Results of the ROTOR-program. II. The long-term photometric variability of weak-line T Tauri stars

1.5 MB·English

by  K. N. Grankin

Astronomy & Astrophysics manuscript no. 8476ms (cid:13)c ESO 2008
February 2, 2008
Results of the ROTOR-program
⋆
8 II. The long-term photometric variability of weak-line T Tauri stars
0
0
1 2 3 1
2 K.N. Grankin , J. Bouvier , W. Herbst , and S.Yu. Melnikov

n
a 1 Astronomical Instituteof the Uzbek Academyof Sciences, Tashkent, Uzbekistan,700052
J 2 LaboratoiredAstrophysique,ObservatoiredeGrenoble,Universit´eJosephFourier,B.P.53,F-38041GrenobleCedex9,France

3 3 Astronomy Department,Wesleyan University,Middletown, CT 06459
2

Received .../ Accepted ...
]
h
p ABSTRACT
-
o
Context.TTauristarsexhibitvariabilityonalltimescales,whoseoriginisstilldebated.OnWTTSthevariabilityisfairlysimple
r
t and attributed to long-lived, ubiquitouscool spots.
s
a Aims. We investigate the long term variability of WTTS, extending up to 20 years in some cases, characterize it statistically
[ and discuss its implications for our understandingof these stars.
Methods.Wehaveobtainedaunique,homogeneousdatabaseofphotometricmeasurementsforWTTSextendingupto20years.
1
It contains more than 9 000 UBV R observations of 48 WTTS. All the data were collected at Mount Maidanak Observatory
v
(Uzbekistan) and they constitute thelongest homogeneous record of accurate WTTS photometry everassembled.
3
Results.Definitiverotationperiodsfor35ofthe48starsareobtained.Phasedlightcurvesover5to20seasonsarenowavailable
4
5 foranalysis.Lightcurveshapes,amplitudesandcolourvariationsareobtainedforthissampleandvariousbehaviorsexhibited,
3 discussed and interpreted.
. Conclusions. Our main conclusion is that most WTTS have very stable long term variability with relatively small changes of
1
amplitude or mean light level. The long term variability seen reflects modulation in the cold spot distributions. Photometric
0
periods are stable over many years, and the phase of minimum light can be stable as well for several years. On the long term,
8
0 spot properties do change in subtle ways, leading to secular variations in the shape and amplitudes of the light curves.
:
v
Keywords.stars:rotation–stars:fundamentalparameters–stars:starspots–stars:variables:general–stars:pre-mainsequence
i
X – stars
r
a
1. Introduction days and were in agreement with spectroscopic estimates
of their rotational velocities. It was assumed that the pe-
Thethirdcatalogofpre-main-sequenceemission-linestars
riodic light variations were due to the nonuniform distri-
assembled by G. Herbig and collaborators includes 742
bution of cool photospheric spots over the stellar surface.
objects(Herbig&Bell1988).Ofthese,aboutfiftyobjects
Rotation periods are now available for some hundreds
were classified as weak-line T Tauri stars (WTTS).These
of pre-main sequence and recently arrived main sequence
includeobjectsfromX-raysurveysofseveralstar-forming
stars of solar-like mass in five nearby young clusters: the
regionsandfromasurveyofstarswithCaIIHandKemis-
OrionNebulaCluster,NGC 2264,α Per,IC2602andthe
sionlines.WTTSexhibitaweak,narrowHαline[W(Hα)
Pleiades(Mandel&Herbst1991;Attridge&Herbst1992;
< 10˚A],a strongLiI absorptionline (6707˚A) with W(Li)
Eaton et al. 1995; Edwards et al. 1993; Choi & Herbst
> 0.1 ˚A, and a substantial CaII H and K emission lines.
1996;Bouvieretal.1997a).Incombinationwithestimates
The first photoelectric UBVR observations of these
of stellar radii these data allow us to construct distribu-
stars revealed periodic light variations in most WTTS
tionsofsurfaceangularmomentumperunitmassatthree
(Rydgren & Vrba 1983; Rydgren et al. 1984; Bouvier et
different epochs: nominally, 1, 2 and 50 Myr (see Herbst
al. 1986, 1993, 1995; Grankin 1992, 1993, 1996; Vrba et
& Mundt 2005). Recent work is extending the age range
al. 1993). Their photometric periods ranged from 1 to 10
to 200 Myr and adding many new clusters (Irwin et al.
⋆ UBVR photometric data described in Table 1 are only 2007).
available in electronic form at the CDS via anonymous ftp The study of long-termvariations in the main param-
to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u- eters of the light curves for young spotted stars is also of
strasbg.fr/cgi-bin/qcat?J/A+A/ considerableinterest.Onewouldexpectlight-curveshapes
2 K.N. Grankin et al.: Resultsof theROTOR-program.II. The long-term photometric variability of WTTS
to evolveas the spots change size, shape, temperature, or where the star contains only a single spotted region in a
location, and a latitudinal migration of spots could cause high latitude zone that is always visible, because increas-
changes in period, if the surfaces are in differential rota- ing the size of the spot (as required to increase the am-
tion, as in the Sun. It would, of course, be very interest- plitude) should decrease the maximum brightness of the
ing to find any cyclic pattern that could be interpreted star. It is possible to explain such behavior by invoking a
as evidence for a magnetic cycle. Unfortunately, most of star covered with mutiple spots at different latitudes. In
the photometric programsof observations of WTTS stars this case the amplitude will not depend just on the total
havebeencarriedoutepisodically,inanintervalfromone area of the spots, but will also depend on the distribu-
tothreemonths.Onlyoneobject(V410Tau)hasbeenin- tion of these spots on the stellar surface. Similar results
vestigatedin detailoverseveralseasons(Vrba et al.1988; havebeenobtainedrecentlyfor 24WTTSstarsinthe ex-
Herbst 1989; Petrov et al. 1994). These authors showed tremely young cluster IC 348 over five observing seasons
thattherewereatleasttwoextendedandlong-livedspot- (Cohenetal.2004).Ithasbeenshownthatthestabilityof
ted regions on the surface of V410 Tau during several averagemagnitudefromseasontoseasonmostlikelyindi-
years. The evolution of the shape and amplitude of the catesthatspotsontheseWTTSstarstendtoredistribute
lightcurvefromseasontoseasonwasexplainedbychanges themselvesandundergochangesinsize,temperature,and
in the spot sizes, temperatures, and relative locations. locationratherthansimplyappearordisappearenmasse.
The first systematic photoelectric BVR observations The observations to date support to the possible exis-
for about thirty WTTS in dark clouds in Taurus-Auriga tence of stellar activity cycles on WTTS. In an attempt
began in 1990 at the Maidanak Observatory (Grankin to find and study such activity cycles we have contin-
et al. 1995). During 1990-1993 rotation periods were dis- ued to monitor some tens of WTTS at Mt. Maidanak
covered for 12 WTTS and refined for another 9 WTTS. Observatory over many years. In this paper, we employ
A fundamental result of the analysis of the photometric the unique and extensive Mt. Maidanak database to in-
behavior of these WTTS was the stability of the initial vestigateWTTS variability ona time scaleof many years
epochs androtationperiods for17 WTTSona time scale and, in some cases,multiple decades.In Section 2,we de-
from 2 to 4 years. In addition, there is a high detection scribe the stellar sample and the observations carried out
rate of rotationperiods among WTTS in the sample con- forthelast20yearsatMt.Maidanak.InSection3,wedis-
sidered. It is generally believed that the stability of the cussthephenomenonofrotationalmodulationofthelight
initial epochs and rotation periods over several years in- curvesof36WTTS.InSection4,wedescribeaspotmodel
dicates that the active region in each WTTS remains on and some results of modeling. In Section 5, we define the
a definite meridian over this time scale. Variations in the statistical parameters used to characterize the long term
maximumbrightnesslevels,theamplitudesandtheshapes variabilityofWTTS.Furthermodelingofthelightcurves
of the light curve for many WTTS is evidence for migra- will be presented in a later paper in this series.
tion of the spots, within the limits of an active zone, and
for changes in their size. It is interesting to note, that
2. Star sample and observations
RS CVn and BY Dra stars show the same kind of long-
term photometric behaviour and that active longitudes All UBVR data were obtained at Mount Maidanak
have long been reported on the Sun (Losh 1939). For RS Observatory(longitude:E4h27m47s;latitude:+38◦41′;al-
CVn stars, active longitudes appear to persist for a num- titude: 2709 m) in Uzbekistan. Results of astroclimate
ber of years (Butler 1996). Thus, an activity mechanism studies at Maidanak observatory have been summarized
with some similarities to that operating on the Sun may byEhgamberdievetal.(2000),whoshowthatitisamong
be indicated by these common observational characteris- the best observatoriesin the world, in many respects. We
tics with WTTS. targetted48WTTSforlong-termmonitoring,mostlyfrom
Longer term observations have shown, that the phe- the list of Herbig & Bell (1988). More than 9000 UBVR
nomenon of stability of the initial epochs is most pro- magnitudes were collected for these objects between 1990
nounced in seven WTTS: LkCa 4, LkCa 7, V410 Tau, and 2004, although the number of U magnitudes is rela-
V819 Tau, V827 Tau, V830 Tau and V836 Tau (Grankin tivelysmallcomparedtotheothercolorsduetothefaint-
1997,1998,1999).Changesinthephaseofminimumlight nessofthestarsatthosewavelengths.Alltheobservations
forthesestarsdidnotexceed±7%oftheperiodonatime wereobtainedatthreetelescopes(two0.6andone0.48m
scale from 7 to 12 years.Similar results were obtainedfor reflectors)usingasingle-channelpulse-countingphotome-
23 WTTS in the young Orion Nebula Cluster (Choi & ter with photomultiplier tubes. As a rule, each program
Herbst 1996). starwasmeasuredoncepernightatminimalairmass.We
Some interestingresultshavebeenreceivedfromanal- secured between 12 and 30 (U)BVR measurements for
ysisoflong-termlightcurvesof30WTTSand80RSCVn each sample target during each observational season last-
and FK Com stars (Grankin et al. 2002). These authors ingseveralmonths.Thenumberofmeasurementsdepends
have found that in 18 of the 110 stars monitored, an in- on the object’s visibility from Mt. Maidanak. The largest
crease in the amplitude of the periodic variability accom- number ofmeasurements wasthus obtainedfor WTTS in
paniesa riseofthe maximumbrightnesslevel.This result Taurus, and fewer in Ophiuchus and Orion. Magnitudes
is difficult to understandin the contextofa simple model areprovidedintheJohnsonUBVRsystem.Thermserror
K.N. Grankin et al.: Resultsof theROTOR-program.II. The long-term photometric variability of WTTS 3
of a single measurement in the instrumental system for a termined by the commonly used Lomb-Scargle method
star brighter than 12m in V is about 0m.01 in BVR and and these are reported in Table 2.
m
0 .05 in U. False-alarm probabilities (FAP1) for the period were
Observations were carried out either differentially us- computed using a Fisher randomization test, or Monte-
ing a nearby reference star (see Strauzis 1977) or directly Carlo method (see, for example, Nemec & Nemec 1985).
by estimating the nightly extinction (Nikonov 1976). In FAP1 represents the proportion of permutations (ie. shu-
the latter case, several reference stars were observed ev- fied time-series) that contained a trough lower than (in
ery night to derive the extinction coefficients in each fil- thecaseofthechi-squaredmethod)orapeakhigherthan
ter. Selected standard stars (Landolt 1983, 1992) were (in the case of the Lomb-Scargle periodogram analysis)
observed and used to transform instrumental magnitudes that of the periodogram of the unrandomized dataset at
into the Johnson/CousinsUBVR system.We then trans- any frequency. This therefore represents the probability
formed the magnitudes to the Johnson UBVR system that, given the frequency search parameters, no periodic
using the relationship from Landolt (1983) : (V-R)C = component is present in the data with this period. To en-
-0.0320 + 0.71652×(V-R)J. The formal accuracy of this sure reliable signicance values, the minimum number of
reductionstepis0m.01.Allobservedlocaltimeshavebeen permutations was set to 1000.If the false alarmprobabil-
converted to heliocentric julian days (JDH). A detailed ities lie between 0.00 and 0.01, then the quoted period is
descriptionofthe equipment,observationtechniques,and a correctone with 95% confidence. Periods were searched
data processing is given in Shevchenko (1989). for within an intervalranging from 1 day to 20 days. The
Results of the Mt. Maidanak program of homoge- periodogram is computed at 1000 frequencies between 0
neous, long-term photometry of WTTS are summarized and 0.05 d−1.
in Table 1. Columns are: star’s name, star’s number in A search for a periodic component has been made for
the Herbig & Bell (1988) catalogue, spectral type, time all stars in Table 1. Results of the periodogram analysis
span of observations in JD, number of seasons observed, arelistedinTable2forthe36starswhichshowedasignif-
photometricrangeintheV band,number ofobservations icantperiodicity inone seasonofobservationormore.No
in the V band, and average values of B−V and V −R significantperiodicitywasfoundfortheother12stars.We
colors. In the last column we give a multiplicity indica- givethevaluesofperiodsforwhichtheFAP1liesbetween
tor, as follows: spectroscopic binary (SB), visual binary 0.00 and0.01.If the false alarmprobabilitieslies between
(VB), and visual tertiary (VT). The complete Maidanak 0.01and0.05,theperiodisdesignatedbyasign”:”.Ifthe
databaseforWTTSisavailableinelectronicformatCDS, FAP1 lies between0.05and0.10,the period is designated
Strasbourg, via anonymous ftp to cdsarc.u-strasbg.fr. by a sign ”?”. Absence of any periodicity is designated
by a sign ”-”. In last column the most significant period,
Most of the objects are located in the Taurus-Auriga
based on a periodogram for the entire observing interval
region (40 of the 48) and only 8 WTTS are in other star
(i.e. for all seasons) is presented.
formingregions.TherangeofspectraltypesisfromG0to
We have tried to improve the period and ephemeris
M4.Thereareeightstarsinthe rangeG0 toG9,eighteen
for each star in Table 2 by the following procedure. Each
between K0 and K5, ten between K6 and K9, and nine
seasonal lightcurve was folded with its mean period to
between M0 and M4.
determine the time of minimum T by fitting a polyno-
0
mial to the folded lightcurve. We used the value for the
periodgiveninthe lastcolumnofthe Table 2to compute
3. Results of periodogram analysis
the numberofcycleselapsedbetweeneachofthe seasonal
The light curves obtained during the ROTOR campaign points T and the time ofminimum observedby us. Then
0
were analyzed using the PERIOD software time-series we computed the O-C diagram for the minima T as a
0
analysis package (see Starlink User Note). Periods were function of cycle number. The residuals in this diagram
searched for each season using two different methods, a can be minimized by modifying the period. In this way a
chi-squaredtechniqueandtheLomb-Scargleperiodogram bestfitperiodandnewephemerisforeachstararefound.
analysis. The first method is straight-forwardand the in- See Stelzer et al. (2003) for an example of the use of this
put data are simply folded on a series of trial periods. At methodforupdatingoftheperiodandephemerisforV410
each trial period, the data are fitted with a sine curve. Tau.Thenewperiodandephemerisforeachstararegiven
The resulting reduced-χ2 values are plotted as a function in Table 3. We adopt this ephemeris and period for all
of trial frequency and the minima in the plot suggest the further analysis.
most likely periods. See Horne et al. (1986) for an exam-
ple of the use of this method, which is ideally suited to
4. Rotation modulation phenomena
the study any sinusoidal variations. The second method
is a novel type of periodogram analysis, quite powerful Thirty-six of our 48 WTTS exhibit periodic light varia-
for finding, and testing the significance of, weak periodic tionsduringoneormoreseasons.Alistoftheseobjectsis
signals in unevenly sampled data (see Horne & Baliunas given in Table 3. Columns are: star’s name, the epoch of
1986;Press&Rybicki1989).Asbothmethodshaveshown ourobservations,theminimumandmaximumamplitudes
very similar results,here we simply adopt the periods de- of the periodic light variations (∆Vmin and ∆Vmax), the
4 K.N. Grankin et al.: Resultsof theROTOR-program.II. The long-term photometric variability of WTTS
initial epoch, the rotational period, and two columns of be noted,thatthe majorityofthese stars(6of7)alsoare
references. The first column with references contains the amongthestarswiththehighestphotometricamplitudes,
papers in which there is a first mention of a period. The i.e. they are the most active variable stars in our sample.
second column with references specifies the papers from We suppose, that the phenomenon of stability of ϕmin is
which we have taken the initial epoch and the more pre- connected somehow with level of activity.
cise value for a period. Allthe starsinoursample showsignificantchangesin
Minimum amplitudes of the periodic light variations amplitude and shape of phased light curves from season
are in the range of 0m.05 to 0m.4 in the V band (see toseasonwithoutanydependence ontheirstability orin-
Figure 1) but more than 80% of stars have minimum am- stability of minimum phase. For example, in the case of
plitudes in the intervalfrom0m.05 up to 0m.1.Maximum V410 Tau, the amplitude changes from 0m.39 till 0m.63.
m
amplitudes of the periodic light variations range from InthecaseofLkCa7theamplitudechangesfrom0 .33to
0m.15 to 0m.8 in V and 75% of the stars show a maxi- 0m.58.Itisworthnotingthatthe mostsymmetricphased
mum amplitude within the limits of 0m.15 to 0m.3. The lightcurve aroundϕmin generallycorrespondsto the sea-
peak of this distribution is at 0m.15. The stars with the son with the maximum amplitude. On the other hand,
highest ampli- tudes of periodic light variations, achiev- the most asymmetrical phased light curves typically cor-
ing0m.4−0m.8intheVband,are:LkCa4(0m.79),V410 respond to seasons with the minimum amplitudes of light
Tau (0m.63), V836 Tau (0m.62), LkCa 7 (0m.58), V827 variability(seeFigure3-4).Wenotethatoneobjectinour
Tau (0m.51), and V830 Tau (0m.45). Such large ampli- sample showed a very unusual shape for a phased light
tudes of the light variation indicate the existence of very curve in some seasons. This is LkCa 4, which in 1992,
extended spottedregionsonthe stellarsurface.Note that 1993, and 1995 displayed a flat portion near minimum in
some stars were observed at fewer epochs than others, so thephasedlightcurve(seeFigure5).Allotherstarsshow
we cannot be sure that the quoted values of ∆Vmin and constantlychanging,inmanycasesnearlysinusoidallight
∆Vmax, especially in these cases, are truly representative curvesasarule.Inaddition,thisstarhasshowntherecord
ofthestarsbehavioronatimescaleofdecades.Theactual amplitude in 2004, of about 0m.8 in the V band. We do
extrema in these values may be largerthanis represented not know of another star of any type with such a large
on Figure 1. amplitude caused by the phenomenon of rotational mod-
Of the 36 targets with periods,35 lie within the range ulation.
0.48 to 9.9 days (see Table 3). The star TAP 4 shows the While some stars (such as V410 Tau, LkCa 7, and
shortestperiod,P=0.482d,andTAP45showsthelongest LkCa 4) show gradual changes of amplitude and shape
period of these 35, with P= 9.9d. The most common pe- from season to season, there are examples of other be-
riodsarewithinthe interval0.5to4d(seeFigure2).The haviour. The amplitude of the periodic light variations
exceptional star Is V501 Aur. Its photometric period is may appreciably change by as much as a few tenths of a
close to 56 days, and it is most likely not a rotation pe- magnitude fromoneseasontothe next,asincaseofTAP
riod. We may estimate the luminosity and radius of this 41. We can see from Figure 6 that the phased light curve
star,assuming, that it is associatedwith the Taurus dark remainsstablefortwoseasons,1992and1993,afterwhich
clouds at a distance of 140 pc. In that case, if the pho- itsinitialphaseandshapeevolverapidly.Duringsuchpe-
tometric period corresponds to the period of rotation, its riodsofrapidlightcurveevolution,itisoftennotpossible
equatorialspeedofrotationwouldbeabout3km/s,which to detect the star asa periodic variableor,if detected, its
contradictsitsmeasuredvalueor25-27km/s.Itispossible amplitude is quite small, as in 1994 and 1998.
thatthisobjectbelongstoanotherclassofvari-ablestars; Itmaybenoted,thatforthemajorityofstarstheaver-
spectral observations are required to confirm or deny this ageleveloflightdoesnotchangeevenastheamplitudede-
guess. creasesconsiderably.TAP 41nicely illustrates this.It has
Perhapsthemostinterestingresultfromourlong-term beenshownthatthestabilityofaverageleveloflightfrom
observations is that the phase light curve (ϕmin) may be seasontoseasonmostlikelyindicatesthatspotsonWTTS
conserved for times as long as several years. This phe- tend to redistribute themselves and undergo changes in
nomenonofstabilityismostpronouncedinV410Tau(see size, temperature, and location rather than to appear or
Figure 3). Over 19 years of observation, the changes of disappear en masse. However,itis alsonecessaryto note,
ϕmin have not exceeded 0.16 P, where P is the rotation that some stars do show significant changes in their av-
period(Stelzeretal.2003).Wecanseeanotherexampleof erage level of light from season to season. Examples are:
phasestabilityextendingfor15yearsinLkCa7(Figure4). TAP 50, V819 Tau, V827 Tau, V836 Tau, and VY Tau.
Outofthetotalsample,7starsshowsuchstabilityofϕmin Thereisonemoreexampleofunusualphotometricbe-
for time intervals between 5 and 19 years, namely: LkCa haviour among our sample of WTTS. It may be seen on
4, LkCa 7, V410 Tau, V819 Tau, V827 Tau, V830 Tau, Figure 7 that the amplitude of the light curve of V830
and V836 Tau. Such long-term stability of ϕmin is prob- Tauchangedbyafew tenths ofa magnitude fromits nor-
ably due to the existence of so-called active longitudes at mal value during the 2002 and 2003 seasons. During this
which the (shorter-lived)extended spotted regionsare lo- period of time the phase light curve also had a complex
cated (Grankin et al. 1995). Such active longitudes have shapeinthesensethattwomaximaandtwominimawere
been reported on the Sun and RS CVn stars. It should observedper cycle.Suchshapesoflightcurvescanbe the
K.N. Grankin et al.: Resultsof theROTOR-program.II. The long-term photometric variability of WTTS 5
result ofthe existence of two extended spotted regionson ners.Someshowspecificdependenciesbetweenamplitude,
opposite sides of the star. Similar light curves were ob- Vmin, Vmax and Vmean, but these are in various direc-
served at two epochs for V410 Tau in 1981/1982 and in tionsandsomestarsshownosuchdependencies.Detailed
1983/1984(see Herbst 1989). modeling of these behaviors is beyond the scope of the
Preliminary analysis of our long-term observations re- present paper and will be presented elsewhere. However,
vealedaninterestingrelationbetweenthe variationofthe here we have used a simple model of the spots to analyze
amplitude of the variability and the change in the level some features of the light curves and suggest reasons for
ofmaximumbrightnessbetweendifferentseasons.We no- the phenomena exhibited above.
ticedthatsomeWTTSshowanincreaseofthe amplitude
of their variability accompanied with the rise of the max-
5. Preliminary Spot model and Some Results
imum level of brightness. The maximum brightness as a
function of the amplitude of the light curve for 4 such Models of light curves of TTs have been made based on
WTTS are shown in Figure 8. The increase of the am- assumed geometries of the spots, e.g. one or two circu-
plitude with the maximum level of brightness is clearly lar spots (Bouvier & Bertout 1989; Herbst 1989), while
visible on this Figure. This result is difficult to explain in othermodelshaveusedonlycertainpropertiesofthelight
amodelofastarspottedwithasingle,highlatitudespot. vari-ationssuchasamplitude asafunctionofwavelength
Increasingtheareaofsuchanalmost-polarspotwouldde- to infer a spotted regions (SR) general parameters, with-
crease the maximum brightness while increasing the am- outassumptionsaboutitsgeometry(Bouvieretal.1993).
plitude of the light curve, which is opposite to our mea- Assessmentofadvantagesanddisadvantagesofparticular
surements. A model with two nearly-polar spots in oppo- modelsisbeyondthescopeofourstudyanditiscertainly
site hemispheres can explain the observations if the incli- a good idea to model the data in a variety of ways. Here
nation angle of the star is sufficiently large so that both we simply note that the non-uniqueness of light curve so-
spots contribute to the light variations. In this case, it lutions means that the choice of particular geometries for
wouldbethemotionsofthespotsinlongitudethatwould the spots needs to be motivated by something other than
account for the amplitude variation, not the growth or the light curve data themselves. For instance, Alekseev
decay of a spot (see Grankin et al. 2002). & Gershberg (1996a) justifiably criticize attempts to use
In this connection we have investigated how Vmin, parametric models to study the surface nonuniformity of
Vmax and Vmean change with amplitude. We found four reddwarfstars with solar-typeactivity.Such models nor-
groupsofstarswithdifferentdependences betweenVmin, mallyassumetheexistenceoftwohigh-latitudespotsnear
Vmax, Vmean and amplitude. The first group of stars thestarsmagneticpoles,whilelong-termphotometricob-
includes V410 Tau, LkCa 1, LkCa2, LkCa 7, TAP 26, servations of red dwarfs provide evidence for the exis-
TAP57, and SR 9. In all these cases, when the amplitude tenceoflow-latitudespottedzones.Accordingly,Alekseev
increases, Vmax decreases (i.e. the star brightens), while &Gershberg(1996b)proposeamodelofzonalspottedness
Vmin increases, and the mean light level remains about forthesestars,inwhichacollectionofstarspotsisapprox-
constant. In Figure 9, the long term variations of Vmin, imated by two symmetric (about the equator)dark strips
Vmax and Vmean as a function of V amplitude for V410 with a variable spot-filling ratio in longitude. For WTTS,
Tau are presented. We can see that Vmax increases, and the situation with the choice of a particular spottedness
Vmin decreases when the amplitude increases. However, model is not yet so certain.
as the lower right panel of the figure shows, there is no On the one hand, the first detailed Doppler images of
correlation between Vmax and Vmin. the surfaces of the two brightest WTTS (V410 Tau and
A second group of stars exists which does show real HDE 283572), which were obtained by analyzing varia-
dependence between Vmax and Vmin (they decrease or tions in the line profiles over the rotation period, sug-
increase simultaneously). These stars are: LkCa 19, TAP gested that there were large cool spots at high latitudes
35, TAP 40, TAP 50, V819 Tau, V836 Tau, V1200 Tau (Joncour et al. 1994a,b). The origin of such high-latitude
and V1202 Tau. It may be noted, that these stars do not spots can be explained by the existence of a dipole mag-
show any reliable dependence between amplitude, Vmax netic field, whose presence is assumed by some current
and Vmin. A third group of stars shows dependence be- modelsthatdescribetheinteractionbetweenayoungstar
tweenamplitudeandVmin,butdoesnotshowdependence andadisk(seeforexampleShuetal.1994).Onthe other
betweenVmax,Vmeanandamplitude.Theseare:Anon1, hand, we discussed above that, based on the photometry
HD283572,LkCa 3,LkCa 4,Wa Oph/2,WaOph/3,V827 of 36 periodic WTTS, there is a similarity in behavior
Tau,andSR12.Afourthgroupdoesnotshowanydepen- with main-sequence dwarfs, BY Dra stars, and with RS
dences.Thesestarsare:LkCa11,V1197Tau,V1207Tau, CVn stars. So, it is arguable that some similarities exist
Wa Oph/1, VY Tau. In addition there are 3 stars which tosolar-typeactivity.Inthiscase,thelong-termevolution
we cannot classify unequivocally as belonging to any of ofthe photometriclightcurvesforWTTSmaybe improp-
these groups, namely TAP 45, V830 Tau, V1199 Tau. erly explained in terms of a model with only one or two
To summarize, all of the stars in Table 3 exhibit large, high-latitude spots.
the phenomenon of rotational modulation. But evolu- Here we will assume that there are many spots or
tion of phased light curves occurs in a variety of man- groups of spots on the surfaces of WTTS, including at
6 K.N. Grankin et al.: Resultsof theROTOR-program.II. The long-term photometric variability of WTTS
high latitude. Analysis of the Doppler images of the sur- ness of the star. Many authors assume that the observed
face of V410 Tau obtained by Rice & Strassmeier (1996) maximum brightness of the star (Vmax) corresponds to a
provides evidence for the existence of both high-latitude spot-free configuration. In this case, however, the phased
and low-latitude spots, consistent with this assumption. light curve may be expected to have a plateau at maxi-
We believe that the number of spots and their distribu- mum light., something that is rarely or never seen. Also,
tion over the WTTS surface remains an open question. inthiscaseastar’smaximumbrightnesscouldnotdepend
Accordingly, for our quantitative analysis of the spotted- onthe amplitude ofvariations,asfound forsome stars.It
ness parameters for the WTTS, we used a model whose may be seen on Fig. 8 that a decrease in periodicity am-
parametersdo not dependonthe number,shape,andpo- plitude is accompanied by a decrease in the star’s max-
sitions of the spots. This non-parametric model allows imum brightness in these cases. This demonstrates that,
only the total area and mean temperature of the spots forthesestars,the brighterstellarhemisphereisnotcom-
in the visible stellar hemisphere to be estimated. A de- pletelyfreefromspots.ThestellarphotospheresofallTTs
tailed description of this model can be found in Bouvier mostlikelyremainspottedtosomedegreeatallphasesof
et al. (1993); Grankin (1998, 1999). axialrotation.Thus,theobservedmaximumbrightnessof
Vogt (1981) showed that the light variations of a star a star is not the absolute maximum brightness of a spot-
due to the spottedness of its photosphere can be written ted star.It is quite clear,therefore,that only lowerlimits
as on the parameters of spotted regions can be determined
by using the observed maximum brightness of the star as
abs
(V ) (see also the discussion in Bouvier et al. 1993).
1−[1−S(λ)]Gmax(λ) max
△m(λ)=−2.5log , (1) Weattemptedtoobtainmorerealisticestimatesofthe
(cid:26)1−[1−S(λ)]Gmin(λ)(cid:27)
SRparametersby usinga linearrelationbetweenthe am-
whereS(λ) is the ratioofthe surfacebrightnessofthe SR plitudes of the periodicity in V and R. At minimum spot
to the brightness of the photosphere; and Gmax(λ) and visibility, Vmabasx is related to Vmax by
G (λ) are the spot areas at maximum and minimum
min
SR visibility, respectively. The spot area depends on the
abs
wavelength via the limb-darkening coefficient of the star. Vmax−Vmax =−2.5log{1−[1−LV]Gmin}. (4)
If we know the absolute maximum brightness of the star, We see from (4) that for Vabs to be determined, we
max
when its visible hemisphere is completely free from spots must know the degree of spottedness of the stellar sur-
(Gmin = 0), then equation (1) for the time of maximum face at minimum spot visibility. The following system of
SR visibility can be written as equations can be used to estimate Gmin:
abs
mmin(λ)−mmax(λ)=−2.5log{1−[1−S(λ)]Gmax(λ)}, 1− [1−LV]Gmax
VA = −2.5log
(2)  (cid:18)1−[1−LV]Gmin (cid:19)
(5)
where mambasx(λ) is the star’s absolute maximum bright-  1− [1−LR]Gmax
ness, and mmin(λ) is its minimum brightness in a specific RA = −2.5log(cid:18)1−[1−LR]Gmin (cid:19),
observing season. 
If the limb-darkening effect is ignored, then the spot whereVA andRA arethe amplitudesoftheperiodicityin
area can be assumed to be independent of wavelength. In VandR,respectively.We derivedthe equationfor VA by
the case of a broadband photometric system, relation (2) subtracting equation (4) from (3). The equation for RA
for V then takes the form was derived in a similar way.
From the set of G values obtained by solving (5),
min
we choose only those which satisfy the relation
abs
Vmin−Vmax =−2.5log{1−[1−LV]Gmax}, (3)
Vabs −Rabs ∼=(V−R) , (6)
where L = ( I (λ)Φ (λ)dλ) ( I (λ)Φ (λ)dλ), max max o
V sp V ph V
Iph(λ)andIsp(λ)-Raretheenergydist(cid:14)ribRutionsinthepho- where (V−R)o is the normal color index of the star that
tosphereandtheSR,respectively;Φ (λ)-istheresponse corresponds to its spectral type; Vabs and Rabs are the
V max max
curveoftheVfilter;V istheminimumVbrightnessfor maximum V and R brightness of the star estimated by
min
aspecificobservingseason;andVabs istheabsolutemax- substituting G into equation (4)written for the V and
max min
imum V brightness of the star.Equation(3) contains two R bands, respectively.
free parameters - the integral of the energy distribution In other words, the star’s Vabs − Rabs color index
max max
for the SR, which is uniquely related to the SR effective corrected for the reddening due to the spottedness of the
temperature,andthespotareaatmaximumSRvisibility. stellar surface must essentially match its normal color in-
These two free parameters can be determined by solving dex.Inthiscase,weobtainanupperlimitonVabs ,which
max
the system of two equations of type (3) written for the V obviously differs from the observed value V . The SR
max
and R bands. parameters determined from the upper limit on Vabs are
max
It may be noted that results of the computer simu- overestimated compared to their values calculated by as-
lation strongly depend on the assumed spot-free bright- suming that Vmabasx = Vmax. For this reason, we call the
K.N. Grankin et al.: Resultsof theROTOR-program.II. The long-term photometric variability of WTTS 7
SRparameterscalculatedbytheabovemethodthe upper as much as 20 years and proposed an empirical classifica-
limits on the spottedness parameters. tion scheme. We here apply the same statistical analysis
With the goal of testing of our model we have esti- to the long term variability of WTTS.
mated the spottedness parameters for VY Ari and com- AsinPaperI,wefirstdefineasetofstatisticalparam-
pared our results with the results that were obtained by eters which allow us to characterize the long term photo-
Alekseev & Gershberg (1996a,b) by using their model of metric variability of WTTS. In order to get robust sta-
zonalspottedness.The testing showsthatthe twomodels tistical estimates, we consider only the 33 stars that have
yieldsimilarresults,despite the significantdifferences be- at least 5 observing seasons containing at least 12 pho-
tween the two algorithms. For example, the difference in tometric measurements per season. As shown in Paper I,
the estimated effective spot temperatures (∆T) is 100 K, thisselectionprovidesreliablestatisticalestimatesoftheir
while the difference in the estimated fractionalspot areas variability. For each object, we compute the mean light
(∆G/G)does notexceed2.5-3.5%.Allthesefacts suggest level (Vm(i)) in each season (i) and the corresponding
that,despiteitssimplicity,ourmodelallowsthemainspot photometric range (∆V(i)). The mean of (Vm(i)) over all
parameterstobeestimatedwithasufficientaccuracy(see
seasonsyieldsthemeanlightleveloftheobject(Vm)while
Grankin 1998).
its standard deviation (σVm) measures the scatter of the
For the stars with the highest light curve amplitudes,
seasonalmeans.Similarly,wecomputetheaverageV band
thismodelshowsthatthespottedregionscoverfrom17to ∆V(i)
photometric amplitude over all seasons (∆V = ,
73% of the visible stellar hemisphere and that the mean PNs
temperature of the spots is 500-1400 K lower than the whereNs –numberofobservationalseasons)anditsstan-
ambient photosphere. An analysis of the calculated spot dard deviation (σ∆V). We also make use of the ratio
σ∆V . Two additional parameters were defined in Paper I,
parameters of V410 Tau revealed that there is a real ∆V
correlation between the amplitude of periodicity (∆V) namely C1 =< Vmed∆−VVmin >, where Vmed is the median
and the spot distribution nonuniformity (∆G), which is light level of the object in a given season, Vmin its maxi-
defined as the difference of spot coverage in the visible mum brightness level and ∆V its photometric amplitude
hemispheres of the star at maximum and minimum light: during this season and the bracket indicates an average
∆G=(Gmax−Gmin)∗100%,andGmax andGmin arethe over all seasons, which measures the prefered brightness
areaofthespottedregionatmaximumandminimumspot state of the object, and C2 = σVmin/σVmax, which char-
visibility, respectively. As the amplitude increases from acterizes the relative seasonalvariability of the maximum
0m.39 to 0m.63, the degree of nonuniformity in the spot and minimum light levels.
distribution increases from 21 to 37%. By contrast, the In addition to the statistical parameters above, we
amplitude is essentially independent of the variations in also characterize the long term photometric behaviour of
total spot areaS, where S =0.5∗(Gmax+Gmin)∗100%. WTTS by investigating their colour variations. Previous
Therefore, the change in the amplitude has to be caused studiesofthe shorttermvariabilityofWTTShaveshown
by a change in the distribution of the star spots rather that most stars tend to redden in colour indices (such as
than by a change in the total spot area. This is shown in V −R) when fading (e.g. Herbst et al. 1994)). This be-
Fig. 10 on the upper panel, where we plot the amplitude havior can result from surface cold spots (cf. Bouvier et
versus the degree of non-uniformity in the spot distribu- al. 2005). Some illustrations of the linear relations found
tion (∆G) and versus the total spot area (S). for most objects between the V −R colour and V magni-
Besides, the computer simulation has shown that the tude are given on Fig. 11. We characterize the colour be-
average magnitude (V) depends on the total spot area haviour of WTTS by computing the color slopes ∆(B−V)
∆V
(S) and it does not depend almost on the degree of non- and ∆(V−R) fromleast-squarefits,andthecorrelationco-
uniformity in the spot distribution (∆G). As the aver- ∆V
m m efficients ρB−V and ρV−R. We used the full set of data
age magnitude decreases from 10 .80 to 10 .95, the to-
pertaining to each object in order to compute these pa-
tal spot area increases from 44 to 53% (see Fig. 10, in-
rameters.
ferior panel). Thus, the cycles of star activity should be
The resulting values of the statistical and colour pa-
exhibited in quasi-cyclic variations of the average magni-
rameters for 33 WTTS whose light curves are shown in
tudefromseasontoseason.SomeWTTSfromoursample
Fig.12a and 12b are listed in Table 4. The columns in
may demonstrate such quasi-cyclic variations of the aver-
Table 4 provide the star’s name, the number of seasons
agemagnitude.We aregoingto continueourphotometric
∗
N with at least 12 measurements, the mean brightness
monitoring of selected spotted stars in an effort to detect s
and study the cycles of stellar-activity. level (Vm) and its seasonal standard deviation (σVm), the
averagephotometricrange(∆V,averagedoverallseasons)
and its seasonal standard deviation (σ∆V), the fractional
6. The long term variability of WTTS variation of photometric amplitude as measured by the
ratio σ∆V , the color slope ∆(B−V), their correlationcoef-
InPaperIwehaveundertakenastatisticalanalysisofthe ∆V ∆V
long-term light curves of classical T Tauri stars (CTTs) ficient ρB−V, the color slope ∆(∆VV−R) together with their
(Grankin et al. 2007). We have presented and character- correlation coefficient ρV−R, and the parameters C1 and
izedthelongtermphotometricvariationsof49CTTsover C2.
8 K.N. Grankin et al.: Resultsof theROTOR-program.II. The long-term photometric variability of WTTS
6.1. General photometric properties Fig. 17 and 18 show plots of the statistical param-
eters against each other that had allowed us in Paper
WTTS usually exhibit a low level of variability. A his-
I to identify various photometric subgroups within the
togramoftheaverageV-bandamplitudeforthe33WTTS
CTTS sample, corresponding to specific sources of vari-
inoursampleisshowninFig.13.Thedistributionisquite
ability(coldspots,hotspots,circumstellarextinction).In
peaked, with ∆V ranging from 0m.1 to 0m.55. Indeed, 28
contrast, WTTS appear in all these plots as an homoge-
WTTS (85%) in our sample exhibit small ranges of vari-
neous pho- tometric group characterized by a low level
ability between 0m.1 and 0m.3, and only 5 (15%) have
of variabil- ity as compared to CTTS. This confirms that
average V-band amplitudes larger than 0m.4 (LkCa 4,
the pho- tometric variability of WTTS is dominated by
LkCa7,SR 9,V410Tau,andV836Tau). The meanlight
a single process, namely the rotational modulation of the
level of WTTS also appears very stable over the years,
stellar flux by coldsurfacespots. Inother words,the usu-
withanexceedinglysmallstandarddeviationσVm.Itsdis- ally very stable long term (years) photometric variability
tribution is shown by the histogram in Fig. 14, with the
ofWTTSmerelyreflectsspotmodulationonmuchshorter
vast majority of WTTS having σVm ≤ 0m.05. Only one timescales(weeks).Althoughwedonotfindanyclearcor-
object, V836 Tau, exhibits significant changes in average
relationinWTTSbetweenthe variousvariabilityproxies,
brightnessovertheyears,withσVm =0m.2.Similarly,the the same trends found for CTTS over a much larger pho-
variationsofphotometricamplitudefromseasontoseason
tometricrangeareseen,suchas,e.g.,acorrelatedincrease
are small, amounting to less than 0m.1 for most WTTS,
of averageamplitude and its seasonal variations (Fig.17).
as shown by the histogram of σ∆V in Fig. 15. The more complicated C1 and C2 parameters proved
WTTS also exhibit a fairly straightforward V − R useful to distinguish the various sources of photometric
colour behaviour, turning redder when fainter. For most variabilityinCTTS(seePaperI).WTTSareshowninthe
objects in our sample, the (V −R) index scales linearly sameplotinFig.18.ExceptforonepeculiarWTTS,V830
with brightness,with a correlationcoefficient higher than Tau, all WTTS scatter around the mean value of these 2
0.47 for 26 WTTS. An illustration is provided in Fig. 11. parameters. This indicates that they have no preferred
Only 7 stars do not show any reliable dependence of brightness state (C2), and that their extreme brightness
V −Ronbrightness(correlationfactoroflowerthan0.47) levels(C1),highandlow,varybyaboutthesameamount
when averaged over all seasons. These stars are: SR 12, (see,e.g.,LkCa7,V410Tau,TAP50inFig.11b).Theiso-
TAP 35, V501 Aur, V1197 Tau, V1207 Tau, Wa Oph/2, lation of V830 Tau on this diagramoccurs because σVmax
and Wa Oph/3. The linear relation is replaced by a wide is three times greater than σVmin. No WTTS are found
scatter of points on the diagram for these stars. in the lower left corner or in the upper right corner of
A histogramof ∆(V−R) color slopes for the 26 WTTS this plot, which were shown in Paper I to correspond to
∆V
withlinearcolorvariationsisshowninFig.16.Itstrongly UXor-type circumstellar extinction events and hot spot
peaksatvaluesof0.2–0.4.InWTTS,brightnessandcolor dominated variability, respectively. This is again consis-
variations result from the rotational modulation of the tent with the cold surface spots being the dominant and
stellar flux by cold surface spots. We showed in Paper I probably single source of variability in WTTS.
thatCTTSexhibitthesameaverage ∆(V−R) colorslopeas Conversely,wenotethatmanyCTTSarefoundinthe
∆V same locationas the WTTS in this diagram,eventhough
WTTS.Thismightbeanindicationthatthephotometric
CTTS photometric variability is probably due to a mix-
variability of CTTS is also dominated by cold spots, but
ture of hot and cold surface spots (see Paper I). This is
hot spots as well as circumstellar extinction can produce
not unexpected, however : as long as the surface spots
this kind of V − R color variations as well (Bouvier &
never disappear from view as the star rotates, the sys-
Bertout 1989).
tem’smeanlightlevelaswellasitsextremawillbedriven
A similar analysis was carried out for the B −V in-
by spot modulation, regardlessof the spot’s temperature.
dex. Unlike the V −R index, B−V variationsshow little
Hence, the system will have no preferred brightness state
correlation with brightness, as seen from the low value of
(C2 ≃0.5) and its extreme values will exhibit about the
the correlation coefficients listed in Table 4. Only 3 stars
same amount of variability (C1 ≃1.). More extreme val-
(TAP50, V410 Tau, and V827 Tau) show a reliable de-
uesoftheC1andC2parametersareexpectedonlyinthe
pendenceofB−V onbrightness(correlationfactorlarger
particular case of a low latitude hot spot located at the
than 0.47) when averaged over all seasons. The lack of a
surfaceofahighlyinclinedsystem,inwhichcasethe spot
correlation between brightness and B-V colour could be
disappears for part of the rotational cycle.
due to flares and/or chromospheric variability.
That CTTS share the same location as WTTS in this
diagramthus does notimply thattheir sourceofvariabil-
6.2. Correlated properties ity is the same.It does imply, however,that surface spots
in most CTTS, as in most WTTS, never disappear from
In Paper I, we investigated the relationships between the view as the system rotates. In turn, this suggests that
various statistical parameters we defined for CTTS. We hotaccretionspotsinCTTSarelocatedatrelativelyhigh
do the same herefor WTTSandcontrastthe resultswith latitudes on the stellar surface, as expected from accre-
those obtained for CTTS. tionfromthe innerdisk edgeontoaslightlytilted dipolar
K.N. Grankin et al.: Resultsof theROTOR-program.II. The long-term photometric variability of WTTS 9
magnetosphere. In addition, the impact of hot spots on ity of phase of minimum light most strongly over many
photometric variations is expected to be more conspicu- years.The datapresentedhereshouldproveuseful infur-
ous at shorter wavelengths (e.g., U and B-bands) than at therinvestigationsofthenatureandevolutionofspotson
V (Bouvier & Bertout 1989). WTTS.
Acknowledgements. The authors wish to thank O. Ezhkova,
7. Conclusions M. Ibrahimov, V. Kondratiev, S.Yakubov,S. Artemenkoand
many other observers and students, who worked or are still
Our main conclusion is that most WTTS have very sta-
workingin theTashkentAstronomical Institute,for theirpar-
ble long term variability with relatively small changes of
ticipation in the photometric observations. We are particu-
amplitude or mean light level. The long term variability larly grateful to C. Dougados, C. Bertout, and F. M´enard
seen merely reflects modulation in the cold spot distribu- for their comments and suggestions pertaining to this work.
tions. Photometric periods are stable over many years,as Support of the American Astronomical Society, European
is the phase of minimum light for most objects, within Southern Observatory (grant A-02-048), and International
some range. On the long term, the spot properties do Science Foundation by Soros (grant MZA000) and a CRDF
change in subtle ways, leading to some variations in the grant (ZP1-341) is acknowledged. This work was also sup-
ported by a NATO Collaborative Linkage grant for European
shape and amplitudes of the light curves. The long term
countries(PST.CLG.976194)andbyanECO-NETprogramof
variability of WTTS is thus perhaps best understood by
the French Ministry of Foreign Affairs, which we both grate-
assuming that they are covered by a number of spots un-
fully acknowledge. W.H. gratefully acknowledges the support
evenly distributed on the stellar surface and located at
of NASA through its Origins of Solar Systems Program. We
preferential longitudes and/or latitudes, much like active
especially thank the referee F. Vrba for helpful comments on
belts in the SunandRSCVn systems,ratherthanresult- theoriginal version of this manuscript.
ing from a single polar spot. Such an uneven spot distri-
butionwouldaccountforthereportedcorrelationbetween
8. References
amplitude and brightness level, as well as for the quasi-
sinusoidal shape of the light curves, which indicates that Alekseev, I. Y. & Gershberg, R. E. 1996a,AZh, 73, 589
the unspotted photosphere is not seen in these stars at Alekseev, I. Y. & Gershberg, R. E. 1996b,AZh, 73, 579
any rotational phase. It also implies that the coverage of Attridge, J. M. & Herbst, W. 1992, Astrophys.J. (Lett.),
the stellar photosphere by cold spots may be much larger 398, L61
thananticipatedfromsimplemodellingofthelightcurves, Berdnikov, L. N., Grankin, K. N., Chernyshev, A. V., et
whichonlyprovidelowerlimitstothespotarealcoverage. al. 1991, Soviet Astron. Lett., 117, 23
Doppler imaging of a sample of typical WTTS could be Bouvier, J. & Bertout, C. 1989, A&A, 211, 99
an effective means to obtain further constraints on the Bouvier,J.,Bertout,C.,Benz,W.,etal.1986,A&A,165,
distribution of cold spots at the surface of WTTS. 110
Modelling ofthe lightcurvesforV819Tau,V827Tau, Bouvier, J., Boutelier, T., Alencar, S., et al. 2005, in
V830 Tau and V836 Tau indicates that the spotted re- ProtostarsandPlanetsV(LPIContributionNo.1286.),
gions cover as much as 30 to 90% of the visible stellar 8150
hemisphere and that the mean temperature of the spots Bouvier, J., Cabrit, S., Fernandez, M., et al. 1993, A&A,
is 500–1400K lower than the ambient photosphere. More 272, 176
detailedmodelcalculationsofthelightcurveofV410Tau Bouvier, J., Covino, E., Kovo,O., et al. 1995, A&A, 299,
showed that: 89
(i) The decrease in mean brightness is attributable to Bouvier, J., Forestini, M., & Allain, S. 1997a, A&A, 326,
the increase in totalspot areafrom 47 to 53%andthat it 1023
is essentially independent of the degree of nonuniformity Bouvier, J., Wichmann, R., Grankin, K., et al. 1997b,
in the spot distribution over the surface. A&A, 318, 495
(ii) The amplitude of the phased light curve depends Butler, C. J. 1996,Proc. IAU Symposium, 176, 423
on the degree of nonuniformity in the spot distribution Choi, P. I. & Herbst, W. 1996, Astron.J., 111, 283
more strongly than on the stars total spot area. An in- Cohen, R., Herbst, W., & Williams, E. 2004, Astron.J.,
crease in amplitude was accompanied by an increase in 127, 1602
the degree of nonuniformity in the spot distribution over Covino, E., Terranegra, L., Franchini, M., et al. 1992,
the stellar surface from 21 to 35%. A&AS, 94, 273
(iii) There is a weak correlationbetween the star’s to- Eaton, N. L., Herbst, W., & Hillenbrand, L. 1995,
tal spot area and its degree of nonuniformity in the spot Astron.J., 110, 1735
distribution with the correlation coefficient k=0.71. The Edwards, S. E., Strom, S., & Hartigan, P. H. 1993,
increase in the stars total spot area from 47 to 53% was Astron.J., 106, 372
accompaniedbyadecreaseinthedegreeofnonuniformity Ehgamberdiev, S. A., Baijumanov, A. K., Ilyasov, S. P.,
in the spot distribution from 35 to 21%. et al. 2000, A&AS, 145, 293
The most active variable stars in our sample (i.e. Ghez, A. M., Neugebauer, G., & Matthews, K. 1993, AJ,
those with the largest amplitudes) demonstrate stabil- 106, 2005
10 K.N. Grankin et al.: Resultsof theROTOR-program.II. The long-term photometric variability of WTTS
Grankin, K., Melnikov, S., Bouvier, J., et al. 2007, A&A, Shu, F., Najita, J., Ruden, S., et al. 1994, ApJ, 429, 797
461, 183 Stelzer,B.,Fernandez,M.,Costa,V.M.,etal.2003,A&A,
Grankin, K. N. 1991, Inform. Bull. Var. Stars., N3658 411, 517
Grankin, K. N. 1992, Inform. Bull. Var. Stars., N3720 Strauzis,V.1977,MulticolorStellarPhotometry(Vilnius:
Grankin, K. N. 1993, Inform. Bull. Var. Stars., N3823 Mokslas)
Grankin, K. N. 1994, Inform. Bull. Var. Stars., N4042 Vogt, S. S. 1981, ApJ, 250, 327
Grankin, K. N. 1996, Inform. Bull. Var. Stars., N4316 Vrba, F. J., Chugainov,P.F., Weaver,W. B., et al. 1993,
Grankin, K. N. 1997, Astron. Lett., 23, 700 AJ, 106, 1608
Grankin, K. N. 1997,in Low Mass Star Formation - from Vrba, F. J., Herbst, W., & Booth, J. 1988, Astron.J., 96,
Infall to Outflow., ed. F. Malbet & A. Castets (Proc. 1032
IAU Symposium N. 182. Dordrecht: D. Reidel Publ. Walter, F. M., Brown, A., Linsky, J. L., et al. 1987, ApJ,
Company.), 281 314, 297
Grankin, K. N. 1998, Astron. Lett., 24, 580 White, R. J. & Ghez, A. M. 2001, ApJ, 556, 265
Grankin, K. N. 1999, Astron. Lett., 25, 611 Zakirov, M. M., Azimov, A. A., & Grankin, K. N. 1993,
Grankin, K. N., Granzer, T., & Strassmeier, K. 2002, in Inform. Bull. Var. Stars., N3898
1st Potsdam Thinkshop Poster Proceedings. (Potsdam,
Germany, May 6-10), 77
Grankin, K. N., Ibragimov, M. A., Kondratiev, V. B., et
al. 1995, AZh, 72, 894
Herbig,G.H.& Bell,K.R.1988,Lick Obs.Bull.,1111,1
Herbst, W. 1989,Astron.J., 98, 2268
Herbst, W., Herbst, D. K., Grossman, E. J., et al. 1994,
AJ, 108, 1906
Herbst, W. & Mundt, R. 2005, ApJ, 633, 967
Horne, J. H. & Baliunas, S. L. 1986, AJ, 302, 757
Horne,K.,Wade,R.A.,&Szkody,P.1986,MNRAS,219,
791
Irwin, J., et al. 2007, MNRAS, 380, 541
Joncour, I., Bertout, C., & Bouvier, J. 1994a, A&A, 291,
L19
Joncour,I., Bertout, C., & Menard, F. 1994b,A&A, 285,
L25
Landolt, A. U. 1983, AJ, 88, 439
Landolt, A. U. 1992, AJ, 104, 340
Leinert, C., Zinnecker, H., Weitzel, N., et al. 1993, A&A,
278, 129
Losh, H. M. 1939, Pub. Zurich Obs, 2
Mandel, G. N. & Herbst, W. 1991, Astrophys.J. (Lett.),
383, L75
Mathieu, R. D., Walter, F. M., & Myers, P. C. 1989, AJ,
98, 987
Mundt, R., Walter, F. M., Feigelson, E. D., et al. 1983,
ApJ, 269, 229
Nemec, A. F. L. & Nemec, J. M. 1985, AJ, 90, 2317
Nikonov, V. 1976, Izvestiya KrAO, 54, 3
Petrov, P., Shcherbakov, V., Berdyugina S. et al. 1994,
Astron. Astrophys. Suppl. Ser., 107, 9
Press, W. H. & Rybicki, G. B. 1989, ApJ, 338, 277
Reipurth, B. & Zinnecker, H. 1993, A&A, 278, 81
Rice, J. & Strassmeier, K. 1996, A&A, 316, 164
Rydgren, A. E. & Vrba, F. J. 1983, ApJ, 267, 191
Rydgren, A. E., Zak, D. S., Vrba, F. J., et al. 1984, AJ,
89, 1015
Shevchenko,V. S. 1989,Herbig Ae/Be Stars (in Russian)
(Tashkent: FAN)
Shevchenko, V. S., Ezhkova, O. V., Kondratiev, V. B., et
al. 1995, Inform. Bull. Var. Stars., N4206
Shevchenko, V. S. & Herbst, W. 1998, AJ, 116, 1419