X-ray Evidence for a Pole-Dominated Corona on AB Dor

1.3 MB·English

by  Jeremy J. Drake

Toappear in the Astrophysical Journal
PreprinttypesetusingLATEXstyleemulateapjv.04/20/08
X-RAY EVIDENCE FOR A POLE-DOMINATED CORONA ON AB DOR
Jeremy J. Drake1, Sun Mi Chung1,2, Vinay L. Kashyap1 and David Garcia-Alvarez1,3,4
1SmithsonianAstrophysicalObservatory,MS-3,
60GardenStreet,
Cambridge,MA02138
2 DepartmentofAstronomy,TheOhioStateUniversity,4055McPhersonLaboratory,140West18thAvenue,Columbus,OH43210-1173
3 Instituto deAstrofsicadeCanarias,E-38205LaLaguna, Tenerife,Spainand
4 Dpto. deAstrofsica,UniversidaddeLaLaguna,E-38206LaLaguna,Tenerife,Spain
5
To appear in the Astrophysical Journal
1
0
ABSTRACT
2
A fine analysis of spectral line widths and Doppler shifts employing Fourier transform and cross-

n correlation techniques has been applied to Chandra HETG spectra obtained in 1999 October of the
a rapidly rotating young star AB Doradus in order to investigateits coronaltopology. The observation
J
lasted 52.3 ks, covering 1.2 rotation periods. The X-ray light curve obtained from integrating the

3 dispersed signal revealed a moderate intensity flare midway through the exposure in which the count
2 rate increased sharply by about 50% and subsequently decayed over the next 10 ks. We find no

significant Doppler shifts in the spectra or modulation of the light curve that could be attributed to
]
R rotationofdominantcoronalstructures atthis epoch. Individualspectralline widths arestatistically
consistentwith thermal broadeningand formally require no rotationalbroadening,while the 1σ limit
S
to rotational broadening corresponds to a compact corona restricted to latitudes > 57deg. Fourier
.
h analysissuggestsasmallamountofrotationalbroadeningispresentconsistentwithacoronarestricted
p largelyto the poles,andexcludes models with surfacerotationalbroadeningorgreater. Theseresults
- present direct spectroscopic evidence that the dominant coronal activity on rapidly-rotating active
o
stars is associated with the dark polar spots commonly seen in photospheric Doppler images, and
r
t support models in which these spots are of mixed magnetic polarity that forms closed loops.
s
Subject headings: stars: activity — stars: coronae — X-rays: stars — stars: winds, outflows — stars:
a
[ magnetic field — stars: late-type — stars: rotation

1
v 1. INTRODUCTION velocities and rotationally modulated Doppler shifts in
6 magnetically active stellar systems, both binaries (e.g.
The Sun is the only star for which we can presently
4 Brickhouse et al. 2001; Ayres et al. 2001; Chung et al.
image coronal X-ray emission directly. In order to un-
8 2004; Huenemoerder et al. 2006; Ishibashi et al. 2006;
derstandhowcoronaeonotherstarsmightbestructured
5
Hussain et al. 2012) and single stars (e.g. Hussain et al.
wemustresorttoindirectmeans,suchaseclipseorrota-
0
2005;Drake et al. 2008).
. tionalmodulation,andspectroscopicdensitydiagnostics.
1 Theadventofthe“highresolution”(λ/∆λ∼1000)capa- Inaddition to detecting Doppler shifts in the Chandra
0 HETG spectrum of Algol caused by the orbital motion
bilityoftheX-raytransmissiongratingspectrometerson
5 of Algol B, Chung et al. (2004) also found spectral line
the Chandra X-ray Observatory opened up further pos-
1 widths to have excess line broadening amounting to ap-
sible means of probing coronal structure. One of these
: proximately 150 km s−1 above that expected from ther-
v is through the Doppler shifts of spectral lines in the X-
malmotionandsurfacerotation. The excessbroadening
i ray emitting plasma that arise as a result of orbital or
X implied that a significant component of the corona at
rotational motion.
r Forlate-typestars,thevelocitiesinvolvedaretypically temperatures less than 107 K has a scale height of order
a oforder10-100kms−1—easilysufficientforopticalstud- the stellar radius. A similar line width analysis applied
to the rapidly rotating giant FK Com by Drake et al.
ies of rotationally-drivenchanges inspectralline profiles
(2008) revealed Doppler shifts consistent with localized
thatarenowroutinely“inverted”tomakequitedetailed
emissionon one hemisphere with a scale height of about
Doppler images of surface features of varying brightness
a stellar radius.
(see,e.g.,Strassmeier2002),andZeemanDopplerimages
The young K-type dwarf AB Doradus, with a pro-
of surface magnetic features (e.g. Donati & Landstreet
jected rotational velocity of 90-100 km s−1 (Rucinski
2009). However, for instruments with a resolving power
1985;Vilhuetal.1987;Donati&CollierCameron1997),
of∼1000,suchvelocitiesonlyamounttoafractionofthe
presentsaplausible,thoughchallenging,caseforDoppler
instrumentalwidth,andDopplerstudiesarechallenging.
inference of coronal structure based on Chandra spec-
Nevertheless,severalstudies havenowdemonstratedthe
tra. Hussain et al. (2005) found evidence for rota-
utility of Chandra Low- and High-Energy Transmission
tional Doppler shifts in Chandra Low Energy Transmis-
Grating(LETG,HETG)spectraforprobingbothorbital
sionGrating(LETG)spectra,whileHussainetal.(2007)
Electronicaddress: [email protected] combined Chandra data with Zeeman Doppler imaging
Electronicaddress: [email protected] (ZDI)ofthestellarsurfacetoinfercoronalstructureand
Electronicaddress: [email protected] scaleheight. Cohenetal.(2010)havealsoemployedZDI
Electronicaddress: [email protected]
mapsinordertoinfercoronalstructurebasedondetailed
2 J.J. Drake et al.
magnetohydrodynamic(MHD)coronaandwindmodels. scopic observational clues as to the structure of the
Here, we bring further, potentially more sensitive, coronaof AB Dor. Rotational modulation studies based
analysistechniques to bearonthe Chandra HighEnergy on EUV-X-ray observations of coronal emission can, in
Transmission Grating (HETG) spectra of AB Dor. The principle, render some limited spatial information. Evi-
analysis partly follows methods developed in the study dence for such modulation has been only very marginal
ofAlgolHETGspectraby Chung et al.(2004),to which in GINGA and EXOSAT observations (Collier Cameron
the reader is referred for a more detailed technical dis- et al. 1988; Vilhu et al. 1993), and essentially absent in
cussion. We usecross-correlationandFouriertechniques EUVE and ASCA data (White et al. 1996). A lack of
to to determine where the bulk of the observed X-ray strong rotational modulation implies either one or more
emission originates in this system at this epoch. AB of the following: emission is distributed fairly uniformly
Dor is introducedin the lightofexisting workin §2,and in azimuth; emission is extended with a scale height of
the Chandra observations and analysis are described in order the stellar radius or larger; emission is concen-
§3. The results of the analysis are discussed in §4 before trated at the stellar poles. Later extensive monitoring
drawing the main conclusions from the study in §5. with ROSAT revealed modest ∼5−13% modulation in
pointedobservationsand19%modulationinall-skysur-
2. ABDORANDITSCORONALACTIVITY vey data (Kuerster et al. 1997), indicating the presence
ABDoradus(HD36705)isarelativelybright(V=6.9), of some lower latitude structure non-uniform in stellar
rapidly rotating K0 star at a distance of about 15 pc, longitude. Maggio et al. (2000) reported an observation
with a period P = 0.514d (Pakull 1981). Its mass is es- ofacompactflare(height.0.3R )whichtookarotation
⋆
timated to be 0.86M⊙ and it is in orbit with a distant periodtodecayandshowednoevidenceofself-eclipse,in-
companion of mass 0.09M⊙ (Guirado et al. 1997, 2010). dicatingahighlatitudelocation. Atlowerchromospheric
Based on the similarity of its space velocity with that of and transition region temperatures (∼104-105 K), rota-
the Pleiades moving group (Innis et al. 1985), and short tional modulation was seen in the fluxes of FUV lines
period and high Li abundance (Rucinski 1985; Vilhu (Schmitt et al. 1997; Ake et al. 2000). More recently,
etal.1987),AB Dor wascommonlyacceptedasayoung Lalitha & Schmitt (2013) did not find evidence for per-
star coeval with the stars of the Pleiades (∼ 100 Myr) sistentrotationalmodulationbasedonXMM-Newtonob-
and that is just evolving onto the main-sequence. How- servationsobtainedoverthe pastdecade,andattributed
ever,theexactageofABDorhasbeenatopicofcontin- observedvariabilitytostochasticprocessessuchasflares.
uing controversy, with estimates ranging from as young Perhapsmoreinterestingarespectroscopicconstraints.
as 30 Myr to as old as 125 Myr (e.g. Collier Cameron & Garc´ıa-Alvarezet al. (2005) found the coronalspectrum
Foing 1997; Zuckerman et al. 2004; Luhman et al. 2005; essentially identical to that of the Hyades tidally-locked
Jansonetal.2007;Torresetal.2008;daSilvaetal.2009; close K1 V+DA binary V471 Tau that has been spun
Guirado et al. 2011; Barenfeld et al. 2013; McCarthy & up to a very similar rotation period. Both spectra ex-
Wilhelm 2014; Wolter et al. 2014). The preponderance hibit a fairly broad range of coronal temperatures up
of these studies favor an age of at least 100 Myr or so. to 107 K or so, and coronal abundances that deviate
The radius of AB Dor was recently measured to be from the solar mixture in according to an “inverse First
0.96 ± 0.06R⊙ based on near infrared interferometry Ionization Potential” effect pattern that is typical of ac-
(Guirado et al. 2011). Commensurate with youth, ro- tive stars (see, e.g., Brinkman et al. 2001; Drake et al.
tational modulation of the photometric light curve of 2001;Drake 2003). Sanz-Forcada et al. (2003b) deduced
AB Dor, as well as extensive optical Doppler imaging acoronalscaleheightoflessthanthestellarradiusbased
studies, suggest that its surface is covered with large, onelectrondensitiesestimatedfromXMM-Newtonspec-
cool starspots or “maculae”, switching between active tra, similar to density and optical depth constraints on
longitudes on a 5.5 yr cycle and probably modulated scale height for other active stars (Sanz-Forcada et al.
with a cyclic period of about 20 years (e.g. Rucinski 2003a;Ness et al. 2004; Testa et al. 2004a,b, 2007).
1985;Vilhuetal.1993;Donatietal.1999;J¨arvinenetal. Hussain et al. (2005) found evidence for rotational
2005;Budding etal.2009;Arzoumanianet al.2011,and Doppler shifts in lines of O VIII observed using the
references therein). The detailed distribution of these Chandra Low Energy Transmission Grating Spectro-
spots has been studied in surface brightness maps ob- graph (LETGS) in 2000 December, suggesting the pres-
tained over many years. They show a persistent polar ence of low-latitude compact emitting regions. Analysis
cap, together with variable mid- to low-latitude spots of HETGS Fe XVII λ15.01 and FUSE Fe XVIII λ974
(e.g.,Donati&CollierCameron1997;Jeffersetal.2007). line profiles indicated a coronalscale heightof .0.5 R .
⋆
The related technique of ZDI has been extensively em- Hussainetal.(2007)combinedtheChandraobservations
ployed on AB Dor to study its surface magnetic field with ZDI reconstructions of the surface magnetic field
distribution and evolution. The magnetic field maps re- anditsextrapolationintothecorona,andconcludedthat
veal strong, complex field distributions. Donati et al. coronalstructuresareno morethan0.3–0.4R inheight.
⋆
(1999) reported at least 12 different radial field regions Cohen et al. (2010) used a ZDI surface magnetic map
of opposite polarities located all around the star from based on spectropolarimetric observations obtained in
observations obtained in 1996 December. They found a 2007DecembertodriveaglobalMHDmodelofthewind
degree of five or greater for a spherical harmonics ex- and corona of AB Dor. They found the global structure
pansion of the underlying large-scale poloidal structure. ofthestellarcoronaatlowerlatitudeswasdominatedby
Thereisalsoastrongandoftenunidirectionalazimuthal strong azimuthal wrapping of the magnetic field due to
field encircling the boundary of the polar cap found in the rapid rotation. Lalitha et al. (2013) obtained simul-
the spot maps. taneous radio, optical, and X-ray observations covering
There are several existing photometric and spectro- a multi-component flare and found flaring filling factors
A Pole-Dominated Corona on AB Dor 3
of 1–3% of the stellar surface. nored here. Flares and rotational modulation caused by
At cooler temperatures, rotational broadening has dominant active regions are of particular interest since
been detected in lines of both C III (λ977, λ1175) and the location of their X-ray source might be betrayed by
O VI (λ1032, λ1037) in ORFEUS and FUSE spectra rotationally-inducedDoppler shifts, providing direct ob-
(Schmitt et al. 1997; Ake et al. 2000). Schmitt et al. servational clues as to the locations of coronal activity.
(1997) note that this does not exceed the photospheric The X-ray light curve obtained from both HEG and
vsini value, suggesting that the observed C III and MEG dispersed events binned at 100s intervals is illus-
O VI emission is produced close to the stellar surface. trated in Figure 2. We also show in this figure the ro-
Based on later FUSE spectra obtained in 2003 Decem- tational “phase” computed according to the ephemeris
ber, Dupree et al. (2006) infer activity at mid-latitudes of Innis et al. (1988), HJD = 2444296.575+0.51479E.
withascaleheightof∼1.3–1.4R . Opticalspectroscopy There are several very small flare-like brightenings visi-
⋆
has also revealed the presence of prominences, initially ble,butthe lightcurveis dominatedbyamoderateflare
through discrete absorption features in Hα (Robinson occurring midway through the observation. There is no
& Collier Cameron 1986; Collier Cameron & Robinson obviousimpulsive phase and the apparentflare risetime
1989), and subsequently also in the light of Mg II and is of order 2000s, which might be considered long for a
Ca II (Collier Cameron et al. 1990). These prominences flareofthissizewhosedecaytimescaleisoforder10000s.
comprisecool(8-10,000K)cloudsofneutral,ornearneu- It is possible that an impulsive phase was occulted by
tral, hydrogen at, and also perhaps beyond, the Keple- the stellar disk just prior to rotating into view, though
rianco-rotationradius. CollierCameronetal.(1990)es- Dopplershiftmeasurementsdiscussedbelowsuggestthis
timatedthatbetween5and20prominenceswerepresent might not be the case.
in 1988December, eachwith a mass ofa few 1017 g. Ul- While the light curve does not appear to show any
travioletspectroscopywiththe HST GoddardHighRes- structure that might be commensurate with rotational
olutionSpectrographrevealednarrowchromosphericline modulation, the relatively short duration of the obser-
cores superimposed on very broad line wings, the latter vation covering only slightly more than a single phase,
beingconsistentwithalocationcommensurateofthatof combined with the flare, does hinder our ability to de-
the optically-detected prominences (Brandt et al. 2001). tect such modulation if it were present. The flatness of
Analogous structures have also been detected in the K light curve outside of the large and smaller flares indi-
dwarf component of V471 Tau based on C II and C IV cates that the amplitude of any rotational modulation
absorptionin FUSE spectra by Walter (2004). Young G can only be of the order of 10% or less.
andKdwarfsoftheαPerseiclusteralsoshowevidenceof
the samebehavior,indicatingthat suchprominencesare 3.2. Phase-Related Doppler Shifts
likelyacommonfeatureofrapidly-rotatingstars(Collier
As noted above, Doppler shifts of spectral lines as a
Cameron & Woods 1992).
function of time might betray the presence of particu-
All these observations provide a rather complex, and
larly dominantcoronalstructures. The equatorialveloc-
sometimesinconsistent,pictureofthecoronaofABDor. ity of AB Dor is about 95 km s−1, which amounts to
In the following sections we examine the only existing approximately 25% of the width of the O VIII 18.97 ˚A
Chandra HETG spectrum of AB Dor, and the highest
Ly doublet as seen by the MEG; such a shift should
resolution X-ray spectrum of the star obtained to date α
be easily detectable in the brighter spectral lines of the
that presents lines bright enough for detailed study, for
AB Dor soft X-ray spectrum.
further clues as to its outer atmospheric structure.
3. OBSERVATIONSANDANALYSIS 3.2.1. Analysis of Individual Spectral Lines
AB Dor was observed using the Chandra High En- InthefirstpartofouranalysiswesearchedforDoppler
ergyTransmissionGrating(HETG)andACIS-Sdetector shifts of individual spectral lines as a function of time.
on 1999 October 9 UT11:21 for a total net exposure of Lines used in this analysis are listed in Table 1. These
52.3ks,orapproximately1.2stellarrotationperiods. The represent the strongest lines in the HETG spectrum of
dataanalyzedherewereobtainedfromtheChandrapub- AB Dor longward of 8 ˚A. While H-like and He-like lines
lic archive1. The final extracted spectrum showing the of Si are also reasonably bright, the resolving power of
spectral lines used in this analysis is illustrated in Fig- the Chandra gratingsis generally too low at these wave-
ure 1. Our analysis methods described below, involving lengths to be of significant additional value in this line-
light curves, cross-correlationtechniques and line profile by-line part of the study.
modeling, are similar to those described by Chung et al. Dispersed events within wavelength ranges of interest
(2004)andDrakeetal.(2008),towhichthereaderseek- for our chosen lines were binned over different time in-
ing more detail is referred. tervals, depending on the number of counts in each line,
so as to achieve approximately the same signal-to-noise
3.1. Light Curve ratio in each bin. Positive and negative orders were co-
added, then analyzed. Line wavelengths were measured
Priorto performing detailedspectralanalysis,the dis-
by fitting modified Lorentzian functions (“β-profiles”)
persedphotoneventswerefirstexaminedtoascertainthe
described by the relation
level at which AB Dor varied in X-rays during the ob-
servation. Owing to the ACIS-S 3.2s frame time, 0th λ−λ
order events are significantly affected by photon pile- F(λ)=a/[1+( 0)2]β (1)
Γ
up and do not yield accurate photometry and are ig-
where a is the amplitude and Γ is a characteristic line
1 http://asc.harvard.edu/cda width. Foravalueofthedenominatorexponentβ =2.5,
4 J.J. Drake et al.
Fig.1.— The Chandra HETG spectrum of AB Dor, for both HEG and MEG binned at 0.0025 and 0.005 ˚A intervals, respectively.
Emissionlinesthatwereusedinouranalysesarelabeledinalargerfontsizethanlinesthatwerenotused.
A Pole-Dominated Corona on AB Dor 5
for a secular trend with a single point near φ ∼ 0.8 ex-
hibitinga2σ variationfromthezerolevel,butthistrend
is opposite that which one might be tempted to see in
O VIII λ16.01; the latter is actually perfectly consistent
with a zero net velocity shift.
3.2.2. Cross-correlation Analysis
In addition to measuring individual emission lines,
we also utilized a cross-correlation technique to obtain
Doppler shifts as a function of rotational phase. The
method involves comparisonof the spectra extractedfor
the different time bins with a reference spectrum in or-
der to determine whether or not there is a net Doppler
shift between the two. This technique was first devel-
oped during earlier analyses of Chandra HETGS obser-
vationsofAlgol(Chungetal.2004)andFKCom(Drake
et al. 2008), and we refer the reader to those works for
Fig. 2.—TheobservedX-raylightcurveofABDorderivedfrom a more detailed description. The advantage of this type
dispersedHEGandMEGevents,plottedasafunctionofrotational of cross-correlation technique over the analysis of indi-
phase. Thetopaxisshowstherotationalphasecomputedwiththe
vidual spectral lines is that it utilizes the signal from
ephemeris of Innis et al. (1988), and the bottom axis shows the
elapsedtimeindayssincethestartoftheobservation. the whole spectrum—strong and weaker lines, isolated
andblended—andistherefore,atleastinprinciple,much
moresensitive. Thereareabout12stronglineslongward
TABLE 1 of10˚Ainthe MEGthathavethe highestvelocitysensi-
Alist of emission linesused in our analyses,includingthe
tivityandwillprovidethe greaterpartofthesignal,and
rest wavelength,elementandion,and grating.
asimilarnumberintheHEGspectrum,although,again,
Wvl [˚A] Ion Grating Analysis† all features in the spectrum contribute. The disadvan-
8.42 Mg XII MEG,HEG DopplerShifts tageofthetechniqueisthatitpotentiallyconfusesstruc-
12.13 NeX MEG,HEG Both tures with different characteristic temperatures since it
14.20 Fe XVIII MEG Both uses lines formed over a fairly large temperature inter-
15.01 FeXVII MEG,HEG Both val.We return to this in §4.1.
Eventswerebinnedintofivetimeintervalscorrespond-
16.01 O VIII MEG Both
ing to different rotational phases, and spectra were ex-
16.78 FeXVII MEG Both
tracted for each phase bin. These spectra were then
18.97 O VIII MEG Both
cross-correlated with the reference spectrum, which in
24.78 N VII MEG Both
this case was the spectrum extractedfrom the entire ex-
†IndicationofwhetherthelineswereusedinDopplershiftorline posure, in order to determine the velocity shift at which
broadeninganalyses. ourcorrelationsignal(representedby a χ2 statistic) was
minimized. As inthe analysisof Algol,the uncertainties
this function has been found to be a good match to ob- in this procedure were estimated using a Monte Carlo
served HETGS line profiles, which are not well-matched technique in which the analysis was repeated a number
by Gaussian profiles (Drake 2004). Fitting was per- of times for different Poisson realizations of the spectra.
formedusingthePackageforINTerativeAnalysisofLine TheanalysiswasundertakenforboththeHEGandMEG
Emission (PINTofALE)2 (Kashyap&Drake2000)IDL3 spectra separately. The full rangeof eachspectrum that
software routine fitlines. Uncertainties at the 1σ level containedsignificantsignalwasused. These rangeswere
weredeterminedfromathoroughsearchofthegoodness- 2–26 ˚A and 2–18 ˚A for MEG and HEG, respectively.
of-fit surface. Figure4illustratestheline-of-sightvelocityofABDor
Since the HETG observation covered slightly more asafunctionofrotationalphaseobtainedfromthecross-
than one full rotation period, we determined line posi- correlation method, for the MEG (upper) and HEG
tions in the individual time-filtered bins relative to the (lower)data. Thereareclearlynolargevelocityshiftsde-
wavelengths measuredfor the same lines from the entire tected, with the more sensitive, by virtue of the number
observation. In this way, we avoid complications from ofphotoncounts,MEGdataplacingquitestringentlim-
smallwavelengthcalibrationerrorsoranylong-termdrift its on average net velocity excursions of less than about
inthedispersionrelation. Themeasuredrelativelinepo- 20km s−1. In the contextofthe projectedsurface equa-
sitions as a function of time are illustrated in Figure 3. torial rotational velocity of 95 km s−1, this lack of obvi-
The resulting line positions are fairly stable with little oussystematicDopplershiftsindicatesthatthecoronaof
change as a function of orbital phase. There is a sug- AB Dor is not dominated by one or two low-latitude ac-
gestion of a redshift at phase φ∼0.9 in Fe XVII λ16.78 tiveregions;theX-rayemissionmustbemoreevenlydis-
andMgXIIλ8.42,butthissignatureisnotseeninother tributed over the surface, or else resides predominantly
lines. The O VIII λ18.96 line also shows some evidence toward polar regions for which projected rotation veloc-
ities are small.
2 PINTofALE is publicly available at http://http://hea-
www.harvard.edu/PINTofALE/ 3.3. Spectral Line Widths
3 Interactive DataLanguage, ExelisInc.
6 J.J. Drake et al.
Fig. 3.—Theobservedline-of-sightorbitalvelocityand1σerrorbarsasafunctionofrotationalphaseforlineslistedinTable1,expressed
relativetothemeasuredwavelengthfortheentireobservation.
A Pole-Dominated Corona on AB Dor 7
uncertaintiesfortheseexcesslinewidthsrelativetoµVel
correspond to the quadrature propagation of the uncer-
tainties of the individual AB Dor and µ Vel line widths.
Alsoshownarethetheoreticalline widthscorresponding
to the case of no rotation, rotation at the stellar sur-
face, and rotation at one stellar radius above the stellar
surface, all relative to µ Vel. Here, we define the scale
heightasthe heightabovethe stellarsurface. Note that,
under this definition, negative scale heights are possible
and correspond to the case where rotational broadening
is less than that induced by rotation of uniform surface
emission.
Fig. 4.— The line of sight velocity as a function of rotational
phase for MEG and HEG spectra, obtained by cross-correlating
spectra from different time intervals with the spectrum from the
entireobservation.
Thetwoscenariosmentionedabovecaninprinciplebe
diagnosed by examining spectral line widths to search
for excess rotation-related broadening. In our analysis,
we compared line widths of observed data to those of
modelprofiles,whichincludetheeffectsofthermal,rota-
tional,andinstrumentalbroadening. Theprocedurewas
again developed from that originally discussed in detail
by Chung et al. (2004) and Drake et al. (2008).
Inordertominimizeuncertaintiesinthe calibrationof
Fig.5.— Illustration of the observed line widths and 1σ un-
theinstrumentlineresponsefunction,wecarriedoutthe
certainties of emission lines measured from the MEG and HEG
AB Dor line width analysis relative to an evolved star spectrum of AB Dor, with the corresponding µ Vel line widths
µ Vel, which is known to have a very small projected subtracted. The horizontal lines represent the model line widths
rotation velocity of vsini = 6 km s−1 (de Medeiros & of AB Dor, relative to µ Vel. The solid black horizontal line in-
dicates predicted line widths based on a realistic optically-thin
Mayor 1995). Synthetic line profiles were calculated for
model, without rotational broadening. The solid gray and dot-
µ Vel based on the DEM obtained from the Chandra ted gray horizontal lines represent the predicted line widths for
HETG spectrum by Garc´ıa-Alvarez et al. (2006). surfacerotationalbroadeningandrotationalbroadeningatascale
Lines used in this analysis are listed in Table 1. The heightof1R⋆ abovethestellarsurface,respectively.
MgXIIλ8.42linewasexcludedinthelinewidthanalysis
because the dispersion at this wavelength is insufficient In most cases the observed line widths in Figure 5 are
to clearly discriminate between line widths of theoreti- consistent with the theoretical profiles corresponding to
cal profiles with no rotational broadening versus those zero rotation, within observational errors. Most of the
broadened by surface rotation. Theoretical line profiles lines are also consistent, within errors, with theoretical
were synthesized by convolving the thermal, rotational, profiles that include rotational broadening at the stellar
andinstrumentallinebroadeningcomponents. Detailsof surface. In order to determine to what extent the obser-
theoretical line synthesis may be found in Chung et al. vations of individual lines can constrain the scale height
(2004). Thermal broadening was computed using the of the emission of AB Dor, we combined the individual
differential emission measure as a function of temper- resultsinthe followingway. ForeachAB Dorline width
ature, Φ(T), derived from the same HETG spectra by we subtracted the appropriate µ Vel line width, then
Garc´ıa-Alvarez et al. (2005). For rotational broadening generated 100 Monte Carlo realizations within a normal
weassumedsolidbodyrotationofthestellarsurface(e.g. distribution corresponding to the observed AB Dor line
Gray1992),correspondingtotheprojectedrotationalve- width(relativeto µ Vel) and1σ uncertainty. Line width
locity vsini = 95 km s−1. The stellar radius, R , was realizations were interpolated onto a model curve that
⋆
taken to be 1R⊙, which is consistent with the interfer- describes the line width as a function of scale height,
ometric result 0.96±0.06R⊙ of Guirado et al. (2011). to obtain a distribution of scale heights for each line.
Wealsosynthesizedprofilesfordifferenteffectiveradiito Finally, we computed the error weighted mean of these
simulate the effects of rotation of a corona with a scale distributions, which is shown in Figure 6. The median
height significantly above the stellar surface. scale height of this distribution occurs at -0.75R , with
⋆
Observed line widths were measured as described in a 1σ lower limit of -0.98R , and 1σ and 3σ upper limits
⋆
§3.2.1. Table 2 lists the line widths of AB Dor and of-0.46R and0.07R , respectively. Physically,this cor-
⋆ ⋆
µ Vel for observed and model profiles, together with the responds to the case in which emission is concentrated
AB Dor excess widths relative to µ Vel. We also illus- toward the stellar poles. The median scale height maps
trate the AB Dor excess line widths in Figure 5. The to a stellar surface latitude of 75deg for very compact
8 J.J. Drake et al.
TABLE 2
Observed andmodelline widths forAB Dor andµ Vel.
Full-WidthatHalf-Maximum(˚A)
Rest Observation Modela ABDorexcess
Grating Wvl(˚A) ABDor µVel ABDor µVel relativetoµVelb
MEG 12.13 0.021±0.001 0.020±0.001 0.023 0.020 -0.001
MEG 14.20 0.021±0.002 0.019±0.002 0.023 0.020 -0.001
MEG 15.01 0.021±0.001 0.018±0.001 0.022 0.019 -0.000
MEG 16.01 0.022±0.002 0.017±0.003 0.024 0.021 0.002
MEG 16.78 0.022±0.002 0.015±0.001 0.023 0.020 0.005
MEG 18.97 0.024±0.001 0.019±0.003 0.026 0.024 0.002
MEG 24.78 0.027±0.007 0.012±0.006 0.029 0.026 0.011
HEG 12.13 0.014±0.001 0.015±0.002 0.015 0.013 -0.003
HEG 15.01 0.011±0.002 0.012±0.003 0.013 0.011 -0.003
aModel line widths include instrumental, thermal, and surface
rotationalbroadening.
bExcess line widths refer to (wobs − wmod)ABDor − (wobs −
wmod)µVel, where wobs and wmod refer to observed and model
linewidths,respectively.
emission with respect to the stellar radius, while the 1σ other lines somewhat weaker than our sample the blend
limit corresponds to 57deg (the 3σ upper limit allows contributions become more significantand resulting sys-
very compact emission over the whole of the stellar sur- tematic uncertainties in measured line widths commen-
face). surately larger.
In a Fourier approach, it is the distribution of power
that matters and the exact placement of the myriad of
weaker lines is less important. Similar Fourier tech-
niqueshavebeenappliedtohighresolutionopticalspec-
tra of stars, as pioneered by D. Gray and co-workers
(e.g. Smith&Gray1976)arealsoinprinciplecapableof
separating rotational broadening from other broadening
mechanisms such as turbulence with Gaussian velocity
distributions. However, Chandra grating spectra cover
a decade in resolving power from short to longer wave-
lengths and the broadening signatures we seek amount
to, at maximum, only a fraction of the instrumental
width and such fine differentiation will not be possible.
Our method is to compare the power spectra of the
observedAB Dor HETG spectra with those of synthetic
spectra that have been broadened by different rotation
velocities. Syntheticspectrawerecomputedusingasim-
ilarapproachtothatdescribedaboveforindividualspec-
tral lines, using the emission measure distribution with
Fig.6.— The error weighted mean distribution of scale heights
temperature, Φ(T), in addition to element abundances,
based on a Monte Carlo analysis of observed and predicted line
widths of the MEG and HEG data, as described in text. Scale of Garc´ıa-Alvarez et al. (2005). Owing to the mass de-
heightsarerelativetothestellarsurfaceandassumesphericalsym- pendency of thermal broadening, this needs to be ac-
metry,suchthataheightofzerocorrespondstoauniformcorona countedfor separately for the different elements prior to
on the stellar surface with negligible vertical extension. Negative
convolutionwith the rotationalbroadeningfunction and
scaleheights implythecorona isrestrictedtohighlatitudes. The
1σlowerlimit,alongwiththe1σand3σupperlimitsareindicated instrumental profile.
byverticallines. Since a given rotational broadening contributes more
to an observed line width at longer wavelengths where
the instrumental resolving power is highest, power spec-
3.4. Fast Fourier Transform Analysis tra generated from synthetic spectra are fairly sensitive
ThegeneralideabehindusingFastFourierTransforms totherelativeintensitiesofthestrongestlinesacrossthe
(FFTs) to probe line broadening is to use the combined wavelength range. While our simulated AB Dor spec-
signal in the whole of the spectrum, rather than just a tra matched the observations very well in general (see,
small handful of bright, well-measured lines. Also cru- e.g. Garc´ıa-Alvarez et al. 2005), some of the intensities
cial to the analysis of individual line widths is accurate of stronger Fe lines, in particular, differed by ∼ 30% or
knowledgeofthestrengthandlocationblendsthatmight so from those observed. These problems are largely at-
significantlyaffecttheobservedlinewidths. Theanalysis tributable to difficulties and complexities in theoretical
above was based on single well-exposed lines for which predictions of the relative line strengths themselves—a
blend contributions can be estimated reasonably well, problem discussed at length in the case of Fe XVII in
provided the temperature structure and chemical com- recent work of Doron & Behar (2002) and Gu (2003).
positionofthe coronaarewell-understood. However,for We therefore adjusted the simulated intensities of the
A Pole-Dominated Corona on AB Dor 9
strongest lines to match the observed intensities. titativeconstraintsonthecoronalscaleheightandstruc-
Uncertainties resulting from Poisson counting statis- ture of the rapidly rotating corona on AB Dor. This in-
tics wereestimated for the FFT ofthe observedAB Dor formation is encoded in the observed spectrum through
spectrum using a Monte Carlo method. We constructed Dopplershiftsofthesourceplasma. TheseDopplershifts
100 realizations of the observed spectrum by randomiz- amount to only a fraction of the instrumental broad-
ing the counts in eachspectralbin within their observed ening and are not easily or reliably detected in single
Poisson errors. An FFT was then computed for each of line profiles or centroids. However, the emphasis of the
the 100 realizations, and the 1 σ confidence limits on study presented here is that the cross-correlation and
themeanFFTofthe observedcountsspectrumwereob- FFT techniques we have exploited use the signal in the
tained from the resulting FFT distributions. In order whole of the observed spectrum and can be more sensi-
to facilitate comparisonbetween FFTs ofmodel and ob- tive than analyses based on single lines.
served spectra, the FFTs were summed over intervals of Measuredwavelengthsofindividualspectrallinesillus-
10 bins, where the bin size was 0.005 ˚A. tratedinFigure3shownoobviousorsignificantDoppler
shifts relative to the mean frame of rest, although there
is a hint of a redshift at phase φ = 0.9 in lines of
Mg XII λ8.42 and Fe XVII λ16.78 that is also perhaps
present in O VIII λ18.97. The phase φ = 0.9 corre-
sponds exactly to the peak of the flare evident in the
light curve in Figure 2 and it is tempting to ascribe the
weak velocity shift signature to it. If so, it would im-
plythe flareweresituatedonthe recedinghemisphereof
AB Dor. We noted in §3 that it is possible that the im-
pulsivephaseoftheflarewasobscuredbythestellardisk.
Werethisthecasethoughwemighthaveexpectedtosee
a blueshift rather than redshift, as the flare approached
along the line-of-sight around the limb, and the lack of
any net blueshift at this phase tends to argue against
such an explanation. One might also expect to see blue-
shifted plasma as a result of chromospheric evaporation
within flaring loops on the visible hemisphere in which
loops are likely to be at least partly aligned along the
line-of-sight (although to our knowledge no convincing
Fig.7.—Comparisonbetween fastFourier transformsof model
blue-shifts due to chromospheric evaporation have been
and observed spectra in the spectral scale size region of interest.
Model spectra were computed as described in the text, and were detected by Chandra to date). That the redshift is not
convolvedwitharotationalbroadeningfunctionwithdifferentscale seen in the brighter Fe XVII λ15.01 line, however, sug-
heights. Here,thescaleheightsrefertotheradiusassumedinthe geststheredshifthintmostprominentinFeXVIIλ16.78
rotationalbroadeningfunction,ratherthantotheadditionalheight
is spurious with an origin in some degree of systematic
above surface rotation as in the preceding figure and in the text
(e.g. Thermal+0.1R⋆ implies a rotational broadening component uncertainty not accounted for in the analysis.
corresponding to a scale height of −0.9R⋆). The shaded regions The cross-correlation of phase-resolved spectra pro-
indicatethe±1σand±3σuncertaintyboundsofthedataobtained vides a much more sensitive measure of Doppler shifts
throughMonteCarlosimulations.
than any of the individual lines (Figure 4). Figure 4
shows that Doppler shifts are almost exclusively within
The observed power spectrum and uncertainties are 1σ of 0 km s−1 and are perfectly consistent with no
comparedwiththoseofthesyntheticspectrainFigure7.
significant net velocity shift. The lack of net Doppler
Thisanalysisindicatesthatspectrawithonlyinstrumen- shifts larger than ∼ 20 km s−1 implies that either coro-
talbroadeningarenotagoodmatchtotheobservations,
nal plasma at low latitudes was relatively uniformly dis-
andsomeadditionalbroadeningisrequired. TheFFTof
tributedinlongitude,orthatplasmawasconcentratedat
the model spectrum with thermal broadening and very
the poles during the 1999 October epoch analyzed here.
small additional rotational broadening corresponding to
Wenotedin§3.2.2thatthecross-correlationtechnique
a very small scale height of 0.1R (essentially equivalent
⋆ does not distinguish between lines formed at different
to the case of no rotational broadening) provides the
characteristic temperatures. In this sense, our measure-
best match to the observations, although models with
ments are essentially a signal-weighted average Doppler
slightly larger scale heights—up to ≤ 1R or so cannot
⋆ shift. Since the longer wavelengths are also more sensi-
be excluded. The model corresponding to surface ro-
tive to velocity, the weighting for the MEG spectrum is
tation scale height 1R exceeds the 3σ error bounds at
⋆ going to be more toward the H-like Ne X Lyα line and
scales corresponding approximately to the line FWHM.
FeXVIIandOVIIIfeatureslongwardofthis. Theseions
This indicates that the model line core is broader than
aregenerallyformedinthetemperaturerange2–6×106,
observations indicate. Models with scale heights > 1R
⋆ although the increasing emission measure toward higher
are strongly excluded.
temperatures (e.g. Garc´ıa-Alvarez et al. 2005) means
thatweightingwillbe towardthe highendofthis range.
4. DISCUSSION
TheHEGspectrumwillbemoresensitivetohighertem-
4.1. Summary and Interpretation of Results
perature features, including H- and He-like Si, Mg and
A careful analysis of Chandra HETG spectra using Ne. These are generally formed at temperatures of 5–
cross-correlationandFFTtechniqueshasprovidedquan- 15×106 K. While the cross-correlationtechnique might
10 J.J. Drake et al.
masksomesubtledifferencesinradialvelocitywithtem- unfortunately,however,theveryweakforbiddenFe lines
perature, the agreement of HEG and MEG results, and are compromised by the presence of neighboring strong
thefactthattheindividuallinesformedatdifferenttem- lines and line blends.
peraturesdo notshow anysigns ofsignificantly different A salient point that the long FUSE observation, and
behavior, indicates that there is no temperature schism theChandraLETGandHETGobservations,wereallob-
in the structure of the AB Dor corona. tained at significantly different epochs, should be borne
The degeneracy between a corona uniformly dis- in mind: while particular active longitudes apparently
tributed in longitude or one concentrated at the poles do exist on AB Dor (J¨arvinen et al. 2005), details of
indicated by the lack of significant Doppler shifts can the coronal topology would be expected to change on
be removedby examining spectral line widths, which we shorter timescales and there is no reasonthat particular
would expect to exhibit palpable broadening were the features hinted at by one observation should be present
corona to be uniformly distributed about the star, or in another. Our observations indicate that the bulk of
concentrated at low latitudes. The line widths, how- the coronal emission persists at high latitudes. Both
ever, show no evidence for strong additional rotational the Doppler shifts and photometric rotational modula-
broadening, in contrast to the HETG spectra of Algol tion found by Hussain et al. (2005) suggest that some
presentedbyChungetal.(2004). BothFFTandindivid- detectable emission can also occur at lower latitudes.
ual line width analyses favor only very small additional This picture is supported by the pattern of ambigu-
broadeningabovethatinducedbythermalvelocitiesand ousEUV-X-rayrotationalmodulationevidencediscussed
theinstrumentalprofile. Themediancoronalscaleheight in §2: while some observations found significant rota-
from the Monte Carlo simulations of all the lines com- tional modulation, others, including the extensive study
bined (Figure 6) is h=−0.75R ; ie less than the stellar of Lalitha & Schmitt (2013), did not.
⋆
radiusasmeasuredfromthestellarcentre. The1σupper Further clues as to the temporal variationof the coro-
limitis−0.46R —alsolessthanthestellarradius. Physi- nal emission of AB Dor can be gleaned from Doppler
⋆
cally,these“negative”scaleheightscanbeinterpretedin and ZDI maps obtained in different years. Donati et al.
termsofthecoronabeingrestrictedtowardhighlatitude (2003)presentedboth spot (Doppler imaging) and mag-
whererotationalbroadeningissmaller. Formally,the 1σ netic field (ZDI) maps for AB Dor for epochs spanning
upper limit corresponds to a corona limited to latitudes 1998-2002. All epochs exhibited an extensive dark polar
> 57deg. Similarly, the FFT analyses also suggest the spot covering latitudes above 70deg or so (see also Jef-
corona lies at restricted higher latitudes. fersetal.2007),consistentwithourinferenceoftheloca-
These results provide direct spectroscopic evidence tion of the bulk of the coronal emission, and all showed
thatthedominantcoronalemissioninarapidly-rotating some degree of structure at lower latitudes. However,
active star such as AB Dor is largely associated with qualitatively, there is quite a striking difference between
the dark polar spots commonly found in Doppler imag- mapspresentedforepoch1999.97,whichisfairlycloseto
ing and ZDI analyses of photospheric spectra (e.g. Vogt the epoch of our 1999 October observations, and those
et al. 1999; Strassmeier 2002; Jeffers et al. 2005). The presented for 2001.99 in the sense that the latter con-
results are not, however, definitive: the 3σ upper limit tainmuchmoreextensive features andstructure atmid-
to the scale height based on individual lines is h < 0R andlow-latitudes. Suchstructureisalmostabsentinthe
⋆
(surfacerotationorless). Arigorousformallimitismore 1999.97 maps, even considering the more limited phase
difficulttodefinefortheFFTanalysis,butthedatasug- coverage of those observations. This matches expecta-
gest strongly that h < 0R . It is also not possible to tions from the 1999 and 2002 Chandra Doppler shift
⋆
rule out some small fraction of the emission as emanat- results reported here and by Hussain et al. (2005), re-
ing from lower latitudes. Such emission would give rise spectively. The late 1990’s also corresponds to the peak
to broadened line wings, of which we see no evidence in in brightness—and presumably the minimum in spot
the spectra. It is, however, possible that of the order coverage—of AB Dor based on the photometric moni-
of 10% of the emission could be in a somewhat broader toring of J¨arvinen et al. (2005).
spectral component.
4.3. Implications for Coronal Magnetic Field
4.2. Comparison with Other Epochs Extrapolation and Models
Thelackofphase-relatedDopplershiftsinthe1999Oc- As noted in §1, the type of spectroscopic constraints
tober spectra of AB Dor contrasts with the modulation on the topography of coronal plasma reported here rep-
seenbyHussainetal.(2005,seealsoHussainetal.2007) resent potentially important observational tests of coro-
in the light of O VIII λ18.97 in the LETG observation nal structure extrapolated from ZDI maps of the photo-
of 2002 December, which exhibited a to peak-to-peak spheric magnetic field. Our deduction of predominately
velocity change of 60 km s−1 and betrayed low-latitude polar coronalactivity on AB Dor is in qualitative agree-
structure during that epoch. Hussain et al. (2005) also ment with the ubiquitous presence of extensive polar
investigatedconstraintson the coronalscale height from spots on AB Dor, and with such coronalfield extrapola-
both Chandra LETG and FUSE spectra. They found tionbyJardineetal.(2002a,b),andHussainetal.(2002).
h<0.75R (1σ)basedontheFeXVII15.01˚Alineinthe These authors inferred that, although the corona might
⋆
2002 December epoch LETG spectra. Based on FUSE be quite extended, much of the model emission comes
observationsfrom1999Decemberand2003Decemberof from high-latitude regions close to the stellar surface.
the forbidden lines Fe XVIII λ974 and Fe XIX λ1118, It has been especially noted by McIvor et al. (2003),
they obtained h = 0.45±0.3R . In principle, the much however, that ZDI cannot reveal the nature of the mag-
⋆
higher FUSE resolution (λ/∆λ ∼ 20000) should render netic field in polar regions and whether field structures
tighterconstraintsonlineprofilesthanChandra spectra; are predominantly closed or open. These authors have