Table Of ContentAstronomy & Astrophysics manuscript no.
(will be inserted by hand later)
In Hot Pursuit of the Hidden Companion of η Carinae: An X-ray
Determination of the Wind Parameters
J.M. Pittard1 and M.F. Corcoran2,3
2
0
0 1 Department of Physics& Astronomy,The University of Leeds, Woodhouse Lane, Leeds, LS29JT, UK
2 2 Universities Space Research Association, 7501 Forbes Blvd,Ste 206, Seabrook, MD 20706, USA
n 3 Laboratory for High Energy Astrophysics, Goddard Space Flight Center, Greenbelt, MD 20771, USA
a
J Received ¡date¿ / Accepted ¡date¿
8
Abstract. We present X-ray spectral fits to a recently obtained Chandra grating spectrum of η Carinae, one
1
of the most massive and powerful stars in the Galaxy and which is strongly suspected to be a colliding wind
v
binary system.Hydrodynamicmodels of colliding windsare usedto generatesyntheticX-rayspectra for arange
5
ofmass-lossratesandwindvelocities.TheyarethenfittedagainstnewlyacquiredChandragratingdata.Wefind
0
thatduetothelowvelocityoftheprimarywind(≈500kms−1),mostoftheobservedX-rayemission appearsto
1
1 arisefromtheshockedwindofthecompanionstar.Weusethedurationofthelightcurveminimumtofixthewind
0 momentumratioatη=0.2.Wearethenabletoobtainagoodfittothedatabyvaryingthemass-lossrateofthe
2 companion and the terminal velocity of its wind. We find that M˙ 2 ≈ 10−5 M⊙yr−1 and v∞2 ≈ 3000 kms−1.
0 Withobservationallydeterminedvaluesof≈500−700 kms−1 forthevelocityoftheprimarywind,ourfitimplies
h/ a primary mass-loss rate of M˙ 1 ≈2.5×10−4 M⊙yr−1. This value is smaller than commonly inferred, although
we note that a lower mass-loss rate can reduce some of the problems noted by Hillier et al.(2001) when a value
p
- as high as 10−3 M⊙yr−1 is used. The wind parameters of the companion are indicative of a massive star which
o mayormaynotbeevolved.Thelinestrengthsappeartoshowslightlysub-solarabundances,althoughthisneeds
r furtherconfirmation.Basedontheover-estimationoftheX-raylinestrengthsinourmodel,andre-interpretation
t
s of theHST/FOS results, it appears that thehomunculusnebula was produced bytheprimary star.
a
:
v Key words.stars:binaries:general –stars:early-type–stars:individual:η Carinae–stars:Wolf-Rayet–X-rays:stars
i
X
r
a 1. Introduction 5.5 yr period in the variability of the He I 10830 ˚A line.
Furtherphotometricandradialvelocitystudies(Damineli
The superluminous star η Carinae (HD 93308, HR 4210)
et al.1997, 2000), X-ray observations (Tsuboi et al.1997;
continues to be extensively studied over a host of differ-
Corcoran et al.2000 and references therein), and radio
ent wavelengths, yet remains intriguingly enigmatic. It is
data(Duncan etal.1995,1999)havesupportedthe 5.5yr
amongstthemostunstablestarsknown.Inthe1840s,and
period and the binary hypothesis. However, the ground
againinthe1890s,itunderwentaseriesofgiantoutbursts
based radial velocity curve was not confirmed by higher
(e.g. Viotti 1995) which ejected large masses of material
resolution spectra with STIS, indicating that at least the
into the surrounding medium. HST images of the result-
time of periastron passage is not well defined by the UV
ing bipolar nebula (e.g. Morse et al.1998), known as the
andopticalspectra(Corcoranetal.2001a).Acomparison
Homunculus, show it to be amongstthe most spectacular
oftheabundancesfromthecentralobject(s)andthecom-
in our Galaxy. The central object is now largely obscured
position of the Homunculus nebula has also determined
by dust, and the cause of the outbursts and the nature of
thatthere areatleasttwostarsinthissystem(Lamerset
the underlying star (at outburst and today) remain spec-
al.1998).
ulative. The source continues to show brightness fluctua-
tionsandemission-linevariations.Furtherdetailsofη Car η Car is often classified as a luminous blue variable
can be found in the review by Davidson & Humphreys (LBV). These are massive stars believed to be in a rapid
(1997). and unstable evolutionary phase in which many solar
In recent years evidence for binarity in this system massesofmaterialareejectedintotheinterstellarmedium
has been accumulating. Damineli (1996) first noted a over a relatively short period of time ( 104 yr). LBVs
≈
are regarded as a key phase in the evolution of massive
Send offprint requests to: J. M. Pittard, e-mail: stars, during which a transition into a Wolf-Rayet star
[email protected] occurs (e.g. Langer et al.1994; Maeder & Meynet 2001).
2 Pittard & Corcoran: In Hot Pursuit of theHidden Companion of η Carinae
Duetotheirrarityandcomplexnaturehowever,weunfor- Small scale quasi-periodic outbursts in the X-ray
tunately still have no definitive theory for mass-loss dur- lightcurve have also been detected (Corcoranet al.1997).
ingtheLBVstage.Themajorityofproposedmechanisms Estimates of changes in the timescale between succes-
to drive LBV instabilities, the onset of higher mass-loss sive flares as a function of phase were made by Davidson
rates and underlying eruptions, are concerned with the et al.(1998) for a variety of assumed orbital elements.
importance of radiation pressure within the outer enve- RXTE X-ray observations obtained after the X-ray min-
lope of the LBV, and for example utilize pulsational in- imum seem to show a lengthening of the flare timescale
stabilities (e.g. Guzik et al.1999), dynamical instabilities (Ishibashietal.1999),whichindirectlysupportthebinary
(e.g. Stothers & Chin 1993), or presuppose Eddington- model. The latest published X-ray observation of η Car
like instabilities. The latter could arise from an enhance- is of a high resolution grating spectrum taken with
ment in opacity as the star moves to lower temperatures the Chandra X-ray observatory (Corcoran et al.2001b).
(e.g. Lamers 1997), or from the influence of rotation (e.g. Preliminary analysis has revealed the presence of strong
Langer1997;Zethsonetal.1999).Alternatively,thepossi- forbidden line emission, which suggests that the density
bility thatbinarityplaysafundamentalroleinexplaining of the hot gas, ne < 1014cm−3. This can be contrasted
observed LBV outburst properties has also been consid- withthenewlypublishedX-raygratingspectraofthesin-
ered (Gallagher 1989), though most LBVs are not known gle stars θ1 Ori C (Schulz et al.2000), ζ Ori (Waldron &
binaries. Clearly, determining the wind and stellar prop- Cassinelli2001),andζ Pup(Kahnetal.2001),allofwhich
erties of LBV stars is paramount (see, for example, the have weak forbidden lines (indicative of either high den-
discussions in Leitherer et al.1994 and Nota et al.1996). sities or high UV flux near the line forming region). This
An importantquestion is the degree to whichbinarity lends further support to a wind-wind collision model, al-
influences the properties of LBVs (i.e. do LBVs in bina- though it is possible that some of the forbidden emission
ries evolve differently than single LBVs?). So while the may be related to the surrounding nebula.
presence of a companion can be exploited to help mea-
IfηCarisinfactabinarysystem,theorbitalelements
sure the mass of such stars, we must bear in mind that
and stellar parameters are not yet tightly constrained
binary LBVs and single LBVs may be quite distinct ob-
by current observations. Ground-based observations (for
jects.Therefore,inordertouseη Cartounderstandsome
which good phase coverage exist) are hampered by poor
ofthedefiningLBVcharacteristicssuchastheirextremely
spatial resolution and thus suffer contamination from
highmass-lossrates,wefirstneedtodeterminebeyondall
strong nebular emission. High-spatial resolution spectra
doubtthatηCarisinfactabinary,andthentodetermine
have been obtained by STIS but phase coverage is cur-
the influence of the companion on the system.
rently very limited. HST STIS observations at two differ-
Investigations over the last few years have already
entphasesofthe5.52yearcycle(Davidsonetal.2000)did
helped to form a basic picture of η Car. The orbital
not confirm the predicted variationsin the radial velocity
parameters, although uncertain, indicate the presence of
of the emission lines based on the ground-based radial
anearly-typecompanionstar,whichwillalsohaveapow-
velocity curve (Damineli et al.2000). If η Car is a binary,
erfulstellarwind.Insuchbinaries,aregionofhotshocked
itis vitally importantto determine the stellarparameters
gaswithtemperatures inexcessof10 millionK is created
of the companion so that the effect of the companion on
where the stellar winds collide (Prilutskii & Usov 1976;
observationscanbeunderstoodandthecorrectstellarpa-
Cherepashchuk 1976). The wind-wind collision (WWC)
rameters of the primary can be derived.
region is expected to contribute to the observed emission
from this system, particularly at X-ray and radio wave-
lengths. Previous X-ray observations revealed extended 1.1. X-ray Emission from Colliding Winds
softemissionfromthenebulaandstrong,hard,highlyab-
sorbed,andvariableemissionclosesttothestar(Corcoran The wealth of information contained in X-ray spectra
et al.1995; Weis et al.2001), in contrast to the emis- of colliding wind binaries (e.g. the density, temperature,
sion characteristics from single stars, which are typically velocity, abundance, and distribution of the shocked gas
softer, much less absorbed, substantially weaker and rel- in the wind collision region) has been a strong motivat-
atively constant in intensity. Since 1996 Feb η Car has ing force for observers and theorists alike in this field.
been continuously monitored by RXTE in the 2–10 keV Since the hot plasma in most colliding wind shocks is op-
band (e.g. Corcoran et al.2001a). The lightcurve (Fig. 1) tically thin and collisionally ionized, and is generally as-
contains remarkable detail showing a slow, almost linear, sumed to be in collisional equilibrium, Raymond-Smith
rise to maximum over a period of 1 yr, followed by a (Raymond & Smith 1977) or MEKAL (Mewe et al.1995)
≈
rapid drop to approximately 1/6 of the peak intensity for spectral models are normally fitted to such data (e.g.
3months,analmostassharprisetoapproximately1/2 Zhekov & Skinner 2000; Rauw et al.2000; Corcoran et
≈
of the peak intensity level, and then almost constant in- al.2001b).However,the multi-temperature,multi-density
tensity for 3/4 of the proposed 5.5 yr orbital period. nature of the WWC regionmeans that at best simple fits
≈
The drop to minimum was successfully predicted from withone-ortwo-temperatureRaymond-Smithmodelscan
numerical models of the WWC (Pittard et al.1998) be- only characterize the broad properties of the emission. In
fore being actually observed. this wayonecanestimatean‘average’temperatureofthe
Pittard & Corcoran: In Hot Pursuit of theHidden Companion of η Carinae 3
30
PCU2 L1 net counts
Colliding wind lightcurve (Pittard et al. 1998)
25
-1s
s 20
t
n
u
o
c
1
L 15
2
U
C
P
t
e
N 10
5
1.0 1.5 2.0 2.5
Orbital Phase
Fig.1.LightcurveofηCarobservedwiththeRXTEsatelliteandphasedtothe5.5yrorbitalperiod.Plottedarecounts
detected in layer 1 of the second proportional counter unit (PCU2) and a predicted lightcurve (Pittard et al.1998)
fromanumericalmodelofthewind-windcollision.Thetwoagreewell,particularlythedurationoftheminimum.The
rise from minimum is not in good agreement, but this is thought to be due to the limitations of modelling the wind
collisionin2D.Therapidchangeinpositionangleofthe starsthroughperiastronpassageskewsthe shockconewhich
causes the line of sight in fully 3D models to remain in the denser wind of the primary until later phases, increasing
the absorption at these times (Pittard 2000)
.
shocked gas, and an ‘average’ absorbing column, but lit- duction in the distance to this star from Hipparcos data1.
tle is learned of the underlying stellar wind parameters. We note that this method can also provide insights into
Atworsttheapplicationofone-ortwo-temperaturemod- thevaluesofparameterswhichareotherwisevirtuallyim-
els to what is inherently multi-temperature emission can possibletoestimate,suchasthemass-lossrateofthecom-
lead to spurious values of some of the fit parameters, e.g. panion, M˙ 2, or the characteristic ratio of the pre-shock
abundances (cf. Strickland & Stevens 1998). electron and ion temperature (Zhekov & Skinner 2000).
The quality of recently available X-ray grating spectra
now gives us access to important X-ray emission line di-
agnostics which should severely constrain models of the
Complexnumericalhydrodynamicalmodelshaveoften X-ray emissiondistribution. This means that stellar wind
been applied to gain insight into colliding wind systems parameters can in principle be reliably estimated from
(e.g. Stevens et al.1992, Pittard et al.1998). However, analysis of X-ray grating spectra of colliding wind bina-
while undoubtedly useful, their interpretation can be ries.
difficult, and to date there have been only two published In addition to testing the binary hypothesis, the
paperswhereobservedspectraaredirectly fittedwithsyn- ChandragratingspectrumofηCar(Corcoranetal.2001b)
thetic spectra from such models. In the pioneering work provides the ideal opportunity to test the method de-
ofStevens et al.(1996),medium resolutionASCA spectra veloped by Stevens et al.(1996) against a spectrum of
oftheWolf-Rayetbinaryγ2 Velorumwerefittedagainsta much higher spectral resolution, and to pin down impor-
grid ofsynthetic spectra.Inthis fashionthey wereableto tant physical parameters of the system. In this paper we
obtain direct estimates of the mass-loss rates and termi- therefore fit the X-ray grating spectrum using a grid of
nal velocities of the individual stellar winds. As mass-loss colliding wind emission models to i) test the binary hy-
ratesobtainedfrommeasuresofradiofluxorspectralline pothesis, and ii) to attempt to obtain accurate estimates
fits depend on a variety of untested assumptions, the im- of the wind parameters of each star. The fact that we
portance of a new independent method to complement are able to obtain good fits, with sensible model param-
estimates from free-free radio or sub-mm observations, or eters, gives us further confidence in the binary hypoth-
from Hα or UV spectral line fitting, cannot be stressed esis. We also find that unlike the UV and optical work
enough. Rates derived by Stevens et al.(1996) with this
new method were significantly lower than the commonly 1 The thermal radio flux, S ∝ M˙ 4/3D−2 (where D is the
accepted estimates for γ2 Velorum based on radio obser- ν
distance to the source) whereas the X-ray flux from an adia-
vations, but an indication of the future benefits of this baticwindcollisionisF ∝M˙ 2D−2.ThereforeM˙ ∝D3/2
ν radio
methodwasrealizedwhenbothsetsofestimateswerelater whereas M˙ xray ∝ D. If D is revised downwards, M˙ radio de-
brought into agreement following a surprisingly large re- creases faster than M˙ xray.
4 Pittard & Corcoran: In Hot Pursuit of theHidden Companion of η Carinae
where fits to the primary are made difficult by signifi- al.(2001a)is 4 1014cm.Thusthereiseither100or150
≈ ×
cant contamination from the companion star, instead the grid cells between the stars. The large separation means
X-ray emission arises from the shocked wind of the com- thatthewindsarelikelytocollideatveryneartheirtermi-
panionandsuffersessentiallyzerocontaminationfromthe nal velocities. We therefore assume that we can treat the
wind of the primary. Therefore the X-ray data uniquely windsasbeinginstantaneouslyacceleratedtotheirtermi-
samples parameters of the companion, in contrast to the nalvelocities,anddonotconsideranyradiativedrivingef-
optical analysis which probes the nature of the primary. fects.Incomparisonwiththeworkonγ2Velorum(Stevens
In this sense our analysis is entirely complementary to et al.1996), assuming terminal velocity winds and negli-
the complex fits to the UV and optical HST spectrum gible binary rotation is more valid for η Car. We further
of η Car by Hillier et al.(2001). Our analysis also pro- assume that the winds are spherically symmetric.
vides us with a new estimate of the mass-loss rate of the
To compute a grid of synthetic spectra we initially
primary star. For details of the Chandra observation and varied four parameters (M˙ 1, M˙ 2, v∞1, v∞2) in the
an initial analysis of the data the reader is referred to
hydrodynamic models. During our investigation we also
Corcoranetal.(2001b).Hereweonlynotethatthereisno
included the separation of the stars, D, as an additional
significant contamination of the dispersed spectrum from
free parameter. From fits at this point it was found that
any spatially resolved emission (i.e. in the Homunculus). D 4 1014 cm with a small uncertainty, in good agree-
In Section 2 we discuss the creation and variation of the ≈ ×
ment with the expected value from our current under-
modelspectralgrid;inSection3wedescribethefitresults;
standing of the orbit. We therefore fixed it at this value
and in Section 4 we summarize and conclude.
for the rest of our analysis. However,we found that there
were large uncertainties on the values of M˙ 1 and v∞1.
2. The Synthetic Colliding Wind Spectra With the benefit of hind-sight this is not too surpris-
ing given the known slow speed of the primary wind
TinheSemcteitohnod1aipspalisedfoblylowStse.vWenes efitrsatl.c(a1l9c9u6l)ataesddaiscwushsoelde (v∞1 ≈500−700 kms−1),whichmeansthattheshocked
primary wind is not a strong source of X-ray emission at
hostofhydrodynamicalmodelswithdifferentstellarwind
hard energies. Therefore for our final grid we fixed the
parameters. We then generated a synthetic X-ray spec- terminal velocity of the primary star at 500 kms−1 and
trumfromeachmodel.Finally,wefitthegridofsynthetic adjusted M˙ 1 to obtain a desired value for the wind mo-
stapiencetdrafotroetahcehpacatruaamledteartao.fBinetsetr-efistt (vea.lgu.eMs˙a1r,eMt˙h2e,nv∞ob1-, mv∞en2tausmfrereatpioa,raηm=eteMr˙s.2 v∞2/(M˙ 1 v∞1), with M˙ 2 and
v∞2 etc. ). Specific points in relation to this method are Therangeofthe freeparametersusedinourfinalgrid
highlighted below.
is given in Table 1. To restrict the number of models to a
manageablenumberthe parameterstepsarefairlycoarse.
2.1. Hydrodynamical Models of η Carinae In future papers we will use a much finer grid. The range
in the value of η corresponds to either the wind of the
The colliding wind models were calculated using VH-1
primary (η = 0.1) or the secondary (η = 5) dominating,
(Blondin et al.1990), a Lagrangian-remap version of the
or the winds having equal momentum fluxes (η =1). The
third-order accurate Piecewise Parabolic Method (PPM;
distance of the stagnation point from the centre of the
Colella & Woodward 1984). The stellar winds are mod-
primary star is given by
elled as ideal gases with adiabatic index γ = 5/3.
Radiative cooling is included via the method of opera-
torsplitting,andiscalculatedasanopticallythin plasma
1
in ionization equilibrium. The cooling curve for the tem- r = D, (1)
perature range 4.0 < log T < 9.0 was generated using 1+√η
the Raymond-Smith plasma code. Despite some evidence
to the contrary (see Corcoran et al.2001b), we have used
and ranges from 1.2 1014 cm to 3.0 1014 cm. In the
solarabundances throughoutthis work,since it keeps the
× ×
most extreme cases, this is still of order ten to a hundred
problem as simple as possible in this first investigation.
timestheradiusofthestars,andjustifiesouruseoftermi-
We aim to model non-solar abundances in a later paper.
nalvelocitywinds.Thekineticpoweroftheprimarywind
The simulations were calculated assuming cylindri-
rangedfrom4.7 1034 ergs−1 to 7.9 1038 ergs−1, and
cal symmetry of the wind collision zone - orbital effects
are negligible at the phase of the Chandra observation from 7.1 1035 ×ergs−1 to 7.9 1038×ergs−1 for the sec-
× ×
ondary wind. The combined kinetic power of the winds
(φ =0.60). Grid sizes spanned a range from 300x 300 to
ranges from 7.6 1035 ergs−1 to 1.6 1039 ergs−1. The
550x450 cells. Each grid cell was square and of constant
× ×
half-opening angle of the contact discontinuity measured
size on an individual grid. The linear dimension of each
cellwaseither2.67 1012or4.0 1012cm.Themaximum from the line between the secondary star and the shock
distance from the ×axis of symm×etry was 1.2 1015 cm apex ranges from 50 120◦ (cf. Eichler & Usov 1993).
≈ −
×
in all cases. At the phase of the observation, the orbital The effect of radiative cooling can be quantified by
separationofthe starsusingtheephemerisofCorcoranet the parameter χ, the ratio of the cooling timescale to the
Pittard & Corcoran: In Hot Pursuit of theHidden Companion of η Carinae 5
Table 1. Our final grid of stellar wind parameters for expected, however,since the dynamicaltimescale is much
the hydrodynamical models used to generate synthetic longer.Twoexamplesof‘time-averaged’syntheticspectra
spectra. The models fix the terminal velocity of the pri- are shown in Fig. 2, next to density plots of the corre-
mary wind at 500 kms−1 and the stellar separation at sponding hydrodynamic calculation.
D =4.0 1014 cm.Themass-lossrateoftheprimarystar
is given ×by M˙ 1 =M˙ 2 v∞2/(500η). rangTehe1.s2y6n–t1h0etkiecVsp(e1c0t–ra1.w26er˚Ae craelscpuelacttievdeloyv)e,ratnhdehenaevregya
resolution of 0.005 ˚A. The actual grating spectrum shows
Parameter 1 2 3
significant absorption below 1.5 keV and contains es-
η 0.1 1.0 5.0
M˙ 2(M⊙yr−1) 10−6 10−5 10−4 sentially no useful information below our lower limit of
v∞2 (kms−1) 1500 3000 5000 1.26 keV.The spectral resolutionof our synthetic spectra
isapproximatelytwiceashighasthegratingdatathatwe
model.UseoftheRaymond-Smithplasmacodeimplicitly
assumesthattheplasmaisinthermalequilibrium.Thisis
dynamical timescale of the system. For shocked gas near
generally true for colliding wind binary systems (see Luo
the localminimum in the coolingcurve atT 2 107 K,
≈ × et al.1990) and is a good assumption for η Car.
v84d12
χ , (2)
≈ M˙ −7 2.2. Variations with η, M˙ 2, and v∞
2
where v8 is the wind velocity in units of 1000 kms−1,
d12 is the distance to the contact discontinuity in units In Fig. 3 and the following subsections we reveal how the
of 1012 cm, and M˙ −7 is the mass-loss rate in units of shape andnormalizationofthe calculatedspectradepend
10−7 M⊙yr−1 (cf. Stevens et al.1992). This equation is on the various free parameters of the grid.
valid for post-shock temperatures in the range 107 <T <
108.2 K (680/√µ < v < 2700/√µ kms−1 where µ∼mH ∼is
the averagepartic∼le ma∼ss in grammes).For material with 2.2.1. Variation with η
solarabundance(µ=0.6),this correspondsto 0.9<v8 <
3.5. For winds with slower velocities, the shocked g∼as lie∼s Due tothelowpreshockvelocityoftheprimarywind,the
onthenegativeslopeofthe coolingcurve.Inthiscasethe X-ray emission from the WWC is almost entirely from
dependence of χ on the velocity of the wind is steeper: theshockedsecondarywind.Agreaterfractionofthesec-
ondary wind passes into the wind collision zone as the
v85.2d12 relative momentum of the primary wind is increased, so
χ . (3)
≈ M˙ −7 we expectthe luminosityto increaseasη decreases,asin-
deed the top panel of Fig. 3 shows. An important point,
Inourgridofsimulations,theshockedwindoftheprimary
however,is that the shape of the spectra do not seem de-
star is almost always strongly radiative (χ1,min << 1.0) pendent on the value of η, contrary to our expectations
whilethesecondary’sisneverstronglyradiative(χ2,min = before starting this study.
2.0). However, for some choices of the 3 parameters in
Table1,theprimary’swindcanapproachthepointwhere
it starts to become adiabatic (χ1,max ≈1.0). In Fig. 2 we 2.2.2. Variation with M˙ 2
showtwoexamplesofthehydrodynamiccalculationsused
tocalculatesyntheticspectra.Duetothedifferenceinter-
As we increase the mass-lossrate of the secondary star in
minal velocity of the two winds, the velocity shear at the
our models, the kinetic power and the density of its wind
wind interface always generates Kelvin-Helmholtz insta-
alsoincrease.Therefore,foragivenwindmomentumratio,
bilities in our models. The rapid cooling of at least one
the rate of conversionof kinetic energy to thermal energy
of the two winds means that thin-shell instabilities also
increases, as does the density of the postshock gas. Thus
always occur in our models. The colliding winds region is
there is more available energy to radiate and a greater
most unstable when both shocked winds rapidly cool (cf.
efficiency of radiation. Hence we should expect the X-ray
Stevens et al.1992). luminosity to scale strongly with increasing M˙ 2. This is
The spectrum from each hydrodynamic model was
indeedwhatweseeinthemiddlepanelofFig.3,wherean
averaged over 3 ‘snapshots’ each spaced by about 70 d. orderofmagnitudeincreaseinM˙ 2 leadstoanalmosttwo
This is of order the wind dynamical timescale and serves
order of magnitude increase in X-ray luminosity, indicat-
to approximate a time-averaged spectrum. It is particu-
ing thatthe calculationsinthis panelareinthe adiabatic
larly important to adopt this approach for models where regime(L M˙ 2;seeStevensetal.1992).However,there
x
the wind collision region is very unstable since in these ∝
isnoevidenceforasofteningofthespectrumwithincreas-
cases the flux can vary by greater than ±50% from one ing M˙ 2. This is againcontraryto our initialexpectations
snapshot to the next. As already noted by Corcoran et
(note, however, the discussion in the next section).
al.(2001b) no variability is seen during the 90ksec ex-
≈
posure of the Chandra grating spectrum. This is to be
6 Pittard & Corcoran: In Hot Pursuit of theHidden Companion of η Carinae
38
10
37
10
−1V)
e
k
−1s 1036
g
r
e
ux ( 1035
Fl
34
10
1 10
Energy (keV)
37
10
36
10
−1V) 35
e 10
k
−1s
g 1034
r
e
x (
u 33
Fl 10
32
10
1 10
Energy (keV)
Fig.2. Hydrodynamic simulations and theoretical spectra of the colliding winds in η Car. The top panels show
the results from a model where the momentum of each wind is equal (η = 1), whereas in the bottom panels the
primary wind has a momentum 10 times greater than the secondary wind (η = 0.1). In both cases a density plot
(gcm−3) from the hydrodynamical grid is shown on the left and the resulting intrinsic X-ray spectrum shown on
the right (no absorption). On each hydrodynamical grid the primary star is located at (0,0) and the secondary star
is at (4.0 1014,0). The shape and structure of the shocked region varies with the momentum balance between the
×
winds and the respective value of χ for each shocked wind. The full parameters used in these models were: upper
panels - M˙ 1 = 10−3 M⊙yr−1, M˙ 2 = 10−4 M⊙yr−1, v∞1 = 500 kms−1, v∞2 = 5000 kms−1; lower panels -
M˙ 1 =3×10−4 M⊙yr−1, M˙ 2 =10−5 M⊙yr−1, v∞1 =500 kms−1, v∞2 =1500 kms−1. The luminosity and shape
of the X-ray spectrum are a direct consequence of these parameters.
2.2.3. Variation with v∞ shocked gas near the stagnation point (E˙ n2), which
2 ∝
acts to slightly suppress the hardflux. A plot of the aver-
Isfhothcke ptermespheorcaktuvreeloicnictyreaosfeas w(Tin∝d ivs2i)n.cTrehaesreedf,ortehewpeoesxt-- aalgseodreenvseitaylsagtahiantstfTorfo1r0v6.∞32<=1T500<, 3100070.,45t0h0e0 akvmersa−g1e
popfeocwtthetrehoesfemcthooneddwealirnsypdewicnitncrradetaiossehsinawcrdreeeaanlsseaods.etxhBpeeecpcatruetsshheeotclhukemvkienlionocseiitttiyyc dv∞en2sit=y i3s00h0ighkemr sw−h1e,nwvh∞ic2h=te5n0d0s0tokmkese−p1 utphatnhewshoefnt
emission relative to the hard emission. This appears to
to increase. The variation of the spectrum with v∞2 is be because there is some mixing at the interface be-
showninthebottompanelofFig.3.Herewefindthatour
tween the primary and secondary wind, and the shocked
edtvwx∞opee2esenci=tnavc∞tr3ieo02an0s=0sea−w1r5eit50oh00n0v−l0y∞3p2k0,am0ar0tnsida−klm1ltyh.semA−se1npt,e.icbTntuvhrtueesmiottivgsdeaoortfaetilsoelnnhlusaimrbndteienotnwotsebhieteinys- p(1tMh5r˙ei0ms01e,a=ir3ny0t0e3wr0×m,ine51dd00i0−ai0ts4e,kdtm6eemn×ss−pe11er0r)−a.wt4Tu,hhree1ens0.m−vi3∞xe2Md⊙g=aysr−t5e10n0d0fosrtkovm∞b2es−a=1t
surprising finding offers the following explanation.
For fixed η and M˙ 2, and variable v∞2, the density of Theoverallneteffectisthattheemissionfromthehot
tchreeawseisn,dwvhaircihesreadsuρce∝s tMh˙e/vra∞d2i.atIifvve∞e2ffiicsieinnccyreaosfetdheρhdoet- gthaes isspseuctprpurmessferdomreltahteivme toodetlhewcitoholve∞r g2a=s, w50h0ic0hksmoftse−n1s
Pittard & Corcoran: In Hot Pursuit of theHidden Companion of η Carinae 7
34 η = 0.1
)
1
−V η = 1.0
e
1 k 33 η = 5.0
−
s
g
er 32
(
x
u
Fl 31
0
1
g
o
L 30
1 10
E (keV)
.
) M = 10−6
−1 36 .2
V M = 10−5
e .2
k M = 10−4
1 2
−
s
g 34
r
e
(
x
u
Fl 32
0
1
g
o
L
30
1 10
E (keV)
37
v = 1500
1) 2
−
eV 36 v2 = 3000
k
−1 v2 = 5000
s
g 35
r
e
(
x
u 34
Fl
0
1
g
o 33
L
32
1 10
E (keV)
Fig.3. Variation in the spectral shape and normalization of the theoretical colliding winds spectra in η Carinae.
The top panel shows the variation with η (M˙ 2 = 10−6 M⊙yr−1, v∞2 = 3000 kms−1). The middle panel shows
the variation with M˙ 2 (η = 5.0, v∞2 = 1500 kms−1). The bottom panel shows the variation with v∞2 (η = 0.1,
M˙ 2 =10−5 M⊙yr−1).
relative to the model with v∞2 =3000 kms−1. These in- In summary, we find that varying M˙ 2 can actually have
ferences are supported by spectra calculated with v∞2 = a small effect on the shape of the spectrum in some parts
5000 kms−1 andη =0.1,andvariableM˙ 2 (Fig.4). This ofparameterspace,aswellasthe moreobviousandmuch
shows that the spectrum hardens as M˙ 2 increases from greater effect on the luminosity. The power of M˙ 2 on af-
10−6 M⊙yr−1 to 10−4 M⊙yr−1 (the spectral index α, fectingthespectralshapeis,however,muchlessthanthat
wweheerxepFecνt∝froνmα,ouinrcrperaiosersinbfyeraenbcoeusts0in.1c)e. aThhiisghiserwMh˙a2t of v∞2, which is the primary influence.
helps to make postshock gas with a preshock velocity of
v∞2 =5000 kms−1 somewhatmoreefficientatradiating.
8 Pittard & Corcoran: In Hot Pursuit of theHidden Companion of η Carinae
lying medium to simulate the combined absorptionof the
.
M = 10−6 circumstellar (nebular) material in the Homunculus, the
.2
38 M = 10−5 ISM, andthe windfrom the companion(allofwhich may
.2
M = 10−4 contribute to the X-ray absorption at some level). Since
2
the stellar wind absorption depends on the companion’s
−1) mass-loss rate (at the phase of the Chandra observation)
V
e
−1s k 36 faobrsocropntsiiosntendciryecwtley,sbhuoutldthimsoisdebletyhoinsdcotmheposcnoepnet ooff tthhee
g present paper. Because of the low number of counts per
r
e
x ( spectral bin in the high-resolution grating spectrum, and
Flu 34 because background does not contribute significantly to
g 10 the observedspectrum atenergiesabove2 keV,we fit the
o gross spectrum using the C-statistic (Cash 1979), which
L
is appropriate for Poisson-distributeddata.
The fact that the shapes of our model spectra are not
32
dependent on the value of η introduces a degeneracy into
our grid as both η and M˙ 2 primarily influence the nor-
1 10 malization of the spectra. This means that various com-
E (keV) binations of η and M˙ 2 can provide similar quality fits to
the data.However,it is possible to obtain anestimate for
Fig.4. Variationin the spectralshape and normalization η fromthedurationofthelightcurveminimum( 100d).
for a very fast secondary wind (v∞2 =5000 kms−1) and To do this we have constructed a simple model o≈f the ob-
a fixed wind momentum ratio (η =0.1).As M˙ 2 increases served X-ray emission. We assume that the intrinsic flux
the spectrum becomes slightly harder. varies as 1/D, and that the absorption from the shock
apex along the line of sight is negligible when viewing
2.2.4. Summary of Spectral Dependence on η, M˙ 2, through the less dense secondary wind, but total when
viewing through the very dense primary wind. We use
and v∞
2 the latest orbital parameters (Corcoran et al.2001a) and
For the models investigated in this paper, we find that assumethattheskewangleoftheshockconefromtheor-
tchaen shpaercdternalsslhigahptelyisasi)Mi˙ns2eninsictrievaesetos (tihneovtahluere poafrηts, ioi)f tbhitearlevseullotcs,itsyc,avloerdb,soistδha≃t Larxct=an1(vaotrbp/evr∞ia1st)r.oFni.gT. 5heshskoewws
parameter space, e.g. strongly radiative shocks, it may of the shock breaks the symmetry of the observed emis-
soften with increasing M˙ 2), and iii) generally hardens sion so that the post-minimum flux is lowerthan the pre-
with increasing v∞2, but can sometimes soften. The minimumflux,asobserved.Thedurationoftheminimum
luminosity increases with i) decreasing η (since η Car is decreases with increasing η (for η = 0.1,0.2,0.3 the du-
unusual in the sense that there is no discernible contri- ration is 133,92,71 d), and is best matched by η 0.22.
≈
bution to the X-rays from the shockedprimary wind, bar Therefore we adopt this value for the rest of our analysis.
mixing), ii) increasing M˙ 2, and iii) increasing v∞2. We attempted to fit the grid of synthetic colliding
wind spectra to the observed MEG +1 order spectrum.
Wealsoconstrainedthe spectrumnormalizationtoliebe-
2.3. The Spectral Grid
tween 0.8 and 1.2, which fixes the distance to the star
ThesyntheticspectrawereinputintoaFITS-style‘Table’ between2300and1900pc,closeto thecanonicaldistance
model for use with the XSPEC data-analysis package, as of 2100 pc. In Fig. 6 we show the best fit interpolated
specified by Arnaud (1999). The fitting procedure within spectrum from our grid in the range 1.5 7.5 keV. Fig. 7
−
XSPEC is able to interpolate between the parameter val- shows a close-up of the fit to the Si and S emission lines
ues on the spectral grid so that best-fit values of M˙ 2 between 1.8 2.8 keV. Both figures demonstrate the ex-
−
etc. are obtained from fitting the Chandra data. In the cellent agreement found between the data and the mod-
2 10 keV band, the intrinsic luminosity on our grid els and highlight the progress made in both the observa-
ra−nges from 1.8 1031 ergs−1 to 1.6 1037 ergs−1, tional and theoretical study of colliding winds over the
× ×
which brackets the observationally determined value of
4 1034 ergs−1 (Corcoran et al.2001b). 2 Incidently,thelightcurveminimumcomputedwiththe2D
× hydrodynamical model in Pittard et al.1998 (redisplayed in
Fig. 1 at the beginning of this paper) also matches the dura-
3. Fits to the Chandra grating spectrum tion of minimum very well (although not the post-minimum
flux because the skew of the shock could not be computed
We compared the model intrinsic colliding wind spectra
with a2D calculation). Althoughdifferentmass-loss ratesand
with the observed grating spectrum allowing the mass- a slightly less eccentric orbit were used, the wind momen-
loss rate and wind terminal velocity of the companion to tum ratio adopted was also η = 0.2, which provides a certain
vary.Weinadditionincludedabsorptionfromacoolover- robustness for thisvalue.
Pittard & Corcoran: In Hot Pursuit of theHidden Companion of η Carinae 9
Variation with opening angle (or η) 4. Conclusions
1.0
In this paper our aimhas been to test the binaryhypoth-
0.8 esisofη Carbydirectlyfitting itsX-rayspectrumusinga
gridofspectracalculatedfromhydrodynamicalmodels of
0.6 thewind-windcollision.Whileouranalysisdoesnotprove
thatitisabinary,wefindthatthecollidingwindemission
Lx
0.4 model naturally provides for the range of ionization seen
intheemissionlinegratingspectrumforreasonablevalues
0.2 of the wind parameters. We have not shown that it is in-
consistentwithemissionfromasinglestar,buthavenoted
0.0 that it is unlike any of the other single stars observed so
1997.6 1997.8 1998.0 1998.2 1998.4
far at high energies and dispersion.
Time (years)
The technique applied in this paper has only been
demonstrated once before and is the first time that it has
Fig.5. The duration of the X-ray minimum predicted
been used with a high quality grating spectrum. Due to
from simple models. The wind momentum ratio in the
thelowvelocityoftheprimarywind( 500kms−1),most
three models shown is η = 0.2,1.0,5.0 (solid, dots, ≈
of the observed X-ray emission arises from the shocked
dashes),whichgivesadurationof92,33,16drespectively.
wind of the companion star. We find it difficult therefore
The observed duration is 100d, so the data is best ap-
proximated by η =0.2. ≈ to fit both M˙ 1 and v∞1 as free parameters.However,the
duration of the observed X-ray minimum can be used to
estimate the wind momentum ratio of the stars, η. With
Ttraabl glerid2.tTohtheebgesrtatfiintgpadraatma.eWteresfifrxotmhethteerfimtinofalthveelsopceitcy- η fixed at 0.2, and M˙ 2, and v∞2 as free parameters, we
are able to obtain a good fit to the data.
ofthe primarywindat500 kms−1,the stellarseparation
14 We find that the mass-loss rate of the companion is
aavattrD0y..2=S,oa4lna.d0ra×abll1uo0nwdaMcn˙mc2e,,savwn∞ed2r,ethNaesHswuaimnnddedtm,haoenmndeoanrtmcuoamlldizreaaxttitioeonrn(ηtao)l Mw˙in2d≈is 1v0∞−25≈M3⊙00y0r−1kmasn−d1.thTehteesremvianlaulesvesluogcigteystofthiatst
the companion is probably an Of supergiant (O-stars
absorbing column was applied. The resultant normaliza-
with similar wind parameters - e.g. HD 15570 (O4If),
tion is very close to 1.0, which indicates that the model
HD93129A(O3If),HD93250(O3Vf),HD151804(O8If),
and the values of D and η are sensible. Alternatively, it
and Cyg OB2 #9 (O5If) - are listed in Howarth& Prinja
implies thatourassumeddistanceto η Caristoo farbya
1989), or is possibly a WR star. The velocity of the pri-
factorof1.077,ifweimaginethisasthesolesourceofdis-
mary wind has been determined to lie in the range 500
crepancy. This would revise the source distance down to 700 kms−1 (e.g. Hillier et al.2001). Hence our fit implie−s
2.1/1.077=1.95kpc,whichiswellinsideofobservational
a primary mass-loss rate of M˙ 1 2.5 10−4 M⊙yr−1.
uncertainties. The implied mass-loss rate of the primary ≈ ×
star from our fit is M˙ 1 =2.5 10−4 M⊙yr−1. From the uncertainty in the value of η, and the interpo-
× lation on our grid, we estimate the uncertainty on our
Parameter Value derived value for M˙ 1 as approximately a factor of 2.
η 0.2 (fixed) Our best-fit estimate of M˙ 1 is smaller than typi-
M˙ 2 (M⊙yr−1) 0.98+−00..0098×10−5 cally inferred (cf. Davidson & Humphreys 1997; Hillier
v∞2 (kms−1) 3000+−335400 et al.2001) However, we note that a lower mass-loss rate
NH (cm−2) 7.68+−00..1177×1022 for the primary star can reduce some of the problems
Normalization 1.16 noted by Hillier et al.(2001) who fitted a value as high
as 10−3 M⊙yr−1. In particular, the models of Hillier et
al.(2001) suffered from absorption components that were
too strongandelectron-scatteringwings whichwereover-
last 10 years. The continuum shape and level from the estimated. Both indicate that their chosen mass-loss rate
models matches closely that of the data. All strong lines is too high. Paradoxically both the Hα and Hβ emission
(andmost weakones)whichappear inthe observedspec- lines were weaker than observed, indicating that their
trumarematchedalsointhebestfit.Thismeansthatthe mass-loss rate is too low. However, it is well known that
temperature distribution seen in the grating spectrum is the wind collisionzone canbe a strongsource of emission
matched by the model. However most of the strong lines lines (e.g. HD 5980, Moffat et al.1998), which would re-
are significantly overpredicted by the model fit. This dis- solve this problem. Their inferred minimum column den-
crepancy is in the opposite sense to the fit results from sity is also larger than the observed X-ray value, again
simple one- and two-temperature Raymond-Smith mod- implying an overestimate of M˙ 1. To increase the mass-
els, and is perhaps revealing that our assumption of solar loss rate of the primary towards the value estimated by
abundancesneedstobemodified.Thebestfitparameters Hillier et al.(2001), we require either a reduction in the
are summarized in Table 2. wind velocity to 100 kms−1, which in turn is in con-
≈
10 Pittard & Corcoran: In Hot Pursuit of theHidden Companion of η Carinae
t3Fh0ii0gs0.i6mk.mpBlisee−ss1tt,hfiηatt=tMo˙0t.12h,e=NC2Hh.5a=nd7r1.7a0−×g4r1a0Mt2in2⊙gycmrs−p−1e2c.,tAraunsmds.etehTnehfeorvofiemrtatpllhaneraofimrgmueatreleir,zsathtwieoenrceownMat˙isn21u.u=1m6.0lI.ef9v8wel×eits1a0vk−eer5vy∞Mw1e⊙=llyfi6r−t0t01ed,kvmb∞ys2−th1=e,
×
interpolated model.
flict with previous estimates, or a reduction in the wind little evidence for this in the current spectrum, other or-
momentum ratio to η < 0.1, which is in conflict with the bital phases may be more favourable in this regard. The
observed duration of ∼the X-ray minimum. Finally, it is addition of Doppler effects has already been incorporated
worth noting that our results indicate a value for M˙ 1 in modelled X-ray spectra (Pittard et al.in preparation),
which is closer to the value inferred for the Pistol star andshouldprovidefurther informationonwind velocities
(M˙ 4 10−4 M⊙yr−1; Figer et al.1998), an extreme and the structure of the wind-wind collision region.
≈ ×
early-type star with similarities to η Car.
The over-prediction of the X-ray lines in our models
Since current observations and theoretical modelling
perhapsindicatesthatthecompanionhassub-solarabun-
of the optical spectrum are unable to determine the ef-
dances, which favours an O-type over a WR classifica-
fective temperature and the stellar radius of the primary
tion, although we would need to perform a more detailed
without first determining M˙ 1 (cf. Hillier et al.2001), our analysis to confirm this possibility. As the primary has
independent estimate may prove to be extremely useful
slightlyenhancedabundancesofCandNcomparedtoso-
in this regard. It will be interesting to see if the results
lar, this suggests that to date there has been no mass ex-
from this paper are consistent with future X-ray obser-
change between the stars. Lamers et al.(1998) suggested
vations, and whether estimates of M˙ 1 from observations that the star which dominates the UV GHRS spectrum
at X-rayand other wavelengthscan be reconciled.Future
is not the star which ejected the nebula since the abun-
X-ray grating observations should also help us to fix the
dances in the GHRS spectrum are not as evolved as the
value of the wind momentum ratio more accurately.
abundances in the nebula (which are indicative of CNO-
As the secondary wind dominates the X-ray spec- cycle products). As the UV bright source is probably the
trum, and its terminal velocity appears to be high ( companion (Hillier et al.2001) this indicates that it was
3000 kms−1), we should expect to see signs of Dopple≈r theprimarywhichejectedthenebula.Therearealsosome
broadening and shifts in the line profiles. While there is caveats about the analysis in Lamers et al.(1998) since
