Evidence for a Link Between Fe K-alpha Emission Line Strength and QPO Phase in a Black Hole

0.12 MB·English

by  J. M. Miller

DRAFTVERSIONFEBRUARY2,2008
PreprinttypesetusingLATEXstyleemulateapj
EVIDENCEFORALINKBETWEENFEKαEMISSIONLINESTRENGTHANDQPOPHASEINABLACKHOLE
J.M.MILLER1,2ANDJ.HOMAN3
Subjectheadings:Blackholephysics–relativity–stars: binaries–physicaldataandprocesses:accretiondisks
DraftversionFebruary2,2008
ABSTRACT
In X-ray binaries, the frequencies revealed in X-ray quasi-periodic oscillations (QPOs) are often interpreted
5
as characteristic frequenciesin the inner accretion disk, though the exact oscillation mechanism is unknownat
0
0 present. BroadenedFeKα linesare alsoexcellentdiagnosticsoftheinneraccretionflow, iftheir broadeningis
2 indeedduetoinnerdiskreflection.Herein,wepresenttwocaseswherethefluxandequivalentwidthoftheFeKα
emissionlinesinspectraoftheGalacticblackholeGRS1915+105varywiththephaseofstrong1Hzand2Hz
n
QPOsintheX-rayflux.TheseresultsprovidestrongevidencethatbothQPOsandtheFeKαlinesoriginateinthe
a
innerdisk.Ifthe1HzQPOisonlyaKeplerianorbitalfrequency,theQPOcomesfromadistanceof84±26R
J Schw.
fromtheblackhole;the2HzQPOimpliesaradiusof50±15R . Attheseradii,relativisticshapingofadisk
8 Schw
lineisinevitable. Moreover,thelinkholdsinradio–brightandradio–faintphases,signalingthatinsystemslike
1
GRS1915+105,theFeKαlineisadisklineandnotajetlineasperSS433.Aparticularlyinterestingpossibility

1 isthatastablewarpintheinnerdisk,e.g.duetoLense-Thirringprecession,mayproducetheobservedQPOsand
v linemodulations.Morebroadly,theFeK–QPOlinkprovidesanunprecedentedmechanismforrevealingtheinner
1 accretionflowandrelativisticregimeinaccretingsystems,inthatitgivestwomeasuresofradius:foragivendisk
7 QPOmodel,thefrequencytranslatesintoaspecificradius,andrelativisticlinemodelsyieldradiidirectly.
3
1
1. INTRODUCTION further. We report the discovery of a link between discrete
0
timingfeatures(QPOs)andspectralfeatures(FeKαemission
5 Inaccretion-poweredsources,agreatdealoftheoreticaland
0 observationaleffortis devotedto the studyof the inneraccre- lines): Fe Kα emission line strength varies with QPO phase
/ in radio–bright and radio–faint states of the “microquasar”
h tionflow,andtousingtheaccretionflowitselfasatooltostudy GRS 1915+105. Our results provide the first indication that
p the centralcompactobject. High frequencyQPOs in Galactic
thesediagnosticsoftheinneraccretionflowarerelated.
- black hole systems may be related to the Keplerianfrequency
o
attheinnermoststablecircularorbit(forzero-spinblackholes,
r
t ν =220 Hz 10 M⊙/MBH; e.g., Strohmayer2001, Miller et al. 2. DATASELECTIONANDREDUCTION
s
a 2001, Remillard et al. 2002, Homan et al. 2004), but they are WechosetoinvestigateGRS1915+105asstrongQPOs(see,
v: onlyobservedinahandfullofsources.QPOsatlowerfrequen- e.g., Morgan, Remillard, & Greiner 1997) and Fe Kα emis-
cies, typically 1–10 Hz are much more common. Although
i sionlines(Munoetal.2001,Martocchiaetal.2002,Milleret
X their origin is unclear, interpreting them as a Keplerian fre-
al. 2004a) have been reported in this source. The high mass
ar qsiuoenncfryeqpuuetsncthyeamt tahte∼<i1n0n0erRdSicshkw..(eI.fg.t,hedsueeQtoPOfrsamareedarapgregcinegs-, ofGRS 1915+105(MBH =14.4±4.4M⊙, Harlaftis& Greiner
2004) means that for a given QPO frequency, the QPOs may
see Markovic& Lamb 1998), theyproberegionsmuch closer
trace regions closer to the black hole in this source than in
to the black hole. Broad, asymmetric Fe Kα emission lines lower-mass black holes. GRS 1915+105 displays a wide va-
are foundin the spectra of bothsupermassiveblack holesand
riety of radio states. Steady radio emission is associated with
stellar-mass Galactic black holes (Reynolds & Nowak 2003).
compactjets(Fender2004),andthisfactcanbeexploitedtoex-
These lines appear to be imprinted with the extreme Doppler
aminewhetheranyrelationbetweenFeKαlinefluxandQPOs
shiftsandgravitationalred-shiftsexpectedneartoablackhole,
dependsonthepresenceofajet.
butthecaseisnotentirelyshut.
To extract QPO phase-selected spectra, QPOs should be
A natural evolution of the means by which inner accretion
strong enough to dominate the X-ray variability and be di-
flows are studied is to bringspectralandtiming constraintsto
rectly visible in the X-ray lightcurves. Morgan, Remillard,
bearjointly.Ithasbeenshownthatthediskreflectionspectrum
& Greiner (1997) found large amplitude, sinusoidal QPOs in
(theFeKαlineisthemostprominentpartofthereflectedspec- GRS 1915+105 that could be seen in the naked lightcurve.
trum;seeGeorge&Fabian1991)inGalacticblackholesvaries
The QPOs were found to be quasi–periodic largely due to
withbroad-bandfrequency(Gilfanov,Churazov,&Revnivtsev
random jumps in phase. We selected two observations of
2000). Thisisstrongevidencethattimingandspectralproper- GRS 1915+105available in the RXTE public archive: 20402-
tiesareintimatelyrelated,andsupportsmodelswhereinFeKα
01-15-00 (obs. date: 9 Feb. 1997) and 20402-01-50-01 (obs.
emissionlinesariseintheinnerdisk.
date:16Oct.1997).Thespectralandtimingpropertiesofthese
Inthiswork,wetakespectralandtimingconnectionsastep
observations(includinganFeKαemissionline)
1Harvard-SmithsonianCenterforAstrophysics,60GardenStreet,Cambridge,MA02138,[email protected]
2NSFAstronomyandAstrophysicsFellow
3CenterforSpaceResearchandDepartmentofPhysics,MassachusettsInstituteofTechnology,Cambridge,MA02139–4307,[email protected]
1
2 TheIronLine–QPOConnection
radio bright radio faint
FIG. 1.—Thepowerdensityspectraoftheradio-brightobservation(black)
andradio-faintobservation(red)areshownabove. ThestrongestQPOshave
frequenciesof1.052(3)Hzand2.260(2)Hz,andamplitudesof14.7(3)%rms FIG. 2.— Approximately 20 cycles of the QPO wave from randomly
selected intervals in each observation are shown above. Clearly the QPOs
and13.6(1)%rms,respectively.
stronglydominatethelightcurves. Solidlinesmarkthemeancountrate,and
have previously been reportedon by Muno et al. (2001). Im- dashedlinesaboveandbelowmarkthecountratelevelsusedtoselectthehigh
portantly, Muno et al. (2001)also studied the radio properties andlowphasesoftheQPOwaves.Theradio-brightdataarebinnedto0.128s,
ofGRS1915+105duringtheseobservations;thefirstoccurred andtheradio-faintdataarebinnedto0.064s.
ina“radio–faint”state(hereafter,“RF”;thesourcewasnotde- 0.01–100HzrangewithLorentzianfunctionsintheν–maxrep-
tected at 8.3 GHz), and the second in a radio-brightor radio- resentation(see,e.g.,Homanetal.2004).EachPDSisstrongly
plateaustate(74±6mJyat8.3GHz;hereafter“RB”). dominatedbyasingleQPO(seeFigure1). ThestrongestQPO
ToolswithinLHEASOFTversion5.3andCIAOversion3.1 in the RF obs. has a frequency of 2.273(4) Hz, a Q–value of
were usedto reduceandanalyzethese observations. Standard 6.0(2),andanamplitudeof11.8(2)%rms(errorsare1σ). The
RXTE data screening and good time selections were applied strongestQPOintheRBobs.hasafrequencyof1.050(3)Hz,a
(e.g.,forSAAavoidance).Wefurtherscreenedthedatatoonly Q–valueof7.9(4),andanamplitudeof11.1(2)%rms. Assum-
include times duringwhich all five PCUs were operated. The ingablackholemassofMBH=14.4±4.4M⊙,ifthesefrequen-
nettotalgoodtimefortheRFobs.(15-00)was10.1ksec,and ciesare merelyKeplerianorbitalfrequencies,theycorrespond
the nettotal goodtime forRB obs. (50-01)was 4.5 ksec. All toradiiof84±26R and50±15R respectively.
Schw. Schw.
spectra and lightcurves were generated using the tool “saex- Lightcurves from the “B_8ms_16A_0-35_H” mode data
trct”, and all response matrices were generated with the tool fromeachobservationwereanalyzed,andthetotalmeancount
“pcarsp”. As GRS 1915+105is very bright and we are inter- rateandmeancountratein100sintervalswerecalculated.The
ested in relative variations, backgroundspectra were not sub- meanrateintheRFobs.is3532c/s,witharangeof3298–3727
tracted. We made time-averaged broad-band PCA spectra by c/swhenmeasuredin100sintervals. ThemeanrateintheRB
combiningdatafromalllayersofallPCUstakenin“Standard- obs.is6602c/s,witharangeof6496–6793c/s.
2” mode (129 energy channels between 2 and 60 keV, taken As the QPOs in each observation dominate the X-ray vari-
every16s). Spectraandlightcurveswerealsomadefromdata ability(seeFigure2),andbecausethemeancountrateineach
takenin“B_8ms_16A_0-35_H”mode(16energychannelsup observationisverysteady,weappliedsimplecount-rateselec-
tochannel35–roughly13keV–takenevery8ms). tionstoisolatethemaximaandminimaoftheQPOwaves. For
To accurately estimate relative flux differences in data ac- the RF obs. selecting periods when the flux was 15% above
quired with the same detector, it is only important to under- orbelowthemeaneffectivelyisolatedthemaximaandminima.
stand the degree to which systematic errors may change over For the RB obs. there is less noise apart from the QPO, and
time. Forthispurpose,wereducedandanalyzedCrabspectra periodswhenthefluxwas10%aboveorbelowthemeanwere
obtained before and after each observationof GRS 1915+105 found to effectively isolate maxima and minima. The CIAO
(spectra obtained on 31 Jan. 1997 and 16 Feb. 1997, and 12 tool“dmgti”wasusedtogenerateadditionalgoodtimefilesof
Oct.1997and27Oct.1997).Absorbedpower-lawfitstothese themaximaandminima. Thesefileswerethanappliedwithin
spectra reveal that most channels below 10 keV (those most “saextrct”toproducespectraofthemaximaandminima.
importantforFeKαlinestudies)differby0.2%orless. Tobe All spectral analysis was done using XSPEC version 11.3
conservative, we added 0.2% systematic errors to the spectra. (Arnaud 1996) and IDL version 5.4. Analysis of the time–
Thisislessthanthe0.5–1.0%systematicerrorsoftenaddedto averagedstandard-2spectrawasperformedinthe3.0–20.0keV
PCAspectrawhenabsolutefluxesareofinterest. band. ThePCAiscalibratedwellinthisenergyrange,andthis
rangeisnotmuchgreaterthantherangeofthe“B_8ms_16A_0-
3. ANALYSISANDRESULTS
35_H”modedata.Fitstothespectrawithanumberofcommon
Wemadepower-densityspectra(PDS)oftheX-rayfluxfrom modelsrevealed the Fe Kα emission line previouslynoted by
eachobservationusingallavailabledata,andfitthe Munoetal.(2001).Ineachcase,theadditionofasimple
Miller&Homan 3
high phase
low phase
FIG. 3.— Fitstothehighandlowphasespectrafromtheradio–faintob- FIG. 4.— Theplotaboveshowstherelative intensityoftheradio-bright
servation ofGRS1915+105areshownabove. Thespectrawerefitwiththe and radio-faint spectra of GRS 1915+105 (and a “control” observation of
model described in Table 1, using the fixed line centroid and width (which H1743- 322)inhighandlowcountratephases. Thelowcountratespectra
givesasmallerdifferenceinthelinefluxesthaniftheseparametersfloat).The weresubtracted fromthehighcountrate spectra, andthedifference was di-
linefluxwassettozeroontheratioplottoshowthedifferenceinFeKαline videdbythemeancountratefortheentireobservation. Errorbarsareplotted
intensitybetweenhighandlowQPOphases. butareverysmall.Channelbinswereconvertedtoenergyspacebutthedetec-
torresponsehasnotbeenremoved(sotheXeLedgecomplexbetween4–6keV
Gaussiancomponenttomodelthelinewassignificantatmore isseen). UnliketheH1743- 322differencespectrum,theFeKαlinebinsare
than the 8σ level of confidence. We find that disk reflection dominantintheGRS1915+105difference spectra. Thismodel–independent
modelsprovidethebestoverallfittothebroad-bandspectrum analysisconfirmsthattheFeKαlineintensityvarieswithQPOphase.
anddonotrequirea diskthatisprominentin theRXTEband- timescales of seconds, but had a steady mean count rate on
pass. Ourmodeldoesnotincludeadisk,butthisonlyreflects 100 s scales in this window. Spectroscopy of H 1743- 322in
thefactthatacooldiskwithmoderatefluxisnoteasilyseenin outburst did not reveal an Fe Kα emission line (Miller et al.
theRXTEbandpass,especiallywhenN ishigh. 2004b), and the Fe Kα line bins are not globally dominantin
H
Wefitthetime-averaged,highphase,andlowphasespectra thedifferencespectrumshowninFig.4.
with absorbed cut-off power-law (for the radio-bright phase)
4. DISCUSSIONANDCONCLUSIONS
or brokenpower-law (for the radio-faintphase) models, mod-
ified by the addition of a Gaussian component (to model the Themainresultsofthisworkmaybesummarizedasfollows:
FeKαemissionline)andsmearededgecomponent(“smedge” • Fe Kα line flux (and possibly FWHM and centroid energy)
in XSPEC) to mimic a reflected continuum. Trudolyubov depends on QPO phase in 1–2 Hz QPOs in GRS 1915+105,
(2001)alsofoundthatthesedifferingspectralmodelswerere- linkingtwoindependentdiagnosticsoftheinneraccretionflow.
quired in RF and RB states. The “phabs” model was used to •TheQPOfrequenciesatwhichtheFeKαlinefluxismodu-
accountfor absorptionin the neutralISM. The “smedge” was latedcorrespondtoradiiof84±26R and50±15R ,if
Schw. Schw.
notstatisticallyrequiredinallfits,anditsparameterscouldnot theyaremerelyKeplerianorbitalfrequencies. Thislinklikely
be well constrained. However, the smedge effectivelymimics ties Fe Kα lines in Galactic black holes to the inner disk and
a disk reflection spectrum at energies above the Fe Kα emis- furthersupportsevidence that the observedline broadeningis
sion line, so we fixed the model parameters to modest values dueto dynamicsin the disk (Dopplershifts, gravitationalred-
consistentwiththedata(E=8.5keV,τ =0.3,width=10keV). shifts)closetotheblackhole.
Theparametersobtainedfromthespectralfitsare shownin • The presence of Fe Kα lines, QPOs, and the link between
Table 1. Inallcases, the linefluxesandequivalentwidthsare themdoesnotdependonjetactivity(takingradiofluxasajet
significantly different in the high and low phase spectra (see indicator). Althoughthebaseofafailedjetmaybeasourceof
Fig.3). Theconfidenceintervalsdonotoverlapevenwhenthe hardX-rayswhichirradiatethedisk,FeKαlinesandQPOsdo
1σ error bars are multiplied by 5. There is evidence that the notariseinanextendedjet.
Fe Kα emissionline fluxisbroaderandslightlyshiftedto the
redinthehighphaserelativetothelowphase. Blobs in the inner accretion disk might create QPOs and
To demonstrate that the line flux varies in a model– could give a quasi-periodically changing reflector area. Sim-
independentmanner, we subtracted the low countrate spectra ilarly, if the height of hard X-ray emitters (flares, or the base
fromthe highcountrate spectra, anddividedthe resultby the of a jet) changes quasi-periodically, QPOs and Fe Kα line
mean count rate for the entirety of each observation. Using variations might be expected. However, while both explana-
theenergytochannelboundsfoundintheresponsematrixfor tions are possible, such explanations seem inconsistent with
each observation, the bins in the difference spectra were con- the strength and constancyof the QPOs found in these obser-
verted to energy bounds; however, the detector response was vations of GRS 1915+105, and with the fact that the Fe K–
not removed and no spectral fitting was performed. In both QPOconnectionholdsoverafactoroftwoinfluxandinboth
theradio–brightandradio–faintobservations,themostpromi- radio-brightandradio-faintphases.Moreover,associatinglow-
nentdifferencebetweenthehighandlowphasesistheFe Kα frequencyQPOswithKeplerianfrequenciesisproblematicfor
line (see Fig. 4). For a “control” observation, we extracted tworeasons: (1)X-rayproductioninaccretiondisksshouldbe
highandlowphasespectra(10%above/belowthemean)from centrallyconcentrated,withlittleemissionfromr≥100R ,
Schw.
a 1.2 ksec slice of an observation of the Galactic black hole and (2) QPOs are strongerat higher energies, suggesting they
H 1743- 322obtainedon28May2003. Liketheobservations are also centrally produced (see, e.g., Homan et al. 2001). A
ofGRS1915+105,H1743- 322washighlyvariableon stablewarpattheinnerdisk,e.g.duetoLense-Thirringpreces-
4 TheIronLine–QPOConnection
TABLE 1
FitstoQPOPhaseSpectra
NH Γ1,Γ2 Ebreak(keV) Norm. EGauss(keV) FWHM flux(10- 2ph/cm2/s) EW(eV) χ2/ν
RFavg. 5.40(6) 2.18(1),1.922(5) 11.4(1) 4.55(6) 6.58(5) 1.9(1) 1.13(7) 150(10) 70.5/38.0
RFhigh† 5.40 2.125(3),2.5(1) 11.4 5.45(3) 6.58 1.9 2.00(8) 200(8) –
RFlow† 5.40 2.335(6),1.00(5) 11.4 4.42(2) 6.58 1.9 0.66(3) 120(5) –
RFhigh 5.40 2.122(4),2.3(1) 11.4 5.37(4) 6.32(6) 2.7(2) 2.8(2) 260(20) –
RFlow 5.40 2.328(6),1.29(9) 11.4 4.32(4) 6.72(4) 1.1(1) 0.52(3) 100(6) –
NH Γ1 Ecut(keV) Norm. EGauss(keV) FWHM flux(10- 2ph/cm2/s) EW(eV) χ2/ν
RBavg. 5.96(8) 1.97(2) 29(1) 7.3(2) 6.43(3) 1.9(1) 4.2(2) 280(10) 189.2/39
RBhigh† 5.96 1.927(2) 29 8.27(3) 6.43 1.9 5.6(1) 300(5) –
RBlow† 5.96 2.044(1) 29 6.89(2) 6.43 1.9 3.13(4) 250(10) –
RBhigh 5.96 1.925(3) 29 8.18(5) 6.33(3) 2.4(1) 6.7(2) 360(10) –
RBlow 5.96 2.046(1) 29 6.96(2) 6.53(1) 1.4(1) 2.59(4) 220(4) –
NOTE.—“RF”refers totheradio-faint observation (fitwithabroken power-law), and“RB” totheradio-bright observation (fitwithacut-off power-law). A
“smedge”withE=8.5keV,τ=0.3,andwidth=10keVwasincludedinallfits.Fitsto“avg”spectraarefitstostandard-2datainthe3–20keVband.Allotherfitsare
tolowerresolution“B_8ms_16A_0-35_H”datainthe3–13keVband.†DenotesfitsinwhichtheFeKαlinecentroidandFWHMwerefixedtothevaluesmeasured
intheaveragespectrum.Whereerrorsarenotgiven,parametersfromthestandard-2fitswerefixed.Systematicerrorsof0.2%wereaddedtoallspectrapriortofitting
toestimatethedriftindetectorresponse.Fitstothephase-selectedspectrawithlinecentroidenergyandFWHMfixedtotheaveragevalue,andwithparametersfree,
arebothreportedforcomparison.Allerrorsare1σerrorstoallowconfidencestobeinferreddirectly.Formallyacceptablefitsareobtainedwithsystematicerrorsset
to0.6%,whichistypicalforspectroscopywhereinabsolutefluxmeasurementsareimportant.
sion,couldcauseQPOsandwouldalsoservetocreateaquasi- Young & Reynolds 2000), and observations of disk hot spots
periodicallychangingreflectorarea,modulatingthestrengthof orbitingclosetotheblackholesinAGN(e.g.,Iwasawa,Mini-
FeKαlineemission.IthasbeensuggestedthatLense-Thirring utti, & Fabian 2004). Long RXTE exposures with carefully
precessionmaybethecauseoflow-frequencyQPOsinaccret- chosen PCA modes are needed to obtain additional data for
ingsystems(e.g.,Markovic&Lamb1998),andtheFeK–QPO new studies. The large effective areas of XMM-Newton and
connectionmaybeevidenceforthisGeneralRelativisticeffect. Astro-E2maysupportsuchstudiesaswell,andmayevenallow
Whether or not Lense-Thirring precession can account for studiesofthelineshapewithQPOphase.AnewX-raymission
the Fe K–QPOconnection,theFe K–QPO connectionhasthe withanareaof2–10m2andCCDspectralresolution(orbetter)
potential to reveal the innermostregime in accreting systems. mayfullyexploittheFeK–QPOconnection.
Foragivendisk–drivenQPOmodel,theFeK–QPOconnection
givestwomeasuresofradius: frequenciesimplyspecificradii, We wish to thank Ed Bertschinger, Andy Fabian, Keith Ja-
andrelativisticdisklinemodelsconstrainradiidirectly(Fabian hoda, Fred Lamb, Cole Miller, Ed Morgan, and Mike Nowak
et al. 1989, Laor 1991). The connection over–constrains the for helpful discussions. We thank Keith Arnaud, Aneta
system,ifQPOsarediskfrequencies. Siemiginowska,andTodStrohmayerforguidancein handling
Work of this kind in Galactic black holes may have impor- systematic errorsin this work. J.M.M. acknowledgesfunding
tantimplicationsforFeKαlinereverberationmappinginAGN fromtheNSF,throughitsAAPFprogram. Thisworkwaspar-
withplannedmissionssuchasConstellation-XandXEUS(e.g., tiallysupportedbyfundingfromtheRXTEGOprogram.
REFERENCES
Arnaud, K.A., 1996, ADASSV,eds. G.Jacoby andJ.Barnes, ASP Conf. Martocchia,A.,Matt,G.,Karas,V.,Belloni,M.,&Feroci,M.,2002,A&A,
Series101,17 387,215
Fabian,A.C.,Rees,M.J.,Stella,L.,&White,N.E.,1989,MNRAS,239,729 Miller,J.M.,etal.,2001,ApJ,563,928
Fender,R.P.,2004,“JetsfromX-rayBinaries”,toappearin“CompactStellar Miller,J.M.,Fabian,A.C.,Nowak,M.A.,&Lewin,W.H.G.,2004a,inthe
X-raySources”eds. W.H.G.Lewin&M.vanderKlis,Cambridge,2004, Proc. ofthe10thMarcelGrossmannMeetingonGeneralRelativity,astro-
seeastro-ph/0303339 ph/0402101
George,I.M.,&Fabian,A.C.,1991,MNRAS,249,352 Miller,J.M.,etal.,2004,ApJ,subm.,astro-ph/0406272
Gilfanov,M.,Churazov,E.,&Revnivtsev,M.,2000,MNRAS,316,923 Morgan,E.H.,Remillard,R.A.,&Greiner,J.,1997,ApJ,482,993
Harlaftis,D.,&Greiner,J.,2004,A&A,2004,414,13 Muno,M.P.,etal.,2001,ApJ,556,515
Homan,J.,etal.,2001,ApJS,132,377 Remillard,R.A.,Muno,M.P.,McClintock,J.E.,&Orosz,J.A.,2002,ApJ,
Homan,J.,etal.,2004,ApJ,inpress,astro-ph/0406334 580,1030
Iwasawa, K.,Miniutti, G., &Fabian, A.C., 2004, MNRAS,inpress, astro- Reynolds,C.S.,&Nowak,M.A.,2003,PhR,377,389
ph/0409293 Strohmayer,T.,2001,ApJ,552,L49
Laor,A.,1991,ApJ,376,90 Trudolyubov,S.P.,2001,ApJ,558,276
Markovic,D.,&Lamb,F.K.,1998,ApJ,507,316 Young,A.J.,&Reynolds,C.S.,2000,apJ,529,101