Free Access
Issue
A&A
Volume 636, April 2020
Article Number A48
Number of page(s) 31
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/201937271
Published online 15 April 2020

© ESO 2020

1. Introduction

At the end of their lives, essentially all low- and intermediate mass stars (roughly ∼0.9 to ∼10 M on the main sequence) will go through the (super)-asymptotic giant branch (AGB) phase. They end up as ∼0.55−1.4 M white dwarfs, which means that a large fraction of the initial mass of the star is lost to the interstellar medium. An important characteristic of AGB stars is that they pulsate, and they are classically divided into stars with small amplitudes (the semi-regular variables, SRVs) and the large-amplitude Mira variables. It is now common to use the term long-period variable (LPV) regardless of pulsation amplitude for a pulsating star on the AGB. Pulsation-induced shock waves and radiation pressure on dust is the most promising mechanism to explain wind driving, especially regarding the more evolved AGB stars with low effective temperatures, large pulsation amplitudes, and high mass-loss rates (MLRs; see the review by Höfner & Olofsson 2018).

It was known from observations in the Large Magellanic Cloud (LMC) that Miras follow a period-luminosity (PL) relation (Glass & Evans 1981; Feast et al. 1989), but the breakthrough came with the advent of micro-lensing surveys. Wood et al. (1999) and Wood (2000) showed that late-type stars in the LMC follow five sequences (labelled A, B, C, D, and E). Subsequent work demonstrated that sequence B consists actually of two sequences (B and C′) and that an additional sequence (A′), includes possible substructure (Ita et al. 2004; Soszyński et al. 2007). Sequence D consists of long secondary periods (LSPs), while sequence E is due to binary stars. A theoretical interpretation using linear radial non-adiabatic pulsation models and a population synthesis model showed that sequences A′, A, B + C′, and C, correspond to third, second, and first overtone and fundamental mode pulsation, respectively (Trabucchi et al. 2017). The LPVs with the largest amplitudes, the classical Miras, dominate sequence C.

The Mira PL-relation has been used as a distance indicator, traditionally inside the Milky Way galaxy in the pre-Gaia era (e.g. Groenewegen et al. 2002; Ramstedt & Olofsson 2014). The method has gained recent interest in the context of the distance ladder as an independent check on Cepheids or the tip of the red giant branch distances; example are recent works on the mega-maser galaxy NGC 4258 (Huang et al. 2018) or the SN host galaxy NGC 1559 (Huang et al. 2020). Because Miras are as bright as Cepheids in the near-IR (NIR) they will be important secondary calibrators in the upcoming era of ground-based extremely large telescopes and the James Webb Space Telescope.

The currently largest survey of LPVs in the Magellanic Clouds (MCs) is the Optical Gravitational Lensing Experiment OGLE-III catalogue, which contains 1667 Mira stars, 11 128 SRVs and 79 200 OGLE small-amplitude red giants (OSARGs) in the LMC (Soszyński et al. 2009a), and 352 Mira stars, 2222 SRVs and 16 810 OSARGs in the Small Magellanic Cloud (SMC; Soszyński et al. 2011).

However, OGLE and other current surveys in the optical domain will miss the reddest, most obscured AGB stars. At the very end of the AGB the (dust) MLR may become so high that the object becomes very faint, beyond the OGLE I-band detection limit of about 21 mag. The dust grains in the circumstellar envelope (CSE) scatter and absorb the emission in the optical to re-emit it in the NIR and mid-infrared (MIR).

These stars are known to exist in the LMC. They were typically selected as having Infrared Astronomical Satellite (IRAS) colours similar to obscured AGB stars in our Galaxy. Wood et al. (1992) reported periods for nine sources in the LMC. Periods range between 930 and 1390 d, with peak-to-peak amplitudes in K between 0.3 and 2.1 mag, and (J − K) colours that range from 2.1 to 5.7 mag (an additional 7 LMC and 3 SMC sources were monitored, but showed small amplitudes, and no periods were given). Wood (1998) monitored 12 sources, of which nine were LPVs with periods in the range 530 to 1295 d. Amplitudes in K are between 0.85 and 1.9 mag, and colours range from (J − K) = 3.9 to 6.1 mag (two stars were not detected in J). Similarly, Whitelock et al. (2003) reported periods for two dozen stars with an IRAS identifier. Periods range from 540 to 1390 days, K-band amplitudes are between 0.52 and 1.8 mag, and (J − K) colours range from 1.9 to 4.0 mag (several are not detected in J). The faintest stars in these works have (mean light) magnitudes in the range K = 12−13 mag.

The ESO public VISTA Magellanic Cloud (VMC) survey is a photometric survey in three filters, Y, J, and Ks performed at the VISTA telescope using the VIRCAM camera. The latter provides a spatial resolution of 0.34″ per pixel and a non-contiguous field of view of 1.65 deg2 sampled by 16 detectors. To homogeneously cover the field of view it is necessary to fill these gaps using a six-point mosaic. This is the unit area of VISTA surveys, called a tile, and it covers an area of 1.5 deg2 uniformly with at least two exposures per pixel (Emerson & Sutherland 2010).

The VMC survey covers an area of approximately 170 deg2 (110 tiles) of the MC system and includes stars as faint as 22 mag in Ks (5σ, Vega mag), see Cioni et al. (2011) for a description of the survey. The large areal coverage and the survey depth are the main strengths of the VMC survey compared to earlier works in the IR. Unlike the VMC papers on classical variables (Type-II and Classical Cepheids, RR Lyrae, e.g. Ripepi et al. 2012, 2015, 2016; Ripepi et al. 2017; Muraveva et al. 2018), the expected periods for AGB pulsators are much longer than the baseline of the VMC observations. Therefore the VMC data are combined with K-band data from the literature when available to increase the time span.

In this paper we inspect K-band light curves (LCs) for a large number of candidate dust-obscured AGB stars. The sample is selected based on colour-magnitude and colour-colour criteria derived from the properties of known AGB stars, using both VMC and other IR data.

The paper is organised as follows. Section 2 discusses our selection of the sample of potential LPVs, which is based on different photometric catalogues, and the creation of the K-band LCs. Section 3 describes our analysis of the LCs. Section 4 presents the results. The sample of potential LPVs is further reduced by considering the shape of the spectral energy distributions (SEDs).

Preliminary results of this work were shown or used in Groenewegen et al. (2016), Cioni et al. (2017), and Groenewegen & Sloan (2018, hereafter GS18), but the results on the LC parameters are superseded by this paper.

2. Sample selection

In this section the sample of candidate obscured AGB stars is generated. It is based on three different photometric catalogues. The first selection uses only VMC data1, but requires a detection in J and Ks for reliability (sample 1). The second selection combines the VMC Ks-band data with WISE data from the AllWISE catalogue (Cutri et al. 2013) (sample 2). The third selection starts with data that are exclusively taken from the Surveying the Agents of a Galaxy’s Evolution (SAGE) survey of the MCs, and then searches for a possible counterpart in the VMC data (sample 3). During this selection procedure, only the mean magnitudes as given by the VISTA Science Archive (VSA; Cross et al. 2012) are used, and the quality flags indicating warnings and possible problems (the ppErrBits) are not considered. Only in the second step are the time-resolved VMC Ks-band data used and combined with literature data to produce an LC.

2.1. Sample 1: VMC data alone

Figure 1 shows the VMC (Ks, (J − Ks)) colour-magnitude diagram (CMD) for a region in the Bridge between the two Clouds and a region located in the bar of the LMC. The region in the Bridge is used to delineate the locus in colour space occupied by extended objects, most of which are background galaxies, but can also result from blends (colour-coded in red)2, while the region in the bar shows the well-known sequence of AGB stars redder than (J − Ks)∼1.5 mag at relatively bright magnitudes. At the brightest level (Ks ≲ 10.5 mag), we note the effect of saturation. This is not expected to influence the selection of obscured AGB stars for which the distribution in the CMD bends to faint magnitudes. This is shown more clearly in Fig. 2.

thumbnail Fig. 1.

VMC (Ks, (J − Ks)) CMD in a region in the Magellanic Bridge (left-hand panel; a strip at 42° < RA < 52° and −72.5° < Dec < −73.8°) and in the LMC bar (right-hand panel; a box defined as 80° < RA < 82°, and −69° < Dec < −70°). Objects that are (probable) stars are indicated in black, and (probable) galaxies (extended objects) are indicated in red. Objects classified differently are indicated in blue. The line, K = 3 ⋅ (J − K) + 10 mag, indicates the approximate boundary of galaxies.

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thumbnail Fig. 2.

Left-hand panel: all VMC stars with a detection in J and Ks, redder than (J − Ks) = 1.5 mag and above the line Ks = 3 ⋅ (J − Ks)+10 mag. The second-order polynomial is a fit to the red sequence of AGB stars, shifted downward by two magnitudes for comparison purposes (see text). Objects that are (probable) stars are indicated in black, and (probable) galaxies are indicated in red. Objects classified differently are indicated in blue. Right-hand panel: synthetic photometry from GS18 for 29 SMC and 133 LMC O- (open circles) and C-rich (filled circles) AGB stars with pulsation periods longer than 450 days. The pulsation periods of the objects marked in red are derived from K/Ks or WISE-band data, and the black points are derived from optical data (OGLE, EROS, and MACHO).

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In a subsequent step, all (about 7000) stars in VMC with a detection in J and Ks, (J − Ks) > 1.5 mag, and Ks <  3 ⋅ (J − Ks)+10 mag were selected to represent candidate obscured AGB stars. Their CMD distribution is shown in the left-hand panel of Fig. 2, and it shows that there is still a high contribution by background galaxies and other extended objects. This CMD also clearly exhibits the sequence of increasing mass loss along the AGB. A fit was made to this sequence, Ks = 10.318 + 0.287 ⋅ (J − Ks)+0.0306 ⋅ (J − Ks)2 mag, and this relation, which was shifted by two magnitudes to fainter magnitudes to delineate the approximate lower boundary of this sequence, is shown as well.

Another consideration in selecting the stars is that the primary interest is in studying the reddest pulsating AGB stars. These objects that are too faint for current optical surveys such as OGLE-III and OGLE-IV, which have a limiting magnitude in the I-band around 20−21 mag.

GS18 fitted the SEDs and spectra taken with the Spitzer Infrared Spectrograph (IRS, Houck et al. 2004) of almost 400 AGB and red supergiant (RSG) stars in the MCs, and determined periods for a large fraction of them. The periods were derived by analysing existing optical data (from the OGLE, Massive Compact Halo Objects (MACHO), and Expérience de Recherche d’Objets Sombres (EROS) surveys), or data in the K and Ks bands (including VMC data) and in the WISE W2 band for the reddest objects.

The right-hand panel of Fig. 2 shows the I, (J − Ks) CMD for about 150 O- and C-rich AGB stars in the MCs with a pulsation period longer than 450 days, based on synthetic photometry, that is, the simulated magnitudes taking into account the filter transmission curves and photometric zero-points in many filters using the best-fitting model to the SEDs in GS18. Marked in red are stars where the pulsation period is based on K/Ks or W2 data, the other periods are derived from optical data (mainly OGLE). The diagram shows that the I-band limit of 20 mag is reached for stars that have a (J − Ks) colour of ∼4 mag.

To have sufficient overlap with the optical surveys and to be on the conservative side, a limit of (J − Ks) = 3 mag was chosen. Sample 1 consists of the 857 stars in the VMC survey that have a detection in J and Ks, (J − Ks) > 3 mag and Ks <  12.318 + 0.287 ⋅ (J − Ks)+0.0306 ⋅ (J − Ks)2 mag.

2.2. Sample 2: VMC and WISE data combined

While sample 1 has the advantage that it uses exclusively data from the VMC survey, the reddest AGB stars by their very nature will become J-band dropouts for high enough MLRs. The aim of constructing samples 2 and 3 was to combine VMC Ks-band data with data at longer wavelengths, in particular, WISE (sample 2) or IRAC (sample 3). The advantage of WISE is that it is an all-sky survey, covering the complete area observed by the VMC survey.

The AllWISE catalogue (Cutri et al. 2013) is available as a table in the VSA and the queries were therefore performed within the VSA. A search radius of 1″ was used and an error on the W1 magnitude of less than 0.2 mag was imposed (equivalent to w1snr > 5).

The left-hand panel of Fig. 3 shows the (W1, Ks − W1) CMD for a region in the Bridge, with the same colour-coding for background galaxies and stars as in Fig. 1. The line W1 = 1.0 ⋅ (Ks − W1)+10.5 indicates the approximate boundary beyond which (at bright magnitudes and red colours) the number of galaxies significantly decreases. In the second panel, all sources are shown which have (Ks − W1) > 1 mag, (W1 − W2) > 0.5 mag, and are brighter than this boundary. The corresponding colour-colour diagram (CCD) is shown in the bottom half of the right-most panel.

thumbnail Fig. 3.

WISE-VMC (W1, Ks − W1) CMD and (W1 − W2)−(Ks − W1) CCDs. Left-most panel: CMD in a region between the SMC and LMC (a strip at 30° < RA < 60°). The line W1 = 1.0 ⋅ (K − W1)+10.5 mag indicates the upper boundary of the region predominantly occupied by galaxies. Second panel from the left: all WISE-VMC sources that are brighter than the boundary line in the left-hand panel, (Ks − W1) > 1 mag and (W1 − W2) > 0.5 mag. Objects that are (probable) stars are indicated in black, and (probable) galaxies (extended objects) are indicated in red, while objects classified differently are indicated in blue in these two panels. The provenance of the line in the second panel is explained in the next panel. The corresponding CCD is shown in the bottom half of the right-most panel. Third panel from the left: synthetic CMD based on GS18 for 29 SMC and 133 LMC O- (open circles) and C-rich (filled circles) AGB stars with pulsation periods longer than 450 days. The pulsation periods of the objects marked in red are derived from K/Ks or WISE-band data, and the black points are derived from optical data (OGLE, EROS, and MACHO). The line W1 = 0.7 ⋅ (Ks − W1)+10.0 mag is the empirical lower boundary to the reddest AGB stars, and it is also shown in the second panel from the left. The corresponding CCD diagram is shown in the top half of the right-most panel with the lines (W1 − W2) = 0.8 mag and (W1 − W2) = 0.37 ⋅ (Ks − W1)−0.2 mag, which indicates the empirical lower boundary to the reddest AGB stars, and is also shown in the panel below it.

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The third panel from the left shows a synthetic CMD based on the AGB stars studied by GS18. The line W1 = 0.7 ⋅ (Ks − W1) + 10.0 is the empirical conservative lower boundary to the reddest AGB stars, and is also shown in the second panel from the left. The corresponding CCD is shown in the top-half of the right-most panel with the lines (W1 − W2) = 0.8 mag and (W1 − W2) = 0.37 ⋅ (Ks − W1)−0.2 mag.

The final selection is based on a detection in Ks, a signal-to-noise ratio (S/N) in the W1 band > 5, (W1 − W2) > 0.8 mag, W1 <  0.7 ⋅ (Ks − W1)+10.0 mag, and (W1 − W2) > 0.37⋅ (Ks − W1)−0.2 mag for a total of 1317 sources.

2.3. Sample 3: SAGE data first

SAGE (Meixner et al. 2006) and SAGE-SMC (Gordon et al. 2011) are surveys of the LMC and SMC with the Spitzer telescope. The advantage of Spitzer is that it has a smaller point spread function than WISE, and confusion is less of a problem. On the other hand, the SAGE observations do not entirely cover the area sampled by the VMC survey. The combined LMC and SMC source catalogue in the [3.6], [4.5], [5.8], and [8.0] bands is available electronically3.

Figure 4 shows in the left panel the ([8.0], [3.6]−[8.0]) CMD of all sources with detections in all four bands. The region occupied by background galaxies is clearly visible, as is a tail of bright red AGB stars.

thumbnail Fig. 4.

Left-hand panel: ([8.0], [3.6]−[8.0]) CMD of LMC and SMC objects in the SAGE survey. Only every tenth star is plotted. The line at [3.6]−[8.0] = 0.8 mag indicates the blue limit of red AGB stars, and the two other lines indicate the limits of the region that is mainly occupied by background galaxies (see text). Top right-hand panel: ([3.6]−[4.5], [5.8]−[8.0]) CCD of all sources that are located in the upper right of the CMD delineated by these lines. Bottom right-hand panel: same diagram with synthetic CCD based on GS18 for 29 SMC and 133 LMC O- (open circles) and C-rich (filled circles) AGB stars with pulsation periods longer than 450 days. The pulsation periods of the objects marked in red are derived from K/Ks or WISE-band data, and the black points are derived from optical data (OGLE, EROS, and MACHO). The background sources in this panel are randomly picked from the S3MC survey (Bolatto et al. 2007).

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Boyer et al. (2011) used this diagram to select very red AGB stars, and we followed their work in selecting stars with [3.6]−[8.0] > 0.8 mag. Our elimination of background galaxies is less conservative than theirs, and we selected objects above the line [8.0] < 13.0 − ([3.6]−[8.0]) (for [3.6]−[8.0] < 4 mag), and [8.0] < 9.0 + ([3.6]−[8.0]−4.0) mag for redder objects.

The ([3.6]−[4.5], [5.8]−[8.0]) CCD of sources that meet these conditions is plotted at the top of the right-hand panel of Fig. 4. The bottom panel shows the synthetic photometry based on GS18; a region delineated by the lines [3.6]−[4.5] >  −0.6 ⋅ ([5.8]−[8.0]) + 0.6 (for ([5.8]−[8.0]) < 1 mag), and [3.6]−[4.5] > 1.7 ⋅ ([5.8]−[8.0]) − 1.7 (for ([5.8]−[8.0]) > 1 mag) is defined. The initial sample consisted of 1958 SAGE sources that meet these constraints.

The next step was the correlation with the VMC database. After inspecting the results using a search radius of 1″, we determined the final correlation by returning all VMC counterparts within 0.8″ of the SAGE coordinates. Multiple counterparts were listed for ten sources, but there was no reason not to take the closest match in any case. In the sample 35 SAGE stars had no counterpart in VMC, and in eight cases the counterpart lacked Ks-band data, leaving 1915 objects.

The selection so far was based on SAGE colours and positions. An additional consistency check between the IRAC and the Ks-band VMC magnitude was performed. Based on the synthetic photometry from GS18, we imposed a limit of Ks − [3.6] > 1.5 mag (which is consistent with the limit (J − Ks) > 3 mag in selecting sample 1). This removed over 300 sources for a final sample size of 1562.

2.4. Final sample

2.4.1. Sample statistics

The three samples were combined and together contain 2014 unique sources. This sample is almost of the same size as that of the known Mira population in the MCs, indicating that the initial sample selection based on colour criteria was not very restrictive.

As the main interest in the present paper is determining new red and (very) long-period pulsating stars, the next step was a correlation with lists of known LPVs. To be able to compare the properties (in terms of period, amplitude, etc.) of known Miras and LPVs with the new objects, known LPVs with periods longer than 450 days were kept, while LPVs with shorter periods were removed. This is an arbitrary choice but a good compromise, because including stars with shorter periods would increase the sample by including stars that would essentially never become optically obscured and where the period from the relatively poorly sampled IR LC would never be able to compete in quality with period(s) determined from OGLE data. At the same time the cut at 450 days allows overlap with OGLE to verify our procedures and compare periods and amplitudes.

A comparison with the OGLE-III catalogue of LPVs in the LMC (Soszyński et al. 2009a) and SMC (Soszyński et al. 2011) removed about 450 stars and kept about 480 LPVs with periods longer than 450 days. Similar correlations were made with the list of MACHO-detected LPVs in the LMC (Fraser et al. 2008) and the catalogues of LPVs detected in the EROS-2 survey (Spano et al. 2011; Kim et al. 2014).

2.4.2. Light curves

The final sample of stars for which the LCs were analysed contains 1299 objects, and for these, the Ks-band epoch data were retrieved from the VSA archive. The information for all these objects is given in Appendix A. Table A.1 lists general information on the objects: the right ascension and declination (from VMC, all epochs in this paper are J2000), some common names and object type (from SIMBAD4), (selected) spectral types (from Skiff 2014), the variability type as listed in the second Gaia data release (GDR2, Gaia Collaboration 2018; Holl et al. 2018), and the classification based on the MIR Spitzer IRS spectrum; see the footnote to the table for more information. Table A.2 lists known periods and related information from the literature, while Table A.3 lists the results of the period analysis (see Sect. 3 for details).

The LCs consist of the VMC Ks-band data with K/Ks-band data found in the literature added (as detailed in Cols. 7 and 8 of Table A.3). For some of the brightest stars the VMC photometry is influenced by non-linearity or saturation. A correction is applied in the VISTA pipeline for this (Irwin 2009), but for the brightest stars, it does not correct sufficiently. In the LC fitting this was accounted for by shifting the VMC Ks-band photometry to externally available photometry (see the remarks in Col. 10 of Table A.3). The shift was determined from the difference in the median of the VMC and the external photometry. The shifted VMC photometry was also assigned an error bar of 0.25 mag.

No attempt was made to bring the various K-band measurements into a common system. The main reason is that colour transformations from one system to another almost always depend on the (J − K) colour (Carpenter 2001; Koen et al. 2007). A J-band magnitude observed simultaneously with the K-band data is not always available, the error on the J-band magnitude is typically large for these red sources, and the (J − K) colour is outside the range considered in the transformation formula. This would make a colour transformation particularly complicated and uncertain in many cases. This is a limitation, and in Appendix B we estimate the possible effect and conclude that this is typically smaller than the error bar quoted for mean magnitudes, amplitudes and periods in Table A.3. In the following text we refer to the K band for simplicity unless we address a specific survey.

3. Modelling

The automatic analysis of the LCs was made with the Fortran codes available in numerical recipes (Press et al. 1992) as described in Appendix A of Groenewegen (2004). The codes were tuned at that time to analyse OGLE-II LCs with hundreds of data points, while the current LCs have between 6 and 73 data points (92% of the stars in the sample have 15 or more data points). This complicates determining the pulsation period through Fourier analysis (using the subroutine FASPER). Therefore the LCs of most stars in the sample were analysed manually with the code PERIOD04 (Lenz & Breger 2005) as well. After an initial guess of the period was determined (either through the automatic routine, a period found in the literature, or from the manual fitting of the LC) a function of the form

(1)

was fitted to the LC using the weighted linear least-squares fitting routine MRQMIN. This results in the parameters listed in Table A.3, mean magnitudes, periods (exp(−f)), and amplitudes () with their associated uncertainties. Equation (1) implies that the LC can be described by a single period. It is well known that the LCs of LPVs are not strictly single-periodic. The OGLE team typically fits three periods to the LC. However with the limited number of data points available in the IR LCs we are not able in general to comment on the presence of more than one period. The exception is the few stars that have been monitored extensively from the ground. Table A.3 sometimes lists a long secondary period (LSP). Those were derived from the manual fitting of the LC using PERIOD04.

When no initial period was known from the literature, it was taken from the Fourier analysis. The reliability of this period determination (also) depends on the number of data points in the LC. We selected from Table A.3 stars without an initial period listed and a S/N >  3 on the final period and amplitude. This shows that the minimum number of useable data points is 12.

A comparison of the LC with the fit sometimes suggested that alternative periods may be possible as well. These cases were inspected by manual fitting of the LC using PERIOD04, and alternative periods are sometimes indicated in Col. 9 of Table A.3.

The table also includes the reduced χ2, defined as , with m, o, and σo indicating the model magnitude, the observed magnitude, and the error, N is the number of data points, and Np = 1 or 4, depending on whether Eq. (1) is fitted without or with the period. The in Table A.3 ranges from 0.2 to 3900, with a median of 70. These values are far higher than an expected value of unity for a model that described the data correctly and with correct estimates of the error bars. This probably indicates that the internal error bars of the Ks band photometry in the VSA (typically at the millimagnitude level) are likely underestimated when compared to other photometry on an absolute external scale, but also that differences in filter curves between the different sets of photometry, and the simplicity of the model (a single period) play a role. In the next section we perform a selection that eliminates stars with a , which represents about 10% of the sample.

4. Analysis and selection of new red LPVs

4.1. Comparison to known Miras

The next step was a comparison of the results of the IR LC fitting to the periods of known Miras from OGLE-III. To compare between the OGLE and the IR pulsation properties we selected from Table A.2 the stars classified by OGLE to be Miras whose amplitude for the second listed period is smaller than that listed for the primary period (as given by OGLE). As mentioned above, many LPVs show an LSP, sometimes with a large amplitude, and this choice enables a more direct comparison of periods and amplitudes. After removing three stars for which our analysis revealed no significant period, 294 stars remain to make the comparison, and the results are shown in Fig. 5. The panel on the left compares the primary period found by OGLE to the period we derived. The dotted line marks the one-to-one relation and shows that the agreement is very good in most cases. The middle panel compares the amplitudes in the K band as found in our analysis with the amplitude in the I band as found by OGLE. There is no strong correlation. The cut-off in I-band amplitude reflects the common definition (as used also by the OGLE team) that the I-band amplitude of Miras is expected to be larger than 0.9 mag. The solid line is plotted to guide the eye and indicates an amplitude in K that is half that in I. The right-hand panel shows the relative error in the period determination plotted against period. The period determination of most stars is better than a few percent. The middle and right-hand panels identify outliers by the red symbols, stars where the amplitude is ill defined (the error on the amplitude is larger than the amplitude itself), and by plus signs stars for which the in the LC fitting is >430. Using the following selection criteria, we selected 291 of the 294 known Miras (based on I-band data) with low amplitude secondary periods as those for which the error in the period determination is better than 4%, the error in the amplitude smaller is than the amplitude itself, the amplitude is larger than 0.1 mag in the K band, and the in the LC fitting procedure is smaller than 430.

thumbnail Fig. 5.

Pulsation properties of 294 confirmed Miras by OGLE compared with our results. Left panel a: directly compares the periods in the upper part; the dotted line marks the one-to-one relation. The lower part indicates the difference in periods as a function of the period found by OGLE. The star at P = 1858 d (log P = 3.26) in the top panel is located outside the plot at ΔPeriod = 216 d in the bottom panel. Middle panel b: compares the amplitude in the K band to that in the I band. The OGLE team defines amplitude as the minimum-to-maximum variation, while we use the traditional definition (see Eq. (1)). Stars with a are marked by a plus sign, and stars where the error on the K-band amplitude is larger than the amplitude are marked in red. The dotted line indicates the cut-off value of 0.1 mag we used to select the maximum number of known Miras from our sample. The solid line has a slope 0.5 to guide the eye. Right-hand panel c: relative error of the period determination against the period. Stars with a are marked by a plus sign, and stars where the error on the K-band amplitude is larger than the amplitude are marked in red. The dotted line indicates the cut-off value of 4% error on the period determination we used to select Miras from our sample.

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When these criteria were applied to the full sample (we also enforced P >  100 days to eliminate a few known Type-II Cepheids), 634 objects of the 1299 showed pulsation properties as derived from the IR LCs that were consistent with those of known Miras (as defined based on I-band data). This includes the 291 stars that were used to define the criteria, but also known OGLE LPVs that were not used in the comparison (those with larger LSP amplitudes). In addition, for some objects, the classification of the Spitzer IRS spectrum indicates that they are not AGB stars (see Table A.1). The amplitude cut-off of 0.1 mag does not imply that these are Miras (as opposed to SRVs). They are (candidate) LPVs, and we did not distinguish between the two classes. The middle panel in Fig. 5 shows considerable scatter between the amplitude in the I and K band, but it also demonstrates that the majority of stars that have been classified as Miras based on I-band data have K-band amplitudes > 0.2 mag, in line with expectations.

In a subsequent step, all known OGLE objects were removed, with the exception of stars with periods longer than 1000 days because they are of prime interest here. This limit for a long period is arbitrary, but a limit of 1000 days has also recently been used by Menzies et al. (2019). Stars detected by MACHO or EROS (and not by OGLE) were also removed when the period listed by these surveys was in good agreement with the period found here (and not longer than 1000 days). Although these sources were not retained for further detailed analysis, the pulsation properties derived from the LC fitting are still available in Table A.3.

In a final step, the Spitzer IRS spectra of all stars classified in the literature as not being of an O- or C-rich AGB star (see Table A.1) were inspected visually using the CASSIS tool5 (combined atlas of sources with Spitzer IRS spectra, Lebouteiller et al. 2011). All spectra appeared consistent with the literature classification, and thus unlike those of O- or C-rich AGB stars. Therefore they were removed from the sample of candidate LPVs. The exception is SMP LMC 11 (72.907608 −67.088019). Although it is classified as a planetary nebula (PN) in SIMBAD, and the literature classification of its Spitzer IRS spectrum is that of a C-rich post-AGB star, its spectrum is technically speaking consistent with that of a very red C-rich AGB star. It was therefore retained. At this point, the sample of stars that was investigated further was reduced to 254.

4.2. Creating and fitting the SEDs

As a further step in distinguishing AGB stars from non-AGB stars, the SEDs of the 254 selected stars were constructed and fitted to a large sample of synthetic template SEDs of AGB stars and some non-AGB stars (created from some of the non-AGB stars previously discarded that have MIR spectra).

The procedure is largely outlined in GS18. Photometry was collected from AllWISE, SAGE, Akari, IRAS, OGLE, and GDR2. In the NIR we used the mean K-band magnitude derived from the LC fitting. The VMC Y and J magnitude were downloaded from the VSA. The Ks band listed in the VSA was also downloaded and assigned a large uncertainty of 0.1 mag so as to give this point less weight in the template fitting. As mentioned in Sect. 2.4.2, for some of the brightest stars the VMC photometry is influenced by non-linearity or saturation. For the SEDs the corresponding data points are plotted with large error bars (arbitrarily set at 0.25 mag) to identify them immediately and in order to avoid affecting the fitting procedure. In some cases the Y and J magnitudes may also be affected by saturation, and these were also assigned large error bars.

The magnitudes were then fitted to the synthetic photometry of several hundred templates. This indicates with high reliability whether the SED of a star is consistent with that of an O-rich, C-rich, or young stellar object (YSO) or other non-AGB objects. Details are given in Appendix C. The SEDs of all 254 objects with their best-matching template are plotted in Fig. C.2.

Based on all available information (spectral type, MIR spectral classification, and template fitting), the 254 stars were divided into 217 most likely AGB stars, and 37 most likely non-AGB stars; see Table C.2. The latter group is no longer discussed, although it contains sources with variability properties that have similarities to those of LPVs. Figure 6 shows the LCs of a YSO and a B1 emission-line star as examples. Table A.1 lists a total of about 200 sources that have been associated with YSOs. An analysis of the VMC-based IR LCs of Spitzer-identified massive YSOs in a ∼1.5 deg2 area in the LMC will be presented in Zivkov et al. (2020).

thumbnail Fig. 6.

Examples of LCs of objects where the literature classification and the template fitting indicate a non-AGB nature. Top panel: probable YSO object 2MASS J04573274−6959032 (based on a photometric classification; Table 10 in Gruendl & Chu 2009), and bottom panel: B1 emission-line star [BE74] 621. Data points (with error bars) in black show the VMC, green points represent 2MASS, dark blue points 2MASS-6X, and light blue points the IRSF.

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The classification based on the SED fitting was compared with that introduced by Lebzelter et al. (2018) for those AGB candidates for which the Gaia DR2 photometry is available (73 stars), as shown in Fig. 7. Lebzelter et al. (2018) divided between O- and C-rich stars according to their position in a specific diagram involving the difference between two Wesenheit functions obtained by combining the J, Ks, GBP, and GRP photometric bands, WRP, BP − RP − WKs, J − Ks (see the left panel of Fig. 1, and Table A.1 of Lebzelter et al. 2018). The Wesenheit functions are defined as

(2)

thumbnail Fig. 7.

Classification of the AGB candidates in this work based on the VISTA Ks band and Gaia DR2 photometry (Lebzelter et al. 2018). The solid line indicates the separation between oxygen-rich (O) stars (to the left of the curve) and C stars, while the dashed line separates C stars from the most extreme dust-enshrouded stars. All the stars are colour-coded according to their (J − K) colours.

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where J and Ks are the VISTA bands, and:

(3)

Of the selected stars, 65 sources are classified as C-rich and 8 as O-rich. We find that 72 sources are classified as carbon (C) stars by both methods, while only 6 sources are classified as extreme stars by Lebzelter et al. (2018) are classified as O-rich by the SED template fitting developed here. Two stars out of eight that are O-rich for Lebzelter et al. (2018) are classified as O-rich on the basis of the templates. When the classification by Lebzelter et al. (2018) is considered, the SED classification method therefore yields a comparable result for C stars but disagrees on O-rich stars. Based on the SED fitting classification method, of the 217 AGB candidates, 22 are O-rich, 1 is a PN, and the remainder are C-rich stars.

The AGB candidates were also fitted using the public database of synthetic spectra and photometry for C stars presented in Nanni et al. (2019). These spectra are obtained by consistently computing the growth of dust grains of different species (amorphous carbon and silicon carbide for C stars) coupled with a stationary dust-driven wind (Nanni et al. 2013, 2014) and a dust radiative transfer code (Groenewegen 2012). The optical constants for amorphous carbon dust are selected to reproduce the photometry in the IR and in the Gaia bands (Nanni et al. 2016; Nanni 2019). We here adopted the data set of Hanner (1988) combined with small grains < 0.04 μm. The metallicity of the synthetic models is Z = 0.004 and 0.006 for the SMC and LMC, respectively. As in Nanni et al. (2019), we selected only the models of those that were computed for which the outflow was accelerated through dust-driven wind when the input MLR was log () ≧ −5.5 M yr−1. The best fit between the observed and synthetic photometry allows us to estimate the (gas) MLR, the dust production rate, and the luminosity of each star, without the need to assume quantities such as the gas-to-dust ratio and the wind speed of the outflow. The results for the luminosity and MLRs derived from the fitting procedure are provided in Table D.1. In Fig. 8 the MLRs derived in this work and from Nanni et al. (2019) for sources in common are compared. We find that the results agree well, with a scatter of 0.23 dex.

thumbnail Fig. 8.

Comparison between the MLR obtained by Nanni et al. (2019) with the rate we derived for stars in common. The solid black line is the one-to-one relation.

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Only 44 and 8 C stars we analysed are missing from the analysis of Nanni et al. (2019) for the LMC and the SMC, respectively. These sources were not included in the catalogues matched by Nanni et al. (2019) (which included C stars from Riebel et al. 2012; Ruffle et al. 2015; Srinivasan et al. 2016; Jones et al. 2017, GS18). The total dust production rate of these missing stars was calculated, and we found that their total contribution is negligible with respect to the total dust production rate of the entire AGB population in these galaxies.

The properties derived for the sources we analysed in this work (period, bolometric luminosity and MLRs) were compared with those derived by Nanni et al. (2019) for the entire population of C stars in the LMC for which the period has been determined (Riebel et al. 2012). The results are shown in Fig. 9, where we correlate the luminosity with the period, the MLR with the luminosity, and the MLR with the period. The sources we analysed span the entire range of Mbol, while the periods are usually between 2.4 <  log P (d) <3.1. The estimated MLR is in general greater than ≈10−6M yr−1 and correlates with the luminosity, even though the scatter is large, and with the period.

thumbnail Fig. 9.

Top panel: bolometric luminosity vs. period obtained from the SED fitting of the C stars selected in this work: C stars in the SMC are indicated with red dots, and C stars in the LMC are plotted with blue triangles. For comparison, we overplot the population of C stars in the LMC for which the period has been determined from Riebel et al. (2012), which have been fitted by Nanni et al. (2019). To avoid superposition in the plot, Mbol has been changed by a random number between −0.25 and +0.25 mag. The sources for which the period has been flagged with a superscript “a” or “b” in Table C.2 are indicated with a cross. Middle and bottom panels: relations between MLR vs. the bolometric luminosity and MLR vs. period, respectively.

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5. Discussion

5.1. Comparison with periods from Gaia

Table 1 contains 32 sources that are listed in GDR2 with a “MIRA_SR” classification and a period. The comparison with the period derived from the NIR data in the present paper is excellent; the value of (PGaia − PNIR)/σGaia ranges from −2.2 to +2.4 with a median value of +0.1. The periods that are presented here are more precise (the median error in the period is 70 days in the Gaia data and 8 days here), but the error in the period determination by Gaia is expected to decrease significantly with further data releases.

Table 1.

Comparison of periods for sources in common between our study and Gaia DR2.

5.2. Comparison with the IRSF monitoring data in the SMC

The NIR monitoring data for three stars has recently been published by Ita et al. (2018) using the InfraRed Survey Facility (IRSF, Kato et al. 2007). These data were not used in our LC analysis and can therefore serve as an independent test. The K-band data (H band for 12.627600 −72.858307) were analysed in the same way as the VMC data and literature data. Table 2 compares the periods and amplitudes. For the first two stars the agreement is good. In the last case the periods do not agree within their mutual error bars, but this is a faint source for the IRSF survey (K ∼ 15.5 mag), while our analysis might be hampered by the relatively small number of data points (18 in total).

Table 2.

Comparison with three sources in the IRSF survey.

5.3. LPVs with periods over 1000 days

Of the likely AGB stars, 34 stars have periods longer than 1000 days6. The longest period we find is 3108 d, but this object has alternative periods that are much shorter. Six other stars also have shorter possible periods, and therefore the periods beyond 1000 days are only tentative in these cases. It will be interesting to analyse the IRSF data for the LMC objects when they become available (cf. the SMC data presented in Ita et al. 2018).

Nine stars with periods over 1000 days in the MCs were previously reported by Wood et al. (1992) and Whitelock et al. (2003) based on NIR observations. Recently, Menzies et al. (2019) presented a compilation of Miras with periods over 1000 days in the Milky Way (17), SMC (3), and LMC (18), while Karambelkar et al. (2019) published a list of 417 luminous IR variables, of which 86 have periods over 1000 days, located in seven galaxies (the majority in M 83 (49 objects), and M 81 (11 objects)). The compilation by Menzies et al. (2019) was based on Wood et al. (1992) and Whitelock et al. (2003), OGLE data in the SMC and LMC (Soszyński et al. 2011, 2009a), and GS18 (which is partly based on a preliminary analysis of VMC data). Of the 21 MC objects, 18 are confirmed with updated periods. Three objects are not in our list. One object (IRAS 05506−7053) is too red; the period in GS18 is based on WISE data. The two others (HV 888 and HV 11417) are too blue to have passed the selection criteria, and both have been classified as RSGs (GS18, Kraemer et al. 2017).

The longest period in the study of GS18 of almost 400 AGB stars with Spitzer IRS spectra is 1810 d based on a re-analysis of OGLE-III data for MSX SMC 055 (also known as OGLE-SMC-LPV-08137 and IRAS 00483−7347). No errors on the period are given in GS18 because they are very hard to reliably estimate for these long periods. The period in the OGLE-III release is 1859 d, which gives some indication of the uncertainty. In Groenewegen et al. (2009) such a long-period has been recognised based on OGLE-II data and, it was suggested that the object may be a candidate super-AGB star, based on its long period and very high luminosity. Updated parameters were given in GS18, where a current pulsation mass of about 9 M was derived. It has a large amplitude (0.8 mag in I), but its LC is not very regular in shape (see the middle panel of Fig. 7 in Soszyński et al. 2011). Based on the IR LC a period of 2075 ± 15 d is derived here, about 4 σ away from the optically determined period considering the mutual error bars.

Our sample of likely AGB stars contains two stars that have very long periods7. They are VMC J052454.84−682958.02 (81.228480 −68.499449), with P = 2261 ± 41 d and amplitude 0.20 ± 0.02 mag, and VMC J045211.18−701244.83 (73.046582 −70.212454), with P = 2510 ± 67 d and amplitude 0.15 ± 0.06 mag. Little is known about the former source. It is not listed in SIMBAD. Its SED is very well fitted by that of a dusty O-rich star, but its luminosity based on the template fitting is low (L ∼ 1500 L) and its amplitude small for a Mira variable. The latter source is listed as a candidate post-AGB object. In ViZieR some catalogues are associated with a source classified as a PN, but often located at about 2″ away. VMC Y- and Ks-band images were inspected. The finding chart in Morgan (1994) (object 9) suffers from poor resolution and is not clear. A slightly better chart was published by Leisy et al. (1997) but does not allow us to unequivocally distinguish between two sources in the VMC images. The coordinates published there and in Reid & Parker (2006, RP 1607) refer to a source located at about 2.2″ to the SE of the very red VMC source referred to in this paper. In any case, the luminosity based on the template fitting is low (L ∼ 3000 L), and its amplitude small for a Mira variable.

One of the original ideas behind this work was to find stars with very long periods as a tracer of the most massive AGB and super-AGB stars. The nature of the two stars with 2000+ day periods would be interesting to investigate but they are unlikely to be as massive as the about 9 M estimated for MSX SMC 055 (GS18).

5.4. Bolometric PL-relation

Figure 10 shows the bolometric PL-relation. The top panel shows all 254 objects for which the template fitting was performed. The likely C-rich objects (i.e. listed as “C” in Col. 10 in Table C.2) are plotted as open squares, the likely O-rich objects (i.e. listed as “O” in Table C.2) are plotted as open triangles, the other AGB stars (i.e. listed as O(AGB), O(OTH), and C(AGB) in Table C.2) as filled circles. The 37 likely non-AGB stars are plotted as dots. The likely C-rich Miras (with an amplitude >0.2 mag) are plotted in the middle panel. The blue dashed line is a fit to the data, excluding seven outliers (plotted as dots) based on iterative 3σ clipping. The fit is Mbol = (−2.27 ± 0.20) ⋅ log P + (1.45 ± 0.54) mag using 182 stars and with an rms of 0.41 mag using a linear bi-sector fit (using the code SIXLIN from Isobe et al. 1990). When we restrict the sample to LMC objects (144 objects) or eliminate the objects for which an alternative period cannot be excluded, the coefficients of the fit or the rms value do not change significantly.

thumbnail Fig. 10.

Bolometric PL-relations for all the 254 objects for which the template fitting was performed (top panel), and the subsets of likely C-rich Miras (middle panel), and O-rich Miras (bottom panel). The likely C-rich objects are plotted as open squares, the likely O-rich objects are plotted as open triangles, and the other AGB stars as filled circles, see the main text for details. The 37 likely non-AGB stars are plotted as dots. The likely C-rich Miras (with an amplitude >0.2 mag) are plotted in the middle panel. The objects in the LMC are plotted with open symbols, and those in the SMC with filled symbols. The blue dashed line is a fit to the data, excluding outliers (plotted as dots). The likely O-rich Miras (with an amplitude >0.2 mag) are plotted in the bottom panel. The blue dashed line is a fit to the data, excluding outliers (plotted as dots). The red dotted lines in the two panels indicate relations from the literature derived at shorter periods, see the main text for details.

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The likely O-rich Miras (with an amplitude >0.2 mag) are plotted in the bottom panel. The blue dashed line is a fit to the data, excluding two outliers (plotted as dots) based on iterative 3σ clipping. The fit is Mbol = (−2.97 ± 0.09) ⋅ log P + (2.59 ± 0.28) mag based on 11 stars and with an rms of 0.36 mag. The red dotted lines in the two panels indicate relations from Feast et al. (1989) for C- and O-rich Miras in the LMC respectively. These relations were derived for P <  420 d and were shifted using an LMC distance modulus of 18.477 mag from Pietrzyński et al. (2019).

6. Summary

Based on CCD and CMD diagrams and the properties of known Mira variables detected by the OGLE survey, we selected a sample of 1299 sources as (candidate) LPVs with periods longer than 450 days. Multiple VMC Ks-band data were combined with literature data to construct LCs. A limitation is that magnitudes from different K-type filters are mixed because it is almost impossible to uniformly and consistently convert all data into a uniform system. The LCs were analysed for periodic variations. Mean magnitudes are published for all stars, and periods and amplitudes for 949 stars. Based on the pulsation properties of known OGLE Miras and when we remove all stars with a known period (except for those longer than 1000 days), a sample of 254 stars was retained for further study. The SEDs of these stars were derived and fitted with template distributions of known objects. A final list of 217 candidate LPVs was obtained. Thirty-four objects have periods longer than 1000 days, but some have a viable alternative period that is shorter. The Mira with the longest known period in the MCs from OGLE data (with P = 1810 d) was derived to have a period of 2075 d based on its IR LC. Two stars were found to have longer periods, but the luminosities and pulsation amplitudes of both are unlike those of Miras. The bolometric magnitude – period relation was derived for both likely O- and C-rich stars in the sample.


1

All VMC data refer to observations obtained until the end of September 2016, including complete observations of the SMC.

2

Indicated by the mergedClass parameter which is −9 for a saturated source, −3 for a probable galaxy, −2 for a probable star, −1 for a star, 0 for noise, and +1 for a galaxy.

3

ViZieR catalogue II/305/archive.

4

As of January 2019.

6

We included one star with a period of 997 ± 12 days.

7

Excluding 70.632433 −74.796568 with P = 3108 d because a shorter period might be the correct one as well, and 81.098476 −65.536337 with P = 2125 d but a rather poor fit and an uncertain amplitude of 0.38 ± 0.18 mag.

Acknowledgments

We thank the Cambridge Astronomy Survey Unit (CASU) and the Wide Field Astronomy Unit (WFAU) in Edinburgh for providing calibrated data products under the support of the Science and Technology Facility Council (STFC) in the UK. M.-R.L.C. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No 682115). A.N. acknowledges support from the Centre National d’Etudes Spatiale (CNES) through a post-doctoral fellowship. This publication is partly based on the OGLE observations obtained with the Warsaw Telescope at the Las Campanas Observatory, Chile, operated by the Carnegie Institution of Washington. This paper utilises public domain data originally obtained by the MACHO Project, whose work was performed under the joint auspices of the U.S. Department of Energy, National Nuclear Security Administration by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48, the National Science Foundation through the Center for Particle Astrophysics of the University of California under cooperative agreement AST-8809616, and the Mount Stromlo and Siding Spring Observatory, part of the Australian National University. This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. This research has made use of the SIMBAD database and the VizieR catalogue access tool, both operated at CDS, Strasbourg, France. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

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Appendix A: Sample, literature, and period analysis

Tables A.1A.3 provide the first entries of the tables that are available at the CDS. They provide information about the 1299 sources for which the K-band LCs were analysed. Table A.1 provides basic information about the sample, Table A.2 provides information on the known periodicity from the literature, and Table A.3 provides the results of the LC analysis. The meaning of the columns is explained in the footnotes to the tables.

Figure A.1 shows examples of the LC fitting. The complete set for the 1299 objects is available at https://zenodo.org/record/3714889. The model is represented by the (red) solid line. At the top of the plot, the identifier and the period (in days) are listed.

Table A.1.

Sample for which a period analysis and LC fitting was performed.

Table A.2.

Literature data.

Table A.3.

Results from the period analysis.

thumbnail Fig. A.1.

Examples of the LC fitting (red solid lines) to the observed time photometry At the top of the plot the identifier and the period (in days) are listed. Data points (with error bars) are identified as black for the VMC, green for 2MASS, dark blue for 2MASS-6X, light blue for IRSF, magenta for DENIS, and orange for other sources (see references in the footnote to Table A.3). Black crosses indicate points that were excluded from the fits. The complete set of LC is available at https://zenodo.org/record/3714889.

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Appendix B: Effect of mixing different K-band filters in the analysis

No attempt was made to bring the various K-band measurements into a common system. Various reasons (see Sect. 2.4.2) would make a colour transformation particularly complicated and uncertain in many cases. This is a limitation, and we try to estimate the possible effect now.

Examination of the bolometric corrections computed by Aringer et al. (2009, 2019), limited to the coolest of their spectra (Teff = 2600 K), reveals that the expected magnitude differences between a K passband (from Bessell & Brett 1989) and a 2MASS Ks filter are typically smaller than 0.04 mag for O-rich stars, and smaller than 0.015 mag for C-rich stars. These differences are smaller for stars with hotter photospheres.

We also investigated the synthetic photometry of the best fits to the SEDs and IRS spectra of almost 400 AGB and RSG stars (GS18) that span a very wide range in colour. We compared K-band magnitudes in the VISTA, DENIS, IRSF, 2MASS and SAAO systems. For stars with moderate circumstellar reddening ((J − K)≲2) the differences between VISTA and DENIS, and VISTA and 2MASS are of the order quoted above, that is, ≲0.02 mag. For redder stars, the differences are about 0.03−0.04 mag at (J − K) = 5. The effect in the IRSF filter is weaker, and in the SAAO system it is greater, up to 0.2 mag for the redder stars. These colours are much redder than the transformation formula given in Koen et al. (2007), which are derived in the range −0.087 ≤ (J − K) ≤ 1.390.

The effect of a 0.2 mag change in the externally available photometry (independent of the filter system) was tested on eight stars monitored by Whitelock et al. (2003) without detection in the J band, which based on their (H − K) colour, have an estimated (J − K)≳4 mag. Their periods range from 550 to 1375 days and their amplitudes from 0.4 to 0.9 mag. The corresponding offset was applied to each of the stars considered, and the period analysis repeated. The absolute differences in the mean magnitudes are 0.01−0.07 mag, and this corresponds to at most a 1.2σ difference with respect to the quoted error bar (for six stars the difference is <0.5σ). The absolute differences in periods are 1−8 days, and this corresponds to at most a 1.8σ difference with respect to the quoted error bar (for six stars the difference is <0.3σ). The absolute differences in amplitudes are 0.01−0.06 mag, and this corresponds to at most a 1.3σ difference with respect to the quoted error bar (for five stars the difference is <0.3σ).

We threfore conclude that the differences between different filter systems is in most cases smaller than the quoted error bars and do not influence the results of this paper.

Appendix C: Spectral energy distributions and template fitting

To obtain insights into the nature of the objects, the SEDs were constructed and compared in a quantitative way to the synthetic SEDs of sources of known composition. For the AGB stars we used as templates the synthetic photometry of the best fits to the SEDs and Spitzer spectra of O-rich AGB stars, RSGs, and C-rich AGB stars from GS18, which are 82, 76, and 204 objects, respectively. These stars cover a wide range in effective temperatures, MLRs and dust compositions. The distinction made in GS18 between O-rich AGB stars and RSGs is based on a number of properties, including luminosity and pulsation period, following the discussion in Sect. 5.1 in Groenewegen et al. (2009).

From Table A.1 and the discussion in Sect. 4.1 it is clear that the main interlopers among possible LPVs on the AGB are YSOs, but objects classified as H II regions, hot stars (Be stars or blue supergiants (BSG)), Wolf-Rayet (WR) stars, or post-AGB/PN stars might also be among the sample of 254 candidate LPVs. To represent the types of sources in the templates, a few sources were picked and analysed in detail, as outlined in the next section.

C.1. Fitting of some non-AGB templates

One PN, one Wolf-Rayet star, one H II region, three blue BSGs, and six (candidate) YSOs with IRS spectra were selected for a detailed study from the objects in Table A.1. The exception was iras05216 (80.37_−67.85), which was initially considered by GS18 as an AGB star but was eliminated in the process because its SED and IRS spectrum were not consistent with that of an AGB star. Information on these stars is provided in Table C.1.

Table C.1.

SED and spectra fitted to some non-AGB stars.

We followed GS18 and fitted the SEDs and the Spitzer IRS spectra with the code more of DUSTY (MoD, Groenewegen 2012), an extension of the radiative transfer code DUSTY (Ivezić et al. 1999). For a given set of photometry and spectra as input data the programme determines the best-fitting luminosity, dust optical depth, dust temperature at the inner radius, and slope of the density profile.

The stars are hotter than AGB stars and the PHOENIX model atmospheres (Hauschildt et al. 1999) were used to represent the central star8. The dust is a combination of amorphous silicates, corundum, and metallic iron, or amorphous carbon and silicon carbide similar to that in GS18. The proportions between the species were chosen so that they fit the dust continuum and broad dust features of the Spitzer spectrum reasonably well. The actual dust composition may be more complicated, but it is not our aim to study this in detail here.

The fits are shown in Fig. C.1. Overall, the fits are reasonable representations of the photometric data, and this is the main purpose of this exercise. The synthetic photometry corresponding to these fits can serve as representative templates.

There are also clear shortcomings. For example, the spectra show polycyclic aromatic hydrocarbon and other features that are not included in the model. In addition, DUSTY and MoD are one-dimensional codes, but the geometry around the YSOs is often clearly non-spherical. For this reason the fit parameters are not discussed in detail because they are sometimes unphysical, such as dust temperatures at the inner radius above 2000 K.

C.2. Fitting the SEDs to the templates

Given a template with luminosity (Lt), distance (dt) and synthetic absolute magnitudes in many filters (Mt) and an object with observed absolute magnitudes with errors (Mo, σ) for an assumed distance (do), the comparison between template and object is

(C.1)

where the sum runs over the observed magnitudes in different filters. Because the template was originally fitted to the photometric and spectroscopic data of a star for a certain distance resulting in a best-fitting luminosity there is a degeneracy as a template could fit any observed SED by a simple offset (o) in magnitude.

Setting the derivative of χ2 to zero, the offset that will provide the best fit is

(C.2)

which is the weighted mean difference between observed and template magnitudes.

The SEDs of the 254 targets were compared in this way to a total of 374 templates. As additional constraint, we imposed that in order to be a valid template a C star had to have a predicted luminosity above 1000 L and below 70 000 L, an O-rich AGB star had to have a luminosity higher than 500 L, and for an O-rich RSG, it had to be above 5000 L. This resulted in an ordered list of χ2s with the type of the template and the luminosity of the target (for an assumed distance of 50 kpc to the LMC and 61 kpc for the objects in the SMC).

Fifty objects of the 254 were fitted by GS18. This allowed us to check the level of contamination: if a star is a known C-rich object, is the best-fitting template that of a C star, and at what level of χ2 is a non-C star considered a possible match. This is not a trivial exercise because the SEDs used in GS18 and constructed here are not the same. For example, GDR2 photometry and VMC magnitudes were not used by GS18. Instead NIR photometry was taken from the available 2MASS, 2MASS6X, IRSF, and DENIS data. In addition, the fits in GS18 were made to the photometry and Spitzer spectra, which leads to different synthetic magnitudes than if only the photometry were fitted, as we did here. For the 35 known C stars, the best-fitting template is always that of a C star and the best-fitting O-rich template has a χ2 that is (when ordered) 1.36, 1.99, 2.05, etc. times larger than the χ2 of the best-matching template. Of the 15 known O-rich stars, the best-fitting template is always that of an O-rich star, and the best-fitting C-rich template has a χ2 that is 1.28, 1.31, 1.32, 1.51, 1.65, etc. times larger than the χ2 of the best-matching template.

thumbnail Fig. C.1.

SEDs and Spitzer spectra of a C-rich post-AGB/PN star (top left), a WR star (top right), an HII region (bottom left), and a Be star (bottom right). See the notes to Table C.1 for the spectroscopic classification. In the panels with the Spitzer IRS spectra, the models (blue lines) are scaled to the observed spectra based on the average flux in the 12−13 μm region. For simplicity, the identifiers are the RA and Dec from Table A.1 truncated to two decimal figures.

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thumbnail Fig. C.2.

continued. The SEDs and Spitzer spectra of two Be stars (top panels) and two YSOs (bottom panels). See the notes to Table C.1 for the spectroscopic classification.

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thumbnail Fig. C.3.

continued. The SEDs and Spitzer spectra of four YSOs. See the notes to Table C.1 for the spectroscopic classification.

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Based on this result, the list of templates with a χ2 lower than 1.5 times that of the best-fitting template was retained and used in the classification. In this case, 34 stars were classified as “C” (all templates are of C stars), one as “C (AGB)” (the best-fitting template is C, and the alternative(s) is (are) (an) O-rich AGB stars or RSGs), 12 as “O” (all templates are O-rich AGB stars or RSGs), and 3 as “O (AGB)” (the best-fitting template is that of an O-rich AGB star or RSG, and the alternative(s) is (are) C stars).

Gullieuszik et al. (2012) also reported that the classification of AGB stars based on a fit to the SED gives reliable results, and that the success rate of classification is better for C than for O stars. They fitted the SEDs of 374 stars in one VMC field selected to be AGB stars based on CCDs and CMDs both with a C star atmosphere model and carbonaceous dust grains, and an O star model and silicate dust grains. They then selected the best model based on a χ2 comparison. Eighty-seven stars in the field were spectroscopically identified as C stars and the SED fitting classified 87% of them correctly, even 100% for stars with (J − Ks) > 1.5 mag. They also fitted the SEDs of stars with a known classification from Spitzer spectra in the MCs. The classification was correct in more than 90% of the cases for C stars and about 75% for the O-rich stars.

When the list of templates includes a non-AGB star, this is marked by OTHER, for example, “C(OTH)”. The best-fitting template could be a YSO, and in this case, the classification might be “YSO” (all templates are those of YSOs), “YSO(AGB)” (the best-fitting template is that of a YSO, and the alternatives are only O-rich AGB stars, RSGs, or C-rich stars), or “YSO(OTH)” (the best-fitting template is that of a YSO, and the alternatives could be (an) AGB star(s), RSG(s), WR, Be star, HII, or PN).

The results of the template fitting are listed in Col. 10 in Table C.2 with the predicted luminosity in Col. 11 (the error in L is estimated to be 15% based on the typical scatter in luminosity among the best-fitting templates). The SEDs of all 254 objects with their best-matching templates are plotted in Fig. C.2. In total, 197 stars are classified as C-rich (in two cases the matching templates include O-rich stars, and in three cases the matching templates include “other”; objects). The luminosities are between 1000 and 29 000 L, in agreement with GS18, who derived luminosities for 225 C stars between 1125 and 56 700 L. All three objects marked as “C(OTH)” are at relatively low luminosities between 1250 and 2850 L, and based on a visual inspection of their SED and additional information (one object is classified as an emission-line object) the three are classified as likely non-AGB stars. In total, 22 stars are classified as O-rich (in five cases the matching templates include C-rich stars, and in two cases the matching templates include “other” objects). The luminosities are between 7000 and 98 000 L, with one exception (1500 L), in agreement with GS18. For 82 stars classified as O-rich AGB stars, they found a range between 1500 and 107 000 L, and for 76 stars they classified as RSG, a range from 24 500 to ∼250 000 L. This means that 217 stars are very likely AGB stars, and the period analysis has revealed LPV like properties.

Twenty stars are classified as YSOs; in five cases AGB stars are among the best-fitting templates. Fifteen have luminosities between 400 and 2800 L, while five have luminosities between 4500 and 20 000 L. Two stars are classified as PNe, six as HII regions and seven as Be stars.

thumbnail Fig. C.4.

Examples of the fitting of a template (the solid line) to the observed photometry. The top right corner lists the identifier of the star (RA and Dec truncated to two decimal figures), and below it the type of the template. The complete set of 254 SEDs is available at https://zenodo.org/record/3714889.

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Table C.2.

Sample of stars with fitted energy distributions.

Appendix D: Results of the fits to synthetic spectra from Nanni et al. (2019)

Table D.1 lists the first entries of the table available at the CDS. It provides the results of the SED fitting performed to synthetic spectra from Nanni et al. (2019) for the 217 objects classified as AGB stars in this work.

Table D.1.

Results from the SED fitting performed to synthetic spectra from Nanni et al. (2019) for all AGB candidates selected in this work.

The calculation of the uncertainty on the MLR and luminosity is the same as that described by Nanni et al. (2018, 2019). The synthetic photometry that best fits the observations provides . Each of the synthetic fluxes are randomly modified within the observed flux errors, and a new value of χ2 between the observed and modified flux is calculated. Such a procedure is reiterated 100 times and an equal number of χ2 values are computed. From the 100 χ2 we extract the minimum and the 34th values (corresponding to 1σ). The difference between the minimum and the 1σ value provides the statistical variation of Δχ2 and thus the maximum acceptable value of χ2, . We then select from the grid of models those that yield a value of χ2: , and we compute their average and standard deviation, which provides the corresponding uncertainty of the quantity calculated. If fewer than 4 models satisfy the condition , the stellar quantities are assumed to be represented by the best-fitting value and zero uncertainty.

All Tables

Table 1.

Comparison of periods for sources in common between our study and Gaia DR2.

Table 2.

Comparison with three sources in the IRSF survey.

Table A.1.

Sample for which a period analysis and LC fitting was performed.

Table A.2.

Literature data.

Table A.3.

Results from the period analysis.

Table C.1.

SED and spectra fitted to some non-AGB stars.

Table C.2.

Sample of stars with fitted energy distributions.

Table D.1.

Results from the SED fitting performed to synthetic spectra from Nanni et al. (2019) for all AGB candidates selected in this work.

All Figures

thumbnail Fig. 1.

VMC (Ks, (J − Ks)) CMD in a region in the Magellanic Bridge (left-hand panel; a strip at 42° < RA < 52° and −72.5° < Dec < −73.8°) and in the LMC bar (right-hand panel; a box defined as 80° < RA < 82°, and −69° < Dec < −70°). Objects that are (probable) stars are indicated in black, and (probable) galaxies (extended objects) are indicated in red. Objects classified differently are indicated in blue. The line, K = 3 ⋅ (J − K) + 10 mag, indicates the approximate boundary of galaxies.

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In the text
thumbnail Fig. 2.

Left-hand panel: all VMC stars with a detection in J and Ks, redder than (J − Ks) = 1.5 mag and above the line Ks = 3 ⋅ (J − Ks)+10 mag. The second-order polynomial is a fit to the red sequence of AGB stars, shifted downward by two magnitudes for comparison purposes (see text). Objects that are (probable) stars are indicated in black, and (probable) galaxies are indicated in red. Objects classified differently are indicated in blue. Right-hand panel: synthetic photometry from GS18 for 29 SMC and 133 LMC O- (open circles) and C-rich (filled circles) AGB stars with pulsation periods longer than 450 days. The pulsation periods of the objects marked in red are derived from K/Ks or WISE-band data, and the black points are derived from optical data (OGLE, EROS, and MACHO).

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In the text
thumbnail Fig. 3.

WISE-VMC (W1, Ks − W1) CMD and (W1 − W2)−(Ks − W1) CCDs. Left-most panel: CMD in a region between the SMC and LMC (a strip at 30° < RA < 60°). The line W1 = 1.0 ⋅ (K − W1)+10.5 mag indicates the upper boundary of the region predominantly occupied by galaxies. Second panel from the left: all WISE-VMC sources that are brighter than the boundary line in the left-hand panel, (Ks − W1) > 1 mag and (W1 − W2) > 0.5 mag. Objects that are (probable) stars are indicated in black, and (probable) galaxies (extended objects) are indicated in red, while objects classified differently are indicated in blue in these two panels. The provenance of the line in the second panel is explained in the next panel. The corresponding CCD is shown in the bottom half of the right-most panel. Third panel from the left: synthetic CMD based on GS18 for 29 SMC and 133 LMC O- (open circles) and C-rich (filled circles) AGB stars with pulsation periods longer than 450 days. The pulsation periods of the objects marked in red are derived from K/Ks or WISE-band data, and the black points are derived from optical data (OGLE, EROS, and MACHO). The line W1 = 0.7 ⋅ (Ks − W1)+10.0 mag is the empirical lower boundary to the reddest AGB stars, and it is also shown in the second panel from the left. The corresponding CCD diagram is shown in the top half of the right-most panel with the lines (W1 − W2) = 0.8 mag and (W1 − W2) = 0.37 ⋅ (Ks − W1)−0.2 mag, which indicates the empirical lower boundary to the reddest AGB stars, and is also shown in the panel below it.

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In the text
thumbnail Fig. 4.

Left-hand panel: ([8.0], [3.6]−[8.0]) CMD of LMC and SMC objects in the SAGE survey. Only every tenth star is plotted. The line at [3.6]−[8.0] = 0.8 mag indicates the blue limit of red AGB stars, and the two other lines indicate the limits of the region that is mainly occupied by background galaxies (see text). Top right-hand panel: ([3.6]−[4.5], [5.8]−[8.0]) CCD of all sources that are located in the upper right of the CMD delineated by these lines. Bottom right-hand panel: same diagram with synthetic CCD based on GS18 for 29 SMC and 133 LMC O- (open circles) and C-rich (filled circles) AGB stars with pulsation periods longer than 450 days. The pulsation periods of the objects marked in red are derived from K/Ks or WISE-band data, and the black points are derived from optical data (OGLE, EROS, and MACHO). The background sources in this panel are randomly picked from the S3MC survey (Bolatto et al. 2007).

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In the text
thumbnail Fig. 5.

Pulsation properties of 294 confirmed Miras by OGLE compared with our results. Left panel a: directly compares the periods in the upper part; the dotted line marks the one-to-one relation. The lower part indicates the difference in periods as a function of the period found by OGLE. The star at P = 1858 d (log P = 3.26) in the top panel is located outside the plot at ΔPeriod = 216 d in the bottom panel. Middle panel b: compares the amplitude in the K band to that in the I band. The OGLE team defines amplitude as the minimum-to-maximum variation, while we use the traditional definition (see Eq. (1)). Stars with a are marked by a plus sign, and stars where the error on the K-band amplitude is larger than the amplitude are marked in red. The dotted line indicates the cut-off value of 0.1 mag we used to select the maximum number of known Miras from our sample. The solid line has a slope 0.5 to guide the eye. Right-hand panel c: relative error of the period determination against the period. Stars with a are marked by a plus sign, and stars where the error on the K-band amplitude is larger than the amplitude are marked in red. The dotted line indicates the cut-off value of 4% error on the period determination we used to select Miras from our sample.

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In the text
thumbnail Fig. 6.

Examples of LCs of objects where the literature classification and the template fitting indicate a non-AGB nature. Top panel: probable YSO object 2MASS J04573274−6959032 (based on a photometric classification; Table 10 in Gruendl & Chu 2009), and bottom panel: B1 emission-line star [BE74] 621. Data points (with error bars) in black show the VMC, green points represent 2MASS, dark blue points 2MASS-6X, and light blue points the IRSF.

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In the text
thumbnail Fig. 7.

Classification of the AGB candidates in this work based on the VISTA Ks band and Gaia DR2 photometry (Lebzelter et al. 2018). The solid line indicates the separation between oxygen-rich (O) stars (to the left of the curve) and C stars, while the dashed line separates C stars from the most extreme dust-enshrouded stars. All the stars are colour-coded according to their (J − K) colours.

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In the text
thumbnail Fig. 8.

Comparison between the MLR obtained by Nanni et al. (2019) with the rate we derived for stars in common. The solid black line is the one-to-one relation.

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In the text
thumbnail Fig. 9.

Top panel: bolometric luminosity vs. period obtained from the SED fitting of the C stars selected in this work: C stars in the SMC are indicated with red dots, and C stars in the LMC are plotted with blue triangles. For comparison, we overplot the population of C stars in the LMC for which the period has been determined from Riebel et al. (2012), which have been fitted by Nanni et al. (2019). To avoid superposition in the plot, Mbol has been changed by a random number between −0.25 and +0.25 mag. The sources for which the period has been flagged with a superscript “a” or “b” in Table C.2 are indicated with a cross. Middle and bottom panels: relations between MLR vs. the bolometric luminosity and MLR vs. period, respectively.

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In the text
thumbnail Fig. 10.

Bolometric PL-relations for all the 254 objects for which the template fitting was performed (top panel), and the subsets of likely C-rich Miras (middle panel), and O-rich Miras (bottom panel). The likely C-rich objects are plotted as open squares, the likely O-rich objects are plotted as open triangles, and the other AGB stars as filled circles, see the main text for details. The 37 likely non-AGB stars are plotted as dots. The likely C-rich Miras (with an amplitude >0.2 mag) are plotted in the middle panel. The objects in the LMC are plotted with open symbols, and those in the SMC with filled symbols. The blue dashed line is a fit to the data, excluding outliers (plotted as dots). The likely O-rich Miras (with an amplitude >0.2 mag) are plotted in the bottom panel. The blue dashed line is a fit to the data, excluding outliers (plotted as dots). The red dotted lines in the two panels indicate relations from the literature derived at shorter periods, see the main text for details.

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In the text
thumbnail Fig. A.1.

Examples of the LC fitting (red solid lines) to the observed time photometry At the top of the plot the identifier and the period (in days) are listed. Data points (with error bars) are identified as black for the VMC, green for 2MASS, dark blue for 2MASS-6X, light blue for IRSF, magenta for DENIS, and orange for other sources (see references in the footnote to Table A.3). Black crosses indicate points that were excluded from the fits. The complete set of LC is available at https://zenodo.org/record/3714889.

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In the text
thumbnail Fig. C.1.

SEDs and Spitzer spectra of a C-rich post-AGB/PN star (top left), a WR star (top right), an HII region (bottom left), and a Be star (bottom right). See the notes to Table C.1 for the spectroscopic classification. In the panels with the Spitzer IRS spectra, the models (blue lines) are scaled to the observed spectra based on the average flux in the 12−13 μm region. For simplicity, the identifiers are the RA and Dec from Table A.1 truncated to two decimal figures.

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In the text
thumbnail Fig. C.2.

continued. The SEDs and Spitzer spectra of two Be stars (top panels) and two YSOs (bottom panels). See the notes to Table C.1 for the spectroscopic classification.

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In the text
thumbnail Fig. C.3.

continued. The SEDs and Spitzer spectra of four YSOs. See the notes to Table C.1 for the spectroscopic classification.

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In the text
thumbnail Fig. C.4.

Examples of the fitting of a template (the solid line) to the observed photometry. The top right corner lists the identifier of the star (RA and Dec truncated to two decimal figures), and below it the type of the template. The complete set of 254 SEDs is available at https://zenodo.org/record/3714889.

Open with DEXTER
In the text

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