arXiv:astro-ph/0102262v1 15 Feb 2001
Scientific correspondence should be directed to Geoffrey C.
The MACHO Project LMC Variable Star Inventory: X.
The R Coronae Borealis Stars
C. Alcock1,2, R.A. Allsman3, D.R. Alves4, T.S. Axelrod5, A. Becker6, D.P. Bennett1,7,
Geoffrey C. Clayton8,9, K.H. Cook1,2,9, N. Dalal2,10, A.J. Drake1,5, K.C. Freeman5, M.
Geha1, K.D. Gordon9,11, K. Griest2,10, D. Kilkenny12, M.J. Lehner13, S.L. Marshall1,2, D.
Minniti1,14, K.A. Misselt15, C.A. Nelson1,16, B.A. Peterson5, P. Popowski1, M.R. Pratt6,
P.J. Quinn17, C.W. Stubbs2,5,6, W. Sutherland18, A. Tomaney6, T. Vandehei2,9, and D.L.
Welch19, (The MACHO Collaboration)
– 2 –
We report the discovery of eight new R Coronae Borealis (RCB) stars in the
Large Magellanic Cloud (LMC) using the MACHO project photometry database.
firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
Livermore National Laboratory,Livermore,
2Center for Particle Astrophysics, University of California, Berkeley, CA 94720
Facility, AustralianNational University, Canberra, ACT0200,Australia;
4Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218; email@example.com
5Research School of Astronomy and Astrophysics, Canberra, Weston Creek, ACT 2611, Australia;
firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
ofAstronomyandPhysics, Universityof Washington, Seattle,WA 98195;
7Department of Physics, University of Notre Dame, Notre Dame, IN 46556; email@example.com
of Physics & Astronomy, Louisiana State University, Baton Rouge, LA 70803; gclay-
9Visiting Astronomer, Cerro Tololo Inter-American Observatory
10Department of Physics, University of California at San Diego, San Diego, CA 92093;
firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
11Steward Observatory, University of Arizona, Tucson, AZ 85721; email@example.com
African AstronomicalObservatory,P.O. Box9, Observatory7935, South Africa;
13Department of Physics, University of Sheffield, Sheffield S3 7RH, England, UK; firstname.lastname@example.org
deAstronomia, P.UniversidadCatolica, Casilla 104, Santiago22,Chile;
15Infrared Astrophysics Branch, Code 685, NASA/Goddard Space Flight Center, Greenbelt, MD 20771;
16Department of Physics, University of California at Berkeley, Berkeley, CA 94720
17European Southern Observatory, Karl Schwarzchild Strasse 2, D-8574 8 G¨ arching bei M¨ unchen, Ger-
of Physics,University ofOxford, OxfordOX13RH, England,UK;
19McMaster University, Hamilton, Ontario Canada L8S 4M1; email@example.com
– 3 –
The discovery of these new stars increases the number of known RCB stars in
the LMC to thirteen. We have also discovered four stars similar to the Galactic
variable DY Per. These stars decline much more slowly and are cooler than the
RCB stars. The absolute luminosities of the Galactic RCB stars are unknown
since there is no direct measurement of the distance to any Galactic RCB star.
Hence, the importance of the LMC RCB stars. We find a much larger range of
absolute magnitudes (MV = -2.5 to -5 mag) than inferred from the small pre-
MACHO sample of LMC RCB stars. It is likely that there is a temperature -
MV relationship with the cooler stars being intrinsically fainter. Cool (∼ 5000 K)
RCB stars are much more common than previously thought based on the Galactic
RCB star sample. Using the fairly complete sample of RCB stars discovered in
the MACHO fields, we have estimated the likely number of RCB stars in the
Galaxy to be ∼3,200. The SMC MACHO fields were also searched for RCB stars
but none were found.
Subject headings: Large Magellanic Cloud, R Coronae Borealis stars, Stellar
The R Coronae Borealis (RCB) stars are rare, hydrogen-deficient, carbon-rich super-
giants which undergo spectacular declines in brightness of up to 8 magnitudes at irregular
intervals as dust forms along the line of sight (Clayton 1996). Their rarity may stem from
the fact that they are in an extremely rapid phase of evolution toward white dwarfs. So
understanding the RCB stars is a key test for any theory which aims to explain hydrogen
deficiency in post-Asymptotic Giant Branch (AGB) stars. AGB and post-AGB stars are
the dominant formation sites for refractory grains subsequently injected into the interstellar
medium, and therefore they play an important role in any theory of dust condensation.
There are two major evolutionary models for the origin of RCB stars: the Double
Degenerate and the Final Helium Shell Flash (Iben, Tutukov, & Yungleson 1996a). The
former involves the merger of two white dwarfs, and the latter involves a white dwarf/evolved
Planetary Nebula (PN) central star which is blown up to supergiant size by a final helium
shell flash. In the final flash model, there is a close relationship between RCB stars and
PN. The connection between RCB stars and PN has recently become stronger, since the
central stars of three old PN’s (Sakurai’s Object, V605 Aql and FG Sge) have had observed
outbursts that transformed them from hot evolved central stars into cool giants with the
spectral properties of an RCB star (Kerber et al. 1999; Asplund et al. 1999; Clayton & De
– 4 –
Marco 1997; Gonzalez et al. 1998).
However, the absolute luminosities of the RCB stars are unknown. There is no direct
measurement of the distance to any Galactic RCB star (Alcock et al. 1996 and references
therein). A group of RCB stars were measured by HIPPARCOS but the data provided
only lower limits on their distances (Cottrell & Lawson 1998; Trimble & Kundu 1997). So
the only source of distances and absolute luminosities for the RCB stars is the LMC. The
distance to the LMC is fairly well determined, m-M = 18.4 mag (e.g., Nelson et al. 2000).
Until recently, only three RCB stars were known in the LMC (Feast 1972). On the basis of
this small sample of stars, an absolute magnitude range of MV = -4 to -5 is inferred. Alcock
et al. (1996) reported the discovery of two additional LMC RCB stars. These two stars were
both fainter, MV ∼ -3.5 but one of the two is a member of the subclass of hot RCB stars
and may not be comparable to the cooler stars.
This paper reports the results of a more extensive search of the MACHO database for
new RCB stars.
The MACHO Project (Alcock et al. 1992) is an astronomical survey experiment designed
to obtain multi-epoch, two-color CCD photometry of millions of stars in the LMC (also, the
Galactic bulge and SMC). The survey makes use of a dedicated 1.27m telescope at Mount
Stromlo, Australia and because of its southerly latitude is able to obtain observations of the
LMC year round (Hart et al. 1996). The camera built specifically for this project (Stubbs et
al. 1993) has a field of view of 0.5 square degrees which is achieved by imaging at prime focus.
Observations are obtained in two bandpasses simultaneously, using a dichroic beamsplitter
to direct the “blue” (∼4400-5900˚ A) and “red” (∼5900-7800˚ A) light onto 2x2 mosaics
of 2048x2048 Loral CCD’s. These bandpasses are referred to as VMACHO and RMACHO,
respectively. Images are obtained and read out simultaneously. The 15 µm pixel size maps
to 0.′′63 on the sky. The data were reduced using a profile-fitting photometry routine known as
SODOPHOT, derived from DoPHOT (Schecter, Mateo, & Saha 1993). This implementation
employs a single starlist generated from frames obtained in good seeing. The results reported
in this survey comprise only a fraction of the planned data acquisition of the MACHO project.
The MACHO data were acquired for 82 LMC fields covering approximately 40 square degrees
and were monitored for about 7 years from 1992 to 1999. Most of the data come from the
top-22 fields which contain approximately 9 million stars (Alcock et al. 1997a, 1999). These
– 5 –
data have been searched for variable stars and microlensing candidates and over 40,000
variables have been found, most newly discovered. The great majority of these fall into
four well known classes: there are approximately 25,000 very red semi-regular or irregular
variables, 1500 Cepheids, 8000 RR Lyraes, and 1200 eclipsing binaries (Cook et al. 1995).
Typically, the dataset for a given star covers a timespan of about 2700 days and contains
up to 1500 photometric measurements (multiple observations are obtained on a given night
whenever conditions allow). The output photometry contains flags indicating suspicion of
errors due to crowding, seeing, array defects, and radiation events.
The MACHO lightcurves for the RCB candidate stars, including all available data, are
shown in Figure 1. Tables containing all the MACHO photometric data for these stars are
given in the Appendix. HV 12842 lies outside the MACHO fields and so has no lightcurve.
Only data free from suspected errors are plotted and included in the tables. Typical photo-
metric uncertainties are in the range 1.5-2 %. The VMACHOand RMACHObandpasses have
been converted to Kron-Cousins (KC) V and R bandpasses using transformations determined
from the internal calibrations of the MACHO database (Alcock et al. 1999). Three stars
in the sample, 16.6541.22, 20.5036.12, and 21.7407.7 lie outside the top-22 fields which have
been photometrically calibrated. The V and R magnitudes for these fields were obtained by
bootstrapping from the top-22-field calibration and should be viewed with caution. Also,
18.3325.148, 20.5036.12, and 21.7407.7 are the three brightest stars in the sample and suffer
from possible saturation problems. In particular, the MACHO V-R colors for 21.7407.7 are
∼-0.2 but are actually ∼0.2 (Goldsmith et al. 1990). The (V −R)KCcolors for each star are
also plotted in Figure 1. The stars are listed in Table 1. Two designations are given for each
MACHO star, the MACHO name which includes the position of the star, and the standard
field.tile.sequence number which refers to a particular star in the database. Finding charts
for the stars are shown in Figure 2.
2.2. JHK Photometry
The Cerro Tololo Infrared Imager (CIRIM) uses a 256x256 HgCdTe NICMOS 3 array.
There were two runs in 1996 and 1999 on the CTIO 1.5m telescope. The data are listed
in Table 2. The typical 1-σ errors are 0.02-0.03 mag in the J-band and 0.04-0.05 mag in
the H- and K-bands. None of the data from the 1999 run are included because of their
large uncertainties. In addition, 2MASS photometry is now available for most of the sample.
These data are also listed in Table 2. The typical 1-σ 2MASS errors are 0.03 mag in all three
bands. The Julian Dates of the observations are also listed in Table 2.
– 6 –
Spectroscopic observations were obtained from 1995 to 1998. In 1995-1996, the spectra
were obtained with the Reticon photon-counting system on the image-tube spectrograph on
the SAAO 1.9m telescope at Sutherland, South Africa. The grating used gives a reciprocal
dispersion of 100˚ A mm−1and a resolution of approximately 4˚ A, giving a useful range of
about 3600-5200˚ A at the angle setting used. The spectrograph is a two-aperture instrument
recording the star and sky simultaneously. Normal operating procedure is to measure the
star through one aperture and then the other, so the sequence goes arc, star in A, arc, star
in B, arc. Each star is then wavelength calibrated by the two arcs on either side and the
results of star in A and B are added together after flat-field correction and sky subtraction.
Flux calibration is done by observing one standard star each night. The fluxes are given in
erg cm−2s−1˚ A−1. In 1997-1998, the spectrograph was adapted to take a SITe CCD chip.
The observations were taken using a grating with a reciprocal dispersion of 210˚ A mm−1and
a resolution of approximately 5˚ A, giving a useful range of about 3500-7600˚ A at the angle
Spectra have been obtained for all the stars in Table 1 except 6.6575.13 and 16.5641.22.
A spectrum of the latter star is shown in Bessell & Wood (1983). No spectrum exists for
6.6575.13 since it has been continuously in decline since 1993. A spectrum of the hot RCB
star, 11.8632.2507, is shown in Alcock et al. (1996). Further spectra are shown in Clayton
et al. (2001). The spectra of the remaining stars are shown in Figure 3. All of the spectra
were obtained when the stars were at or near maximum light. These spectra are sums of all
3. New RCB Stars in the LMC
From the night in 1795 when Edward Pigott first noticed that R CrB had apparently
disappeared from the sky, RCB stars have been characterized primarily on the basis of their
lightcurves. They are the only intrinsic variables that undergo sudden and severe drops
in brightness from their light maximum at irregular intervals. However, this definition has
resulted in many irregular variables with poor lightcurve coverage being identified as RCB
stars (Payne-Gaposchkin & Gaposchkin 1938). Spectroscopic confirmation has been used
to weed out non-RCB stars from the class. Many turn out to be symbiotic, cataclysmic
or semi-regular variables (Lawson & Cottrell 1990a). Much of this sorely needed spectro-
scopic work has been performed by Kilkenny and collaborators (Clayton 1996 and references
therein). However, if a well sampled lightcurve is available then an identification with the
RCB class may be made with fairly high confidence because of the distinctive nature of the
– 7 –
RCB declines. Following the definition of Payne-Gaposchkin & Gaposchkin (1938), a typical
RCB lightcurve has:
• uniform brightness at maximum which may last for months or years.
• A sudden drop in brightness of more than three magnitudes taking a few days or weeks.
• Recovery to maximum light, which is typically slower, taking months or years.
When spectra are obtained, we see in addition that the typical RCB star has:
• Weak or absent hydrogen lines and molecular bands (CH).20
• Strong carbon lines and molecular bands (CN, C2).
• Little or no13C.
Other observables of the typical RCB star are:
• Regular or semi-regular pulsations with ∆V of a few tenths of a magnitude and periods of
• An infrared excess.
• Effective temperature between 5000 and 7000 K. A small subclass is much hotter with
effective temperatures of about 20,000 K.
The first RCB star to be discovered in the LMC was HV 966 (W Men, 21.7407.7)
(Luyten 1927). He identified it as an RCB star on the basis of its irregular and sudden dips
in brightness. Much later, spectra confirming its resemblance to R CrB and its membership
in the LMC were obtained (Feast 1956; Rodgers 1970; Feast 1972). Subsequently, two other
stars, HV 5637 (Hodge, & Wright 1969) and HV 12842 (Payne-Gaposchkin 1971), were
identified as members of the RCB class on the basis of their lightcurves. Confirming spectra
were soon obtained of these stars (Feast 1972). A fourth star, HV 12671, was listed by
Payne-Gaposchkin (1971) as an RCB star. It is now thought to be a carbon-symbiotic star
(Allen 1980; Lawson et al. 1990). Two new RCB stars were previously discovered using the
MACHO database, HV 2671 (11.8632.2507) and 81.8394.1358 (Alcock et al. 1996).
The final database of MACHO variables for the top-22 fields was searched for stars which
underwent large sudden brightness variations. Candidates were selected from the thousands
of variable star lightcurves by selecting out those with large amplitude variations that were
not periodic. These lightcurves were then viewed by eye and candidates were selected as
having distinctive RCB lightcurve behavior.
20V854 Cen, one of the most active RCB stars, shows fairly strong Balmer lines and CH band (Kilkenny
& Marang 1989; Lawson & Cottrell 1989).
– 8 –
In addition, the MACHO lightcurves for stars listed as irregular variables of large
range by Payne-Gaposchkin (1971) were examined.
(18.3325.148) were found to be RCB stars. Stars listed by Hughes (1989) as having RCB-
type lightcurves were also checked. None of those lying in MACHO fields turned out to be
RCB stars. However, three other variables in the Hughes list are members of the MACHO
RCB star sample. Of the stars in our sample, three appear in the list of carbon stars in the
LMC compiled by Sanduleak & Phillip (1977). However, none appear in the carbon star
catalogs of Westerlund et al. (1978) or Blanco & McCarthy (1990).
HV 942 (6.6696.60) and HV 12524
In addition to the five RCB stars already known in the LMC, eight stars (6.6575.13,
6.6696.60, 12.10803.56, 16.5641.22, 18.3325.148, 79.5743.15, 80.6956.207, and 80.7559.28)
which show lightcurves with deep, sharp declines are clearly RCB stars. See Figure 1. Two
stars, 6.6575.13 and 6.6696.60 were independently discovered to be RCB stars by Wood &
Cohen (2001). As summarized in Table 3, these stars share most or all of the photometric
and spectroscopic criteria listed above for the typical RCB star. In particular, with the
exception of 18.3325.148, as shown in Figure 1, all of these stars show the unique sharp,
deep, irregular declines characteristic of RCB stars. This has been quantified in Table 3 as
dm/dt, the number of magnitudes per day that the star fades. The lightcurve for 18.3325.148
shows only the long recovery from a decline often seen in Galactic RCB stars. Subsequently,
spectra were obtained for all except 6.6575.13 showing that they are indeed RCB stars. The
star, 6.6575.13, entered a very deep decline early in the MACHO era and has never recovered
enough for a spectrum to be obtained. It is likely to be an RCB star based on its lightcurve
The star, 6.6696.60, joins HV 12842 and W Men as members of the warm (6000-7000
K) RCB stars showing only weak molecular bands. The others are similar to HV 5637 which
is typical of the cooler (5000 K) RCB stars which have much stronger molecular bands. See
Figure 3. A low dispersion spectrum of 16.5641.22 (HV 2379) was previously obtained and
is also very similar to HV 5637 (Bessell & Wood 1983). The spectra were examined for
evidence of hydrogen by looking at the Balmer lines and the G-band of CH at 4300˚ A. The
presence of13C was searched for in the isotopic bands of C2and CN. In particular, the Swan
bands,12C13C and13C13C near 4700 A, other C2bands in the 6000-6200˚ A region, and the
13CN band near 6250 A were examined. The results are summarized in Table 3.
Several other stars show irregular, fairly deep (2-3 mag) declines but fade much more
slowly than typical RCB stars. In their lightcurve behavior, these stars resemble the unusual
Galactic RCB star, DY Per (Alksnis 1994). This star has very deep (>4 mag) declines at
irregular intervals like an RCB star but the declines are very slow. The DY Per declines
appear much more symmetrical than the prototypical RCB decline which features a much
– 9 –
faster drop than rise. Further spectroscopic analysis has shown that DY Per is very cool,
Teff ∼3500 K (Keenan & Barnbaum 1997). This is significantly cooler than the coolest
known Galactic RCB stars, S Aps, WX CrA, and U Aqr which have estimated Teff∼5000
K (Lawson et al. 1990). Keenan & Barnbaum (1997) suggest that DY Per may be hydrogen
deficient. The G-band is fairly weak. The evidence for the abundance of isotopic carbon is
mixed. The isotopic Swan bands,12C13C and13C13C near 4700 A are clearly seen but the
13CN band near 6250 A is not. The LMC DY Per stars share these characteristics. Four
stars, 2.5871.1759, 10.3800.35, 15.10675.10, and 78.6460.7, show significant but slow declines
of at least 2 magnitudes. See Figure 1d. They also closely resemble DY Per spectroscopically.
See Figure 3c. The DY Per spectrum is from Barnbaum, Stone & Keenan (1996). Table 3
itemizes the major differences between the RCB and DY Per stars. The RCB declines are
deeper and they fade faster as shown in the dm/dt column of the table. The DY Per stars
show evidence for significant amounts of13C and they are cooler than the RCB stars. The
molecular bands in the cool RCB stars and the DY Per stars are of comparable strength but
the DY Per spectra are intrinsically much redder. The spectra of the DY Per stars resemble
R-type carbon stars (Barnbaum et al. 1996). Many carbon stars also show irregular small
(≤1 mag) declines. In addition, other stars produce dust such as carbon Miras and the V
Hya stars. But these stars also show large regular variations not seen in either the RCB or
DY Per stars (e.g., Feast et al. 1984; Lloyd Evans 1997). Until more extensive observations
and analysis are done, it is not clear whether the DY Per stars are related to either the RCB
stars or the carbon stars.
4. Individual Stars
Using SIMBAD, each star was checked for previous identifications. These are included
in Table 1. Previous observations from the literature for the sample stars are listed below.
This is the only star in the sample that lies in an area of the LMC not covered by
MACHO. It was first listed as an RCB star (mpg= 14.15-17.92 mag ) by Payne-Gaposchkin
(1971). Several declines have been noted (Morgan, Nandy, & Rao 1986; Lawson et al. 1990;
Lawson, Cottrell, & Pollard 1991). Coordinates are from the HST Guide Star Catalog. HV
12842 is possibly an IRAS source. In the Faint Source Catalog, F05447-6425, lies within
7′′of HV 12842. At 12µm, it is 0.09 ± 0.01 Jy. This is within a factor of 2 of the expected
IRAS brightness of a Galactic RCB star seen at the distance of the LMC. This star had a
– 10 –
median mpg=15.2 mag and ∆m = 2.5 mag in the early 1900’s (Hodge & Wright 1967 and
4.2. 20.5036.12 (HV 5637)
This star was first listed as an RCB star by Hodge & Wright (1969). They found that
HV 5637 (Vmax= 14.99 mag , Bmax= 16.19 mag) had one decline of ∆ B ≥ 2.36 mag around
JD 2425000. This star had a median mpg=16.5 mag and ∆m = 2.0 mag in the early 1900’s
(Hodge & Wright 1967 and references therein). It is listed as an RCB star (mpg= 16.38-18.20
mag) by Payne-Gaposchkin (1971). Butler (1978) noted small variations (∆V = 0.2 mag).
No further declines were noted during the seven years of MACHO coverage. See Figure 1.
4.3. 21.7407.7 (W Men)
This star was first identified as an RCB star by Luyten (1927). Several declines have
been noted (Milone 1975; Glass 1988; Lawson et al. 1990). This star is HV 966 which had
a median mpg=14.4 mag and ∆m = 1.2 mag in the early 1900’s (Hodge & Wright 1967 and
references therein). It is listed as an RCB star (mpg= 13.37-17.57 mag) by Payne-Gaposchkin
4.4. 11.8632.2507 (HV 2671)
This star had a median mpg=16.4 mag and ∆m = 1.8 mag in the early 1900’s (Hodge
& Wright 1967 and references therein). Kurochkin (1992) reports a maximum brightness of
B= 15.5 mag and one deep decline with B <19 mag (JD 2439849.9 and 2439852.75).
126.96.36.19996.60 (HV 942)
This star had a median mpg=15.8 mag and ∆m = 2.0 mag in the early 1900’s (Hodge
& Wright 1967 and references therein). It is listed as an irregular variable of large range
(mpg= 14.44-17.74 mag) by Payne-Gaposchkin (1971). This star is also possibly detected
by IRAS (Schwering 1989). As with HV 12842, the IRAS brightness is consistent with an
RCB at the distance of the LMC.
– 11 –
188.8.131.5241.22 (HV 2379)
This star had a median mpg=16.5 mag and ∆m = 1.8 mag in the early 1900’s (Hodge &
Wright 1967 and references therein). Wright & Hodge (1971) report that in 1958, HV 2379
was seen at B=17.6 and then was below the plate limit for 95 days. They also summarize
several hundred Harvard plates taken between 1896 and 1949 where the star varied between
16.2 and fainter than 18.6 at B. It is listed as a long period variable (mpg = 15.89-18.45
mag) by Payne-Gaposchkin (1971). Feast et al. (1984) suggest that HV 2379 is related to
the carbon Mira, R For, but the MACHO lightcurve, shows a typical irregular RCB-star
behavior with no sign of a Mira-type pulsation. This star is also possibly detected by IRAS
(Trams et al. 1999). As with HV 12842, the IRAS brightness is consistent with an RCB at
the distance of the LMC. HV 2379 was also observed with ISO (van Loon 1999).
4.7. 18.3325.148 (HV 12524)
This star had a median mpg=15.9 mag and ∆m = 0.6 mag in the early 1900’s (Hodge &
Wright 1967 and references therein). It is listed as an irregular variable of large range (mpg
= 15.27-17.12mag ) by Payne-Gaposchkin (1971).
This star is also SHV 0523154-690100 (< mI> = 15.36 mag, ∆mI= 1.16 mag) (Hughes
This star is also SHV 0526537-690959 (< mI> = 14.74 mag, ∆mI= 1.24 mag) (Hughes
This star is also SHV 0546548-710843 (< mI> = 13.90 mag, ∆mI= 1.14 mag) (Hughes
– 12 –
Most of the sample has been observed one or more times in the near-IR. We have plotted
the J-H vs. H-K colors in Figure 4. The typical RCB star colors evolve as dust forms and
then disperses. Feast (1997) shows the behavior of a large sample of Galactic RCB stars.
The colors evolve from those typical of the RCB star photosphere toward those of a dust
shell of ∼900 K. The colors for a combination of a 5500 K star and a 900 K shell are plotted
in Figure 4. The LMC RCB star colors are consistent with the behavior of the Galactic RCB
stars. With the exception of W Men, HV 2379, and HV 12842 (Bessell & Wood 1983; Glass,
Lawson, & Laney 1994), each of the LMC stars has been observed only once or twice at a
random point in its lightcurve. So, when plotted together, the ensemble of stars includes
observations at maximum light and in declines. Together these observations map out an
RCB star color evolution similar to that seen for the Galactic stars (Feast 1997). Since there
are a range of photospheric and shell temperatures, Figure 4 shows more scatter than the
plot of individual stars as shown by Feast (1997). Another interesting feature of Figure 4
is that the DY Per stars are well separated from the RCB stars and show colors typical
of carbon stars (Westerlund et al. 1991). The two DY Per stars plotted were observed at
Most or possibly all of the RCB stars are pulsators (Lawson et al. 1990). As listed in
Table 3 and seen in Figure 1, most of the LMC RCB stars pulsate as well. We inspected the
lightcurves for “dormant” sections - places where the lightcurve was within a magnitude or
two of maximum brightness and where, if it was changing, it was increasing slowly with no
obvious dust dropouts. The long-term trend in the dormant sections was subtracted, leaving
just the shorter timescale oscillations. The baseline-subtracted, dormant sections of the V-
band lightcurves was run through the Discrete Fourier Transform Fortran code of Roberts,
Lehar, & Dreher (1987). The default frequency spacing was used, with a maximum period
of one per day. In cases where there was an obvious signal, the period corresponding to the
frequency with the highest power is reported. In most instances, the frequency spacing was
about 5E-4 per day. Among the RCB stars, we were able to extract periods for 18.3325.148
(83.8 d), 11.8632.2507 (60.0 d), 12.10803.56 (50.5 d), 21.7407.7 (240 d, questionable signif-
icance), and 79.5743.15 (53.3 d). For the DY Per stars, we extracted periods for 78.6460.7
(208 d), 2.5871.1759 (138 d), 10.3800.35 (206 d),and 15.10675.10 (116 d). Theses two classes
differ also in their typical pulsation period. The RCB stars in the LMC like their Galactic
counterparts have periods between 50 and 84 days while the periods of the DY Per stars lie
– 13 –
between 100 and 210 days. These differences are at least qualitatively in agreement with the
results of theoretical models of pulsations in RCB stars (Weiss 1987). Theoretical periods
for ‘Case 1’ of Weiss for M=0.825 M⊙show ∼40 d for Teff∼7000 K, ∼100 d for Teff∼5000
K, and ∼300 d for Teff∼4000 K. Figure 32 of Lawson et al. (1990) shows the Galactic RCB
stars plotted with Weiss ‘Case 1’ for comparison.
In a color-magnitude diagram (CMD), most of the of the RCB stars lie within the
instability strip defined by the MACHO-discovered BL Her, W Virs, and RV Tauri stars
extrapolated to higher luminosities (Alcock et al. 2000). These LMC variables are believed
to be low-mass Population II stars. In the CMD, the one hot RCB (11.8632.2507) lies
blueward of the blue edge of the instability strip as defined by the bluest BL Her and W Vir
stars. The DY Per stars lie in the same region of the CMD as carbon-rich red variables, and
are brighter/redder than the other observed sequences of red variables. With the exception
of 11.8632.2507, the RCB and DY Per stars form an extension of the W Vir and BL Her
star W-logP relation, where W = V - 2.0*(V-R), to higher luminosities and longer periods,
although there may be a “roll over” at long periods.
7. Absolute Luminosity of RCB Stars
The Galactic foreground reddening varies significantly across the face of the LMC rang-
ing from E(B−V)Gal=0.00 to 0.17 mag (e.g., Schwering & Israel 1991; Oestreicher, Gocher-
mann, & Schmidt-Kaler 1995). Schwering & Israel (1991) estimate that most of the LMC
bar, where the MACHO fields are centered, has a Galactic foreground reddening of E(B-
V)Gal=0.06-0.08. The dust inside the LMC is patchy also but a good estimate of the
reddening due to dust inside the LMC foreground to the RCB stars is E(B-V)LMC ∼0.1
(Oestreicher & Schmidt-Kaler 1996). There will also be a small amount (E(B-V)∼0.1 mag)
of circumstellar reddening around each RCB star even at maximum light. We will ignore
that component. The total reddening due to Galactic foreground and LMC intrinsic dust is
E(B-V)∼0.17 mag or AV ∼0.5 mag.
The RCB and DY Per stars are plotted in Figure 5 in a V vs. V-R CMD. The values of
V and V-R plotted are those measured for each star at maximum light. A reddening vector
is also plotted. In addition, a line is plotted representing the change in V and V-R with
temperature assuming LV ∝ T4with stellar radius held fixed. Temperatures and colors
are assumed to be those for normal supergiants (Cox 2000). On the basis of the three pre-
MACHO RCB stars, Feast (1979) noted that the cool RCB star, HV 5637 is significantly
fainter than HV 12842 and W Men. He suggested that there might be a relationship between
absolute magnitude and effective temperature for the RCB stars. The new observations
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reported here reinforce this suggestion. The intrinsically brightest RCB stars at V are the
warm (∼7000 K) stars and the faintest are the cool (∼5000 K) stars. There is a much wider
range of absolute luminosity in the RCB stars than given by the canonical, MV = -4 to -5
mag. The foreground reddening of individual stars is somewhat uncertain but the brightest
RCB stars have MV ∼-5 mag and the faintest are about MV ∼-2.5 mag. The DY Per stars
are cooler and fainter still, with a maximum absolute brightness of MV ∼-2.5 mag.
It seems likely that 6.6696.60 is fairly heavily reddened. From Figure 3a, it can be
seen that the spectrum of 6.6696.60 closely resembles W Men and HV 12842. Therefore,
it is likely that the effective temperatures and colors are similar for these three stars. For
6.6696.60, Vmax= 15.0 and (V-R)max=0.6 compared to Vmax= 13.8 and (V-R)max=0.2 for
the other two stars. The simplest explanation is that some combination of circumstellar and
interstellar dust in front of 6.6696.60 is responsible. The high value of reddening implied,
E(B-V)∼0.8 is unlikely to be primarily interstellar reddening. More likely, a large portion
of this reddening is circumstellar. From the lightcurve of 6.6696.60, seen in Figure 1b, it is
quite possible that the star was never at maximum light during the the seven years of the
MACHO data. This is supported by earlier photometry of this star, previously discovered
as HV 942, which found the maximum brightness to be mpg=14.4 (Payne-Gaposchkin 1971).
This corresponds to B∼14.3 mag. So assuming the same B-V color as W Men, then 6.6696.60
would have V∼13.85 mag which is the same as W Men and HV 12842 at maximum light.
Similarly, 10.3800.35 maybe more reddened than the other DY per stars.
8. The Population of RCB stars
The MACHO LMC sample of RCB stars allows us to attempt something not possible
in the Milky Way, which is to estimate the total population of RCB stars in a galaxy. Figure
6 shows an image of the LMC with the locations of the RCB and DY Per stars plotted. As
mentioned in the introduction there are two suggested evolutionary paths leading to the RCB
stars, the Double Degenerate and the Final Helium Shell Flash (Iben et al. 1996a). Both
these suggestions imply that the RCB stars are an old population. The distribution of these
stars on the sky and their radial velocities give clues to their origin. The space distribution
and radial velocities of the Milky Way RCB stars are similar to those of distant planetary
nebulae implying that these stars may be a bulge population (Drilling 1986). However, the
scale height is 400 pc for the RCB stars assuming MBol=-5 (Iben and Tutukov 1985). So the
RCB stars may be more like old disk/Population I stars. Either of the evolutionary scenarios
predicts significantly more than the ∼30 RCB stars which are known in the Milky Way. For
instance, Webbink (1984) estimates a population of ∼1000 RCB stars making reasonable
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assumptions for the Double Degenerate scenario. However, it should be pointed out that
Sch¨ onberner (1986) suggests that the estimated lifetimes for both scenarios are too short to
account for the number of RCB stars. Iben, Tutukov, & Yungleson (1996b) estimate that
final flashes could produce 30-2000 RCB stars at any given time depending on the core mass.
They estimate that the Double Degenerate or binary merger scenario could produce ∼300
Most of the Galactic RCB stars were discovered early in the century on the Harvard
Observatory plate survey. The detection limit was about B= 11.8 mag on these blue sensitive
plates. Stars near or below this limit, reddened stars and intrinsically red stars would have
been missed (Lawson & Cottrell 1990b; Lawson et al. 1990). The results for the LMC RCB
stars imply that many Galactic RCB stars are significantly fainter than previously believed,
making them even less likely to have been detected.
Using evolutionary models of the pulsation periods of RCB stars, one can estimate the
crossing time as a function of temperature (Lawson et al. 1990 and references therein). The
model results imply relative populations of RCB stars with Teff = 5000, 6000 and 7000 K
of 30:5:1. Most of the known RCB stars in the Galaxy fall in the warmest subgroup. The
observed population ratio is 1:1:4. Lawson et al. (1990) suggest that the apparent lack of
cool RCB stars is a selection effect. Lawson & Cottrell (1990b) estimate that if all RCB
stars have MV ∼-5, then the real number would be 200-300 or even larger if the number of
cool stars equaled the number of warm stars. The results of this study for the LMC imply
that the ratio is 7:2:1 which is consistent with the theoretical ratio given above. If this is the
intrinsic ratio in the Galaxy also, then there are ∼ 103RCB stars in the entire Milky Way,
most yet to be discovered.
We can estimate the number of RCB stars in the LMC from the results of the MACHO
sample. The MACHO lightcurves for most stars have extremely good coverage for ∼2500
days spanning the years 1993 through 1999. This is long enough to catch most but not
all RCB stars in decline. RCB stars are true irregular variables. The historical lightcurve
of R CrB itself, which now stretches back over two hundred years, shows that it has gone
up to 10 years with no decline and at other times has had several declines in one year
(Mattei, Waagen, & Foster 1991). The characteristic time between declines is 1000-2000
days (Clayton, Whitney, & Mattei 1993). So any search over a short time period will detect
only a fraction of the RCB stars. HV 5637 is an LMC RCB star but it is relatively inactive
(Hodge & Wright 1969). It shows no evidence for a decline during the 7 years of MACHO
coverage. One of the Galactic RCB stars, XX Cam, shows similar behavior. It has had only
one recorded decline this century (Bidelman 1948; Yuin 1948). The AAVSO monitors 31
RCB stars including R CrB, V854 Cen and XX Cam. Over the same timespan covered by