Revisiting binary stars in population synthesis models
aa r X i v : . [ a s t r o - ph . C O ] F e b Mon. Not. R. Astron. Soc. , 1–13 (2013) Printed 1 October 2018 (MN L A TEX style file v2.2)
Revisiting binary stars in population synthesis models
Fabiola Hern´andez-P´erez , ⋆ and Gustavo Bruzual A. Centro de Investigaciones de Astronom´ıa, CIDA, Av. Alberto Carnevalli, M´erida, Venezuela. A.P. 264, C.P. 5101 Postgrado de F´ısica Fundamental, Universidad de Los Andes, M´erida, Venezuela Centro de Radioastronom´ıa y Astrof´ısica, CRyA, UNAM, Campus Morelia, Michoac´an. M´exico. A.P. 3-72, C.P.58089
Accepted 2013 February 22. Received 2013 February 22; in original form 2012 December 20
ABSTRACT
We report results of a population synthesis model that follows the evolution ofsingle and binary stars. In this model we include the 2HeWD merger channel,suggested by Han et al. (2002), for the formation of EHB stars. The physicalparameters of the resulting EHB stars are derived from the BaSTI database,and are thus realistic and observationally supported. The predictions of thismodel are in good agreement with traditional population synthesis models,except when the spectrum of the stellar population is dominated by binarystars or their products, e.g., EHB stars in the UV of ETGs. We reproducesuccessfully the observed CMD and SED of the metal rich open cluster NGC6791. The stellar population in this cluster may be archetypal of the stellarpopulation in ETGs that show the UVX phenomenon. Our models should beappropriate to study the UV upturn in ETGs.
Key words: galaxies: elliptical and lenticular – ultraviolet: galaxies – stars :binaries – stars: horizontal branch
Stellar population synthesis models are a useful tool tointerpret the spectrum and colours of the light emit-ted by galaxies, as well as the properties of resolvedstellar populations in the colour-magnitude diagram(CMD). Crucial ingredients for these models are com-plete sets of evolutionary tracks that describe in detailthe time dependence of the physical properties of starsof different initial mass and chemical composition inthe Hertzsprung-Russell diagram (HRD). Equally com-plete spectral libraries are needed to compute the spec-trophotometric properties of the stars at each positionin the HRD. Weighting the stellar spectrum by the num-ber of stars at each of these positions at any giventime, we obtain the integrated spectrum of the stellarpopulation at this age. The number of stars of eachmass born whenever there is a star formation eventis given by the initial mass function (IMF), and themass of gas transformed into stars as a function of timein each of these events is provided by the star forma- ⋆ E-mail: [email protected] tion rate (SFR). See, e.g., Fioc & Rocca-Volmerange(1997), Bruzual & Charlot (2003), hereafter BC03, andMaraston (2005) for details.Despite considerable progress in recent years inboth the quality and quantity of the ingredients avail-able to the population synthesis modelers, i.e., stellartracks and spectra, these models still suffer from limi-tations in some specific regimes. In general, the prob-lems arise from our poor understanding of short-livedand/or not well characterized phases of stellar evolution,e.g., the thermally pulsing asymptotic giant branch (TP-AGB) and the extreme horizontal branch (EHB). Thesestars are relatively bright and contribute considerablyto the total luminosity of a simple stellar population(SSP). Thanks to the work of P. Marigo and collabora-tors (Marigo et al. 2008), we now have a better under-standing of TP-AGB stars of intermediate mass. Thesestars contribute at least 50% of the near infrared (NIR)light in a 1-2 Gyr old SSP (Bruzual et al. 2013).Progress has not reached as far in the other sideof the spectrum. Stellar evolution models explain natu-rally the existence of canonical horizontal branch (HB)stars, but the formation mechanism and the evolution- c (cid:13) F. Hern´andez-P´erez and G. Bruzual ary path of EHB stars is not well understood. EHBstars, being less luminous but hotter than canonicalHB stars, are almost invisible in the optical range, butcontribute significantly in the ultraviolet (UV), espe-cially in old stellar populations. Even though we do notunderstand well how EHB stars form (for many yearsthese stars were hypothetical), the observational fact isthat they have been observed in many open clusters(Kaluzny & Udalski 1992), globular clusters (Catelan2009), and nearby galaxies like M32 (Brown et al. 2000).See Catelan (2009) for a review of open problems andthe status of observations of EHB stars.It has long been thought that EHB stars are re-sponsible of the UV upturn phenomenon observed inthe spectrum of early type galaxies (ETGs). This in-crement in the flux emitted shortward of 2000 ˚A, alsoknown as UV excess (UVX), was first detected in ETGsby Code & Welch (1979). Since then, its origin has beena topic of debate. Carter et al. (2011), Bureau et al.(2011), and Smith, Lucey & Carter (2012) have shownbeyond doubt that the UV upturn is present in passivelyevolving galaxies with no sign of recent star formation.Thus, the UV upturn must arise from evolved stars, andnot from residual star formation. Were the UV excessproduced by young stars, it should show signs of evo-lution, e.g. the temperature of the UV spectrum shouldevolve in time. This is not supported by observationsof ETGs (Smith et al. 2012; Carter et al. 2011). It isthus fundamental to include properly the evolution ofEHB stars in population synthesis models that describeETGs.Several mechanisms have been proposed for the ori-gin of EHB stars. Single star evolution provides one suchmechanism. When a low mass star ascends the red giantbranch (RGB), its evolution is governed by the mass ofthe stellar envelope. If the mass loss rate is low, the starforms a deep and optically thick envelope, and, when theHe flash occurs, the star reaches the HB. In high metalli-city and enhanced He abundance stars, mass loss is moreeffective and the star may loose all, or nearly all, of itsenvelope. The star then becomes bluer and fainter, andreaches the hottest region of the HB, the so called EHB.RGB stars of all metallicities with envelope mass < . M ⊙ evolve into the EHB (Dorman, Rood & O‘Connel1993). The EHB evolutionary phase is short-lived ( ∼ yr) (Pietrinferni et al. 2004). However, the number ofexpected EHB stars rises with age. This suggests that ifthe UV upturn is related to the presence of EHB stars,the strength of the upturn should increase with metalli-city and age (Smith et al. 2012).The evolution of binary stars leads naturally to theformation of EHB stars. Han et al. (2002, 2003) haveshown that there are three channels by which interact-ing binaries may form EHB stars, referred to as hotsubdwarf stars in their papers: ( a) the stable Rocheoverflow (RLOF) channel, which results in the forma- tion of hot subdwarf binaries with long orbital peri-ods, ( b) the common envelope (CE) ejection channel,which results in the formation of hot subdwarf binarieswith short orbital periods, and ( c) the merger of twoHe white dwarfs (2HeWD) to form a single hot sub-dwarf star. In the RLOF channel, the donor star fillsits Roche lobe near the tip of its first giant branch as-cend, experiences stable mass transfer until its envelopeis stripped off, resulting in a naked He core with a thinH envelope. In the CE ejection channel, the donor staralso fills its Roche lobe near the tip of its first giantbranch ascend, but dynamically unstable mass transferleads to the formation of a CE. The ejection of this CEproduces a naked He core with a thin H envelope. Inboth cases, the He core ignites to produce a hot sub-dwarf star. In the 2HeWD merger channel, a close HeWD pair coalesces due to angular momentum loss viagravitational wave radiation. The merger product ig-nites He to become a hot subdwarf. This binary scenariosuccessfully explains the main observational character-istics of field hot subdwarf stars: their distributions inthe orbital-period vs. minimun-companion-mass and inthe effective-temperature vs. surface-gravity diagrams;their distribution of orbital periods and mass function;their binary fraction, and the fraction of hot subdwarfbinaries with WD companions; their birth rates; andtheir space density. In a stellar population, the forma-tion of EHB from binary stars dominates the far-UVpart of the population’s SED at ages above 1 Gyr (seeFigure 9 of Han et al. 2007). The fraction of EHB starsformed through the 2HeWD merger channel becomeslarger than 50% after 10 Gyr (Figure 1 of Han 2008).This channel produces more massive and more luminousEHB stars, which are the major sources of the FUV fluxafter 3.5 Gyr (Figure 7 of Han et al. 2007).Both scenarios for EHB star formation (single andbinary) are plausible. However, the properties of the re-sulting EHB star depend on the formation channel, sincethe distributions of the basic properties of their progen-itors are different (Han et al. 2007). Smith et al. (2012)measured the UV upturn as a function of a few spectralindices and stellar velocity dispersion. They find thatthe ( F UV − i ) colour anti-correlates with age, contrary tothe predictions of Han et al. (2007), and conclude thatbinary evolution as the source of the UV upturn is in-consistent with the observations.In this paper we revisit the inclusion of binary starevolution in population synthesis models, paying specialattention to the predicted UV spectrum. First, we con-struct evolutionary tracks for single and binary stars us-ing the Hurley et al. (2002) public code. We add to thiscode the possibility that EHB stars form via the 2HeWDchannel proposed by Han et al. (2002). The physical pa-rameters ( T eff , L ) of the resulting EHB stars are ob- c (cid:13) , 1–13 inary stars in population synthesis models tained from the BaSTI database. From our tracks wecompute isochrones for stellar populations that includeboth single and binary stars, and build the correspond-ing spectral energy distribution (SED). We compare ourmodels with the BC03 models, based on single star evo-lutionary tracks.The structure of the paper is as follows. In § § § § As indicated in §
1, close binary systems may be progen-itors of EHB stars through mass transfer or coalescence.We want to explore the effects of including binary stars,and hence EHB stars, in population synthesis models.We take a Monte Carlo approach to build from scratcha stellar population formed by both single and binarystars. To include the binary star population we mustspecify: ( a ) the mass distribution of the primary (themore massive) and secondary stars in the binary pairs,( b ) the binary fraction as a function of the mass of theprimary star, and ( c ) the distributions of the orbital pe-riod and orbit eccentricity of the binary pairs. For thesedistributions we follow as close as possible the obser-vations reported in the literature, as explained in thefollowing subsections. The first step in our approach is to generate the massdistribution of the primary and secondary stars in eachbinary pair. First, we build the distribution of the mass M of the primary star. The values of M are obtainedby populating stochastically the IMF, which we choose,without loss of generality, to follow the Chabrier (2003) Bag of Stellar Tracks and Isochrones (BaSTI) is a ro-bust and fast interface which uses the evolutionary tracks ofPietrinferni et al. (2004, 2006) to obtain the stellar param-eters of HB stars in old stellar populations, including EHBstars. The tracks by Pietrinferni et al. (2004, 2006) are com-puted with realistic stellar physics. The good agreement be-tween their theoretical predictions and observations is clear.We do not include their α -enhanced stars in our database. Table 1.
Binary fraction in function of spectral typeSpectral Binary ReferenceType FractionO 0.72 Mason et al. (1998)O-B 0.65 Preibisch et al. (1999)B-A 0.62 ± ± ± ± parametrization: ξ (log m ) ∝ exp (cid:20) − (log m − log m c ) σ (cid:21) , if m ⊙ ,m − . , if m > ⊙ , where m c = 0 .
08 M ⊙ , and σ = 0.69. For the lowerand upper mass cutoffs we adopt m L = 0 . ⊙ , and m U = 100 M ⊙ , respectively. Each star of mass M willbe the primary star in a pair according to the probabilitydiscussed in the next subsection and listed in Table 1.Stars in our initial pool that are not selected as binariesremain as single stars.In order to obtain the mass M of the secondarystar, it is necessary to establish a mass ratio distribu-tion. Milone et al. (2012) studied the properties of pho-tometric binaries in 59 Galactic globular clusters ob-served with the HST
WFC/ACS, and concluded thatthe distribution of the mass ratio q = M /M is almostflat. Therefore, we assume that M follows from a uni-form distribution in q : f ( q ) = 1 with 0 q < . (1)It should be remarked that our procedure does not alterthe global IMF. Adding the binary and single star massdistributions we recover the original IMF. In the last decades, surveys of binary systems haveshown that stellar multiplicity is not the same forall spectral types. For example, Duquennoy & Mayor(1991) find a multiplicity fraction of 0.58 ± ± a ) most( ∼
69 %) of the stars in the Galaxy are single, and ( b )the binary fraction depends on the stellar spectral typeof the primary star in such a way that this fraction in-creases with the mass of the primary star. Table 1 sum-marizes these results. A binary pair is also characterized by its orbital periodand orbit eccentricity. Surveys of binary systems have c (cid:13) , 1–13 F. Hern´andez-P´erez and G. Bruzual shown that the distribution of the orbital period is notuniform. We assume that the orbital period of our bi-nary pairs follows the gaussian (in log P ) distribution ofperiod found by Duquennoy & Mayor (1991): f (log P ) = C exp " − (log P − log P ) σ P , (2)where P is the period in days, log P = 4.4, and σ log P = 2.3. For the orbit eccentricity e , we assumethat it follows a uniform distribution (Zhang et al. 2004,2005a): f ( e ) = 1 with 0 e < . (3) One important limitation to include binary stars inpopulation synthesis models is the lack of evolutionarytracks computed ex professo for binary stars, which areneeded to evolve in time the binary pairs described in § § M ⊙ of metallicity Z from 0.0001 to 0.03.The orbital period and orbit eccentricity of the pairare input to the BSE code. In Figure 1 we show anexample of how the values of these parameters affectevolutionary tracks. In the top left panel of Figure 1 weshow the evolution of an Algol-like system. The binaryinteraction leads to the formation of an EHB star (log L ∼ − . T eff ∼ . L ∼ P ), eccentricity ( e )and mass. Their single star counterparts are shown inthe bottom middle and right panels. The luminosity atthe tip of the RGB is lower if the stars evolve in a bi-nary system. The origin of these differences is the masstransfer between the stars in binary systems. A plus ofthe BSE code is that it can follow the entire evolution ofeven the most complex binary systems in a small amountof CPU time (near to one second per system). The codeis thus ideal to compute tracks for large populations ofbinaries considering realistically their interactions. Hurley et al. (2002) assume in their BSE code that if2HeWD stars coalesce, the temperature becomes hotenough to start the triple- α process, and the mergertransforms into a COWD. The process of this trans-formation, i.e., the EHB phase, is not followed in detail.However, Han et al. (2002) conclude that under specificconditions the 2HeWD star merger can lead to the for-mation of a single EHB (see also Webbink 1984). Thismechanism becomes very important in populations olderthan ≃ § c (cid:13) , 1–13 inary stars in population synthesis models BSE binary star tracksP = 5.2e = 0.0M1 = 3.1M2 = 1.1 l og L BSE binary star tracksP = 836.0e = 0.2M1 = 5.2M2 = 2.1 BSE binary star tracksP = 1.7e = 0.0M1 = 1.1M2 = 1.0
SSE single star tracksM1 = 3.1M2 = 1.1 log T eff l og L SSE single star tracksM1 = 5.2M2 = 2.1 log T eff SSE single star tracksM1 = 1.1M2 = 1.0 log T eff Figure 1.
Evolutionary tracks computed with the BSE (binary) and SSE (single) stellar evolution code of Hurley et al. 2002.The top panels show tracks for binary stars with different period ( P ), eccentricity ( e ) and masses. Note the differences in thetracks when the same star evolves as a single star (bottom panels). The track of the secondary star of the pair is shown in gray colour. The stellar masses are given in units of M ⊙ and the orbital periods are in days. merger. The conditions for He to ignite depend on themass of the more massive component, its accretion his-tory, and other parameters related to its thermal struc-ture. In order to determine these parameters, Han et al.(2002) performed a series of calculations that allowedthem to follow in detail the evolution of the two WDs,the merger, and its products. An important result oftheir work is the mass distribution of the merger prod-ucts. This mass is restricted to a narrow range from ∼ ∼ ⊙ . This result is not sensitive to the ste-llar metallicity. If a 2HeWD star merger occurs in one ofour BSE binary star tracks, we assume that the mass ofthe product is the sum of the mass of the two mergingWDs at the moment of the coalescence. The resultingsingle star will ignite He if its mass is in the range indi-cated above.When He ignition happens in the merger prod-uct, we must assign an effective temperature and aluminosity to the star. This is done by interpolationin mass in a database constructed for this purposefrom the output of the BaSTI web tool (ver. 5.0.1). The resulting effective temperatures are in the range20000 K . T eff . The isochrone describing the position of single and bi-nary stars in the HRD at time t is built by interpo-lation in our set of BSE evolutionary tracks for thespecific metallicity. Blue Stragglers (BS) are presentin these isochrones. BS are stars which are currentlyburning H in the core, but their mass is larger thanthe turn off mass. They are located above and blue- c (cid:13) , 1–13 F. Hern´andez-P´erez and G. Bruzual log T eff l og L log T eff log T eff Figure 2.
5, 9 and 13 Gyr isochrones for solar metallicity derived from the binary and single star evolutionary tracks computedwith our implementation of the Hurley et al. (2002) BSE code, assuming the Chabrier 2003 IMF, and the binary fractiondescribed in § ward of the turn off point in a CMD. This suggeststhat BS form through a mechanism that permits thestar to stay in the main sequence (MS) despite itsold age. There are two possible mechanisms to formBS. Both require that H is replenished in the stellarcore by chemical mixing. One possibility is the coales-cence of two MS stars to form a more massive MS star(Sigurdsson et al. 1994). Other possible mechanism ismass transfer in a binary system (McCrea 1964). Herewe focus on the mass transfer model, included in theBSE tracks. Collisions are important mostly in highstellar density environments (Sigurdsson et al. 1994).BS have been observed in all stellar systems: globularand open clusters (Milone et al. 2012; Sigurdsson et al.1994; Cenarro et al. 2010; de Marchi et al. 2006), dwarfspheroidal galaxies (Mapelli et al. 2009), ultra faintdwarf galaxies (Okamoto et al. 2012), elliptical and spi- ral galaxies, and even in our own Milky Way galaxy(Monachesi et al. 2011; Clarkson et al. 2011).Another important aspect of the BSE isochrones isthe presence of EHB stars, formed as described above.It should be noticed that HB stars in single star evo-lutionary tracks do not reach as hot temperatures asthe EHB stars, even at the lowest metallicities. In Fi-gure 2 we show isochrones corresponding to the evolu-tionary tracks computed using the recipes described in § c (cid:13) , 1–13 inary stars in population synthesis models l (A (cid:176) ) Log F ( l ) + C on s t Figure 3.
Spectral evolution of an SSP of solar metallicitycomputed with our model. The age in Gyr is indicated nextto each SED.
The integrated SED of the stellar population is obtainedby adding the spectrum of the star at each position inthe HRD along the isochrone, weighted by the numberof stars at this position given by the IMF (see BC03 fordetails on the isochrone synthesis approach). We use theBaSeL 3.1 stellar spectral library (Westera et al. 2002)to compute the spectrophotometric properties of all themodels discussed in this paper. The Chabrier (2003)IMF is used throughout.Figure 3 shows the evolution in time of the SED of asolar metallicity SSP computed from our BSE tracks. Atthe youngest ages the UV light is dominated by short-lived massive MS stars, which rapidly evolve and leavethe MS, causing a drop in the UV flux. At ages olderthan 1Gyr, the evolution of binary systems triggers theformation of EHB stars through the 2HeWD merger me-chanism. Even though these stars are also formed atyounger ages through the CE and RLOF channels, itspresence is not apparent because massive MS stars areabout 100 times more luminous and dominate the UVspectrum. When the massive stars leave the MS, theEHB stars are responsible for the far ultraviolet emis-sion.The Hurley et al. (2002) evolutionary tracks showthe expected behavior with stellar metallicity, e.g., ste-llar lifetime increases with metallicity; the evolution ofsingle low mass stars through the RGB phase determinesthe position of the star in the HB, at fixed initial stellarmass, lower metallicity stars evolve into hotter HB starsafter the He flash. However, the formation of EHB starsthrough binary interactions depends only on the orbitalparameters of the binary pair and not on the stellar me-tallicity. Thus, everything else being equal, the numberof EHB stars present in a stellar population, should notdepend on metallicity. This has been reported previouslyby Han et al. (2002, 2007). Figure 4 shows the expected l (A (cid:176) ) Log F ( l ) + C on s t Z=0.03Z=0.02Z=0.008Z=0.004Z=0.0004Z=0.0001
Figure 4.
SED of SSPs of different metallicities at 12 Gyr.The SEDs have been shifted in the vertical direction for clar-ity. The UV upturn short ward of 2000 ˚A is present at allmetallicities. similarity of the SED of SSPs of different metallicity at12 Gyr, the UV upturn is clearly seen at all metallicities.In Figure 6 we compare the evolution of the UV-optical colours predicted by our models for SSPs of diffe-rent metallicities. FUV and NUV refer to the GALEXfilters of the same name, and i and r to the SDSS filters.The four colours shown in the figure become bluer as thepopulation ages. The behavior of the FUV-NUV colouris quite remarkable. This colour is dominated at olderages by EHB stars, and becomes very blue for the fourhigher metallicities shown in the figure. In the two lowermetallicity SSPs, the NUV flux is increased at older agesby HB stars, making FUV-NUV less blue than in theirhigher metallictiy counterparts. Most of the population synthesis models availablein the literature (Fioc & Rocca-Volmerange 1997,Leitherer et al. 1999, BC03, Maraston 2005) are basedon evolutionary tracks for single stars and do not followthe evolution of the binary stars known to be present inall stellar populations. Despite this fact, these modelsreproduce surprisingly well the spectra of most galaxiesat all redshifts that have been sampled. This has beenused as an argument in favour of the idea that binarystars are irrelevant in modeling the spectral evolutionof galaxies. However, in the last decade there have beenseveral important efforts to include binary star evolu-tion in population synthesis models. In this session wecompare some results of our models with previous work.In Figure 5 we plot the spectrum of a 12 Gyr oldstellar population of solar metallicity computed withthree different codes. It is clear that below ∼ c (cid:13) , 1–13 F. Hern´andez-P´erez and G. Bruzual F U V − NU V Age (Gyr)
Z=0.03Z=0.02Z=0.008Z=0.004Z=0.0004Z=0.0001 NU V − r Age (Gyr)0 2 4 6 8 10 12123456 NU V − i Age (Gyr) 0 2 4 6 8 10 12123456 F U V − r Age (Gyr)
Figure 6.
UV-optical colour evolution for SSPs of different metallicity. Although the appearance of EHB stars is independentof metallicity, the presence of an extended HB in the lower metallicity populations increases the NUV flux and makes theFUV-NUV less blue than for the higher metallicity SSPs. with the model that uses the SSE tracks, which is com-pletely flat in this wavelength range. The BC03 modelshows a modest increment in the UV flux because ofthe contribution of the central star of planetary nebulae(CSPNe) included in this model, and not in the othertwo. Figure 7, analogous to Figure 6, compares theevolution of the UV-optical colours of our models for Z = 0 .
008 and 0.02 with the BC03 models for the samevalues of Z . In the NUV-optical colours, the BC03 mod-els remain red as the population ages, whereas the mod-els with binaries become bluer by more than one magni-tude. In the colours including the FUV filter the BC03models also get bluer with age, due to the appearanceof the CSPNe, but much less than our present models,dominated in this wavelength region by EHB stars.Zhang et al. (2004) and Zhang, Li & Han (2005b) also use the Hurley et al. (2002) evolutionary tracksto follow binary star evolution in their models. Howe-ver, we adopt the default BSE values for the physi-cal parameters governing the RLOF and CE channels.The CE efficiency parameter ( α CE ) is taken as 3.0, theReimmer mass loss coefficient ( η ) is assumed to be 0.5,and the tidal enhancement parameter is taken as 0.0.Zhang et al. (2004) and Zhang, Li & Han (2005b) use adifferent set of values. The models by Li & Han (2008)also use the Hurley et al. (2002) tracks. They assumethe binary fraction to be 50% for all spectral types, andexamine mostly the optical range and NIR, and com-pute the Lick indices. We think that our approach thatuses observationally supported distributions of orbitalperiods and binary fractions makes our models more re-alistic.The Binary Population and Spectral Syn- c (cid:13) , 1–13 inary stars in population synthesis models BSM Z=0.02BSM Z=0.008BC03 Z=0.02BC03 Z=0.008 F U V − NU V Age (Gyr) 0 2 4 6 8 10 1201234567 NU V − r Age (Gyr) NU V − i Age (Gyr) 0 2 4 6 8 10 122468 F U V − r Age (Gyr)
Figure 7.
Comparison of the UV-optical colour evolution for two of our SSPs with the BC03 models of the same metallicity.The CSPNe dominate the FUV flux in the BC03 models at late ages and make the model become bluer, but never as much asour present models, dominated by EHB stars in this wavelength range. thesis (BPASS) code (Eldridge et al. 2008;Eldridge & Stanway 2009; Eldridge et al. 2011) followsthe evolution of fast rotating massive stars in binarysystems (Eldridge & Stanway 2012), according to theirown evolutionary tracks, including the modeling of theinterstellar gas surrounding the stars. Their main goalis to study the effects on stellar lifetime due to themass loss induced by binary interactions. Our goal isdifferent, since we aim at studying how the integratedproperties of stellar populations are modified by thepresence of interacting binaries. Comparing our modelswith either the BPASS, the Zhang et al. (2005b), orthe Li & Han (2008) models would be an importantexercise, since they study the same process governingdifferent problems.
The open cluster NGC 6791 is an interesting stellar sys-tem which shows several particular features: ( a ) it lacksRGB stars (Kalirai et al. 2007), ( b ) the mass distribu-tion of its WD cooling sequence is bimodal (Kalirai et al.2007; Bedin et al. 2008), and ( c ) shows bimodality in theHB morphology (Buzzoni et al. 2012). All of these pecu-liarities are thought to be driven by a mechanism of en-hanced mass loss. Particularly, Bedin et al. (2008) haveshown that the observed fraction of submassive WDs inthis cluster can be naturally accounted for if ∼
34% ofthe WDs in NGC 6791 are in binary systems. Addition-ally, from asteroseismology observations by the
Kepler space mission, Stello et al. (2011) found evidence of theexistence of unresolved binaries in this cluster. It is thusplausible that the origin of these peculiarities is related c (cid:13) , 1–13 F. Hern´andez-P´erez and G. Bruzual l (A (cid:176) ) N o r m a li z ed F ( l ) Present model (binary)Present model (single)BC03
Figure 5.
SED of a solar metallicity stellar population at12 Gyr computed with three different synthesis codes. Fromtop to bottom in the UV: ( a ) Present models, ( b ) BC03, and( c ) SED corresponding to the evolutionary tracks computedwith the Hurley et al. (2000) SSE code. ( a ) includes and ( b,c )ignore the evolution of binary stars. Table 2.
Open cluster NGC 6791Observational parameter ReferenceAge ∼ / H] = 0.4 ± α/ Fe] = solar Origlia et al. (2006)Y = 0.3 Brograad et al. (2012)m-M = 13.51 Brograad et al. (2011)E(B-V) = 0.09-0.18 Carney et al. (1999) to the evolution of a large number of binary star systemspresent in the cluster.The bimodality of the HB morphology in this clus-ter is relevant for our study. EHB and red clump (RC)stars co-exist in this cluster, suggesting that a fractionof its RGB stars were subject to enhanced mass loss,evolving into EHB stars, while another fraction evolvednormally into RC stars. To explore the HB morphologyof this cluster, we compute a synthetic model with thecharacteristics of this cluster, following the prescriptionsof §
2. The main observational parameters of the clusterare listed in Table 2. The metallicity of the cluster isZ=0.03.Figure 9 shows that there is very good agreementbetween the observed (left panel) and the synthetic(right panel) CMD of NGC 6791 in (
B, B − V ). Theposition and the extension of the region occupied bythe BS are very well accounted for. The locations of theRC, the RGB and the EHB are also in good agreementin both diagrams. A remarkable feature is that in ourmodel the bimodality in the HB is evident. It is impor- Log F ( l ) + C on s t l (A (cid:176) ) Figure 8.
SED of NGC 6791 computed with our model.
Table 3.
Colours of the open star cluster NGC 6791Color This model Buzzoni et al. (2012)U- B 0.602 0.60B - V 0.956 0.97V - R 0.625 0.60V - I 1.154 1.18V - J 2.115 2.08FUV - V 4.074 5.22NUV - V 4.066 5.01 tant to emphasize that the points located at the rightof the MS in the synthetic CMD represent stars thatare members of a binary system with a BS companion.These stars have lost a considerable amount of mass, be-coming fainter and cooler as they evolve through the subgiant and RGB phase corresponding to their lower mass.This suggests that it is possible that the mechanismof enhanced mass loss mentioned above (Kalirai et al.2007; Bedin et al. 2008; Buzzoni et al. 2012), could bedriven by binary interactions. This will explain in a nat-ural manner why only a fraction of the stars passingthrough the RGB experience enhanced mass loss, lead-ing to the coexistence of a EHB and a RC normal forthis metallicity and He abundance.In our simulated cluster, the fraction of EHB starswith respect to the total of He burning stars is 20%.Kalirai et al. (2007) argues that ∼
30% of the HB starsare hot, which is a extreme value for a high metallicitycluster. However, Dorman et al. (1995) using populationsynthesis models found that for the highest UV upturngalaxies a fraction of 15% - 20% hot HB stars is enoughto produce the observed colours.Figure 8 shows the SED corresponding to our syn-thetic model for NGC 6791, computed as described c (cid:13) , 1–13 inary stars in population synthesis models B−V V Figure 9.
Left panel:
Observed CMD of NGC6791. The small gray dots are the data from the Stetson et al. (2003) photometriccatalog, the open triangles are the 75 BS candidates from Ahumada & Lapasset (2007), and the open diamonds are the EHBstars from Kaluzny & Udalski (1992).
Right panel:
Synthetic CMD. The dark gray line (in both panels) shows the isochronecomputed for the cluster parameters listed in Table 2. in § ∼ λ & c (cid:13) , 1–13 F. Hern´andez-P´erez and G. Bruzual
Table 4.
Colours of NGC 6791 vs. ETGssynthetic observedColor NGC 6791 ETGsFUV - V 4.074 4.95NUV - V 4.066 4.56FUV - NUV -0.008 0.4993NUV - r 4.459 5.3465 computed from our synthetic SED with those listed byBuzzoni et al. (2012). Both sets of colours are in goodagreement. However, the NUV - V and FUV - V coloursare bluer in our model. The bluer FUV - V colour mayindicate a lack of RGB stars in our model. There areseveral possibilities to explain a low number of RGBstars. i ) If the donor star in a binary pair is in the subgiant or RGB phase, it may loose enough mass to not beable to reach the tip of the RGB. This may be due to theadopted CE ejection efficiency parameter. ii ) The initialorbital period distribution or binary fractions adoptedin this paper may not be good enough for NGC 6791.In reality there may be more binary interactions pre-venting the primary star (star 1) of the pair to reachthe RGB. We should keep in mind that CE evolution isthe most important but the least understood process inbinary evolution (Podsiadlowski 2001).The study of old metal rich open clusters may pro-vide an important clue to the study of the UV up-turn in ETGs, since in the clusters it is possible toresolve the hot component of the HB, which couldact as a proxy to constrain the source of the UV ex-cess in ETGs. Recent work by Rosenfield et al. (2012)shows that emission from EHB stars can be responsi-ble of the UV upturn in ETGs. In a subsequent paper(Hern´andez-P´erez & Bruzual 2013) we consider a sam-ple of ( ∼ SDSS /DR8 and the
GALEX /GR6 surveys, and an-alyze the possible scenarios that can influence the for-mation of EHB stars in these galaxies, determining thevariety observed in the UV spectrum of ETGs.In Table 4 we compare our synthetic clustercolours with the typical UV-optical colour of UVstrong ETGs. FUV-V and NUV-V are taken fromTable 1 of Buzzoni et al. (2012), which is con-structed from a sample of ETGs from Bureau et al.(2011) and Buzzoni & Gonz´alez-L´opezlira (2008).The FUV-NUV and NUV - r colours are fromHern´andez-P´erez & Bruzual (2013). This samplecontains ∼
340 UV strong ETGs with no signs of recentstar formation. The values listed in the table are theaverage colours for all of these galaxies. The syntheticcluster defines a blue limit to the observed averages.
We have built a population synthesis model that in-cludes, using a simple approach, the evolution of binarystars. In this model we include the 2HeWD merger chan-nel, suggested by Han et al. (2002), for the formation ofEHB stars. An important aspect of our model is theuse of the Pietrinferni et al. (2004, 2006) evolutionarytracks to estimate the stellar parameters of the EHBstars produced via the 2HeWD merger process.The predictions of our model are in good agree-ment with other well established single star models (e.g.,BC03), except in those instances where the spectrum ofthe stellar population is dominated by the binary starsor their products (e.g., EHB stars in the UV of ETGs).The CMD diagram predicted by our model for themetal rich open cluster NGC 6791 is in very good agree-ment with the observed CMD of this cluster. Our modelreproduces well the position and relative number of BSand EHB stars seen in this cluster (Figure 9), as well asits expected SED (Figure 8) computed by Buzzoni et al.(2012).Despite the good match between model predictionsand observations, the formation of EHB stars via the2HeWD merger process is still debated. The frequencyof occurrence of this process in real stellar populationsremains as an open question.
ACKNOWLEDGMENTS
We are grateful to the referee, Dr. Zhanwen Han, forvaluable suggestions and comments which helped to im-prove this paper. Support for this work was provided bythe National Autonomous University of M´exico, throughgrants IA102311 and IB102212. FHP acknowledges thehospitality of the UNAM Centro de Radioastronom´ıa yAstrof´ısica during the last stages of this investigation.FHP acknowledges support from CIDA during her PhDthesis work partially reported in this paper. This workhas made use of BaSTI web tools.
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