RUNAWAY AND HYPERVELOCITY STARS IN THE GALACTIC HALO: BINARY REJUVENATION AND TRIPLE DISRUPTION

A close pass of a binary star near an MBH results in an exchange interaction, in which one star is ejected at high velocity, while its companion is captured by the MBH and is left bound to it. Such interaction occurs because of the tidal forces exerted by the MBH on the binary components. Typically, a binary (with mass, M_bin = M_e + M_c and semimajor axis, a_bin), is disrupted when it crosses the tidal radius of the MBH (with mass M_BH), given by

$$\begin{equation} r_{t}=\left(\frac{M_{\rm BH}}{M_{\rm bin}}\right)^{1/3}a_{\rm bin}, \end{equation} \tag{ 1 }$$

and one of the stars (with mass M_c) is captured close to the MBH and the other (with mass M_e) is ejected at high velocity of about (Hills 1991; Bromley et al. 2006)

$$\begin{eqnarray} v_{\mathrm{\rm BH}} & = & 1800\;{\rm km\;s^{-1}} \nonumber \\ & & \times\, \left(\frac{a_{\rm bin}}{0.1\;{\rm AU}}\right)^{-1/2}\left(\frac{M_{e}+M_{c}}{2\;M_{\odot }}\right)^{1/3}\!\left(\frac{M_{\rm BH}}{4\!\times \!10^{6}\;M_{\odot }}\right)^{1/6}\nonumber\\ &&\times\,\left(\frac{2M_{c}}{M_{e}+M_{c}}\right)^{(1/2)}. \end{eqnarray} \tag{ 2 }$$

The same scenario could be extended to a triple disruption by an MBH. Triple stars have a stable configuration if the semimajor axis of the outer binary, a_o is much larger than the semimajor axis of the inner binary, a_i (i.e., a_i ≪ a_o). In such hierarchical triples, the outer binary could be disrupted by the MBH while the inner closer binary is kept bound. In this case a triple disruption could produce a hypervelocity binary, or alternatively a captured binary star near the MBH. The ejection velocity in Equation (2) is strongly dependent on the semimajor axis of the binary (the outer binary in the triple case) and on the mass of the stellar binary (triple in this case). Both of these parameters vary by much between the population of low-mass stars and high-mass stars.

For low-mass stars (M_triple ∼ 3 M_☉, for equal-mass stars) such as those studied by Lu et al. (2007), one requires a_bin = a_o ∼ 0.4 AU for ejection of a hypervelocity binary at ∼900 km s⁻¹. Such close binaries are infrequent (only a few percents of the binary population; Duquennoy & Mayor 1991), and the fraction of low-mass triples with such close outer binaries is negligibly small (Tokovinin et al. 2006).

For higher mass stars such as the observed young B-type HVSs in the Galactic halo, m_⋆ ∼ 2–4 M_☉, corresponding to a triple mass of M_triple ∼ 6–12 M_☉ (assuming equal-mass stars). In this case even a semimajor axis of a_o ∼ 0.6–1 AU is sufficient for the ejection of a hypervelocity binary. High-mass binary stars are known to have higher binary fraction (probably f_bin > 0.8, e.g.; Abt et al. 1990; Mason et al. 1998; Kobulnicky & Fryer 2007) and different semimajor axis distribution than low-mass stars, with a large fraction of them (f_cbin ∼ 0.4) in close binaries (a_bin < 1 AU, e.g., Abt 1983; Morrell & Levato 1991). The triple fraction and distribution of massive stars is still uncertain, but it is strongly suggestive of a high triple fraction among binaries. Evans et al. (2005) find that most if not all of the massive binaries they observed (in Cepheids) are likely to be triple systems. Some f_triple ∼ 0.8 of the wide visual binaries in stellar associations are in fact hierarchical triple systems, where typically the more massive of the binary components is itself a spectroscopic or even eclipsing binary pair (Zinnecker 2005). Fekel (1981) compared the properties of close multiple stars. He finds a fraction $f_{\frac{1}{2}\,\rm yr}\sim 0.2$ of the more massive systems (we choose systems with total mass of > 6 M_☉) to have outer binary periods shorter than half a year, corresponding to a_o ≲ 1 AU, i.e., with characteristics allowing for the ejection of hypervelocity binary if they were disrupted by an MBH. The fraction of close triples (such as those in Fekel 1981) out of the total triple population is unknown. Lacking a better estimate, we assume this fraction to follow the fraction of close binaries; i.e., we take the fraction of close triples out of the full triple population to be $f_{\rm ctriple}=f_{\rm cbin}\cdot f_{\frac{1}{2}\,\rm yr}=0.4\times 0.2=0.08$ (note that the fraction of close triples might in fact be higher, since f_cbin is taken for binaries with a_bin < 1 AU where as Fekel's sample also contain triples with wider outer binaries). Taken together we can estimate the triple fraction of hypervelocity binary potential progenitors to be f_prog = f_bin · f_triple · f_ctriple ≃ 0.05 (taking a binary fraction of 0.8 of which 0.8 are triples, and 0.08 of those have outer binaries with period <0.5 yr). We note that there is some weak trend for more massive stars to have higher multiplicity, however, more observational data are required for a better resolution of the mass dependence of the multiplicity, and the quoted values are assumed to represent all MS B stars.

Note that very few studies on observed massive triples have been done, and therefore we also try to estimate the appropriate triple fraction differently, based only on the better known characteristics of massive binaries, where we follow the method used by Fabrycky & Tremaine (2007). Again, we assume that the orbital and stellar characteristics of the third component in a given triple could be chosen from the same distributions of the binaries¹. We pick a sample of randomly chosen triple systems taken from the appropriate binary distributions. For our sample we choose many triples with initial orbital distributions such that both their inner and outer binaries are taken from the best-fit observed distributions of Kobulnicky & Fryer (2007). Each given triple has an inner binary with semimajor axis a_i and masses m₁ and m₂; and an outer companion with mass m₃ in an orbit with semimajor axis a_o. The period is chosen from a distribution of orbital separations which is flat in log space, f(log p) ∝ const, corresponding to f(r) ∝ 1/r (i.e., Öpik's law). The minimum value for the appropriate semimajor axis is taken to be twice the radii of the binary stars, i.e., separation of a contact binary which does not immediately merge. The maximal value is taken to be 1000 AU, following the best-fit distribution found by Kobulnicky & Fryer (2007). The mass ratio, q, is chosen from a power-law distribution (f(q) ∝ q^−0.4); we also tried other distributions suggested in the literature and found only minor effects on the final calculated fraction. The mass of the tertiary companion, m₃, was determined by choosing q = m₃/m₁ + m₂ from the same mass ratio distribution. This approach implies that the mass of the third star was correlated with the mass of the inner binary, but we do not believe that this correlation has any significant effect on our results.

Two periods and eccentricities were picked in the same manner discussed in Fabrycky & Tremaine (2007). The smaller (larger) period was assigned to the inner (outer) orbit. The semimajor axes were computed from these masses and periods assuming noninteracting Keplerian orbits. The mutual inclination distribution of the tertiary is assumed to be isotropic with respect to the inner binary. After these parameters were selected, we used the empirical stability criterion used in Fabrycky & Tremaine (2007; see their Equation (37), originally formulated in Mardling & Aarseth 2001) to determine whether the system is hierarchical or if it will disrupt in a small number of dynamical times. If the semimajor axes obeyed this criterion then we accepted the triple as stable, otherwise, we assumed it disrupted. We then found the fraction of stable triples, such that their disruption by the MBH in the GC could eject a hypervelocity binary, i.e., have outer semimajor axis small enough for the ejection velocity to be high.

From a large sample of triples (10⁵) we find that about 0.03 of potentially formed triples are stable triples that could serve as hypervelocity binaries progenitors, where these results are not very sensitive to the prime mass m₁ of the inner binary component. This is generally consistent with the observation based estimates given before. We conclude that ∼0.03–0.05 of all massive HVSs could have been ejected with a binary companion or have left a close binary captured in an orbit very close to the MBH.

Given the observed high velocity of HE 0437−5439, a dynamical scenario for this star would most likely require an interaction with an MBH. Gualandris & Portegies Zwart (2007) have suggested that a tidal disruption of a binary by an IMBH in a young stellar cluster in the LMC could produce HVS such as HE 0437−5439 at a rate of 5 × 10⁻⁸ yr⁻¹. We note that such IMBH have not yet been observed in the LMC (or elsewhere). Moreover, Gualandris & Portegies Zwart (2007) have not taken into account a few important considerations. (1) The travel time from the LMC to our Galaxy for such an HVS is about 20 Myr, very close to the ages of the clusters they suggested as possible hosts of an IMBH. For these clusters the HVS should have been ejected immediately after the formation of the IMBH (assuming that the IMBH have formed quickly enough in the cluster to begin with), probably during less than 1 Myr, in order to achieve its current position. Given the calculated ejection rates, only N_eject ∼ 10⁶ × 5 × 10⁻⁸ = 0.05 HVSs could have been ejected, on average, in the relevant time. (2) The stellar mass function has not been taken into account by Gualandris & Portegies Zwart (2007). The fraction of stars as massive as 8.5 M_☉ or more (the estimated mass of HE 0437−5439) is very small, only a fraction of f_IMF ∼ 0.01 of the stellar population is in such massive stars (and likely even smaller, as most of these more massive stars were likely to fuel the growth of the IMBH). (3) The ejection of HVSs is isotropic, and therefore only a fraction of them f_MW < 0.1 would be directed to the Milky Way. Taking together the average number of observable massive (> 8.5 M_☉) HVSs from the LMC (similar to HE 0437−5439) should be about N_eject × f_imf × f_MW = 5 × 10⁻⁵, making this possibility highly unlikely.

Recently, it was suggested that HVSs might be produced through binary–binary dynamical interactions of massive binaries in a dense cluster (Gvaramadze et al. 2008). Leonard (1991) has studied such encounters. He found that the lowest mass star participating in the interaction could attain the highest velocity. Such velocity would be comparable to the escape velocity from the most massive star participating in the encounter. If HE 0437−5439 was ejected from the LMC, it would require an ejection velocity of > 900 km s⁻¹ in order to acquire its current position during its lifetime (Gualandris & Portegies Zwart 2007; Przybilla et al. 2008). For this to happen HE 0437−5439 would need to encounter stars more massive than itself. Even then the fraction of encounters where such velocity could be attained by this star is f_high ∼ 10⁻⁴(4 × 10⁻⁴, 2 × 10⁻³; see Leonard 1991) for encounters where the masses of the other stars are larger than 15 M_☉(30 M_☉, 60 M_☉, respectively). Since binary–binary encounters usually lead to the disruption of one of the binaries, one would require ∼1/f_high such binaries to exist in order for one of them to potentially be ejected at such high velocity. Such conditions, i.e., the existence of hundreds (thousands) of > 30 M_☉ (greater than 15 M_☉) stars in a super dense cluster core are not known to exist in any young cluster in the Galaxy or in the LMC. We conclude that the scenario for ejection of HE 0437−5439 through a dynamical interaction with massive stars in a cluster is highly unlikely.

Recently, Bonanos et al. (2008) and Przybilla et al. (2008) have found the metallicity of the HVS HE 0437−5439 to be low relative to solar metallicity. They suggested this as a possible evidence for an LMC origin of this star rather than a Galactic origin. However, an LMC origin would be difficult to explain dynamically, as discussed above. Moreover, in the following we show that the current metallicity measurements do not rule out a Galactic (and GC) origin for HE 0437−5439.

It is known that the observed abundances of some elements in Galactic B stars are depressed relative to the established solar values (see, e.g., Martin 2004; 2006; and the Appendix). Therefore, one should compare the metallicity of B-type stars such as HE 0437−5439 with large surveys of similar B-type stars. Przybilla et al. (2008) made a comparison with a single galactic B star and a single LMC B star that may not representative of the large scatter in the abundances shown in larger samples. Bonanos et al. (2008) made a comparison with a large B stars survey in the LMC, but for the comparison with the Galactic abundances they took the solar abundances rather that Galactic B stars surveys. Figure 2 shows the spread in the measured chemical abundances for different samples of stars (LMC, Milky Way and the GC stars) found in the literature (see caption of Figure 2). For small samples (with 10 stars or less) the data for each of the stars are shown rather than the mean abundance, since given the very small samples the mean may not be a good representative of the underlying distribution of abundances. For the larger samples the 1σ spread around the mean (i.e., where 68% of the measured values are found) is shown.⁴ We can use these data samples and compare them with the chemical abundances of HE 0437−5439. The results by Przybilla et al. (2008) have systematically smaller error bars, and also contain the abundances for more elements (C, N, O, Mg, Si, and Fe) compared with the results obtained by Bonanos et al. (2008; which do not show the Fe abundance), and are therefore used in the comparison. Nevertheless, given the large differences that exist between the chemical abundances obtained by Przybilla et al. (2008) and those found by Bonanos et al. (2008), the latter results are also shown in Figure 2 for completeness.

Zoom In Zoom Out Reset image size

Comparison of the chemical abundances of HE 0437−5439 as found by Przybilla et al. (2008) to those found in surveys of B-type stars throughout the Galaxy (Daflon et al. 2001 show that its metallicity is highly consistent with their metallicities⁵). Most (greater than 50%) of the stars in the sample have more extreme elemental abundances than that of HE 0437−5439 (for each of the elemental abundances observed; see Figure 2, bottom panel), showing that the elemental abundances of HE 0437−5439 are quite typical of the Milky Way chemical abundances.

Although a galactic origin is most consistent with the metallicities of HE 0437−5439, its high velocity would require an interaction with an MBH, currently known to exist only in the GC. Therefore, its metallicities should be compared with the metallicities of similar unevolved B stars in the GC. Unfortunately, metallicity measurements of stars in the GC region exist only for a small number of stars, none of which are similar to HE 0437−5439 (although some of these GC stars have similar masses, they are at a very different evolutionary stage; Cunha et al. 2007). Therefore, given the current data, drawing conclusions on the origin of HE 0437−5439 based on metallicity comparisons with GC stars is premature. Nevertheless, we shortly discuss such metallicity comparison, but caution that this should not be taken as evidence for the origin of HE 0437−5439, but at most as a possible clue until further measurements of the metallicity of GC stars are available.

The chemical abundances of stars in the GC are known mostly for cool evolved stars (Cunha et al. 2007). Data on two additional highly massive (∼150 M_☉) LBV stars exist (Najarro et al. 2009), but given their very different stellar type and evolution, comparing their abundances with that of HE 0437−5439 is not justified, and we do not use their data. The number of data points (stars) for each element are 10, 7, 6, and 5 for the elements Fe, O, C, and N, respectively. The C, O, and Fe abundances of HE 0437−5439 are found to be consistent with GC values (see Figure 2⁶), but the N abundance is not (with all five stars in the GC sample have higher abundances than those found for HE 0437−5439). We note that better agreement is observed for those elements for which more data exist. The N abundance of HE 0437−5439 is lower than those of the GC stars. However, since CNO cycle mixing can convert these elements in the GC stars (see, e.g., Carr et al. 2000; Cunha et al. 2007) and in HE 0437−5439, one should be careful and also check the sum of these elements and not only compare each of these elements by itself. We find that the sum of these elements is consistent with that of the GC sample stars, i.e., not even the N abundance of HE 0437−5439 could be interpreted as an evidence against a GC origin. Moreover, given the low statistics of the GC sample, the lower N abundance is not statistically significant, even by itself. Given the wide range of abundances found in different Galactic B-type stars surveys (see the Appendix), it is possible that this specific HVS B star may have lower abundances of these specific element.

The middle panel of Figure 2 shows the comparison of the elements abundances of HE 0437−5439 to those found in the LMC. The metallicities of B stars in the LMC were found by several groups (the largest samples by Korn et al. 2002; Hunter et al. 2007), where we show the values obtained by Hunter et al., for which a large sample exists (30), whereas the sample by Korn et al. contains only four stars. The comparison shows much poorer agreement with LMC abundances than with the Milky Way abundances. The N, Fe, and the Si abundances of HE 0437−5439 are found to be consistent with LMC values, but the C, O, and Mg abundances are not (all 30 stars in the LMC samples have higher abundances than those found for HE 0437−5439 for these elements). We do note, however, that the metallicities of HE 0437−5439 obtained by Bonanos et al. (2008) are consistent with those of the LMC for all elements. In addition the results of Przybilla et al. (2008) are better consistent with LMC values found by Korn et al., which are systematically higher.

These comparisons show that the metallicities obtained by Przybilla et al. (2008) are more consistent with the GC abundances than the LMC abundances shown here (and best consistent with a Galactic origin). However, we caution again that the small statistics and the different type of stars included in the GC sample of stars, the large differences inferred for the metallicities of HE 0437−5439 by different authors (Bonanos et al. 2008; Przybilla et al. 2008); and the different analysis methods used by different groups, suggest that it is still to early to draw conclusions from such metallicity comparisons. It is clear from the above discussion, however, that none of the suggested origins for HE 0437−5439, including the Galactic disk, the LMC, and the GC can be ruled out based upon current metallicity data.

As discussed in the previous sections, young halo stars such as HE 0437−5439 could have evolved from two lower mass members of ejected hypervelocity binaries. The binary components either merge completely, or may evolve through a strong mass transfer from the more massive binary component to its initially lower mass companion, which becomes a rejuvenated massive star. The later possibility would give a strong observable signature in the form of a high mass ratio binary with a period of tens of days. The observations of Przybilla et al. (2008) and Bonanos et al. (2008) rule out the possibility of such a binary, and therefore if this HVS is a rejuvenated star its binary progenitor fully merged. As can be seen in Figure 1, a binary progenitor with 4.8 and 4.3 M_☉ components, for example, could have propagated for more than 60–80 Myr and then merge to form a 9 M_☉ star, consistent with the required travel time from the GC (Edelmann et al. 2005). We note that binaries with other high mass ratio components (not shown here), but with a total binary mass of ∼9 M_☉, could also produce such a merged star with the appropriate evolutionary timescales. Given the tendency of massive binaries to have high mass ratios, it is likely that most ejected binaries should have mass ratios in the relevant parameter space as to produce a merged star similar to HE 0437−5439. All the hypervelocity binaries have initial semimajor axis smaller than ∼0.2 AU (4–5 R_☉), since they were originally part of the inner binaries in close stable triples. In addition, the KCTF mechanism in triples (see Section 4) can evolve such inner binaries into even closer contact configuration at a very short timescale (Myr). It is therefore expected that most hypervelocity binaries would be at very tight orbits or a few R_☉ separations, such as those required to eventually form a merged starlike HE 0437−5439 (see Figure 1). In other words the rejuvenation scenario is a likely scenario for the formation and ejection of HE 0437−5439. The estimate in Section 3.2.1 suggests f_prog = 3%–5% of the HVSs could be ejected as close hypervelocity binaries or leave a binary star close to the MBH. The fraction of rejuvenated HVSs is therefore f_rej = f_prog · f_inner · f_merged · f_lifetime where f_inner is the fraction of disrupted triples that eject the inner binary, f_merger is the probability the binary merges, f_lifetime is the fractional lifetime of the merger remnant to the original stars lifetime. Simulations of binary disruptions by an MBH (Miller et al. 2005; Bromley et al. 2006) suggest that there is no preference for the primary or the secondary in the binary to be ejected, i.e., they have equal ejection probability; I therefore take f_inner = 0.5. Estimating the probability of binary merger is very uncertain. Taking the observed triples sample of Fekel (1981), I find that the inner binaries in the HVSs binaries possible progenitors have periods of a few days, which together with the binary stellar evolution simulations (see Figure 1) suggest that > 0.75 of them would merge due to stellar evolution. I therefore take f_merger = 0.75. The question of f_lifetime is more complicated. The merger remnant has a lifetime of t_mrej as discussed in Section 5.1, and the maximal lifetime of its progenitor is at most $t_{\frac{1}{2}\rm mrej}$. A rejuvenated star therefore has a fractional lifetime to the original stars of $t_{\rm mrej}/t_{\frac{1}{2}\rm mrej}$. Taking the stellar evolution MS lifetimes from the Geneva stellar evolution tracks (Schaller et al. 1992), I find this to be approximately 0.2. However, on average, the HVSs are ejected after half their lifetime. In addition, the ejected stars are observed only after their propagation for t_prop = few × 10⁷–10⁸ yr (the flight time to distances of 10–100 kpc from the GC where they are currently observed), the fraction of the merger remnant lifetime to the time spent by the progenitor at observable regions is $t_{\rm mrej}/(0.5\cdot t_{\frac{1}{2}\rm mrej}+t_{\rm prop})>0.4$. A reasonable estimate is therefore f_lifetime = 0.2–0.6. Taken together, we find f_rej ≃ 0.003–0.012.⁷ Given the current estimate of N_HVS ∼ 100–650 3–4 M_☉ B-type HVSs in the galactic halo Brown et al. (2007b); Perets et al. (2009b), we may expect to find N_HVS · f_rej = 0.25–8 rejuvenated (more) massive HVSs in a full sky survey (compare with the value of 5 × 10⁻⁵ massive stars expected to originate from the LMC in the IMBH scenario, if such IMBH indeed exist there in a young massive cluster).

We summarize this section by concluding that current suggestions for the hypervelocity ejection of HE 0437−5439 from the LMC (either by an IMBH or through interactions with other massive stars) are highly unlikely, and suggest that HE 0437−5439 was ejected from our GC (where we stress that this scenario is not ruled out by current metallicity comparisons) in a hypervelocity binary following a triple disruption by the MBH.

We note that the HVS US 708, which is not a young star but an evolved sdO star, was suggested to evolve from a merger of a close binary (Hirsch et al. 2005). In that respect, we find that when the evolution of close binaries such as studied here is followed to later times (not shown here) such white dwarfs are indeed formed in some cases. It is therefore possible that US 708 was also ejected as a binary star from a triple disruption that later on evolved and merged to form an sdO star, in a similar way to the rejuvenated young halo star studied here (as suggested by W. Brown 2007, private communication). However, the unique evolution and a merger of two white dwarfs is only poorly followed in the evolutionary code used here, and further studies should be made to check this possibility.