations.

Reddening
We adopted the same values of foreground reddening for each RRL star as Bersier & Wood (2002) with an uncertainty of 0.02 mag. These values are on average 0.008 mag smaller that the mean reddening E(B − V ) = 0.03 ± 0.02 mag towards Fornax adopted by Pietrzyński et al. (2009). The difference is however negligible, being smaller than the reddening uncertainty. If we adopted the same reddening value as Pietrzyński et al. (2009) for all stars in our sample, the distance moduli would be smaller by 0.004 mag and 0.001 mag in the J-and K-band, respectively. This exercise demonstrates a very limited impact of reddening in the NIR domain.

Metallicity
Because of its non-trivial star formation history, it is troublesome to determine the metallicity of even the oldest Fornax stellar population. With no spectroscopic measurements of Fornax RRL stars, other methods of metallicity determination have been employed: metallicity dependence on visual RRL brightness (Lee et al. 1990;Cacciari & Clementini 2003), metallicity dependence on RRL pulsational period (Sandage 1993), CMD comparison (Saviane et al. 2000). Moreover, the results were delivered in various metallicity scales. For example, Bersier & Wood (2002) used Sandage's periodmetallicity relation to get [Fe/H] = −1.6 dex in Butler-Blanco (BB) metallicity scale 3 (used by Sandage 1993). Metallicities [Fe/H] = −1.78 dex in the BB scale (Greco et al. 2005) and [Fe/H] = −1.8 dex in the Zinn & West (1984) scale  for Fornax field RRL stars are also present in the literature. In this study, we follow Bersier & Wood (2002) and adopt the average metallicity [Fe/H] = −1.6 ± 0.2 dex. The large uncertainty addresses the inconclusive metallicity of Fornax old population. In addition to the large metallicity dispersion of Fornax RRLs, the metallicity scales in Eqs. (1)−(3) are not uniquely defined. In the worst case scenario, the systematic differences between scales can reach 0.2 dex (Layden 1994). This would constitute a maximum systematic error of 0.046 mag, which we include to the final error budget.

Alteration of the zero point by single-phase measurements
Here we explore the possibility that at the moment of observations a significant number of RRL stars from our sample could have brightnesses above (below) their mean magnitudes. Since we approximated mean magnitudes by single-phase magnitudes, these stars would bias the zero point of the distance modulus fit towards higher (lower) values. In order to evaluate this error, we gen-erated 77 RRL light curves, drew from each light curve a single data point which served as an approximation of the mean brightness, and calculated distance modulus in the same manner as described in Section 3. Next, we repeated this procedure but this time we took the mean brightness of each star from its complete light curve. We compared the differences in calculated distance moduli for 1000 sets and concluded that the mean offset between distances derived from complete light curves and from random-phase measurements is 0.002 ± 0.01 mag. Therefore we adopt 0.01 mag as additional source of the systematic error. We recall that in the case of stars with a couple of observation points, we took a straight average of random-phase magnitudes, which led to a better approximation of the mean magnitudes for these stars, and to a reduction in the uncertainty of the zero point fit.

Uncertainties
All sources of errors which affected to any extent our results are summarized below in two groups: systematic and statistical errors. The statistical error (expressed as the standard deviation from the fit) contributes in values of 0.015 mag (J) and 0.013 mag (K) to the overall distance error, and accounts for: (i) the intrinsic scatter caused by single-phase measurements, (ii) the photometric error on each observation, and (iii) the uncertainty of atmospheric extinction and color corrections. The systematic error is associated with: (i) the uncertainty of adopted metallicities, (ii) the uncertainty of the metallicity scale, (iii) the uncertainty of the reddening correction, (iv) the uncertainty of the photometric zero point, (v) the uncertainty of literature zero point, and (vi) the uncertainty of the zero point fit altered by single-phase measurements. Systematic errors significantly surpass the statistical ones, and are dominated by the uncertainties of metallicity and the literature zero point. As in the case of the statistical error, we conservatively assumed the final systematic error to be the largest one among systematic errors presented in Table  5. Ultimately, taking into account errors of both origins, our best distance determination to the Fornax galaxy is 20.818 ± 0.015 (statistical) ± 0.116 (systematic) mag.

Comparison with previous results
In spite of continuous effort in determining the distance to the Fornax galaxy with various standard candles, still quite large spread in the results is observed (Table 1). For example, in the visual domain the difference between measurements of Bersier (2000) and Mc-Namara (2011) reaches almost 0.3 mag. In the NIR domain the difference of 0.1 mag is observed between distance moduli determined by Gullieuszik et al. (2007) and Pietrzyński et al. (2003Pietrzyński et al. ( , 2009). Our result is closer to Pietrzyński's results, although agrees also with Gullieuszik et al. (2007) within uncertainties.
The spread in the distances presented in Table 1 can result from a variety of reasons, among which we mention three. Different techniques employed for distance determinations could introduce a systematic shift between the results, as seen in the case of Gullieuszik et al. (2007) and Pietrzyński et al. (2003Pietrzyński et al. ( , 2009, both deriving Fornax distance from the red clump and the tip of the red giant branch stars. 4 Dispersion in results among studies conducted in the visual domain can be also attributed to the reddening, which is more severe in V and I filters than in J and K. Finally, in the case of RRL stars, the choice of the absolute magnitude is inextricably linked to the distance determination, as discussed by McNamara (2011). Combination of these effects could resolve the differences in distance moduli to some extent, but might not be able to provide a full coherence of all results. A thorough comparison of methodologies and values of crucial parameters (e.g. absolute magnitude, metallicity) across all distance determinations should disclose the sources of systematic differences in distance moduli, but such a study is beyond the scope of this paper.
Our result is based on four calibrations, but more NIR PLZ relations for RRL stars exist in the literature. Some are genuinely new empirical calibrations (Navarrete et al. 2017;Marconi et al. 2015;Braga et al. 2015), others use the coefficients standing by the logarithmic period from previous theoretical studies, or correct for the zero points (Benedict et al. 2011;Dékány et al. 2013). Our choice of calibrations was dictated by the consistency we wanted to hold with our similar previous studies of distance determinations from RRL stars (Pietrzyński et al. 2008;Szewczyk et al. 2008Szewczyk et al. , 2009Karczmarek et al. 2015).

CONCLUSIONS AND SUMMARY
We determined the distance to the Fornax Dwarf Spheroidal Galaxy from single-phase near-infrared Jand K-band observations of 77 RR Lyrae stars. We employed four different theoretical and empirical calibrations of the near-infrared PLZ relation for RRL 4 Two techniques differed in detection method of the tip of the red giant branch stars (Maximum Likelihood Algorithm versus Sobel edge-detection filter) and in the correction on population effects. The population correction, implemented by Gullieuszik et al. (2007) to the red clump and the tip of the red giant branch, was argued by Pietrzyński et al. (2003Pietrzyński et al. ( , 2009 to be negligible in the K-band and therefore omitted. stars, averaged the results, and determined a reddeningfree distance modulus to the Fornax galaxy of value 20.818 ± 0.015 (statistical) ± 0.116 (systematic) mag. The method requires very modest observational effort, because NIR single-phase measurements of RRLs can successfully approximate their mean magnitudes. Our results are consistent and agree with other distance determinations obtained from a number of independent techniques and in various wavebands, especially with the red clump stars and the tip of red giant branch, examined also in the NIR domain (Pietrzyński et al. 2003. Our study adds to existing distance determination a new, competitive measurement with the precision at 5% level. The method presented in this paper is expected to reach a precision level of 3%, once the zero point of the PLZ calibration is refined thanks to the Gaia mission. We have consistently used NIR PLZ relations for RRL stars to measure distances to five member galaxies of the Local Group (LMC, SMC, Sculptor, Carina, and Fornax) within the Araucaria Project, and proved its quality as a tool for accurate and precise distance determination, particularly for galaxies and clusters which lack young standard candles, like Cepheids. With the use of the world largest telescopes equipped with NIR detectors this method allows to measure distances up to 300 kpc.
We gratefully acknowledge the anonymous referee, whose thorough reading and insightful comments im-proved the content of this paper. The research leading to these results has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (grant agreement No 695099), and from the Polish National Science Centre grant MAESTRO 2012/06/A/ST9/00269. GP and WG acknowledge financial support for this work from the BASAL Centro de Astrofisica y Tecnologias Afines (CATA) PFB-06/2007. WG and MG also acknowledge financial support from the Millenium Institute of Astrophysics (MAS) of the Iniciativa Cientifica Milenio del Ministerio de Economia, Fomento y Turismo de Chile, grant IC120009. The data presented here were acquired under ESO programmes 082.D-0123(B) and 092.D-0295(B), granting of which is gratefully acknowledged. We thank the staff of the ESO Paranal and La Silla observatories for their help in obtaining the observations. This research has made use of the 2MASS Database, the NASA's Astrophysics Data System Service, and the NASA/IPAC Extragalactic Database.