Oxygen- and carbon-rich variable red giant populations in the Magellanic Clouds from EROS, OGLE, MACHO, and 2MASS photometry

Abstract

The carbon-to-oxygen (C/O) ratio of asymptotic giant branch (AGB) stars
constitutes an important index of evolutionary and environment/metallicity
factor. We develop a method for mass C/O classification of AGBs in photometric
surveys without using periods. For this purpose we rely on the slopes in the
tracks of individual stars in the colour-magnitude diagram. We demonstrate that
our method enables the separation of C-rich and O-rich AGB stars with little
confusion. For the Magellanic Clouds we demonstrate that this method works for
several photometric surveys and filter combinations. As we rely on no period
identification, our results are relatively insensitive to the phase coverage,
aliasing, and time-sampling problems that plague period analyses. For a
subsample of our stars, we verify our C/O classification against published C/O
catalogues. With our method we are able to produce C/O maps of the entire
Magellanic Clouds. Our purely photometric method for classification of C- and
O-rich AGBs constitutes a method of choice for large, near-infrared photometric
surveys. Because our method depends on the slope of colour-magnitude variation
but not on magnitude zero point, it remains applicable to objects with unknown
distances.

Full text

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arXiv:1104.0200v1 [astro-ph.SR] 1 Apr 2011
Astronomy & Astrophysics manuscript no. 14319
April 4, 2011
c ? ESO 2011
Oxygen- and carbon-rich variable red giant populations in the
Magellanic Clouds from
EROS, OGLE, MACHO, and 2MASS photometry.
M. Wi´ sniewski1, J.B. Marquette2,3, J.P. Beaulieu2,3, A. Schwarzenberg-Czerny1,4, P. Tisserand5,6,´E. Lesquoy6,2,3
1Nicolaus Copernicus Astronomical Centre, Bartycka 18, 00-716 Warsaw, Poland
2UPMC Universit´ eParis 06,UMR7095,
(marquett,beaulieu,lesquoy)@iap.fr
3CNRS, UMR7095, Institut d’Astrophysique de Paris, F-75014, Paris, France
4Adam Mickiewicz University Observatory, ul. Słoneczna 36, PL 60-286, Pozna´ n, Poland, e-mail: alex@camk.edu.pl
5Research School of Astronomy & Astrophysics, Mount Stromlo Observatory, Cotter Road, Weston ACT 2611, Australia, e-mail:
tisseran@mso.anu.edu.au
6CEA, DSM, DAPNIA, Centre d’´Etudes de Saclay, 91191 Gif-sur-Yvette Cedex, France
Institutd’AstrophysiquedeParis, F-75014,Paris,France,e-mail:
Received ...; accepted ...
ABSTRACT
Context. The carbon-to-oxygen (C/O) ratio of asymptotic giant branch (AGB) stars constitutes an important index of evolutionary
and environment/metallicity factor.
Aims. We develop a method for mass C/O classification of AGBs in photometric surveys without using periods.
Methods. For this purpose we rely on the slopes in the tracks of individual stars in the colour-magnitude diagram.
Results. We demonstrate that our method enables the separation of C-rich and O-rich AGB stars with little confusion. For the
Magellanic Clouds we demonstrate that this method works for several photometric surveys and filter combinations. As we rely on
no period identification, our results are relatively insensitive to the phase coverage, aliasing, and time-sampling problems that plague
period analyses. For a subsample of our stars, we verify our C/O classification against published C/O catalogues. With our method
we are able to produce C/O maps of the entire Magellanic Clouds.
Conclusions. Our purely photometric method for classification of C- and O-rich AGBs constitutes a method of choice for large,
near-infrared photometric surveys. Because our method depends on the slope of colour-magnitude variation but not on magnitude
zero point, it remains applicable to objects with unknown distances.
Key words. Methods: data analysis, Techniques: photometric, Surveys, Stars: oscillations (including pulsations), Stars: AGB and
post-AGB, Magellanic Clouds
1. Introduction
Low and intermediate mass stars evolve through three late
stages. After passing the red giant branch (RGB) they reach
maximum luminosity at its tip (TRGB) followed by a luminos-
ity drop after the helium flash. Next they grow again and move
along the asymptotic giant branch (AGB). According to their
spectra, the AGB stars split into oxygen-rich stars (O-rich, M-
stars, or K-stars) and carbon-rich stars (C-rich, C-stars, or N-
stars). The M-stars have more oxygen than carbon in their at-
mospheres (C/O < 1). When the abundance of oxygen equals
that of carbon the AGB type is S. Classification of the lat-
ter is difficult and also involves intermediate MS and SC types
(Cioni & Habing 2003).
Stars entering the AGB phase are rich in oxygen, how-
ever, subsequent dredge-up caused by thermal pulsation may
enrich their atmospheres in carbon (Iben & Renzini 1983). On
the AGB, several thermal pulses (TP-AGB) may occur, resulting
in dredging up the matter enriched in carbon nuclei by nuclear
fusion. In this way the O-rich stars are converted after at least
several pulses into the C-rich ones (Marigo et al. 2008 and ref-
erences there).
Send offprint requests to: A. Schwarzenberg-Czerny
It is believed that the rate of conversion of O-stars into
C-stars depends on the efficiency of the third dredge-up and
the extent and time variation in the massloss (e.g. Iben 1981;
Marigo et al. 1999). Mass loss is expected to be stronger in
metal-rich stars, givingto shorter AGB life and eventuallyyield-
ing a C-star. These thermal pulses result in the luminosity varia-
tions with the peak-to-peakamplitude up to a few magnitudes at
visual wavelengths.
According to Iben & Renzini (1983), the lower the metallic-
ity the less carbon needed to be dredged-up in order to convert
an O-star into a C-star, hence the correlationbetween metallicity
and the C/M ratio. For lower metallicity, the AGB evolutionary
tracks move to higher temperatures; for very low metallicity a
post-horizontal-branch star may become a white dwarf without
first becoming an AGB star. Since O and C stars reveal very dif-
ferent spectra, it is relatively easy to spectroscopically identify
C-rich stars even at large distances. The differences in molecu-
lar blanketing and dust creation result in an observed sharp di-
chotomy in infrared colours of O- and C-rich stars. Thus the O-
and C-stars are often identified using narrow filters. The J − K
colour of the C-rich stars is > 1.4 mag and systematically red-
der than that of O-rich stars (Frogel et al. 1990; Costa & Frogel
1996; Cioni et al. 2000a). These effects influence the luminosity

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2 Mariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds
functionof O- andC-richAGB stars. TheMagellanicClouds are
good test-beds of theories of the late stages of stellar evolution.
Theyarenearbyandyetfarenoughto ignoretheLMC thickness,
so that all stars are approximately at the same distance.
Late evolutionary stages are often associated with long
period- (LPV), semi-, and irregular-variability. A wealth of
data on this variability was collected as a by-product of
the microlensing surveys. All yielded catalogues of numer-
ous variable stars. In these data the period-luminosity rela-
tions of the LPV’s on the AGB are well documented for both
the Large and Small Magellanic Clouds (Wood et al. 1999;
Wood 2000; Cioni et al. 2001, 2003; Noda et al. 2002, 2004;
Lebzelter & Hinkle 2002; Ita et al. 2004a,b; Kiss & Bedding
2003, 2004; Soszynski et al. 2004a,b, 2005; Groenewegen2004;
Fraser et al. 2005; Raimondo et al. 2005).
The period-luminositydiagram for red variables at advanced
evolutionary stages reveals six sequences for different classes
of objects (Ita et al. 2004b). Miras and some low-amplitude
semiregulars pulsating in the fundamental mode form the se-
quence C. Other semiregular stars pulsating in the second and
third overtone modes occupy sequences A, B, and C, and the
RGB eclipsingbinariesformtheirownsequenceE.Theoriginof
the sequence D corresponding to long-secondary periods (LSP)
remains ambiguous. Wood et al. (2004) considered a number of
possible explanations of LSP (radial and non-radial pulsations,
rotations, orbiting companions, chromospheric activity, orbiting
dust clouds), but none fit the observations satisfactorily.
Soszynski et al. (2004a) combined the OGLE-II and OGLE-
III data and found the multiperiodicity of the red giants to be
variable with a small amplitude. They exhibited two modes
closely spaced in their power spectrum. This is likely to indi-
cate non-radialoscillations. They also show that members of the
short-period P–L sequences below the TRGB constitute a mix-
ture of the RGB and AGB variables. Recently, Soszynski et al.
(2004a, 2005); Soszy´ nski (2007), and Derekas et al. (2006) have
demonstrated that the sequence E overlapped with the sequence
D, which may be evidence for a binary origin of the sequence D.
There are differences between the O-rich and C-rich LPVs,
too. Cioni et al. (2003) note that C-stars have a larger amplitude
than O-stars. Ita et al. (2004a) confirm that O- and C-rich Miras
follow different period vs. (J − K) colour relations (Feast et al.
1989). The I-band amplitude of C-rich Miras tends to grow with
the redder mean (J − K) colour, while the amplitude of O-rich
Miras is colour independent (Matsunaga et al. 2005).
The evidence has provided new and significant con-
straints for theoretical pulsation models. Models and obser-
vations are compared in three ways: using stellar isochrones
(e.g. Bressan et al. 1996; Bruzual & Charlot 2003; Mouhcine
2002; Marigo et al. 2003; Groenewegen & de Jong 1993),
stellar tracks (Groenewegen & de Jong 1993; Marigo et al.
1999; Mouhcine & Lanc ¸on 2002; Lanc ¸on & Mouhcine 2002;
Mouhcine & Lanc ¸on 2003), and the fuel consumption theorem
by Renzini & Buzzoni (1986) and Maraston (1998, 2005).
The synthetic characteristics of AGB stars are derived either
from complete evolution tracks, semi-empirical fits to the core
mass-luminosity relation, or from the core mass-interpulse pe-
riod relation and the mass-loss rate as a function of stellar pa-
rameters. The examples of such calculations are provided by
Groenewegen & de Jong (1993) and Izzard et al. (2004).
Recent attempts have been made to include the TP-AGB
phase in evolutionary population synthesis models. Both im-
provements in the low-temperature opacities and peculiarities
of the actual surface chemical composition have such profound
consequences that the whole AGB evolutionary scenario be-
came significantly affected (Marigo et al. 2008). Use of the
molecular opacities reflecting the actual chemical composition
leads to a significant decrease in Tef f as soon as C/O > 1
(Marigo et al. 2008 and references therein). This decrease is
confirmed by observations of galactic AGB stars (Bergeat et al.
2001; Marigo et al. 2003), and it naturally explains the presence
of a red tail in the (J − K) colour-magnitude diagram of C stars.
The mass loss is driven by pulsation in a complicated way.
The pulsation pushes a fraction of the atmosphere above the
photosphere, creating a cool and dense environment where dust
grains form and grow efficiently. The radiation pressure on the
dust combined with the momentum carried in the shock waves
drives the mass loss (Wood 1979; Bowen & Willson 1991;
Hoefner et al. 1996, e.g.)
Lebzelter & Wood (2005) compared the observations of
LPV in 47 Tuc with the models. On one hand, they find that
the models without mass loss fail to reproduce the observed pe-
riodsofthesmallamplitudepulsators.Ontheother,the K−logP
sequence of the large amplitude variables, such as the Miras, is
inconsistentwiththe mass-oss modelsandconsistentwith theno
mass-loss models. Only models involving the non-linear funda-
mental mode yield periods consistent with the Miras in 47 Tuc
(Olivier & Wood 2005).
The past decade has brought results of extensive pho-
tometric surveys – OGLE (Paczynski et al. 1994), OGLE II
(Udalski et al. 1997), EROS (Aubourg et al. 1995), MACHO
(Alcock et al. 1997), and MOA (Bond et al. 2001) – covering
several optical and infrared bands, sometimes simultaneously.
They have provided a wealth of observations of red variable
stars, thus enabling the study of their population properties. In
particular, use of infrared colours and/or pulsation periods have
enabled the classification of C- and O-rich stars. We discussed
above the relevant observational and theoretical results.
In the present paper, we attempt to analyze the photomet-
ric properties of red variables in the visual region without re-
course to their periods. Our analysis should be complementary
to any traditional methods while suffering less, if at all, from
aliasing andseasonal interference.We employcorrelationslopes
of colour and magnitude variability introduced by Wood et al.
(2004). In this paper the slope aRof the correlation of R magni-
tude and V − R colour variations revealed no relation with any
otherpropertyof red variables.We employa differentfilter com-
bination in our attempt of photometricclassification of C and O-
rich red variable stars. Our results should not depend much on
the number of pulsation cycles covered by a given survey. Our
practical requirement that data span at least one pulsation cycle,
is met in most large surveys.
In Sect. 2 we describe data employed in the present study.
Our calculation methods are described in Sect. 3. In Sect. 4 we
propose new methods of selection O- and C-rich stars. Due to
large differences in filters and time span, we present our results
for each survey separately. We give an estimate of the C/O ratio
forvariablestars in the MagellanicClouds.In Sect. 5 we employ
a simple model to demonstrate how observed effects may arise.
Possible peculiarvariables are discussed in Sect. 6. We conclude
in Sect. 7.
2. The data
Our paper is based primarily on the EROS-2 photometric survey
of the Magellanic Clouds cross-referenced with the 2MASS in-
frared magnitudes (Sect. 2.1). We explicitly indicate when these
are supplemented by the OGLE and MACHO photometry and
four catalogues of C-and O-rich stars (Sect. 2.2 – 2.4).

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Mariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds3
2.1. EROS-2 survey
The Exp´ erience de Recherche d’Objets Sombres (EROS-2)
project employed extensive photometry obtained with the 1-
meter MARLY telescope at La Silla Observatory, Chile, to
search for the baryonic dark matter of the Galactic halo
by means of the gravitational microlensing (Afonso et al.
2003; Lasserre et al. 2000; Palanque-Delabrouille et al. 1998;
Tisserand et al. 2007). The observations were performed be-
tween July 1996 and February 2003 through a dichroic plate-
splitting light into two wide field cameras covering 0.7× 1.4oin
right ascension and declination each, yielding two broad pass-
bands. The so-called blue channel (420 − 720 nm, hereafter BE
band) overlapped the standard V and R standard bands, while
the red one (620− 920 nm, hereafter REband) roughly matched
the standard I filter. Each camera constituted a mosaic of eight
2k × 2k CCDs with a pixel size on the sky of (0.6”)2.
Ten fields covered the SMC and 88 fields covered the LMC.
The photometryfromindividualimages was combinedinto light
curves using the Peida package developed specifically for the
EROS experiment(Ansari 1996). The estimated accuracy of this
photometry is discussed by Derue et al. (2002). For uniformity,
the SMC data were analysed again with the more recent version
of Peida.
The RGB and AGB variable stars were selected from the
SMC and LMC lists of EROS variables using their location in
the colour-magnitude diagram. In this way we selected 28914
stars in LMC and 5930in SMC. Theyconstituteoursampleused
in further analysis.
2.2. OGLE data
The Optical Gravitational Lensing Experiment (OGLE-II) data
were collected with the 1.3 m Warsaw Telescope at the
Las Campanas Observatory, Chile, operated by the Carnegie
Institution of Washington. The I-band data span about 3000
days: from January 1997 to April 2005. The V-band measure-
ments were obtained from 1997 to 2001 (Zebrun et al. 2001), so
they span a shorter time baseline. Up to 70 V-band points per
star are available. In the I-band, 500 to 900 measurements were
available, depending on the field (Soszynski et al. 2005). In the
present work we use data on 3586 LPV from LMC published
by Soszynski et al. (2005), downloaded from the OGLE home-
page1.
We cross-identified EROS and OGLE objects within a 1.3”
radius. The OGLE-II fields cover only the bar of LMC, i.e. a
much smaller field than for EROS, hence there are relatively few
stars in common.
2.3. MACHO data
The MAssive Compact Halo Objects (MACHO) project
(Alcock et al. 1997) comprises eight years of observations of
the Large and Small Magellanic Clouds and of the Galactic
Bulge. For the present purposes we selected LMC stars from the
MACHO catalogue of variable stars (Alcock et al. 2003). Using
the MACHO2interface, we downloaded 2868 individual light
curves of the stars classified as the red giant variables (classified
as Wood A, B, C, and D sequences).
1http://sirius.astrouw.edu.pl/∼ogle/
2http://wwwmacho.mcmaster.ca/
2.4. 2MASS survey data.
The Two Micron All Sky Survey (2MASS)3employed two 1.3-
m robotic telescopes, one at Mt. Hopkins, Arizona, and one at
CTIO, Chile. Each telescope was equipped with a three-channel
camera, capable of observing the sky simultaneously at J (1.25
microns), H (1.65 microns), and Ks(2.17 microns). The south-
ernfacility begancollectingSurveydatain March1998andcon-
ducted its final scan in February 2001.
We extracted 2MASS data for each of the EROS fields sep-
arately. Then cross-identification was done separately for each
field. During the cross-identification of EROS and 2MASS, we
employed a 3” search radius. We selected only stars with pho-
tometry available in all three bands J,H, and Ks. AGB stars are
among the brightest stars of the LMC. If an area of the order of
16 square degrees contains 25000 AGB stars, their average sep-
aration is 1.5 minutes of arc, so the probability of blending two
of them within the search radius is (1.5∗60/3)−2= 0.0006, thus
correspondingto fewerthan 15stars in thewhole sample.This is
negligible compared to the blur of our photometric plots. At this
point it is worth discussing the contamination of our AGB sam-
ple of IR colours with mistaken cross-identification with RGB
stars. For stars brighter than TRGB (K < 12 for LMC and
K < 12.7 for SMC), this problem does not exist. Suppose, for
an EROS AGB star, that IR colours for an RGB one were fit-
ted, then the star would land leftwards of the vertical lines on
aV versus K diagrams. One possible problem is mixing faint
AGBswithRGBs, causingpollutionofRGBs withAGBsbutnot
otherwise [i.e. faint AGB remain clean, if possibly incomplete].
Kiss & Bedding (2004) consider the same problem in more de-
tail for stars from OGLE and 2MASS and conclude that con-
tamination is insignificant, possibly no more than 0.3%, for their
searchradiusof1”,correspondingtoless than3%contamination
for our radius of 3”. Since there were selected MACHO objects
than for EROS, we cross-identified MACHO and 2MASS with-
out subdivision into fields and with the same 3” radius. Again
we only selected stars with photometry in all three bands J,H,
and Ks.
2.5. The catalogues of C-rich stars
We selected 1707 C-rich stars from the SMC identified
by Rebeirot et al. (1993) in the low-resolution spectroscopic
survey employing the ESO 3.6 m telescope and 1185
stars identified in the Siding Spring Observatory survey by
Morgan & Hatzidimitriou (1995).
A catalogue of 7760 C-rich stars in the LMC was presented
by Kontizas et al. (2001). These stars were identified during a
systematic survey of the objective-prism plates taken with the
UK 1.2 m Schmidt Telescope. To these we added the list of C-
rich stars from Groenewegen (2004).
Soszynski et al. (2005) demonstrate a new method of dis-
tinguishing between O-rich and C-rich Miras, SRVs and stars
with long secondary periods, relying on their V and I-band pho-
tometry and periods. The list of stars selected from the LMC in
this way was downloadedfrom the OGLE homepage.All C-rich
stars from these catalogues were cross-identified with the EROS
and MACHO stars within a 3” radius.
3http://www.ipac.caltech.edu/2mass/

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4 Mariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds
3. Data pre-processing
The analysis outlined in this paper was performedseparately for
EROS LMC and SMC, OGLE LMC and MACHO LMC data.
We used data from all surveys to study a path in the colour-
magnitude diagram traversed by each variable star. We investi-
gated correlation of the average slope of the path with the chem-
ical composition of the objects. The results of this analysis are
summarised in diagrams described in the Sect. 4.
The EROS surveyproducedsimultaneouslight curvesin two
spectral bands. By applying time filters to each band light curve
we obtained a smooth, low-pass filtered light curve and its com-
plementaryhigh-passlightcurve.Thesumofthetworeproduces
the original light curve. In this way for each spectral band we
obtained 3 light curves: raw, low-, and high-pass, six in total. In
further analysis we study correlations of stellar properties with
the properties derived from these light curves.
3.1. Photometric calibrations.
Both EROS and MACHO obtained simultaneous expositions in
two bands termed “red” (REand r, respectively) and “blue” (VE
and v, respectively) for nearly all observations. We simply ig-
nored observations made in just one filter.
FollowingTisserand et al. (2007),we convertedthe rawpho-
tometryintothestandardKron-Cousinssystemusingthefollow-
ing relations:
VEROS = 1.666VE− 0.666RE
IEROS = RE.
(1)
(2)
The MACHO data from the web database are available in
the raw instrumental system. Following Alcock et al. (1997), we
converted the raw photometry into the standard Kron-Cousins
system using the following relations:
VMACHO = v + 23.699− 0.1804(v− r)
RMACHO = r + 23.412− 0.1825(v− r)
where v and r are instrumental magnitudes and VMACHO and
RMACHOare in the Kron-Cousins standard system. These cali-
bration formulae are estimated to have an overall absolute ac-
curacy of ±0.10 mag in VMACHOor RMACHOand ±0.04 mag in
(V − R)MACHO(Alard et al. 2001).
The OGLE survey employs one camera, so observations in
different filters are not simultaneous. Observations in V filter
were obtained much less frequently than in I. For each V ob-
servation, we searched the nearest I observations.If two I points
before and after a V observation separated by no more than 2
days, we performed a linear interpolation at the time of V obser-
vation. For just one I point nearby, no more than one day from
the V observation,we assume they were measured nearly simul-
taneously. In this way for most V observations we found its cor-
responding I magnitudes. Other V observations were ignored.
Because we only analyse stars with long periods, this procedure
proved reliable for our purposes.
(3)
(4)
3.2. Time filtering
Through the whole paper except for Sect. 6, we used the raw
light curves. Light curves for Sect. 6 were filtered in the time
domain. The low-pass curve was obtained from the raw one by
means of the “moving median”. The purpose of time filtering is
to separate short period pulsations in some stars from the LSP.
Since ourproceduredoesnot dependonactual detectionof these
-0.4
-0.2
0
0.2
0.4
-1-0.5 0 0.5 1
∆ V-I
∆ V
-0.4
-0.2
0
0.2
0.4
-1-0.5 0 0.5 1
∆ V-I
∆ V
Fig.2. Sample plot of raw colour and magnitude variations for
the same 2 stars as in Fig. 1. We also plot the regression lines.
Their inclination parameter is aV, discussed in the text.
periods, we applied it to all EROS red variables. We selected
a window of width w centred on a given point and replaced its
valuewith thewindowmedianvalue.In practicewe filteredeach
light curve twice consecutively using windows of width w1and
w2dependent on average Ksluminosity:
w1 = 10(K−D)/(−3.9)
w2 = 10(K−D+1)/(−3.9)
(5)
(6)
where the D magnitude is equal to 19.4 for the LMC and to 21.1
for the SMC. These windows were selected to have intermediate
length between the short period and LSP (see Sect. 6 for discus-
sion of these periods). As both periods depend on mean stellar
brightness K, so do our window widths. The slope of −3.9 cor-
responds to a border line between the short period sequences
and the LSP sequence in the period-luminosity (P − L) diagram
(Ita et al. 2004b; Soszynski et al. 2004a). As this area is virtu-
ally devoid of stars, its exact value is of no consequence for the
current considerations.
We found that a light curve smoothed with two moving
medians reveal LSP more clearly than when smoothed only
once. Any short-period variations are filtered out. The high pass
curve was obtained by subtracting the low pass one from the
raw data. Only short time variations are left in the high-pass
light curve. Sample light curves are plotted in Fig. 1. A simi-
lar procedure was employed by Wood et al. (2004) except that
we did not use the short period as the parameter determining fil-
ter window to avoid confusion for multi-periodic/irregular red
giants (Soszynski et al. 2004a). For EROS and MACHO colours
(V − I)EROS, (V − R)MACHOwere calculated for each time point.
Subsequently we filtered colours similarly to how magnitudes
are filtered. In this way we got the colour variation for raw data,
LSP, and short time scale variations separately. For OGLE the
number of V observations was too small to filter.
3.3. Analysis of colour variations
In further analyses we considered variations in colour against
magnitude, for all possible combinations of light curves (raw,
long-, and short-time scale colours against raw, long- and short-
time scale V and I magnitudes). Sample plots are presented in
Fig. 2. Next we fitted by the least squares the regression lines,
(V − I) = aII + bI
(V − I) = aVV + bV
where aVand aI denote the slope of the corresponding colour
- magnitude relation. This kind of linear equation was fitted for
EROS, OGLE and MACHO data.
To verify the quality of our slope parameter, we calculated
the correlation coefficient ρ and the statistic t in the following
(7)
(8)

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Mariusz Wisniewski et al.: Populations of variable red giants in the Magellanic Clouds5
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
500 1000 1500 2000
Vraw
time
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
500 1000 1500 2000
Vlong
time
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
500 1000 1500 2000
Vshort
time
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
500 1000 1500 2000
Vraw
time
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
500 1000 1500 2000
Vlong
time
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
500 1000 1500 2000
Vshort
time
Fig.1. Sample EROS light curves for two stars with spectral types assigned by Cioni et al. (2001): DCMC J052618.12-694100.0
of type C (top row) and DCMC J052446.91-694949.9 of type M (bottom row). The left, middle, and right panels present the raw,
low-pass, and high-pass light curves, respectively. For details of filtering see Sect. 3.2
way:
ρ =Cov{V,V − I}
σVσV−I
t =
?1 − ρ2
1
n
i
(9)
ρ
√n − 2 where (10)
Cov{V,V − I} =
n ?
(V − V)[V − I − (V − I)].
(11)
Results are shown in Fig 3. For the null hypothesis H0assuming
no correlation, i.e. ρ = 0, a t statistic obeys the Student distribu-
tion with n − 2 degrees of freedom, where n is number of points
per star (Fisz 1963). For a probability of 0.995, t is equal to 2.6.
For most stars the correlation coefficient is greater than 0.5, and
t is as significant as 15 or more.
3.4. Analysis of amplitude variations
The amplitude of the luminosity variation was calculated from
the distance of the maximum and minimum in the correspond-
ing, possibly filtered light curve. We derived the amplitude of
the colourvariation as the distance between points on these lines
corresponding to extreme magnitudes. In this way we dimin-
ished the influence of individual colour errors on the colour am-
plitude.Theseamplitudeswerecalculatedforeachfilter,andraw
, long-, and short time-scale data.
4. Photometric chemical classification of red
variable stars
4.1. The slope-amplitude diagram.
Wood et al. (2004) have introducedthe variabilityslope parame-
ter aR. They note it has no obvious relation to any other property
of red variable stars. Noticing that red giants have greater am-
plitude in the blue filter results in better accuracy for the slope
estimates. We adopted the aVslope parameter as a better substi-
tute. In the left panels of fig. 4 we plot the slope aVof the colour
- blue magnitude relation against amplitude, for all EROS red
variable stars in the LMC and SMC. For completness we also
plot aV against the near infrared magnitude and colour in the
middle and right panels. In the rest of the present section, we in-
vestigateourslopeparameteraVas a toolforthechemicaland/or
evolutionarystatus classificationof redvariablestars. We defera
discussion of the classification corresponding to the middle and
right panels until Sects. 4.3 and 4.4. Anticipating our result, we
adopted in Fig. 4 different colour coding for O-rich RGB stars,
O-rich, and C-rich AGB stars as green(light grey), blue(black),
and red(dark grey) dots, respectively. The colour-coded selec-
tion, for all diagrams, comes from the third method presented in
the right panels.
The left panels in Fig 4 display plots of the slope aVagainst
the colour amplitude ampVIfor EROS LMC and SMC data, re-
spectively. Note the conspicious two-modal distribution of aV
suggesting separate clustering of C- and O-rich AGB stars. In
these plots there are two distinct branches corresponding to
steep and shallow slopes, i.e. for large and small aV. For both
branches, the slope initially grows and then, for amplitudes over
0.3, saturates at the constant values of 0.65 and 0.3. These two
groups can be separated by the curve with the equation
aV= 0.52tanh(ampVI/0.15).
(12)
The same border holds for both EROS LMC and SMC data. In
the following sections we demonstrate by cross-checking in the
catalogues that the stars above and below the curve are respec-
tively O- and C-rich. Thus our Eq. (12) constitutes the new clas-
sification criterion for C- and O-rich stars. Its importance and
novelty stem from using the visual photometry alone with no
recourse to periods. Our criterion does work for an incomplete
phase coverage and even for data spanning as small an interval
as a typical Mira period. Moreover,at this point there are no ob-
stacles totest the usefulnessofournew methodforthe semi- and
irregular red variables. Problems in using aIfor low-amplitude
variables are illustrated in Fig. 5. The two clusters merge for low
amplitudes. In this way we confirm that the slope aVis indeed