The VMC Survey. VIII. First results for Anomalous Cepheids

The VMC Survey. VIII. First results for Anomalous Cepheids1


The VISTA near-infrared survey of the Magellanic Clouds System (VMC, PI M.-R. L. Cioni) is collecting deep –band time–series photometry of the pulsating variable stars hosted in the system formed by the two Magellanic Clouds and the Bridge connecting them. In this paper we present for the first time –band light curves for Anomalous Cepheid (AC) variables. In particular, we have analysed a sample of 48 Large Magellanic Cloud ACs, for which identification and optical magnitudes were obtained from the OGLE III and IV catalogues. The VMC –band light curves for ACs are well sampled, with the number of epochs ranging from 8 to 16, and allowing us to obtain very precise mean magnitudes with errors on average of the order of 0.01 mag. The values were used to build the first Period–Luminosity and Period–Wesenheit relations in the near-infrared for fundamental-mode and first overtone ACs. At the same time we exploited the optical () OGLE data to build accurate Period–Luminosity, Period–Luminosity–Colour and Period-Wesenheit relations both for fundamental-mode and first overtone ACs. For the first time these relations were derived from a sample of pulsators which uniformly cover the whole AC instability strip. The application of the optical Period–Wesenheit relation to a sample of dwarf galaxies hosting a significant population of ACs revealed that this relation is a valuable tool for deriving distances within the Local Group. Due to its lower dispersion, we expect the Period–Wesenheit relations first derived in this paper to represent a valuable tool for measuring accurate distances to galaxies hosting ACs when more data in near-infrared filters become available.

Stars: variables: Cepheids– galaxies: Magellanic Clouds – galaxies: distances and redshifts – surveys

1 Introduction

The Magellanic Clouds (MCs) play a fundamental role in the context of stellar populations and galactic evolution studies (see e.g. Harris & Zaritsky, 2004, 2009). Together with the Milky Way they form the closest example of ongoing complex interaction among galaxies (see e.g. Putman et al., 1998; Muller et al., 2004; Stanimirović et al., 2004; Bekki & Chiba, 2007; Venzmer, Kerp & Kalberla, 2012; For, Staveley-Smith & McClure-Griffiths, 2013). Moreover, since they are more metal poor than our Galaxy and host a significant population of younger populous clusters, the MCs represent an ideal laboratory for testing physical and numerical assumptions of stellar evolution codes (see e.g. Matteucci et al., 2002; Brocato et al., 2004; Neilson & Langer, 2012).

In the framework of the extragalactic distance scale, the Large Magellanic Cloud (LMC) represents the first crucial step on which the calibration of Classical Cepheid (CC) Period-Luminosity () relations and in turn of secondary distance indicators relies (see e.g. Freedman et al., 2001; Walker, 2012; Riess et al., 2011; de Grijs, 2011, and references therein). Similarly, the LMC hosts several thousand RR Lyrae variables, which represent the most important Population II standard candles through the well known –[Fe/H] and near-infrared (NIR) metal dependent relations. Hence, the LMC is the ideal place to compare the distance scales derived from Population I and II indicators (see e.g. Clementini et al., 2003; Walker, 2012, and references therein).

In this context NIR observations of pulsating stars (see e.g. Ripepi et al., 2012a; Moretti et al., 2013, and references therein) are very promising. Such observations over the whole Magellanic system, including the relatively unexplored Bridge connecting the two Clouds, represent one of the most important aims of the VISTA near-infrared survey of the Magellanic Clouds system (VMC; Cioni et al., 2011, hereinafter Paper I). The VMC ESO public survey is acquiring deep NIR photometric data in the , and filters on a wide area across the Magellanic system, with the VIRCAM camera (Dalton et al., 2006) of the ESO VISTA telescope (Emerson, McPherson & Sutherland, 2006). The principal scientific aims of VMC are the reconstruction of the spatially-resolved star-formation history (SFH) and the determination of the 3D structure of the whole Magellanic system. The observational strategy, planned to go as deep as mag (Vega) at Signal to Noise ratio (S/N)=10, will allow us to detect sources encompassing most phases of stellar evolution, namely the main-sequence, the subgiant branch, the upper and lower red giant branch (RGB), the red clump, the RR Lyrae and Cepheid location, the asymptotic giant branch (AGB), the post-AGB and planetary nebulae (PNe) phases, but also supernova remnants (SNRs), etc. These different stellar populations will allow us to study age and metallicity distributions within the whole MC system.

The properties of the CCs and RR Lyrae stars observed by the VMC survey are addressed by Ripepi et al. (2012a, b). In these papers, the authors provide important results on the calibration of the distance scales for both these important standard candles. Beyond these two classes of variables, other kinds of pulsating stars play an important role both as distance indicators and stellar population tracers. In particular, Anomalous Cepheids (ACs) are Pop.II stars, according to their low metallicity, with periods shorter than 2 days and brighter than RR Lyrae stars by an amount that typically ranges from 0.3 mag for the shortest period to 2 mag for the longest period pulsators (see e.g. Caputo, 1998; Marconi et al., 2004; Caputo et al., 2004, and references therein). From the evolutionary point of view these variables are usually associated with the central He burning phase of stars with masses from 1.3 to 2.1 and metallicities lower than ([Fe/H]1.7 dex, for ) (see Caputo, 1998; Marconi et al., 2004, for details). In this low metallicity regime the Zero Age Horizontal Branch (ZAHB) is predicted to show a turnover at lower effective temperatures. Indeed, as the mass increases along the ZAHB, the effective temperature decreases down to a minimum value beyond which both the effective temperature and the luminosity increase up to the values corresponding to the transition mass limit (see e.g. Caputo, 1998, for details). Above this limit, the star ignites the triple– reaction quiescently and burns central Helium along the blue loop phase, becoming a CC when crossing the instability strip. The location of the ACs in a period magnitude plane is therefore the downward extension of the distribution of metal poor classical Cepheids, and in the short period range the discrimination between the two classes can be risky, as extensively discussed in Caputo et al. (2004). These authors have also demonstrated that both the predicted limiting magnitude for massive pulsators and the magnitude of RR Lyrae stars, depend on the assumed metallicity, with the difference between these magnitudes increasing with the metal content.

In the LMC there are 86 ACs (Soszyński et al., 2008, 2012). An investigation of the properties of these pulsators in the optical bands has been recently presented by Fiorentino & Monelli (2012), using these objects as stellar population tracers. These authors derived pulsation constraints on their mode identification and mass estimate. Nevertheless, optical Period–Luminosity–Colour () and Wesenheit () relations (see Madore, 1982; Madore & Freedman, 1991, for a detailed discussion) for the LMC ACs are still lacking in the literature. These relations are important tools providing an alternative and independent estimate of the distance to the LMC. Furthermore, for the reasons discussed above, we expect significant advantages when deriving similar relations in the NIR bands.

The VMC data for the ACs are presented in Section 2. The , , and relations in the optical (on the basis of the OGLE data) and in the NIR (on the basis of the VMC data) derived for Fundamental-mode (F) and First Overtone (FO) ACs are discussed in Sections 3 and 4. The zero-point calibrations of the AC , , and relations and their application are presented in Section 5. Finally, a summary of the main results is presented in Section 6.

Figure 1: Distribution of the known ACs over the LMC (projected in the sky adopting deg and deg). Grey and black filled circles show the ACs observed by OGLE and those falling in the VMC tiles considered in this paper, respectively. The red filled circles represent the only two stars without a VMC counterpart within 1.0 arcsec (see text). Thin blue and thick green squares (distorted by the projection into the sky) show part of the VMC tiles in the LMC and the 11 tiles treated in this paper, respectively. The thick red and light blue lines show the areas covered by OGLE III and IV (released up to now), respectively.

2 Anomalous Cepheids in the VMC survey

ACs in the LMC were identified and characterized in the optical bands by Soszyński et al. (2008, and references therein) as part of the OGLE III project5. For the LMC tile 8_8 (including the South Ecliptic Pole, or SEP) which lies outside the area imaged by OGLE III, we used results of an early release of stage IV of the OGLE survey (Soszyński et al., 2012). In these surveys, a total of 86 ACs were found (83 by OGLE III and 3 by OGLE IV), of which 66 are F and 20 are FO pulsators.

In this paper we present results for the ACs included in eleven“tiles” (1.5 sq. deg.) completely or nearly completely observed, processed and catalogued by the VMC survey as of March 2013, namely the tiles LMC 4_8, 5_3, 5_5, 5_7, 6_4, 6_5, 6_6, 6_8, 7_3, 7_5, and 8_8 (see Fig. 1). Tile LMC 6_6 is centred on the well known 30 Dor star forming region, tiles LMC 5_5, 6_4 and 6_5 are placed on the bar of the LMC, whereas the remaining tiles lie in less crowded regions of the galaxy. We note that tile LMC 8_8 encompasses the South Ecliptic Pole (SEP) which will be observed by the Gaia satellite during its commissioning phase (Lindegren & Perryman 1996; Lindegren 2010).

The general observing strategy of the VMC survey is described in detail in Paper I, whereas the procedures specifically applied to the variable stars can be found in Moretti et al. (2013). Here we only recall that to obtain well sampled light curves, the VMC -band time series observations were scheduled in 12 separate epochs distributed over ideally several consecutive months. The VMC data, processed through the pipeline (Irwin et al., 2004) of the VISTA Data Flow System (VDFS, Emerson et al., 2004) are in the VISTA photometric system (Vegamag=0). The time-series photometry used in this paper was retrieved from the VISTA Science Archive (VSA, Cross et al., 2012)6. For our analysis we used the VMC data acquired until the end of March 2013.

According to OGLE III/IV, 48 ACs are expected to lie in the 11 tiles analysed in this paper. Figure 1 and Tab. 1 show the distribution of such stars in the VMC tiles. The OGLE III and IV catalogues of ACs were cross-correlated against the VMC catalogue to obtain the light curves for these variables.

All but one of the 48 ACs were found to have a counterpart in the VMC catalogue (see Tab. 2). The only object without VMC counterpart in the VSA within 3 arcsec (see Fig. 2) is OGLE-LMC-ACEP-024, which is expected to fall well within the tile LMC 6_4. This star has has a luminosity =17.679 mag and =17.986 mag and no remarks in the OGLEIII catalogue. There is a match if we enlarge the pairing radius to 5 arcsec, but the corresponding star is clearly too bright (12.8 mag). An inspection of the VMC image reveals that the star is placed in the outskirts of the cluster NGC 1252, in a rather crowded region. This could explain the lack of a detection. For one of the objects with VMC identification, i.e. OGLE-LMC-ACEP-065 in tile LMC 6_6, the VSA database did not return any time-series data. This is likely because the star is located at the very edge of the frame, where the sensitivity is low and the target cannot be detected in the single epoch frames. Looking in more detail at this object on the VMC image (see Fig. 2), it appears that some crowding is present but the target should be easily detected at least in the neighbour tile LMC 5_6 which was not observed yet.

As shown in Tab. 2, the sample of ACs discussed here includes 36 F and 10 FO-mode pulsators. This sample represents more than 50% of the total number of ACs in the LMC. The VMC time-series photometry for these 46 objects is provided in Table 3, which is published in its entirety in the on-line version of the paper.

Tile RA (center) DEC (center) #ACs Epochs OGLE
LMC J(2000) J(2000) (VMC)
4_8 06:06:32.95 72:08:31.2 2 10 III
5_3 04:58:11.66 70:35:28.0 4 11 III
5_5 05:24:30.34 70:48:34.2 8 15 III
5_7 05:51:04.87 70:47:31.2 3 8 III
6_4 05:12:55.80 69:16:39.4 8 14 III
6_5 05:25:16.27 69:21:08.3 10 9 III
6_6 05:37:40.01 69:22:18.1 3 14 III
6_8 06:02:21.98 69:14:42.4 2 14 III
7_3 05:02:55.20 67:42:14.8 6 16 III
7_5 05:25:58.44 67:53:42.0 1 14 III
8_8 05:59:23.14 66:20:28.7 1 16 IV
Table 1: Number of Anomalous Cepheids in the 11 VMC tiles analyzed in this paper, according to OGLE III/IV.
Figure 2: Sky pictures for nine problematic stars extracted from the VMC (lower panels) and the OGLE III (upper panels) archives. The target is identified in the single-epoch VMC images by a label showing the last 8 digits of the VMC identification. Similarly the corresponding OGLE III identification is reported with three digits (i.e. without the prefix “OGLE-LMC-AC-”).
ID RA DEC M Period Epoch VMC-ID Tile n Notes
J2000 J2000 d d mag mag
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
OGLE-LMC-ACEP-035 5:18:22.19 69:03:38.4 FO 0.446049 52115.88331 18.143 18.658 558355019633 6_4 14
OGLE-LMC-ACEP-013 4:59:56.62 70:42:24.9 FO 0.500923 52166.70918 17.963 18.488 558359106778 5_3 11
OGLE-LMC-ACEP-043 5:24:35.40 68:48:22.6 FO 0.50647 52167.59135 17.913 18.593 558356009732 6_5 9
OGLE-LMC-ACEP-028 5:13:10.02 68:46:11.9 FO 0.599253 50457.56427 17.574 18.322 558354835825 6_4 14 a
OGLE-LMC-ACEP-068 5:51:09.02 70:45:42.6 F 0.625645 52194.18981 18.265 18.809 558360489508 5_7 8
OGLE-LMC-ACEP-049 5:28:03.58 69:39:15.2 F 0.644796 52167.32917 18.011 18.451 558356666394 6_5 9
OGLE-LMC-ACEP-071 5:54:43.24 70:10:16.1 FO 0.676209 52187.35869 17.330 17.755 558360071488 5_7 8
OGLE-LMC-ACEP-045 5:26:24.68 68:57:55.0 F 0.678431 52167.43289 18.325 18.976 558356105371 6_5 9
OGLE-LMC-ACEP-051 5:30:14.23 68:42:31.1 F 0.708606 52167.2697 18.200 18.845 558355948009 6_5 9
OGLE-LMC-ACEP-023 5:07:52.42 68:50:28.8 FO 0.723433 50726.2685 17.194 17.763 558354917807 6_4 14
OGLE-LMC-ACEP-034 5:17:11.15 69:58:33.1 F 0.734298 52123.77557 17.874 18.474 558355708277 6_4 14
OGLE-LMC-ACEP-008 4:58:24.59 71:05:11.5 FO 0.749068 52166.14121 17.300 17.911 558359341685 5_3 11
OGLE-LMC-ACEP-024 5:08:44.05 68:46:01.2 F 0.794464 50726.76849 17.679 17.986 558354864345 6_4 0 b
OGLE-LMC-ACEP-009 4:58:51.29 67:44:23.9 FO 0.80008 52166.34228 17.344 17.913 558351428166 7_3 16
OGLE-LMC-ACEP-081 6:09:38.40 69:34:04.1 F 0.800838 52194.39949 17.917 18.504 558354433783 6_8 14
OGLE-LMC-ACEP-067 5:48:22.08 70:45:49.3 F 0.820921 52168.84504 17.786 18.451 558360481966 5_7 7 c
OGLE-LMC-ACEP-010 4:59:00.10 68:14:01.1 F 0.834201 52166.34125 18.068 18.723 558351741077 7_3 16
OGLE-LMC-ACEP-078 6:06:58.20 72:52:08.7 FO 0.856556 52187.11324 16.979 17.417 558367620049 4_8 10
OGLE-LMC-ACEP-041 5:21:14.35 70:29:39.5 F 0.878142 50831.14818 17.625 18.200 558361532603 5_5 15
OGLE-LMC-ACEP-063 5:37:54.39 69:19:28.7 F 0.893031 52187.44348 18.013 18.756 558357554473 6_6 14
OGLE-LMC-ACEP-007 4:57:31.48 70:15:53.6 F 0.896399 52166.18452 17.688 18.247 558358821009 5_3 11
OGLE-LMC-ACEP-017 5:02:03.13 68:09:30.4 F 0.929995 52166.07849 17.585 18.190 558351666932 7_3 16
OGLE-LMC-ACEP-040 5:21:13.22 70:34:20.7 F 0.960577 50831.32386 17.433 18.037 558361590075 5_5 15
OGLE-LMC-ACEP-054 5:31:06.72 68:22:29.8 F 0.980222 52167.47834 17.901 18.798 558353586650 7_5 14
OGLE-LMC-ACEP-039 5:20:44.47 69:47:46.5 F 0.992407 50455.25698 17.660 18.245 558356832178 6_5 9 c
OGLE-LMC-ACEP-011 4:59:38.09 70:37:45.5 F 0.99859 51999.6182 17.671 18.254 558359538067 5_3 3 c
OGLE-LMC-ACEP-050 5:28:57.71 70:07:15.5 FO 1.044691 50454.74962 16.609 17.049 558361189093 5_5 15
OGLE-LMC-ACEP-042 5:23:34.60 69:10:58.2 F 1.079036 52167.36992 17.897 18.715 558356267143 6_5 5 c
LMC571.05.5070 6:01:41.77 65:58:53.5 F 1.087061 55557.82471 17.181 17.686 558349409852 8_8 16
OGLE-LMC-ACEP-077 6:04:35.73 71:40:35.8 F 1.122498 52187.66068 17.459 18.099 558367137280 4_8 10
OGLE-LMC-ACEP-056 5:31:49.45 70:33:22.6 F 1.124003 52167.63676 17.284 17.877 558361558150 5_5 15
OGLE-LMC-ACEP-079 6:07:02.01 69:31:55.2 F 1.15517 52176.92756 17.149 17.634 558354405855 6_8 14
OGLE-LMC-ACEP-037 5:19:16.67 70:11:58.4 F 1.25774 52156.5207 17.132 17.743 558361296449 5_5 15 a
OGLE-LMC-ACEP-036 5:18:58.85 69:26:47.8 F 1.257982 50455.67396 17.160 17.787 558355324744 6_4 23
OGLE-LMC-ACEP-052 5:31:01.53 70:42:22.2 F 1.262555 52167.0715 17.008 17.577 558361664456 5_5 15
OGLE-LMC-ACEP-046 5:26:27.17 69:58:57.0 F 1.263717 50454.39955 17.264 17.851 558356990050 6_5 9
OGLE-LMC-ACEP-021 5:06:37.49 68:23:40.3 F 1.295843 50725.62518 17.188 17.827 558351789022 7_3 16
OGLE-LMC-ACEP-044 5:25:54.11 69:26:52.9 F 1.308509 50455.10639 17.052 17.609 558356474792 6_5 9
OGLE-LMC-ACEP-032 5:15:56.13 69:01:29.1 F 1.316022 50456.81167 17.167 17.780 558355007611 6_4 14
OGLE-LMC-ACEP-065 5:40:03.04 70:04:47.8 F 1.3215432 50725.78028 17.041 17.508 558358103119 6_6 0 b
OGLE-LMC-ACEP-016 5:01:36.69 67:51:33.1 F 1.54567 52166.4502 16.926 17.448 558351480147 7_3 16
OGLE-LMC-ACEP-048 5:27:12.12 69:37:19.6 F 1.545893 50454.48193 16.718 17.324 558356636279 6_5 9
OGLE-LMC-ACEP-055 5:31:41.11 68:44:37.7 F 1.606665 52189.7241 17.011 17.603 558357237330 6_6 14
OGLE-LMC-ACEP-057 5:31:49.88 70:46:30.0 F 1.710008 52167.36219 16.813 17.455 558361710363 5_5 15
OGLE-LMC-ACEP-026 5:10:42.62 68:48:19.6 F 1.738745 50457.22581 16.816 17.483 558354874727 6_4 14
OGLE-LMC-ACEP-053 5:31:06.20 68:43:45.3 F 1.888099 52166.63019 16.738 17.299 558355958053 6_5 23 a
OGLE-LMC-ACEP-047 5:27:05.27 71:23:33.4 F 2.177985 52166.33026 16.881 17.482 558362082677 5_5 15
OGLE-LMC-ACEP-014 5:00:08.26 67:54:04.3 F 2.291346 52164.63844 16.639 17.241 558351518318 7_3 16
stars showing significant blending but with useful light curves (see Figs.  2,  3, and Fig. 4)
stars without VMC data (see Fig. 2)
stars showing significant blending and having unusable light curves (see Fig.  2 and  5)
Table 2: Cross-identification and main characteristics of the Anomalous Cepheids in the 11 “tiles” analysed in this paper. The columns report: 1) OGLE identification; 2) right ascension (OGLE); 3) declination (OGLE); 4) mode of pulsation; 5) period; 6) epoch of maximum light; 7) intensity–averaged magnitude (OGLE); 8) intensity–averaged magnitude (OGLE); 9) VMC identification; 10) VMC Tile; 11) Number of epochs; 12) Notes on individual stars
HJD-2 400 000
56267.81039 17.118 0.039
56316.64476 16.921 0.032
56318.55354 16.899 0.030
56322.63275 17.170 0.036
56328.57027 16.925 0.030
56334.54372 16.933 0.036
56341.53132 17.200 0.042
56347.56046 17.036 0.032
56371.53252 16.923 0.034
56372.51981 16.952 0.034
56375.52238 17.112 0.034

Table 3 is published in its entirety only in the electronic edition of the journal. A portion is shown here for guidance regarding its form and content.

Table 3: time-series photometry of the ACs

Periods and Epochs of maximum light available from the OGLE III catalogue were used to fold the –band light curves produced by the VMC observations. The OGLE IV catalogue provides only the period for the AC LMC571.05.5070, hence we obtained the Epoch of maximum from the analysis of the star -band light curve. The –band light curves for a sample of 42 ACs with useful light curves are shown in Figs. 3 and 4. Apart from a few cases these light curves are generally well sampled and nicely shaped. Intensity-averaged magnitudes were derived from the light curves simply using custom software written in C, that performs a spline interpolation to the data with no need of using templates. Some evidently discrepant data points in the light curves were excluded from the fit but were plotted in the figure for completeness (note that most of these “bad” data points belong to observations collected during nights that did not strictly meet the VMC quality criteria). The final spline fit to the data is shown by a solid line in Figs.  3 and 4. Final magnitudes are provided in Table 4.

Four objects in our sample were excluded, namely: OGLE-LMC-ACEP-011, 039, 042, 067. Their light curves are displayed in Fig. 5, whereas their finding charts are shown in Fig. 2. A quick analysis of the finding charts reveals that all these stars have significant problems of crowding/blending (particularly, star 011).

ID M Period V-I
d mag mag mag mag mag
(1) (2) (3) (4) (5) (6) (7) (8)
OGLE-LMC-ACEP-035 FO 0.446049 17.585 0.026 0.17 0.07 0.026
OGLE-LMC-ACEP-013 FO 0.500923 17.334 0.033 0.06 0.03 0.068
OGLE-LMC-ACEP-043 FO 0.50647 17.186 0.051 0.08 0.09 0.013
OGLE-LMC-ACEP-028 FO 0.599253 16.399 0.010 0.08 0.06 0.040
OGLE-LMC-ACEP-068 F 0.625645 17.490 0.049 0.26 0.06 0.042
OGLE-LMC-ACEP-049 F 0.644796 17.412 0.028 0.12 0.04 0.003
OGLE-LMC-ACEP-071 FO 0.676209 16.790 0.015 0.12 0.07 0.053
OGLE-LMC-ACEP-045 F 0.678431 17.499 0.045 0.33 0.11 0.008
OGLE-LMC-ACEP-051 F 0.708606 17.437 0.023 0.17 0.10 0.000
OGLE-LMC-ACEP-023 FO 0.723433 16.444 0.005 0.13 0.08 0.052
OGLE-LMC-ACEP-034 F 0.734298 17.186 0.022 0.26 0.13 0.028
OGLE-LMC-ACEP-008 FO 0.749068 16.567 0.007 0.14 0.08 0.072
OGLE-LMC-ACEP-009 FO 0.80008 16.575 0.014 0.16 0.06 0.081
OGLE-LMC-ACEP-081 F 0.800838 17.147 0.017 0.13 0.07 0.090
OGLE-LMC-ACEP-010 F 0.834201 17.225 0.015 0.35 0.11 0.077
OGLE-LMC-ACEP-078 FO 0.856556 16.372 0.018 0.16 0.09 0.057
OGLE-LMC-ACEP-041 F 0.878142 16.790 0.020 0.17 0.09 0.021
OGLE-LMC-ACEP-063 F 0.893031 16.990 0.026 0.20 0.18 0.020
OGLE-LMC-ACEP-007 F 0.896399 17.002 0.020 0.25 0.06 0.073
OGLE-LMC-ACEP-017 F 0.929995 16.810 0.015 0.25 0.06 0.070
OGLE-LMC-ACEP-040 F 0.960577 16.644 0.012 0.18 0.09 0.021
OGLE-LMC-ACEP-054 F 0.980222 16.781 0.029 0.17 0.26 0.000
OGLE-LMC-ACEP-050 FO 1.044691 16.016 0.011 0.14 0.07 0.003
LMC571.05.5070 F 1.087061 16.479 0.007 0.25 0.08 0.072
OGLE-LMC-ACEP-077 F 1.122498 16.608 0.002 0.08 0.07 0.062
OGLE-LMC-ACEP-056 F 1.124003 16.527 0.019 0.19 0.06 0.002
OGLE-LMC-ACEP-079 F 1.15517 16.471 0.013 0.26 0.05 0.085
OGLE-LMC-ACEP-037 F 1.25774 15.332 0.007 0.04 0.08 0.024
OGLE-LMC-ACEP-036 F 1.257982 16.388 0.022 0.13 0.08 0.023
OGLE-LMC-ACEP-052 F 1.262555 16.316 0.011 0.27 0.07 0.001
OGLE-LMC-ACEP-046 F 1.263717 16.570 0.016 0.35 0.03 0.008
OGLE-LMC-ACEP-021 F 1.295843 16.377 0.027 0.20 0.07 0.058
OGLE-LMC-ACEP-044 F 1.308509 16.380 0.024 0.48 0.06 0.007
OGLE-LMC-ACEP-032 F 1.316022 16.360 0.010 0.20 0.06 0.032
OGLE-LMC-ACEP-016 F 1.54567 16.261 0.006 0.30 0.05 0.073
OGLE-LMC-ACEP-048 F 1.545893 15.958 0.018 0.25 0.07 0.005
OGLE-LMC-ACEP-055 F 1.606665 16.188 0.010 0.26 0.08 0.003
OGLE-LMC-ACEP-057 F 1.710008 16.006 0.017 0.43 0.07 0.001
OGLE-LMC-ACEP-026 F 1.738745 15.932 0.011 0.27 0.08 0.046
OGLE-LMC-ACEP-053 F 1.888099 15.682 0.011 0.26 0.11 0.002
OGLE-LMC-ACEP-047 F 2.177985 16.181 0.009 0.31 0.07 0.012
OGLE-LMC-ACEP-014 F 2.291346 15.862 0.008 0.29 0.04 0.076
Table 4: Results for the 42 Anomalous Cepheids with useful light curves analysed in this paper. The columns report: 1) OGLE identification; 2) mode of pulsation; 3) period; 4) intensity–averaged magnitude; 5) uncertainty on the ; 6) peak–to–peak amplitude in ; 7) adopted reddening; 8) correction in magnitude due to the deprojection.
Figure 3: –band light curves for 27 of the 42 ACs with usable data discussed in this paper. Stars are displayed in order of increasing period. Solid lines represent spline best-fits to the data (see text). In each panel we report OGLE’s identification number and period.
Figure 4: As in Fig. 3 but for the remaining 15 ACs of our sample.

It is important to remember that all the photometry presented in this paper is in the VISTA system. To make it easy to compare our results with the widely used 2MASS system, we note that the two systems are very close to each other. In particular, the VMC magnitude depends only mildly on the () colour. Indeed, the empirical results available to date7 show that: ()(2MASS)=1.081(-)(VISTA) and (2MASS)=(VISTA)0.011(-)(VISTA). Unfortunately, for the majority of our targets we only have a few measurements (4 phase points), hence a star-by-star correction based on the colour is likely to introduce larger errors than the correction itself. Furthermore, since the measured ( ) of our AC sample typically ranges from 0.2 to 0.5 mag, the average correction over the 42 ACs considered here, is as small as 1.0 mmag and can be safely neglected. In conclusion, for ACs, as well as for CCs (see Ripepi et al., 2012b), to a very good approximation, the VISTA and 2MASS can be considered equivalent.

3 Optical Period-Luminosity, Period-Luminosity-Colour and Period-Wesenheit relations

Before presenting the results in the NIR bands, in this section we derive the coefficients of the optical () , and Wesenheit– relations, based on the OGLE data, since they are still lacking in the literature. Indeed, neither Soszyński et al. (2008) nor Fiorentino & Monelli (2012) published these relations, although they showed them in some figures. In this case we have used the whole sample of ACs detected in the LMC by the OGLE III/IV surveys.

The first step is to correct for reddening, which unfortunately is rather variable in the LMC, hence needs to be evaluated locally. To this aim, we adopted the recent estimates by Haschke, Grebel & Duffau (2011). Individual () reddening values for the 42 ACs with useful VMC data are reported in column 7 of Table 4. In Sect. 5 we will check the soundness of these reddening values.

The second step consists of accounting for the inclination of the LMC disc-like structure by de-projecting each AC with respect to the LMC centre. We followed the procedure outlined in van der Marel & Cioni (2001) and adopted their values of the LMC centre, inclination, and position angle of the line of nodes (see column 8 of Tab. 4).

Finally, we performed least-squares fits to the data of F and FO-mode variables separately, adopting equations of the form Mag= log, with Mag. The best-fitting relationships are shown in the left panels of Fig. 6, their coefficients are provided in the first portion of Table 5. We note that in all panels of this figure, the stars plotted with crosses and open circles were rejected from the fit because they are 2.5-3 off the regression line. In particular, the three objects with the longest periods, namely OGLE-LMC-ACEP-014, 033, 047 (crosses in Fig. 6) are likely not ACs but rather members of some different variable classes such as BL Herculis stars. Indeed, looking at Fig. 1 in Soszyński et al. (2008) it is clear that some confusion can be possible between ACs and BL Her pulsators at the periods of interest. Additional stars that were not used in at least one of the regressions are OGLE-LMC-ACEP-022, 024, 028, 042, 059, 083. All these objects, with the possible exception of 022, show some observational problems. In particular, the stars 024, 042, 028 will be discussed in detail in the next section, since they are problematic also in the VMC data (see Fig. 2). As for the remaining three, we inspected the OGLE images and light curves, finding that in the case of the star 083 there is a strong background variation close to the object (possibly close to an edge of the CCD) and the star light curves appear to be rather noisy. Stars 022 and 059 are surrounded by a number of close companions and both of them show a rather noisy light curve, especially star 059, that has also a large colour (1.2 mag).

Figure 5: Light curves for four problematic stars (see text).

In addition to the relations we can also derive the and relations. The advantages of using these relations instead of a simple have been widely discussed in the literature (see e.g. Marconi et al., 2004, in the case of ACs). Briefly, these relations include a colour term with a coefficient that, in the case of the relation, takes into account the colour distribution of the variable stars within the instability strip, whereas in the case of the Wesenheit function corresponds to the ratio between total-to-selective extinction in the filter pair (Madore, 1982; Caputo, Marconi & Musella, 2000), thus making the Wesenheit relations reddening free by definition. We expect these relations to have much smaller dispersion than a simple relation, even if the scatter reduction for ACs is not as significant as in the case of CCs (see e.g. Marconi, Musella, & Fiorentino, 2005; Marconi et al., 2004). In fact, for CCs a strict Mass-Luminosity () relation is predicted to exist by stellar evolution computations for He burning intermediate mass stars, which makes the a relation holding for each individual pulsator (see e.g. Caputo, Marconi & Musella, 2000, for details). Unfortunately, the ACs are not characterized by such a strict relation, thus the resulting and relations include the possible effect of mass differences at fixed luminosity level.
The and relations are usually calculated using the colour. The coefficients of the relations derived with this procedure for the LMC ACs are provided in the lower portions of Table 5. The relations are shown in the right panels of Fig. 6. The dispersion of the and relations is of the order of 0.15 mag (see Tab. 5), hence smaller than for the relation but larger than in the case of CCs (see e.g. Soszyński et al., 2008, who found a =0.08 mag for the relation).

mode r.m.s.
=+ log
F 17.90 0.03 3.21 0.21 0.20
FO 17.20 0.09 3.14 0.37 0.23
=+ log
F 17.38 0.02 3.22 0.19 0.18
FO 16.74 0.06 3.23 0.25 0.16
F 16.59 0.02 3.41 0.16 0.15
FO 16.05 0.05 3.44 0.22 0.13
F 16.71 0.09 3.40 0.14 2.34 0.16 0.14
FO 16.24 0.13 3.34 0.18 2.14 0.28 0.12
Table 5: Optical , and relations for F and FO Anomalous Cepheids. The Wesenheit function is defined as: .
mode r.m.s.
=+ log
F 16.74 0.02 3.54 0.15 0.10
FO 16.06 0.07 4.18 0.33 0.10
F 16.58 0.02 3.58 0.15 0.10
F 15.93 0.07 4.14 0.33 0.10
Table 6: NIR and relations for F and FO-mode Anomalous Cepheids. The Wesenheit function is defined as: =0.13 (). Note that all the results are in the VISTA photometric system.
Figure 6: Optical , and relations for F and FO Anomalous Cepheids. The Wesenheit function is defined as: . In each panel, green and black filled circles are OGLE F pulsators, blue and magenta filled circles are OGLE FO pulsators, with (in green and magenta) or without (in black and blue) VMC measurements. Empty circles and crosses mark pulsators that were discarded in the derivation of the and (and the optical ) relations. In particular, the three stars with longest periods (crosses) likely are not ACs and rather belong to a different type of variability. In all panels, the red lines show the best-fits to the data, with the corresponding relationships labelled at the bottom.

4 -band Period-Luminosity and Period-Wesenheit relations

By analogy to the optical bands, we can calculate the , and relationships in the -band. Our sample consist of 32 F-mode and 10 FO-mode ACs that are sufficient to provide statistically meaningful and relations. For both modes of pulsation our sample maps the whole range of periods covered by the LMC ACs, as shown in Fig. 6, where we have plotted in green and magenta colours the F and FO-mode objects observed by VMC, respectively. The -band and relations obtained are displayed in Fig. 7, whereas their coefficients are summarized in Tab. 6. Three F-mode and one FO-mode stars were excluded from the fit because they are more than 2 off the regression lines. The stars OGLE-LMC-ACEP-037 and 028, a F and FO-mode pulsators respectively, are shown with empty circles in Fig. 7. They have rather “normal” light curves, but at least the star 037 is clearly blended (see Fig. 2). The star 028 also exhibit an unusual colour (see Sect. 5 and Fig. 9) and we hypothesize that it may be blended, however, we do not have enough resolution to detect the contaminant star. The two additional F-Mode ACs excluded from the fit (namely, OGLE-LMC-ACEP-014 and OGLE-LMC-ACEP-047, shown as crosses in Fig. 7) are the stars with the longest periods. They were excluded also in the optical analysis as we suspect they could possibly belong to a separate class of variables. We note that, as for CCs, moving to the NIR the dispersion of the AC and relations decreases. We also made an attempt to calculate relations in the form =, but the colour term coefficient turned out to be statistically equal to zero. This is not very surprising given the relatively small number of pulsators and the almost identical dispersions of the and relations. Hence, according to this dataset, in the NIR filters it seems that there is no great advantage in using the AC or pseudo relations instead of the .

Figure 7: Top panel: -band relation for F and FO-mode ACs (red and blue symbols, respectively). Filled circles show the objects used for the least square fits. Stars marked by open circles and crosses were discarded (see text for detail). The solid lines is the least squares fit to the data. Bottom panel: as for the top panel but for the Wesenheit function, which is defined as labelled in the figure.

5 Comparison with literature and application to real cases

To compare our s for ACs with the relations available in the literature, we first need to set the absolute zero points. This can be done by assuming a proper value for the distance to the host galaxy, the LMC. We have adopted our own evaluation based on the absolute calibrations of the , and relations for CCs in the LMC presented in Ripepi et al. (2012b). In that paper we used the trigonometric parallaxes of Galactic Cepheids as well as Baade-Wesselink measurements of Cepheids in the LMC to evaluate mag (see Ripepi et al., 2012b, for full details.). This distance modulus is in very good agreement with current literature estimates for the distance to the LMC as nicely reviewed by Walker (2012), and with the very recent and precise value by Pietrzyński et al. (2013), based on eclipsing binaries. Results of this comparison in the optical are summarized in the first part of Tab. 7 and graphically shown in Fig. 8 for the and the Wesenheit relations, respectively.

The upper panel of Fig. 8 shows the comparison of our s with the relations derived empirically by Pritzl et al. (2002) and Marconi et al. (2004) on the basis of a few tens of ACs belonging to a number of dwarf Spheroidal galaxies (dSph) orbiting the Milky Way and M31 spirals. There is a clear disagreement between our results and the literature. This is likely due to a number of reasons: i) the very different coverage of the AC instability strip, which is much more uniformly and completely covered in the LMC sample; ii) at shorter periods (P0.4-0.5 d) it is easy to confuse F– and FO–mode pulsators, especially in the dSphs where samples are generally rather small; iii) the non-homogeneous dSph sample. A better agreement, at least for the F-mode pulsators, can be seen in the bottom panel of Fig. 8, where we compare our function with those by Marconi et al. (2004), the only published relation to date. The better agreement in this case is probably due to the much lower dependence of the with respect to the on the way the pulsators populate the instability strip.

Marconi et al. (2004) also published mass-dependent, and Wesenheit (the latter only for F-mode pulsators) relations for ACs calculated on the basis of non–linear, non–local time-dependent convective pulsation models. The lower portion of Tab. 7 reports the comparison between Marconi et al. (2004) theoretical models and our results. There is good agreement for the slope of the relations, however, our zero point implies a stellar mass of , at the lower end of the allowed range for ACs.

As for the , both the slopes and the zero point disagree by more than 1 . We do not have a clear explanation for these discrepancies, however, if the reddening values we have adopted for the ACs are correct, the disagreement could in principle be related to uncertainties in the theoretical colour-temperature relations.

There are no other empirical NIR relations in the literature we are aware of, hence we can compare our results only with the colour-colour and the relations derived by Marconi et al. (2004) from the theory of stellar pulsation. The top panel of Fig. 9 shows this comparison for the 42 pulsators analysed in this paper in the plane. Overall the agreement is very satisfactory. The residual discrepancy can be minimized by a difference in the adopted reddening of only mag. This is a confirmation that the reddening values adopted in this paper are well–established. An inspection of the figure confirms that the two stars OGLE-LMC-ACEP-037 and 028 (empty circles), previously excluded from the and derivation, are highly deviant also in the colour-colour plane. In addition, we find a third discrepant star in this plane: OGLE-LMC-ACEP-053 (empty star). Also this object is clearly blended (see Fig. 2), so that its strange position in the colour-colour plane can be easily explained. Since this AC shows a rather normal light curve and it is not deviant e.g. in the relation, we conclude that its photometry is only mildly affected by the blending star.

The lower panel of Fig. 9 shows the comparison between our F-mode relation and theoretical predictions (not available for FO-mode pulsators), for three different choices of the AC mass encompassing approximately the whole range of allowed values for this parameter, namely and . There is a good agreement for the slope of the relations, whereas, as already found for the optical , our zero-point seems to favor the smallest value of , for the mass.

Figure 8: Comparison between the optical (top panel) and relations (bottom panel) for F and FO-mode ACs derived in this paper with the literature results.
Figure 9: Top panel: versus plot for the F-mode ACs analysed in this paper. Symbols are as in Fig. 7. The solid line represents the theoretical relation by Marconi et al. (2004). The theoretical was converted to the 2MASS system using the relations in Tab. 7. Bottom panel: comparison between the observed Wesenheit -band relation for F-mode (solid line; note that the FO-mode relation is shown, too) and the predictions by Marconi et al. (2004) for three different choices of the pulsator mass (dashed lines, see labels).
mode r.m.s. source
=+ log
F 0.04 0.21 0.20 This paper
F 0.03 0.17 Pritzl et al. (2002)
F 0.14 0.14 Marconi et al. (2004)
FO 0.09 0.37 0.23 This paper
FO 0.07 0.20 0.25 Pritzl et al. (2002)
FO 0.25 0.25 Marconi et al. (2004)
F 0.04 0.16 0.15 This paper
F 0.20 0.20 Marconi et al. (2004)
F 0.20 0.20 Marconi et al. (2004)
FO 0.06 0.22 0.13 This paper
FO 0.20 0.20 Marconi et al. (2004)
F 0.09 0.14 2.34 0.16 0.14 This paper
F 2.73 0.01 Marconi et al. (2004)
FO 0.13 0.18 2.14 0.28 0.12 This paper
FO 2.67 0.01 Marconi et al. (2004)
F 0.04 0.15 0.10 This paper
FO 0.07 0.33 0.10 This paper
F 0.04 0.15 0.10 This paper
F 0.04 Marconi et al. (2004)
FO 0.07 0.33 0.10 This paper
Theoretical, the value of the mass ranges from 1.3 to 1.9
Models transformed to the Johnson system: for ACs (Johnson) (SAAO)
(see Bessell & Brett, 1988). (2MASS)(SAAO)(SAAO) (Carpenter, 2001)
Table 7: Literature values for the coefficients of the , and relations, for F and FO Anomalous Cepheids. The Wesenheit functions are defined as: and . In the , the photometry of previous studies was converted to the 2MASS system, for consistency with our results (see Section 2).

5.1 Application of the optical relation

In the previous sections we have shown that the relation is likely the best tool we have to use the ACs as standard candles. Indeed, the relation does not depend on the reddening and on how the pulsators populate the instability strip. This obviously holds also for the . However, at present the lack of NIR observations of ACs in other galaxies limits severely the use of this relation. On the contrary, data are available for a significant number of ACs belonging to a few dwarf galaxies in the Local Group that can be used to verify the ability of our to estimate the distance to the host systems by comparing AC-based and RR Lyrae-based distance determinations.

Figure 10: Optical relations for ACs in a number of Local Group dwarf galaxies in comparison with the results obtained in this paper. F and FO-mode ACs are marked by filled and empty circles, respectively; starred symbols refer to objects with uncertain classification that were not used in calculating the distances. Red and blue lines show present work for F and FO-mode ACs, respectively. True distance moduli estimated from these relations are labelled.

To our knowledge, there are only three dwarf galaxies with a significant number of ACs measured in the bands, namely, Fornax (Bersier & Wood, 2002), Leo T (Clementini et al., 2012), and Phoenix (Gallart et al., 2004). There is no clear separation between F and FO-mode pulsators in these galaxies (see Pritzl et al., 2002; Marconi et al., 2004), hence we used our own relation to perform a tentative subdivision of the samples into the two modes. The result of the overall procedure is shown in Fig. 10, where the different panels report the results for the three afore-mentioned galaxies. The distance moduli labelled in the figures were obtained trying to adjust simultaneously F-mode and FO-mode pulsators, and weighting the results to take into account the number of pulsators in each of the two modes. Errors on the derived distances are dominated by the dispersion of the LMC , whereas the uncertainty of the LMC distance is significantly smaller.

In Table 8 we compare the distances obtained from the ACs and literature values based on RR Lyrae or other distance indicators. Our distance modulus for the Fornax dSph is systematically smaller than all the other determinations, but still in agreement with most of them within 1. On the contrary, the agreement is rather good for Leo T and excellent for Phoenix. On this basis, it is not easy to explain why we find such shorter distances for Fornax dSph. New observations, including the complete sample of ACs belonging to this very large galaxy are needed to clarify this point.

Concluding, the derived in this paper is a reliable tool for the determination of the distance to galaxies hosting significant samples of ACs.

method Reference
Fornax: (ACs)=20.500.16 mag (15 ACs)
TRGB 20.760.20 (1)
Red Clump 20.66 (2)
TRGB 20.650.11 (2)
Red Clump 20.860.01 (3)
RR Lyrae 20.720.10 (4)
TRGB 20.750.19 (5)
HB 20.700.12 (6)
TRGB 20.840.18 (7)
RR Lyrae 20.660.07 (8)
Leo T: (ACs)=22.880.16 mag (11 ACs)
TRGB 23.10.2 (9)
SFH-Fitting 23.05 (10)
RR Lyrae 23.060.15 (11)
Phoenix: (ACs)=23.150.16 mag (11 ACs)
TRGB 23.00.1 (12)
TRGB 23.210.08 (13)
TRGB 23.11 (14)
Mira 23.100.18 (15)
TRGB 23.090.10 (16)
(1) Buonanno et al. (1999); (2) Bersier (2000);
(3) Pietrzyński, Gieren, & Udalski (2003); (4) Greco et al. (2005);
(5) Gullieuszik et al. (2007); (6) Rizzi et al. (2006);
(7) Pietrzyński et al. (2009); (8) Greco et al. (2009);
(9) Irwin et al. (2007); (10) Weisz et al. (2012);
(11) Clementini et al. (2012);
(12) Martínez-Delgado, Gallart & Aparicio (1999);
(13) Held, Saviane & Momany (1999);
(14) Holtzman, Smith & Grillmair (2000);
(15) Menzies et al. (2008); (16) Hidalgo et al. (2009);
Table 8: Comparison between distances derived from the ACs in this paper and the literature values for the Fornax, Leo T, and Phoenix Local Group dwarf.

6 Summary and Conclusions

We have presented the first light curves in the NIR -band for Anomalous Cepheids. In particular, our sample consists of 46 AC pulsators (36 F-mode and 10 FO-mode) located in the LMC and observed by the VMC survey. Our light curves are well sampled with the number of epochs ranging from 8 to 23. In spite of the faintness of the LMC ACs, these data allowed us to obtain very precise mean magnitudes for the pulsators, with average errors of the order of 0.01 mag.

The magnitudes were used to build the first and relations in the NIR for F and FO-mode ACs. At the same time we exploited the OGLE optical () data for ACs to construct accurate optical , and relations both for F- and FO-mode ACs. These relations were obtained for the first time from a sample of pulsators covering in a uniform and complete way the AC instability strip.

The application of the relation to three dwarf galaxies hosting significant populations of ACs, revealed that this relation is a valuable tool for deriving distances within the Local Group. Due to the lower dispersion, we expect that the first derived in this paper will become an even better tool for measuring distances to galaxies hosting ACs. More NIR (-band in particular) data for ACs in other Local Group galaxies are needed to properly exploit the properties of the relation.


We thank our anonymous Referee for his/her very helpful comments that helped in improving the paper. V.R. warmly thanks Roberto Molinaro for providing the program for the spline interpolation of the light curves. We thank K. Bekki and R. Guandalini for helpful discussions. Partial financial support for this work was provided by PRIN-INAF 2011 (P.I. Marcella Marconi) and PRIN MIUR 2011 (P.I. F. Matteucci). We thank the UK’s VISTA Data Flow System comprising the VISTA pipeline at the Cambridge Astronomy Survey Unit (CASU) and the VISTA Science Archive at Wide Field Astronomy Unit (Edinburgh) (WFAU) for providing calibrated data products supported by the STFC. RdG acknowledges research support from the National Natural Science Foundation of China (NSFC) through grant 11073001.


  1. thanks: Based on observations made with VISTA at ESO under programme ID 179.B-2003.
  2. pagerange: The VMC Survey. VIII. First results for Anomalous Cepheidsthanks: Based on observations made with VISTA at ESO under programme ID 179.B-2003.LABEL:lastpage
  3. thanks: Based on observations made with VISTA at ESO under programme ID 179.B-2003.
  4. pubyear: 2002


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