Asymmetric Wolf-Rayet winds: implications for GRB afterglows

1.2 MB·English

by  J. J. Eldridge

Mon.Not.R.Astron.Soc.000,1–5(2002) Printed5February2008 (MNLATEXstylefilev2.2)
Asymmetric Wolf-Rayet winds: implications for GRB
afterglows.
⋆
J. J. Eldridge .
Astronomy Research Centre, School of Maths & Physics, Queen’sUniversity Belfast,Belfast, BT7 1NN, Northern Ireland, UK
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n
a ABSTRACT
J
RecentobservationsofWolf-Rayet(WR)binariesWR151andWR155inferthattheir
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stellar winds are asymmetric. We show that such asymmetries can alter the stellar-
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wind bubble structure, bringing the wind-termination shock closer to the WR star.

If the wind asymmetry is caused by rotation, the wind density and distance to the
1
v wind-terminationshockarebothdecreasedalongtherotationaxisbyafactorofafew
7 fortheobservedequator-to-polewinddensityratioofWR151.Ifthisasymmetrylasts
0 until core-collapse the time taken to reach the wind-termination shock by supernova
7 ejecta or a gamma-ray burst jet is reduced. This leads to a distorted structure of the
1 supernova ejecta and makes it more likely a constant density environment is inferred
0 from gamma-ray burst afterglow observations.
7
0 Key words: stars: Wolf-Rayet – circumstellar matter – stars: individual: WR151 –
/ stars: winds, outflows – gamma-rays:bursts
h
p
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r
t 1 INTRODUCTION some GRB are found to occur in constant density en-
s
a vironments rather than a freely expanding wind where
: Wolf-Rayet (WR) stars are the most massive stars in the ρ ∝ 1/r2 (Chevalier, Li & Fransson 2004; Panaitescu 2005;
v final stages of evolution and have lost (or in the process of
van Marle et al. 2006). Stellar-wind bubbles do have a re-
i losing the last remnants of) their hydrogen envelopes. Ob-
X gion where the wind density structure is approximately a
servationally they are very luminous, with broad emission
r constantdensity.Theexpandingwindgoesthroughawind-
lines indicating a fast and dense wind. WR stars are the
a termination shock (a hydraulic jump) when the ram pres-
preferred progenitors of type Ibc supernovae (SNe) due to
sureofthefree-winddropsbelowthepressureofthestalled-
the lack of a hydrogen envelope. They have also become
windregion(Castor, McCray & Weaver1975).Thisstalled-
theleading candidates to betheprogenitors of Gamma-ray
wind region has a density profile that is roughly constant.
bursts (GRB). A GRB is thought to occur at core-collapse
Therefore if the free-wind region is small, the GRB jet can
if a black hole forms and thecore material surrounding the
traverse it before the afterglow emission begins and a con-
blackholepossessesenoughangularmomentumtoresidein
stant density environment would be inferred. Simulations
an accretion disk. This disk can then feed material to the
show it is very difficult to shrink the free-wind region to a
blackholeresultinginahighlyrelativisticjet.Iftheprogen-
smallenoughradiusforittoremainunobservedintheGRB
itoriscompactthejetwillemergeatthesurfacetoproduce
afterglow (van Marle et al. 2006; Eldridge et al. 2006). The
thepromptemissionandlatertheafterglow.Thesupporting required radius is roughly 1018cm, a fraction of a parsec
evidenceisthatGRBsoccurinstarformingregionsoftheir
(Chevalier, Li & Fransson2004).Thereareanumberofpos-
hostgalaxies,someGRBshaveassociatedtypeIbcSNeand
sible physical processes that might shrink the free-wind re-
someafterglowlightcurvesareconsistentwiththejetpropa-
gionasoutlinedbyvan Marle et al.(2006)butfactorsmust
gatinginafree-wind environmentexpectedaroundmassive
becombinedtoproduceafree-windregionwiththerequired
stars(forarecentreviewseeWoosley & Bloom(2006)).The
radius.
evidence for stellar progenitors from absorption lines in af-
One possible process that may have an effect is asym-
terglow spectra has weaken due to the recent findings of
metry in WR star winds. The cause of asymmetric winds
Chen et al. (2006).
would typically be the result of stellar rotation or du-
However when the circumburst environment (CBE)
plicity, however, as we discuss below there is some uncer-
density structure is inferred from afterglow observations
tainty in predicting how rotation affects the WR winds.
Wind asymmetry can be estimated by performing po-
larimetry on stars as asymmetry induces strong polari-
⋆ E-mail:[email protected] sation (Brown, McLean & Emslie 1978). Polarimetry sur-
2 J.J. Eldridge
veys of WR stars have been performed and for most the orbit shrank to its current size, the hydrogen envelope
WR stars the polarisation is low with only 20 percent was lost and the helium core became a WN star. For the
of the stars showing any noticeable intrinsic polarisation secondary,weassumethattheprimary’shydrogenenvelope
(Harries, Hillier & Howarth 1998). The observations indi- waslostrapidlyandthesecondaryaccretedverylittlemate-
cateamass-lossasymmetrybetweenthehighest andlowest rial from the primary. Therefore we assume that the initial
wind density to be between a factor of 2 to 3. There is one mass of the secondary was similar to its current mass of
important case of stronger polarisation from the close WR 30M⊙. When we compare the wind strengths we find the
binaryWR151(Villar-Sbaffi et al.2006).Inthissystemthe primarywinddominatessoweignorethesecondary’swinds
light is polarised by 4 percent and modelling indicates that when modelling the wind bubble.
theequator-to-pole density ratio (α) is 5. Our stellar-wind bubblemodel is made using thesame
Villar-Sbaffi et al. (2006) suggest that the difference is codeasdescribedinEldridge et al.(2006).Weusethemass-
due to rotation redistributing the mass-loss from the pole loss rates and wind velocities from the solar metallicity
to the equatorial region as in the wind-compressed zone 60M⊙model with an initial ISM density of n0 = 10cm−3.
model of Ignace, Cassinelli & Bjorkman (1996). If this is We turn on the wind asymmetry when the star has lost its
the case then there is a direct implication for the CBE of hydrogen envelope and assume that M˙(θ) ∝ 1+β(sinθ)2
GRB progenitors which are thought to be rapidly rotat- where beta is β = α−1. We normalise the mass-loss rate
ing WR stars but the effect of stellar rotation on stellar so that thetotal mass-loss from thestar is unchangedfrom
winds is somewhat uncertain. The effect on B star winds the symmetric case. Also we assume that the wind speed
has been well studied. Bjorkman & Cassinelli (1993) and isunchanged.Weselect thestellar-wind bubblemodelwith
Ignace, Cassinelli & Bjorkman (1996) first suggested that an age of 3.8 Myrs as the mass-loss rate and wind velocity
inertial effects due to rotation reduce the polar wind den- are broadly in agreement with the observed parameters of
sity and increase the equatorial wind density. A more rig- WR151.
orous approach from Owocki, Cranmer & Blondin (1994), Figure1showsagreyscaleplotofthewindbubbleden-
Owocki, Cranmer & Gayley (1996) and Petrenz & Puls sity structure with and without the asymmetric mass-loss.
(2000) suggest the converse is true when the distortion of The dense shell in the stalled-wind region is the RSG wind
thestellarsurfacebyrotationandtheradiativedrivingforce that has been swept up by the faster WR wind. The differ-
are taken into account. ence between the symmetric and asymmetric cases is clear
However only Ignace, Cassinelli & Bjorkman (1996) with the distance to the wind termination shock in the po-
have considered WR winds. WR winds are different from lar direction reduced by nearly a factor of two. This is due
winds of other hot stars as they are optically thick and hy- to the reduction in wind density in the polar direction and
drodynamicmodelsofthewindsarequitecomplexandcom- therefore a reduction in the ram pressure compared to the
putationalintensive(Grfener & Hamann2005).Theresults stalled-wind ambient pressure which remains constant.
forBstarwindscannotbedirectlyappliedtoWRwindsbe- Figure 2 compares density profiles through this envi-
cause although they are both line driven the optical thick- ronment. In this plot it is easier to compare the change
ness may cause important differences and possibly result in the position of the wind termination shock in the polar
in the inertial terms dominating and causing the winds to andequatorialdirections.Itisimportanttonotethatwhile
be distorted as predicted by Ignace, Cassinelli & Bjorkman the polar distance is decreased the equatorial distance to
(1996). thewindterminationshockisincreasedbecausetheslightly
In this letter we use the observed asymmetry of higher density of the wind leads to a greater ram pressure.
WR151’swindtoproduceamodelwindbubbleforthissys- Also in these plots the asymmetry we have introduced has
tem and study the effect which the asymmetry has on the onlyjustbeenswitchedonwithinthesimulation andthere-
bubble structure. However we do not consider what might fore thestalled wind region is similar between the two sim-
causetheasymmetry.Thisavoidstheuncertaintyinthedif- ulations.
ferent models for wind distortion byrotation. Wethen per- If we continue the simulations for another 0.34 Myrs
form a small parameter survey varying the initial interstel- up until the end of the stellar models (about a year before
lar medium (ISM) density and the size of the wind-density core-collapse) and we assume the asymmetry remains the
asymmetry and estimate the time it would take a GRB jet distortionincreasesasthestalled-windregionisalsoaltered.
to reach thestalled-wind region. Thisisimportantasthesupernovaorgamma-rayburstthat
mayoccuratthattimewillpropagatethroughthisenviron-
ment. The resulting wind-bubble structures are shown in
Figures3and4.Bothwithandwithouttheasymmetrythe
2 THE CURRENT AND FUTURE STELLAR
stalled-windregionhassomedenserswirls.Thesearedueto
WIND BUBBLE OF WR151.
instabilitiesinthewind(Garcia-Segura, Langer & Mac-Low
Firsttomodelthestellar-windbubblewemustselectastel- 1996)thathavegrowntoproducegreatdensityvariationsas
larmodeltouse.InWR151thecurrentmassoftheWRstar foundbyEldridge et al.(2006).Wefindwiththeasymmet-
is estimated to be 23M⊙. To obtain the correct mass from ric wind acting for a long time the magnitude and number
oursinglestarmodelweadoptasolarmetallicity(Z =0.02) of these swirls are greater. Overall we find the distance to
starwithaninitialmassof60M⊙ thathasalongWNphase. the wind-termination shock, RSW is decreased in the polar
WethereforeassumethatWR151wasinitiallyawidebinary direction by a factor of approximately 3.
where the 60M⊙ star became a red supergiant, filling its If a SN was to occur in such a medium the ejecta
RocheLobeandgrowingtoaradiusgreaterthanthebinary would reach the wind-termination shock in the polar direc-
orbitsothatcommonenvelopeevolutionoccurs.Duringthis tion sooner than along the equatorial region and therefore
Asymmetric Wolf-Rayet winds: implications for GRB afterglows. 3
Figure 1.Greyscaleplotsofthestellar-windbubblestructurewithin12.5parsecsoftheWRstar.TheWRstarhadaninitialmassof
60M⊙ and is pictured here at an age of 3.8Myrs, the initial ISM density was 10cm−3. The left panel shows the case for a spherically
symmetric windwhile the right panel shows the case when the equator-to-pole wind density ratio, α=5. The polar direction is along
thex-axisinbothfigures.
deceleratemorequicklybyaccretingmorematerial.TheSN
remnant would be distorted to an oblate shape rather than
beingspherically symmetric.IfaGRBwastooccurinsuch
astructuretheafterglowjetwouldreachthestalled-windre-
gioninashortertimeandthereforetheafterglowwouldap-
pear to be traversing a constant density environment. This
is in comparison to the symmetric wind bubble case where
a freely expandingwind would be inferred.
There is another reason why the RSW is more un-
even in Figure 3. Eldridge et al. (2006) found that the po-
sition of the wind-termination shock is not alway directly
related to the initial ISM density as the analytic relation
of Castor, McCray & Weaver (1975). This is because if the
wind speed and wind density of the source star are vary-
ing on the same timescale as the time it takes for the wind
toreachthewindterminationshockthentheboundarywill
move.Asthattimenowvariesbetweenthepoleandequator
so too does themagnitude of this timescale effect.
3 A PARAMETER SEARCH.
Figure2.DensityprofilesthroughthesimulationsshowninFig-
We have performed a parameter search varying the wind ure 1. The solid and dotted lines are through the spherically-
symmetric wind while the dashed and dash-dotted lines are
asymmetry, α, and the initial ISM density, n0, around the
through the asymmetric simulation along the pole and equator
star to investigate the resulting change in the polar dis-
directionsrespectively.
tance to the wind-termination shock. In table 1 we show
the distance in parsecs to the wind termination shock and
thewinddensityalongthepolardirection.Clearlytheeffect
ofincreasingthewindasymmetryisthatbothRSW andA∗ similar timescale the wind-termination shock will respond
decrease.TheeffectofincreasingtheinitialISMdensityde- to any change on a different timescales.
creases RSW, as expected. There is one exception when at Withthesedistancesandwinddensitiesitispossibleto
the highest ISM density, RSW increases. This is due to the estimatehowlongitwouldtakeforaGRBjettotraversethe
wind-terminating shock becoming highly distorted so the distancetothebeginningofthestalled-windatRSW.Rather
timeforthewindtotravelfromthestartotheshockvaries than perform adetailed afterglow calculation we usea sim-
from pole to equator. Therefore if the wind is varying on a plemodelofisotropicrelativisticejectawithEiso=1053ergs
4 J.J. Eldridge
Figure 3.Similarto Figure1 but 340,000 years later, a few years beforecore-collapse. The leftpanel shows the case for aspherically
symmetricwindwhiletherightpanel shows thecasewhenthe equator-to-pole winddensityratiois5. Thepolar directionisalongthe
x-axisinbothfigures.
Table 1 show that the asymmetries greatly reduce the
time for thejet to reach RSW. However a high density ISM
is still required to reduce the size of the wind-bubbles. The
timeofaroundanhourisshortenoughthattheearlyX-ray
afterglow of GRBs may show some sign of occurring in a
free-wind region while later emission may show a constant
density profile. This agrees with Panaitescu et al. (2006)
where for the first few hours of a sample of GRB after-
glows a free-wind CBE is preferred while after a few days
a constant density CBE become more common (Panaitescu
2005). Therefore we may see the transition from free-wind
tostalled-windregionsinsomeGRBafterglowswithoutany
bump in the lightcurve when the jet encounters the wind
termination shock.Itisimportanttonotethatourtimees-
timate is approximate, if for example the Lorentz factor or
thekineticenergyoftheejecta ishigherthenthetimescan
be reduced further. Although our results demonstrate that
evenmoderateasymmetriesinthewindreducethetimesby
an order of magnitude.
4 DISCUSSION AND CONCLUSIONS.
Figure4.DensityprofilesthroughthesimulationsshowninFig-
ure 3. The solid and dotted lines are through the spherically- While the asymmetry in WR winds of WR151 and other
symmetric wind simulation while the dashed and dash-dotted WR stars could be dueto rotation, duplicity or some other
lines are through the asymmetric simulation along the pole and
factor, it is the asymmetry itself that has a large effect
equator directionsrespectively.
on the stellar-wind bubble structure. It may also affect
the evolution of the star since angular momentum loss will
depend on how much mass is lost at equatorial latitudes
andΓinitial=100.Astheejectaexpandsitsweepsupmate- (Meynet & Maeder 2007). It will effect the evolution of a
rial decreasing it’s velocity.Therefore shorterdistances and SNorGRBifitoccurswithinsuchadistortedwind-bubble.
lower wind-densities both shorten the time for the jet to SphericallysymmetricSNejectawillbeforcedintoanoblate
reach RSW. We note that we calculate the observer time form. For a GRB if we assume that the observed asymme-
that includes the effect of time dilation by viewing along try is caused by rotation and that the direction of the low-
the expanding ejecta direction of motion. However it does est wind density is the rotation axis then the GRB jet will
notincludecosmological time-dilation thereforethesetimes propagateinthatdirection.Thereforethemoreasymmetric
are a lower limit and will belonger for higher redshifts. the WR wind the more quickly it will encounter the wind-
Asymmetric Wolf-Rayet winds: implications for GRB afterglows. 5
InconclusionsomeWRstarsareobservedtohaveasym-
Table 1. Position of the wind-termination shock from the WR
stars with different initial ISM densities and different equator- metric winds and this has a large effect on the position of
to-pole density ratios during the WR phase. Also listed is the thewind-terminationshock.Thereductionofthewindden-
winddensityinthepolardirectionforthedifferentdensityratios, sityinonedirectioncanleadtothewind-terminationshock
A∗ =(M˙/10−5M⊙yr−1)/(vwind/1000kms−1). Also show is the movingcloser tothestar. IfaGRBjet was totravelinthis
timetakenforejectatoreachthewind-terminationshockRSWfor direction then with the lower wind density and shorter dis-
asimpleisotropicmodelwithEiso=1053ergsandΓinitial=100. tance, a constant density CBE is more likely to be inferred
from theobservations of the afterglow.
n0/cm−3= 103 102 101
RSW tSW RSW tSW RSW tSW
α A∗ /pc /hrs /pc /hrs /pc /hrs ACKNOWLEDGEMENTS
1 0.66 0.76 24.4 2.67 794 5.25 5831 This work, conducted as part of the award “Understand-
2 0.33 0.47 7.2 2.02 356 3.80 2227 ing the lives of massive stars from birth to supernovae”
3 0.22 0.37 4.1 1.89 295 3.31 1485 made under European Science Foundation EURYI Awards
5 0.13 0.31 2.7 1.41 130 2.18 443
scheme. JJE would also like to thankAllard-Jan van Marle
7 0.09 0.25 1.6 1.08 62.2 2.18 443
andNorbertLangerforusefuldiscussion,SeppoMattilafor
10 0.07 0.31 2.7 1.08 62.2 1.70 219
thecarefulproofreadingthisletterandtherefereefortheir
15 0.04 0.22 1.3 0.70 19.7 1.05 57.6
comments that haveimproved this letter.
20 0.03 0.20 1.1 0.66 16.9 1.05 57.6
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