Destruction of wide binary stars in low mass elliptical galaxies: implications for initial mass function estimates
aa r X i v : . [ a s t r o - ph . GA ] M a r Mon. Not. R. Astron. Soc. , 1–5 () Printed 29 July 2018 (MN L A TEX style file v2.2)
Destruction of wide binary stars in low mass ellipticalgalaxies: implications for initial mass function estimates
Thomas J. Maccarone
Department of Physics, Texas Tech University, Box 41051, Lubbock TX 79409-1051, USA
ABSTRACT
We discuss the effects of destruction of wide binaries in the nuclei of the lower massgiant elliptical galaxies. We show that the numbers of barium stars and extrinsic Sstars should be dramatically reduced in these galaxies compared to what is seen inthe largest elliptical galaxies. Given that the extrinsic S stars show strong Wing-Fordband and Na I D absorption, we argue that the recent claims of different initial massfunctions from the most massive elliptical galaxies versus lower mass ellipticals maybe the result of extrinsic S stars, rather than bottom-heavy initial mass function.
Key words: stars:binaries – stars:chemically peculiar – galaxies:stellar content –supernovae:general
Despite the fact that most stars are members of binary systems, binary stellar evolution is usually neglected in modelling ofthe spectral energy distributions of galaxies (although see e.g. Han et al. 1995). This decision is made as a basic simplication, inpart because it has not, to date, been clear how binary evolution would affect most of what is seen in optical light, and in partbecause binary population synthesis is extremely complicated, with large numbers of parameters which are not particularlywell-constrained by observations (see e.g. Belczynski et al. 2008 for a discussion of a particular binary population synthesiscode). Furthermore, while we will show evidence to the contrary in this paper, one might initially expect that the effects ofbinary evolution would not vary much from galaxy to galaxy.Heggie’s Law (1975) states that hard binaries get harder while soft binaries get softer – i.e. binaries whose binding energyis larger than the mean kinetic energy of single stars in their local neighborhood will tend to become closer with time, whilebinaries with binding energies less than the local mean stellar kinetic energy will tend to become wider with time until theyare eventually dissolved into two single stars. The consequences of Heggie’s Law are generally well-appreciated, if not fullyunderstood, in the context of globular clusters. For example, the hardening of binaries in globular clusters supplies kineticenergy to the single stars in the clusters, holding up the collapses of star clusters in a manner somewhat analogous to themanner in which nuclear fusion holds up the collapses of stars (see e.g. Sugimoto & Bettweiser 1983; Fregeau 2008).In the context of field populations of galaxies, it has been shown that the absence of wide binaries in the Galactic halo canbe taken as evidence against massive compact halo objects (i.e. MACHOs) supplying the bulk of the dark matter in the MilkyWay (Yoo et al. 2004). There has been relatively little appreciation, however, of how removing long period binaries from astellar population affects integrated stellar light. Traditionally, in fact, stellar population synthesis models for understandinggalaxy evolution have ignored binaries almost entirely, except with respect to binary models for producing the ultravioletupturn in elliptical galaxies (e.g. Han et al. 2002; Han et al. 2007), and, of course population synthesis calculations aimed atunequivocally binary populations like X-ray binaries and double neutron stars (e.g. Belczynski et al. 2008). In this Letter, Iwill show that the cutoff period varies considerably through different classes of stellar systems, and that this difference affectswhether Roche lobe overflowing red giants will be present in different classes of galaxies. I will show further that these binarysystems may then have profound implications for the observational appearance of different classes of galaxies.
Binney & Tremaine (2009) give the dissolution timescale of a binary as: c (cid:13) RAS
Maccarone et al. t d = 15Gyr (cid:16) K diff . (cid:17) (cid:18) σ rel / sec (cid:19) (cid:18) M b M ⊙ (cid:19) (cid:18) M p M ⊙ (cid:19) − (cid:18) . − n (cid:19) (cid:18) AU a (cid:19) , (1)where K diff = . (and Λ = σ rel aGM p ), so that K diff ≈ .
002 for nearly all galaxies; σ rel is the velocity dispersion of thescattering stars, M p is the mass of the star perturbing the binary, M b is the mass of the binary, n is the number density ofstars in the local region, and a is the orbital separation of the binary.Now, let us consider two relatively extreme giant elliptical galaxies: M87, the central galaxy in the Virgo Cluster, andNGC 4458, a small galaxy in the Virgo Cluster. For M87, the central velocity dispersion is about 400 km/sec, and the centraldensity is about 200 stars per cubic parsec (Gebhardt & Thomas 2009). For NGC 4458, the central density is about 2800 L ⊙ /pc (Gebhardt et al. 1996), and the central velocity dispersion in 85 km/sec (van Dokkum & Conroy 2011). In general, thefundamental plane relation (Dressler et al. 1987) shows giant elliptical galaxies which fit on the plane will become significantlydenser and have significantly lower velocity dispersions as their masses drop. For a 10 Gyr old population in a dynamicalenvironment like that of M87, binary separations of up to about 20 AU will be possible in the core; for a galaxy like NGC 4458,binary separations of about 0.4 AU will be possible. Two important classes of objects have orbital periods of order 1 year. They may be destroyed in the cores of the smallestgiant elliptical galaxies, but not in the cores of the largest galaxies. They are symbiotic stars, and barium stars/extrinsic Sstars.First, let us consider the case of symbiotic stars. These are binary systems which contain compact objects which accretefrom a highly evolved companion star – either a red giant or an asymptotic giant branch star. While there are a few neutronstar symbiotic binaries, the vast majority of the symbiotic stars have white dwarf accretors (Belczynski et al. 2000). Theorbital periods of the catalogued symbiotic stars range from a little over 200 days to 5700 days (Belczynski et al. 2000). Eventhe shortest period symbiotics have separations of about 0.9 AU (assuming P = 250 days and a total system mass of about1 . M ⊙ ). One reason for particular interest in the symbiotic stars is that a disproportionate fraction of recurrent novae occurin symbiotic stars, as are a disproportionate fraction of the steady supersoft sources (e.g. Sokoloski 2003). It is not generallyconsidered that these objects represent a large fraction of Type Ia supernovae (e.g. Schaefer 2014), but searching for a deficitof central Type Ia’s in dense galaxies would represent an additional possible test.The other class is a group of stars with enhancements in their s-process element abundances – barium stars, CH starsand extrinsic S stars (sometimes called Tc-poor S stars). Barium stars (see Bidelman & Keenan 1951 for the discovery of theclass, and e.g. Warner 1965; McClure 1985 for a working definition of the class) are G/K giants which show exceptionallystrong absorption lines from s-process elements - especially barium and strontium. CH stars (Keenan 1942) represent thePopulation II analogs of the barium stars. S stars in general represent the class of cool stars rich in s-process elements (Merrill1922 – although at the time of the establishment of the category, they were called S stars with the letter S being chosen,apparently, arbitrarily with the connection to the s − process coincidental). It has become appreciated in recent years that all barium stars are found in wide binaries (i.e. with orbital periods of at least 600 days – Jorissen & Mayor 1992) with whitedwarf companions, in accord with theoretical predictions (e.g. Iben & Renzini 1983). This finding has led to a model for theirproduction in which a star donates most of its envelope to its companion star after it evolves off the main sequence, so that thecompanion star’s new abundances become the abundances of the interior of the originally more massive star (see e.g. McClure& Woodsworth 1990; Han et al. 2002). Extrinsic S stars are the S stars thought to form through binary stellar evolution,as descendants of the barium stars. There also exist intrinsic S stars, which are thought to form as s-process elements areraised to the surface in the third dredge-up in the evolution of a moderately massive single stars. The most common means ofdistinguishing between the two is by searching for lines from Tc, an s-process element with a half-life of order a million years– similar to the lifetimes of the intrinsic S stars, but much shorter than the lifetimes of the extrinsic S stars. The implications for our understanding of Type Ia supernova progenitors are quite clear. If symbiotic stars dominate theprogenitors of Type Ia supernovae in old stellar populations, then there should be a strong deficit of such objects seen fromthe centers of small elliptical galaxies. The Type Ia supernova rates on the outskirts of these galaxies, where the stellar densityhas dropped, should not be affected. Searching the centers of the highest surface brightness galaxies is not easy, but maypay large dividends. On a related note, any elements predominantly produced in recurrent novae may be preferentially moreabundant in the largest giant ellipticals than in smaller giant ellipticals. c (cid:13) RAS, MNRAS , 1–5 inary destruction in ellipticals Figure 1.
The spectra of two similar temperature stars from the IRTF library (Rayner et al. 2009). The upper curve, in black, is thespectrum of HD18191, an M6III star. The lower curve, in red, is the spectrum of SU Mon, a S6 star. The continua shortward of theWing-Ford band are similar, while the spectrum along the Wing-Ford band shows suppressed flux for the S star, indicating that itsWing-Ford band strength is much larger. Some S stars show even deeper Wing-Ford bands, but these are not in the IRTF libraries.
The use of certain near-infrared spectral features to constrain the initial mass function of stars has been suggested for quitesome time. Whitford (1977) suggested that the suggested that the FeH band at 9916 ˚A(discovered by Wing & Ford in 1969,and hence often called the Wing-Ford band) could be used to estimate the amount of light from dwarf stars in old stellarpopulations, but did not detect the band in a sample of seven galaxies he observed. Hardy & Couture (1988) did detect theband, but noted that the presence of a nearby TiO feature would often complicate the interpretation of such measurements.Using more sophisticated models for the integrated light from galxies, van Dokkum & Conroy (2010) showed that the Wing-Ford band in the centers of giant elliptical galaxies is much stronger than expected from standard simple stellar populationsmodels. Later, in Conroy & van Dokkum (2011), they argued further that the much smaller elliptical galaxy NGC 4458 hadan initial mass function much closer to the Salpeter IMF, again on the basis of its Wing-Ford band. An alternative method fortesting the initial mass function has also been proposed recently, and has also found a higher M/L ratio in the most massivegalaxies than is expected from a Salpeter, Kroupa, or Chabrier IMF (Cappellari et al. 2012), but this work examines only thestellar mass to light ratio, and can give the same results for a bottom-heavy IMF dominated by dwarf stars, or a top heavyIMF with larger numbers of black holes, neutron stars and white dwarfs.It has also been found, however, that stars rich in s-process elements show strong Wing-Ford bands (Wing 1972; Lambert& Clegg 1980), leading to a flux reduction of about 0.1-0.2 magnitudes. This can also be seen from the IRTF spectra of Sstars (Rayner et al. 2009 – see also figure 1). Since the Wing-Ford feature in the giant elliptical galaxies is only about 0.02magnitudes deeper than expected from a Salpeter initial mass function, only about 10% of the giants’ light needs to comefrom S stars for the S stars to explain the deviation from the predictions of a Salpeter IMF. Since the Wing-Ford band itselfis quite broad with the deep part of the absorption spanning about 40 ˚A, and the whole band spanning more than 100˚A,the smearing due to the few hundred km/sec velocity dispersions in elliptical galaxies will be negligible – unlike the case fornarrow spectral features which might be strongly affected.It should be noted that the empirical spectral libraries used by van Dokkum and Conroy (2010) explicitly excluded giantsof unusual chemical composition, rather than attempting to estimate the number of such stars and weigh their empiricalspectra accordingly. As a result, their models are missing single-star channel S stars for all galaxies, and is also missing thebinary channel S stars for galaxies where they can exist. The single star channels are not likely to be especially important forearly type galaxies, since the s-process elements reach the surface only during the third dredge up phase of stellar evolution,a process which happens only for relatively high mass stars.In order to estimate the magnitude of the effect on the Wing-Ford band, we need an estimate of the fraction of giantswhich are S stars. This is not straightforward to do from the literature, as the number of very cool giants is rather small, andin the CCD era, only recently has there been good enough sensitivity at 9900 ˚Afor spectra at that wavelength to be common.As one manner of estimating the number of S stars, we can rely on the number densities of barium stars, which are identifiedby features around 4400 ˚A, and which are thought to be progenitors of the extrinsic S stars, and we can assume that the ratioof S stars to M giants will be similar to the ratio of barium stars to earlier type red giants. We also note that roughly half ofthe S stars seen in the Milky Way in flux limited surveys are intrinsic and roughly half are extrinsic (e.g. Yang et al. 2006). c (cid:13) RAS, MNRAS , 1–5
Maccarone et al.
Following a suggestion by Han et al. (1995), we restrict the counts of the two classes of objects to those stars brighterthan 6th magnitude, so the stars will be members of the Bright Star Catalog (Hoffleit & Warren 1995), and also allows usto be reasonably confident that most of the barium stars will have been identified as such. We also note that the bariumstars have been found to show typically the same absolute magnitudes as other G/K giants (e.g. Kemper 1975; Hakkila 1990).Restricting ourselves to giants with spectral classes from G5 to K5, we find 61/1194, or 5.5% of the stars are barium stars – weregard this number as a lower limit, since there does not exist a definitive paper with upper limits that definitively show thatall the barium stars are accounted for. This limit is considerably higher than what was estimated through a similar procedureby Warner (1965) – however Warner noted that the barium stars in his sample already skewed toward being around K0 inspectral type, and that relatively fewer normal giants were in that temperature range than is the case for later K-types.Similarly, about 4% of the M giants in the Bright Star Catalog (Hofleit & Warren 1995) correspond with S stars in thecatalog of Stephenson (1984). Keenan (1954) found that roughly 10% of M giants were S stars as well, and no more recentsystematic attempt seems to have been made to estimate the fraction of stars occupying the M-giant region of the colormagnitude diagram which are S stars. CH stars account for roughly 30% of halo giants (e.g. Lucatello et al. 2005).We can thus conclude that removal of the extrinsic S stars from a galaxy will have a significant effect on its apparentinitial mass function if the mass function is measured using the Wing-Ford band. If ∼ half of the barium stars are as yetunidentified, then the extrinsic S stars may explain the entire effect on the Wing-Ford band, with no need for an altered stellarinitial mass function. Another issue, whose effect is not clear, is whether the binary fractions of galaxies vary systematically.Within the Galaxy, there is some suggestive evidence that metal rich stars have a higher binary fraction than metal poorstars (e.g. Riaz et al. 2008), which might also boost the number of S stars in massive galaxies relatively to that in lower massgalaxies. Studies have been done of extragalactic binary fractions only in a few very nearby galaxies. They are within a factorof the few of the disk binary fraction, but with large statistical uncertainties (e.g. Geha et al. 2013).One clear prediction of a scenario where the S stars are significant contributors to the Wing-Ford band fluxes of galaxiesis that the ZrO bands should be stronger in such galaxies as well. In the most comprhensive analysis to date of ellipticalgalaxies (van Dokkum & Conroy 2012), there is no real sensitivity to these bands. In integrated light, the strong bands near4600 ˚Awill be swamped out by the light from turnoff stars, while the strong band around 6470 ˚Ais not covered in the spectra,and the region around the strong infrared band of ZrO at about 9300 ˚Ais in the region of strong sky background.We note that the Na I D absorption line was also presented by van Dokkum & Conroy (2010) as part of the evidence for abottom heavy initial mass function in giant elliptical galaxies. This line is also strongly enhanced in barium stars and S stars– Warner (1965) estimates that the sodium abundances of the barium stars are roughly 1.2-1.8 times larger than expectedfor stars of the same iron abundance. Additionally, the [Na/Fe] abundance ratio increases with increasing [Fe/H], at leastfor super-solar stars in the Milky Way disk (e.g. Edvardsson et al. 1993). The use of solar metallicity template spectra willtherefore affect sodium absorption lines much more strongly than most other lines.An alternative test of the scenario is to look at the central region of the Milky Way. Dynamical encounters there havebeen suggested to affect the formation rates of X-ray binaries (Maccarone & Patruno 2013; see also a similar suggestion forthe inner bulge of M31 from Voss & Gilfanov 2007). In the central regions of the Milky Way, the stellar density can be ∼ stars per pc (i.e. in the nuclear star cluster – Genzel et al. 2010). The density remains greater than a few thousand solarmasses per cubic parsec out to several parsecs. Since the absolute K band magnitudes of the extrinsic S stars are about -5.7(van Eck et al. 1998), they should have apparent magnitudes of roughly 14 at the distance of the Galactic Center, assuminga distance of 8 kpc, and 5 magnitudes of extinction – these sources should be detectable as S stars in surveys of the GalacticCenter, e.g. with FLAMINGOS-2 (Eikenberry 2008). Binary destruction in the cores of the smaller giant elliptical galaxies is expected. A lack of S stars in these galaxies canprovide an alternative explanation for the recent claims of steeper initial mass functions in the biggest giant elliptical galaxiesthan in smaller ellipticals, eliminating the need to deal with the conflict between those results and other estimates of the darkmatter content of the Universe. This idea can be tested by searching for the ZrO bands in giant elliptical galaxies, and byspectroscopic follow-up of giants in the center of the Milky Way relative to giants elsewhere in the Milky Way.If the Wing Ford band can be confirmed to be dominated, or even affected, by the S stars, the results from Cappellariet al. (2012) showing higher M/L in higher velocity dispersion galaxies remain unaffected by the conclusions of this work.However, the results of Cappellari et al. (2012) have some degeneracies between the functional form of the dark matter densitydistribution and the stellar mass-to-light ratio. They can also produce higher-than-standard M/L ratios either through topheavy or bottom heavy initial mass functions, with the former producing high M/L ratios due to having more compact objects,and the latter due to having more low luminosity M-dwarfs. Understanding all the systematic effects in stellar populationmodels is thus a key for understanding the root cause of the results of Cappellari et al (2002). c (cid:13) RAS, MNRAS , 1–5 inary destruction in ellipticals I thank Anthony Gonzalez, Steve Zepf, Claudia Maraston and Dave Sand for useful discussions.
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