ON THE AGE OF GLIESE 504

In recent years, the study of nearby stars has steadily increased the number of mass transfer systems or potential candidates. Thus, for Regulus, the nearest B-type star in the sky, Gies et al. (2008) have found a 40 day spectroscopic orbit with a likely white dwarf companion. The intriguing prospects then potentially ahead of Regulus—notably that it could be much older than previously thought—are described in Rappaport et al. (2009). As for the famous binary systems Sirius and Procyon, our recent comparative study of the nearby Gl 86 (Fuhrmann et al. 2014) reveals that both must have been subject to significant wind accretion from their now degenerate companions. In other words, we meet here the rebirth of stars—the blue straggler phenomenon—right in the immediate solar neighborhood.

Clear-cut evidence for further mass transfer systems among nearby solar-type stars was also found for the spectroscopic binaries HR 4657 (Fuhrmann & Bernkopf 1999) and HR 3220 (Fuhrmann et al. 2011). Both are ancient Population II members that usually exhibit very low $v{\rm sin} i\simeq 1$ km s⁻¹ projected rotational velocities. Since both are found to match the Rappaport et al. (1995) period–white dwarf mass relation there is a straight explanation for their currently enhanced rotation and nominal young age in terms of degenerate mass donors.

For other nearby stars that are part of common-proper-motion systems one can encounter yet another kind of oddity in that some display one component being chromospherically active, while the other is not. Examples of this kind are HD 137763/HD 137778, HR 5, 37 Cet, and ζ Ret, and it appears difficult to reconcile the observations with the notion of a common birthplace and evolution, unless one allows for a planetary or stellar merger of a formerly close companion on the now chromospherically active component. Indeed, observations of close stellar binaries rather often exhibit distant "control" stars (Tokovinin & Smekhov 2002; Tokovinin et al. 2006; Allen et al. 2012; Chini et al. 2014) that potentially drive the merger of the inner system.

In our previous study on a major subset of bright stars of the solar neighborhood (Fuhrmann 2004, hereafter F04) it became already clear that—among several other sources—the G-type star Gl 504 (59 Vir, HR 5011, HD 115383, HIP 64792) was an odd object in terms of a turn-off stage of evolution and a solar-like age, but with an incredibly short P_rot = 3.33 day rotation period (Donahue et al. 1996), reminiscent of a young star. Recently, Kuzuhara et al. (2013) found a fairly distant substellar companion to Gl 504 by direct imaging observations. On account of a presumed young age of $160_{-60}^{+350}$ Myr for the G-type primary, they consider this companion to be a similarly young $4_{-1.0}^{+4.5}$ M_J Jovian exoplanet. In this paper, however, we shall revisit the observational evidence that Gl 504 A is very likely about as old as the Sun and—by inference—its faint companion a low-mass brown dwarf.

A model atmosphere analysis of Gl 504 A based on high-resolution spectra secured in 1998 June with the FOCES échelle spectrograph (Pfeiffer et al. 1998) was previously presented in F04. As mentioned in the Introduction, Gl 504 A was herein found to be an odd star and likely subject to a recent accretion of a giant planet or a brown dwarf. In 2004 February we re-observed Gl 504 A with the FOCES spectrograph, yet the spectrum was not further investigated since then. However, in the light of the recent discovery of a substellar companion to Gl 504 A by Kuzuhara et al. (2013), we do present here a merged, updated, and consistent set of the basic stellar parameters of Gl 504 A. This also includes the use of the revised evolutionary tracks by VandenBerg et al. (2006) as well as the improved Hipparcos parallax by van Leeuwen (2007).

The model atmospheres (convection, opacities, abundances, Balmer lines, Stark and resonance broadening) and line formation (oscillator strengths, damping parameters, non-thermal velocities, rotational broadening, instrumental profile, LTE ionization equilibrium) have been described at length in Fuhrmann et al. (1993, 1997). In brief, the effective temperature is derived from the Balmer line wings and the surface gravity results from the pressure-dependent damping wings of the Mg Ib triplet lines at 5167, 5172 and 5183 Å. The Balmer line wings generally lead to effective temperatures that agree very well with precision values from interferometrically determined stellar radii (cf. Fuhrmann 2011). Similarly, and as we have already demonstrated in Fuhrmann et al. (1997) and F04, the spectroscopic surface gravities from the Mg Ib triplet lines are mostly reliable to within 0.1 dex. Thus, in the case of Gl 504 A we derived in F04 a surface gravity ${\rm log} g=4.17$, which comes close to ${\rm log} g=4.23$ that results from a comparison of the Hipparcos astrometric parallax, π = 56.95 ± 0.26 mas, with the spectroscopic parallax ⁴

$$\begin{eqnarray*}\begin{array}{ccccccccccccccc} {\rm log} \pi & = & 0.5([g]-[M])-2[{{T}_{{\rm eff}}}] \\ {} & {} & -0.2(V+B{{C}_{V}}-{{M}_{{\rm bol},\odot }}+5). \\ \end{array}\end{eqnarray*}$$

For consistency with the precision value from the van Leeuwen (2007) Hipparcos parallax we also give preference to this astrometric surface gravity ${\rm log} g=4.23$ in Table 1 that summarizes our stellar parameters on Gl 504 A.

Table 1.  Basic Stellar Parameters of Gl 504 A

Teff	5978 ± 60 K
${\rm log} g$	4.23 ± 0.10 cgs
[Fe/H]	+0.13 ± 0.06 dex
[Fe/Mg]	−0.02 ± 0.05 dex
ξt	1.13 ± 0.20 km s−1
ζRT	(fixed) 4.9 km s−1
v sin i	6.6 ± 0.6 km s−1
V	5.191 ± 0.005 mag
Mbol	3.87 ± 0.05 mag
BCV	−0.10 ± 0.05 mag
Radius	1.36 ± 0.04 R⊙
Mass	1.16 ± 0.05 M⊙
Nominal age	4.5$_{+2.0}^{-1.5}$ Gyr

Note. The entries ξ_t and ζ_RT denote the micro- and macroturbulence velocities, respectively. The bolometric correction refers to Alonso et al. (1995). All given uncertainties represent 2σ errors.

Download table as:  ASCIITypeset image

In our previous work, Gl 504 A has also been part of a volume-complete sample of nearby solar-type stars (cf. Fuhrmann 2011) that is reproduced in the T_eff-${\rm log} g$ plane in the left panel of Figure 1. There are basically two things to learn from this figure: first, the position of Gl 504 A, given by the dark blue circle, implies the star is close to its turn-off stage, and second, the red circle that represents the stellar parameters by Valenti & Fischer (2005) and to which Kuzuhara et al. (2013) refer in their work, leads to an implausible position in the H–R diagram. This result immediately follows from the above Hipparcos parallax in comparison with the spectroscopic parallax ${{\pi }_{{\rm sp}}}=76.51_{-3.47}^{+3.81}$ mas derived from the T_eff and ${\rm log} g$ parameters of Valenti & Fischer (2005) and the stellar mass M = 1.22 ± 0.08 M_⊙ used by Kuzuhara et al. (2013, their Table 1). ⁵ In other words, the high ${\rm log} g=4.60\pm 0.02$ surface gravity value that Kuzuhara et al. (2013) take as evidence for a young main-sequence star for Gl 504 A is instead the result of an inconsistent model atmosphere analysis. The ${\rm log} {{g}_{{\rm iso}}}=4.32$ given by Valenti & Fischer (2005) directly reflects this circumstance.

Zoom In Zoom Out Reset image size

That Gl 504 A is indeed an evolved star is shown in the right panel of Figure 1 with reference to the VandenBerg et al. (2006) evolutionary tracks for a metallicity [Fe/H] = +0.13. The precise absolute bolometric magnitude of Gl 504 A in this figure directly refers to the solid Hipparcos astrometry and irrespective of the comparatively large uncertainty with the effective temperature of Gl 504 A that allows for an age range from 3 to 6 Gyr, a much younger case can safely be excluded.

At this point, we repeat our previous concern that in a Bottlinger V–U diagram of the nearby stars (cf. Figure 28 in F04) Gl 504 A is also not in a region where the young stars can be found. Thus, and as Kuzuhara et al. (2013) also concede in their work, there appears to be no local young open cluster or moving group that Gl 504 A could somehow belong to.

As an evolved star of about solar age, it follows that the putative exoplanet discovered by Kuzuhara et al. (2013) must be more massive than derived by these authors. Thus, if we also refer to the work of Baraffe et al. (2003), Figure 2 illustrates the situation for the 1.6 μm H-band. ⁶ The absolute magnitude M_H = 18.92 ± 0.14 depicted by the blue horizontal bar refers to the Kuzuhara et al. (2013) photometry, H = 20.14 ± 0.14, and the (m − M)_V = 1.22 mag distance modulus from the van Leeuwen (2007) Hipparcos parallax. From the solid curves that denote the Baraffe et al. (2003) COND H-band isochrones for 0.1, 0.5, 1, 5, and 10 Gyr a 4 M_J planetary companion follows for a system age of 160 Myr as favored by Kuzuhara et al. (2013), whereas a 25 M_J brown dwarf mass is derived for an evolved system of about solar age. With reference to the slightly revised photometry M_H = 18.77 ± 0.10 by Janson et al. (2013) we note that the mass of Gl 504 B would only be increased by about 2 M_J. Also, it is worth mentioning that an upper limit for the brown dwarf mass of M_B ≃ 35 M_J applies to the 8 Gyr thin-disk formation time scale.

Zoom In Zoom Out Reset image size

The second aspect of an evolved turn-off stage for Gl 504 A is that the only viable explanation to account for the short P_rot = 3.33 day rotation period (Donahue et al. 1996), the coronal (Hünsch et al. 1999) and chromospheric activity, remains a recent mass and angular momentum transfer. As already pointed out in F04, in this case one must assume that the accreted object was more likely a giant planet or a brown dwarf, i.e., predominantly a source of angular momentum for its primary that mostly left Gl 504 A in the evolved stage that is currently observed. The fact that Gl 504 A still possesses strong lithium absorption is relevant to this argument, for if Gl 504 A would have started as a ∼0.1 M_⊙ less massive, solar-like star it would have depleted most or all of its lithium. Yet, it is important to understand that in case of a small, but significant mass accreted by Gl 504 A, our age derived from the evolutionary tracks in Figure 1 could only be a nominal, a lower limit. A former, say, M_A = 1.12 M_⊙ progenitor in Figure 1 would instead be very likely older than the Sun, but, at the same time, must not exceed the 8 Gyr age limit for thin-disk stars. This provides us with yet another argument that the accreted object should have been restricted to a substellar mass.

In the following we will briefly consider the case of a giant planet accreted by its host star. We adopt for the angular momentum of the Sun (e.g., Iorio 2012, and references therein)

$$\begin{eqnarray*}&&{{J}_{\odot }}=I\cdot {\Omega }\simeq 1.92\times {{10}^{48}}\;{\rm g}\;{\rm c}{{{\rm m}}^{2}}\;{{{\rm s}}^{-1}},\end{eqnarray*}$$

where I = k² M R² is the moment of inertia and Ω the angular velocity. The scaling factor k is the radius of gyration, which for the case of the Sun leads to k_⊙ ≃ 0.26.

The orbital angular momentum of the giant planet is given by

$$\begin{eqnarray*}&&{{J}_{{\rm orb},p}}={{m}_{p}}\cdot a\cdot v={{m}_{p}}\cdot a\cdot {{(G{{M}_{\star }}/a)}^{1/2}},\end{eqnarray*}$$

where m_p , a, and v are the mass, orbital separation, and orbital velocity of the giant planet.

If we say that the entire stellar angular momentum J_⋆ was caused by the accretion of the giant planet's angular momentum at some radial separation a, we can write

$$\begin{eqnarray*}&&{{m}_{p}}\cdot a\cdot {{(G{{M}_{\star }}/a)}^{1/2}}={{k}^{2}}\cdot {{M}_{\star }}\cdot R_{\star }^{2}\cdot {\Omega }.\end{eqnarray*}$$

With

$$\begin{eqnarray*}&&{{P}_{\star }}=2\pi \cdot R_{\star }^{3/2}/{{(G\cdot ({{M}_{\star }}+{{m}_{p}}))}^{1/2}}\simeq 2\pi \cdot R_{\star }^{3/2}/{{(G{{M}_{\star }})}^{1/2}}\end{eqnarray*}$$

defined as the Keplerian orbital period at the stellar surface and P_rot = 2π · Ω⁻¹ as the stellar rotation period, we can write

$$\begin{eqnarray*}&&{{m}_{p}}={{k}^{2}}\cdot {{({{R}_{\star }}/a)}^{1/2}}\cdot {{M}_{\star }}\cdot {{P}_{\star }}/{{P}_{{\rm rot}}}.\end{eqnarray*}$$

The Roche lobe of a giant planet in orbit around Gl 504 A is about 0.05a to 0.10a, which is reached at R_⋆/a ratios of 0.3 to 0.5. Thus, if we take R_⋆/a ≃ 0.4 as the critical radius for Roche lobe overflow and adopt k ≃ k_⊙, and with P_⋆ ≃ 4.1 hr and P_rot = 3.33 days (Donahue et al. 1996) we arrive at

$$\begin{eqnarray*}&&{{m}_{p}}\simeq 2.7\ \;{{M}_{{\rm J}}}\end{eqnarray*}$$

as the (minimum) planet mass to account for the observed stellar spin-up.

For the case of Gl 504 A we add that the spiral-in merger may have been self-triggered by virtue of a strong tidal interaction in response to its expanding stellar radius. However, and since there has been plenty of time for an orbital evolution of the inner subsystem, we are inclined to favor the distant Gl 504 B as the real cause for the former merger. In a three-body system, as we suggest here for the Gl 504 protostar, the effect of a highly inclined outer orbit is to cause cyclic large-amplitude variations of the orbital eccentricity of the inner subsystem (cf. Eggleton & Kiseleva-Eggleton 2001). These Kozai cycles can evoke tidal friction to become important and hence induce orbital decay, eventually followed by a merger. From observations of close binary systems in the solar neighborhood it has in recent years become clear that a remarkable fraction of them do possess a distant companion (cf. Tokovinin et al. 2006, their Figure 10) indicative of a transport mechanism of angular momentum from the inner to the outer orbit. To see that orbital planes of higher level systems must not necessarily be aligned, a brief inspection of the very nearby (d = 8 pc) and prominent solar-type multiple star ξ UMa may also be instructive: here the principal A (F8V) and B (G2V) components that define the outer 60 year orbit possess an orbital inclination i = 121° (Söderhjelm 1999), the P = 1.8 year Aa–Ab subsystem in turn has an almost edge-on i = 91° orbit (Heintz 1996), whereas the short-period P = 3.98 day Ba-Bb binary, provided it is in bound rotation, has a rather face-on i < 20° inclination. ⁷

With respect to the 160 Myr system age given by Kuzuhara et al. (2013) we consider this to be the time elapsed since the engulfment on Gl 504 A took place. Compared to the Sun-like system age that we derive from our analysis this is only a few percent, yet it is only the first few hundred million years after a significant stellar spin-up that the observed age discrepancy is visible at all. The fact that more than a dozen cases among the ∼500 nearest (d ≤ 25 pc) solar-type stars show similar clues of mass accretion like Gl 504 is in line with this assessment. However, should these observational features mostly be erased after, say, a billion years, this also means that on account of this selection effect one may expect a significant percentage of blue stragglers among the field star populations and with a potentially strong impact on our notions of stellar ages or age distributions.

K.F. acknowledges support from the DFG grant FU 198/10-1.