A New Diagnostic of the Radial Density Structure of Be Disks

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by  Zachary H. Draper

Accepted inApJL
PreprinttypesetusingLATEXstyleemulateapjv.11/12/01
A NEW DIAGNOSTIC OF THE RADIAL DENSITY STRUCTURE OF BE DISKS
Zachary H. Draper1, John P. Wisniewski1,2, Karen S. Bjorkman3, Xavier Haubois4, Alex
C. Carciofi4, Jon E. Bjorkman3, Marilyn R. Meade5, Atsuo Okazaki6
Accepted inApJL
ABSTRACT
WeanalyzetheintrinsicpolarizationoftwoclassicalBestarsintheprocessoflosingtheircircumstellar
1 disks via a Be to normal B star transition originally reported by Wisniewski et al. During each of five
1 polarimetric outbursts which interupt these disk-loss events, we find that the ratio of the polarization
0 across the Balmer jump (BJ+/BJ-) versus the V-band polarization traces a distinct loop structure as a
2 function of time. Since the polarizationchangeacrossthe Balmer jump is a tracerof the innermostdisk
density whereas the V-band polarization is a tracer of the total scattering mass of the disk, we suggest
n
a such correlatedloop structuresin Balmer jump-V bandpolarizationdiagrams(BJV diagragms)provide
J a unique diagnostic of the radial distribution of mass within Be disks. We use the 3-D Monte Carlo

8 radiation transfer code HDUST to reproduce the observed clockwise loops simply by turning “on/off”
1 themassdecretionfromthedisk. Wespeculatethatcounter-clockwiseloopstructuresweobserveinBJV
diagrams might be causedby the mass decretion rate changing between subsequent “on/off” sequences.

] Applying this new diagnostic to a larger sample of Be disk systems will provide insight into the time-
R
dependent nature of each system’s stellar decretion rate.
S
Subject headings: circumstellar matter — stars: individual (pi Aquarii) — stars: individual (60 Cygni)
.
h
p
- 1. introduction different physical regions of disk, demonstrate how the
o radial-dependence of the gas density in these disks can
ClassicalBestarsarewellknowntobecharacterizedby
r be observationally constrained. Such works offer promise
t havinggaseouscircumstellardecretiondiskswhicharefed
s for testing the appropriateness of the single power-law
a from mass-loss from their rapidly rotating central stars
adopted by most models.
[ (Porter & Rivinius 2003). As detailed in the review of
Some classical Be stars can exhibit stable decretion
Carciofi (2010),theviscousdecretiondiskmodel(VDDM;
1 disks for decades (e.g ζ Tau; Stefl et al. 2009); however,
Lee et al. 1991) is adept at explaining many of the ob-
v they are also known to experience aperiodic “Be to nor-
1 servational properties of Be star disks, including the ob-
mal B to Be” transitions whereby they lose (and subse-
7 served Keplerian rotation of the disk, and is generally
quently regenerate) all observational signatures of hav-
5 considered the most promising model to explain the Be
ing a disk (Underhill & Doazan 1982; Clark et al. 2003;
3 phenomenon, although alternate models also have been
Vinicius et al. 2006). The frequency of these transitions
. proposed (Bjorkman & Cassinelli 1993; Cassinelli et al.
1 is not well constrained by observations, although the dis-
0 2002). The mechanism(s) responsible for ejecting mate-
covery of 12 new transient Be stars in multi-epoch study
1 rial from the stellar photosphere into a disk is also un-
of eight open clusters suggests that these major events
1 kown, although both observational (Rivinius et al. 1998;
are not rare (McSwain et al. 2009). These systems rep-
: Neiner et al. 2002) and theoretical (Ando 1986; Cranmer
v resent ideal testbeds to diagnose the fundamental mech-
2009)studies suggestthatnon-radialpulsationsmightact
i anism which drives disk formation in Be stars precisely
X to feed at least some of these decretion disks.
because they are known to be actively losing (or gaining)
r While some classical Be stars exhibit observational
a evidence of large-scale asymmetries (Okazaki 1997; a disk. Studying such disks with techniques capable of
diagnosingthe radial-dependence of the gas density, espe-
Vakili et al. 1998; Stefl et al. 2009) interpreted as arising
cially in the inner-most regions of the disk, could enable
from one-armed density waves (Okazaki 1991), the gen-
an enhanced understanding of how these disks form.
eralgasdisk density hastypically beenmodeledby avery
In paper I of this series (Wisniewski et al. 2010), we
simple axisymmetric power law (see e.g. Bjorkman 1997;
analyzed ∼15 years of spectropolarimetric observations
Porter 1999). Recent contemporaneous optical-infrared
of the classical Be stars 60 Cygni and π Aquarii which
(IR) spectroscopic (Wisniewski et al. 2007a), polarimet-
covered one disk-loss episode in each star, and discussed
ric (Carciofi et al. 2007), and optical-IR interferometric
the time-scale and overall evolution of these events. In
studies (Tycner et al.2006; Gies et al.2007; Tycner et al.
this paper, we present a first look at the behavior of
2008; Pott et al. 2010), which are each most sensitive to
1 DepartmentofAstronomy,UniversityofWashington, Box351580Seattle, WA98195,USA,[email protected],[email protected]
2 NSFAstronomy&AstrophysicsPostdoctoral Fellow
3 Ritter Observatory, Department of Physics & Astronomy, Mail Stop 113, University of Toledo, Toledo, OH 43606,
[email protected], [email protected]
4InstitutodeAstronomia,Geof´ısicaeCiˆenciasAtmosf´ericas,UniversidadedeS˜aoPaulo,RuadoMata˜o1226,CidadeUniversit´aria,05508-900,
S˜aoPaulo,SP,BRAZIL,carciofi@usp.br,[email protected]
5 SpaceAstronomyLab,UniversityofWisconsin-Madison,1150UniversityAvenue, Madison,WI53706, [email protected]
6 FacultyofEngineering,Hokkai-Gakuen University,Toyohira-ku,Sapporo062-8605, Japan,[email protected]
1
2
the intrinsic polarization during these events and detail a loop-like structures in Balmer jump-V band polarization
uniquenewdiagnosticwhicheffectivelytracesthegasden- diagrams (hereafter BJV diagram) for both 60 Cyg (Fig-
sity in the inner-most region of the disk. We investigate ure 1, top middle panel) and π Aqr (Figure 1, bottom
these“polarization-loop”signatureswithawellvetted3-D middle panel). The outburst responsible for each of these
MonteCarloNLTEcodeandpresentrepresentativemodel loopsaredepictedinthetopandbottomleftpanelsofFig-
runswhichreproducetheobservationsandsupportourin- ure 1. The duration of the depicted outburst in π Aqr is
terpretation of this phenomenon. Finally, we outline our ∼180daysandtheevolutionofthepolarizationacrossthe
plans to perform more detailed modeling of these signa- Balmerjumptracesaclockwiselooppatternasafunction
tures. ofV-bandpolarization. The durationofthe depicted out-
burst in 60 Cyg is ∼770 days and while the polarization
2. observations traces a clockwise loop pattern during the initial stages
of the outburst, it traces a partial counter-clockwise loop
π Aquariiwasobserved127times between1989August
pattern during the latter stages of the outburst. We find
8and2004October10and60Cygniwasobserved35times
similarclockwiseloopmorphologiesforoneadditionalpo-
between 1992 August 3 and 2004 September 26 with the
larimetric outburst in π Aqr which lasted for ∼160 days,
University of Wisconsin’s (UW) HPOL spectropolarime-
and a counter-clockwise loop morphology for another π
ter,mountedonUW’s0.9mPineBluffObservatory(PBO)
Aqr outburst which lasted for ∼730 days.
telescope. The full details regarding the observation, re-
While these loops are very prominent in the BJV dia-
duction, and calibration of these data, along with basic
gram (middle panels; Figure 1), we also explored whether
properties of the total (interstellar + intrinsic) polariza-
these morphological features would be detectable if one
tion, are presented in Wisniewski et al. (2010), hereafter
simply had broad-bandfilters attheir disposal. We there-
referred to as paper I or WIS2010. In this paper we an-
fore binned ourspectropolarimetricdata to reproduce the
alyze the intrinsic polarization of these data, which were
coverage of the Johnson U- and B-filters, and plotted
obtained by removing the interstellar polarization com-
our data on a (B-filter/U-filter) versus V-filter (hereafter
ponent described in Table 5 of WIS2010 using a modified
BUV)diagram. AsseenintherightpanelsofFigure1,the
Serkowskilaw(Serkowski et al.1975;Wilking et al.1982).
same looplike structures are visible in BUV diagrams (as
We note that the residual instrumental systematic errors
BJV diagrams), albeit at lower amplitude. We therefore
depends mildy on the date of the observationsand ranges
suggest that moderately high precision filter polarimetry
from 0.027-0.095%in the U-band, 0.005-0.020%in the V-
couldalsoprovidethesameeffectivediagnosticasafforded
band, and 0.007-0.022%in the I-band.
by our spectropolarimetric data.
3. results: a new disk density diagnostic
4. discussion
Spectropolarimetry can provide insight into the density
4.1. Modeling the Observed Phenomenon
structure of circumstellar envelopes (see e.g. Bjorkman
2000). Pre- or post-scattering absorption of these As mentioned in the introduction, the viscous decre-
photons by hydrogen in the disk can imprint the tion disk model (VDDM) is currently the most promising
wavelength-dependent opacity signature of hydrogen in candidate to explain the structure, formation and evo-
the polarization if the density of absorbers is signifi- lution of Be disks. While most theoretical approaches
cant (Wood et al. 1996b), producing a “saw-tooth” like so far considered the case of a constant mass decretion
wavelengthdependentpolarizationsignature(Wood et al. rate in the quasi-steady state limit (e.g., Bjorkman 1997;
1997;Wisniewski et al.2007b). Thuswhiletheoverallpo- Bjorkman & Carciofi 2005), more recent studies investi-
larizationis a tracer ofthe electronnumber density, or ef- gated the temporal evolution of the disk surface den-
fective mass of a Be disk, the polarization change across sity fed by an arbitrary mass decretion history (Okazaki
the Balmer jump is a tracer of the largest densities of the 2007; Jones et al. 2008). Here we qualitatively investigate
disk, which are typically found in their innermost regions. whether the VDDM can account for the trends we see in
With thesebasicprinciplesinmind, webeginouranalysis BJV diagrams.
of the intrinsic spectropolarimetric dataset of WIS2010. In order to theoretically reproduce the observed trends
WIS2010 detailed how the gradual disk-loss episodes of shown in Figure 1 with the VDDM model we used a 1-D
60CygandπAqrproceededoveratimescaleof∼1000and hydrodynamicalcode(Okazaki2007)tocomputethetime-
∼2400 days respectively, and how these events were tem- dependent surface density of the disk. This code solves
porarilystalledbyseveralpolarimetricoutbursts(leftpan- the viscous diffusion problem given a prescription for the
els Figure 1; see also WIS2010). We examined the behav- stellar mass decretion rate, and a value for the disk kine-
iorofeachoftheseeventsinstandardJohnsonbroad-band matic viscosity (the α parameter of Shakura & Sunyaev
filters, createdby binning our spectropolarimetric data to 1973). The surface density for chosen epochs of the disk
reproduce the coverage of each filter, and in custom fil- evolutionis then fed to our radiativetransfer code hdust
ters such as one which probed the polarization across the (Carciofi & Bjorkman2006)thatiscapableofturningthe
Balmer jump. This Balmer jump (BJ+/BJ-) filter was structuralinformationthusprovidedintoastrophysicalob-
createdsimply by ratioingdata binned betweenthe wave- servables,suchasemergentspectrumorintensitymapson
lengthrange3650-4100˚A(BJ+)and3200-3650˚A(BJ-). the sky.
During polarimetricoutbursts, we detect clearevidence The correlationloops observedin the BJVdiagramcan
that the polarization across the Balmer jump (BJ+/BJ-) be qualitatively reproduced assuming a prescription for
exhibits a distinctive loop-like evolution when compared the mass decretionrate that involves alternating cycles of
to the V-band polarization. We show examples of such activity (mass decretion on) and quiescence (mass decre-
3
tion off). One such an example is shown Fig. 2. Start- 4.3. Implications and Future Applications of the
ing from no preexisting disk, this sample model assumes Technique
a 3-year long period of activity followed by a 3-year long
The steady-state (Bjorkman & Carciofi 2005) and time
quiescence. This 6-year cycle were repeated many times.
dependent (Okazaki 2007) surface density of Be disks is
In Fig. 2 we show results covering the period between 32
driveninlargepartbytheratioofthestellarmass-lossrate
and 39 years after the beginning of disk formation. The
and the α parameter (both quantities setting the disk de-
polarization forms a clockwise loop in the BJV diagram
cretion rate), although recent modeling work has demon-
that can be described as follows. At the end of the active
strated that the disk temperature can also influence the
phase, the star had built a large and dense circumstellar
surface density, especially in the inner disk regions, when
disk (phase 1). When the mass decretion stops, the inner
thestellarmass-lossrateislarge(Carciofi et al.2008). As
disk quickly reaccretes back onto the star; this causes a
Carciofi et al. (2009) noted, observationally constraining
fast drop of BJ size and the curve follows a track towards
the stellar mass-loss rate is very challenging for systems
the bottom-left of the BJV diagram (phase 2). What fol-
whose disks are truncated by binary companions; more-
lows is a slow secular dissipation of the entire disk along
over, constraining the detailed time dependent decretion
which the BJ size changes little (the inner disk having
rate of non-steady state disk systems (e.g. Rivinius et al.
already reachedvery low densities) but the V-bandpolar-
1998)isalsochallenging. TheBJV(andbroad-bandBUV)
ization diminishes as the disk mass decreases (phase 2 to
diagnosticwehaveintroducedinthispaperoffersoneclear
3). When the next cycle of activity begins (phase 3) the
waytobetterdiagnosethedetailedtime-dependentdecre-
inner disk quickly fills up again and the curve eventually
tion rate of Be disk systems. Application of this tech-
reaches back the top of the BJV diagram.
nique,whenthe requisite low-resolutionblue opticalspec-
The detailed shape of the loop depends on several fac-
tropolarimetry(BJVdiagram)orU-andB-bandfilterpo-
tors: the viewing angle (Fig. 2), the value of α, and the
larimetry is available, to a larger sample of Be systems
mass decretion history assumed. In the simple model
actively gaining/losing their disks would help elucidate
shown here the loops nearly close, because the mass de-
the mechanism(s) responsible for triggering disk forma-
cretion rate assumed for each cycle is the same. The loop
tion in Be stars. We encourage the community to obtain
would not close if the mass decretion rate of subsequent
this type of well time sampled polarimetry for the mid-
cycles were to be different and/or if the length of the ac-
2011 periastron passage of δ Sco, as it would be provide
tive/quiescentphaseswereirregular. Weplantosystemat-
a powerful diagnostic of the type of decretion outbursts
icallyexplorealargerangeofmassdecretionratescenarios
which have been reported in previous periastron passages
in a future publication (Haubois et al 2011,in prep).
(Miroshnichenko et al.2001,2003). Moreover,inclusionof
simpleV-bandphotometryinsuchanalysiscouldhelpob-
servationally determine the α parameter (Carciofi 2010).
4.2. Comparison with CMD loops 5. summary
de Wit et al. (2006) studied the photometric variabil- We have analyzed the intrinsic polarization of 60 Cyg
ity of several hundred Be stars in the Magellanic Clouds and π Aqr as they were in the process of losing their
andfound∼100starswhosephotometricvariationstraced circumstellar disks via a Be to normal B star transition.
loop-like patterns in optical color magnitude diagrams During each of five polarimetric outbursts which interupt
(CMDs). Most (∼90%) objects traced clockwise loops in these disk-loss events, we find that the ratio of the po-
these CMDs while ∼10% traced counter-clockwise loops. larization across the Balmer jump (BJ+/BJ-) versus the
de Wit et al. (2006) suggested that clockwise loops were V-band polarization traced distinct loop structures as a
indicativeofsystemsactivelydecretingmaterialfromtheir functionoftime,andsuggestthatthisdiagnosticprovides
stellar surfaces whereas counter-clockwise loops were in- unique insight into the radial distribution of mass within
dicativeofsystemsinwhichmaterialwasbeingre-accreted Be disks. We observed two clockwise and one counter-
onto the central star. clockwise loop structures in Balmer jump-V band polar-
We note that our models of the loop-like structures we izationdiagrams(BJVdiagragms)ofπ Aqr,while 60Cyg
observeinBJVdiagramsincludetheeffectsofbothdecre- exhibitedacombinedclockwiseandcounterclockwiseloop
tion of materialfrom the centralstar and the re-accretion (i.e. a “figure eight”). We use the 3-D Monte Carlo ra-
of material onto the central star. Hence the large-scale diation transfer code HDUST to reproduce the observed
morphological differences we observe, i.e. clockwise ver- clockwiseloopssimplybyturning“on/off”themassdecre-
sus counter-clockwise loops in BJV diagrams, can not be tion from the disk, and speculate that counter-clockwise
simply attributed to differences in the radial direction of loopstructuresmightbecausedbythemassdecretionrate
motion of material in the disk as invokedby de Wit et al. changingbetweensubsequent“on/off”sequences. Current
(2006). Rather, we speculate that the counter-clockwise andfutureexplorationoftheparameterspaceofourmod-
loops we sometimes observe in BJV diagrams might be els (Haubois 2010; Haubois et al 2011 in prep) will help
caused by a non-constant mass decretion rate or two efforts to identify the definitive origin of these counter-
nearby cycles which have significantly different mass de- clowckwise loop structures.
cretion rates. Our future systematic exploration of the
parameter space of our models (Haubois et al 2011, in We thank Brian Babler for his assistance with HPOL
prep) will enable us to test this speculative hypothesis, data, and Kenneth H. Nordsieck for providing access to
as well as other mass ejection scenarios, to explain these the HPOL spectropolarimeter. We also thank our referee,
counter-clockwise loops. David Harrington,for his suggestions which improvedthe
4
clarityandcontentofthis paper. JPWacknowledgessup- theUniversityofToledo. ACCacknowledgessupportfrom
port from NSF Astronomy & Astrophysics Postdoctoral CNPq (grant 308985/2009-5). XH acknowledges support
Fellowship AST 08-02230 and a Chretien International from Fapesp (grant 2009/07477-1). HPOL observations
Research Grant. ZHD was supported by the University were supported under NASA contract NAS5-26777 with
of Washington Pre-MAP program, a UW College of Arts the University of Wisconsin-Madison.
and Sciences Research Scholarship, and a NSF REU at
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5
Fig. 1.—Thetimeevolutionoftheintrinsicpolarizationof60Cyg(toppanels)andπAqr(bottompanels)isshown. 60Cygischaracterized
by a ∼770 day polarimetric outburst denoted by large, open green circles (top left panel). A clock-wise loop pattern in 60 Cyg’s Balmer
jump-V band polarization diagram (BJV diagram; top middle panel) is observed during the early stages of the star’s outbust, followed by
a counter-clockwise loop during later stages of the outburst. This loop structure is discernible at lower amplitude when the polarization
ratiooftheJohnson B/U filtersisconsideredasafunctionof theV-bandpolarization(toprightpanel). Thetimeevolution oftheintrinsic
polarizationofπAqrischaracterizedbyseveralpolarimetricoutbursts,includinga∼180dayeventdenotedbylarge,filledredcircles(bottom
leftpanel). Abroadclock-wiselooppatternisseeninπAqr’sBJVdiagram(bottommiddlepanel);thisloopstructureisdiscernibleatlower
amplitudewhenthepolarizationratiooftheJohnsonB/UfiltersisconsideredasafunctionoftheV-bandpolarization(bottomrightpanel).
6
Fig. 2.— Upper panel: BJV diagram at two inclinationangles (solid line, 70 degrees and dashed line, 90 degrees) forthe mass decretion
rate described inSect. 4.1. The corresponding phasenumber isreported inboth panels andobserving epochs areindicated and counted in
years. Lowerpanel: TemporalevolutionoftheV-bandpolarizationandpolarizationacrosstheBalmerjumpforbothinclinationangles. The
dotted lineshowsthemassdecretionhistoryarbitrarilyscaledtotherangeofthegraph.