Long Secondary Periods and Binarity in Red Giant Stars

0.72 MB·English

by  I. Soszynski

Draftversion February5,2008
PreprinttypesetusingLATEXstyleemulateapjv.10/09/06
LONG SECONDARY PERIODS AND BINARITY IN RED GIANT STARS
I. Soszyn´ski
WarsawUniversityObservatory,Al.Ujazdowskie4,00-478Warszawa,Poland
Draft versionFebruary 5, 2008
ABSTRACT
Observational arguments supporting the binary explanation of the long secondary periods (LSP)
phenomenon in red giants are presented. Photometry of about 1200 semiregular variables with the
LSPintheLargeMagellanicCloudareanalyzedusingtheMACHOandOGLEphotometry. Forabout
5% of these objects additional ellipsoidal-like or eclipsing-like modulation with the same periods as
7
the LSP is detectable. These double-humped variationsare usuallyshifted inphase comparingto the
0
LSP light curves. I discuss the model of binary system with a red giant as the primary component
0
anda low-massobject asthe secondaryone. The masslostby the redgiantthroughthe wind follows
2
the spiral pattern in the orbit around the primary star and obscures it causing the LSP variations.

n
Subject headings: stars: binaries: close — planetary systems — stars: AGB and post-AGB
a
J
6 1. INTRODUCTION (sequences C and C′), andthe sequence D contains rela-
1 tively much smaller number of carbon-richstars.
Amongnumerousclassesofvariablestarsonlyonetype
of large-amplitude stellar variability remains completely Recently Derekas et al. (2006) presented a period–
1
luminosity–amplitude analysis of variable red giants in
v unexplained. This is the long secondary periods (LSP)
the LMC. They examinedamplitudes ofellipsoidal,LSP
3 observed in luminous red giant stars. The LSP variabil-
6 ity with periods between 200 and 1500 days and with and Mira-like variables using MACHO red (RM) and
4 V-band amplitudes up to 1 mag occurs in ∼ 30% of blue (BM) photometry. The amplitude distribution for
the LSP stars turned out to be different than for ellip-
1 Semiregular Variables (SRVs) and OGLE Small Ampli-
soidalandpulsatingvariables,butblue-to-redamplitude
0 tudeRedGiants(OSARGs). Thisphenomenonhasbeen
7 knownfor decades(Payne-Gaposhkin1954; Houk 1963), ratios of the LSP stars (typically 1.3) is more similar to
0 but an interest in the stars with the LSP has been re- this quantity in pulsating variables (∼ 1.4) than to el-
h/ newedsinceWood et al.(1999)showedthattheseobjects lipsoidal/eclipsing binaries (∼ 1.1). This last feature is
usedinpresentworkforseparationofthe LSPandellip-
p follow a period–luminosity (PL) relation (sequence D).
soidal/eclipsing variability in the same light curves.
- In recent years our knowledge about the LSP phe-
o nomenon has significantly increased, although its origin Various hypotheses have been proposed to explain
r the origin of the LSP variability: rotation of a spot-
remains a mystery. Hinkle et al. (2002) and Wood et al.
t
s (2004) studied spectral features of severalGalactic stars ted star, episodic dust ejections, a radial and non-radial
a pulsation and binary companions including planets or
withtheLSPanddetectedradialvelocityvariationswith
v: amplitudes of a few km/s which agree with photomet- brown dwarfs. Wood et al. (1999) suggested that the
i ric long-period variations. Soszyn´ski et al. (2004) used sequence D stars are components of semidetached bi-
X
nary systems. The matter lost by the AGB star forms
OpticalGravitationalLensingExperiment(OGLE)data
r a dusty cloud around the companion, and regularly ob-
to select and analyze close binary systems in the Large
a
scures the primary componentcausing the LSP variabil-
Magellanic Cloud (LMC) with a red giant as one of the
ity. Hinkle et al.(2002)andthenOlivier & Wood(2003)
components. They noticed that the sequence D in the
mentionedthattheradialvelocitymeasurementsarecon-
PL diagram overlaps and is a direct continuation of the
PL sequence of ellipsoidal and eclipsing red giants1 (se- sistent only with the binary or pulsation explanations of
the LSP. Wood et al. (2004) ruled out the binary hy-
quence E), suggesting that the LSP phenomenon is re-
pothesis,becauseashort(∼1000yr)timescaleonwhich
lated to binarity. Soszyn´ski et al. (2004) also showed
the companion should merge with the red giant. They
that some evident ellipsoidal red giants exhibit simul-
suggested that the most likely explanation of the LSP
taneously OSARG-type variability, thus, it was directly
are low degree g+ pulsation modes trapped in the outer
demonstrated that in some cases the binary explanation
radiative layers of the star.
of the LSP is true. Nevertheless, there is no doubt that
The main goal of this paper is to find observational
the bulk of the LSP variables are not typical ellipsoidal
evidences for or against the binary explanation of the
or eclipsing binaries.
LSP. Since the PL sequence populated by the ellipsoidal
Soszyn´ski et al.(2005)discoveredthatthe sequence D
and eclipsing variables overlaps with the LSP sequence
split into two ridges in the period – Wesenheit index
(WI =I−1.55(V −I)) plane, which corresponds to the (Soszyn´ski et al.2004),itshouldbepossibletofindstars
revealing simultaneously both types of variability. If pe-
spectral division into oxygen-rich and carbon-rich AGB
riodsarethesame,theLSPphenomenonmustberelated
stars. The same feature wasnoticed for MirasandSRVs
to binarity. If not, the LSP is presumably causedby an-
Electronicaddress: [email protected] other reason.
1 if the real orbital periods of binary variables are considered,
i.e. periodstwotimeslongerthanobtainedautomatically.
2 Soszyn´ski
2. DATAANALYSIS
SincetheLSParesometimesaslongas1500days,pre-
sentedanalysisis basedonobservationaldataoriginated
in two sources: MACHO and OGLE surveys. Merged
light curves from both projects covered 15 years of ob-
servations: from 1992 to 2006. The sequence D stars se-
lected by Soszyn´ski et al. (2004) in the OGLE database
were cross-identified with objects collected in the MA-
CHO archive2. I found about 1200 counterparts of the
previously selected variables. Then, RM-band MACHO
observationshavebeenmergedwiththeOGLEpointsby
scaling amplitudes and shifting zero points of the pho-
tometry. The parameters of this transformation have
been found by the least square fitting to the measure-
ments obtained between 1997 and 2000, i.e., when both
projects observed the LMC fields at the same time.
2.1. Searching for orbital periods different than the LSP
Searching for ellipsoidal or eclipsing variability with
differentperiods thanthe LSP wasarelativelyeasypro-
cedure. For each object a third order Fourier series was
fitted to the LSP light curve and subtracted from the
points. Then, the period search was performed for the
residual data. This procedure was repeated until four
additional periods per star have been found.
From these results I selected and visually inspected
light curveswith periods lying betweensequences C and
D,i.e.,whereonecanexpectellipsoidaloreclipsingvari-
ables (automatic procedure gives a half of orbital peri-
ods). Thebestsevenlightcurvesofthattypeareplotted
in Fig. 1. Phased LSP light curves are shown in the left
column, the right column presents the light curves of
these objects after subtracting the LSP variations and
phased with periods two times longer than obtained au-
tomatically.
As one cansee none ofthese secondarymodulations is
distinct, indisputable eclipsing or ellipsoidal light curve.
The most likely explanation of these modulations are
variations of phases or amplitudes of the LSP variabil-
ity which produce such “artificial”variability in residual
light curves. A very similar behavior occurred in eclips-
ing binary described in Section 3. Fig. 1.— Light curves of LSP stars with secondary periods in
thebinarityrange. Leftcolumnshowslightcurvesfoldedwiththe
LSP, and right column presents these data after subtracting the
2.2. Searching for orbital periods the same as the LSP LSPvariabilityandfoldedwithdifferentperiods.
If the LSP is related to binarity, one can expect that They studied MACHO BM and RM photometry of long
a number of objects shows ellipsoidal or eclipsing vari- period variables in the LMC and found that blue-to-
abilityofthesameperiodastheLSP.Unfortunately,de- redamplitude ratiosaredifferentforellipsoidalandLSP
tecting such a modulation in the LSP light curves is not variables. In the ellipsoidal red giants, where the vari-
aneasytask,because(i)the ellipsoidallightcurveshave ability is dominated by the geometric changes, ampli-
usually much smaller amplitudes than LSP, (ii) shorter tudes in different filters are very similar. The median
semiregular variability is superimposed, (iii) the LSP value of A(BM)/A(RM) is equal to 1.1. For the LSP
light curves often change amplitudes, phases and peri- stars A(BM)/A(RM) is more similar to pulsating vari-
ods. A careful investigation of the LSP light curves re- ables and equal on average to 1.3. It means that if the
vealsthatsomeofthemshowshallowsecondaryminima, amplitudes of the RM-band light curves are scaled by a
whatmaybeasignofellipsoidalvariationssuperimposed factor 1.3 and the BM observations are subtracted, the
on the LSP. However,since the LSP light curves appear LSP variations will be canceled, but not the possible el-
inseveralvariants,itispossiblethatsuchbehaviorisnot lipsoidal/eclipsing modulation.
related to binarity. The procedure was as follows. The BM and RM-band
ToseparateLSPandpossibleellipsoidal/eclipsingvari- amplitudesweredeterminedbyfittingthesplinefunction
ations I used a feature noticed by Derekas et al. (2006). to the folded light curves. Then, the RM magnitudes
were converted into flux and linearly scaled to obtain
2 http://wwwmacho.mcmaster.ca/Data/MachoData.html the sameamplitude (in magnitudes)asin theBM band-
Long Secondary Periods and Binarity in Red Giant Stars 3
Fig. 2.— Six LSP star exhibiting additional double-humped variations. Upper diagram in each panel shows MACHO RM-band
photometry,middlediagramcontainsBM-banddata,lowerdiagrampresentstheresidualdataafterscalingRM andsubtractingBM light
curves. The dashed lines show the phases of minimum brightness during the LSP variations. Note that each light curve of given star is
foldedwiththesameperiod.
pass. Thefluxwasagainconvertedintomagnitudes,and residual points. However, for about 5% of stars I found
BM measurements were subtracted point by point from clearperiodsequaltohalftheLSP,i.e. Inoticeddouble-
scaledRM data. The final step of the procedure was fit- humped curves with periods the same as of the LSP.
ting a sinusoid of a period 1 year, and subtracting the All these residual data are available from the electronic
function from the residual data. This way I removed a edition of the Astrophysical Journal. The most promi-
differentialrefractioneffectdistinctly visibleinMACHO nent curves of this type are presentedin Fig. 2. In these
data. cases the residual data seem to arrange in eclipsing-like
For the vast majority of light curves the LSP and pul- or ellipsoidal-like light curves.
sation(semiregular)variability subtracted verywell. No Fig. 3 shows period–WI diagram (where WI = I −
significant long-period variability was detectable in the 1.55(V −I) is the reddening-free Wesenheit index) for
4 Soszyn´ski
lipsoidal/eclipsing light curves. Consistent results were
presentedbyWood et al.(2001),whodiscoveredaphase
D lagof∼1/8betweenLSPlightcurvesandradialvelocity
curves. Such phase offsets between ellipsoidal/eclipsing
and LSP minima agree very well with hydrodynamical
simulationsofawinddrivenaccretionflowinbinarysys-
tems (Theuns & Jorissen 1993; Mastrodemos & Morris
1998; Nagae et al. 2004). These models predict that a
matter lostby a redgiantin a binarysystem follows the
spiralpatternwithmaximumdensitylocatedbehindthe
secondary component.
An exhaustive discussion about possible origins of the
LSP was done by Wood et al. (2004). They argued that
the mergertimescalefor redgiantsandits companionin
E close binary systems is of the order of 103 years, while
thelifetimeintheAGBphaseistwoordersofmagnitude
longer. Thus, 30% of SRVs showing the LSP is highly
inconsistent with the binary scenario.
However,the mass transfer in a binarysystem may be
due to the Roche-lobe overflow (e.g. Paczyn´ski 1971),
or through the stellar wind (e.g. Anzer et al. 1987;
Fig. 3.— Period–WI diagram for the LSP stars and ellipsoidal
Theuns & Jorissen 1993). The former process tends to
redgiants intheLMC.Crossesshowthe LSPstars(sequence D),
emptycirclesindicateellipsoidalredgiants(sequenceE),filledcir- circularize the orbits and to synchronize the spin of the
clesmarktheLSPstarswithdouble-humpedcurvesvisibleinresid- starswiththeorbitalrotation,whichresultsinshrinking
ualdata. the orbits and finally in merging the components. The
stars from sequences D and E. Full circles show the po- latterphenomenonincreasestheeccentricityoftheorbits
sition of the LSP stars with the double-humped curves. and,ifthebulkofthemasslostbytheredgiantsescapes
Notethattheseobjectsappearalongthecompletelength from the system, the distance between components may
of sequence D, although there is an overdensity for even increase. Thus, the main argument of Wood et al.
shorter-periodstars, i.e. where sequences D and E over- (2004) against the binary explanation may be not valid,
lap. Note also that double-humped objects populate ifweassumethattheredgiantsinthebinarysystemsdo
both, O-rich and C-rich, sequences of the LSP stars notfullyfilltheirRochelobe,andthebulkofmasstrans-
(Soszyn´ski et al. 2005). fer is driven by the stellar wind. The non-sinusoidal ra-
It is worth mentioning that the described procedure dialvelocity curves observedby Hinkle et al.(2002) and
doesnotdemandanyassumptionsconcerningperiodsor Wood et al. (2004), which can be explained by the ec-
light curve shapes. It is a simple transformation, the centricity of the orbits, are in good agreement with this
same for each observing point. The only parameter of scenario.
thistransformationisablue-to-redamplituderatioofthe Presentedhypothesisneverthelessrequiresthatatleast
LSP variability, but I checked that the double-humped 30% of AGB stars exist in close binary systems. More-
residual light curves are visible for relatively wide range over,whilethestudiedLSPvariableshavevelocityampli-
ofthis parameter,soitis notveryimportanttomeasure tudesofonlyafewkm/s(Hinkle et al.2002;Wood et al.
amplitudes very accurately. 2004), the confirmed binary systems (sequence E stars)
appeartohavevelocityamplitudesabouttentimeslarger
(Adams et al. 2006). The radial velocity measurements
3. DISCUSSION suggest that the second component in the LSP stars
I have shown that about 5% of sequence D objects may be a brown dwarf. Retter (2005) proposed that
haveellipsoidaloreclipsing-likemodulationwithperiods the Jupiter-like planets may accrete the matter from its
the same as the LSP. In the sample of 1200 sequence hoststarandincreasemassintothebrowndwarfsrange.
DstarsI didnotfind anydistinct ellipsoidalor eclipsing This hypothesis would explain such large number of the
binarywithperioddifferentthantheLSP.Althoughvar- LSP cases among AGB stars, if we assume that plan-
iousscenariosarestillpossible,itisjustifiedtore-invoke ets with a separation of 1–5 AU are common. To test
the binary hypothesis proposed by Wood et al. (1999). the binaryhypothesis itwouldbe interestingto measure
In this explanation the AGB star in a close binary sys- the radial velocity changes for the LSP stars with the
temlossesmasstothesecondarycomponent. Thematter double-humped variations. If these stars are ellipsoidal
forms a dusty cloud around and behind the companion or eclipsing variables indeed, their velocity amplitudes
and regularly obscures the primary star. should be similar to these observed in sequence E stars,
An argument for this hypothesis is a phase lag be- i.e. significantlylargerthanfortheremainingLSPstars.
tweenellipsoidal/eclipsingandtheLSPvariationsclearly The brown dwarf scenario can also explain why only
visible in Fig. 2. Only one object of six – the star 5% of our sample show the double-humped variability.
with the shortest period – does not exhibit such be- For low-mass secondary components the ellipsoidal and
havior. I checked that it might be a rule for the eclipsing variations have too small amplitudes to be de-
shortest period sequence D variables. For longer peri- tected in our procedure. One should remember that the
ods the minima of the LSP brightness variation occur residual data obtained by scaling RM and subtracting
about 0.05–0.10 of a cycle after the minima of the el- BM magnitudes can show variability with amplitudes of
Long Secondary Periods and Binarity in Red Giant Stars 5
Fig. 4.— Three upper panels show LSP stars with variable amplitudes. In the lower panel the probable eclipsing binary is presented.
Leftandrightdiagramscontainunfoldedandfoldedlightcurves,respectively.
about0.2oftheoriginalellipsoidalamplitudes(RM were by an analysis of typical and peculiar cases of the light
scaled by a factor of 1.3 and A(BM)/A(RM) is on av- curves. A common feature of the LSP variations is the
erage 1.1 for ellipsoidal variables). Moreover, presented modulation of the amplitudes and phases. A few such
modeldoesnotassumethattheredgiantfillsentirelythe light curves are shown in in Fig. 4. It seems that the
Rochelobe,becausethebulkofthemassflowisthrough phase shifts are correlated with the depth of minima –
astellarwind,sotheseparationbetweenthecomponents the deeper minimum occurs earlier than the shallower
can be too large to cause significant ellipsoidal variabil- one (see the folded light curve in Fig. 4a). Sometimes
ity. Note also that observed number of possible ellip- the LSP variations completely disappear or appear in
soidalandeclipsingvariablesamongtheLSPvariablesis red giants which did not show such modulation before
in agreement with relative number of sequence E stars. (Fig. 4b). The conclusion that can be drawn from these
The LSP modulation is observed for about 30% of the cases is that the regular (with no LSP) apparent lumi-
AGB stars, so 5% of these objects gives about 1-2% of nosity of the red giants is the same as in the maximum
the wholepopulation. Exactlythe samerelativenumber apparent luminosity of the LSP variations, i.e. the LSP
ofellipsoidaloreclipsing variables is observedfor fainter phenomenon decreases the total luminosity of the star.
red giants (Soszyn´ski et al. 2004), so one should not ex- Thisfactmustbetakenintoconsiderationbyanytheory
pect to detect many more such objects among brighter of the LSP variability.
stars. The hypothesis of a binary system with a mass-losing
Of course, it cannot be absolutely excluded that AGB star seems to agree with these results, because the
the double-humpedvariationshavedifferentexplanation obscuration by a cloud of matter reduces the total lu-
than the binarity. However, the non-binarity model of minosity of the star. The amplitude and phase changes
theLSPphenomenonhastoexplainwhyproducedresid- arelikelyconnectedwiththe variablemasslossrate. An
ual light curves have ellipsoidal or eclipsing-like shapes, interestingLSPlightcurveispresentedinFig.4c. Start-
why it appears only in a few percent of the sequence ingfromthebeginningoftheobservationsthedepthand
D stars, and why there is phase lag between LSP and width of the minima were increasing. After a few cycles
double-humped variations. All these facts can be ex- thisprocessaffectedthemaximumofthelightcurve,and
plained by the binary scenario. thetotalapparentopticalluminosityofthestardropped
Additionalclues on the originof the LSP canbe given down. Then, the object returned, more or less, to the
6 Soszyn´ski
previous stage. This behavior can be interpreted as a tinuation of “binary” sequence E) is a projection of a
sudden rise of a mass loss rate, which caused the whole radius–luminosity relation for red giants. Positive cor-
system to be hidden in the cloud of matter. relation between amplitudes of the LSP variability and
In Fig. 4d I show a probable eclipsing binary system mean luminosity (Soszyn´ski et al. 2004; Derekas et al.
with the AGB star as one of the components. This ob- 2006) may be caused by the increasing mass loss rate
jectpresentsstrikingsimilaritiestothe LSPstars. First, with the luminosity. The dimming during the LSP min-
it is located in the sequence D in the PL diagram. Sec- imaareconsistentwiththeobscurationbyadustycloud
ond, the light curve changes the amplitudes and phases of matter orbiting the red giant. Finally, the radial ve-
ofvariations. Third,aftersubtractingafunctionfittedto locity variations are in agreement with eccentric motion
the primary (eclipsing) variability I obtained secondary ofthelow-masscompanion. Thelong-termprojectofra-
long-periodvariationscausedprobablybymodulationof dial velocity measurements of selected sequence D stars
the primary period. The same behavior I observed for have been recently finished (P. Wood, private communi-
the LSP stars presented in Fig. 1. cation). I expect that these data will definitively solve
the LSP problem.
4. SUMMARYANDCONCLUSIONS
In this paper I show that careful analysis of available
data may shed new light on the nature of the last un-
explained type of stellar variability. Arguments in favor
IamdeeplygratefultoProfessorsW.D.Dziembowski,
ofthe binaryexplanationoftheLSPphenomenonareas
B. Paczyn´ski, A. Udalski, and Dr. Z. Ko laczkowski for
follows:
the careful and critical reading of the manuscript and
1. There are no reliable examples of the LSP stars many useful discussions. I thank the anonymous referee
with ellipsoidal or eclipsing variations with differ- for helpful comments. The paper was supported by the
ent periods. FoundationforPolishSciencethroughthe“HomingPro-
gramme”.
2. At least 5% of the sequence D stars exhibit ellip- This paper utilizes public domain data obtained by
soidaloreclipsing-likevariabilitywiththesamepe- the MACHO Project, jointly funded by the US Depart-
riod as the LSP. ment of Energy through the University of California,
LawrenceLivermoreNationalLaboratoryundercontract
3. Phase lag between ellipsoidal and LSP variations
No. W-7405-Eng-48,bytheNationalScienceFoundation
agreeswellwithmodelsofwindaccretioninbinary
throughthe Center for Particle Astrophysics of the Uni-
systems.
versity of California under cooperative agreement AST-
4. The LSP lightcurveswithvariableamplitudes can 8809616, and by the Mount Stromlo and Siding Spring
be explainedby a variable mass-lossrate in binary Observatory,part of the Australian National University.
systems. This publication is partly based on the OGLE obser-
vations obtained with the Warsaw Telecope at the Las
The binary scenario can explain many features of the CampanasObservatory,Chile,operatedbytheCarnegie
LSP variables. The PL relation (which is a direct con- Institution of Washington.
REFERENCES
Adams, E., Wood, P. R., & Cioni, M.-R. 2006, Memorie della Soszyn´ski, I., Udalski, A., Kubiak, M., Szyman´ski, M. K.,
SocietaAstronomicaItaliana, 77,537 Pietrzyn´ski, G., Z˙ebrun´, K.,Szewczyk, O.,Wyrzykowski, L ., &
Anzer,U.,Boerner,G.,&Monaghan,J.J.1987,A&A,176,235 Ulaczyk,K.2005,ActaAstron.,55,331
Derekas, A.,Kiss,L. L.,Bedding, T.R., Kjeldsen,H., Lah, P.,& Theuns,T.,&Jorissen,A.1993,MNRAS,265,946
Szabo´, G.M.2006,ApJ,650,L55 Wood, P. R., et al. 1999, in IAU Symp. 191: Asymptotic Giant
Hinkle,K.H.,Lebzelter,T.,Joyce,R.R.,&Fekel,F.C.2002,AJ, BranchStars,eds.T.LeBertre,A.L´ebre,andC.Waelkens(San
123,1002 Francisco:ASP),151
Houk,N.1963,AJ,68,253
Wood, P. R., Axelrod, T. S., & Welch, D. L. 2001, ASP
Mastrodemos,N.,&Morris,M.1998,ApJ,497,303
Conf.Ser.229: EvolutionofBinaryandMultipleStarSystems,
Nagae, T., Oka, K., Matsuda, T., Fujiwara, H., Hachisu, I., &
eds.Ph.Podsiadlowski,S.Rappaport,A.R.King,F.D’Antona,
Boffin,H.M.J.2004,A&A,419,335
andL.Burder,233
Olivier,E.A.,&Wood,P.R.2003,ApJ,584,1035
Wood,P.R.,Olivier,E.A.,&Kawaler,S.D.2004,ApJ,604,800
Paczyn´ski,B.1971,ARA&A,9,183
Payne-Gaposhkin, C.1954,HarvardAnnals,113,No.4
Retter, A. 2005, Bulletin of the American Astronomical Society,
37,1487
Soszyn´ski, I., Udalski, A., Kubiak, M., Szyman´ski, M. K.,
Pietrzyn´ski, G., Z˙ebrun´, K.,Szewczyk, O., Wyrzykowski, L .,&
Dziembowski,W.A.2004, ActaAstron.,54,347