A Multi-wavelength study of the M dwarf binary YY Geminorum

0.71 MB·English

by  C. J. Butler

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed19January2015 (MNLATEXstylefilev2.2)
A Multi-wavelength study of the M dwarf binary YY
Geminorum
C.J. Butler1 ⋆, N. Erkan2, E. Budding3, J.G. Doyle1, B. Foing4, G.E. Bromage5,
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1 B.J. Kellett6, M. Frueh7, J. Huovelin8, A. Brown9, J.E. Neff10
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2 1Armagh Observatory, College Hill, Armagh, BT61 9DG, N. Ireland, UK
2Physics Dept., C¸anakkale OnsekizMart University,C¸anakkale, Turkey

n 3Carter Observatory,School of Chemical and Physical Sciences, Victoria University,Wellington, NewZealand
a 4ESA, Postbus 299, 2200, AG Nordwijk, The Netherlands
J 5Jeremiah Horrocks Institute, Universityof Central Lancashire, Preston, UK

6 6Space Science and Technology Department, STFC Rutherford Appleton Laboratory, Oxon, UK
1 7McDonald Observatory,3640 Dark Sky Drive, Texas, USA
8Divisionof Geophysics and Astronomy, Department of Physics, Universityof Helsinki, Finland

] 9Centerfor Astrophysics and Space Astronomy, Universityof Colorado, Boulder, CO, USA
R 10Department of Physics and Astronomy, College of Charleston, Charleston, SC, USA
S
.
h
p 19January2015
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o
r ABSTRACT
t
s
a
We review the results of the 1988 multi-wavelength campaign on the late-type
[
eclipsing binary YY Geminorum. Observations include: broad-band optical and near

1 infra-red photometry, simultaneous optical and ultraviolet (IUE) spectroscopy, X-ray
v (Ginga) and radio (VLA) data. From models fitted to the optical light curves,funda-
0 mentalphysicalparametershavebeendeterminedtogetherwithevidencefortransient
3
maculations (spots) located near quadrature longitudes and intermediate latitudes.
9
Eclipses were observed at optical, ultraviolet and radio wavelengths. Significant
3
drops in 6cm radio emission near the phases of both primary and secondary eclipse
0
indicate relatively compact radio emitting volumes that may lie between the binary
.
1 components. IUE observations during secondary eclipse are indicative of a uniform
0
chromosphere saturated with MgII plage-type emission and an extended volume of
5 Lyα emission.
1 Profilefittingofhigh-dispersionHαspectraconfirmsthechromosphericsaturation
:
v and indicates significant Hα opacity to heights of a few percent of the photospheric
i radius.There is evidence for an enhancedHα emissionregionvisible near phase 0.25-
X
0.35 which may be associated with a large spot on the primary and with two small
r
optical flares which were also observedat other wavelengths:one in microwaveradia-
a
tionandtheotherinX-rays.Forbothflares,L /L isconsistentwithenergyrelease
X opt
in closed magnetic structures.
Key words: Stars: late-type; binaries; eclipsing; flare; starspots
1 INTRODUCTION the brightest known eclipsing binary of the dMe type, YY
Gemisanimportantfundamentalstandardfordefiningthe
YYGeminorum,(BD+321582,SAO60199,Gliese278c),is
low-mass Main Sequence mass-luminosity and mass-radius
ashortperiod(19.54hours)eclipsingbinarywithtwoalmost
relationships (Torres & Ribas, 2002). However, it was clear
identical dM1e (flare star) components. The close binary is
alreadyfromKron’s(1952)pioneerstudythattherearesig-
a subsystem of the nearby Castor multiple star (YY Gem
nificantsurfaceinhomogeneities(starspots)affectingtheob-
= Castor C), at a distance of ∼14.9 pc. The binary nature
served brightness of both components, likely to complicate
was discovered in 1916 (Adams & Joy, 1917) and the first
data analysis. YY Gem was the first star, after the Sun, in
spectroscopicorbitsweregivenbyJoy&Sanford(1926).As
whichsuchmaculationeffectsweredemonstrated.Beforewe
canaccurately definetheintrinsicluminosities ofsuchstars
weneed to clarify thescale of these effects.This is also sig-
⋆ E-mail:[email protected]
(cid:13)c 0000RAS
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nificant for comparing thephotometric parallax with direct
Table1.MultiwavelengthObservationsofYYGem,March1988
measurements,suchasthatfromHIPPARCOS(Buddinget
al., 2005).
Institute Observer Facility Range
ThesystemwasreviewedbyTorres&Ribas(2002)and
Qianetal.(2002),thelatterconcentratingmainlyonappar- ISAS-Tokyo Bromage GINGA MEX-rays
ent variations of the orbital period. Torres & Ribas (2002) VILSPA-ESA Foing IUE UV
gaverevisedvaluesforthemeanmassandradiusofthevery MaunaKea Butler UKIRT IR
similar components as (solar units) M = 0.5992±0.0047, MaunaKea Doyle/Butler 0.6m UBVRI
R = 0.6191±0.0057, with mean effective temperature T = McDonaldObs. Frueh 0.9mMCD UBVRI
JILABoulder Brown VLA 5&1.4GHz
3820±100K,aswellasanimprovedparallaxforthesystem
CrimeaObs. Tuominen 2.6mShajn UBVRI+Hα
of66.90±0.63mas.Fromsuchresults,Torres&Ribasargued
that there had been a tendency to adopt systematically er-
roneousparametersfordwarfstarscomparabletoYYGem,
with wider implications for low-mass stars in general.
intention concerns the various light curves and their analy-
Determinationoftheprecisestructureofthesestars,in
sesintermsofstandardeclipsingbinarymodelsthatinclude
viewoftheabsenceofdefinitiveinformationontheirintrin-
photosphericinhomogeneities. Inaddition, wepresent hith-
sic, spot-free, luminosities, is still rather an open question.
ertounpublished,ultraviolet(IUE),radio(VLA)andX-ray
Torres & Ribas (2002) and Qian et al. (2002) revised the
(Ginga) data, which shouldberelevant tosubsequentstud-
work of Chabrier & Baraffe (1995), giving radiative core
ies. A number of optical flares were observed but only two
radiiofabout70%,leavingtheouter30%toaccountforthe
of these were seen at other wavelengths, one in X-rays by
convective zone. The strong subsurface convective motions,
Ginga and theother in the microwave region bythe VLA.
give rise to large-scale magnetic fields that produce large
starspots (cf. Bopp & Evans, 1973). Moffet first reported
large flare events, and, in subsequent studies, YY Gem has
beenshowntobeveryactive(MoffetandBarnes,1979;Lacy 2 THE 1988 MULTI-WAVELENGTH
et al., 1976; Doyle & Butler, 1985; Doyle & Mathioudakis, CAMPAIGN ON YY GEMINORUM
1990; Doyle et al. 1990).
In late February to early March 1988, YY Gem was the
Doyleetal(1990) havepreviouslydescribedphotomet-
object of a coordinated multiwavelength campaign to ob-
ric observations of repetitive, apparently periodic, flares on
serve the star simultaneously in radio, near infra-red, X-
YYGemwhichwereobservedduringthisprogramme.More
rays,UVandopticalradiation(Butler,1988).Theprincipal
recently,Gao et al. (2008) modelled such periodicity effects
objectives of this programme were: (i) To provide multi-
on the basis of magnetic reconnection between loops on
colour photometry of the light curve in order to establish
the two stars generating interbinary flares. Fast magneto-
(a) the distribution of surface inhomogeneities (starspots),
acoustic waves in plasma trapped in the space between the
and (b) the temperature difference of these inhomogeneous
two components are thought to modulate the magnetic re-
regions from the normal photosphere. (ii) To provide high
connection, producing a periodic behaviour of the flaring
time-resolution photometry in V and K during the eclipses
rate. Doyle et al. (1990) had previously suggested filament
in order to check on possible surface inhomogeneities by
oscillations. Several authors, (see Vrsnak et al. 2007) have
‘eclipse imaging’ — i.e. examining any small disturbances
subsequently reported solar filament oscillations of similar
observed in the light curve during eclipses. (iii) To use op-
duration tothose suggested on YYGem.
ticalspectroscopy,X-rayandradiomonitoringtoprobethe
Multi-wavelength observations of flare activity on YY
outer atmospheres of the components and assess any topo-
Gem were initiated byJackson, Kundu& White(1989) us-
graphicalconnectionbetweenphotosphericspotsandbright
ingradio data from theVLA (seealso, Gary,1986). Stelzer
chromospheric or coronal regions. (iv) To monitor flares on
etal.(2002) usedtheChandraandXMM-Newtonsatellites
YYGeminasmanyseparatewavebandsaspossibleinorder
in simultaneous observations of the X-ray spectrum, while
to check theirenergy distribution and constrain models.
Saar & Bookbinder(2003) carried out far ultraviolet obser-
Theprogrammeinvolvedthefacilitiesandobservations
vations. Impulsive UV and X-ray phenomena, taken to be
giveninTable1.Severalotherorganisationsofferedsupport
essentially flare-like, were shown to be orders of magnitude
tothecampaign, butunfortunately a numberof these were
stronger than those occurring on the Sun (Haisch et al.,
unable to provide useful data due to poor observing condi-
1990). Tsikoudi & Kellett (2000), reviewing X-ray and UV
tions. In Figure 1, we show the overlap between observing
observations of the Castor system, reported a large (EX-
facilities that were successful in obtaining data. Seven ma-
OSAT) flare event with total X-ray emission estimated as
jorfacilitiesprovidedthemostrelevantdataandsixofthese
∼7±1×1033 ergs. Their comparison of X-rayand bolomet-
were operativeon Mar 5 and 6, with a few hoursof overlap
richeatingrates pointedtostrongmagnetic activitywithin
on those two days; and to a lesser extent on Mar 4.
hot coronal components.
In this article, we concentrate on the multiwavelength
campaign initiated from the Armagh Observatory in 1988
(Butler,1988).Ourgeneralaimistobringtogetherresultsof 3 UBVRIK PHOTOMETRY
somework,previouslyreported(e.g.Doyleetal.1990,But-
3.1 Photometric Techniques
ler, et al. 1994, 1995, Budding et al. 1996, Tuominen et al.
1989)withcontemporaneoussatelliteandradioobservations To achieve the photometric aims we required broad-band
thereby allowing an overview of the campaign. Onespecific photometry covering as much of the optical and infra-red
(cid:13)c 0000RAS,MNRAS000,000–000
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Figure 1.Time-lineofvariousfacilitiesusedinthemultiwavelengthcampaignof1988
regionsaspossible.Wethereforeoperatedtwotelescopessi- 3.2 UBVRIK photometry from the 0.6m
multaneously: the University of Hawaii 0.6m telescope on telescope on Mauna Kea
Mauna Kea and the neighbouring 3.8m United Kingdom
Infra-RedTelescope(UKIRT).Someadditionalobservations TheUBVRIphotometry,fromthe0.6m telescopeandTins-
were contributed by Marion Frueh of McDonald Observa- leyPhotometer,wasstandardised totheJohnson UBVand
tory,Texas. Cape/KronRIsystemsusingequatorialandsouthernhemi-
sphere standards from Cousins (1980, 1984). The follow-
All observers were alerted to a particular problem as- ing mean extinction coefficients were adopted: κU = 0.22,
sociated with photometry of YY Gem, namely that the κB =0.16, κV =0.12, κR =0.10 andκI =0.07. Duetothe
manual operation of the Tinsley photoelectric photometer,
close proximity (separation ∼71 arcsec) to YY Gem of the
time-resolution for a single complete UBVRI set of mea-
bright star Castor (A2 type, V ∼1.6) makes it difficult to
surementswasrestrictedtoseveralminutes.Thiswassatis-
obtain repeatable and consistent sky background measure-
factory for the slower variations associated with eclipse ef-
ments, particularly in the U and B bands, where YY Gem
fectsandtherotationalmodulationofspots,butunsuitable
is weak and Castor bright. Kron (1952) commented that,
for flare monitoring. Therefore, two modes of observation
in the vicinity of YY Gem, 30% of the monitored blue
were used on this telescope: (1) UBVRI photometry, with
light originated with Castor and only 70% with YY Gem
low time-resolution (∆t ∼ 2m) during eclipses and approx-
itself (Budding & Kitamura 1974). For this campaign, in
imately once per hour at other phases, and (2) continuous
order to reduce the errors associated with scattered light,
U-band monitoring at (mainly) out-of-eclipse phases. Some
observers were requested to take the mean of two adja-
of thelatter data was reported on byDoyle et al. (1990).
cent sky areas, one to the east and another to the west
of YY Gem. Frequent reference to three nearby compar- Because the 0.6m telescope was set manually it seems
ison stars: BD 32◦1577, BD 31◦1611 and BD 31◦1627, to- likelythatsmallerrorsinpositioningofthebackgroundcom-
getherwithstandardtransformationequationsandmeanex- parison region could be responsible for some of the scatter
tinction coefficients allowed a photometric accuracy ∼ 0.01 intheUandBlightcurveswhichincreasesatshorterwave-
magnitudestobeachieved.Lists of thestandardsused,the lengths.However,small,unrecognised,flareswouldalsocon-
colour equations derived and the reduced photometric ob- tributetothescatter.InFigure2,weshowtheUBVRIlight
servations are given in the supplementary electronic tables curvesforYYGemfromthecombineddataobtainedon2-7
(http://star.arm.ac.uk/preprints/2014/654/). March 1988 with the0.6m telescope.
(cid:13)c 0000RAS,MNRAS000,000–000
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7
8
9
e
d
u
t
i
n
g
10
a
M
11
12
2March
3March
4March
5March
6March
7March
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
Phase
Figure 2.Hawaii0.6mUBVRIlightcurvesofYYGem.
3.3 BVK photometry with UKIRT on Mauna Kea are relatively more prominent in V and flare effects in B, it
wasdecidedtomonitorinKandVduringeclipsesandinK
and B at out-of-eclipse phases. Useful coverage of the out-
The United Kingdom Infrared Telescope (UKIRT) was
of-eclipse phases by UKIRTturnedout to be quitelimited,
scheduled to observe on four half-nights, during which two
however. The auto-guider was not functional at this time,
primary and two secondary eclipses occurred. Continuous
resulting in occasional guiding errors. We used the mean
monitoring in the K-band simultaneously with V or B was
atmospheric extinction coefficients given above in carrying
made possible with a dichroic filter and VISPHOT, a pho-
out the differential reductions (see also Krisciunas et al.,
toelectricphotometersetuptomonitorthereflectedoptical
1987).Aselectionofstandardssuitableforbothopticaland
beam. A nodding secondary mirror provided rapid and re-
infra-redphotometrywasmadeforthedeterminationofthe
peatablebackgroundcorrection.Asspot modulation effects
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Figure 3.UKIRT-BVKlightcurvesofYYGem.
colour equations. One of these (Gleise 699, Barnard’s Star) essary for the UKIRT data for similar reasons). Transfor-
was believed to be in the declining stage of a flare during mations to the Johnson UBVRI system relied on observa-
observation on 4 March 1988. Further details are given in tions of 17 stars listed by Moffat & Barnes (1979) and the
thesupplementary electronic tables. three local standards listed in Section 3.1 (Butler, 1988).
In Figure 2, discrepancies can be seen at some phases The following mean extinction coefficients were employed:
in the B light curves, but there is generally good agree- κU =0.57, κB =0.29, κV =0.17, κR =0.12 andκI =0.09.
ment in V. This is consistent with the greater influence of AsatMaunaKeawehadtransformedtotheKron/Cousins
background irregularities and small flares at shorter wave- R,I system, rather than Johnson’s, the McDonald data was
lengths.InFigure3weshowtheUKIRTB,VandKobser- furthertransformedtotheKron/Cousinssystemusingequa-
vations. The two broadband photometric data-sets (Hawaii tionsformulatedbyBessell(1979).TheUBVRIobservations
0.6m and UKIRT) are comparable over common phase in- ofYYGemonthethreenights4/5/6March1988arelisted
tervals, although theless-scattered UKIRTdatahas poorer inthesupplementaryelectronictables.Thoughnoverylarge
phase coverage. optical flares were recorded at McDonald during this cam-
The cool-spot hypothesis receives support from the paign, a flare of approximately 0.6 magnitudes in U was
smaller amplitude of the out-of-eclipse variation at the observed simultaneously with a substantial increase in the
longer wavelengths. This is quite noticeable in the UKIRT 6-cm microwave fluxrecorded by theVLA.
K-band,butless so in the0.6m I-banddata.
3.4 UBVRI photometry from McDonald 4 MODELLING THE MAUNA KEA V LIGHT
Observatory CURVES
In order to increase the probability of obtaining simulta- The idea of large-scale inhomogeneities in the local surface
neous optical photometry with radio, X-ray or ultraviolet brightness of stars is not new, and, after a period of dor-
observations of flares, YY Gem was placed on the schedule mancy, was revived in the mid-twentieth century, particu-
forthe0.91m telescopeatMcDonaldObservatory,Texason larly after discussion of possible causes of stellar brightness
4, 5and 6th March 1988. The photoelectric McD photome- variation by the careful photometrist G. Kron (1947, 1950,
terwasequippedwithacooledEMI9658Aphotomultiplier. 1952). Subsequently,evidence has accumulated from across
With sequential exposures through U,B,V,R and I filters of the electromagnetic spectrum of magneto-dynamic activity
the Johnson system, a time resolution in each waveband effects on cool stars of a few orders of magnitude greater
ofapproximately20secondswasobtained.Unfortunately,a scale than that known for the Sun. These effects include
computercrashcausedthelossoftheelectronicallyrecorded large areas of the photosphere (spots) with cooler than av-
dataanditwasnecessary tomanuallytypeintherawpho- erage temperature.
ton counts from the printed output (as had also been nec- This subject formed thethemeof IAUSymposium 176
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(Strassmeier & Linsky, 1996), and was reviewed in Chap- group of parameters is located then that direction can be
ter 10 of Budding & Demircan (2007), which outlines the followed in the iteration sequence (‘vector search’), other-
methodologypursuedinthispaper.Ofcourse,theuseofuni- wise the search proceeds by optimizing each parameter in
formcircularareastomodelmaculationeffectsisaphysical turn. For a linear problem, χ2 minimization is equivalent
over-simplification,butitisacomputationaldevicethatal- to the familiar least-squares method (cf. Bevington, 1969),
lowsaneasilyformulatedfittingfunctiontomatchthedata but the parameters in our fitting function are not in a
totheavailablephotometricresolution.Evenwiththehigh- linear arrangement, preventing an immediate inversion to
est S/N data currently available, a macula less than about the optimal parameter set. However, the χ2 Hessian is
5 deg in angular mean radius produces light curve losses calculated numerically for a location in parameter space
only at the milli-magnitude level. Whether a given macu- corresponding to the found minimum. If the location is a
lation region’s shape is circular, or of uniform intensity is true minimum with all the Hessian’s eigenvalues positive,
unfortunately not recoverable. Otherindications on surface usefullightonthedeterminacyofeachindividualparameter
structurehowever,suchascomefromthemoredetailedZee- is thrown.
manDopplerImagingtechniquesforexample(Donatietal, An important issue is the specification of errors. Pho-
2003),tendtosupportsomewhatsimpleanduniformstruc- tometricdatasetsusuallypermitdataerrorstobeassigned
turestomaculae,andtherearesupportingtheoreticalargu- fromthespreadofdifferencesbetweencomparisonandcheck
ments, related to magnetic loop parameters. But it is also stars. We have adopted representative errors based on the
truethat different data sources (e.g. spectroscopy and pho- observation that the great majority of data points for YY
tometry)and analysis techniques(e.g. minimumentropyor Gemarewithin20%ofthemean.Uniformerrorassignment
information limit) do not always lead to one clear and con- weightsthefittingatthebottomoftheminimamorehighly
sistent picture (Strassmeier, 1992; Radick et al. 1998; Petit which is beneficial in fixing the main parameters as these
et al., 2004; Baliunas, 2006). regions of the light curve have relatively high information
Even if real maculae are neither circular nor uniform, content.
there will be certain mean values that can represent their A check on the validity of such error estimates comes
(differential)effecttotheavailableaccuracy.Suchmeanval- from thecorrespondingoptimalχ2 values.Theratiosχ2/ν,
ues, as used in sunspot statistical studies, have validity in where ν is the number of degrees of freedom of the fitting,
tracking and relating data to other activity indicators. So canbecomparedwiththoseinstandardtablesoftheχ2vari-
while the surface structure of active cool stars may well be ate(e.g.Pearson&Hartley,1954)andaconfidencelevelfor
morecomplicatedthanwecanpresentlydiscern,theapprox- thegiven modelwith theadopted errorestimates obtained.
imationsavailablecansummariseobservationalfindingsand If χ2/ν is quite different from unity, we can be confident
stimulate efforts towards more detailed future studies. that either the data errors are seriously incorrect, or (more
Notethatthedifferentialmaculationvariation,thathis- often),thederivedmodelisproducinganinadequaterepre-
toricallycaughttheattentionofobservers,shouldnotcause sentation for the available precision.
the steady background component to be disregarded. The This relates to another well-known aspect of optimiza-
latter, coming from a simultaneously extant, uniform, dis- tionproblems,i.e.thatwhileagivenmodelcanbeadequate
tribution of maculae, can have quite a significant effect, as toaccount foragiven data-set,we cannot besurethat it is
noted by Popper (1998) and Semeniuk (2000), who derived the only such model. This is sometimes called the ‘unique-
systematicdifferencesbetweenthedistanceestimatesofcer- ness’ problem, and, in its most general form, is insoluble.
taincoolclosebinaries,obtainedphotometrically,withthose However,ifweconfineourselvestomodellingwithalimited
fromtheHipparcossatellite.Theyfoundthatthemeansur- set of parameters and the Hessian at the located χ2 min-
face flux of such cool binaries was too low to allow them imum remains positive definite for that set with the χ2/ν
to fit with the normal correlation from their B−V colour ratio also within acceptable confidence limits, then the re-
indices and concluded that a uniform distribution of dark sultsaresignificantwithinthecontext.Ifeitherofthesetwo
spotscould account forthedifference.Buddinget al(2005) conditionsfailthentherearereasonable groundsfordoubt-
confirmedtheseresultsandestimatedthatthemeansurface ingtherepresentation.Providedtheconditionsaremet,the
flux could be underestimated up to a level of about 30% in Hessian can be inverted to yield the error matrix for the
casesofclosebinariessimilartoYYGem(seealsoTorres& parameter-set. The errors listed in Tables 2 and 3 were es-
Ribas, 2002). timated in this way.
Computer programs that model the light curves Tospeedupafullexamination ofparameterspace,the
of eclipsing variables with surface inhomogeneities data can be binned to form normal points with phase in-
were discussed by Budding & Zeilik (1987). This tervals typically 0.5% of the period. The residuals from the
software was developed into a user-friendly for- eclipsemodelwerefirstfittedwithasimpletwo-spot model
mat by M. Rhodes, available as WINFITTER from (for procedural details see Zeilik et al. 1988), but this was
http://home.comcast.net/∼michael.rhodes/. The adopted laterrevised in afittingthat includedabright plage visible
technique is an iterative one that progressively defines nearprimaryminimum,onthebasisofadditionalevidence.
parameters affecting light curves, beginning with those The high orbital inclination of YYGem (∼86◦) results
relating to the binary orbit, and subsequently including in poor accuracy for the spot latitude determination. Spots
those controlling the extent and position of surface spots. of a given size at the same longitudes but in opposite lat-
The procedure involves a Marquardt-Levenberg strategy itude hemispheres would generally show similar light curve
for reducing χ2 values corresponding to the given fitting effects. Attempts to derive a full spot parameter specifica-
function with an assigned trial set of parameters. If an tionsimultaneously tendtorunintodeterminacyproblems:
advantageous direction for simultaneous optimization of a alow-latitudespot might bemovedtowardsthepolein the
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Table2.Parametersusedinorderivedfromthesolutionforthe M⊙), however, are in almost exact agreement with those of
Vlightcurve Torres & Ribas, with our own (slightly lower) value for the
orbitalinclination,i.e.thetwosetsofresultsarewithintheir
error limits of each other. The inclination listed in Table 2
0.6m V Light Curve model
derives from the fit to the binary light curve, however, in
RatioofLuminosities L1/L2 1.02±.005 the separate fitting that allows spot parameters to be esti-
RatioofMasses M1/M2 1.0 mated, a mean value for the inclination has been adopted.
RatioofRadii R1/R2 1.0±.008 This allows the full weight of the difference curve data to
Coeff.LimbDark. u1,2 0.88 go into the determination of the geometrical paremeters of
RadiusofPrimary R1/A 0.154±.001 thestarspots.Thefinalvalueofχ2/ν givenatthebottomof
OrbitalInclination(◦) i 86.0±0.11
Table2isalittlehighfortheadoptedaccuracyofthedata,
as mentioned above. The photometric modelling of these V
Three-spot model for V light curve data,takeninisolation,shouldthenberegardedasafeasible
Long. Lat. Radius Temp.decr. orcoarserepresentation ofreality.Nonethelessitisinkeep-
ingwiththeotherresultsdiscussedinthefollowingsections,
94.8◦ -16◦ 16.4◦ 0.84
250.0◦ 45◦ 10.0◦ 0.84 andthecombination ofevidencegivesaddedsignificanceto
342.7◦ 21◦ 12.3◦ 1.13 themodel.
Note that this modelling alone cannot distinguish be-
Datumerror∆l 0.01 tweenspotsontheprimaryandsecondarycomponents,par-
Goodness offitχ2/ν 1.26
ticularly in the present case with an essentially identical
pair. A given spot can be situated on the primary at the
longitude indicated in Table 2, or on the secondary at that
modelling,butaquitesimilarpatternofvariationcouldthen longitude ±180◦. The longitudes of the darkened regions
be reproduced by a corresponding decrease in size at the are about 5 and 20 deg from quadrature, i.e. they reach
same latitude. On the other hand, spot longitudes were al- their maximum visibility when the two stars are not too
ways fairly well defined. far from greatest elongation. This recalls Doyle & Math-
Weadoptedthefollowingprocedure:(1)Fittheeclipses ioudakis’ (1990) finding that flares tend to occur close to
for the 0.6m V light curve by adjusting the main geometri- quadrature phases, which, in turn, suggests a topological
cal parameters, using the photospheric temperatures listed connection between flaring regions and cool photospheric
by Budding & Demircan (2007: Table 3.2). A normaliza- spots.
tionconstantalsoappearsasafreeparameterforanygiven
light curve.An initial value is usually adopted from setting
thehighest measured fluxto anominal valueof unity.Sub-
5 MODELS FOR THE B, R, I AND K LIGHT
sequent optimization will yield a better representation for
CURVES AND TEMPERATURES OF SPOTS
this. (2) Specify initial values for the longitudes, latitudes
and radii of spots, as in Zeilik et al. (1988). (3) Estimate Following the determination of basic parameters for the V
the relative intensity of spots κ in the V band (compared light curve we processed the light curves from the other fil-
to the unspotted photosphere). We assigned a preliminary ters, assuming the same geometry. We verified that the B,
value of κ ∼0.2, assuming black-body emission and an ap- R, I and K light curves could all be fitted by eclipses hav-
proximate mean temperature difference of ∼500 K between ing closely similar numerical values of themain parameters
spots and photosphere Tp−Ts. The low value of κ entails to those of the V. The large scatter of the U band (0.6m)
thatthespotsizeisnotsosensitivetotheadoptedtemper- data prevented their detailed analysis in this way. In our
ature decrement for the V light curve. Since the V spectral final spot models for the B, R, I and K data we adopted
region lies some way to the short-wavelength side of the longitudes, radii and latitudes of the spots which were the
Planckian peak at the adopted temperature (3770 K), only sameasfortheV,andassumedthatonlythelimb-darkening
in the infra-red will light curves start to show a noticeably and mean surface brightness of the spots, relative to the
decreasedmaculationamplitude.Thiscouldbesimulatedby unspotted photosphere, differed. At a given wavelength the
a smaller spot, but that would not be consistent, of course, optimized value of κ corresponds to a spot mean temper-
withradiiofthesamefeatureobtainedinV.Inotherwords, ature through the implicit relation (1). The photometric
theweightofinformationintheshorterwavelengthphotom- information content thus directs us towards the tempera-
etry goes towards fixing the spot size: at the longer wave- tureestimate.Withlimb-darkeningcoefficientsatthemean
lengths it goes towards determining the temperature. (4) wavelength of the Cape/Kron R, I and Johnson B and K
Optimizefirstspotlongitudes,thenradiiand(possibly)lat- bands taken from van Hamme (1993), we determined the
itudes,usingCURVEFIT.(5)Retrofittheeclipsecurvefor relative surface brightness of thespots in the different pho-
thestellar parameters with thespot modulation removed. tometricbandsusingCURVEFIT.Wecouldthenestimate
FinalparametersfromthisprocedurearegiveninTable the difference in temperature of the spotted regions from
2. Adopting the radial velocity analysis of Torres & Ribas theunspottedphotosphere.Themeansurfacebrightnessbe-
(2002) andthestandarduseofKepler’sthirdlawleadstoa comes adjustable in the fittingof the infra-red light curves.
separation ofthetwomass-centresas 3.898 R⊙,orthat the The geometrical parameters are held constant to allow the
radius of either star is some 0.601 R⊙. This is slightly less fitting to concentrate only on the flux ratio for the infra-
than the value Torres & Ribas calculated due to the differ- red data-sets. The increase in this flux ratio can definitely
enceinthetwolight-curvefittingresults.Ourmasses(0.600 beseen for theinfra-red light curves,though wecannot get
(cid:13)c 0000RAS,MNRAS000,000–000
8
Table 3.Relative Intensities of Dark Spots in V,R,I,K and the derived temperature difference between the spots and
the photosphere
Filter λeff(˚A) Limb darkening Mean intensity Spot Temp. Diff.(◦K) TP - TS
Coefficient κ Method 1 Method 2
V 5550 0.88 0.20
RC 6800 0.73 0.24±.04 630 420
IC 8250 0.60 0.73±.04 200 280
K 22000 0.33 0.30±.08 1000 1320
awayfromtherelativelyhighnoiselevelwhichdetractsfrom typeofstar(cf.diBenedetto,1998;Besselletal.,1998),but
thetemperatureestimation.Thelightcurvesarenormalised a higher assigned temperature would increase this discrep-
in steps, with initially an approximate value used to scale ancy and our adopted 3770 K appears a reasonable com-
the input magnitude differences so that the out of eclipse promise.InTable3,column5,welist thespottemperature
flux level can be approximately unity. The finally adopted differences which satisfy theaforegoing identity.
fractional luminosities are then given in terms of that cor-
Eker’s alternative approach seems less direct, given in-
rected reference light level.
sufficienttransmissiondetailsforthethreeR,IandKwave-
Eker (1994), discussing the determination of spot tem-
bands.Here,weassumethe(V–R),(V–I)and(V–K)colours
peratures from broad-band photometry, suggested two al-
ofspottedregionsarethesameasthoseofa(verycool)star
ternative approaches: (a) Assume that the spots and the
of the same spectral type or temperature. For the R and I
normalphotospherebothradiateasblackbodiesatsettem-
bands, we first interpolated the values in Table 4 of Th´e et
peratures. (b)Assumethattheradiation from aspot is the
al. (1984) to determine spectral types of the relevant spot-
sameasthatarisingfromanormalstellarphotosphereofthe
ted regions, and thence corresponding temperatures (Cox,
given temperature, and then use theBarnes-Evans (Barnes
2000). For the K band we can find a temperature directly
&Evans,1976) relationship betweencolour(V–R)andsur- from therelation for log Te to(V −2.2µ) of Veeder(1974).
face flux fV. Both methods can be criticised; for example, ResultsaregiveninTable3,column6.Inbothmethods,the
black-body radiation is unlikely to provide a very accurate
meanrepresentativetemperaturesofalldarkspotsaffecting
result for localised spectral regions, considering the strong
a given light curveare taken tobe thesame.
influenceofmolecularbandsonthefluxdistributionofdMe
stars. On the other hand, spectrophotometric fluxes, pre- Empirically derivedvaluesforthedifferenceintemper-
dicted by current models, are not always sufficiently close atureofspotsandthenormalphotosphereonYYGemwere
foundtovaryfrom ∼200Kto∼1200K,withthedifference
torealstellarspectratogiveaccuratecoloursoverthetem-
perature range required. Given such issues, we applied the from the K band larger than that from the R and I bands.
firstproceduretotheB,R,IandKlightcurves,andchecked The average results from Table 3 give a temperature differ-
enceof650±300K,whichappearsingoodagreementwith
theresult with thesecond one.
thephotosphere–spottemperaturedifferenceof600±450
In Table 3, column 4 we give the relative intensities of
K found by Vogt (1981) and Eker (1994) for the prototype
the spots derived from the models fitted to the R, I and K
star BY Dra (M0 V).
light curves, adopting the positions and radii of the spots
from the V light curve, specifying, initially, the dark spot The disparity in theresults for the mean temperatures
intensityas 0.2of that ofthenormalphotosphere.Weused of the spotted areas shown in Table 3 render infeasible an
the following identity, where the left side refers to mean accurate resolution into distinct penumbral and umbral re-
fluxes f in spot ‘s‘ and photospheric ‘p‘ regions, and the gions. While the solar case suggests a significant role for
right adopts an appropriate flux formula (e.g. black body) penumbra in large spots (Bray & Loughhead (1964)), the
φ(T,λ): fact that derived temperature differentials for the macula-
tion ofcool activestarsare generally less thanthatof large
(fλ/fV)s = φ(Ts,λ)φ(Tp,V) . (1) sunspots may well be an indication that these active re-
(fλ/fV)p φ(Tp,λ)φ(Ts,V) gionsareheterogeneousindetail,eitherbecauseofcomplex
shapes and groupings of spots, the presence of white-light
Here, λ is the effective wavelength of the R, I or K
faculae,penumbralcomponentsorother,perhapstemporal,
filtersbeingcomparedwithV.Theleftsideconcernsempir-
irregularities.
icallydeterminedratiosofthemaculationamplitudes,while
the right implicitly yields corresponding spot temperatures Several calculations of mean spot temperatures for RS
for given wavelengths if we have some value of the mean CVnstarshavebeenreported,givingvaluesthatdifferfrom
unspotted photospheric temperature Tp. We have adopted thenormalphotospherictemperaturebytypically∼1000K,
the value 3770 K given by Budding & Demircan (2007). (Vogt, 1981; Eker, 1994, Neff et al. 1995, Olah & Strass-
Thiswasdeterminedusinganabsolutefluxcalibration,with meier, 2001, Berdyugina, 2004). This difference is lower for
an adopted flux of 8.82×10−12 W m−2. This temperature M type stars than for the solar type (Vogt, 1981: Rodono,
is higher than many values for M1 stars in the literature, 1986).Atfirstsight,thisisnotsurprising,as,fromtheirrel-
as noted by Torres and Ribas (2002) who preferred a yet ativeareas,onecanexpectpenumbraetodominatetheflux.
higher value of 3820 K. The bolometric correction required However,Dorren(1987) arguedthatthisisunlikely,asonly
tomatchtheVfluxis–1.18mag.Thisissomewhatlessthan spots with umbral areas <10% of the total spot area show
the value –1.25 mag that recent sources would give for this penumbralfluxdomination.Dorrenfound,forpracticallyall
(cid:13)c 0000RAS,MNRAS000,000–000
9
3
x
u 2.5
gII fl
M
2
1.5
3.5
x
u 3
a fl
h
p 2.5
al
y
L 2
1.5
0 0.2 0.4 0.6 0.8 1
Phase
Figure 4.Integrated IUEfluxes(squares)intheultravioletemissionlinesofMgiihandk(top)andtheLyα(bottom)againstphase
withthescaledV-bandmodeleclipselightcurvesforYYGem.TheIUEfluxesareinunitsof10−12 ergscm−2 s−1.Notethereasonable
fitoftheMgiifluxestotheVsecondaryeclipsecurveandthemuchbroadereclipseinLyαx.
cases, that the increased contrast of the umbra weights the Mgiiemittingplages. Atfirst sight,theexistenceof an ap-
result towards the umbralcomponent’s effect. proximatelyuniformchromosphereaboveanevidentlynon-
Berdyugina(2005) has written acomprehensivereview uniformphotospheremight beunexpected.However,thisis
ofcurrenttechniquesforthedeterminationofstarspottem- not the first time that such a situation has been suggested
peratures. In Figure 7 of that publication, starspot tem- byobservations. That theveryactivedMestars maybeto-
perature decrements (TP-TS) are shown to correlate with tally covered (‘saturated’) with chromospheric regions was
the photospheric temperature (TP), with both dwarfs and proposed by Linsky & Gary (1983) as an explanation for
giants scattered about a single mean curve. The mean the high integrated Mg ii flux on BY Dra like stars. Math-
starspottemperaturedecrementwederivehereforYYGem ioudakis&Doyle(1989)reachedasimilarconclusion,taking
(650±300 K) falls close to the mean line in the lower part into account the integrated Mg ii and soft X-ray fluxes of
of Berdyugina’s figure. dM-dMestars.
ThereissomesuggestionofaMgiifluxincreasetowards
theendofourIUEobservationrun.Thiscouldbeassociated
6 SPECTROSCOPIC DATA with alowerlatitudeactiveregion at longitudeabout 230◦,
but thereis insufficient data to confirm this suggestion.
6.1 Ultraviolet Spectra from IUE
In Figure 4 (bottom) we show the flux in the Lyα
Observations of ultraviolet spectra from the International line with the geocoronal emission subtracted. The extrac-
UltravioletExplorerSatellite(IUE)ofYYGemweresched- tion was made using the method of Byrne & Doyle (1988).
uled for 5 and 6 March 1988 from 03:00 to 11:00 UT.A to- Theeclipse light curvein Lyαappears broader thantheV-
talof30spectrawereobtained;9withtheshortwavelength band curve. We should note, however, that there are only
(1000-2000A)SWPcameraand21withthelongwavelength a few data points at relevant phases, and the out-of-eclipse
(2000-3000A)LWPcamera.Toimprovethetimeresolution, scattershowsdeviationsthatarecomparable.Therearetwo
two exposures of 10 minutes duration were taken with the feasible explanations; one of them intrinsic to the star and
LWPcamerabeforetheimagewasdownloaded,whereasex- theothernot.Thefirstalternativewouldbethatthebroad
posures in the SWP camera were single and longer (circa eclipsearisesfromalargervolumeofLyαemittingmaterial
25m). The spectra obtained covered the secondary eclipse than the photosphere of the secondary star, roughly cen-
and some contiguous phases. The Starlink reduction pack- tred on that star. In effect, this extended region would be
age IUEDR was used to extract the emission line fluxes in optically thick in Lyα. Another explanation for the broad
Mg ii (2800A), Ly α, C iv (1550A) and various other lines. declineatsecondary minimuminLyαcouldbevariableab-
Only theMg ii and Lyα results will bedetailed here. sorptionbyinterstellarHastheemissionlinesoftheorbiting
The most noticeable feature of theMg iiemission dur- stars are Doppler shifted across the rest wavelength of the
ing secondary eclipse is that it is fitted reasonably well interstellarabsorptionline.Thisisunlikelytobesignificant,
by the scaled V light curve (see Figure 4 - top). This im- however, due to the small range in radial velocity ∼15% at
pliesthatthesurfaceisapproximatelyuniformlycoveredby eclipseswhenthestellar motionisperpendiculartotheline
(cid:13)c 0000RAS,MNRAS000,000–000
10
1.9
Phase=0.087
1.6
1.9 1.9
Phase=0.947 Phase=0.975 1.3
1.6 1.6
1
1.3 1.3
1 1 6555
6555 6563 Å 6571 6555 6563 Å 6571
1.9
Phase=0.218
1.9 1.9 1.6
Phase=0.003 Phase=0.036
1.6 1.6 1.3
1.3 1.3 1
1 1
6555
6555 6563 Å 6571 6555 6563 Å 6571
1.9
1.9 1.9 Phase=0.281
Phase=0.067 Phase=0.096 1.6
1.6 1.6
1.3 1.3 1.3
1 1 1
6555 6563 Å 6571 6555 6563 Å 6571 6555
1.9 1.9 1.9
Phase=0.123 Phase=0.152 Phase=0.374
1.6 1.6 1.6
1.3 1.3 1.3
1 1
1
6555 6563 Å 6571 6555 6563 Å 6571
6555
1.9 1.9
1.6 Phase=0.166 1.6 Phase=0.206 1.9 Phase=0.405
1.3 1.3 1.6
1 1 1.3
1
6555 6563 Å 6571 6555 6563 Å 6571
6555
1.9 1.9
Phase=0.087 Phase=0.190
1.6 1.6
1.3 1.3
1 1
6555 6563 Å 6571 6555 6563 Å 6571
1.9 1.9
Phase=0.218 Phase=0.247
1.6 1.6
1.3 1.3
1 1
6555 6563 Å 6571 6555 6563 Å 6571
1.9 1.9
Phase=0.281 Phase=0.310
1.6 1.6
1.3 1.3
1 1
6555 6563 Å 6571 6555 6563 Å 6571
1.9 1.9
Phase=0.374 Phase=0.376
1.6 1.6
1.3 1.3
1 1
6555 6563 Å 6571 6555 6563 Å 6571
1.9
Phase=0.405
1.6
1.3
1
6555 6563 Å 6571
Figure 5.Hαlineprofilesof YY Gem obtained on the5 and6March1988 atthe CrimeanAstrophysical Observatory (seeTuominen
etal.1989). Fluxesarenormalisedtothecontinuum. (cid:13)c 0000RAS,MNRAS000,000–000