beyond blue stragglers - kepler & k2 science center · 2018. 1. 23. · beyond blue stragglers:...

Beyond Blue Stragglers: K2 Observations Reveal Post-Mass-Transfer Binaries Hidden on the M67 Main-Sequence

Emily Leiner University of Wisconsin— Madison

Advisor: Robert Mathieu Dwarf Stars and Clusters with K2

January 17, 2018

In collaboration with the K2 M67 project

Geller, Latham, & Mathieu (2015)

M67WIYN Open Cluster Study: Bob Mathieu, Emily Leiner, Ben Tofflemire, Erika Carlson

Many stars in open clusters do not follow the standard path of stellar evolution…

… because of binary interactions and stellar dynamics

Over 30 years of radial velocities from the WIYN Open Cluster Study (WOCS)


WIYN Open Cluster Study: Bob Mathieu, Emily Leiner, Ben Tofflemire, Erika Carlson



blue stragglers

Blue stragglers defy the standard theory of stellar evolution… …because they have been through binary mergers,

mass-transfer, or collisions





blue stragglersyellow stragglers

Yellow stragglers: Evolved blue stragglers?

S1237A red clump giant twice the turnoff

mass of M67(Leiner et al. 2016)

K2 mission asteroseismology allows us to measure the first masses






sub-subgiants

Sub-subgiants a newly recognized class of stars fainter/redder than the giant branch

Formed from mass loss or magnetic inhibition of convection? (Leiner, Geller & Mathieu 2017)



sub-subgiants

Are there other mass-transfer, merger, or collision products in M67?




More

evolv

ed

blue s

tragg

lers?

Lower mass blue

stragglers?

Theoretical Prediction: Mass-transfer and collision products are

rapidly rotating soon after formation

Blue stragglers as stellar collision products 723

rate of the disc. This disc locking is assumed to be important in therotational evolution of pre-main-sequence stars (Konigl 1991; Sills,Pinsonneault & Terndrup 2000; Barnes, Sofia & Pinsonneault 2001),and may well be applicable to blue stragglers (although see Matt &Pudritz 2004). We have added a module to the stellar evolution codewhich allows this disc locking to be turned on for a given amountof time (which is a user-set parameter). The surface rotation rate ofthe star is fixed to be the surface rotation rate immediately after themass was lost. If this module is turned on, the disc locking turns onafter the star has lost at least 0.1 M⊙.

3.2.4 Results

We ran two evolutionary calculations. The collision product wasevolved until it threw off the minimum mass required for disclocking to turn on. Then, we either allowed the star to continueevolving without the disc locking, or locked the star to the discfor 5 million years. The lifetimes for pre-main-sequence discs arethought to range between 0 and 10 million years (Strom et al.1989).

The evolutionary tracks of the collision products with disc lock-ing (solid lines) and without (dotted lines) are presented in Fig. 8.Initially the star lost 0.10 M⊙ during its supercritical rotation pe-riod. The final angular momentum after the mass loss was 9.0 ×1049 g cm2 s−1, and after the star had been locked to a disc for 5 Myrits total angular momentum was 1.5 × 1049 g cm2 s−1 (i.e. the starloses ∼80 per cent of its angular momentum during the 5 Myr disc-locking period). Note that the stars lose ∼90 per cent of their initialangular momentum during the mass-loss phase. The material at theouter edge of the star has very large specific angular momentum, soa little mass can remove a lot of angular momentum.

While both stars initially begin their post-collision evolution inthe lower right portion of this diagram, the star that was lockedto a disc follows a fairly normal evolutionary track. This star isstill significantly brighter than a normal star of the same mass andshows some evidence of rotational mixing and modification of evo-lutionary track and lifetime. The star that was not locked to a disc(dotted line) mixes more hydrogen to the core and helium to thesurface. Its evolutionary track is slightly bluer and brighter, andits main-sequence lifetime is slightly longer than the disc-lockedstar.

Figure 8. Evolutionary tracks in the HR diagram for the M66Q collision,with (solid line) and without (dotted line) disc locking.

Figure 9. Rotation rate as a function of time for the M66Q collision, with(solid line) and without (dotted line) disc locking. The entire region showsthe current range of detected rotation rates for blue stragglers in globularclusters: 200 ± 50 km s−1 (BSS 17 in M3; De Marco et al. 2004) and<50 km s−1 (BSS 11 in NGC 6752; De Marco et al. 2004).

In Fig. 9, we plot the surface rotation velocity in km s−1 as afunction of time for the M66Q collision, with the solid line showingthe star that was locked to a disc, and the dotted line for the starthat was allowed to evolve freely after it lost mass. The differencein surface rotation rates is quite apparent, and directly reflects theamount of angular momentum that was carried away by the disc.Rotation rates of 125 km s−1 are quite fast for stars of 1 M⊙ (our Sunrotates at ∼2 km s−1), but are not completely unreasonable given theobserved rotation rate of a few blue stragglers in a globular cluster.The ordinate of this graph gives the range of observed rotation rates(Shara et al. 1997; De Marco et al. 2004).

An interesting effect of rotation in stars is the amount of rotation-ally induced mixing that can occur. Since rotating stars are subjectto a variety of thermodynamic and hydrodynamic instabilities, moremixing of material can occur than that caused by convection. Thismixing, particularly of hydrogen to the core and helium to the sur-face, is responsible for the extended lifetime of the rotating stars,and is shown in Fig. 10. This plot of surface helium abundance as a

Figure 10. Helium abundance as a function of time for the M66Q collision,with (solid line) and without (dotted line) disc locking.

C⃝ 2005 RAS, MNRAS 358, 716–725

Downloaded from https://academic.oup.com/mnras/article-abstract/358/3/716/1025781by gueston 09 December 2017

Sills, Adams & Davies 2005

The Astrophysical Journal, 764:166 (17pp), 2013 February 20 De Mink et al.

Figure 2. Four annotated examples of the effect of binary interaction on the stellar rotation rates of main-sequence stars for systems with different initial mass ratios(left vs. right panels) and different initial orbital periods (upper vs. lower panels) for Z = 0.008. Each panel shows the evolution of the equatorial rotational velocityvrot of the primary and secondary star (thick lines) as well as the Keplerian rotational velocity vK (thin lines) as long as the stars are on the main sequence. Shadinghighlights the phases during which one of the stars is rotating more rapidly than 200 km s−1. See Section 3.2 for more information.(A color version of this figure is available in the online journal.)

the projected rotational velocity for such a star accountingfor gravity darkening is considerably smaller, by a factor offdark⟨sin i⟩ ≈ 0.55.

We note that the amount by which the massive stars expandover the main sequence is not well constrained. The modelson which this diagram is based (Pols et al. 1998) have beencalibrated to the radii of eclipsing binaries of intermediate mass(Pols et al. 1997; Schroder et al. 1997). In these models theexpansion of massive stars over the course of the main sequenceis limited to a factor of 2–3. In contrast, the models by Brottet al. (2011a), which adopt a larger value for the overshootingparameter, predict expansion by a factor of 3–5 for stars in themass range 5–30 M⊙. While the predictions based on modelswith both codes show excellent agreement at zero age, theKeplerian velocities at the end of the main sequence are smallerby about a factor of 2 in the Brott et al. (2011a) models.

Furthermore we note that in the most luminous stars theeffects of radiation pressure cannot be ignored and the Keplerianlimit should be considered as an upper limit to the physicalmaximum.

3.2. Examples of the Spin Evolution of Binary Systems

In Figure 2 we depict four examples of the evolution of therotational velocity for main-sequence stars in a binary system.In each example, we assumed an initial mass for the primarystar of 20 M⊙, a metallicity of Z = 0.008, and initial rotationalvelocities of 100 km s−1 for both stars. In the top row we showsystems with initial orbital periods of P = 25 days. Thesesystems are so wide that the primary star fills its Roche lobe

only after it leaves the main sequence as it expands during itshydrogen shell burning phase. In the bottom row we assumedan initial orbital period of P = 2.5 days. In these tight systemsthe primary star fills its Roche lobe as a result of expansion onthe main sequence.

The panels on the left show examples in which the initialmass of the secondary is comparable to that of the primary,M2/M1 = 0.75. In these examples, one or more phases of masstransfer eventually lead to spin-up of the companion star. Inthe panels on the right we adopted a more extreme initial massratio, M2/M1 = 0.25. In these systems the onset of mass transferbrings the stars into contact and they merge. Only in the short-period case are the two stars that merge both still main-sequencestars. After the merged star regains its thermal equilibrium, it isexpected to continue to burn hydrogen in the center.

The phases during which one of the stars is rotating morerapidly than 200 km s−1 are highlighted in Figure 2 with grayshading. Note that during the major part of this phase, therapidly rotating star is single or appears to be single. The clearestexample is shown in panel (d) where the rapidly rotating staris the product of a merger between the two stars. In panels (a)and (b) the rapidly rotating star is the spun-up secondary. Theprimary star has lost its hydrogen envelope and is hard to detect,as a result of its reduced mass, its low luminosity, and the wideorbit. When the primary star finishes its nuclear burning andexplodes, it is likely to disrupt the system, leaving the rapidlyrotating secondary behind as a single star.

Besides the drastic effects of mass transfer and coalescence,Figure 2 illustrates the other processes that have a more subtleeffect on the stellar rotation rates, which we describe below.

5

The Astrophysical Journal, 764:166 (17pp), 2013 February 20 De Mink et al.

Figure 2. Four annotated examples of the effect of binary interaction on the stellar rotation rates of main-sequence stars for systems with different initial mass ratios(left vs. right panels) and different initial orbital periods (upper vs. lower panels) for Z = 0.008. Each panel shows the evolution of the equatorial rotational velocityvrot of the primary and secondary star (thick lines) as well as the Keplerian rotational velocity vK (thin lines) as long as the stars are on the main sequence. Shadinghighlights the phases during which one of the stars is rotating more rapidly than 200 km s−1. See Section 3.2 for more information.(A color version of this figure is available in the online journal.)

the projected rotational velocity for such a star accountingfor gravity darkening is considerably smaller, by a factor offdark⟨sin i⟩ ≈ 0.55.

We note that the amount by which the massive stars expandover the main sequence is not well constrained. The modelson which this diagram is based (Pols et al. 1998) have beencalibrated to the radii of eclipsing binaries of intermediate mass(Pols et al. 1997; Schroder et al. 1997). In these models theexpansion of massive stars over the course of the main sequenceis limited to a factor of 2–3. In contrast, the models by Brottet al. (2011a), which adopt a larger value for the overshootingparameter, predict expansion by a factor of 3–5 for stars in themass range 5–30 M⊙. While the predictions based on modelswith both codes show excellent agreement at zero age, theKeplerian velocities at the end of the main sequence are smallerby about a factor of 2 in the Brott et al. (2011a) models.

Furthermore we note that in the most luminous stars theeffects of radiation pressure cannot be ignored and the Keplerianlimit should be considered as an upper limit to the physicalmaximum.

3.2. Examples of the Spin Evolution of Binary Systems

In Figure 2 we depict four examples of the evolution of therotational velocity for main-sequence stars in a binary system.In each example, we assumed an initial mass for the primarystar of 20 M⊙, a metallicity of Z = 0.008, and initial rotationalvelocities of 100 km s−1 for both stars. In the top row we showsystems with initial orbital periods of P = 25 days. Thesesystems are so wide that the primary star fills its Roche lobe

only after it leaves the main sequence as it expands during itshydrogen shell burning phase. In the bottom row we assumedan initial orbital period of P = 2.5 days. In these tight systemsthe primary star fills its Roche lobe as a result of expansion onthe main sequence.

The panels on the left show examples in which the initialmass of the secondary is comparable to that of the primary,M2/M1 = 0.75. In these examples, one or more phases of masstransfer eventually lead to spin-up of the companion star. Inthe panels on the right we adopted a more extreme initial massratio, M2/M1 = 0.25. In these systems the onset of mass transferbrings the stars into contact and they merge. Only in the short-period case are the two stars that merge both still main-sequencestars. After the merged star regains its thermal equilibrium, it isexpected to continue to burn hydrogen in the center.

The phases during which one of the stars is rotating morerapidly than 200 km s−1 are highlighted in Figure 2 with grayshading. Note that during the major part of this phase, therapidly rotating star is single or appears to be single. The clearestexample is shown in panel (d) where the rapidly rotating staris the product of a merger between the two stars. In panels (a)and (b) the rapidly rotating star is the spun-up secondary. Theprimary star has lost its hydrogen envelope and is hard to detect,as a result of its reduced mass, its low luminosity, and the wideorbit. When the primary star finishes its nuclear burning andexplodes, it is likely to disrupt the system, leaving the rapidlyrotating secondary behind as a single star.

Besides the drastic effects of mass transfer and coalescence,Figure 2 illustrates the other processes that have a more subtleeffect on the stellar rotation rates, which we describe below.

5

Mass transfer

Collisions

De Mink et al. 2013 Sills, Adams & Davies 2005

disk

no disk

Vro

t (km

/s)

Observations: Blue stragglers have a wide range of rotation velocities, from very fast (> 100 km/s) to quite modest (< 10 km/s)

Leiner et al. 2018

V

B-V

Some of the blue stragglers in NGC 188 have hot (> 11,000 K) white dwarf companions, allowing us to measure blue straggler ages from white dwarf cooling

IMPLICATIONS FOR BSS FORMATION WITH HST 11

0.4 0.6 0.8 1.0 1.2

16

15

14

13

12

0.4 0.6 0.8 1.0 1.2B - V

16

15

14

13

12

V

18,500 16,000 13,500 11,000Temperature of WD companion (K)

18882679

4230

4348

4540

5350

5379

Fig. 5.— Optical CMD of NGC 188 cluster members with theBSS population highlighted according to binarity and the measuredtemperature of WD companions. The solid black line is the ZAMSfor NGC 188. Binary BSSs are shown as diamonds and non-velocity variable BSSs are shown as large circles. The outlinedsolid black diamonds are the two double-lined BSS binaries thatare not included in this HST study. The BSSs with WD detectionsare shown with a color from dark blue to light blue representing thetemperature of the WD companion, as indicated with the color bar.The sources outlined in grey (two SB1 binaries, one single BSS) arethe three sources without a 3σ detection in F150N.

tribution using all mass transfer-formed BSSs observablebetween 6.0–7.5 Gyr (Geller et al. 2013), and convert thetime since mass transfer ended to a WD temperature(Holberg & Bergeron 2006; Tremblay et al. 2011). Theresulting CDF is shown in Figure 6 as a solid black line.The light gray lines are the result of Monte Carlo boot-strap resampling of the N -body CDF, meant to illustratethe inherent error in the N -body age distribution.We compare the N -body age distribution with the

empirical age distribution, shown in Figure 6 as bluesquares with 500 K error bars. A KS test showsthe empirical distribution and theoretical distributionare consistent with being drawn from the same parentdistribution (p = 0.97). The overall shape of the N -body age distribution is fully consistent with the BSSages detected in this study.Adopting a mass-transfer formation frequency of 67%

for the BSS population implies there are five BSSs inNGC 188 that formed through other formation mech-anisms, such as collisions or the Kozai mechanism, inaddition to the two short-period SB2 systems. Thisnumber is consistent with the number of collisionallyformed BSSs seen in the Geller et al. (2013) N -bodymodel of NGC 188.The fraction of collisionally formed BSSs in the

Geller et al. (2013) study is quite different than observed,however, because the total number of BSSs created istoo low. The model results have an average of six BSSs

12000 14000 16000 18000

0.0

0.2

0.4

0.6

0.8

1.0

12000 14000 16000 18000White dwarf temperature (K)

0.0

0.2

0.4

0.6

0.8

1.0

CD

FFig. 6.— CDF of detected WD temperatures compared to N-

body model predictions. The distribution from the N-body modelof NGC 188 is shown as a black line (Geller et al. 2013). The lightgray lines are from 1000 Monte Carlo bootstrap resamples of the N-body distribution. The seven WDs detected in this study are shownas solid blue squares at the temperatures given in Figures 2 and 3with 500 K error bars. A KS test indicates the CDF of the detectedWD temperatures is consistent with being drawn from the sameparent population as the N-body model distribution (p = 0.97).

in NGC 188 at 7 Gyr, one of which formed from masstransfer. A separate N -body study of the open clusterM67 also fails to create a high fraction of mass transfer-formed BSSs as observed in NGC 188 (Hurley et al.2005), although the progenitor binary period distribu-tions used were not realistic.The lack of BSSs inN -body models (Geller et al. 2013)

may be attributed to an incomplete description of masstransfer processes in the binary population synthesismodels used within the N -body code. Geller et al.(2013) utilize the NBODY6 code (Aarseth 2003), whichrelies similar algorithms to those implemented in theBinary-Stellar Evolution (BSE) code of Hurley et al.(2002) to track binary evolution.Although there are too few BSSs, Geller et al. (2013)

note that the model produces a large number of long-period post-common envelope (CE) binaries that are notobserved in such frequency in NGC 188 or the field. Themass transfer parameterization in BSE may need to beadjusted such that these sources go through stable Rochelobe overflow rather than CE. Converting the post-CEbinaries to BSS+WD binaries would bring the totalmass transfer BSS population to 10 systems at 7 Gyr,for a mass-transfer formation frequency of 67%. Thismatches the inferred mass-transfer formation frequencyof 67% measured in this study for the total NGC 188BSS population.However, if the parameterization of mass transfer is

amended in BSE the consistency of the age distributionsfrom the N -body model and and these results should berevisited.Binary population synthesis models are important

tools for theoretical astronomy that allow full-N modelsof rich open clusters to run in a reasonable amount oftime. We hope that observations such as these helpconstrain the parameterizations used so that populationsynthesis models can be as accurate as possible.

Gosnell et al. 2015

Observations: Rapidly rotating blue stragglers in NGC 188

have young white dwarf companions

Leiner et al. 2018

X

XX

X XXX

Blue stragglers spin down approximately as predicted by standard main-sequence models.

A&A 556, A36 (2013)

Envelope

Core

Fig. 3. Angular velocity of the radiative core (dashed lines) and of the convective envelope (solid lines) as a function of time for fast (blue), median(green), and slow (red) rotator models. The angular velocity is scaled to the angular velocity of the present Sun. The blue, red, and green tiltedsquares and associated error bars represent the 90th percentile, the 25th percentile, and the median, respectively, of the rotational distributions ofsolar-type stars in star forming regions and young open clusters obtained with the rejection sampling method (see text). The open circle is theangular velocity of the present Sun and the dashed black line illustrates the Skumanich relationship, Ω ∝ t−1/2.

mass-loss rate (M⊙ = 1.25−1.99 × 1012 g s−1, see Table 2 fromCranmer & Saar 2011).

The middle panel of Fig. 2 shows the evolution of the mass-loss rate as a function of stellar angular velocity in our models.The saturation of the mass-loss rate again appears around 10Ω⊙,corresponding to the saturation of f∗. We derive the followingasymptotic expressions for the mass loss-rate prescription in theslow and fast rotation regimes, respectively,

Mwind ≃ 1.14 × 1012!Ω∗Ω⊙

"1.58

g s−1, (14)

if 1.5 Ω⊙ ≤ Ω∗ ≤ 4 Ω⊙, and

Mwind ≃ 2.4 × 1013 g s−1, (15)

if Ω∗ ≥ Ωsat, where Ωsat ≈ 15 Ω⊙.

3.3.3. Angular momentum loss rate: asymptotic forms

To highlight the dependency of the angular momentum loss rateon stellar parameters and primarily on stellar angular velocity,we express dJ/dt, in the asymptotic cases of slow and fast ro-tators, as a power law combining Eqs. (3), (4), and (12)−(15)above, to yield

dJdt= 1.22 × 1036 K2

1 R3.1∗

#K2

2 2GM∗ +Ω2∗R3∗$0.22Ω

4.17∗ (16)

if 1.5 Ω⊙ ≤ Ω∗ ≤ 4 Ω⊙, and

dJdt= 2.18 × 1016 K2

1 R3.1∗

#K2

2 2GM∗ +Ω2∗R3∗$0.22Ω∗ (17)

in the saturated regime (Ω∗ ≥ 15 Ω⊙). Figure 2 shows how theangular momentum loss rate varies with angular velocity for thethree rotational models developed below.

4. Results

The free parameters of the model are the initial rotational pe-riod at 1 Myr Pinit, the core-envelope coupling timescale τc−e,the disk lifetime τdisk, and the scaling constant of the wind brak-ing law K1. The value of these parameters are to be derived bycomparing the models to the observed rotational evolution ofsolar-type stars. The models for slow, median, and fast rotatorsare illustrated in Fig. 3 and their respective parameters are listedin Table 2. As explained below, the initial period for each modelis dictated by the rotational distributions of the youngest clus-ters, while the disk lifetime is adjusted to reproduce the observedspin up to the 13 Myr h Per cluster. We did not attempt any chi-square fitting but merely tried to reproduce by eye the run of therotational percentiles as a function of time.

For the fast rotator model (Pinit = 1.4 d), the disk lifetime istaken to be as short as 2.5 Myr, resulting in a strong PMS spinup. This is required to fit the rapid increase of angular velocitybetween the youngest clusters at a few Myr (Ω∗ ≃ 10−20 Ω⊙)and the 13 Myr h Per Cluster (Ω∗ ≃ 60 Ω⊙). The choice of

A36, page 6 of 15

Adapted from Gallet & Bouvier 2013 White dwarfs from Gosnell et al. 2015

Blue stragglers spin up to large rotational velocities at formation

400 Myr white dwarf detection limit


Rotation may be the key to detect recent mass-transfer or collision products on the main sequence




Lower mass blue

stragglers?

Typical M67 rotation periods are 20-30 days

with prior open cluster results), indicating that they havesmaller fractional spotted areas, while the reddest stars arevariable enough to be detectable even from the ground. Starswith spectral types F8-G0 are not detectably spotted. Similarbehaviors were noticed in the younger clusters NGC 6819 andNGC 6811 (see Meibom et al. 2011, 2015).

We are reporting rotation periods for 20 stars of the 106GLM15 member stars outside the area of the central K2superstamp. These are undoubtedly the M67 stars with bothrelatively large spot groups, and also those with rotational axesfavorably inclined with respect to the Earth. The remainder ofthe 106 members include stars where spot evolution does notallow good period determination, those that are either justunfavorably inclined, and those that had insufficiently asym-metric spot distributions and/or smaller-than-detectable spotsizes during the K2 observations.

There are a half dozen additional periodic stars with lowervariability levels among the 106 members. Although their lightcurves are less convincing than the ones reported here (at thecurrent levels of light curve correction), they lie in the sameregions of the CMD and CPD currently occupied by oursample. This fact informs us that the CPD displayed in Figure 3is robust against the particular choice of variables displayed.Other researchers might construct M67 rotator samples usingslightly different choices for individual stars and may choosedifferent data reduction strategies. However, we opine that theCPD presented here is unlikely to be altered significantly bysuch choices.

Finally, we note that the P = P(t, M) surface for M67 isexpected to be intrinsically thinner than, for example, that ofthe 2.5 Gyr cluster NGC 6819, because rotational evolution ishighly convergent (e.g., Kawaler 1988; Barnes & Kim 2010)under normal circumstances (i.e., for stars that are not locatedin close binary systems or are otherwise pathological). Themeasured surface presented here is wider. We attribute this

scatter to the long rotation periods of the sample stars relativeto the K2 observing baseline. In contrast, the availability ofmultiple quarters of Kepler data for NGC 6819 enabledmultiple determinations of each star’s period (see Meibomet al. 2015) and the calculation of a corresponding mean stellarrotation period.

3.3. Rotational Age for the Cluster

Clearly all these stars, with or without determined rotationperiods, have a single age equal to the cluster age, ∼4 Gyr(Demarque et al. 1992; VandenBerg & Stetson 2004; Belliniet al. 2010). However, by treating the individual measured starsindependently (i.e., as field stars, each sampling the cluster age),we can examine the extent to which gyrochronology yields thesame age for individual cluster stars and the uncertainties withwhich ages for similar field stars might be derivable.We therefore proceed to derive rotational ages, ti, for the

individual periodic rotators in M67 from the periods, Pi. Variousmodels may be used for this purpose, beginning with those ofEndal & Sofia (1981) for solar-mass stars. We use the relationship

⎛⎝⎜

⎞⎠⎟

tt

= + -tk

PP

kP Pln

21

C

I

0

202( ) (( ))

from B10 because of its prior success relative to other modelsin describing similar observations in a series of younger openclusters, including most recently the 400Myr old cluster M48(Barnes et al. 2015) and the 2.5 Gyr-old cluster NGC 6819(Meibom et al. 2015).11 Here P0 = 1.1 d, and kC =0.646 dMyr−1, kI = 452Myr d−1are two-dimensionless con-stants, retained unchanged from B10. (The dispersion from therange (0.12–3.4 d) of possible initial rotation periods isnegligible by the age of M67.) The convective turnover

Figure 4. Color–period diagram for M67 together with rotational isochronesfor the mean (4.15 Gyr) and median (4.3 Gyr) ages, constructed using themodel of Barnes (2010). The current Sun is located approximately 1σ abovethese isochrones. The majority of the data scatter about the isochrone isobservational. We also display isochrones for certain younger ages for whichthe model has been tested against key cluster observations.

Figure 5. Histogram of gyrochronology ages (red) for the individual M67 stars.All stars but one have 3.4 Gyr < Age < 5.3 Gyr with a median age of 4.28 Gyr(mean = 4.15 Gyr) and standard deviation of 0.7 Gyr (=17%). The equivalentMH08 chromospheric age distribution for the single cluster members ofGiampapa et al. (2006) is also displayed for comparison. These ages have amedian of 3.95 Gyr (mean = 4.2 Gyr) and a standard deviation of 1.6 Gyr(=38%). The arrows indicate the final chromospheric (4.1 Gyr) andgyrochronology (4.2 Gyr) ages for M67 (see text).

11 Lanzafame & Spada (2015) (see Brown 2014) have also shown that this modelis better than others at describing the mass dependence of rotation. By includingthe turnover timescale, and therefore the Rossby number, Ro, this model alsoconnects to chromospheric activity work by Noyes et al. (1984), and a body ofdynamo-related work going back to at least Durney & Latour (1978).

5

The Astrophysical Journal, 823:16 (16pp), 2016 May 20 Barnes et al.

Barnes et al. 2016

We searched K2 light curves for main sequence stars with

periods less than 10 days

P= 4.5 days

P= 2.2 days

Light curves from Andrew Vanderburg


K2 reveals 13 rapidly rotating stars on the main sequence we hypothesize have been through mass-transfer or collisions

These stars have a lot in common with the blue stragglers, including a 70% binary frequency, long orbital periods with low

eccentricities, and UV excesses consistent with white dwarf companions

Leiner et al. in prepPeriods around 1000 days and low eccentricities

GALEX UV excesses

Leiner et al. 2018


This work gives us a first look at the low-mass end of the blue straggler distribution, providing a new test of binary

evolution theory.

These stars are difficult to form with standard mass-transfer

models.

Post-common envelope?


Binary evolution impacts many stars 50% of solar-type stars are binary or higher-order systems

~30-40% of these are in close enough orbits to interact

What is next?

• Studies of more clusters with Kepler/K2 light curves or v sini measurements to expand our sample

• Population modeling to understand the formation frequencies and lifetimes of the post-interaction population

• Binary evolution modeling to understand the detailed physical processes that produce these stars

• For the first time, we can integrate studies of blue stragglers with their lower-luminosity and evolved counterparts

Questions?

beyond blue stragglers - kepler & k2 science center · 2018. 1. 23. · beyond blue stragglers:...

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