Placing the spotted T Tauri star LkCa 4 on an HR diagram

4.4 MB·

by  Michael A. Gully-Santiago

Accepted to ApJ
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
PLACING THE SPOTTED T TAURI STAR LKCA 4 ON AN HR DIAGRAM
Michael A. Gully-Santiago,1 Gregory J. Herczeg,1 Ian Czekala,2 Garrett Somers,3,18 Konstantin Grankin,4
Kevin R. Covey,5 J.F. Donati,6,7 Silvia H. P. Alencar,8 Gaitee A.J. Hussain,9,10 Benjamin J. Shappee,11,12
Gregory N. Mace,13 Jae-Joon Lee,14 T. W.-S. Holoien,15,16 Jessy Jose,1 Chun-Fan Liu17,1
Accepted to ApJ
ABSTRACT
Ages and masses of young stars are often estimated by comparing their luminosities and effective
temperaturestopre-mainsequencestellarevolutiontracks,butmagneticfieldsandstarspotscomplicate
7 both the observations and evolution. To understand their influence, we study the heavily-spotted
1
weak-lined T-Tauri star LkCa 4 by searching for spectral signatures of radiation originating from the
0
starspot or starspot groups. We introduce a new methodology for constraining both the starspot filling
2
factor and the spot temperature by fitting two-temperature stellar atmosphere models constructed
n from Phoenix synthetic spectra to a high-resolution near-IR IGRINS spectrum. Clearly discernable
a spectralfeaturesarisefrombothahotphotosphericcomponentT ∼4100Kandtoacoolcomponent
hot
J T ∼2700−3000 K, which covers ∼80% of the visible surface. This mix of hot and cool emission
cool
4 is supported by analyses of the spectral energy distribution, rotational modulation of colors and of
2 TiO band strengths, and features in low-resolution optical/near-IR spectroscopy. Although the revised
effective temperature and luminosity make LkCa 4 appear much younger and lower mass than previous

] estimates from unspotted stellar evolution models, appropriate estimates will require the production
R
and adoption of spotted evolutionary models. Biases from starspots likely afflict most fully convective
S young stars and contribute to uncertainties in ages and age spreads of open clusters. In some spectral
. regions starspots act as a featureless “veiling” continuum owing to high rotational broadening and
h
p heavy line-blanketing in cool star spectra. Some evidence is also found for an anti-correlation between
- the velocities of the warm and cool components.
o
Subject headings: stars: fundamental parameters — stars: individual (LkCa 4) — stars: low-mass –
r
stars: statistics
t
s
a
[ 1. INTRODUCTION The causes of age uncertainties and of large luminosity

spreads in young clusters are controversial (see reviews
1
v 1KavliInstituteforAstronomyandAstrophysics,PekingUni- by Preibisch 2012; Soderblom et al. 2014). Absolute ages
3 versity,YiHeYuanLu5,HaidianQu,100871Beijing,People’s are usually inferred from comparisons between observed
0 RepublicofChina stellar properties and pre-main sequence evolutionary
7 2KIPAC,PhysicsandAstronomy,StanfordUniversity,Stan- models, which are sensitive to stellar birthlines and the
ford,CA
6 3DepartmentofPhysicsandAstronomy,VanderbiltUniversity, input physics that controls the contraction and internal
0 6301StevensonCenter,Nashville,TN,37235,USA heating. Within clusters, any real differences in ages
. 4CrimeanAstrophysicalObservatory,Nauchny,Crimea298409, between stars may be masked by observational uncertain-
1 Russia
ties in temperature and luminosity measurements (e.g.
0 5DepartmentofPhysics&Astronomy,WesternWashington
7 University,BellinghamWA98225-9164,USA Hartmann 2001; Slesnick et al. 2008).
6CNRS,IRAP/UMR5277,Toulouse,14avenueE.Belin,F- Magnetic activity is a likely source of significant un-
1
31400France certainty in both the models and observations of young
v: 7UniversitédeToulouse,UPS-OMP,IRAP,14avenueE.Belin, low-massstars. Convectionattheseyoungagesgenerates
Toulouse,F–31400France
Xi 8DepartamentodeFìsica–ICEx–UFMG,Av. AntônioCar- strong magnetic fields, as measured by Zeeman broad-
los,6627,30270-901BeloHorizonte,MG,Brazil ening and polarimetry (e.g. Johns-Krull 2007; Donati &
r 9EuropeanSouthernObservatory,Karl-Schwarzschild-Str. 2, Landstreet 2009) and as seen in starspots (e.g. Stauffer
a 85748GarchingbeiMünchen,Germany
10InstitutdeRechercheenAstrophysiqueetPlanétologie,Uni- etal.2003;Grankinetal.2008). Evolutionarymodelsare
versitédeToulouse,UPS-OMP,F-31400Toulouse,France justnowstartingtoimplementprescriptionsforhowspots
11CarnegieObservatories,813SantaBarbaraStreet,Pasadena, andmagneticfieldsaffecttheinteriorstructure(MacDon-
CA91101,USA ald & Mullan 2013; Jackson & Jeffries 2014; Somers &
12Hubble,Carnegie-PrincetonFellow
13Department of Astronomy, The University of Texas at Pinsonneault 2015a; Feiden 2016). Stellar evolution mod-
Austin,2515SpeedwaySt,Austin,TX,USA els that include these effects can make a coeval 10 Myr
14KoreaAstronomyandSpaceScienceInstitute,776Daedeok- population exhibit apparent age spreads of 3−10 Myr.
daero,Yuseong-gu,Daejeon305-348,Korea. Mass estimates may also be biased to lower masses, as
15DepartmentofAstronomy,TheOhioStateUniversity,140
measured for some eclipsing binaries (e.g. Stassun et al.
West18thAvenue,Columbus,OH43210,USA
16CenterforCosmologyandAstroParticlePhysics(CCAPP), 2014;Rizzutoetal.2016). Observationally,starspotsmay
The Ohio State University, 191 W. Woodruff Ave., Columbus, also be responsible for biases in stellar effective tempera-
OH43210,USA
tures derived by different methods. For example, the ef-
17InstituteofAstronomyandAstrophysics,AcademiaSinica
(ASIAA),Taipei10617,Taiwan fective temperatures for 3493 young stars measured using
18VIDAPostdoctoralFellow theAPOGEEspectrograph(1.5−1.70µmatR=22,500
2 Gully-Santiago et al.
Wilson et al. 2010) are offset from and usually cooler Kraus et al. 2011; Daemgen et al. 2015)19 or from RV
than prior measurements made at optical wavelengths searches (Nguyen et al. 2012) and high-precision Zeeman
(Cottaar et al. 2014). Similarly, near-IR spectral types Doppler Imaging (Donati et al. 2014). This single star
of young stars have sometimes been evaluated as later demonstrates a large amplitude of sinusoidal photometric
than optical spectral types (Bouvier & Appenzeller 1992; variability indicative of large spots (Grankin et al. 2008;
Vacca & Sandell 2011). Xiao et al. 2012). The variability amplitude cannot arise
Rotational modulation from starspots is understood from an eclipsing binary since the large RV variations
as the cause of cyclic variations in weak-lined T Tauri would have been seen in spectroscopic monitoring. All of
stars (WTTSs) and some classical T Tauri stars (e.g. these observations indicate that the spectrum of LkCa
Vrba et al. 1986; Herbst et al. 1994). Spots have recently 4 should be devoid of complicating factors like near-IR
been observed with exceptional photometric precision excess veiling, accretion excess, or close binarity.
from monitoring surveys targeting exoplanet transits (e.g LkCa 4 has recently been examined with ZDI (Donati
Harrison et al. 2011; Davenport et al. 2015). The sin- et al. 2014), revealing a complex distribution of cool and
gle band light curves from such surveys cannot separate warm spots in brightness map reconstructions. Dark
the relative areas and temperatures of the emitting re- polar spots extend to about 30◦ from the pole, with
gions, and therefore cannot yield estimates for the filling about 5 appendages reaching down to about 60◦ from
factor of spots without making assumptions about the the pole. There is also evidence for a hot spot in the
relative temperature contrast. Contemporaneous or near- reconstructed ZDI map. These spot maps demonstrate
contemporaneous panchromatic photometric monitoring that multiple temperature components contribute to the
(Herbstetal.1994;Petrovetal.1994;Bouvieretal.1995; broadbandemissionfromthestar, whichmayexplainthe
Grankin et al. 2007; Cody et al. 2014) can break the largedifferencesbetweenthe4100Keffectivetemperature
degeneracy between starspot filling factor and starspot measurement obtained from high-resolution optical spec-
temperature, but these measurements are still limited tra (Donati et al. 2014) compared with 3600 K obtained
to detecting large longitudinally asymmetric starspots. from an analysis dominated by TiO bands (Herczeg &
Transiting planets or eclipsing binaries passing in front Hillenbrand 2014).
of starspots (Desert et al. 2011) can break geometric In this work, we measure the starspot properties of
degeneracies, providing estimates for the characteristic LkCa 4 with four complementary techniques.20 Section 2
sizes and lifetimes of starspots or starspot groups, but describes the full spectroscopic and photometric dataset
the number of such transiting systems and demands of and quantifies the optical variability of LkCa 4 over the
high photometric precision limit wider application. Zee- last 31 years based on all available photometric monitor-
man Doppler Imaging (Donati et al. 2014, ZDI) produces ing; acollectionofspectralobservationsatvariousphases
the latitudinal and longitudinal distribution of starspots ofvariabilityisintroduced. Section3andAppendixAde-
in reconstructed brightness maps based on models for scribeaspectralinferencetechniqueaimedatgeneralizing
spectro-polarimetric line shapes but would be unable to linedepthratioanalysis,whichisappliedtoahighresolu-
identify uniform distributions of small spots. All of these tion H and K near-IR spectrum of LkCa 4 in Section 3.5.
techniques would tend to underestimate the fractional Section 4 shows results from SED fitting, polychromatic
coverage of starspots distributed isotropically on the sur- photometric monitoring, and optical TiO line-depth ratio
face, stars viewed pole-on, or stars with longitudinally fitting. All lines of evidence are ultimately combined to
symmetric bands of starspots. build a consistent picture of the spectral and temporal
Spectroscopic strategies have the power to measure evolution of LkCa 4. Section 5 describes how the two-
both the starspot areal coverage and temperature in any temperature fit affects the placement of LkCa 4 on the
geometric configuration. For WTTSs, SED modeling HRdiagramandwhatcanbeunderstoodaboutpre-main
indicated the presence of cool spots (Wolk & Walter sequence stellar evolution from this exemplar. Finally,
1996), while spot temperatures have been estimated from Section 6 describes how our results should be interpreted,
rotationalmodulationofopticalcolors(e.g.Grankin1998; the implications for analyses of spots in high-resolution
Venuti et al. 2015; Koen 2016). The TiO bands in optical spectra, and methodological limitations.
spectra have been used to measure spots on WTTSs
(Petrov et al. 1994), stars with ages of 125 Myr in the 2. OBSERVATIONS
Pleiades (Fang et al. 2016), and evolved stars (e.g. Neff
2.1. IGRINS Spectroscopy
etal.1995;O’Nealetal.2001,2004). Recentspectroscopic
WeacquiredobservationsofLkCa4withtheImmersion
detections of spots on young stars have focused on TW
GratingInfraredSpectrograph,IGRINS(Parketal.2014)
Hya, an active accretor, and DQ Tau, a close binary in
on the Harlan J. Smith Telescope at McDonald Observa-
which both components are accreting (Debes et al. 2013;
toryon2015-11-1809h UTC.IGRINSisahighresolution
Bary & Petersen 2014).
near-infraredechellespectrographprovidingsimultaneous
The star LkCa 4, a WTTS member of the Taurus
R(cid:39)45,000 spectra over 1.48-2.48 µm. The spectrograph
Molecular Cloud (Herbig et al. 1986; Strom et al. 1989a;
has two arms with 28 orders in H−band and 25 orders
Downes & Keyes 1988; Strom et al. 1989b) is an ideal
in K−band. The data were reduced with the Pipeline
exemplar for a spotted pre-MS star because it does not
have any mid-IR or mm excess (e.g. Andrews & Williams
2005; Furlan et al. 2006; Buckle et al. 2015) and is not 19 Thestatusforwidecompanionsislessclear;seeStaufferetal.
(1991);Itohetal.(2008);Kraus&Hillenbrand(2009);Krausetal.
actively accreting (e.g. Edwards et al. 2006; Cauley et al.
(2011);Herczeg&Hillenbrand(2014)
2012). LkCa 4 has no evidence for a close companion 20 Some data, Python code, Starfish configuration files, and
from either direct imaging searches (Karr et al. 2010; otherdocumentsrelatedtothispaperareavailableontheproject’s
GitHubrepositoryathttps://github.com/BrownDwarf/welter
Starspots on LkCa 4 3
Package (Lee 2015). Telluric correction was performed
TABLE 1
by dividing the spectrum of LkCa 4 by a spectrum of HR
Estimated BVR magnitudes
1237, an A0V star observed immediately before LkCa 4 ,
bothatairmass1.1. ThebroadhydrogenlinesintheA0V
JD−2450000 Instrument B V R
star produced excess residuals in the spectrum of LkCa 4.
Noeffortwasmadetomitigatethesefluxexcessresiduals, 781.7106 2MASS 14.02 12.61 11.25
4830.5637 TripleSpec ··· 13.02 ···
which affect several spectral orders. These orders were
4830.7719 DoubleSpec ··· 12.94 ···
ultimately excluded from further analyses. 6665.7204 ESPaDOnS 14.36 12.87 11.71
6666.8505 ESPaDOnS 14.15 12.69 11.65
2.2. ESPaDOnS Spectroscopy 6667.7727 ESPaDOnS 14.31 12.87 11.63
6668.8699 ESPaDOnS 14.44 12.94 11.75
We used ESPaDOnS on CFHT to obtain twelve high- 6672.8995 ESPaDOnS 14.25 12.80 11.56
resolution optical spectra of LkCa 4 from 8-21 Jan. 2014 6673.8408 ESPaDOnS 14.12 12.67 11.62
6674.7746 ESPaDOnS 14.46 12.99 11.85
as part of the MaTYSSE Large Program. These spectra
6675.7396 ESPaDOnS 14.40 12.90 11.73
cover 3900−10000 Å at R∼68,000 and were obtained in 6676.7954 ESPaDOnS 14.18 12.72 11.65
spectropolarimetry mode. The Zeeman Doppler Imaging 6677.8699 ESPaDOnS 14.29 12.86 11.61
obtainedfromtheseobservationswereanalyzedbyDonati 6678.7419 ESPaDOnS 14.53 13.02 11.80
6678.8950 ESPaDOnS 14.47 12.97 11.75
et al. (2014). In this paper, we concentrate on the inten-
7344.8610 IGRINS 14.24 12.84 11.38
sity spectrum. To calculate TiO indices, the relative flux
calibrationwasobtainedfromanapproximateinstrument
Integral-OMC obtained 138 V−band measurements from
sensitivity calculated from observations of 72 Tau. The
2006−2008 (Alfonso-Garzón et al. 2012). The AAVSO
spectral shapes match the flux calibrated low-resolution
archive (Kafka 2016) includes 385 V, 23 B and 10 R
spectra described in §2.3.
measurements from 2013−2016. Unpublished data from
2.3. Low-resolution optical and near-IR spectra the ASAS-SN survey (Shappee et al. 2014) were obtained
from 2012 January – 2016 March in 186 visits. Finally,
A flux-calibrated low-resolution optical spectrum of
recent photometry from the ongoing Crimean Astrophys-
LkCa 4 was obtained using Palomar/DBSP (DBSP, Oke
ical Observatory (CrAO) ROTOR project (Grankin et al.
&Gunn1982)on30Dec. 2008at06:30UT.Thesespectra
2008) is presented here for the first time. The CrAO
cover 3200–8700 Å at a spectral resolution R∼500. The data includes 43 BVR visits from August 2015 - March
data reduction and a spectral analysis are described by 2016. Figure 1 displays all the V−band photometry over
Herczeg & Hillenbrand (2014) within the context of a the interval 1985-2016. HJD, BJD, and JD are simply
larger survey. referred to as JD, which is accurate to the precision of
Near-infraredspectraofLkCa4wereobtainedat 01:30 available data.
UT on Dec. 30, 2008, a few hours earlier than the DBSP Figure 2 shows all available V−band data grouped by
spectra, using the TripleSpec spectrograph on the Astro- the 22 observing seasons and phase-folded by the period
physical Research Consortium (ARC) 3.5 meter telescope P =3.375 days obtained from multiterm Lomb-Scargle
at Apache Point Observatory in Sunspot, New Mexico. periodograms(Ivezićetal.2014). Thegeneralappearance
LkCa 4 was observed for a total integration time of 90 s of the phase-folded lightcurves does not change with per-
using an ABBA dither sequence along the slit to remove turbations to the period on the scale of 0.003 days. The
sky emission by differencing sequential exposures. With estimated BVR magnitudes at the time of the spectral
the 1.1(cid:48)(cid:48) slit used for these observations, TripleSpec pro- observations are determined from regularized multiterm
vides nearly contiguous coverage from 0.95 to 2.46 µm fits (VanderPlas & Ivezić 2015, i.e. Fourier series trun-
at a resolution of R ∼3200 (Wilson et al. 2004). Spectra catedtothefirst∼4components)shownasthesolidblue
were reduced with a variant of the SpeXTool pipeline, lines in Figure 2. Table 1 lists the estimated BVR pho-
originallydevelopedbyCushingetal.(2004)andmodified tometry and the observing epoch for data from IGRINS,
for use with TripleSpec data. Spectra were differenced, ESPaDOnS, 2MASS (Skrutskie et al. 2006), DBSP, and
flattened, extracted, and wavelength calibrated prior to TripleSpec.
telluric correction and flux calibration; the latter two
corrections were performed using the XTELLCOR IDL 3. FITSTOHIGHRESOLUTIONSPECTRA
package (Vacca et al. 2003) and a spectrum of HD 25175,
Starspots possess a spectrum distinct from the ambient
a nearby A0V star observed directly after LkCa 4 at a
photosphere. Approaches like ZDI and line-bisector anal-
similar airmass.
ysis (e.g. Prato et al. 2008; Donati et al. 2014) target the
modulationofstellarphotosphericlinesasstarspotsenter
2.4. Photometric monitoring
and exit the observable stellar disk. In contrast, the tech-
Photometry in B, V, and/or R-bands in 1216 distinct nique described in this Section measures the spectrum
epochs was assembled from published and unpublished that emerges from both the hot and the cool surfaces of
data sources spanning 31 years in 22 observing seasons. the photosphere.
Published data targeting LkCa 4 is composed of 29 BVR Starspotlinedepthratioanalysishastraditionallybeen
visitsfrom1985−1986(Vrbaetal.1993),26BVRepochs limited to isolated portions of spectrum that possess
from 1990−1991 (Bouvier et al. 1993), 284 visits in V- absorption lines attributable only to cool photospheric
band (278 with B and 268 with R) from 1992 August - components and spectral lines arising from the warmer
2004 October (Grankin et al. 2008), and 10 BVR visits ambient photosphere (e.g. Neff et al. 1995; O’Neal et al.
from 2013 (Donati et al. 2014). ASAS3 (Pojmański 2004) 2001). The apparent veiling of the lines and their respec-
acquired 63 V−band measurements from 2002−2004. tive temperature dependences can be combined to solve
4 Gully-Santiago et al.
12.2
12.4
12.6
12.8
V
Vrba et al. 1993 AAVSO
13.0 Bouvier et al. 1993 Grankin unpublished
Grankin et al. 2008 2MASS
13.2 ASAS3 TripleSpec
Integral-OMC DoubleSpec
Donati et al. 2014 ESPaDOnS
13.4 ASASSN IGRINS
2448000 2450000 2452000 2454000 2456000
JD
Fig. 1.— Overview of LkCa 4 V−band photometric monitoring from 1986−2016. The vertical lines denote the observing epochs of
2MASS,IGRINS,ESPaDOnS,DBSP,andTripleSpec. ThenearcontemporaneousDBSPandTripleSpecepochslayontopofeachotheron
thisscale,asdothe12ESPaDOnSepochs. Theabscissarangeisequaltothecurrentlifespanofthefirstauthorofthispaper.
for the cool photosphere and ambient photosphere tem- Appendix of C15). The forward model includes calibra-
peratures and relative areal coverages. This line depth tion parameters, line spread functions, and a Gaussian
ratio method suffers from the need to identify portions of process noise model to account for correlations in the
the spectrum that possess easily identifiable strong lines, residual spectrum. We employed the Phoenix grid of
and from the need to assemble large atlases of observed pre-computed synthetic stellar spectra, which are pro-
spotlessspectraltemplatestowhichthespottedstarspec- vided at high spectral resolution over a wide wavelength
trum can be compared. In this section, we introduce a range at 100 K intervals in stellar photospheric tempera-
generalization of the line depth ratio analysis which em- ture22 in our range of interest (Husser et al. 2013). The
ployspixel-by-pixelmodelingofallechellespectralorders. modularframeworkwasalteredtoaccommodatestarspot
Byusingallthespectraldata,thisstrategyhasthepower measurements in two ways. First, the single photospheric
to constrain starspot properties at relatively low filling componentwasupdatedtoincludetwophotosphericcom-
factors and to identify weak lines that originate from the ponents. Second, the MCMC sampling strategy was
cool photosphere. altered to accommodate the additional free parameters
We took two approaches to characterizing the photo- added by the two component model.
spheric temperature from a spotted-star spectrum. First, The stellar photosphere is characterized as two photo-
using the spectral fitting approach introduced in Section spheric components with a cool temperature T and
cool
3.1, we separately fit the optical (ESPaDOnS) and near- hot temperature T , with scalar solid angular coverages
hot
IR (IGRINS) spectra with distinct, single photospheric Ω and Ω , respectively23. The choice of nomen-
cool hot
componentmodels;thesefitsaredescribedinSections3.2 clature depends on the physical origin of the emission
and 3.3 respectively, and then compared in 3.4. Second, region, which is not directly observable without ancil-
we use a two temperature mixture model to perform a lary information. For many applications, it could be
fit to the near-IR spectra in Section 3.5. The near-IR reasonably assumed that the cool photospheric compo-
spectral range is preferred over the optical, since the cool nent corresponds to a sunspot or sunspot group, and the
photosphereemitsmostofitsfluxinthenear-IR,enhanc- hot component corresponds to the ambient photosphere.
ing the likelihood of direct detection of emission from the However, acoolambientphotospherepossessinglocalized
cool component. hot spots—like plages on the sun—could yield the same
or similar two-temperature composite spectrum. In prin-
3.1. Methodology ciple, the physical origin could be assessed with detailed
Czekala et al. (2015, hereafter C15) developed a mod- comparison of average surface magnetic field strengths
ular framework21 to infer stellar properties from high- through Zeeman line broadening or other magnetic-field
resolutionspectra. TheC15techniqueforwardmodelsob- sensitive techniques. For now, we index the two pho-
tospheric components in the most general way possible,
served spectra with synthetic spectra from pre-computed
model grids. The intra-grid-point spectra are “emulated”
in a process similar but superior to interpolation since 22 SinglecomponentPhoenixphotospheresareindexedbythe
it seamlessly quantifies the uncertainty attributable to label“effectivetemperature”,orTeff,whichpresupposesthatthe
emergentspectrumiscomprisedofonlyasinglephotosphericcom-
the coarsely sampled stellar intrinsic parameters (see
ponent. Inthisworkweavoidlabelingthephotosphericcomponents
byT ,andinstead,refertothemassimply“photospherictemper-
eff
21 Theopensourcecodebaseanditsfullrevisionhistoryisavail- atures”.
able at https://github.com/iancze/Starfish. The experimen- 23 For flux calibrated spectra, the total solid angle Ω can be
talforkdiscussedinthispaperisathttps://github.com/gully/ constrained, but for typical echelle spectrographs only relative
Starfish. valuesofΩcool andΩhot canbeinferred.
Starspots on LkCa 4 5
10/1985-3/1986 11/1990-1/1991 8/1992-12/1992 8/1993-10/1993
12.4
V 12.8
13.2
8/1994-12/1994 8/1995-11/1995 10/1996-11/1996 9/1997-11/1997
12.4
V 12.8
13.2
9/1998-10/1998 8/1999-12/1999 8/2000-10/2000 8/2001-9/2001
12.4
V 12.8
13.2
10/2002-3/2003 8/2003-1/2004 8/2004-10/2004 8/2006-8/2006
12.4
V 12.8
13.2
1/2008-3/2008 8/2008-9/2008 1/2012-3/2012 9/2013-4/2014
12.4
V 12.8
13.2
7/2014-3/2015 7/2015-3/2016 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
12.4 phase phase
V 12.8
13.2
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
phase phase
Fig. 2.— Phase-folded lightcurves constructed assuming P = 3.375 days for all 22 observing seasons. The blue solid lines show a
“multiterm” regularizedperiodicfit,thatis,keepingthefirstMmax=4Fouriercomponents(VanderPlas&Ivezić2015). Theverticallines
showtheepochsatwhichspectraorancillaryphotometrywereobtained,withthesamelinestylesandcolorsasFigure1. LkCa4shows
secularchangessinitslightcurvemorphology. TheIGRINSspectrumwasacquirednearthemedianfluxleveloftheseason.
6 Gully-Santiago et al.
4500 stellarandnuisanceparametersarefitsimultaneouslyina
single spectral order, making stellar parameter estimates
θ unique for each spectral order o, whereas the C15
o
4000 strategy had the power to provide a single set of stellar
parameters θ that was based on all N spectral orders.
K) ord
T (eff 3500 ingInftreormprethtiengsatmheetpwhoo-ttoesmppheerreatruerqeumireixstsuirnegmleosdtaerlsa,soarraist-
leastdoublestarswith extremelylarge (>100)luminosity
ratios or wide separations. Unresolved single-lined or
3000
double-lined binaries could mimic a signal that would be
0.6 misattributed to starspots. As pointed out earlier, LkCa
Black body 4 has no detected companion from direct imaging, and
0.5 Phoenix models
its RV variations are consistent with starspot modula-
0)
10 0.4 tion, so any binary companion would have to have an
4
0)/f(λ 0.3 eitxcuenpdteiotencatlalybllearwgiethluomuirnospsietcytr(aolrimnfaesrse)ncreatmioe,trheonddoelroinggy
280 0.2 with the finite signal to noise available in the IGRINS
f(λ data. The absence of a detectable disk around LkCa
0.1 4 means that the spectral modeling requires no further
parameters like veiling or accretion.
0.0
Further details of the spectral inference methodology
5000 10000 15000 20000 25000
are described in Appendix A.
λ(Å)
Fig. 3.—Toppanel: thebest-fittemperaturemeasuredfromour 3.2. Single temperature fitting to the ESPaDOnS
fullspectrumfittingtoeachof58spectralordersintheopticaland spectrum
infrared portions of the spectrum, assuming a single component
We performed spectral fitting on an ESPaDOnS spec-
photosphere. Thebest-fittemperaturemeasuredintheK−band
is about 800 K lower than that derived in optical. The triangles trum acquired on 2014 January 11 (JD 2456668.9). The
in the H-band show upper limits with best fits near the edge of spectrum was split into subsets of N = 26 chunks, cor-
ourgrid. Bottompanel: Thefluxratiobetweenthecoolandhot responding approximately to spectral order boundaries.
componentsincreasestothenear-IR,whichexplainstheobserved
Fitting was performed separately on each spectral chunk.
trendinthebest-fittemperature.
The spectral emulator was trained on stellar parameters
simply cool and hot. in the range logg ∈ [3.5,4.0], [Fe/H] ∈ [−0.5,0.5], and
The two photospheric components share the same photospheric temperatures T ∈[3500,4200] K.
average intrinsic and extrinsic stellar parameters Standard MCMC convergence criteria were assessed.
vsini,logg,[Fe/H],v . The composite mixture model Typical spectral chunks show photospheric temperature
z
for observed flux density is: point estimates in the range 4000 ± 130 K. Figure 3
displays the point estimates with 5th and 95th percentile
Smix =ΩhotB(Thot)+ΩcoolB(Tcool) (1) errorbarsplacedatthecentralwavelengthofeachspectral
chunk. The spectral chunk from 8473−8707 Å is an
where B(T) is the spectral radiance from model spectra.
outlier, showing an estimated photospheric temperature
The filling factor of the starspots is:
of ∼3500 K.
Ω
fcool = Ω +cooΩl (2) 3.3. Single temperature fitting to the IGRINS spectrum
hot cool
We selected a subset of 32 of the 54 available IGRINS
The term fcool represents an instantaneous, observa- spectral orders24 with low telluric absorption artifacts.
tional fill factor seen on one projected hemisphere, not We performed unique spectral fitting on each order, with
fspot, the“ratioofthespottedsurfacetothetotalsurface free stellar parameters θ =(Teff,logg,[Fe/H]). The same
areas” (Somers & Pinsonneault 2015a). In the limit of analysisproceduredescribedfortheESPaDOnSspectrais
homogeneously distributed starspots and assuming the used here, though in the K-band the temperature search
cool photosphere arises from starspots, fcool tends to range is expanded to T ∈[3000,4200] K.
fspot, but in general fspot is not a direct observable since We find a larger dispersion in the point estimates for
some circumpolar regions of inclined stars will always thestellarparametersderivedfromtheIGRINSdatathan
face away from Earth; fcool can vary cyclically through those derived in the optical spectrum. The most conspic-
rotational modulation, whereas fspot changes secularly uous trend is in the derived photospheric temperature as
through starspot evolution that is not yet understood. a function of wavelength shown in Figure 3. The photo-
The two component mixture model includes two more spheric temperature peaks at values of ∼4200 K in the
free parameters than the standard C15 model, namely shortwavelengthendofH−bandandsaturatesat<3500
Tcool and fcool. The addition of these two parameters K at the long wavelength end of H−band. The K−band
makes the MCMC sampling much more correlated than shows even lower derived photospheric temperatures of
it was for single component models. This challenge moti- ∼3300 K, or 700 K cooler than estimated from optical.
vated a second technical change to the spectral inference No single photospheric temperature can describe all the
framework, switching from Gibbs sampling (c.f. C15) to
ensemble sampling using emcee (Foreman-Mackey et al. 24 Theprohibitivecomputationalcostlimitedusfromrunning
2013). The practical effect of this switch is that all 14 allthespectralorders.
Starspots on LkCa 4 7
0.40 fTTcohcoooolt −l = ==2 6 3σ218 7.9199%6 fTTmcohcoooeolt dl = ==ia 6 4n280 7f.1i83t9:%4 fTTcohcoooolt +l = ==2 7 4σ231 7.1694%9 0.7 fTTcohcoooolt −l = ==2 5 3σ259 8.1864%4 fTTmcohcoooeolt dl = ==ia 6 3n258 7f.9i88t3:%0 fTTcohcoooolt +l = ==2 7 4σ220 9.2211%2
0.35 0.6
0.30 0.5
flux density000...122505 flux density00..34
0.2
0.10
0.05 Cool 0.1 Cool
Hot Hot
0.00 0.0
0 5 10152025303540 0 5 10152025303540 0 5 10152025303540 5 0 5 10 15 20 25 5 0 5 10 15 20 25 5 0 5 10 15 20 25
λ 15020Å λ 17100Å
− −
fTcohoolt − ==2 53σ65 .783% fTmcohooelt d ==ia 74n94 f.4i3t3:% fTcohoolt + ==2 84σ44 .454% fTcohoolt − ==2 53σ15 .542% fTmcohooelt d ==ia 73n56 f.4i4t2:% fTcohoolt + ==2 84σ41 .375%
0.6 Tcool = 2879 Tcool = 3126 Tcool = 2944 0.6 Tcool = 2781 Tcool = 2882 Tcool = 2817
0.5 0.5
0.4 0.4
flux density00..23 flux density00..23
0.1 Cool 0.1 Cool
Hot Hot
0.0 0.0
0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 5 10152025303540 0 5 10152025303540 0 5 10152025303540
λ 17750Å λ 20430Å
− −
2σ median fit: +2σ 2σ median fit: +2σ
fcool −= 87.1% fcool = 90.3% fcool = 92.9% fcool −= 71.8% fcool = 78.2% fcool = 85.4%
Thot = 4427 Thot = 4441 Thot = 4240 Thot = 3496 Thot = 3717 Thot = 4101
Tcool = 2908 Tcool = 2957 Tcool = 2712 Tcool = 2760 Tcool = 2706 Tcool = 2901
0.7 0.7
0.6 0.6
0.5 0.5
flux density00..34 flux density00..34
0.2 0.2
0.1 Cool 0.1 Cool
Hot Hot
0.0 0.0
0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 5 10152025303540 0 5 10152025303540 0 5 10152025303540
λ 21500Å λ 22800Å
− −
Fig. 4.—ExamplesofspectralfeaturesintheobservedIGRINSspectrum(lightgrayline). Thecompositespectrummodel(purplethin
line)isconsistentwiththeobservedspectrumforarangeoffillfactors,withexamplesofthemedianfillfactor(middlepaneloftriptych)and
±2σ fillfactorsdemarcatedonthespectralpostagestamps. TheupperrighttriptychshowsaZeeman-sensitiveMgIlinethatismodeled
withnoattentiontomagneticfield,whichmaybiasestimatesofT and/orf forindividualspectralorders.
hot cool
spectral lines present in the high resolution optical and wavelengthuntilasymptoticallyapproachingafixedvalue
IR spectra. Sources with such discrepancies have been on the Rayleigh-Jeans tail (Wolk & Walter 1996). The
seenpreviously,forexampleinFigures4and5inBouvier bottom panel of Figure 3 shows the flux density ratio for
& Appenzeller (1992). These discrepancies are circum- patches of 2800 K and 4100 K photospheres with equal
stantial evidence for the detection of spectral features areas (50% filling factor). The black-body ratios predict
attributable to a second photospheric component. smooth flux ratio increases with wavelength, while the
ratio of Phoenix models shows wavelength regions with
3.4. Heightened sensitivity to starspot spectral lines in heightened sensitivity to starspot fluxes, for example in
the infrared J−band. The visible portion of the spectrum will be
The heightened sensitivity to starspot spectral lines as dominated by the warm patches. The infrared spectrum
a function of wavelength can be understood in the fol- will have a lower overall spot contrast and will have more
lowing way. Starspots are cooler than their surrounding net starspot flux than optical emission.
photosphere and will, therefore, have a longer wavelength Some care should be taken when directly comparing
of peak emission. The average ratio of flux density be- resultsbetweentheESPaDOnSandIGRINSspectrasince
tween starspot and bulk photosphere will increase with they were not taken at the same time. The particular ES-
8 Gully-Santiago et al.
IGRINS Spectral Order Central Wavelength (Å)
14620 14735 14853 14972 15093 15216 15341 15469 15598 15731 15865 16002 16284 16428 16576 16726 16879 17036 17195 17357 17522 17691 17863 18986 19185 19390 19598 19811 20029 20252 20480 20713 20953 21198 21448 21705 21969 22239 22515 22800 23091 23391 23698 24014 24338 24671
4500
)
K
(
ot
h
T
4000
3500
)
K
(
ol3000
o
c
T
1.0 12312212112011911811711611511411311211010910810710610510410310210110094 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72
0.8
0.6
ol
o
c
f
0.4
0.2
0.0
12312212112011911811711611511411311211010910810710610510410310210110094 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72
IGRINS Spectral Order Index (o)
Fig. 5.—Marginalprobabilitydistributionsmirroredthroughtheverticalaxis(Waskometal.2014,“Violinplot”)for48IGRINSorders
forT (blueshadeinthetoppanel),T (redshade,top),andfillfactorf (yellowshade,bottom). Thestellarparametersarederived
hot cool cool
independently in each spectral order. Spectral orders show differing levels of constraint on the cool photosphere and hot photosphere
properties,includingsomeorders(o=104,102,100,88,83)thatyieldespeciallytightcoolspotfillingfactors. Thestarspottemperatureis
consistentwithvaluesevenlowerthan2700K,thelowerlimitofthetemperaturerangeused. ManyoftheK−bandordersthatshowlower
estimatesforthehotphotosphereareunreliableduetospectrallineoutliersanduncorrectedtelluricresiduals(lightshadeddistributions).
PaDOnSspectrumusedinSection3.2wasobtainedwhen
TABLE 2
LkCa 4 had an estimated V−band brightness of 12.94
Adopted values of LkCa 4
mag,comparedwith12.84magatthetimeoftheIGRINS from IGRINS spectra
spectrum. The fainter magnitude during the ESPaDOnS
spectrum acquisition implies a greater coverage fraction Thot Tcool fΩ
of cool material than during the IGRINS spectrum ac- K K %
quisition. The photospheric temperature derived in the
4100±100 2750+250 80±5
optical bands and short-wavelength end of H-band yield −50
similar values of ∼4100 K, suggesting the bulk25 spectral
Note. — These are the val-
features are broadly consistent with emission from a sin-
ues at the epoch of the IGRINS
gle temperature component. A single ESPaDOnS order
spectrumacquisition.
surrounding the TiO bands shows an exceptionally low
signatures than the shorter wavelength portions.
estimated T . The long wavelength portion of H−band
eff
andallofK−bandaremoresensitivetostarspotspectral
3.5. Two-temperature fitting to IGRINS spectra
25 The bulk appearance and disappearance of spectral lines is Full-spectrum fitting was performed for 48 of the 54
mostly controlled by the temperature of the emitting region of availableIGRINSspectralorders,omittingonlytheorders
the local photosphere. In other words, most of the variance in with the most pathological telluric spectral artifacts. We
a spectrum is attributable to temperature, assuming near-solar
appliedthemixturemodelasdescribedinSection3.1and
metallicity. Starspotsimbuedearthsoffluxinthelineprofilesof
optical spectra, but these are secondary to the mere presence of Appendix A. Standard MCMC convergence tests were
temperature-sensitivelines. evaluated. The stellar parameter ranges were logg ∈
Starspots on LkCa 4 9
[3.5,4.0] and [Fe/H] ∈ [−0.5,0.5]; the Phoenix model
spectrumtemperaturerangewasT ,T ∈[2700,4500].
hot cool
H−band fits had normal distribution priors in place:
solar metallicity to ±0.05 dex, logg = 3.8 ± 0.1, and
vsini=29±5 km/s.
The fit quality is first assessed by examining the consis-
tency of the point estimates of v and vsini across the
z
spectralorders. Thedistributionofv andvsiniexposed
z
extremely poor fits in two orders (o=91 and 94), with
all other orders demonstrating v =12.4±2.6 km/s and
z
vsini=28.8±2.0 km/s.
Overplotting forward-modeled spectra with the ob-
served IGRINS spectra yielded insights on why some
spectral orders perform better than others in assessing
stellar properties. Orders with extremely poor telluric
correction residuals, large spectral line outliers, and un-
corrected H line residuals from A0V standard division, Fig. 6.— The SED of LkCa 4 (red) compared with the two-
temperaturespectrumobtainedfromthebestfittotheIGRINS
are all excluded from our final stellar parameter compi-
spectra (black), scaled to AV =0.3 and logL/L(cid:12) =0.20 at the
lation. Several orders in K−band were rejected due to epochofthe2MASSobservation(see§5n).
poor spectral fits influenced by deep metal lines. Metal model spectrum overplotted.
lines can be biased by Zeeman broadening, which could Figure 5 shows the distribution of T (blue shading),
hot
explain poorer fit quality with wavelength (Johns-Krull T (red shading), and f (yellow shading) for all of
cool cool
2007; Deen 2013). Some orders were also discarded be- the spectral orders, with the rejected orders grayed out,
cause their fits were mediocre or uninformative. The and the reliable order subset shown in bold. The point
remaining orders are relatively devoid of spectral line estimates for each spectral order are listed in Appendix
outliers and include the most information rich portion of Table 3.
the spectrum. Best fit values for the stellar parameters are listed in
TheIGRINSspectrumdemonstratessomefeaturesthat Table2. Remarkably,thefillingfactorofcoolphotosphere
are present only in the hot photosphere model, and some exceeds 50%, with a best fit value of f =80±5%.
cool
features that are present only in the cool photosphere
model. Figure 4 shows a selection of six such spectral 4. THETWOTEMPERATUREFITTOTHESEDAND
features for a range of plausible fill factors. In some cases STELLARROTATION
(e.g. the top two panels), featureless cool photosphere In the previous section, we established that the high
spectra veil isolated spectral lines predicted in the hot resolution optical and near-IR spectra of LkCa 4 may
photosphere models. In other cases (e.g. the middle row be explained by a two-temperature photosphere. In this
and lower left panel), the hot photosphere model veils section, we test the two component fit by comparing the
sequences of shallow spectral features predicted in the combined spectrum to observed spectral features and
coolphotospheremodel. Thecoolspectralmodelspredict rotational modulation. We adopt the best-fit two temper-
shallow features because line blanketing from multiple ature model to the IGRINS spectrum, with components
indistinctmolecularbandsoverlapsfromrotationalbroad- of 2750 K covering 80% of the visible stellar surface and
ening; any feature of interest will be biased to non-zero 4100Kcovering20%ofthestellarsurface,obtainedwhen
veiling. LkCa 4 had an estimated brightness of V =12.84 mag.
The combination of line blanketing and high vsini has The cool and hot temperatures and the filling factor are
probablyhamperedeffortstoidentifyisolatedspectralfea- blindly adopted without any adjustments to attempt to
tures suitable for line-depth-ratio analysis in the spectra improve fits to the SED or broadband spectra.
of rotationally broadened young stars. One such feature, Figures 6–7 compare synthetic spectra from the two-
the OH 1.563 µm line analyzed by O’Neal et al. (2001), component photosphere to the SED and flux-calibrated
shows a clear pattern of 3 lines in our data, with the spectra of LkCa 4. The only free parameters in this com-
central line exceeding the depth of the adjacent two lines. parison, the luminosity and extinction, are both scaled to
The Phoenix models predict a non-negligible hot pho- match the spectrum (see §5.1-5.2). The optical-IR SED
tosphere contribution to the middle line for our range of is obtained by estimating photometry from Grankin et al.
hot and cool temperatures. In comparison, the forward- (2008)duringthe2MASSepoch,withV ∼12.61mag(see
modeling technique described in this work thrives in the Table1). TheSEDalsoincludesmid-IRphotometryfrom
presence of long sequences of indistinct yet predictably Spitzer/IRAC (Hartmann et al. 2005), without adjusting
correlated spectral features. The level of veiling of hot for epoch. In the spectroscopic comparison, some minor
photospheric lines is set by the cool photosphere filling discrepancies between the optical and near-IR spectra
factor and temperature, while the level of veiling of the may be introduced because the spot coverage changed in
cool lines is set by the filling factor and temperature the ∼5 hrs between observations (∆V =0.08 mag). The
of the hot photosphere lines. Similar forward-modelling synthetic spectrum is obtained from the Phoenix models,
strategies have successfully identified patterns of weak as in §3, and is extended beyond the longest wavelength
metallinesintheline-blanketedspectraoflowmetallicity (5 µm) to calculate the bolometric luminosity.
stars (Kirby 2011; Kirby et al. 2015). Figures 14 and The synthetic models match the full spectrum reason-
15 in the Appendix show 42 of the H− and K−band ably well. When scaled separately to the red-optical and
spectra on a log scale with a single random composite near-IR spectra, the synthetic models match even better
10 Gully-Santiago et al.
Fig. 7.— Top: The low-resolution optical/near-IR spectrum of LkCa 4 obtained from Palomar/DBSP and APO/Triplespec on 30
December2008(black),comparedtoasyntheticspectrumofatwotemperaturephotosphere(4100Kwith20%fillfactorand2750Kwith
80%fillfactor,reddenedbyAV =0.3mag;purplelines),a3900Kspectrumreddenedby1.3mag(bluelines),anda3500Kspectrum
withnoreddening. AllsyntheticspectraarefittotheJ-bandspectrumofLkCa4. Theobservationsingrayandthesingletemperature
photospheresarescaledbyfactorsof3and9forvisualpurposes. Bottom: Sameasthetoppanel,butthesyntheticspectraarescaled
separatelytotheopticalspectrumat0.75µmandtothenear-IRspectrumat1.5µm. Warmphotospheresaccuratelyreproducemolecular
bandsat0.7µmbutfailtofitthespectralfeaturesatlongerwavelengths. Coolerphotospherespredictmolecularbandsat<0.7µmthat
aremuchdeeperthanobserved. Thetwotemperaturephotosphereaccuratelyfitsspectralfeaturesinbothopticalandnear-IRwavelengths.
(bottompanelsofFigure7),whilesingletemperaturepho- The V-band brightness reflects the instantaneous fill-
tospheres fail to reproduce large spectral features. The ing factor of the cool and hot components. In the two-
3900 K component fits the TiO bands at <7400 Å but temperature photosphere, the V-band emission is domi-
fails to reproduce molecular bands at longer wavelengths. nated by the hotter component and is, therefore, a good
The3500Kcomponentsuffersfromtheoppositeproblem, proxy for the visible surface area of the hot component.
yielding molecular bands at short wavelengths that are Figure9showsthewinter2015–2016ASAS-SNlightcurve,
too deep. The two temperature photosphere with the converted into a cool spot filling factor. During this pe-
parameters from the best-fit calculated in §3 reproduces riod, the brightest and faintest phase corresponds to cool
the TiO bands, the hump in the H-band, and the jump componentfillfactorsof74%and86%,respectively. Since
in flux at the long-wavelength end of the J-band. This 1992 the V band photometry has been as bright as 12.3
latter feature is caused by opacity in H O bands and is mag, which corresponds to a cool component fill factor
2
only seen when the fraction of emission from the cool of 65%, and as faint as 13.2 mag, or a cool component
component is high (Figure 8). fill factor of 87%. This drastic change in visible area of
These spectral features should be rotationally modu- the hot spot (35% to 13%) is needed to explain the full
lated as the filling factors of the visible hot and cool ∼1 mag range in brightness, assuming no temperature
components change. In §4.1, we first use our fit to the change in either component.
IGRINS spectrum to convert the V-band brightness to
thefillingfactorofthetwocomponents. Wesubsequently 4.2. Rotational Modulation of Colors
calculate the color changes expected based on this spot Therelativecontributionsfromthehotandcoolcompo-
coverage and compare these results to historical data nents change as LkCa 4 rotates, leading to color changes.
(§4.2), and confirm our basic approach by demonstrating We model this rotational modulation using the main se-
that TiO band depths vary with rotation (§4.3). quence colors (compiled by Pecaut & Mamajek 2013),
which should have less contribution from spots than pre-
main sequence colors. The Cousins R photometry from
4.1. The V-band lightcurve and spot coverage
Pecaut & Mamajek (2013) is converted to Johnson R for