Rejuvenation of stellar mergers and the origin of magnetic fields in massive stars

0.76 MB·

by  Fabian R. N. Schneider

MNRAS000,1–12(2015) Preprint21January2016 CompiledusingMNRASLATEXstylefilev3.0
Rejuvenation of stellar mergers and the origin of magnetic
fields in massive stars
F.R.N. Schneider1(cid:63), Ph. Podsiadlowski1, N. Langer2, N. Castro2, and L. Fossati3
1Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom
2Argelander-Institut fu¨r Astronomie der Universit¨at Bonn, Auf dem Hu¨gel 71, 53121 Bonn, Germany
3Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
6
AcceptedXXX.ReceivedYYY;inoriginalformZZZ
1
0
2
ABSTRACT

n Approximately 10% of massive OBA main-sequence (MS) and pre-MS stars harbour
a strong, large-scale magnetic fields. At the same time there is a dearth of magnetic
J
stars in close binaries. A process generating strong magnetic fields only in some stars

9 must be responsible with the merging of pre-MS and MS stars being suggested as one
1
such channel. Stars emerging from the coalescence of two MS stars are rejuvenated,

appearing younger than they are. They can therefore be identified by comparison
]
R with reference clocks. Here we predict the rejuvenation of MS merger products over
a wide range of masses and binary configurations calibrated to smoothed-particle-
S
hydrodynamical merger models. We find that the rejuvenation is of the order of the
.
h nuclear timescale and is strongest in the lowest-mass mergers and the most evolved
p
binary progenitors with the largest mass ratios. These predictions allow us to put
-
o constraints on the binary progenitors of merger products. We show that the mag-
r netic stars HR 2949 and τ Sco are younger than the potential binary companion
st HR 2948 and the Upper-Sco association, respectively, making them promising merger
a candidates. We find that the age discrepancies and the potential binary progenitors
[ of both are consistent with them being rejuvenated merger products, implying that

their magnetic fields may originate from this channel. Searching for age discrepancies
1
v in magnetic stars is therefore a powerful way to explore which fraction of magnetic
4 stars may have obtained their strong magnetic field in MS mergers and to improve
8 our understanding of magnetism in massive stars and their remnants.
0
5 Key words: stars: general – binaries: general – blue stragglers – stars: individual:
0 τ Sco – stars: individual: HR 2949
.
1
0
6
1 1 INTRODUCTION Carrier et al. (2002) in Ap stars and now confirmed by the
: BinaMIcS project in more massive OB stars: the magnetic
v About7–10%ofmain-sequence(MS)OBAstarshoststrong,
incidence in close, massive binaries is no more than about
Xi large-scale magnetic fields (e.g. Donati & Landstreet 2009; 2%(Neiner&Alecian2013;Alecianetal.2015;Neineretal.
Ferrario, Melatos & Zrake 2015; Fossati et al. 2015) and a
r 2015).Asoftodaythereisonlyonebinarywithamagnetic
a similar B-field incidence is found in pre-MS Herbig Ae/Be fielddetectioninbothcomponents,theeccentric(e=0.27),
stars (Wade et al. 2007; Alecian et al. 2013). Among these,
4.56d B-star binary (cid:15) Lupi (Shultz et al. 2015b).
Babcock’s star (HD 215441), a chemically peculiar A0 star
withasurfacepolarmagneticfieldstrengthof34kG,isthe The origin of these strong magnetic fields is still un-
current record holder. The strong field pre-MS stars show known but from the rather low magnetic-star incidence of
similar magnetic fluxes to those found in magnetic1 OBA theorderof10%itisclearthatsomethingspecialmusthave
stars, indicating a common origin. Interestingly there is a happened to these stars. In the literature, three formation
dearth of magnetic stars in close binaries, first noted by channels are typically discussed: (i) strong B-fields inher-
ited from the star forming cloud (e.g. Mestel 2001; Moss
2001), (ii) a dynamo generating strong magnetic fields and
(cid:63) E-mail:[email protected]
1 In the following, we use the term “magnetic stars” for stars (iii) mergers of pre-MS and/or MS stars creating B fields
withstrong,large-scalesurfacemagneticfields.Sub-gausssurface because of strong shear (Ferrario et al. 2009; Langer 2012,
magneticfieldshavenowbeenobservedaswellinsomestars(e.g. 2014;Wickramasinghe,Tout&Ferrario2014).Scenarios(i)
Ligni`eresetal.2009;Petitetal.2011)andmaybeubiquitous. and(ii)havedifficultiesexplainingwhyonlysomestarsshow
(cid:13)c 2015TheAuthors
2 Fabian R.N. Schneider et al.
strong,large-scalesurfacemagneticfieldsandnotallofthem products will be rejuvenated (e.g. Hellings 1983; Podsiad-
given that they formed from the same molecular cloud and lowskietal.1992;Braun&Langer1995;Dray&Tout2007),
are governed by the same physical processes, respectively. i.e. they will appear younger than other stars that formed
Neutronstars(NSs)andwhitedwarfs(WDs)alsocome at the same time such as other cluster members or binary
in a highly and a less magnetic group. There is the class companions (e.g. van Bever & Vanbeveren 1998; Schneider
of highly magnetised neutron stars, so-called magnetars, et al. 2014b). Pre-MS mergers will not rejuvenate and will
with inferred surface magnetic fields of about 1013–1015G not show hydrogen-burning products on their surface. Ap-
(Olausen & Kaspi 2014) and the class of strong-field WDs, parent age discrepancies are therefore strong hints towards
among them the Polars, with surface magnetic fields in ex- aMSmergeroriginofsomemagneticstarsandmayfurther
cess of 106G. Liebert, Bergeron& Holberg (2003) find that allowustoestimatethefractionofstarsthatobtainedtheir
at least about 10% of WDs with B-field strengths greater strong magnetic field in MS mergers.
than about 2MG are highly magnetic. Because of the sim- Age discrepancies have recently been reported in two
ilar fractions of magnetic WDs and AB stars, Landstreet magnetic stars. In the HR 2949 and 2948 visual binary, the
(1992)proposethatthemagneticABstarsmaybethepro- more massive and magnetic star HR 2949 is found to be
genitors of magnetic WDs. younger than the non-magnetic, potential binary compan-
No highly magnetic WD has been found in a detached ion HR 2948 (Shultz et al. 2015a). Also, the magnetic star
binary.StrongmagneticfieldshaveonlybeenfoundinWDs τ Sco appears to be significantly younger than the Upper
in cataclysmic variables (Roche-lobe overflowing binaries) Scorpius association of which it is a proper motion member
andinsomeapparentlysingleWDs(Toutetal.2008).Based (Nieva & Przybilla 2014). Triggered by these findings, we
on that, Tout et al. (2008) suggest that the strong mag- investigatewhetherthemergerhypothesisisabletoexplain
neticfieldsinWDsaretheresultofadynamooperatingbe- the observed age spreads. To that end, we explore the reju-
causeofdifferentialrotationandconvectionduringcommon- venation of MS mergers (Sec. 2) and apply our findings to
envelopeevolutionthat(nearly)leadtoamerger.Inthispic- HR 2949 and τ Sco (Sec. 3). We show that both stars may
turenearmergersgiverisetomagneticcataclysmicvariables indeed be the products of MS mergers and put constraints
andcompletemergerstohighlymagnetisedsingleWDs.Fol- ontheirprogenitorsystems.Wediscussourresultsandfur-
lowingtheworkofToutetal.(2008),Wickramasingheetal. thertestablepredictionsofthemergerhypothesisinSec.4,
(2014)proposeanΩdynamo2thatgeneratesmagneticfields and summarize our conclusions in Sec. 5.
from differential rotation that could act during common-
envelope evolution and in mergers. Wickramasinghe et al.
(2014) further find that the magnetic flux per unit mass in
2 REJUVENATION OF MERGER PRODUCTS
highlymagnetisedWDsissimilartothatofmagneticOBA
starsandthereforesuggestthatthemagneticfieldsinstrong Wedefinetheageofastarasthetimethathaspassedsince
fieldWDsandOBAstarsmayhavebothbeengeneratedby corehydrogenignition(zero-ageMS;ZAMS).Arejuvenated
similar processes. star is a star whose appearance suggests an apparent age
A scenario accounting for the observations mentioned thatisyoungerthanitsrealage.Rejuvenationcantherefore
aboveisthatmagneticstarsareproducedbymergersofpre- only be defined with respect to a comparison clock.
MSandMSstars.Mergerscannaturallyexplainwhyonlya The merging of pre-MS stars leads to merger products
fractionofstarshavestrong,large-scalemagneticfields(e.g. thatreachtheZAMSatdifferenttimescomparedtopre-MS
deMinketal.2014predictthatabout8%ofallmassiveMS genuinesinglestarsofthesamemass.Themergerproducts
stars are merger products), why the magnetic field charac- may reach the ZAMS earlier because of the decreased con-
teristicsofmagneticpre-MSstars,MSstarsandstrongfield tractiontimescaleduetotheincreasedmassbutitcanalso
WDs are so similar and why there is a dearth of magnetic reach the ZAMS later because of the additional orbital en-
MS stars in close binaries. The merging can occur during ergy that has to be radiated away before the core heats up
thepre-MSby,e.g.,tidalinteractionwithcircumstellarma- enoughtostarthydrogenburning.Thedelayis,inanycase,
terial(Stahler2010;Korntreff,Kaczmarek&Pfalzner2012) of the order of the thermal timescale and therefore practi-
aswellasduringtheMSby,e.g.,binarystarevolution(e.g. cally undetectable.
Podsiadlowski, Joss & Hsu 1992; Langer 2012). In MS mergers the rejuvenation is of the order of the
Main-sequencemergerproductsarehardtodistinguish nucleartimescaleandhencedetectable.Inthefollowing,we
fromgenuinesinglestarsbecausetheirinternalstructuread- predicttherejuvenationandhenceapparentagedifferences
justs to the new mass such that it may be quite similar to ofMSmergerproductstopavethewayfortheidentification
thatofsinglestars.However,mergersmayshowsurfaceen- of MS mergers by apparent age discrepancies. To that end,
hancements of hydrogen-burning products such as nitrogen we extend the approach of Glebbeek & Pols (2008) by also
and helium, they may be rapid rotators if not spun down takingstellarwindmasslossintoaccountwhichisimportant
efficiently, e.g. by magnetic fields coupled to outflows, and inmassivestars.Weassumethattheaveragehydrogenmass
there may be circumstellar material ejected prior to and/or fraction,
during the merger process. More importantly, MS merger
1 (cid:90) M
(cid:104)X(cid:105)= X(m)dm=(1−Q f)X , (1)
M c 0
0
2 Strictlyspeaking,thisisnotapureΩdynamobecauseWickra- decreases linearly with time from its initial value of
masingheetal.(2014)introduceanartificialmechanismthatgen- (cid:104)X(cid:105)ZAMS =X0toitsfinalvalueof(cid:104)X(cid:105)TAMSattheterminal-
erates a poloidal field component from the decay of the toroidal ageMS(TAMS).InEqs.(1),M isthetotalmassandmthe
component. masscoordinate,andwehavedefinedthefractionalMSage
MNRAS000,1–12(2015)
Origin of magnetic fields in massive stars 3
f =t/τ (withtbeingtheageandτ theMSlifetimeof Q = Q ≈ 0, we recover the average hydrogen mass
MS MS m,2 m,i
a star) and the effective core mass fraction, fraction and the apparent fractional MS age of the merger
products of Glebbeek & Pols (2008),
(cid:104)X(cid:105) −(cid:104)X(cid:105) X −(cid:104)X(cid:105)
Q = ZAMS TAMS = 0 TAMS. (2)
c (cid:104)X(cid:105)ZAMS X0 (cid:104)X(cid:105) =1− 1 Qc,1f1+Qc,2f2q, (7)
X 1−φ 1+q
In an ideal situation, i.e. no wind mass loss, no receding 0
convective cores during the course of the MS evolution, no
additionalmixingetc.,theabovedefinedeffectivecoremass f = 1 1 Qc,1f1+Qc,2f2q. (8)
fractiongivesQc =Mc/M formassivestarswithconvective app αQc(M)1−φ 1+q
cores of mass M . In non-ideal cases such as those encoun-
c Glebbeek & Pols (2008) and Glebbeek et al. (2013) con-
teredinthiswork,Eq.2givestherelativedifferencebetween
duct smoothed-particle hydrodynamical (SPH) simulations
the average initial and end-of-MS hydrogen mass fractions
of head-on collisions of massive MS stars and calibrate the
which can be viewed as an effective core mass fraction (for
extra mixing parameter α. To that end they import the
simplicity we call Q the effective (convective) core mass
c structure of their SPH merger products into a 1D stellar
fraction from here on). The big advantage of this definition
evolutionarycodeanddeterminetheremainingMSlifetime
is that it can also be applied to stars with radiative cores
of the merged stars, t = τ (1 − f ). Knowing t
MS MS app MS
and it properly accounts for stellar wind mass loss, addi-
from the evolution of the SPH merger products, Glebbeek
tional mixing, receding convective cores etc.
&Pols(2008)inferamixingparameterofα=1.67forlow-
We further assume that the stellar mass, M, decreases
massmergers(lessthan1.2M )andGlebbeeketal.(2013)
(cid:12)
linearly with time because of winds,
α = 1.14 for high-mass mergers (5–40M ) at solar metal-
(cid:12)
M =(1−Q f)M . (3) licity. We adopt α=1.14 for our rejuvenation prescriptions
m ini
of high-mass MS mergers.
In the last equation, Mini is the initial mass of a star and In order to understand the basic behaviour of rejuve-
Qm the fraction of mass lost on the MS, nation, it is instructive to consider the case of equal-mass
Q = Mini−MTAMS (4) mergers with negligible wind mass loss (M1 = M2, q = 1,
m Mini f1 = f2 = f and Qm,1 = Qm,2 = Qm,i = 0). Equation (8)
then reads
with M being the mass of a star at the TAMS.
TAMS
f 1 Q (M )
As Glebbeek & Pols (2008), we assume that a fraction app = · c 1 . (9)
φofthetotalmassofabinaryislostinthemergingprocess f 1−φ αQc(M)
andthatthecompositionofthelostmaterialisthesameas This equation shows that rejuvenation is the stronger the
the initial composition. The latter assumption breaks down lower the fraction of lost mass, φ, the larger the increase
ifthosepartsofstarslostinthemergerprocessarealready oftheeffectivecoremassfraction,Q (M)/Q (M ),andthe
c c 1
enrichedinhydrogen-burningproducts,e.g.,bystellarwind larger the mixing into the core, α. Equation (9) further il-
mass loss or rotational mixing. From head-on collisions of lustratesthattheabsoluterejuvenation,∆f =f−f ∝f,
app
massiveMSstars,Glebbeeketal.(2013)findφ=0.3q/(1+ is larger in more evolved mergers.
q)2 with q =M2/M1 being the mass ratio and M1 and M2 Physically,anequal-massmergeratf =1,i.e.amerger
themassesoftheprimaryandsecondarystaratthetimeof oftwostarswithpureheliumcores,onlyrejuvenatesbythe
the merging, respectively. The mass of the merger product additional mixing of fresh fuel into the newly formed core.
is then M =(1−φ)(M1+M2). However,thedetailedmergersimulationsofGlebbeeketal.
Using the above definitions and assumptions, the av- (2013)showtheformationofathickhydrogen-burningshell
erage hydrogen mass fraction of the merger product, (cid:104)X(cid:105), around the inert helium cores that burns hydrogen for a
followsfromM(cid:104)X(cid:105)=M1(cid:104)X(cid:105)1+M2(cid:104)X(cid:105)2−φ(M1+M2)X0, significant fraction of time: the merger of a 20.0+19.8M(cid:12)
binaryatcorehydrogenexhaustionoftheprimaryproduces
(cid:104)X(cid:105) (1−Q f )(1−Q f −φ)
= m,1 1 c,1 1 amergerproductthatburnshydrogeninathickshellforap-
X (1−φ)[(1−Q f )+(1−Q f )q]
0 m,1 1 m,2 2
proximately 1.4Myr, a duration that corresponds to about
(1−Q f )(1−Q f −φ)q
+ m,2 2 c,2 2 . (5) 18% of the MS lifetime of the former primary star. This
(1−φ)[(1−Q f )+(1−Q f )q]
m,1 1 m,2 2 phaseofthickhydrogenshellburningtakesplaceintheblue
Theindices1and2refertotheprimaryandsecondarystar, part of the Hertzsprung–Russell (HR) diagram where gen-
respectively. The apparent fractional MS age of the merger uinesinglestarsundergocorehydrogenburningandEqs.(6)
product, f , is then related to the fractional MS age, f, and (8) still give a good approximation to the remaining
app i
ofagenuinesinglestarofinitialmassM thathasthesame hydrogen-burningtimeforsuchmergerproducts(Glebbeek
i
mass (M = (1 − Q f)M) and average hydrogen mass etal.2013).However,theevolutionarytrackofsuchmerger
m,i i i
fraction ((cid:104)X(cid:105) = (1−Q f)X ) as the merger product. In- products in the HR diagram do no longer resemble those of
c,i i 0
troducingtheparameterαthataccountsforpotentialextra single stars. The internal structure does not adjust to that
mixingoffreshfuelintothecoreofthemergerproduct(see of a single star with the same mass and the apparent age
also Glebbeek & Pols 2008), we find for the apparent frac- inferred for such merger products from their position, e.g.,
tional MS age in the HR diagram might be different from what we can
predict from the above simplified model (see also Sec. 2.2).
f 1−(cid:104)X(cid:105)/X
f = i = 0. (6) Let t = f τ (M ) = f τ (M ) be the real and
app α αQ real 1 MS 1 2 MS 2
c,i t =f τ (M)theapparentageofthemerger.Theab-
app app MS
In case of negligible stellar wind mass loss, i.e. Q = soluteamountbywhichthemergerapparentlyrejuvenates,
m,1
MNRAS000,1–12(2015)
4 Fabian R.N. Schneider et al.
(b) τMS/Myr
97.5 23.3 8.5 4.5
f
e
ag f ∆τMS=74.2Myr ∆τMS=4.0Myr
e
c
n
ue ∆f f
q ∆
se fapp
n- f
ai app
m
al
n
o ∆t=t t =fτ f τ f∆τ
cti ⇒ real−app MS,1− app MS,2≥ MS
a
Fr
5 10 20 40
M/M
fl
Figure 1. Cartoons illustrating the two contributions to the overall rejuvenation in the case of equal-mass mergers with no mass loss.
Stars rejuvenate because of (1) the mixing of fresh fuel into the core and (2) shorter lifetimes connected with more massive stars (not
toscale;seemaintextfordetails).In(a)wedepicttherealrejuvenationina10+10M(cid:12) merger,i.e.thereductionofthecorehelium
mass fraction Yc. Convective cores are indicated by the grey shaded regions. The parameter α describes the extra-mixing that occurs
during the merger process. The real rejuvenation is stronger in more massive stars because they have larger effective convective cores,
Qc, and in older stars because they have larger core helium mass fractions. In (b) we show the overall rejuvenation in the fractional-
MS-agevs. stellar-mass planeformergersof5+5M(cid:12) and 20+20M(cid:12) forthecases ofrejuvenating (∆f =f−fapp >0;bluearrows)
and not rejuvenating (∆f = 0; red arrows) the cores of the merger products. The overall rejuvenation, ∆t = treal−tapp, is at least
∆t=f[τMS(M)−τMS(2M)]=f∆τMS (no real rejuvenation), i.e. it is of the order of the nuclear timescale of stars. Also, the overall
rejuvenation is stronger in relatively older stars (larger fractional MS ages f) and in lower-mass stars (larger MS-lifetime differences
∆τMS).Intermsofmassratiosq=M2/M1,rejuvenationtendstowardszeroforverylow-masscompanions.
binarymergers.InTab.1,weprovidetheinitialandTAMS
Table 1. Initial mass Mini, TAMS mass MTAMS, effective con-
vectivecoremassfractionQc andMSlifetimeτMS ofBrottetal. masses, the MS lifetimes and the effective convective core
(2011a) solar-metallicity stellar models used to compute the re- masses of these models. Within this table, we interpolate
juvenationofmergerproducts. linearly in mass to obtain M and Q , and logarithmi-
TAMS c
callyinmasstogetτ .Withthesedataandinterpolations
MS
Mini/M(cid:12) MTAMS/M(cid:12) Qc τMS/Myr we map the rejuvenation, ∆t/τMS, as a function of primary
3.0 3.0 0.23 340.4 and secondary mass for fractional MS ages of the primary
5.0 5.0 0.26 97.5 star of f1 ≡f =0.2, 0.5 and 0.8 in Fig. 2 and as a function
10.0 9.9 0.33 23.2 ofprimarymassandfractionalMSageforafixedmassratio
20.0 19.3 0.45 8.5 of q = 1 in Fig. 3. The MS lifetimes of the primary stars,
40.0 32.9 0.67 4.5 τ ,areindicatedontheupperx-axesofFigs.2and3from
MS
50.0 33.6 0.86 3.9 which the time of the merger follows as t =fτ . At
merger MS
60.0 39.5 0.88 3.5
thetimeofthemerger,theprimarystarfillsitsRochelobe.
80.0 45.2 0.96 3.1
Approximating the Roche lobe radius R by
100.0 49.4 0.98 2.8 L
R q−1/3
L =0.44 for 0.1≤q−1 ≤10 (12)
a (1+q−1)1/5
∆t=t −t , is then given by
real app
(Eggleton2006)withabeingtheorbitalseparation,wefind
∆t=f τ (M )−f τ (M), (10)
1 MS 1 app MS for the orbital period, P ,
orb
and the relative amount by
(cid:115)
(cid:18) M (cid:19)1/5 R3
∆t =1− fapp τMS(M). (11) 1+ M1 Porb =2π GM 0L.443, (13)
t f τ (M ) 2 1
real 1 MS 1
Equation (11) demonstrates that the rejuvenation of MS where G is the gravitational constant. Note that M and
1
mergers is of the order of the real age of the merger, i.e. M are present-day masses. From further interpolations of
2
of the order of the nuclear timescale of stars, and further stellar radii, we compute the orbital periods of the merg-
shows the two different contributions to the overall rejuve- ing binaries following Eq. (13). Because (1+M /M )1/5 is
1 2
nation (see also Fig. 1). The first factor, f /f , describes a weak function of the mass ratio (approximately 1.15 for
app 1
therealrejuvenationintermsofthemixingoffreshfuelinto M = M and 1.62 for M = 10M ), the orbital periods
1 2 1 2
the core of the merger product whereas the second factor, given on the second top x-axis in Fig. 2 are close to the
τ (M)/τ (M ), describes the apparent rejuvenation be- orbital periods of the binaries at the time of the merger.
MS MS 1
cause of the shorter lifetimes associated with more massive As already discussed above and illustrated in Fig. 1,
stars (τ (M)<τ (M ) because M >M ). the overall rejuvenation is stronger in more evolved stars
MS MS 1 1
Wenowusethesolar-metallicity(X =0.72739)stellar (cf. Fig. 3 and Eq. 9). For fixed fractional MS ages, the re-
0
modelsofBrottetal.(2011a)tocomputetherejuvenationof juvenation is more in binaries with larger mass ratios, i.e.
MNRAS000,1–12(2015)
Origin of magnetic fields in massive stars 5
1+M1/M2 0.2Porb/days τMS/Myr
0.69 0.83 ¡ 1.06 ¢ 1.36 1.96 1.0340.4 97.5 23.2 8.5 3.9 0.81
50340.4 97.5 23τ.M2S/Myr 8.5 3.9 0.65 age 0.73 0.65 q=1.0 0.73
(a) f=0.2 000...556050 uence 0.8 0.57 0.49 00..5675
tmerger=f·τMS 00..4405 n-seq0.6 0.41 00..4419/τMS
M/M2fl10 000...233505∆t/τMS nal mai0.4 0.205.33 00..2353∆t
0.12 0.09 0.20 ctio0.2 0.17 0.17
0.15 0.06 000...011925 Fra0.0 00..0091 00..0019
3 10 50
0.06
M /M
3 1
0.03 fl
3 10 50
M /M
1 fl Figure 3. Apparent rejuvenation, ∆t/τMS, as a function of the
1+M1/M2 0.2Porb/days initialmass,Mi,1,andfractionalMSageoftheprimarystar.The
0.95 1.11 ¡ 1.41 ¢ 1.85 3.04 initialmassratioqi=Mi,2/Mi,1 issetto1.Thetopx-axisgives
τMS/Myr the MS lifetime of the primary stars from which the time of the
50340.4 97.5 23.2 8.5 3.9 0.65 mergerfollowsastmerger=f·τMS.
0.60
(b) f=0.5
0.55
0.50 in more massive binaries, mainly because of shorter life-
tmerger=f·τMS 0.45 times associated with more massive mergers. Fixing the
0.40
fractional MS age and the mass ratio (e.g. dashed diago-
/Mfl 00..3305/τMS nal lines for equal-mass mergers in Fig. 2), the overall re-
M210 0.25∆t juvenation is more in less massive binaries. For example,
0.35 0.30 0.25 0.20 00..1250 τinMSa(M3)+/τ3MMS((cid:12)M1m)e=rg0e.r23atwhfer=eas0f.o5r, afa3p0p/+f130=M(cid:12)0.8m2eragnedr
0.150.12 00..0192 fvaepnpa/tfio1n=,t0h.e60maixnidngτMoSf(fMres)h/τfuMeSl(iMnt1o)t=he0c.6o0r.eTofhtehreeamlerregjuer-
0.06
3 0.03 product, is greater in more massive stars (smaller fapp/f1
3 10 50 values)becauseQ increasesmoresteeplywithmassathigh
M /M c
1 fl masses than at low masses (cf. Eq. 9 and Tab. 1). The
1+M1/M2 0.2Porb/days overall apparent rejuvenation, however, is more in lower-
1.7 1.9 ¡ 2.43 ¢ 3.48 9.92 massstars(smallerτ (M)/τ (M )values)becauseofthe
τMS/Myr MS MS 1
340.4 97.5 23.2 8.5 3.9 largermass-luminosityexponentandhencelargerdifferences
50 0.65
in MS lifetimes.
0.60
(c) f=0.8
0.55 From Fig. 3 we can infer the age of the apparently
0.50 youngest merger product in coeval star clusters of various
tmerger=f·τMS 0.45 ages. The apparently youngest and at the same time one of
0.40 the most massive merger products stems from equal-mass
Mfl 0.35 MS mergers at f ≈ 1. In a 3.9Myr star cluster, the age of the
/ 0.30/τ
M210 0.25∆t apparently youngest merger product is about 1.9Myr and
0.55 0.45 0.40 0.35 00..1250 ianreac3o4m0pMaryarbsletatroctlhuossteerfoitunisdabbyoSucth6n8eMideyrr.eTtahle.s(e20n1u5m)baenrds
0.60 0.50 0.300.250.20 000...001692 hthigahnlitghhetytrheaatllbyinaarery,pportoednutciatsllycabnialosionkgsiingfneirfirceadnctlluysyteorunaggeesr
towardstooyoungageswhenneglectingthatthemostmas-
3
0.03
3 10 50 sive and hence most luminous stars are likely products of
M /M
1 fl binary mass transfer (Schneider et al. 2014b, 2015).
Figure2.Apparentrejuvenation,∆t/τMS,asafunctionofinitial
primarymass,Mi,1,andsecondarymass,Mi,2,forthreedifferent 2.1 Model uncertainties
merger times: the stars merge at a fractional MS age of (a) f =
0.2, (b) f =0.5 and (c) f =0.8 of the primary star. The upper Ourrejuvenationmodelhasessentiallytwophysicalparam-
twox-axesindicatetheMSlifetimeoftheprimarystar,τMS,and eters, the mixing parameter α and the fraction of mass
theorbitalperiod,P ,ofthebinaryatthetimeofthemerger.
orb lost in a merger φ, and further three parameters set by
Theorbitalperiodsdependslightlyonthepresent-daymassratio
the stellar models, the fraction of mass lost on the MS
ofthebinary.
Q , the effective core mass fraction Q and the MS life-
m c
timeτ .Wevariedtheseparametersandreportthedevia-
MS
tionsoftherejuvenationwithrespecttoourstandardmodel,
MNRAS000,1–12(2015)
6 Fabian R.N. Schneider et al.
mostmassivebinaries.Alsothedeviationsfromourstandard
Table 2.Uncertaintiesintheamountofrejuvenationbecauseof
uncertainties in the mixing parameter α, the fraction of mass modelaresmallerforyoungerfractionalMSages.Switching
lost in a merger φ, the fraction of mass lost by stellar winds wind mass loss totally off (Qm = 0) reduces the rejuvena-
Qm and switching wind mass losses totally off, Qm = 0.0. Tab- tion by at most 20% for the most massive binaries consid-
ulated values are relative deviations from our standard model ered here and leaves the rejuvenation nearly unchanged in
([∆tstandard−∆t]/∆tstandard) with negative deviations indicat- intermediate-mass binaries (approximately 10M(cid:12)).
ingmorerejuvenationandpositiveless.Thequotednumbersare
forf =0.8.
2.2 Systematic uncertainties
M1= 3M(cid:12) 10M(cid:12) 50M(cid:12)
q= 1.0 0.2 1.0 0.2 1.0 0.2 The age differences of our model relate to the available fuel
α+0.2 −4% – −6% −21% −17% −31% in the cores of stars. This age difference is not the same
α=1.0 +3% – +6% +20% +16% +28% anobservermightinferfromthesurfacepropertiesofstars.
Thiscancausesystematicdifferencesbetweenthepredicted
φ·2 +8% – +12% +20% +12% +17%
rejuvenation of our models and that inferred from observa-
φ/2 −3% – −5% −9% −6% −8%
tions.Suchdifferencesareexpectedtobelargeriftheinter-
Qm·1.2 ±0% – ±0% ±0% −12% −2% nalstructureofmergedstarsdeviatesignificantlyfromthat
Qm·0.8 ±0% – ±0% ±0% +7% +2% of genuine single stars of the same mass. In the models of
Qm=0 ±0% – +1% +1% +18% +9% Glebbeek et al. (2013) this applies to mergers of stars near
the end of core hydrogen burning that undergo a phase of
thick hydrogen shell burning.
Generally, merger products have larger average mean
(∆t −∆t)/∆t ,inTab.2.Varyingtheeffective
standard standard molecular weights, µ, and are therefore over-luminous and
core mass fraction by a factor that is independent of mass
havelargerradii(hencesmallersurfacegravities)compared
will not affect the rejuvenation in our models (see Eqs. 5, 6
to genuine single stars of the same mass (e.g. see Fig. 7 in
and8).Anymass-independentchangeoftheMSlifetimewill
Glebbeeketal.2013).Thusweexpectthatapparentagesin-
linearly affect the rejuvenation for fixed fractional MS ages
ferredfromcomparingthepositionsofmergerstosingle-star
(seeEq.10):prolongingMSlifetimesby,e.g.,10%,leadsto
models in HR diagrams are younger than what our models
10%increasesoftherejuvenationandviceversa.Overallthe
predictbecauseofshorterMSlifetimesassociatedwithmore
deviations are of the order of 10–20% and in general larger
luminous stars. In contrast, we expect older apparent ages
for higher-mass binaries.
when comparing mergers to single-star models in the so-
In low-mass stars (less than about 1.2M ) the mixing
(cid:12) called Kiel diagram (effective temperature vs. surface grav-
parameter α is 1.67 (Glebbeek & Pols 2008) whereas it is
ity diagram) because of older ages associated with stars of
1.14 in high-mass stars (Glebbeek et al. 2013). Increasing
smaller gravities. Inferring ages by matching effective tem-
(decreasing)themixingparameterresultsinmore(less)re-
peratures, luminosities and surface gravities simultaneously
juvenation. Setting α = 1.0 corresponds to no mixing of
to stellar models may cancel some of the biases.
fresh fuel into the core of the merger product. There is a
mass dependence in the deviations because the mixing pa-
rameter always assumes that a fraction of the effective core
2.3 Inferring merger progenitor properties
massismixedintothecoreasfreshfuel.Hencetheabsolute
amount of mixed fresh fuel is larger for more massive stars The rejuvenation derived in this work can be used to put
because they have larger convective cores. constraints on pre-merger binaries if the apparent age dis-
TheSPHsimulationsofGlebbeeketal.(2013)arehead- crepancy of merger candidates with respect to comparison
oncollisions.Ontheonehand,onemayexpectlessmassloss clocks,e.g.theageofahoststarcluster,isknownfromob-
in more gentle mergers of orbiting stars but, on the other servations. Imagine there is an apparently single star with
hand, there is a lot of orbital angular momentum that may aninferredmassof18.4M andanapparentageof8.3Myr
(cid:12)
makethemergedstarrotaterapidly,therebyenhancingmass in an otherwise coeval star cluster of 16.6Myr. The age of
loss. Increasing (decreasing) the fraction of mass lost by a thestarclusterimpliesthatthemergermusthavehappened
factor of 2 reduces (enhances) the rejuvenation. Modifying att <16.6Myr.Themassofthemergercandidatere-
merger
thetotalmassofthemergerproductaffectstherejuvenation stricts the potential mass range of pre-merger binaries and
in two ways: (i) it influences the rejuvenation directly via the observed apparent age discrepancy can then be used to
changingφinEqs.(5)and(8)and(ii)indirectlyviachanges determine the mass ratio and the time when the merger
in the effective convective core sizes and the MS lifetimes. occurred. In this example, a 10+10M merger at an age
(cid:12)
Overall the changes are such that the rejuvenation varies of t = 11.6Myr (f = 0.5) leaves a merger product
merger 1
more in higher-mass binaries. of 18.4M that looks younger by 8.3Myr than it really is.
(cid:12)
Stellar-wind mass-loss rates are uncertain. Increasing From the potential binary masses and the time when the
(decreasing) the fraction of mass lost during the MS evo- merger occurred, we can further determine the orbital pe-
lution leads to more (less) rejuvenation because the initial riod of the pre-merger binary as P =1.23days. The pre-
orb
mass of the genuine single star that matches the mass of mergerbinaryconfigurationcanthenbecomparedtobinary
the merger product and the average hydrogen mass frac- modelstocheckwhethersuchabinaryisindeedexpectedto
tion is larger (smaller) for more (less) mass lost and the merge. According to the models of Schneider et al. (2015),
corresponding MS lifetimes are hence shorter (longer). En- a binary composed of two 10M stars in a 1.23days orbit
(cid:12)
hancing/reducing the mass loss by 20% mainly affects the (a=13R ) will indeed merge.
(cid:12)
MNRAS000,1–12(2015)
Origin of magnetic fields in massive stars 7
Generally speaking, the problem is to constrain four In order to quantify the age discrepancy including ro-
parameters, the primary and secondary mass, the orbital busterrorbars,weusetheBayesiantoolBonnsai3 (Schnei-
period and the time when the merger occurred, from three deretal.2014a).Wesimultaneouslymatchtheobservedlu-
observables, the inferred mass and apparentand real age of minosities,effectivetemperatures,surfacegravitiesandpro-
the merger product. This is obviously a degenerate situa- jected rotational velocities derived by Shultz et al. (2015a)
tion where no unique solution exists unless in special cases to the stellar models of Brott et al. (2011a) to determine
where it is possible to, e.g., obtain the time of the merger the masses and ages of HR 2949 and HR 2948. We assume
from the expansion age of a shell that was ejected in the a Salpeter initial mass function (Salpeter 1955) as initial
mergerprocess.Althoughitisgenerallynotpossibletofind mass prior, a Gaussian with mean of 100 and FWHM of
auniquesolution,onecanusestatisticsandadditionalprior 250kms−1 as initial rotational velocity prior (cf. Hunter
knowledgesuchasdistributionfunctionsof,e.g.,binarype- et al. 2008a), a uniform prior in age and that the rotation
riods and mass ratios to evaluate the likelihood of different axes are randomly oriented in space. We find initial (and
merger progenitors. In some cases this may allow us to ex- present-day) masses of 5.8+0.4 and 4.0+0.4M , and ages
−0.2 −0.3 (cid:12)
clude significant parts of the parameter space. of 27.2+7.9 and 59.8+29.2Myr for HR 2949 and HR 2948,
−11.1 −32.2
respectively. From the full age posterior probability dis-
tributions of the two stars, we find an age difference of
35.0+31.3Myr, which means that HR 2949 appears to be
3 MAGNETIC MERGER CANDIDATES −32.6
younger than HR 2948 with a confidence of 87.8%.
The procedure of constraining pre-merger binaries relies on Taking this age discrepancy at face value, we investi-
accurate and reliable merger models, and precise age and gate a potential merger origin of HR 2949 (see Sec. 2.3).
mass determinations of the merger candidate and the com- In this scenario, the HR 2949 system was a triple-star sys-
parison clock. We now apply this new technique to the teminwhichtheinnerbinarymerged.Theinferredmassof
magnetic merger candidates HR 2949 (Sec. 3.1) and τ Sco HD 2949 requires the merger to leave a remnant of about
(Sec. 3.2). 5.8M . Mergers of 3+3M , 4+3M and 5+2M stars
(cid:12) (cid:12) (cid:12) (cid:12)
mayproducetheobservedmassofHR2949andweplotthe
predicted rejuvenation of such merger products as a func-
3.1 HR 2949
tionofthetimeofthemergerinFig.4.Withinourmodels,
HR2949andHR2948formavisualpairofB-typestarsata the apparent rejuvenation is a linear function of the (frac-
Hipparcos distance of 139+24pc (van Leeuwen 2007), sepa- tional MS) age when the two stars merge (see Eq. 8 and
−18
ratedby7.3arcsecontheskywithradialvelocitiesidentical recall that f2 = f1τMS(M1)/τMS(M2)). We indicate the 1σ
withintheirerrorbars(Shultzetal.2015a).Ifthetwostars range of the real age of the merger, the age of the com-
weretoformabinarysystem,theirorbitalseparationwould parison clock HR 2948, by the shaded region in Fig. 4 and
be larger than 2×105R . Shultz et al. (2015a) argue that highlighttheinferredagedifferenceofHR2949withrespect
(cid:12)
HR2948andHR2949maynotbegravitationallyboundbe- to the comparison clock by the hatched area4. The inferred
causetheirrelativepropermotionsaretoolarge,rathersug- agedifferencedependsontherealageandvarieswithinthe
gesting a chance superposition. However they caution that 1σ uncertaintyoftheageofthemergercandidateHR2949.
their analysis is not fully conclusive because of the proper Ourmergermodelsareabletoexplaintheobservablesifthey
motionuncertainties.IfHR2948andHR2949weretoform predictanagedifferencethatislargerthanthelowerbound
a gravitationally bound binary, they would share the same oftheinferredagedifferences,i.e.iftheycrossorareabove
age. But even if they are not gravitationally bound, their the lower bound at any time younger than the real age of
proximity on the sky and similar radial velocities suggest the HR 2949 system (younger than 89Myr). In the present
thattheyatleastformedtogetherinthesamestar-forming case all considered merger models provide the right merger
cloud and may therefore also share the same age. In the remnantmassandapparentagedifferencewhenmergingat
following, we assume that both stars are born at the same ages younger than 89Myr.
timeeitherinagravitationally-boundmultiplesystemorin Predicting the right amount of rejuvenation and post-
a star cluster/association. mergermasswithinacertaintimewindowisanecessarybut
Themoreluminousandmoremassivestar,HR2949,is notsufficientconditiontoexplainHR2949byaMSmerger
aHe-weakB3pIVstarwithadetectedsurfacemagneticfield induced by binary evolution. Depending on the initial mass
ofB =2.4+0.3kG(Shultzetal.2015a).Shultzetal.(2015a) ratio and orbital period, Roche-lobe overflow (RLOF) ini-
p −0.2
further report that HR 2949 appears to be about 100Myr tiated during the MS evolution of the more massive donor
younger than the non-magnetic companion, HR 2948. The starmayleadtostablemasstransferandnotamerger.The
ages in Shultz et al. (2015a) have been determined by com- oldest possible merger time to explain the observed rejuve-
paringthepositionsofHR2949andHR2948intheHRdia- nation in case of the considered 3+3, 4+3 and 5+2M(cid:12)
gramtostellarmodelsofEkstr¨ometal.(2012).However,the binariesis89Myr.Thistranslatesintomaximumorbitalpe-
isochronesintheirHRdiagram(Fig.4ofShultzetal.2015a) riods of 0.64, 0.91 and 2.20days, respectively, to explain all
have been mislabelled (and the provided age uncertainties
have been underestimated), requiring a re-determination of
3 TheBonnsaiwebserviceisavailableathttp://www.astro.uni-
thestellarages.Correctlylabellingtheirisochrones,wefind
bonn.de/stars/bonnsai.
that the 1σ error bars of HR 2949 extend from the 10 to 4 Wenotethattheoutermostcornersofthehatchedareaarenot
the 30Myr isochrone and those of HR 2948 from the 60 to within1σoftheobservedagesofHR2949andHR2948andthat
the 100Myr isochrone. ThusHR 2949indeedappears tobe aproper1σcontourhasanellipticalshape.Forclaritywedonot
50–90% younger than HR 2948. showtheproper1σ contourhere.
MNRAS000,1–12(2015)
8 Fabian R.N. Schneider et al.
80 Table3.Stellarparametersofτ Sco.EffectivetemperaturesT ,
eff
70 treal 3 +3 M fl tsourrifaalcerogtraatvioitneasllovgelgo,ciltuimesinvossiintiiesalroegfLro/mL(cid:12)Maonkdiepmroejetcatel.d(e2q0u0a5-,
60 4 +3 M fl M05), Sim´on-D´ıaz et al. (2006, SD06) and Nieva & Przybilla
(2014, NP14). The ages and masses are derived using Bonnsai
Myr 50 5 +2 M fl asypsptleyminginthSeecs.a3m.1e.sTtehllearinmfeorrdeedlsinanitdialprainodrsparsesfoenrtt-hdeayHmRa2ss9e4s9,
∆t/40 M, are the same. The age difference to that of Upper Sco, ∆t,
30 andtheprobabilitypthattheagedifferenceisgreaterthanzero
arecomputedusingthefullposteriordistributionsoftheinferred
20 stellaragesandtakingtheuncertaintyintheinferredageofthe
Upper Sco association into account. The probability p is there-
10
fore a measure of our confidence that the age of τ Sco is indeed
0 younger than that of Upper Sco and also accounts for a certain
0 10 20 30 40 50 60 70 80 90
finite duration of star formation in Upper Sco through the age
t/Myr
uncertainty of Upper Sco inferred by Pecaut et al. (2012). All
errorbarsare1σ uncertainties.
Figure 4. Apparent rejuvenation, ∆t, as a function of the time
when the merger occurred, t. Shown are models for 3+3M(cid:12), M05 SD06 NP14
4+3M(cid:12) and 5+2M(cid:12) mergers. The vertical dashed line is the
age determined for HR 2948, i.e. the presumed real age of the T /K 31900+500 32000±1000 32000±300
eff −800
HR2949andHR2948pair,andtheshadedregionindicatesthe logg/cms−2 4.15+0.09 4.0±0.1 4.30±0.05
−0.14
corresponding1σarea.Thehatchedareashowstheapproximately logL/L(cid:12) 4.39±0.09 4.47±0.13 4.33±0.06
1σregionoftheinferredagediscrepancy,i.e.theapparentrejuve- vsini/kms−1 5(adopted) ≤13 4±1
nation(notethattheproper1σ areahasanellipticalshapeand
isnotshownhereforclarity). M/M(cid:12) 16.0+−00..86 16.8+−11..01 16.0+−00..44
Age/Myr 2.0+1.3 4.1+1.1 0.0+0.6
−1.3 −1.5 −0.0
∆t/Myr 8.8+2.6 7.2+2.6 10.6+2.2
observations with such binaries (cf. Sec. 2 and Eq. 13). Ac- −2.5 −2.6 −2.3
p(∆t>0) >99.9% 99.8% >99.9%
cording to the binary models of Schneider et al. (2015) all
considered binaries indeed merge. The 5 + 2M binaries
(cid:12)
merge because of the small mass ratio of 0.4 and the 3+3
thestellarparametersanddeterminedmasses,ages,agedif-
and4+3M binariesbecausebothstarsaregoingtoover-
(cid:12) ferences to the age of Upper Sco and the probability that
fill their Roche lobes as a result of stellar expansion on a
τ Sco is younger than Upper Sco in Tab. 3. The apparent
nuclear timescale, leading to a contact phase and a subse-
ageofτ Scoisinallcasessignificantlyyoungerthanthatof
quent merger. We therefore conclude that the properties of
the Upper Sco association.
HR 2949 are consistent with being a merger product.
As in Sec. 3.1, we check whether the found age dis-
crepancy is consistent with the rejuvenation predicted in
3.2 τ Sco our merger models (Fig. 5). To match the observed mass of
τ Sco,weconsidermergersof8.5+8.5,10+7,11+6,12+5,
τ Scoisabright,magneticB0.2Vstar,adjacentinthenight 13+4 and 14+3M binaries5. As in Fig. 4, the shaded
(cid:12)
sky to the red supergiant Antares in the zodiacal constella-
region indicates the age range of the comparison clock and
tionofScorpius.ItisapropermotionmemberoftheUpper
hence the real age of τ Sco (the age of the Upper Sco asso-
Scorpius association for which Pecaut, Mamajek & Bubar
ciation) and the hatched areas the approximate 1σ regions
(2012) estimate an age of 11 ±1(stat.)±2(sys)Myr. Do-
oftheagedifferencesforthethreesetsofstellarparameters
nati et al. (2006) find a surface magnetic field strength of
M05, SD06 and NP14.
τ Sco of about 0.5kG and a surprising complex magnetic
Allmodelscanexplaintheobservablesgiventhestellar
field configuration for hot stars. Because τ Sco was consid-
parameters of SD06, i.e. the models predict a rejuvenation
ered a spectral standard for B0 V stars (Morgan & Keenan
larger than the lower bound of the hatched area. Strictly
1973),manyauthorsdeterminedatmosphericandsometimes
speaking,the13+4M mergerspredictarejuvenationthat
(cid:12)
alsofundamentalparametersofτ Sco(e.g.Kilianetal.1991;
is not compatible with the observations within the 1σ un-
Mokiem et al. 2005; Simo´n-D´ıaz et al. 2006; Hubrig et al.
certainties. We therefore conclude that the minimum mass
2008b;Pecautetal.2012;Nieva&Przybilla2014).Nieva&
ratiorequiredtoexplaintheSD06observationsisabout0.3.
Przybilla(2014)notethattheinferredapparentageofτ Sco
In the case of the stellar parameters of NP14, none of
doesnotcoincidewiththatoftheUpperScoassociationand
our models is able to explain the apparent age discrepancy.
suggest that τ Sco may be a merger product.
Anincreaseofatleast25%oftherejuvenationisneededto
Analogously to Sec. 3.1, we use the Bayesian code
explaintheobservedagediscrepancywiththe8.5+8.5M
Bonnsai (Schneider et al. 2014a) to determine the mass (cid:12)
merger. Given that the uncertainties of our predictions for
and age of τ Sco including robust error bars by matching
the rejuvenation of mergers of 10M stars are of the order
(cid:12)
observedeffectivetemperatures,surfacegravities,luminosi-
of5–10%(Tab.2),itseemsdifficulttoexplaintheapparent
tiesandprojectedrotationalvelocitiessimultaneouslytothe
stellar models of Brott et al. (2011a). The choice of priors
is the same as in Sec. 3.1. We use three sets of observables, 5 The merger of a 9+8M(cid:12) binary is not shown because the
thoseofMokiemetal.(2005,M05),Simo´n-D´ıazetal.(2006, predicted rejuvenation is nearly the same as that of the equal-
SD06)andNieva&Przybilla(2014,NP14),andsummarize mass8.5+8.5M(cid:12) mergers.
MNRAS000,1–12(2015)
Origin of magnetic fields in massive stars 9
14 fields and mergers. As shown in this paper, looking for age
treal discrepancies is a promising way to identify rejuvenated bi-
12 nary products among magnetic stars. The best candidates
8.5+8.5 M fl arethosemagneticstarsforwhichthereisarobustcompari-
yr180 NP14 111210+++567 MMM flflfl saonndcbloincka.ryThaendcomhipghareirs-oonrdcelrocmksucltainplbeescyosetevmalss.taPrroclmusistienrgs
/M 13+4 M fl targets are the SB2 binary V1046 Ori (HD 37017) located
∆t 6 M05 14+3 Mfl in the NGC 1977 star cluster and θ1 Ori C in the Trapez-
iumcluster(havingonebinarycompanionandothercluster
4 SD06 members as comparison clocks) and the triple star ζ Ori
(HD 37742) having two gravitationally bound comparison
2 clocks. Further observations and careful modelling are re-
quired to determine the ages of these stars and their com-
0
4 6 8 10 12 14 parison clocks with high confidence.
t/Myr
Figure 5. As Fig. 4 but for τ Sco. The merger models are for
8.5+8.5,10+7M(cid:12),11+6,12+5,13+4and14+3M(cid:12)binaries.
The age of the Upper Sco association is given by the vertical
dashed line (Pecaut et al. 2012). The hatched areas denote the
4.1 Thermal timescale processes
approximate 1σ areas of the apparent age differences of τ Sco
with respect to the ages derived from the stellar parameters of Stellar mergers and common-envelope phases are dynam-
Mokiem et al. (2005, M05), Sim´on-D´ıaz et al. (2006, SD06) and ical and violent phenomena, and the differential rotation
Nieva&Przybilla(2014,NP14).
they induce is thought to be the key ingredient to gener-
ate strong magnetic fields (Tout et al. 2008; Ferrario et al.
young age of τ Sco inferred from the stellar parameters of 2009; Wickramasinghe et al. 2014). Also mass transfer by
NP14 with our models. Roche-lobe overflow (RLOF) leads to differential rotation
The set of stellar parameters of M05 suggests an age butseemsnottoberelatedtostrongmagneticfields.Some
difference that can be explained by the merger models of, Be stars are expected to be formed from RLOF in binaries
e.g.,8.5+8.5,10+7and11+6M binaries.Mergersofbi- and may be ejected into the field by the supernova explo-
(cid:12)
nariesofthesametotalmassbutsmallermassratiospredict sion of the former donor star (e.g. Pols et al. 1991; Tauris
toolittlerejuvenation.FromFig.5wefindthat,inorderto & van den Heuvel 2006). None of the observed Be stars is
explaintheobservedagedifference,the8.5+8.5M merger found to be magnetic (e.g. Wade et al. 2014). Another ex-
(cid:12)
mustoccuratanagebetween7.5and12.5Myr,whichtrans- ample is θ Car, a single-lined spectroscopic binary with an
lates into an orbital period range of 0.89–1.03days. The orbitalperiodofabout2.2daysintheopenclusterIC2602.
age intervals are approximately 7.8–10.8 and 8.2–9.5Myr The visible component is a nitrogen-enriched B star rotat-
and the corresponding orbital period ranges 1.00–1.14 and ingwithaprojectedrotationalvelocityofabout110kms−1
1.07–1.24days for the 10+7 and 11+6M merger mod- that likely accreted mass during a past RLOF phase giving
(cid:12)
els, respectively. Given these orbital periods and primary rise to its blue straggler appearance (Hubrig et al. 2008a).
and secondary masses, all binaries indeed merge during the Nomagneticfieldhasbeendetectedinthispost-RLOFsys-
MS evolution according to the models of Schneider et al. tem (Borra & Landstreet 1979; Hubrig et al. 2008a). Also
(2015) because of contact phases caused by the nuclear ex- mass accretion during star formation may act on a simi-
pansionofthesecondarystars.Aconsequenceofthepoten- lartimescaletothatofRLOFbutclearlynotallstarshave
tial age ranges of the mergers is that all mergers would be strongsurfacemagneticfields.Roche-lobeoverflowandmass
quite recent, i.e. they would have had to happen less than accretion during star formation proceed at most on a ther-
1–2Myr ago. Nieva & Przybilla (2014) note that the spin- mal timescale and it therefore seems that processes acting
down timescale of τ Sco because of magnetic braking ex- onnear-dynamicaltimescalessuchasmergersandcommon-
ceedstheirinferredyoungage(youngerthan2Myr),posing envelope phases are required to generate long-lived, strong
aproblemforourunderstandingoftheslowrotationofthis surface magnetic fields (Langer 2014).
star.Alsoourmergermodelsfacethesameissue,suggesting A star potentially contradicting this is Plaskett’s star,
more efficient spin-down in the past. HD47129.Plaskett’sstariscurrentlythoughttobeamas-
In conclusion, it is plausible to explain the age differ- sive (Mtotsini = 92.7 ± 2.7M(cid:12)) O star binary with an
encesinferredfromthestellarparametersofM05andSD06 orbital period of 14.4days and a mass ratio of M2/M1 =
with our merger models of close binaries (orbital periods of 1.05±0.05 (Linder et al. 2008). The rapidly rotating sec-
about 1day) and mass ratios larger than 0.3–0.5. At the ondarystaristhoughttobemagnetic(Grunhutetal.2013)
same time it seems difficult to explain the large age differ- and it has been suggested that it gained its fast rotation in
ence derived from the stellar parameters of NP14. a past-RLOF phase (Bagnuolo, Gies & Wiggs 1992; Linder
et al. 2008; Grunhut et al. 2013). However, Plaskett’s star
iscurrentlybeingre-investigatedanditsinferredproperties
are expected to change significantly (J. Grunhut, private
4 DISCUSSION
communication). For the time being, we are therefore left
Unambiguous and a larger number of candidates are re- with a puzzling situation that requires further attention to
quired to fully establish the link between strong magnetic reveal the true nature of this interesting binary.
MNRAS000,1–12(2015)
10 Fabian R.N. Schneider et al.
4.2 Observational consequences of the merger surfacenitrogenenrichmentandmagneticstars(butseealso
hypothesis for the origin of magnetic stars Aerts et al. (2014) who find that magnetic fields have no
predictivepowerforsurfacenitrogenenrichmentinGalactic
The merger model for the origin of strong, large-scale mag-
massive stars). Magnetic fields and/or stellar mergers may
netic fields in massive stars makes clear and testable pre-
therefore help to explain the slowly rotating, nitrogen rich
dictions beyond the rejuvenation discussed in the previous
starsintheHunterdiagramofLMCBstarsthataredefying
sections. Requiring mergers to produce magnetic stars im-
thepredictionsofstate-of-the-art,rotatingsingle-starmod-
pliesthatthereshouldbenomagneticstarinclosebinaries.
els (Hunter et al. 2008b; Brott et al. 2011b; Langer 2012).
To be more precise, there may be rare channels to form
First steps into this direction have been taken by Meynet,
short-period binaries with one or two magnetic stars (e.g.
Eggenberger & Maeder (2011) and Potter, Chitre & Tout
from capturing magnetic stars during the star formation
(2012), who suggest that magnetic braking and the associ-
process or later in cluster like environments) but the in-
atedmixingmaycontributetothegroupofslowlyrotating,
cidenceofmagneticstarsinclosebinariesispredictedtobe
nitrogen-enriched stars.
significantly lower than in apparently single stars or wide
Mergersareexpectedtoejectmassbecauseofthehuge
binaries. Wide binaries such as the potential binary system
surplus of angular momentum. Glebbeek et al. (2013) find
HR2949discussedinSec.3.1couldhavebeenbornastriple
that, depending on the mass ratio of the merging binary,
stars where the inner binary merged. Searches for magnetic
about2–9%ofthetotalmassisejected.Inmergersof mas-
OBA stars in binaries indeed show that there is a signifi-
sive stars this may produce ejecta of a few solar masses,
cantdearthofmagneticstarsinclosebinaries(Carrieretal.
implying that some magnetic stars should be surrounded
2002;Alecianetal.2015;Neineretal.2015),supportingthe by massive nebulae6. As suggested by Langer (2012), the
merger hypothesis.
nitrogen-enriched (5 times solar), young (3000yr), massive
Binary population synthesis simulations predict that (2M ), expanding (350kms−1), bipolar nebula RCW 107
(cid:12)
the rate of MS mergers increases with mass (e.g. de Mink surrounding the magnetic O6.5f?p star HD 148937 (Lei-
et al. 2014; Schneider et al. 2015). In their standard model, therer & Chavarria-K. 1987) may well be the ejecta of a
deMinketal.(2014)findamergerfractionof8%inapop- merger. Also the B[e] supergiant in the wide binary system
ulation of stars more luminous than 104L(cid:12) (roughly cor- R4 (Porb ≈ 21yr) in the Small Magellanic Cloud is sug-
responding to OB stars) and 12% in stars more luminous gestedtobeamergerproductandissurroundedbyayoung
than 105L(cid:12) (O stars). However, given that the present-day (1.2×104yr), nitrogen-enriched, bipolar nebula expanding
populationofmagneticmassivestarswouldbeamixtureof with a velocity of about 100kms−1 (Pasquali et al. 2000).
pre-MSandMSmergers,theoveralltrendoftheincidenceof However the large distance to this star makes it hard to es-
magneticMSstarswithmassisnotreadilyobvious.Itmay tablishwhetherthestarismagnetic.Furthermoresomered
be expected that the incidence of magnetic stars is greater luminous novae, e.g. V4332 Sgr, V838 Mon and V1309 Sco,
in MS than in pre-MS stars if magnetic fields observed in may be stellar mergers (Martini et al. 1999; Munari et al.
the pre-MS phase prevail into the MS and if they do not 2002; Tylenda et al. 2011). In particular the eruption of
disappear from the surface of stars, e.g. by decaying. V838 Mon may have involved rather massive B stars (e.g.
The fraction of MS merger products is expected to be Munari et al. 2005; Tylenda, Soker & Szczerba 2005), mak-
highest in a population of massive blue straggler stars. In ingthistargetapromisingcandidateforprobingtheideaof
the models of Schneider et al. (2015) MS mergers make up magnetic-field generation in massive-star mergers.
about 30% of the blue straggler star population in young
(less than about 100Myr), coeval stellar populations (this
does not include blue stragglers formed by dynamical in-
5 CONCLUSIONS
teractions/collisions in dense clusters). So, if MS mergers
indeed contribute to the magnetic massive star population, Merging MS stars leads to rejuvenation because of mixing
we expect a higher magnetic field incidence in massive blue of fresh fuel into the cores of merger products and shorter
straggler stars. lifetimes associated with more massive stars. We find that
Surface nitrogen enrichment may be achieved by vari- the rejuvenation is of the order of the nuclear timescale
ous mechanisms, for example by rotationally and magneti- of stars, implying that merger products can look substan-
cally induced mixing, but it is also a prediction of the sug- tiallyyoungerthantheyreallyare.UsingtheresultsofSPH
gested merger channel. Glebbeek et al. (2013) find that the merger models of Glebbeek et al. (2013), we show that the
surfaces of merger products of binaries more massive than rejuvenation is the stronger the more evolved the progeni-
about 5–10M(cid:12) show significant nitrogen enrichment. Fur- tors,thelowerthemassesofbinariesandthelargerthemass
thermore they find that the surface nitrogen enrichment is ratios.Givenourmodels,itispossibletoidentifyMSmerger
stronger in more massive and more evolved binary merger productsbytheirrejuvenationandtoputconstraintsonthe
progenitors. Pre-MS stars are not hot and dense enough in merger progenitor from the mass, the apparent age and the
theircorestoactivatetheCN(O)cycleandpre-MSmergers real age of the merger product. The latter can be inferred
therefore cannot have nitrogen-enriched surfaces. Hence, if from comparison clocks such as a binary companions and
mixing processes other than merger mixing are negligible, other coeval cluster members.
the ratio of nitrogen-enriched to nitrogen-normal magnetic Merging of MS and pre-MS stars has been suggested
stars may be used to gain insights into the fraction of MS
mergers among magnetic stars. In that regard it is inter-
esting to note that Morel et al. (2006) and Morel, Hubrig 6 Ejected nebulae disperse and are therefore only visible for a
& Briquet (2008) find a correlation between slow rotation, limitedamountoftime(probablylessthanabout105yr).
MNRAS000,1–12(2015)