The lithium depletion boundary and the age of the Hyades cluster
Eduardo L. Martín, Nicolas Lodieu, Yakiv Pavlenko, Víctor J. S. Béjar
aa r X i v : . [ a s t r o - ph . S R ] F e b Draft version February 21, 2018
Typeset using L A TEX default style in AASTeX61
THE LITHIUM DEPLETION BOUNDARY AND THE AGE OF THE HYADES CLUSTER. ∗ Eduardo L. Mart´ın, Nicolas Lodieu,
2, 3
Yakiv Pavlenko, and V´ıctor J. S. B´ejar Centro de Astrobiolog´ıa (INTA-CSIC), Carretera de Ajalvir km 4, E-28550 Torrej´on de Ardoz, Madrid, Spain Instituto de Astrof´ısica de Canarias (IAC), Calle V´ıa L´actea s/n, E-38200 La Laguna, Tenerife, Spain Departamento de Astrof´ısica, Universidad de La Laguna (ULL), E-38205 La Laguna, Tenerife, Spain Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Ukraine (Accepted February 8th, 2018)
Submitted to ApJABSTRACTDetermination of the lithium depletion boundary (LDB), i.e., the observational limit below which the cores of verylow-mass objects do not reach high enough temperature for Li destruction, has been used to obtain ages for severalopen clusters and stellar associations younger than 200 Myr, which until now has been considered as the practicalupper limit on the range of applicability of this method. In this work we show that the LDB method can be extended tosignificant older ages than previously thought. Intermediate resolution optical spectra of six L-type candidate membersin the Hyades cluster obtained using OSIRIS at the 10.4-m Gran Telescopio Canarias are presented. The Li I 670.8 nmresonance doublet is clearly detected only in the two faintest and coolest of these objects, which are classified as L3.5to L4 brown dwarf cluster members with luminosities around 10 − solar. Lithium depletion factors are estimated forour targets with the aid of synthetic spectra and they are compared with predictions from evolutionary models. ALDB age of 650 ±
70 Myr for the Hyades provides a consistent description of our data using a set of state-of-the-artevolutionary models for brown dwarfs calculated by Baraffe et al. (2015).
Keywords: methods: observational — techniques: spectroscopic — stars: abundances — brown dwarfs— open clusters and associations: Hyades
Corresponding author: Eduardo L. Mart´ı[email protected] ∗ Based on data obtained at the Gran Telescopio Canarias
Mart´ın et al. INTRODUCTIONThe light element lithium (Li) is destroyed by collisions with protons in the cores of stars and high-mass browndwarfs (BDs) with masses above 0.05 M ⊙ in timescales shorter than 1 Gyr (Magazz`u et al. 1993). This nuclearprocess becomes observable as Li depletion in the surface via deep convective mixing. The discovery of Li in BDmembers in the Pleiades cluster (Basri et al. 1996; Rebolo et al. 1996) was an observational confirmation that thislight element is preserved in substellar mass objects as originally proposed by Rebolo et al. (1992). The first attemptto detect Li in very low-mass members in open clusters (Hyades and Pleiades) was reported in Mart´ın et al. (1994).Currently, the so-called Li test for BD candidates keeps on being used to constrain the ages and masses of young BDsin the field (Phan-Bao et al. 2017).The Li depletion boundary (LDB) in young open clusters is a chronometer that provides age estimates independentfrom other methods, such as turn off determination or main-sequence isochrone fitting. The physics involved in usingthe LDB are considered simpler than other methods used for dating clusters and associations (Burke et al. 2004).However, it has been considered that the LDB method is limited in its practical applicability to the age range between20 Myr and 200 Myr, which implies that so far it could be used only in 2 stellar associations and 7 young open clusters(Stauffer et al. 1998; Barrado y Navascu´es et al. 2004; Cargile et al. 2010; Dobbie et al. 2010; Jeffries et al. 2013). Inthis work we search for the LDB in the Hyades cluster, and we show that this method can be extended to significantlyolder ages than previously thought.Located at only 46.3 ± ±
50 Myr (Maeder & Mermilliod 1981), although a much older age of 1200 Myr hasbeen reported using evolutionary models with enhanced convective overshooting (Mazzei & Pigatto 1988). A recentestimate of the Hyades age using models that incorporate rotation has given 750 ±
100 Myr (Brandt & Huang 2015).Both convective overshooting and stellar rotation increase main-sequence lifetimes and thus yield older cluster ages.The Hyades cluster may be part of larger complex that also includes the Praesepe open cluster and a large number offield stars. This complex, known as Hyades supercluster, includes stellar populations with ages ranging from 0.5 Gyrto 1.0 Gyr (Eggen 1998).Even though the Hyades has a paucity of low-mass members with respect to younger clusters (Reid 1992), which isunderstood as evidence for dynamical evolution that makes the lowest mass members disperse from the cluster core(Terlevich 1987), a dozen L dwarf candidates with high probability of membership in the Hyades cluster were identifedfrom photometry and proper motion data presented in Hogan et al. (2008). Moreover, T dwarf candidate memberswere found by Bouvier et al. (2008), and a late L dwarf member was recently reported in Perez Garrido et al. (2017).Hyades brown dwarfs are benchmarks for understanding substellar evolution and they also provide a unique oppor-tunity to extend the LDB method to a stellar cluster older than 200 Myr. In this paper, we present a search for the Li Iresonance doublet centered at 670.8 nm in six L dwarfs selected on the basis of confirmed L-type spectral classificationfrom reconaissance spectra presented in Lodieu et al. (2014).The rest of this paper is organized as follows: In Sect. 2 we present the target selection and the spectroscopicobservations. In Sect. 3, we present the spectral types, spectrophotometric distances and radial velocities of ourtargets, and we estimate their membership probability in the Hyades. We also derive astrophysical parameters such asbolometric luminosities and effective temperatures using empirical calibrations. In Sect. 4, we present the search forLi, as well as for H α in emission, and we give the pseudo-equivalent width measurements of photospheric lines seen inthe spectra. In Sect. 5, we discuss the determination of surface Li abundances in our sample of L dwarfs. Finally, inSect. 6, we estimate the Hyades cluster age using the LDB method. TARGET SELECTION AND SPECTROSCOPIC OBSERVATIONSWe selected 6 targets from the list of 12 L-type Hyades brown dwarf candidates originally identified by Hogan et al.(2008) on the basis of photometric and proper motion criteria. These objects had been confirmed as L-type dwarfsfrom low-resolution optical spectra (Lodieu et al. 2014).All the spectra presented here were taken during dark nights in service mode at the 10.4-m Gran Telescopio Canarias(GTC) for programs GTC20-16B and GTC21-17B (PI, E. L. Mart´ın) using the Optical System for Imaging and LowResolution Integrated Spectroscopy (OSIRIS), Cepa et al. (2000). The instrumental configuration was the long slitmode with R1000R grating, a slit width of 1.2 arcsec, and a detector bining of 2x2. This combination gave a dispersionof 2.62 ˚A/ pixel, and a resolving power (R= λ/ ∆ λ ) of 561 at the central wavelength of 743 nm, corresponding to a he lithium depletion boundary in the Hyades. z -band), another exposure through the same filter to check centeringon the slit, and several exposures in the longslit spectroscopic mode. An offset of 15 arcsec along the slit direction wasapplied between each exposure. All observations were carried out in parallactic angle.As a radial velocity (RV) reference the field L dwarf DENIS-P J0615493 − I =17.0) than the Hyades targets, the exposure times were reduced to20 s for the acquisition image and 900 s for each of the spectroscopic observations. Table 1 lists the targets observedfor our lithium search and the observing details.We used IRAF to reduce the data. Bias subtraction and flat field correction were performed. One-dimensionalspectra were extracted interactively using apsum. Wavelength calibration was made using an arc lamp spectrumobtained the same night as the science spectrum. The spectro-photometric standard Hilt 600, observed with thesame instrumental configuration in one of the same nights as the science spectra, was used to correct for instrumentalresponse. Table 1 . Observing logAbridged names a b Seeing c Weather conditions d coordinates seconds arcsec(1) (2) (3) (4) (5) (6)Hya03 J04102390+1459104 Feb 19th, 2017 2 × × × × × × × × −
01 J06154934 − ×
900 0.8 Spectroscopic a Names of Hyades L dwarfs from Hogan et al. (2008). b Number of exposures × on-target exposure time. c Values taken from GTC log of observations. d Sky conditions reported by the night observers. Spectroscopic means that some clouds were passing during the night.3.
CLUSTER MEMBERSHIPIn Figure 1 we show the calibrated spectra of our targets compared with spectral templates from the Sloan DigitalSky Survey (SDSS) (Schmidt et al. 2010) that provided the best match to our data. The spectral types adopted for ourtargets and their uncertainties are given in Table 2. Our spectral types are systematically later by 0.5 to 2.0 subclassesthan those published by Lodieu et al. (2014), and consequently the spectrophotometric distances of the objects arecloser and more consistent with cluster membership. On the other hand for DENIS J0615-010 we find a spectral typeof L1 which is 1.5 subclasses earlier than the L2.5 type reported by Phan-Bao et al. (2008). Our spectral types oughtto be more reliable than those estimated by other authors because of the higher quality of our data.Spectrophometric distances were derived using the infrared photometry provided by Hogan et al. (2008) andLodieu et al. (2014), and the spectral type versus absolute magnitudes for field L dwarfs in Filippazzo et al. (2015).
Mart´ın et al.
They are given in Table 2. We note that they are consistent with the range of distances expected for cluster members,i.e., between 32 pc and 60 pc according to Hogan et al. (2008).RV measurements were obtained for all the targets from cross correlation with the spectrum of the template DE-NIS J0615-010 using the IRAF task fxcor . Heliocentric radial velocity corrections were derived with the IRAF task rvcor . Instrumental zeropoint correction was applied using a radial velocity of − − ± ± Table 2 . Hyades sample propertiesName
SpT D spec a log (L bol /L ⊙ ) b T eff b RV Memb.pc (K) km/s(1) (2) (3) (4) (5) (6) (7)Hya03 L2.0 ± ± ± ±
113 24 ±
13 95%Hya08 L2.0 ± ± ± ±
113 23 ±
14 95%Hya09 L3.5 ± ± ± ±
113 45 ±
13 98%Hya10 L3.5 ± ± ± ±
113 48 ±
13 95%Hya11 L3.0 ± ± ± ±
113 45 ±
11 95%Hya12 L4.0 ± ± ± ±
113 36 ±
13 98% a Spectrophotometric distances derived from photometry in Hogan et al. (2008) andLodieu et al. (2014) and the spectral type versus absolute magnitude relations forfield L dwarfs (Filippazzo et al. 2015). b Bolometric luminosities and effective temperatures estimated using the calibrationsof those parameters with spectral type given in Filippazzo et al. (2015).
All brown dwarf evolutionary models predict that Li should be preserved at masses below 0.06 M ⊙ , which correspondsto luminosities and temperatures in the realm of L dwarfs for ages younger than about 1 Gyr (D’Antona & Mazzitelli1984; Burrows et al. 1997). The presence of Li is therefore an indication of younger age than the average for field Ldwarfs. In the case of Hya09 and Hya12 we consider the presence of a detectable Li feature as an additional confirmationof membership in a cluster younger than the average age of the field population. Taking into account that the rate of Lidetection in field L4 dwarfs is 40% ±
11% (Kirkpatrick et al. 2008), we add this factor to their membership probability.Thus, the Hyades membership probabilities of the 6 targets considered in this study include the facts that they have he lithium depletion boundary in the Hyades.
Astrophysical parameters
None of our targets show spectroscopic signs of being very young (age <
100 Myr) as defined in Kirkpatrick et al.(2008). Their membership in the Hyades implies that they should have radii and surface gravities close to those offield L dwarfs. Therefore, it is justified to use the calibrations for field L dwarfs of known distance (Filippazzo et al.2015) to calculate their bolometric luminosities ( log (L bol /L ⊙ ) and effective temperatures (T eff ) from the spectraltypes obtained by us. They are given in Table 2.We also tried other approaches, such as using the observed photometry and bolometric corrections fromFilippazzo et al. (2015), and also Spectral Energy Distribution (SED) fitting with theoretical spectra following theprocedures available in VOSA (Bayo et al. 2008), an interactive sofware developed by the Spanish Virtual Observatory.These other approaches gave larger uncertainties and they could be affected by unresolved binarity of the targets,which is known to be at least 10% among brown dwarfs in the Pleiades clusters (Mart´ın et al. 2013; Bouy et al. 2006).The advantage of using directly the calibrations between spectral type and luminosity and temperature is that theresults do not depend neither on the distance nor on the appartent brightness of the objects. Thus, we adopt thosevalues for the analysis of the LDB in the Hyades. ATOMIC LINESWe searched for the Li I resonance doublet at 670.8 nm in all of the targets and did find something in 3 latest objects,namely Hya09, Hya11 and Hya12, as shown in Figure 2. The significance of these detections were estimated using theequation from Cayrel (1988); namely, rms ( pEW ) = 1 . × ( F W HM × Disp. ) / /SN R where in our case the followingparameters apply: FWHM=12 ˚A, Disp.=2.62 ˚A/pix, and the SNR per pixel for each spectrum was computed usingthe key m in the IRAF task splot across the wavelength range from 675 to 680 nm. These SNR estimates were moreconservative than those found using other methods.In the case of Hya09 we found a predicted rms(pEW) for the Li I resonance doublet at 670.78 nm of 0.71 ˚A, whichformally implies a significance of 6.2 ± σ for the detection of this feature with a pEW=4.4 ± ± ± σ , and hence we cannot claim to have a definitive Li detection in Hya10. On the other hand,Hya12 has a Li I feature with a pEW=8.5 ± ± σ for this detection giventhan the predicted rms(pEW) is just 0.64 ˚A, and it is indeed the clearest Li detection in our whole sample. For therest of this paper we will consider as definitive Li detections only the features observed in Hya09 and Hya12, while therest will be treated as upper limits. As a consistency check we also note that the FWHM of the Li I feature in Hya09and Hya12 were consistent with the expected FWHM resolution as measured in other photospheric lines.Independent measurements of the pEW for the Li I features by all the co-authors of this work using the task splotconfirmed that the uncertainties estimated from the Cayrel formula are realistic, although the interactive measurementstended to provide slightly higher error bars. Thus, we have adopted the more conservative uncertainties provided bythe independent measurements and they are given in Table 3. Table 3 summarizes the pEW measurements, upperlimits and uncertainties.We also searched for H α in emission, an indicator of chromospheric activity but we could not find any clear detectionamong the Hyades L dwarfs. Upper limits to the H α pEW are given in Table 3. None of our Hyades targets haveH α emission with pEW larger than about 4 ˚A, which is consistent with recent estimates of about 10% H α emissiondetection rate among field L dwarfs (Pineda et al. 2016).Prominent photospheric lines in L dwarfs of Cs I, Na I and Rb I were present in the observed spectral range. TheirpEWs were measured in a manner analog to that described for the Li I resonance feature. The line wavelengths listedin the NIST Atomic Spectra Database (Kramida et al. 2015) and the pEWs that we measured are given in Table 3.For most of the lines there is good agreement between our pEWs and those listed in Burgasser et al. (2015) for DENISJ0615 − ∼ Mart´ın et al. and highlights the importance of using data of similar resolution when comparing pEW values. We also note thatthe Cs I resonance line at 852.11 nm is stronger in Hya12 than in the other objects. This line is known to be verysensitive to T eff in L dwarfs, becoming stronger for cooler and later objects (Kirkpatrick et al. 1999; Mart´ın et al.1999; Basri et al. 2000), which is consistent with Hya12 being the coolest L dwarf in our sample.
Table 3 . Pseudo equivalent width measurements a Name SNR pEW H α pEW Li I pEW Rb I pEW Rb I pEW Na I pEW Cs I675-680 nm 656.28 nm 670.78 nm 780.03 nm 794.76 nm 818.32, 819.48 nm 852.11 nm(1) (2) (3) (4) (5) (6) (7) (8)Hya03 10.3 > -3.5 < ± ± ± ± > -0.8 < ± ± ± ± > -1.2 4.4 ± ± ± ± ± > -2.0 3.2 ± ± ± ± ± > -2.7 < ± ± ± ± > -2.8 8.5 ± ± ± ± ± ± < ± ± ± ± a pEW measurements are given in ˚A.5. LITHIUM ABUNDANCES IN HYADES L DWARFSPrevious studies of the LDB in young open clusters and associations did not attempt to estimate surface Li abun-dances because the gap in luminosity across the LDB was comparable to observational uncertainties. However, forincreasing age the gap in luminosity from Li bearing BDs to Li naked BDs becomes larger (Figure 3) and this motivatedus to estimate the Li abundances in our targets. We calculated theoretical pEWs for the Li I resonance doublet usingsynthetic spectra for a range of T eff , log g and log N(Li) values that are relevant for our targets. The model namesused in Table 4 denote the T eff in K and log g adopted.The theoretical spectra were synthesized following the procedures described in Lodieu et al. (2015). Fluxes acrossthe Li I resonance doublet are governed mainly by absorption in the extended wings of the K I and Na I resonancelines (Pavlenko et al. 2000). The TiO bands are of marginal strength in L dwarfs. In our computations only depletionof atomic lithium into molecular species (LiOH, LiCl, LiF) was accounted for. Depletion of lithium atoms into dustparticles may reduce the number of absorbing particles in the atmosphere. Unfortunately chemistry and kinematicproperties of phase transition gas-dust are too poorly known to account for this effect.
Table 4 . Predicted Li abundance versus relative pEW Li IModel ∆log N(Li) (pEW Li I) depl /(pEW Li I) max (1) (2) (3)1600/5.0 − − Table 4 continued on next page he lithium depletion boundary in the Hyades. Table 4 (continued)
Model ∆log N(Li) (pEW Li I) depl /(pEW Li I) max (1) (2) (3)1600/5.0 − − − − − − − − − − − − − − − − − − − − − − − − − − − − Hyades brown dwarfs presumably start off their evolution with an initial Li abundance of log N(Li) ≈ ± ± Mart´ın et al. between Li depletion due to Li burning and the ratio of the pEW of the Li I feature with respect to the maximumvalue which corresponds to undepleted Li abundance. These relations are provided in Table 4, and we note that theyare rather insensitive to the T eff and log g adopted in the range of values considered in this work.From the pEW values given in Table 3, and the calculations presented in Table 4, we derive the surface lithiumabundances for our targets that are given in Table 5 assuming as undepleted Li abundance of log N(Li)=3.3. Inparticular, for an L4 dwarf (the spectral type of Hya12) we assume that the initial Li abundance corresponds to pEW(Li I) obs =11 ± ± − ± ± obs =7 ± ± − ± ± Table 5 . Li depletion in Hyades L dwarfsName
SpT (pEW Li I) obs /(pEW Li I) max log N(Li)(1) (2) (3) (4)Hya03 L2.0 ± < < ± < < ± ± ± ± < < ± < < ± ± ± THE HYADES AGEGiven the bolometric luminosity, the effective temperature and the lithium abundance of an L dwarf, it should bepossible to determine its age and mass, or place lower limits on them, using evolutionary models. Our goal in thissection is to combine the Li abundances and upper limits derived in our sample of L dwarfs to check whether ornot we can find consistent age estimates for all of them using two independent sets of models, namely those fromBurrows et al. (1997) (hereafter Bu97) and those by Baraffe et al. (2015) (hereafter BHAC15).The predicted relations between Li depletion and luminosity or temperature for these two models are shown inFigures 3 and 4, respectively. The age limits obtained for the 5 Hyades L dwarfs from comparison of their luminosities,T eff and Li abundances with the two sets of models are given in Table 6. Hya10 is not included because it does notprovide any additional constraint.Using the luminosities and the Bu97 models, we get a cluster age of 800 ±
50 Myr. Using the temperatures, thesame models yield 975 ±
25 Myr. On the other hand, the BHAC15 models give 635 ±
85 Myr with the luminosities and690 ±
110 Myr with the temperatures. Thus, there is a significant region of agreement between the ages obtained fromthe BHAC15 luminosity tracks and the BHAC15 cooling curves, which is not the case for the Bu97 models. This lackof self-consistency in the Bu97 models could be due to the fact that they were mainly aimed at modeling in detailthe properties of brown dwarfs cooler than 1300 K, whereas, for hotter brown dwarfs, such as those considered inthis work, they use grey atmosphere approximations. The BHAC15 models, on the other hand, use detailed modelatmospheres in the range of T eff values considered in this work, and we adopt them for estimating the Hyades LDBage. he lithium depletion boundary in the Hyades. ± ±
50 Myr (Maeder & Mermilliod 1981), although it does not rule out a slightlyolder age, which may be consistent withing the error bars with the age of 750 ±
100 Myr suggested by models thatincorporate the effects of stellar rotation (Brandt & Huang 2015).The study of the LDB in the Hyades has some advantages and some disadvantages with respect to analog studies inyounger clusters such as the Pleiades. On the positive side the LDB in the Hyades is less prone to magnetic activityeffects because L dwarfs are less active than late-M dwarfs, and thus no activity corrections have been attempted inthis work for the Hyades, whereas in younger clusters they have been deemed to be necessary (Juarez et al. 2014;Dahm 2015). Another bonus is that beyond 500 Myr the location of the LDB depends primarily on the cluster ageand almost nothing on the mass of the brown dwarfs. On the other hand, the effects of dust condensation in L-typeatmospheres and how they may impact on the observational properties of L dwarfs and the determination of the LDBare complicated and it could be worthwhile to be investigate them in more detail.
Table 6 . LDB age constraints for Hyades L dwarfsName log (L bol /L ⊙ ) T eff Li depletion Age1 Age2 Age3 Age4K Myr Myr Myr MyrBu97-L Bu97-T Ba15-L Ba15-T(1) (2) (3) (4) (5) (6) (7) (8)Hya03 -3.83 ± ± > > > > > ± ± > > > > > ± ±
113 0%–90% 450-940 550-1150 480–720 500–800Hya11 -3.96 ± ± > > > > > ± ±
113 0%–78% 500-850 600-1000 550-750 500–800
We thank the staff of the GTC who carried out the observations with OSIRIS in service mode for programs GTC20-16B and GTC21-17B, and I. Baraffe for providing a finer sampling of the Li depletion models for ages between500 Myr and 700 Myr. ELM and NL are supported by grants AyA2015-69350-C3-1-P and AyA2015-69350-C3-2-P from the Spanish Ministry of Economy and Competitiveness (MINECO/FEDER). This publication makes use ofVOSA, developed under the Spanish Virtual Observatory project supported from the Spanish MICINN through grantAyA2011-24052. We thank the anonymous referee for numerous comments that helped to improve the manuscript.
Facilities:
GTC(OSIRIS)
Software:
IRAF (Tody 1986) VOSA (Bayo et al. 2008),REFERENCES
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600 650 700 750 800 850 900Wavelength (nm)0246810 N o r m a li z ed F l u x a t - n m Hya03 L2.0Hya08 L2.0Hya11 L3.0Hya10 L3.5Hya09 L3.5Hya12 L4.0DENIS0615-01
Figure 1. GTC/OSIRIS spectra of the Hyades L dwarfs observed in this work and the radial velocity standard.The best matching spectrum from the SDSS database is overplotted on each target and the spectral type ofthe template is labeled. Mart´ın et al.
650 655 660 665 670 675 680Wavelength (nm)01234 N o r m a li z ed F l u x a t - n m LiHya03 (L2.0)Hya08 (L2.0)Hya11 (L3.0)Hya10 (L3.5)Hya09 (L3.5)Hya12 (L4.0)DENIS J0615
Figure 2. Zoom of the spectral region around the Li I resonance doublet at 670.8 nm. The central wavelengthof the Li feature is marked with a dashed vertical line. he lithium depletion boundary in the Hyades. -4.3-4.2-4.1-4-3.9-3.8-3.7-3.6-3.5-3.4 200 400 600 800 1000 1200 1400>99% Li depletion>90% Li depletion>1% Li depletion 0.080 Msol0.070 Msol0.060 Msol0.050 Msol0.040 Msol0.030 Msol0.020 Msol0.010 Msol l og L / L s o l Age (Myr) (a) T e ff ( K ) Age (Myr) (b)
Figure 3. Evolutionary tracks for very low-mass stars and brown dwarfs as a function of age computed byBurrows et al. (1997). Masses and predicted Li depletion factors are labelled. The location of the Hyades Ldwarfs observed in this work are shown. -4.3-4.2-4.1-4-3.9-3.8-3.7-3.6-3.5-3.4 200 400 600 800 1000 1200 1400>99% Li depletion>90% Li depletion>1% Li depletion 0.080 Msol0.075 Msol0.070 Msol0.060 Msol0.050 Msol l og L / L s o l Age (Myr) (a) T e ff ( K ) Age (Myr) (b)(b)