The spectroscopic orbit and the geometry of R Aqr

0.16 MB·

by  M. Gromadzki

Astronomy&Astrophysicsmanuscriptno.raqr˙final c ESO2009
(cid:13)
January14,2009
The spectroscopic orbit and the geometry of R Aqr
M.Gromadzki1 andJ.Mikołajewska1
NicolausCopernicusAstronomicalCenter,Bartycka18,00-716Warszawa,Poland
e-mail:marg,[email protected]
9
0
ReceivedOctober??,????;accepted??????,????
0
2
ABSTRACT

n
a Context.R Aqr is one of the closest symbiotic binaries and the only D-type system with radial velocity data suitable for orbital
J parameterestimation.

4 Aims.TheaimsofourstudyaretoderiveareliablespectroscopicorbitoftheMiracomponent,andtoestablishconnectionsbetween
1 theorbitalmotionandotherphenomenaexhibitedbyRAqr.
Methods.WereanalyzeandrevisethevelocitydatacompiledbyMcIntosh&Rustancomplementedbyadditionalvelocities.
] Results.Wefindaneccentricorbit(e=0.25)withaperiod43.6yr.ThissolutionisinagreementwitharesolvedVLAobservationof
h thissystem.WedemonstratethatthelastincreaseinextinctiontowardstheMiravariablein1974–1981occurredduringitssuperior,
p spectroscopicconjunction,andcanbeduetoobscurationbyaneutralmaterialintheaccretingstream.Wealsoshowthatjetejection
- isnotconnectedwiththeorbitalposition.
o
r Keywords.stars:binaries:symbiotic–stars:binaries:spectroscopic–stars:individual:RAqr
t
s
a
[
1. Introduction McIntosh& Rustan (2007) collectedradialvelocitydataof

4 SiO maser emission of R Aqr (Lepine et al. 1978; Cohen &
v R Aqr is a symbiotic binary surrounded by an hourglass neb- Ghigo 1980; Spencer et al. 1981; Lane 1982; Hall et al. 1990;
9 ula(Solf&Ulrich1985),andbothitscoolandhotcomponents Cho et al. 1996; Boboltz 1997; Hollis et al. 2000; Alcolea et
3 areunique.ThecoolcomponentisaMiravariablewithapulsa- al. 1999; Pardo et al. 2004; McIntosh & Rustan 2007) com-
1 tionperiodof387dwithSiOandH2Omaseremission,whichis plemented by previous radial velocities derived from optical
4
rare, with only three among 48 symbiotics with Miras exhibit- absorption lines (Merrill 1950; Jacobsen & Wallerstein 1975;
.
4 ing thisemission (Whitelock2003). The hotcomponentshows Wallerstein 1986) and near-IR CO and Ti I lines (Hinkle et al.
0 sporadic, jet ejections (e.g. Kellogg et al. 2007 and Nichols et 1989).Allofthesefeaturesareassociatedwiththecoolcompo-
8 al.2007),andNicholsetal.(2007)alsodetecteda1734speri- nentormaterialinitscloseneighborhoodandreflectitsmotion
0 odicoscillationinChandraX-rayobservations,whichsuggested aroundthemasscenter.Inastrophysicalmasers,emissionorig-
:
v thatthehotcompanionisamagneticwhitedwarf.Willsonetal. inating in many maser spots moves around the Mira variable.
i (1981) interpreted a brightness reduction in pulsation maxima Spectra of masers exhibit a series of emission lines with vari-
X
as the eclipsing of the Mira by a companionsurroundedby an ous velocities associated with different maser spots. McIntosh
r extended gas cloud. This interpretation was supported by two (2006) studied changes in the velocity centroid (VC) of SiO
a
facts. First, duringthe last hypotheticaleclipse (1974–1980),a maseremissionfrom76singleevolvedgiants,andshowedthat
minimumwasobservedinthenear-IRlightcurvesimilartothat themeandifferenceintheVCsmeasuredatdifferentepochswas
correspondingtodustobscurationinothersymbioticMiras(e.g., only 0.065 2.00kms 1, and thatthe VC of the emission dis-
−
Whitelocketal.1983).Secondly,aspectrumobtainedduringthe tributioncan±beusedtoderivethevelocityofthestar.Basedon
firstsuchevent(1886–1894)exhibitsonlyfaintemissionlinesof this result, McIntosh & Rustan (2007) adopted the VC in their
hydrogenand no trace of M type spectral features(Townleyet workforallkindsofvelocitydataanalysis.
al. 1928). In the historical, visual, light curve, three phases of
McIntosh & Rustan (2007) also estimated orbital elements
reduced maxima are present spaced at 44 yr intervals and this
using a program developed by Gudehus (2001). They inferred
valuewasadoptedbyWillsonetal.(1981)astheorbitalperiod.
aneccentricorbit,e = 0.52,withaperiod34.6yr.Theirorbital
Additionally,theO Cdiagramshowedvariationwithaperiod
− period was significantly shorter than any previousestimates as
of 22yr.Wallerstein(1986)usedanumberofspectralabsorp-
∼ wellastheperiodderivedinourpresentstudy.Theirotherwere
tionlinesassociatedwiththeMirainanattempttodeterminethe
ofreasonableaccuracyif we interprettheir system mass, equal
orbitalelements of R Aqr. His results were consistent with the
to 0.043 M , as the mass function, and their semi-major axis
44yrperiod,butuncertain.Hinkleetal.(1989)combinedthese
of the syste⊙m, of 3.7 AU, as the semi-major axis of the orbit
archivaldata withradialvelocities(RV) determinedfromnear-
of the Mira component. We also note that not all points listed
IRCO andTiI lines, andobtaineda 44yr periodanda highly
eccentric,e=0.6,orbitalsolution. intheirTable1wereplottedontheirfiguresshowingVCversus
orbitalphase,namely,theydidnotmeasurementfromAlcoleaet
al.(1999).Inthetext,theauthorswrotethatpointsfromHollis
Sendoffprintrequeststo:M.Gromadzki et al. (2000) are listed in their Table 1, althoughthey were not
2 M.GromadzkiandJ.Mikołajewska:ThespectroscopicorbitandthegeometryofRAqr
displayed there. These data points were plotted on the figures negligibleduringsuchaninterval.Thedataobtainedfromdiffer-
showing VC versus Julian days, but they were missing on the entmethodswerebinnedseparately.Sincedifferentmasertran-
figureofVCversusorbitalphase.Theauthorsalsodidnotcom- sitionsareformedatdifferentdistancesfromthestellarsurface,
pare the orbit solution with the resolved image of the binary theywerealsobinnedseparately.We excludedsinglemeasure-
(Hollisetal.1997),norincluderadialvelocitymeasurementsbe- ments for various maser transitions (Allen et al. 1989; Patel et
fore1946(Merrill1935,1950).Thesepointswerealsoignored al.1992;Grayetal.1995;Imaietal.2001)obtainedforepochs
inallpreviouspapersabouttheorbitestimationfromradialve- coveredbymoreextensivedatasets.InTable1,welisttheradial
locities(Wallerstein1986,Hinkleetal.1989).Theauthorsalso velocity data used to derive the orbital elements of R Aqr and
neglected radial velocity measurements of the SiO maser by thenconvertedtolocalstandardofrest(LSR)velocities,which
Zuckermanetal.(1979),Hollisetal.(1986),Halletal.(1987), arealsoplottedinFig.1.
Allen et al. (1989), Heske (1989), Jewell et al. (1991), Patel et WealsodecidedtoexcludefromouranalysistheSiOmaser
al. (1992), Gray et al. (1995), Schwarz et al. (1995), Hollis et dataobtainedduringtheperiodJD2446000–47500(datafrom
al. (2000, 2001), Imaietal. (2001), Cotton etal. (2004, 2006), Hollisetal.1986,Heske1989,Alcoleaetal.1999,andHallet
andKangetal.(2006).Wealsonotethattheobservationsstud- al.1990)becausethemaseremissionshowedatthattimesignif-
iedbyPardoetal.(2004)includedtheobservationsanalyzedby icantlydifferentbehavioure.g.afewfainteremission,irregular
Alcoleaetal.(1999),whichincludedthedatausedbyMartinez contoursthan in later epochs, as well as the masers in isolated
etal.(1988).Thesethreedatasetsarethusnotentirelydifferent, Miras(seePardoetal.2004).TheSiOmasersinRAqrdisplaya
and the later studies were based simply on data collected over ring-likemorphology 31mas( 6.2[d/200pc]AU)indiam-
longertime. eter(Boboltzetal.199∼8).So,the∼semaserslieveryclosetothe
Thispapercontainsananalysisoftherevisedradialvelocity stellarsurface,namelyatadistanceofonly 1.5radiifromthe
data listed in Table 1 of McIntosh & Rustan (2007) and addi- Mira(seeSect.3)inaregiondominatedbyst∼ellarpulsationsand
tionalvelocitydata(listedhereinTable1),aswellasdiscussion permeatedbycircumstellarshocks.Inaddition,theSiOmasers
of the connections between the orbital motion and other phe- canbeseriouslyaffectedbytidalinteractionsduringtheperias-
nomenashownbyRAqr. tronpassagewhenthesizeoftheSiOmaserregionbecamecom-
parabletotheRocheloberadiusoftheMira.Infact,according
toourorbitalsolution(seebelow)theAlcoleaetal.(1999)ob-
2. Orbitdetermination
servationswereobtainedaroundperiastron.Thedeepminimum
The data from Table 1 of McIntosh & Rustan (2007) were re- in both VCs and flux of maser emission that appeared around
vised and supplemented by additional radial velocity measure- JD2446700–47300, coincided with the jet formation(Nichols
mentsfromMerrill(1935, 1950), Zuckerman(1979), Martinez et al. 2007) and a rise in the UV continuum (Meier & Kafatos
etal. (1988),Jewell etal. (1991), Schwarzetal. (1995),Hollis 1995).WesuspectthattheSiOmasersmayhavebeenpartlydis-
et al. (2000, 2001), Cotton et al. (2004, 2006), and Kang et al. ruptedbyrisingUVradiationduringthejetformation,andtidal
(2006). interactionduringtheperiastronpassageandthengraduallyre-
Theblue-violetabsorptionlinesinMiravariablesshowcon- build.
stant shift of between 5 km s 1 and 10 km s 1 with respect
− − To identify the spectroscopicorbit, we first estimated a pe-
− −
tonear-IRvelocities(Hinkleetal.1984;andreferencestherein).
riodofRVvariationsof43.6yrusingOrtfit(basedonthemethod
Inourstudy,ashiftequalto 6kms 1 wasadopted.Theblue-
− ofSchwarzenberg-Czerny1996),andthencalculatedtheorbital
−
violetabsorptionlinesdonotshowanyvariationwithpulsation
parameters:T ,thetimeofperiastronpassage,γ,thebaricentral
0
period and do not need any additional correction. Absorption
velocity, K, the semi-amplitude,ω, the longitudeof periastron,
lines from the red part of the optical spectrum exhibit signifi-
and e, the eccentricity with fixed period. We applied Bertiau’s
cant variation but there is no way of correcting for this effect
program(1967)basedontheLehmenn-Filhe´smethod.Asare-
in a single measurement. For this reason, we did not use three sult,weobtainedaneccentric,e=0.25 0.07,orbitwithreason-
datapointsfromJacobsen&Wallerstein(1975),whichhadbeen ±
ableerrors(Table2).Figure2displaysthedataandthebest-fit
previously used for the spectroscopic orbit determinations by
velocitycurveversusorbitalphase.
Wallerstein(1986),Hinkleetal.(1989),andMcIntosh&Rustan
Figure 1 also compares the RV variations with the O C
(2007). −
dataforthe Mirapulsationsbasedvisualdatacollectedbyam-
In the near-IR,the radialvelocity(RV) variationsofR Aqr
ateur observers from AAVSO. The O–C is a plot showing the
weredominatedbystellar pulsations(∆V 40kms 1).Tore-
∼ − difference between the observed (O) times of maximum light
move changes due to the pulsations, Hinkle et al. (1989) com-
andthevaluescalculatedaccordingtoanadoptedephemeris(C)
plete a linear fit to the infrared velocity curve between phase
asa functionof time.A descriptionof theO–C methodcanbe
0.1and0.8,andthenadoptedasthestellarvelocitiestheresid-
found in a review by Zhou (2003). To derive a new pulsation
ualsremainingaftersubtractingthevelocity-curvefitfromeach
ephemeris,we firstestimatedthetimeofeachmaximuminthe
measurement plus the center-of-mass velocity of the Mira of
light curve by fitting a third-order Fourier polynomial. Then a
29.1kms 1. The value of the center-of-massvelocitywas es-
− − linearephemeris:
timated from the CO ∆ν = 3 velocity at phase 0.36, following
the results of Hinkle, Scharlach & Hall (1984). Unfortunately,
Hinkleetal.(1989)usedanoldephemerisofCampbell(1955). JD(max)=2416070 4+387.30 0.07 E
SinceRAqrdisplayssignificantvariationinitspulsationperiod ± ± ×
(see Fig. 1), we repeated these corrections with the ephemeris
JD(max)=2442404.2( 0.4)+388.1( 0.1) E,derivedforthe was fitted to the obtained times of maxima. The resulting O-C
± ± ×
1975–1989periodcoveringHinkleetal.(1989)observations. diagramshowsaparabolicshapethatcorrespondstoanincrease
Tocalculatetheorbitalsolutionalldatapointswereaveraged intheperiodrateof0.013 0.002daypercycle.Aftersubtracting
±
in387-daybinscorrespondingtothepulsationperiodoftheMira thisparabolictrend,asinusoidalvariationwithaperiodof22.5
component.The velocitychangesdue to the orbitalmotionare yearsandamplitudeofabout8days(Fig.1)isvisible.
M.GromadzkiandJ.Mikołajewska:ThespectroscopicorbitandthegeometryofRAqr 3
11111999992222200000 11111999994444400000 11111999996666600000 11111999998888800000 22222000000000000000
2222200000
1111100000
-1-1-1-1-1V [km s] V [km s] V [km s] V [km s] V [km s] ----------22222222226262626262 --- --- --- --- --- 00000321321321321321000000000000000 O-C [days] O-C [days] O-C [days] O-C [days] O-C [days]
RRRRR
-----3333300000
-----3333344444
2222200000000000000000000 3333300000000000000000000 4444400000000000000000000 5555500000000000000000000
JJJJJDDDDD-----22222444440000000000000000000000000
Fig.1. The O C diagram (top) and RV variations (bottom) for R Aqr. Observations from different sources are marked like in
−
Table1.Thesolidcurverepresentsthefittedorbitalelements(Table2).Thedottedcurverepresentstheorbitalmodelproposedby
Hollisetal.(1997).Thedashedcurverepresentssolution,withmodifiedω=87whichbetterfitstheVLAobservations.Barsshow
timesofhypotheticeclipse,shortarrowsrepresentmomentsofjetejection(Nicholsetal.2007),whilstlongarrowsshowperiastron
passage.
Table2.OrbitalelementsforRAqr. ties in the orbital parameters (see Table 2). The mass function
setsalowerlimittothehotcompanionmass.
Element Value Forfurtherdiscussion,weassumethatthesymbioticbinary
P (day) 15943 471 RAqrconsistaMiravariableandawhitedwarf(WD)compan-
γKo(r(kbkmmss−−11)) -244.0.9±±±00.4.2 Uiornliwchit1h9a8n5)o.rAbistsiunmcliinngedplaatuisi=bl7e0c◦o(m∼p7o2n◦enatcscmoradsisnegs,toMSgo=lf1&–
e 0.25 0.07 1.5M ,andM =0.5–1.4M ,fortheMiraandtheWD,respec-
± h
ωT (deg) 244140061±919728 tively,⊙thetotalmassofsystem⊙ Mtot = Mh+Mgshouldbewithin
Σ(0O C)2 40 ± therange1.5–3M .Thecomponentmassesarealsolimitedby
σ(km−s 1) 1.11 the orbital solution⊙. Therefore, if we consider f(M) = 0.064–
− 0.138 M and M = 1–1.5 M , we derive M = 1.6–2.5 M ,
g tot
M = 0.5⊙7–1.02M ,andthem⊙assratioq = M /M =1.2–2⊙.1
h g h
3. Discussion (Fig.3).Thesevalu⊙esareingoodagreementwiththecommonly
adoptedmodelofsymbioticbinaries.Thesemi-majoraxisofthe
Ourorbitalsolutionyieldsthesemi-majoraxisoftheMiraof
system,a,is14.2–16.8AU,whichcorrespondsto71–84mason
KP theskyforadistanceofd =200pc(seebelow).
a sini= √1 e2 =5.68+0.85AU,
g 2π − 0.83 Our orbital solution can be tested and refined by using re-
−
solved observations of R Aqr (Hege et al. 1991; Hollis et al.
andthemassfunctionof
1997). In particular, the binary componentsof R Aqr were re-
1 (M sini)3 solved by VLA observations (Hollis et al. 1997) obtained on
f(M)= 2πG ·PK3(1−e2)3/2 = (Mhh+Mg)2 =0.096+−00..004322M⊙, t2h0eNVoLvA19im96ag(JeDin=2Si4O50m4a0s7e)r.vT=he1m,Jea=su1red0setpraanrastiitoionnbaentwdethene
−
where M , and M represent masses of the giant and the hot continuumemissionina50MHzbandwidthat43.165GHzas-
g h
component,respectively,andtheerrorsaresetbytheuncertain- sociatedwithanHiiregionsurroundingthehotcompanionwas
4 M.GromadzkiandJ.Mikołajewska:ThespectroscopicorbitandthegeometryofRAqr
Table1.RadialvelocitiesofRAqrusedfororbitalelementsdetermination.
JD RV[kms 1] Spectralrange Symbol References
−
2422255 -21.6 Visual G# Merrill1935
2423039 -22.0 Visual G# Merrill1935
2429581 -30.7 Visual H# Merrill1950
2430336 -30.2 Visual H# Merrill1950
2432235.5 -28.5 Visual H# Merrill1950
2433019.3 -29.0 Visual H# Merrill1950
2441237 -21.7 Visual (cid:8) Jacobsen&Wallerstein1975
2442939 -22.0 Near-IR > Hinkleetal.1989
2443527.5 -26.6 v=1,J=1 0 + Lepineetal.1978,Zuckerman1979
2444078 -25.9 v=1,J=1−0 (cid:4) Cohen&Ghigo1980,Spenceretal.1981,Lane1982
−
2444356 -27.0 v=1,J=1 0 Lane1982
2444509 -25.6 Visual − ×(cid:7) Wallerstein1986
2444748 -30.1 Visual (cid:7) Wallerstein1986
2445535 -27.7 Near-IR > Hinkleetal.1989
2445574.5 -27.6 v=1,J=1 0 N Choetal.1996,Jewelletal.1991
2445862 -30.1 Visual − (cid:7) Wallerstein1986
2445890.6 -28.0 Near-IR > Hinkleetal.1989
2446378.5 -27.8 Near-IR > Hinkleetal.1989
2447247 -28.5 v=1,J=1 0 Martinezetal.1988
2447338 -28.9 Near-IR− △> Hinkleetal.1989
2447634 -28.5 v=1,J=1 0 Martinezetal.1988
2447870 -27.1 v=1,J=1−0 △H Pardoetal.2004
2448240 -27.0 v=1,J=2−1 q Schwarzetal.1995
2448283 -28.3 v=1,J=1−0 H Pardoetal.2004
2448696 -27.4 v=1,J=1−0 H Pardoetal.2004
2448998.4 -26.4 v=1,J=2−1 q Schwarzetal.1995
2449435 -27.0 v=1,J=1−0 H Pardoetal.2004
2449439 -26.3 v=1,J=2−1 q Schwarzetal.1995
2449804 -27.0 v=1,J=1−0 H Pardoetal.2004
2450068.8 -26.8 v=1,J=1−0 Boboltzetal.1997
2450407 -24.0 v=1,J=1−0 2♦ Hollisetal.2000
2450948 -24.0 v=1,J=1−0 2 Hollisetal.2000
2451390.4 -25.6 v=1,J=2−1 D Kangetal.2006,Hollisetal.2000
2451785.8 -23.2 v=1,J=2−1 C Kangetal.2006
2451892 -24.3 v=1,J=1−0 Hollisetal.2001,Cottonetal.2004,McIntosh&Rustan2007
2453253 -23.0 v=1,J=1−0 4⊕ Cottonetal.2006
2453784.3 -22.7 v=1,J=1−0 ▽ McIntosh&Rustan2007
2454112 -22.8 v=1,J=1−0 ▽ McIntosh&Rustan2007
−
ρ = 55 2mas(11[d/200pc] AU), and the position angle was The Hipparcos parallax of R Aqr is 5.07 3.15 mas (Perryman
θ = 18± 2 . This can be compared with the projected com- etal.1993),whichcorrespondstoadistan±ceof197+323pc.Our
◦ ± ◦ 75
ponent separation on the sky plane calculated from our orbital determinationoftheparametersofthespectroscopic−orbitisthus
elements.Theorbitalelements(Table2)combinedwiththeor- inagoodagreement(within 1-σerrorsintheorbitalparame-
≤
bital inclination of i = 70 (Solf & Urlich 1985) inferred the ters) with those inferred from the VLA resolved observations.
◦
projected separation of ρ = 0.44a 31–37[d/200pc] 1 mas, The value of θ = 18 , measured with the VLA, implies that
− ◦
∼
and the difference between the apparent binary position angle Ω=127 .Thus,thepositionofthebinaryorbitontheskyrepro-
◦
and the position angle of the line of nodes (the binary orienta- duceswell the generalpicture of the nebula aroundR Aqr, i.e.
tiononsky)ofθ Ω= 109 . theorbitalplaneisperpendiculartothejets(seeFig.7inSolf&
◦
− −
Our predicted component separation on the sky is consis- Urlich1985).
tentwiththeVLAobservationsonlyifthedistanceissomewhat Theorbitalparametersderivedforthe speckle observations
lowerthan200pcorweunderestimatetheρvalueduetouncer- (Hege et al. 1991) completed on 16 Oct 1983 are inconsistent
taintiesinourorbitalelements. withourorbitinanycase,becausethemeasuredseparation,ρ=
Thepredictedvalueofρshouldinfactincrease,changingω 124 2 mas which corresponding to 25[d/200pc] AU, is too
±
(seealsoFig.4),and/orincreasinge,and/ordecreasingT .For largeforanyorbitalphase.Hegeetal. (1991)probablydidnot
0
example, ρ should increase to 0.65a (46–55[d/200pc] 1 mas) detecttheMiracompanionbutratheranHαemissionregionin
−
just by adopting a lower value of ω = 87, i.e. lower only by theSWcounterjet.
anamountapproximatelyequaltothestandard-deviationuncer- Ourorbitalsolutionpredictsthetimesofspectroscopiccon-
taintyofω. junctionsat T = 2450859(Feb 1998),T = 2443658
conjI conjII
ThedistancetoR Aqris alsorelativelyuncertain,andpub- (May 1978) for the inferior ( the Mira is in front of the hot
lishedestimatesbasedonvariousmethodsareintherange180– component),andthesuperior(theMirabehind)conjunction,re-
260pc(e.g.180pcbySolf&Ulrich1985;181pcbyLepineet spectively.Thesuperiorconjuctioncoincideswith the last dust
al.1978;240pcusingthemostrecentperiod-luminosityrelation obscuration/eclipse(see also Fig. 4). Althoughthe conjunction
fromWhitelocketal. 2008;and260pcbyBaade1943, 1944). timescoulddifferbyupto1–2yearsduetouncertaintiesinthe
M.GromadzkiandJ.Mikołajewska:ThespectroscopicorbitandthegeometryofRAqr 5
ateandminimumpulsationphase,respectively(vanBelleetal.
222
111]]] 1996;Millan-Gabetetal.2005;Raglandetal.2006).Theseval-
---sss ues correspond to the average radius of the Mira component,
m m m
R 2AU. Even during periastron passage, the Mira variable
s [ks [ks [k thger∼eforeremainsrelativelyfarfromfillingtheRochelobe.
rerere ---222 Manydetachedinteractingbinaries,includingthesymbiotic
binariesaswellasmanyX-raybinariesshowevidenceformuch

highermasstransferratethanpredictedbymodelsofspherically
----22222222 symmetric winds. This phenomenon can be accounted for by
wind focused towards the compact component. Podsiadlowski
& Mohamed (2007) proposed a model for o Cet binary sys-
1111]]]]
----ssss tem thatcan explainthis focusing.In their model,a slow wind
m m m m ----22226666 fromMirafillsitsRochelobeandthenthematterfalls–viathe
kkkk
V [V [V [V [ L1 Lagrangian point – into an accreting stream onto an accre-
RRRR tiondiskaroundthe companion.Thismodelisevenmorerele-
vant to R Aqr where the componentseparation is significantly
smallerthanthatin oCet. Inparticular,itcouldexplainthein-
----33330000
creaseinextinctiontowardstheMiraduringthelast“eclipse”in
1974-1981causedbyaneutralmaterialintheaccretingstream.
Accordingtoourorbitalsolution,thestreamingmaterialcanob-
0000....0000 0000....5555 1111....0000 1111....5555
scure the Mira at that time, and in addition, the proximity of
OOOOrrrrbbbbiiiittttaaaallll pppphhhhaaaasssseeee periastron(seeFig.4)couldgiverisetoenhancedmasstransfer.
A similar enhanced, wind-obscuration scenario for R Aqr was
Fig.2. Bottom: The RV data and fitted orbital curve (Table 2) discussed by Mikołajewska & Kenyon(1992), althoughin that
againstorbitalphase.SymbolsarethesameasinFig1.Thesolid case the source of the increased mass loss was proposed to be
curverepresentourorbitalsolution.Thedashedcurverepresents a helium flash above a massive core (M 1.36M ) of the
core
solution,withmodifiedω=87whichbetterfitstheVLAobser- Mira. ∼ ⊙
vations.Top:DifferencebetweentheRVdataandourorbitalfit TheorbitalconfigurationofRAqrcouldalsoexplaintheob-
(solidlineinthelowerpannel). servationsofthe OH andH O masersthatoriginatein circum-
2
stellar regions more distant from the Mira variable (e.g. H O
2
111...222 maserszoneis10–20AU)thantheSiOmaseremissionregion.
The OH and H O maser lines were not detected in 1979 and
2
000...111333888 1984 (Cohen & Ghigo 1980; Norris et al. 1984) when the hot
companion was in front of Mira. Ivison et al. (1994) reported
111...000
detectionof weak OH and H O maser emission in 1993,when
000...000999666 2
theMirawasinfrontofthehotcompanionandthemaserswere
M ]M ]M ]O•O•O• shieldedfromitsradiation.Theyclaimed,however,thattheOH
[ [ [hhh 000...888 000...000666444 maser detection was only tentative, and that the velocity mea-
MMM surementwasveryunusual(anexpansionvelocityof10kms 1
−
is rather large for this system), and only the red peak should
000...666 have been detected, and additional spectra obtained using the
VLAduring1994JunedidnotshowtheOHmaserline(Ivison
et al. 1998). The H O line appeared more promising, although
2
000...444 weak for a Mira variable with relatively strong SiO masers. It
000...888 111...000 111...222 111...444 111...666 111...888 wasalsoclearlydetectedduring3epochsin1993–1995(Ivison
MMM [[[MMM ]]] etal.1998). Ivisonetal. (1998) proposedthreepossiblemech-
ggg OOO•••
anisms that could inhibit the OH and H O maser formation in
2
theirnaturalenvironment,involvingeithertheorbitalmotionof
Fig.3.Thepermittedcomponentmassesconstrainedbytheob-
thecompanionoritsUVradiationandfastwind,orlineobscu-
servedmassfunctionaswellasitsmaximumandminimumval-
rationatlowfrequenciesbyopticallythick,ionizedgas.
ues(solidlineslabeledwiththevaluesof f(M)),andassuming
i = 70 .Dottedanddashedlinesshowthesolutionfori = 75 , Theapparentcorrelationbetweentheorbitalpositionandthe
◦ ◦
andi=90 ,respectively. O CfortheMirapulsationsisextremelyinteresting.Inparticu-
◦ −
lar,minimaintheO Cdiagramoccuraroundtheperiastron(see
−
Fig 1). This may be due to some distortion of the Mira caused
orbitalparameters,especiallyT ,e,andω,theobscurationlasted by tidal interaction during the periastron passage, for example
0
about6 years,andthecoincidencebetweenthese twoeventsis if the Mira became elongated towards the hot component, the
obvious. pulsationmayneedmoretimeforpropagationinthisdirection.
Adopting plausible binary parameters, i.e. the mass ratio According to our orbital model, the main maximum of O C
−
q 1.6, M = 2 M , and a = 15 AU (see above), we esti- appearsclosetotheinferiorconjunction,whentheMiraeclipses
tot
ma∼tetheminimumcom⊙ponentseparationtobea(1 e) 11AU, thehotcompanion,whereasthesecondary,lowermaximumap-
− ∼
and the Roche lobe radiusfor the Mira, to be R 4AU. The pearsinthemiddleofthetwoconjunctions,whenbothcompo-
L
∼
near-IRinterferometryof R Aqr gave the diameterof the Mira nentsarewellseparatedandwecanseetheelongatedside.
expressedasadiameterofuniformdisk,Θ =14.06–20.8mas Finally,theorbitalsolutionproposedisinconsistentwiththe
UD
in K, 17.7 mas in J, and 17.7–19.07 mas in H, in intermedi- 17yrorbitalperiodforRAqrproposedbyNicholsetal.(2007).
6 M.GromadzkiandJ.Mikołajewska:ThespectroscopicorbitandthegeometryofRAqr
1111111111111111111111111111111111..................................5555555555555555555555555555555555
Mira as obscuration by the accretion stream. We also showed
thatthe jet ejection (Nicholset al. 2007) is notconnectedwith
theorbitalposition.Finally,wenotethatSeptember2012should
beaperfecttimetocompleteresolvedimagingofRAqr,since
1111111111111111111111111111111111 theMiracomponentwillthenbeatminimumbrightnessandthe
separation between the componentson sky will be close to its
maximumpossiblevalue.
Acknowledgements. This study made use of the American Association of
0000000000000000000000000000000000..................................5555555555555555555555555555555555
Variable Star Observers (AAVSO) International Database contributed by ob-
EEEEEEEE22222222 EEEEEEEEE111111111 serversworldwide.Wearegratefultotheanonymousrefereeforvaluablecom-
ments.WealsothankRadekSmolecforcomments tothefirstversionofthis
SSSSSS paperandWojtekPychforprovidingtheOrtfitsoftware.Thisworkwaspartly
supportedbythePolishResearchgrantN203395534.
0000000000000000000000000000000000
MMM222
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