Contamination of RR Lyrae stars from Binary Evolution Pulsators
A Binary Evolution Pulsator (BEP) is a low-mass (0.26Mꙩ ) member of a binary system, which pulsates as a result of a former mass transfer to its companion. The BEP mimics RR Lyrae-type pulsations, but has completely different internal structure and evolution history. Although there is only one known...
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| Cite this: | Contamination of RR Lyrae stars from Binary Evolution Pulsators / P. Karczmarek // Advances in Astronomy and Space Physics. — 2015. — Т. 5., вип. 1. — С. 24-28. — Бібліогр.: 7 назв. — англ. |
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| citation_txt | Contamination of RR Lyrae stars from Binary Evolution Pulsators / P. Karczmarek // Advances in Astronomy and Space Physics. — 2015. — Т. 5., вип. 1. — С. 24-28. — Бібліогр.: 7 назв. — англ. |
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| description | A Binary Evolution Pulsator (BEP) is a low-mass (0.26Mꙩ ) member of a binary system, which pulsates as a result of a former mass transfer to its companion. The BEP mimics RR Lyrae-type pulsations, but has completely different internal structure and evolution history. Although there is only one known BEP (OGLE-BLG-RRLYR-02792), it has been estimated that approximately 0.2% of objects classified as RR Lyrae stars can be undetected Binary Evolution Pulsators. In the present work, this contamination value is re-evaluated using the population synthesis method. The output falls inside a range of values dependent on tuning the parameters in the StarTrack code, and varies from 0.06% to 0.43%
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Contamination of RR Lyrae stars
from Binary Evolution Pulsators
P.Karczmarek
∗
Advances in Astronomy and Space Physics, 5, 24-28 (2015)
© P.Karczmarek, 2015
Warsaw University Observatory, Al. Ujazdowskie 4, 00-478, Warsaw, Poland
A Binary Evolution Pulsator (BEP) is a low-mass (0.26M�) member of a binary system, which pulsates as a
result of a former mass transfer to its companion. The BEP mimics RR Lyrae-type pulsations, but has completely
di�erent internal structure and evolution history. Although there is only one known BEP (OGLE-BLG-RRLYR-
02792), it has been estimated that approximately 0.2% of objects classi�ed as RR Lyrae stars can be undetected
Binary Evolution Pulsators. In the present work, this contamination value is re-evaluated using the population
synthesis method. The output falls inside a range of values dependent on tuning the parameters in the StarTrack
code, and varies from 0.06% to 0.43%.
Key words: methods: numerical � variables: RR Lyrae � binaries
introduction
RR Lyrae (RRL) stars reside in a small area of
the instability strip (IS) in the Hertzsprung-Russel
diagram, limited by e�ective temperature and lumi-
nosity given below [2]:
5000K < Teff,RR < 7400K,
16L� < LRR < 100L�.
(1)
Stellar evolution models �nd RRL mass in a narrow
range 0.6 − 0.8M�, which corresponds to RRL age
of 10 − 12Gyr. These properties make RR Lyrae
pulsators precise tools for determining the age and
distance to the hosting galaxies and clusters.
With a growing number of pulsating variables
found in binary systems, it is surprising that no
RR Lyrae binary has been reported so far. The dis-
covery of a RR Lyr-type pulsator in a binary sys-
tem OGLE-BLG-RRLYR-02792 [6] was even more
surprising, as the pulsator's mass was only 0.26M�
� clearly too small for a bona �de RR Lyrae star.
Thus, a RRL-type pulsator is assumed to be the
product of a mass transfer (MT) episode, during
which the initially more massive component removed
most of its envelope and exposed the degenerated he-
lium core, placing itself in a narrow range of e�ec-
tive temperatures and luminosities characteristic for
RR Lyrae IS. The mass transfer was the key stage in
the binary evolution, producing a pulsator with such
a small mass within the Hubble time. Because of
its peculiar evolution, the pulsator earned the name
BEP (Binary Evolution Pulsator).
Preliminarily estimations suggest that approxi-
mately 0.2% of known RR Lyrae stars are actu-
ally BEPs [6] which cannot be distinguished from
bona �de RRLs due to the lack of binarity indica-
tions, e. g. eclipses. This contamination value im-
plies that BEPs should be scarce enough to not a�ect
any statistics-based calculations involving RR Lyrae
stars, like age or distance determinations. To gain
con�dence, the contamination value is revised with
use of a synthesis population code StarTrack [1].
The code, equipped with up-to-date stellar formulae
governing both single and binary evolution, proceeds
the evolution of a large number of binaries (one at
a time), and deliver statistical occurrence of objects
of interest (with predetermined set of parameters) in
comparison with the total sample. First results from
StarTrack, showing various evolutionary tracks for
simulated BEPs, were introduced by Karczmarek in
2012 [4]. In this work, the BEP contamination value
is presented as strongly dependent on the parame-
ters governing MT in the StarTrack code. The dis-
cussion of this result points the direction of further
study devoted to BEP.
StarTrack calculations
The percentage of contamination of RRL stars
from BEPs is given by:
C =
NBEP
NRRL
× 100%, (2)
where NBEP and NRRL are the number of BEP and
RR Lyrae stars found in a given sample, respectively.
For this study, the size of the sample was 105 objects
within a wide mass range 0.3 − 150.0M�, and the
probability of drawing the star of a massm was given
∗pkarczmarek@astrouw.edu.pl
24
Advances in Astronomy and Space Physics P.Karczmarek
by the Initial Mass Function (IMF) [5]:
ξ(m) =
0 if m < 0.1M�,
0.29056m−1.3 if 0.1M� ≤ m < 0.5M�,
0.15571m−2.2 if 0.5M� ≤ m < 1.0M�,
0.15571m−2.7 if m ≥ 1.0M�.
(3)
As Pietrzy«ski stated, 20% of stars with initial
masses in range 0.8− 0.9M� can become RR Lyrae
stars [6]. In this work, the number of RR Lyrae stars,
NRRL, was found by �ltering from a total sample
only 20% of objects with initial masses in a range
0.8− 0.9M�.
The procedure of choosing BEP from a given sam-
ple was more complicated, because it accounted for
not one, but four parameters: initial mass of primary
component m (in units of M�), initial mass ratio q,
initial eccentricity e, and initial separation a (in units
of R�)
1. Noteworthy, 50% of all systems are con-
sidered to be binary or multiple systems. Because
BEP is always a product of binary evolution, the
probability of its occurrence needs to be reduced by
50%, adequately to the occurrence of binary systems
among all systems. Finally, noting that BEP crosses
the Instability Strip (IS) a hundred times faster than
RR Lyrae star, one should expect to detect one hun-
dred times fewer BEP events, than if the IS crossing
times for BEP and RRL were similar. Above consid-
erations are summarized in the following formula:
NBEP = ST (m, q, e, a)× 0.5× 0.01,
where ST (m, q, e, a) represents the StarTrack out-
put, i. e. the number of BEPs found in the sample of
105 binaries.
A simple �lter was implemented to StarTrack
code in order to �nd BEPs in the total sample. The
BEP object was detected if at any stage of binary
evolution all of the following conditions were simul-
taneously satis�ed: (i) the mass of an object was less
than 0.45M�, (ii) the object was evolved at least to
Red Giant stage, (iii) the e�ective temperature and
the luminosity were within the range of values given
by Eq. (1), and (iv) the MT was not ongoing. Fig-
ure 1 shows a mesh of BEPs occurrence as a function
of the initial mass of more massive component A,
M0,A, and mass ratio q = M0,A/M0,B for di�erent
initial periods from 2 to 20 days. The eccentricity
was assumed zero at all times (this was justi�ed, be-
cause the system needs to circularize its orbit prior
to the onset of MT).
Mass transfer can proceed in general in two forms:
stable MT in the form of the Roche Lobe Over Flow
(RLOF) or unstable MT in the form of an instant
phase of Common Envelope (CE). The BEP favours
the stable MT scenario, i. e. the simulations fail
to recover the BEP system assuming CE scenario.
Thus, the algorithm governing MT in the StarTrack
code was tuned to choose RLOF over CE scenario
whenever the status of MT was unclear. The out-
put mesh of BEP occurrence produced by the new
version of StarTrack code is shown in Figure 2. The
comparison of both �gures indicates that more BEPs
with larger mass ratio (up to q = 3) are produced
when �stable MT� option is on.
Finally, the synthesis population was run for both
versions of the StarTrack code. Each time a BEP
was found in the binary, the parameters of this sys-
tem were saved, and the total sum of BEPs in the
sample was increased by one. In this way, two di�er-
ent databases were created and two di�erent contam-
ination numbers were derived � for the original ver-
sion and for the �stable MT� version of the ST code.
The results, especially the contamination number,
are presented in the next section.
results and conclusions
The contamination ratio of RRL stars from BEPs
was calculated from Eq. (2). The number of RRLs
and the number of BEPs were found independently
in a total sample of 105 elements, in a manner de-
scribed in a previous section. In the case of BEP, the
population synthesis was performed for two scenarios
of mass transfer (original MT versus �stable MT� ver-
sion). The contamination ratio C is 0.06% in the case
of the original treating of MT, and 0.43% in the case
of enhanced stability of MT. These values de�ne the
range of the contamination ratio, and Pietrzy«ski's
value 0.2% [6] lies well within this range. It should be
noted that the choice of eccentricity distribution [3]
does not a�ect neither the number of encountered
BEPs nor the characteristics of found BEPs.
A more careful investigation of selected BEP
properties is presented in Figures 3, 4, and 5. Gen-
eral conclusions drawn from these histograms are as
follows. The initial mass of BEP progenitor can be
as high as 4.5M� for both versions of MT treatment
and for both eccentricity distributions, although the
most preferred mass range for BEP occurrence is
approximately 1.7M� and 1.0M� for original and
�stable MT� versions, respectively. BEP masses clus-
ter around values 0.26− 0.27M�, but more massive
cases are also visible � they have higher luminosities
(close to the upper limit from Eq. (1)) and reside in
binaries with wider orbits. Indeed, Figure 5 shows
two distinct peaks for BEP orbital period distribu-
tions, with the smaller peak corresponding to more
massive and more luminous BEPs. This suggest that
BEPs may contaminate not only RR Lyrae stars but
1Initial parameters were drawn from probability distributions as follows: (i) m was drawn from the IMF as given in Eq. (3) over the
same mass range [0.3, 150.0], (ii) q was drawn from uniform distribution over a range [0, 1], (iii) e was drown from two di�erent probability
distributions: f1(e) = 2e, f2(e) = N (0.26, 0.142) [3]; the comparison of outputs for these two distributions is presented in the next section,
(vi) a was drawn from uniform distribution of log10(a) over a range [amin, 10
5]; amin denotes the smallest separation without initial merging
of components. See [1] for details.
25
Advances in Astronomy and Space Physics P.Karczmarek
Fig. 1: The mesh of occurance of Binary Evolution Pulsator (BEP) depending on the initial mass of more massive
component A, M0,A, and mass ratio q = M0,A/M0,B of components in a binary system for four di�erent ranges of
initial periods, from 2d to 20 d, and assuming circular orbits (e = 0). If at any time of a system's evolution, the
properties of a component matched the BEP characteristics (see text for details), this component was considered as
BEP. This simulation used the StarTrack code with the original treatment of mass transfer.
also other pulsating variables up in the Instability
Strip, like type II Cepheids, but the evaluation of
such statement is beyond the scope of this paper.
The obvious and the most important uncertainty
of the contamination ratio C is the treating of mass
transfer. Further evaluation of the mass transfer
phase is crucial to obtain the precise value of contam-
ination ratio. In this work, the range of contamina-
tion values was established for two di�erent methods
of MT treatment, yielding C ∈ [0.06%, 0.43%]. The
upper limit 0.43% is still negligible in the analysis
of large sample RR Lyrae stars, e. g. for determin-
ing clusters' age or distance, as predicted earlier [6].
Nevertheless, the presence of objects with such pe-
culiar properties points an interesting direction of
further studying for pulsation theory [7].
acknowledgement
It is a pleasure to thank G.Pietrzy«ski for sub-
stantive guidance to this project. I am gratefull to
K.Belczynski for sharing the StarTrack code and for
many useful and valuable instructions. This research
is supported by the Polish National Science Centre
grant PRELUDIUM 2012/07/N/ST9/04246.
references
[1] BelczynskiK., KalogeraV., Rasio F.A. et al. 2008, ApJS,
174, 223
[2] BonoG., CaputoF., Cassisi S., IncerpiR. & MarconiM.
1997, AJ, 483, 811
[3] DuquennoyA. & MayorM. 1991, A&A, 248, 485
[4] KarczmarekP. 2012, Advances in Astronomy and Space
Physics, 2, 135
[5] KroupaP., ToutC.A. & GilmoreG. 1993, MNRAS, 262,
545
[6] Pietrzy«skiG., Thompson I. B., GierenW. et al. 2012, Na-
ture, 484, 75
[7] SmolecR., Pietrzy«skiG., GraczykD. et al. 2013, MN-
RAS, 428, 3034
26
Advances in Astronomy and Space Physics P.Karczmarek
Fig. 2: The mesh of occurance of Binary Evolution Pulsator (BEP) depending on the initial mass of more massive
component A, M0,A, and mass ratio q = M0,A/M0,B of components in a binary system for four di�erent ranges of
initial periods, from 2d to 20 d, and assuming circular orbits (e = 0). If at any time of a system's evolution, the
properties of a component matched the BEP characteristics (see text for details), this component was considered as
BEP. This simulation used the StarTrack code with the enhanced stability of mass transfer.
27
Advances in Astronomy and Space Physics P.Karczmarek
Fig. 3: Distributions of the initial mass of BEP progenitor for two initial eccentricity functions; left : original MT,
right : �stable MT�.
Fig. 4: Distributions of the BEP mass for two initial eccentricity functions; left : original MT, right : �stable MT�.
Fig. 5: Distributions of the orbital period of a binary with BEP component for two initial eccentricity functions; left :
original MT, right : �stable MT�.
28
|
| id | nasplib_isofts_kiev_ua-123456789-119821 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 2227-1481 |
| language | English |
| last_indexed | 2025-12-07T18:33:24Z |
| publishDate | 2015 |
| publisher | Головна астрономічна обсерваторія НАН України |
| record_format | dspace |
| spelling | Karczmarek, P. 2017-06-09T20:49:49Z 2017-06-09T20:49:49Z 2015 Contamination of RR Lyrae stars from Binary Evolution Pulsators / P. Karczmarek // Advances in Astronomy and Space Physics. — 2015. — Т. 5., вип. 1. — С. 24-28. — Бібліогр.: 7 назв. — англ. 2227-1481 DOI: 10.17721/2227-1481.5.24-28 https://nasplib.isofts.kiev.ua/handle/123456789/119821 A Binary Evolution Pulsator (BEP) is a low-mass (0.26Mꙩ ) member of a binary system, which pulsates as a result of a former mass transfer to its companion. The BEP mimics RR Lyrae-type pulsations, but has completely different internal structure and evolution history. Although there is only one known BEP (OGLE-BLG-RRLYR-02792), it has been estimated that approximately 0.2% of objects classified as RR Lyrae stars can be undetected Binary Evolution Pulsators. In the present work, this contamination value is re-evaluated using the population synthesis method. The output falls inside a range of values dependent on tuning the parameters in the StarTrack code, and varies from 0.06% to 0.43% It is a pleasure to thank G. Pietrzy«ski for substantive guidance to this project. I am gratefull to K. Belczynski for sharing the StarTrack code and for many useful and valuable instructions. This research is supported by the Polish National Science Centre grant PRELUDIUM 2012/07/N/ST9/04246. en Головна астрономічна обсерваторія НАН України Advances in Astronomy and Space Physics Contamination of RR Lyrae stars from Binary Evolution Pulsators Article published earlier |
| spellingShingle | Contamination of RR Lyrae stars from Binary Evolution Pulsators Karczmarek, P. |
| title | Contamination of RR Lyrae stars from Binary Evolution Pulsators |
| title_full | Contamination of RR Lyrae stars from Binary Evolution Pulsators |
| title_fullStr | Contamination of RR Lyrae stars from Binary Evolution Pulsators |
| title_full_unstemmed | Contamination of RR Lyrae stars from Binary Evolution Pulsators |
| title_short | Contamination of RR Lyrae stars from Binary Evolution Pulsators |
| title_sort | contamination of rr lyrae stars from binary evolution pulsators |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119821 |
| work_keys_str_mv | AT karczmarekp contaminationofrrlyraestarsfrombinaryevolutionpulsators |