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Field Blue Stragglers and Related Mass Transfer Issues

This chapter contains my impressions and perspectives about the current state of knowledge about field blue stragglers (FBS) stars, drawn from an extensive literature that I searched. I conclude my review of issues that attend FBS and mass transfer, by a brief enumeration of a few mildly disquieting observational facts.


The metal-poor halo
The observational requirements for selection of (apparently young) halo FBSSs are parameters that (a) identify stars with the metallicity of the parent population and (b) sort them unambiguously by age. The first of these two parameters must cull halo stars from the much more numerous, metal-rich, and age-heterogeneous populations of the thick and thin discs. Note that there are complications here because of the overlapping abundance distributions of the three principal Galactic populations. The second parameter must separate the "young" FBSSs from the bulk of their older main sequence cousins. If we ignore well-known details about the behavior of O and Na [23], and the poorly-constrained and indirectly inferred He content [19], the gross chemical compositions of most GCs are homogeneous, and their ages can be estimated by fits of isochrones (there is a plethora of these in the literature) to the stellar distributions in colour-magnitude diagrams (CMD). The fits are characterised most sensitively by colours of the main sequence turnoffs (MSTO). Because of the great ages of GCs the variation of turnoff colour with age is small, d(B −V )/dt ∼ 0.008 dexGyr −1 [152]. For this reason a number of small and not-so-small effects mask the age effect: interstellar (IS) reddening , chemical composition, including [Fe/H], and [alpha/Fe], and (assumed) He, the choice of mixing-length parameter, and the effects of radiation pressure and gravitational settling on stellar models. These effects combine to produce a blurred lower bound for temperature-sensitive colour indices of halo main sequence stars.

Photometric criteria: UBV
The UBV photometric system identifies FBSSs [100] with reasonable success because U − B is a sensitive metallicity indicator [146,147,75], and B −V is an adequate, though not ideal, temperature indicator ( [18,141]). The manner in which the UBV two-colour diagram isolates FBS candidates is indicated in Fig. 4.1 taken from [100], which utilised photometry [98] of the HK search for metal-poor stars [3].
A steeply inclined blanketing vector extending upward from the intrinsic twocolour relation for solar-type stars [147] Fig. 4.2, reproduced from [16].  New abundances for stars in the PS00 survey derived from spectra with superior signal-to-noise ratios (S/N) and resolution [16] are plotted against those of PS00 in Fig. 4.3. The solid 45-degree line indicates 1:1 correspondence. Bragaglia et al [16] obtain abundances systematically lower than PS00 by ∼ 0.15 dex. Scatter in this regression contributes to blurring of the lower boundary of the FBS domain.
There is a bright side to this otherwise dreary discussion. The binary fraction of stars in the PS00 survey with thick disc abundances ([Fe/H]> −1) is marginally higher, 0.76, than the fraction, 0.69, for stars with [Fe/H]< −1 and markedly higher than the spectroscopic binary fractions, ∼ 0.15, of the normal stars of the halo ( [59]) and disc near the sun [32]. Evidently, mild (U − B) excesses properly select mildly metal-deficient FBSSs in the thick disc. This result suggests that the bulk of the thick disc stars have similar ages, i.e., the thick disc does not contain a significant component of normal A-type and early F-type stars. Most of the known FBSSs near the solar circle have been identified by UBV photometry. For additions to the list of FBS candidates at distances less than about 2 kpc subsequent to [100], see the compilation by Wilhelm et al. [148].

Photometric criteria: SDSS ugr
Numerous FBS candidates have been identified in the distant halo by use of the (u − g, g − r) equivalent of the (U − B, B − V ) diagram shown in Fig. 4.1 ( [151,124]). Noting that the conversion of (u − g) to (U − B) is not well-defined, Yanny et al. [151] tentatively identify 2715 FBSSs and 1493 BHB stars. Sirko et al. [124], finding that ugr photometry did not separate BHB and FBS satisfactorily, preferred the use of Balmer lines as described in section 4.2.1.5 below.
FBSSs enter most discussions of BHB stars as a nuisance population that complicates the calculation of space densities of BHB stars. I have found little discussion of the apparent FBS population (e.g., space densities, Galactic distribution, clumping, specific frequency, abundance distribution) in the SDSS literature. More about this possibility in section 4.4.1 below.

Other photometric criteria
Morrison et al. [78] used the Washington photometric system to search for halo substructure produced by satellite accretion. They chose BMP stars ( [99]), of which FBSSs are a subset, as one of their halo tracers. Using Washington M − T 2 as a temperature indicator they found 23 BMP to V = 19 in an area of 2.75 deg 2 in accord with expectations (see their Fig. 2). In their discussion apparent magnitude, which limits the sample to heights far above the Galactic plane, isolates stars with low [Fe/H].
FBS candidates have been identified in the Strömgren photometric surveys of Olsen [82,83] who lists 84 candidates in the summary tables of his two papers. Stetson [132] identifies 15 possible metal-poor FBSSs in his Table 9. I found it difficult to assess the reliability of these assignments mainly because of the confusing graphical displays of results. It is my impression that Strömgren filters are not ideal tools for wholesale identification of FBS. Narrow bandwidths of the filters are a major drawback.  [91]; (right panel) abundance calibration of CaII (K) by [64]. The figures are reproduced with permission of the AAS.

Hybrid spectro-photometric methods
Pier [91] pioneered the identification of bona fide metal-poor blue horizontal branch stars (BHB) of the halo field and, thus indirectly, FBS stars by use of B − V as a temperature coordinate, the equivalent width of the CaII K line as an abundance indicator, and the widths of Balmer lines as a gravity (luminosity) indicator. Following [117], he estimated metal abundances by calibration of the CaII K line as shown by the diagrams in Fig. 4.4, hereafter BV K diagrams.
The left panel contains measured equivalent widths. The right panel contains a calibration provided by [64]. Again following [117], Pier [91] showed that FBSSs and BHB stars could be disentangled in a HB candidate list by use of D 0.2 , the full width of a Balmer line (here Hδ ) at a depth 20% below the local continuum level. How well this works is illustrated in Fig. 4  success with which these parameters separate BHB stars and FBSSs is shown in Fig. 4.6 and 4.7.
Concordance of classification assignments based on these three parameters is reassuring. Kinman et al. [52] found that more than half of the A-and F-type stars fainter than V = 13.0 and with (B −V ) 0 < 0.23 are not BHB stars, but have surface gravities more like those expected for main-sequence stars. They remark that the more metal-poor of these are likely to be the blue metal-poor (BMP) stars discussed by [99].
Flynn, Sommer-Larsen & Christensen [35] compared the performance of Strömgren c1, (b − y) and D 0.2 , (B − V ) photometry to separate BHB from FBS . They concluded that both systems work but that the D(0.2), B−V system made more efficient use of telescope time. Finally, Carney et al. [20] found a few (n = 6) FBSSs in their radial velocity survey of high proper motion stars. (B − V ) is their temperature parameter. They derived abundances by matching their spectra to a grid of synthetic spectra. The low proper motion limits, 0.2 yr −1 , of the Giclas and Luyten surveys from which their sample was drawn confines the Carney et al. [20] survey to a small volume of space in which only a few FBSSs are expected. In a most refreshing example of cross fertilisation in astronomy Clewley et al. [26] borrowed the Sérsic [121] function from extragalactic astronomy to make analytical fits of observed Balmer line profiles in A-type stars. They use the Sérsic scale-width parameter b and exponent c to derive gravities and temperatures of Atype stars. Fig. 4.8 shows that the Sérsic exponent c is well-correlated with (B−V ) o , hence, temperature. The scale-width parameter b effects a clean gravity separation of metal-poor main sequence and BHB stars. The BV K diagram provides abundances. Brown et al [17] compare the various hybrid methods for isolation of BHB stars from FBSSs (see their Fig. 5) from which it is evident that the Sérsic parameters do the best job.

Spectroscopic Criteria
Xue et al. [150] used a similar application of the Sérsic function to effect a clean separation of FBSSs from BHB stars as shown in Fig. 4.9, where the Sérsic b and c parameters were derived from measurements of Hγ. Recall that c is a temperature parameter, b is a gravity parameter (the surface gravities of FBSSs exceed those of BHB stars by approximately one order-of-magnitude). Because Xue et al. [150] were primarily interested in kinematic substructure, they confined their analysis to the BHB stars. However, the FBS sample contains a wealth of additional untapped information about the stellar content of the halo.  This remarkable database can be used to resolve the Galactic halo BMP population into FBSSs formed in situ and FBSSs accreted from satellites. Recall that [α/Fe] is systematically low by ∼ 0.2 dex at all [Fe/H] in the red giants of dwarf spheroidal satellites of the Milky Way relative to the bulk of Galactic halo stars. This is illustrated in Fig. 4.10 taken from Venn [145], where black boxes denote red giants in the dwarf spheroidal galaxies Carina, Draco, Fornax, Leo I, Sculptor, Sextans, and Ursa Minor [38,122,123], and the small circles denote various species of Galactic stars.
Note further that two of the three α−elements used to construct Fig. 4.10 possess prominent lines (Mg b, CaII K) that can be measured with modest spectral resolution, say R = 5000. Finally, note that an early exploration (PS00) yields promising results (see Section 4.6 below). This is a project ready to go.

FBS of the thick/thin disc
If McCrea's mass transfer produces most of the FBSSs, then we must be surrounded by lots of them in the thick/thin discs. From an assemblage of star counts Sandage [114] estimated stellar densities of the thin disc, thick disc, and halo to be in the proportions 200:22:1. Scaling the local metal-poor FBS number density, ∼ 350 kpc −3 , at the solar circle, by 100 in round numbers, we expect ∼35000 disc FBSSs brighter than V ∼14.5, of which approximately 140 should be in the Henry Draper catalogue, and 10 in Olsen's surveys which were limited to V < 8.3. By this reckoning Olsen found too many disc FBSSs (see section 4.2.1.3 above).
A convincing procedure for wholesale identification of disc FBSSs, simpler in its application than detailed one-by-one analysis [36,37], has yet to be devised. Perhaps, in view of the high binary fraction, 0.76, among PS00 sample stars with [Fe/H]> −1, we should revisit the UBV identification criteria.

Group Properties of Metal-Poor FBS
This section is devoted to a number of characteristics of metal-poor FBSSs that set them apart from other stellar groups. The first, to which all others are subsidiary, are the colour boundaries which define the group. The boundaries are defined in a number of photometric systems.

Colour boundaries
In all practical cases the red (cool) boundary of the blue straggler domain is defined to be at or near the colour of the MSTO of the stellar system in which they occur, i.e., the boundary of the group is defined by stars which are not members of the group. Such a definition leads to the artificial edge in the beautiful photometry of NGC 6809 [65] indicated by the dashed curve in the right panel of Fig. 4.11. An obvious (to me) sequence of mass transfer binaries extends continuously into the single-star main sequence in the left panel. Such a red extension was a natural ingredient of the PS00 toy model, and the more sophisticated applications of Eggleton's code [34] by, for example, Tian et al. [138] and Chen & Han [24] who, however, did not make calculations for old metal-poor systems considered here. Ryan et al. [110,111] reach the same conclusion, arguing that Li-deficient binaries with greater-than-average axial rotation below the MSTO should be regarded as mass-transfer binaries.
A second logical defect of this definition is dramatised by considering the MSTO (B −V ) o values for two well-studied clusters each of which contains BSS. The clusters M67, and NGC 5466 have MSTO (B −V ) o values of 0.50 [142] and 0.39 [2], a large difference, comparable to the entire colour range of the FBSSs, due primarily to the ∼ 2 dex difference in metallicity. FBSSs with this range in metallicity are common in the halo/disc field, where there are no MSTOs to guide us.
What we realise from this cluster comparison is that there is no one-size-fits-all red (low temperature) boundary to the FBS domain. Furthermore, the field contains sizable numbers of FBSSs with abundances well below the low limit, [Fe/H]∼ −2.5, of the globular cluster population, and a fraction of these are CEMP-s stars, formed by mass transfer from AGB companions, that pay no heed to the MSTO; outstanding, indubitable examples are CS 22964-161 [135] and CS 22949-008 [68]. An even larger fraction is formed by mass transfer from ordinary RGB companions. As we shall see in Sect. 4.6 below, knowledge of the amounts of mass transferred, whether by Roche lobe overflow (RLOF) or wind accretion is now or will soon become important for estimation of dilution of the accreted mass by the receiver envelope, for calculating changes in dilution modified by thermohaline mixing, for accurate calculation of the efficiency of wind accretion in the variety of scenarios posed by binaries with different orbital parameters, and for reconciliation of the relative numbers of MS and giant CEMP-s stars.
It is possible to generalise the cool boundary for metal-poor FBSSs by converting it to a parameter that can be calculated for each star, rather than a parameter defined for the whole group. Because of the large ages of metal-poor halo stars, MSTO colour varies only slowly with age, d(B −V )/dt ∼ 0.008 magGyr −1 [152]. Therefore, with negligible error we may adopt a single, canonical age, say 13.  Lower limits are the best that can be achieved, because the initial masses of the receivers, hence their initial B −V colours, are unknown: they may lie within a considerable range of values at or below their MSTO values (PS00, [111]). The

Specific Frequencies
To estimate the incidence of FBSSs in their parent population we [100] introduced specific frequencies, S BMP , defined as the ratio of space densities of BMP and HB stars near the solar circle. HB stars are a convenient reference population because both theory and observation support the notion that HB density is closely proportional to total population density. The HB models of [60] with typical halo abundance Z = 0.0004 have lifetimes that range from 0.90 × 10 8 yr for mass M/M = 0.52 to 1.14 × 10 8 y for mass M/M = 0.76, and the average number ratio, 1.38, of HB stars to red giants more luminous than the horizontal branch in metal-poor globular clusters [19,153] has a standard deviation of only 0.15. Lower RGB stars with luminosities comparable to those of BSSs [13] or MS stars near the turnoff [24] are not options in the halo field, because such stars cannot be identified unambiguously. We [100] used our high value S BMP = 8 relative to the values < 1 for BSSs in globular clusters to conclude that cluster-type BSSs are a minor constituent of the BMP population, and suggested an extra-Galactic origin. We were overly enthusiastic. Subsequent recognition of the high binary fraction among BMP stars (PS00) produces a lower specific frequency for FBSSs, S BMP = 4.0, that is nevertheless an order-of-magnitude larger than those of the halo globular clusters, as shown in Fig. 4.13. Notice that S BMP values are conspicuously larger in the sparse globular clusters of the outer halo, identified by name in the right panel of Fig. 4.13.
The marked decreases with increasing cluster Luminosity (mass) and the King [51] concentration parameter c played key roles in formulation of the view that collisional disruption of long period (wide) binaries [61,47], by far the most numerous in the orbital period distribution of Duquennoy & Mayor [32], accompanied by merger of the much less numerous short-period binaries ( [69]) are the two physical processes responsible for the low specific frequencies of BSSs in GCs relative to the field. Piotto et al. [96] confirmed the correlation of specific frequency with absolute luminosity and the relatively low specific frequencies with their elegant HST data for 56 GCs shown in Fig. 4.14. The upper bound to specific frequency among the oldest open clusters extended the correlation essentially to the field value of PS00 [31].
The disruption of wide binaries in M22 is contested by Côté et al. [28], in spite of the fact that their own 22 yr search led to a marked deficiency of such binaries rela-  tive to the Galactic field. A related situation was encountered by Mayor, Duquennoy & Udry [70] in ω Cen, who reported that only 2 of 32 CEMP stars in that cluster are spectroscopic binaries, contrary to the expectations of McClure & Woodsworth [71]. At issue is whether CEMP stars in these two clusters are produced by McCrea-type star-by-star mass transfer or by pollution of intra-cluster gas during evolution of a previous generation of stars. This topic has a fascinating history [44,80,143,66,67] beyond the purview of this chapter.

The Distinguishing Characteristics of FBS Binary Orbits
The orbital characteristics of FBSSs, discussed at length by PS00 and Carney et al. [21], are these: (a) the mass functions of FBSSs are smaller by a factor of two than those for binaries of the disc [32] and high proper motion samples [59] as illustrated by the cumulative distributions in the left panel of Fig. 4  Straight-line segments join alternative orbital solutions for a number of FBS binaries obtained by PS00. Such alias periods, three of them for three of the stars, were an unfortunate, inevitable consequence imposed by annual/biennial observing trips to Chile. I included these alternatives in the middle panel of Fig. 4.16 to assure the reader that the conclusions about periods and eccentricities are not sensitive to which alternatives are chosen. It is commonly accepted that periods lengthen during conservative mass transfer after the mass of the donor falls below that of the receiver [45] and that such mass transfer circularises orbits. However, Sepinsky et al. [118,119,120] have revisited mass transfer with and without mass loss in binaries with eccentric orbits and obtain a wide variety of outcomes that depend on initial conditions. Even in the conservative case periods and eccentricities may either increase or decrease on time scales that range from a few million years to a Hubble time. FBSSs and CEMP-s stars provide a rich database with which to test these recent theoretical developments. (c) Finally, PS00 found no double-lined spectroscopic binaries (SB2) among their FBSSs while SB2 comprise 20% of the binaries in the high proper motion sample of Latham et al. [59]. The absence of detectable secondaries among FBS binaries is a natural consequence of the mass transfer hypothesis. I [99] did discover one extremely metal-poor SB2, CS 22873-139 and deduced an age of 8 Gyr from a discussion of the observed colours, suggesting that this binary came to the Milky Way from a satellite like the Carina dSph. This result was challenged by Spite et al. [129] who derived a lower T e f f from the Hα profile. Interestingly, however, they also found low [α/Fe]∼ 0 and did not detect lithium -results expected for a BSS accreted from a dSph (see Fig. 4.10 and the discussion in section 4.6.2) To summarise: the orbital characteristics of the FBS binaries are distinctly different from the ordinary binaries of their parent populations with regard to mass functions, orbital periods, orbital eccentricities, and incidence of detectable secondaries. FBS binaries are a species sui generis. For simplicity of presentation I did not use the much busier update of this diagram in [27]. Supposing that the ranges of age and chemical composition in the GC sample are similar to those encountered in the halo, I estimate from inspection of Fig. 4.17 that the standard deviation of M V for FBSSs on 0.0 < (B − V ) o < 0.4 is σ < 0.5 mag., which translates to 25% errors in distances to individual stars. The range of galacto-centric distances over which SDSS FBS data could be used to calculate space densities is ∼ 20 kpc, so my gloss on the situation is that FBSSs may be useful for investigations of space density on such length scales. How useful they might be would require more careful error analysis. Nevertheless, FBS have not been entirely discounted for such purposes. Univane, & Gilmore [140] used star counts blue-ward of the classical halo turnoff at B − V ∼ 0.4 to estimate that ∼ 10 per cent of the halo could be attributed to accretion of intermediate-age satellites.

The Galactic Bulge
Recently [25] reported the discovery of BSSs in the Galactic Bulge. They identify BSSs produced by mergers of W UMa stars that follow the path of AW UMa [86] to FK Com [15]. They use these BSSs to place a conservative upper limit on the percentage of genuinely young stars in their sample. Such young stars have interesting consequences for the history of the Bulge. The strong resemblance of the Bulge observational material to that of [69] for the GC NGC 5466, indicated by the side-by-side CMDs of NGC 5466 and the Bulge sample in Fig. 4.18, invites a common explanation for at least a portion of the bulge BSSs.  [69] concluded that all of the BSSs in NGC 5466 can be understood as mergers of W UMa stars. This conclusion, coupled with the great preponderance of long-period binaries in the distribution of Duquennoy & Mayor [32], provides a convenient rationale for the disparate specific frequencies of BSSs in GCs and the halo field.
Clarkson et al. [25], working with a much more complicated dataset, cautiously reach a suitably more modest conclusion, namely, that the Bulge BS population with P < 10 d comprises at most half of all bulge BS binaries. This is more or less consistent with their specific frequency for Bulge BSSs, ∼ 1.23, which is markedly smaller than that of the halo field. If (almost) all the remainder are BSS binaries of longer period, an expectation based on halo experience, they arrive at an upper limit of ∼ 3% for the young (< 5Gyr) population of the bulge. Bensby et al. [6] argue for the existence of an intermediate-age population based on spectral analysis of Bulge dwarfs observed during microlensing events. The age distribution of stars in the Bulge has arisen once again, like the Phoenix, as a new direction for research.

Halo Streams
Morrison et al. [78] included BMP stars in their list of tracers to investigate structure in the halo produced by satellite accretion, but I could find no subsequent results based on their use. Newberg, Yanny & Willet [79] identified a new polar-orbit stream (Cetus Polar Stream) spatially coincident with the Sagittarius trailing tidal trail, but with systematically lower metallicity ([Fe/H]= −2.1), in which the specific frequency of BSSs differs from that in Sagittarius. More recently Koposov et al. [55] claim that the BSSs belong mainly to Sagittarius and the BHB belong mainly to the Cetus stream. This conclusion requires gross, unlikely differences in specific frequencies of the two streams. Streams in the halo is a fascinating but difficult subject in its infancy, so interpretation of results best awaits further investigation

Metal-rich A-type Stars Above the Galactic Plane: Another Inconvenient Truth
No review of FBSSs would be complete without a digression to the metal-rich Atype stars far above the Galactic plane. The existence of such stars was first recognised by Perry [88] who sought to determine the force law perpendicular to the Galactic plane by use of early A-type main sequence stars near the north Galactic pole, for which accurate distances could be derived from suitably calibrated Strömgren photometry. Perry [88] constructed a density distribution perpendicular to the plane, shown in the left panel of Fig. 4.19, that produced an unbelievable force law. He was obliged to consider that the A-type stars more than 400 pc above the plane were a mixture of two populations. This result prompted Rodgers [108] to investigate the A-type stars at the south Galactic pole (SGP) identified by [90]. He identified 21 stars on −0.04 < (B − V ) o < 0.32 with "normal" abundances of calcium and thought of no satisfactory explanation. A decade later Rodgers, Harding & Sadler [109] confirmed Rodgers [108] first abundances, used their radial velocities and a believable force law ( [84,48]) to calculate Z max values that range from 1.5 to 8 kpc. They hypothesised that these stars were formed during a recent (< 10 9 yr ago) collision with a gas-rich satellite galaxy.
Lance [57,58]  After considering various alternatives, Lance arrived at the earlier conclusion of Rodgers et al. [109]: about 0.6 Gyr ago a slightly metal-poor, but still gas-rich, satellite merged with the disc of the Galaxy. During the collision stars formed "that do not partake of the usual age-abundance-kinematics relationships shown by other Galactic stellar groupings" (Lance verbatim).
So far as I am aware, Lance's work has never been refuted. Rather, it simply has been ignored because, I suspect, her results do not conform to current dogma about Milky Way satellite encounters. According to ADS her paper ( [58]) has received a total of 56 citations in 24 years, the last being 5 years ago in 2007. In contemporary vernacular, the astronomical community "never lets facts stand in the way of a good idea".

Abundance Issues
Three abundance topics are of particular importance for FBSSs: (a) Li (and Be) as diagnostics of deep mixing in FBSSs and in the RGB/AGB antecedents of their present white dwarf companions (b) the α-elements as possible discriminants for satellite accretion, and (c) neutron-capture elements as constraints on AGB models, thermohaline convection, and dilution. Fig. 4.20 Locations of early A-type stars among RYI isochrones, according to [58]. This figure is reproduced with permission from the AAS.

Lithium
Lithium deficiencies in blue stragglers of various ilks relative to those of the Spite plateau [128] have been recognised for two decades [107,46,39,22]. More recently [9] have added Be deficiencies to the problem. Because 7 Li is burned to 4 He ash at temperatures greater than ∼ 2 × 10 6 K, Li deficits are widely believed to be consequences of mixing processes that are plausible consequences of collision, merger, or mass transfer from a cool giant. These mixers are by no means the only possibilities. Pinsonneault et al. [93,95] consider rotation-driven circulation, while Ryan et al. [111] discuss rotation produced by angular momentum transfer during binary mass transfer. They suggest that such transfer could produce the rapid axial rotations (sic!), v sin i values of 8.3, 7.6, and 5.5 kms − 1, of three Li-deficient stars below the MSTO. This suggestion can be reframed as an hypothesis amenable to observational test. Finally, in consideration of the "Lithium Dip" in young stellar populations [8], it was, perhaps, inevitable that radiative levitation, gravitational settling [76], and associated mas -loss [30] would be investigated.
The link between blue stragglers and the small fraction of Li-deficient stars below the MSTO, required by observation [65], is a natural consequence of power-law mass spectra adopted for the initial primaries and secondaries of primordial binaries used in the toy model of PS00. This link was also noted by Ryan et al. [110,111]. Worry by [110,111] that some Li deficient MS stars are not known binaries will only become a real problem after these stars have been subjected to the same careful long-timescale scrutiny accorded the disc [32], halo [59], and BMP (PS00) samples. Norris et al. [81] note that Li deficiency is not always accompanied by AGB carbon and s-process enrichments. For some unstated reason they do not consider the rational possibility that mass transfer from ordinary RGB companions will deplete Li without affecting other [X/Fe].
Most recently Masseron et al. [68] have made an extensive investigation of Li in CEMP-s stars. Among the several important issues addressed in their paper is the unequivocal demonstration, provided by CS 22949-008, that mass transfer binaries populate the main sequence well below the MSTO. Equally interesting, they present a detailed discussion of the role of dilution, as parameterised by Gallino and his colleagues [7] and modified by thermohaline mixing [143], in creating the dispersion of Li abundance in the Spite plateau. Detailed discussion of their results is beyond the scope of this review; I only note that they [68] provide yet another empirical argument for the notion that FBSSs represent an extension of the family of mass transfer binaries to locations above (hotter than) the MSTO. Finally, Glebbeek et al. [40] calculated surface abundances of blue straggler models and comment that it may be possible to use Li as a tracer to distinguish between formation by mass transfer and formation by collision.
One caution about detection of Li in FBSSs should be mentioned. Due to increasing ionisation of Li I (ionisation potential= 5.4eV) the strength of Li I 6707Å decreases steadily at temperatures above MSTO values, as shown in Fig. 4.21, a plot of equivalent width of Li I 6707Å versus T e f f along the Spite plateau made from data in Table 2 of [137]. Linear extrapolation into the FBS region by use of the line drawn through the data in Fig. 4.21 indicates that equivalent widths for normal Spite-plateau abundances fall below 10 mÅ at T e f f > 6500 K. Considering that most of the FBSSs found in the HK and HES surveys are fainter than V = 14, detection of Li with the requisite resolution (R > 25000) and signal-to-noise ratio (S/N> 50) in most FBSSs can only be accomplished with large telescopes.

Alpha/Fe
The relatively lower values of [α/Fe] found for red giants in Milky Way satellite galaxies (see Fig. 4.10 in section 2 above) suggests the possibility that [α/Fe] might serve as a discriminant with which to distinguish FBSSs accreted from Milky Way satellites from FBSSs home-grown in the halo. The data for FBSSs, summarised in   Table 7 of PS00 first into two groups by metal abundance at [Fe/H]= −1 and then into binary and constant velocity groups within each abundance group. I calculated average values of [α/Fe] for these four groups, first treating Mg and Ca as the α-elements in column 4 of Table 1, and then including Ti, frequently treated as an α-element, in column 6. The two cases are indistinguishable. The last column of Table 1 contains the number of stars in each group. For the FBS stars with [Fe/H]< −1 the average [α/Fe] is lower among the constantvelocity stars by 0.15 dex. The differences in columns 4 and 6 exceed the sums of the standard deviations of the means and are comparable to the amounts by which red giants of satellite galaxies lie below Galactic stars in Fig. 4.11. The differences found for the samples with disc metallicity are insignificant. The abundances were derived from spectra of low-to moderate S/N for modest numbers of stars, so these results should be regarded as tentative. They are presented here as incentive for a definitive investigation.
Finally, we only mention that Ivans [49], on the basis of three stars, promote the existence of yet another population of metal-poor stars ([Fe/H]∼ −2) in the Galactic halo. They are characterised by unusually low abundances of the α-elements Mg, Si, and Ca and the neutron-capture elements Sr, Y, and Ba, and other peculiarities in abundances of the Fe-peak group. One of the three stars, CS 22966-043, that define this putative new population is a pulsating binary blue straggler [102].

The Neutron-Capture Elements
Bisterzo et al. [7] have interpreted the abundances of 94 s-process enriched metalpoor C-stars, the CEMP-s stars, by comparison with appropriate AGB models. I confine my discussion below to 4 FBSSs among the 27 MS stars in their [7] sample. To interpret the observed abundances of any CEMP-s star the following parameters must be specified: (a) chemical abundances, [X/Fe], in the envelopes, hence ejecta, of various AGB models, (b) a set of standard abundances for the companion star, (c) the mass of ejecta captured by the companion, and (d) the envelope mass of the receiving star into which AGB ejecta are mixed.
If mixing were confined to the diminutive convective envelope, 0.001 M/M , of a typical FBSS with T e f f ∼ 6400 K ( [94]), the wind accretion of Boffin & Jorissen [10] would be more than adequate. However, Stancliffe et al. [130] complicated the discussion by noticing that the enhanced molecular weight of overlying He-and C-enriched AGB accreta will induce thermohaline mixing throughout ∼90% of the mass of a typical MS star. In a rejoinder Thompson et al. [135] argue that helium and the heavy elements settle in the surface layers of the receiver during the mainsequence lifetime (∼3 Gyr) of a typical (1.3 M ) AGB star employed by Bisterzo et al. [7], thus creating a stabilising µgradient that confines thermohaline mixing to a thin surface layer until the stabilising µ-gradient is flattened by sufficient accretion of high-µ matter. The various issues of mixing associated with CEMP-s stars are reviewed by Stancliffe et al. [131].
Bisterzo et al. [7] combine items (c) and (d) above into their dilution parameter, dil = log M CE /M AGBacc , the log 10 of the ratio of mass of the convective envelope of the receiver to the mass of AGB accreta. They then try various combinations of AGB compositions and dilution factors to achieve the best agreement between observed and predicted abundances for each star. Details of the AGB models and element-by-element model-fitting procedures are beyond my competence. I restrict my discussion to aspects of their work pertinent to the FBSSs.
Physical data for the four FBSSs studied by Bisterzo et al. [7] are presented in Ta  They are minimum masses because there is no way to know the initial masses. These minimum masses can easily be provided by the wind accretion calculations of Boffin & Jorissen [10], and they are more than sufficient to completely fill the surface convection zones of these stars, but they require dilution parameters of order unity if the AGB material has been mixed into ∼ 0.7 M/M of receiver envelope. I include these calculations merely to indicate that the means are at hand to place additional observational constraints on the AGB models used to explain CEMP-s stars.

How Many Evolved Mass-transfer Binaries Are There?
This topic was belabored by me earlier [105]. To estimate the amount of mass transferred requires a theory of accretion. Boffin & Jorissen [10], in a limited exploration of their parameter space, concluded that accretion in an AGB wind could produce a Ba star like classic ζ Capricorni ( [12]). Subsequently, Han et al. [43] and Theuns, Boffin & Jorissen [134] concurred that accretion from an AGB wind might produce Ba star and CH star companions in binaries with periods up to 100,000 d or more, a range that extends beyond the frequency maximum, near P= 50, 000 d, for F-and Gtype dwarfs in the solar neighbourhood [32]. On the other hand, Boffin & Zaćs [11] observed that overabundances of s-process elements decline systematically with increasing orbital period (separation), as they must, in a recognisable albeit imperfect correlation. Their results are in qualitative agreement with those of Jorissen & van Eck [50] who found a steep drop in numbers of Ba star spectroscopic binaries with P> 3000 d, the number falling to zero at 10,000 d. Failure to find such binaries is not a radial-velocity precision problem, but it may be an observer persistence problem. The K 1 value of a 0.8 M star in a 10,000 d orbit with a 0.5 M white dwarf com-panion is 4 kms −1 , easily detectable by all modern high-resolution spectrographs, if someone has the patience to monitor radial velocities on a 30-year timescale. My gloss on all of this is that any census of CEMP-s stars is conditioned by observer persistence and the sensitivity of survey detection criteria. Thresholds for detection skew the observed orbital period (size) distribution toward lower values and such bias acts to produce a discrepancy between the period distributions of Jorissen & van Eck [50] and Duquennoy & Mayor [32].

Pulsating Blue Stragglers
SX Phe stars are metal-poor pulsating blue stragglers found in GCs and the halo field. See Cohen & Sarajedini [27] and references contained therein. The issues of SX Phe stars are complex and multifarious. I confine my attention here to only two of them.

Non-variable Stars in the SX Phe Instability Strip
PS00 found one large-amplitude SX Phe star and two probable low-amplitude versions [101,102] among 40 BMP binaries. They noted that other low-amplitude pulsators might contribute to the radial velocity residuals of some of their binary orbits, but it is clear from examination of velocity residuals in Fig. 7 of PS00 that velocity amplitudes of putative pulsators in many of these binaries would have to be near or below the 1 kms −1 level. High-amplitude pulsators like SX Phe are a distinct minority among FBS spectroscopic binaries.
Kepler data for the δ Scuti stars, Population I analogues of SX Phe stars, discussed by Balona & Dziembowski [1], pre-empt all previous photometric inquires into this topic. In spite of exquisite photometric precision that permits detection of very low-amplitude (< 100 ppm) variables, they find that the δ Scuti fraction of stars in the instability strip barely reaches 0.5 only in the narrow temperature interval 7500 < T e f f (K)< 8000, and falls to very low levels below 7000 K and above 8500 K. The great majority of FBSSs in the δ Sct instability strip are non-variable even by stringent Kepler standards, a circumstance contrary to all previous experience with the instability strips of the RR Lyrae stars and classical Cepheids. This concentration to a narrow interval of T e f f , less than 300 K, is borne out approximately by the locations of high amplitude δ Scuti and SX Phe stars in the (M V , T e f f ) plane of McNamara [74] reproduced here in the left panel of Fig. 4.22.
McNamara's narrow High Amplitude Delta Scuti (HADS) strip, identified by the letter "M" in the right panel of Fig. 4.22, cannot be predicted theoretically according to Petersen & Christensen-Dalsgaard [89]. Furthermore, stability analysis [87]  does not explain the paucity of SX Phe stars within the much broader temperature boundaries (thick solid lines in the right panel of Fig. 4.22).
SX Phe stars identified in the Fornax dSph galaxy [97] are not confined to the HADS strip of Figure 4.22 above, but the stars are faint and photometric errors blur this conclusion. As in the Kepler field the SX Phe stars comprise only a small fraction of the total BS population of Fornax. Balona & Dziembowski [1] suggest that unspecified damping mechanisms operate to suppress pulsation in many BSSs. According to them, "Perhaps we need to wait for the development of non-linear, non-radial calculations to properly address this problem." Explanations for many SX Phe phenomena are still in disarray.

RRLYR-02792, Archetype of a New Kind of Mass-transfer Pulsator
Pietrzyński et al. [92] describe a new kind of pulsating star found in an OGLE eclipsing binary, RRLYR-02792 [127]. Its light and radial velocity variations resemble, approximately, those of an RRb star with period P = 0.627 d, but its dynamical mass, 0.26 M , is incompatible with a location on the horizontal branch. Pietrzyński et al. [92] believe that they have caught an Algol-type binary in a short-lived evolu-tionary phase following mass exchange, in which the pulsator possesses a partially degenerate helium core and a small H-shell-burning envelope. The pulsator is now shrinking as it evolves toward the hot subdwarf region at a rate compatible with the decline of its pulsation period, 8.4 − 2.6 × 10 −6 d yr −1 . Wonders never cease.

Mass Transfer in Hierarchical Triples
Approximately half of the short-period (P < 30 d) binaries in the solar neighbourhood reside in multiple systems [139], so we expect to find them among main sequence CEMP-s stars, whether above or below the MSTO, if the statistical properties of disc and halo binary populations are similar. Apparent confirmation of such expectation is provided by CS 22964-161 [135] and CS 22949-008 [68], doublelined binaries in which both components are carbon and s-process enriched. Both components of CS 22964-161 have subgiant characteristics in contrast to CS 22949-008, in which both components lie well below the MSTO. In both cases the AGB donor must have been the remote third star of an hierarchical triple. This circumstance puts a lower limit on the semi-major axis of the AGB orbit, hence upper limits on the density of the AGB wind at the close binary and on the accretion of AGB gas by that binary system. Soker [126] initiated inquiry into the very case of interest here, wind accretion by the close binary companions of a remote AGB in an hierarchical triple system. The problem is extremely complex, requiring specification of the inclination angle of orbital planes and treatment anew of Bondi & Hoyle [14] accretion in an AGB wind, including assumptions about cooling times and angular momentum transfer in the accretion column. With regard to the latter Davies & Pringle [29] called attention to a conceptual problem for angular momentum transfer in an inhomogeneous medium that was not resolved in subsequent investigations by Livio et al. [62,63] Accretion rates for the two binary components may differ, in which case they will possess different surface enrichments by the AGB accreta. Investigation of accretion in hierarchical triples adds a new dimension to McCrea's initial ideas.

Heresy
I conclude my review of issues that attend FBS and mass transfer, by brief enumeration of a few mildly disquieting observational facts.
Lithium again. After building a case for AGB enrichment of the surface layers of CS 22964-161, enrichment in gas that has endured deep mixing in cool giant atmosphere, Thompson et al. [135] were obliged to appeal to some process by which lithium is produced in the AGB star prior to mass transfer, and by just the right amount that elevates it to the Spite plateau. Extraordinary coincidence, one may suppose. The process must be a bit less than extraordinary, because it must also account for the detection of appreciable lithium in two additional relatively bright (nearby) MS CEMP-s stars, CS 22898-027 [136] and LP 706-7 [81].
The three aforementioned stars share another property illustrated in Fig. 4.23: extant observations provide no clear evidence for orbital motion. The results for CS 22898-027 and LP 706-7 are taken from [105]; those for CD 22964-161 are velocity residuals with respect to predictions of the binary orbit under continuing investigation by Ian Thompson (private communication). The centre of mass velocity ought to vary sooner or later, if the third AGB relic is present. CS 22880-074 [105] and TY Gru ( [106] are additional examples of apparently misbehaving CEMP-s stars. I leave it to the reader to consider whether the radial velocity behaviours of these stars (never mind Li!) are all statistical flukes, chance consequences of small orbital inclinations, or are they warning signals about the universal AGB paradigm for production of s-process elements.