Flares and variability from Sagittarius A*: five nights of simultaneous multi-wavelength observations

1 MB·English

by  X. Haubois

Astronomy&Astrophysicsmanuscriptno.data07˙final˙version (cid:13)c ESO2013
January22,2013
Flares and variability from Sgr A* : five nights
⋆
of simultaneous multi-wavelength observations.
X.Haubois1,4,K.Dodds-Eden2,A.Weiss3,T.Paumard1,G.Perrin1,Y.Cle´net1,S.Gillessen2,P.Kervella1,F.
Eisenhauer2,R.Genzel2,andD.Rouan1
1 LESIA-Observatoire de Paris, CNRSUMR8109, UPMC Univ Paris 6, Universite´ Paris Diderot, 5 place Jules Janssen, 92195
Meudon,France
e-mail:[email protected]
3 2 MPE,Max-Planck-Institutfu¨rExtraterrestrischePhysik,Postfach1312,D-85741Garching,Germany
1 3 MPIfR,Max-Planck-Institutfu¨rRadioastronomie,AufdemHu¨gel69,D-53321Bonn,Germany
0 4 InstitutodeAstronomia,Geof´ısicaeCieˆnciasAtmosfe´ricas,UniversidadedeSa˜oPaulo,RuadoMata˜o1226,CidadeUniversita´ria,
2 Sa˜oPaulo,SP05508-900,Brazil

n Received18July2011/Accepted11January2012
a
J ABSTRACT

0
2 Aims.Wereportonsimultaneousobservationsandmodelingofmid-infrared(MIR),near-infrared(NIR)andsubmillimeter(sub-mm)
emissionofthesourceSgrA*associatedwiththesupermassiveblackholeatthecenterofourGalaxy.Ourgoalwastomonitorthe

] activityofSgrA*atdifferentwavelengthsinordertoconstraintheemittingprocessesandgaininsightintothenatureoftheclose
A
environmentofSgrA*.
G Methods.WeusedtheMIRinstrumentVISIRintheBURSTimagingmode,theadaptiveopticsassistedNIRcameraNACO,andthe
sub-mmantennaAPEXtomonitorSgrA*overseveralnightsinJuly2007.
.
h Results.The observations reveal remarkable variability in the NIR and sub-mm during the five nights of observation. No source
p was detected in the MIR but we derived the lowest upper limit for a flare at 8.59µm (22.4 mJy with A8.59µm = 1.6±0.5). This
- observational constraint makes us discard the observed NIR emission as coming from a thermal component emitting at sub-mm
o frequencies.Moreover,comparisonofthesub-mmandNIRvariabilityshowsthatthehighestNIRfluxes(flares)arecoincidentwith
r thelowest sub-mmlevels of our five-night campaign involving threeflares. Weexplain thisbehavior bya lossof electrons tothe
t
s systemand/orbyadecreaseinthemagneticfield,asmightconceivablyoccurinscenariosinvolvingfastoutflowsand/ormagnetic
a reconnection.
[
Keywords.blackholephysics–Galaxy:center–Galaxy:nucleus–accretion,accretiondisks
1
v
4
4 1. Introduction massive blackholesin galacticnuclei, makingit the best labo-
6 ratoryfortestingthesupermassiveblack-holeparadigmandfor
Due to its proximity compared to other galaxies, the center of
4 studyingitsuniqueastrophysicalenvironment.
our Galaxy is the best place to study the nucleus of a spiral
1. galaxyanditsstronginfluenceonitsneighborhood.Inthepast One of the peculiarities of Sgr A* is its variability at all
0 wavelengths (see a review in e.g. Genzeletal., 2010). Distinct
twodecades,theadventofNIRadaptiveopticsat10mclasstele-
3 outburstingeventsinthelightcurves,calledflares,havebeende-
scopes has made it possible to track the movementsof stars in
1 tectedondifferenttimescalesfromafewminutestoafewhours,
the innermost regions of the Galaxy. The trajectories of these
: observed in X-rays (e.g., Baganoffetal., 2001, 2003) and the
v stars,whichareperfectKeplerianellipseswithacommonfocus
NIR (e.g., Genzeletal., 2003; Ghezetal., 2004; Cle´netetal.,
i to measurement precision, have demonstrated there is a super-
X 2005). These X-ray/NIRflaresare also sometimesfollowedby
massiveblackholeatthecenteroftheGalaxy(Eckart&Genzel,
r a sub-mm flare with a time delay of 100 min to a few hours
1996,1997;Ghezetal.,1998,2003,2005;Scho¨deletal.,2002,
a (Eckartetal.,2008;Yusef-Zadehetal.,2009;Trapetal.,2011).
2003).
Flaresarestronglypolarizedatthehighestfluxlevels(for are-
Atadistanceofabout8.33±0.35kpc,thisobjecthasamass
view,seeGenzeletal.,2010).Thankstotheirdetailedpolariza-
ofabout4 × 106 M⊙ (Ghezetal., 2008;Gillessenetal., 2009)
tion analysis of some Sgr A* flares, Zamaninasabetal. (2010)
locatedatthepositionofthecompactradiosourcenamedSgrA*
supporttheideaofacompactsourcefortheemission,insteadof
(Boweretal.,2004).TheSchwarzschildradiusoftheblackhole
radiallyextendedshapes.
hasanangularsize ofabout10µasasviewedfromEarth.This
Moreover, these flares display a quasi-periodicity of about
is three times larger than the black holes in M87 (3.66 µas,
20 minutes in the NIR which has been interpreted in terms of
Bettonietal.,2003)andinM31(2.28µas,Benderetal.,2005).
the orbiting motion of a hot spot around a rotating (Kerr) su-
TheGCrepresentsthebestevidencesofarthattherearesuper-
permassive black hole (Genzeletal., 2003; Trippeetal., 2007;
Sendoffprintrequeststo:X.Haubois Meyeretal., 2006; Eckartetal., 2006a). Accelerated electrons
⋆ Basedonmulti-wavelengthobservationsobtainedattheESOVLT of Lorentz factor γ ∼ 103 − 106 are required to produce
Melipal-Yepun telescopes and at the APEX facility (run ID: 179.B- the NIR and X-ray emission via synchrotron emission and/or
0261). inverse Compton scattering (Markoffetal., 2001; Yuanetal.,
1
X.Hauboisetal.:FlaresandvariabilityfromSgrA*:fivenightsofsimultaneousmulti-wavelengthobservations.
2003,2004;Dodds-Edenetal.,2009;Eckartetal.,2006b).The
possibleoriginsofthehotelectronsincludemagneticreconnec-
tion in the accretion flow (Baganoffetal., 2001; Markoffetal.,
2001), stochastic acceleration (Liuetal., 2006), fluctuations in
theaccretionrate,oreventhetidaldisruptionofasmallinfalling
bodysuchasanasteroid(Cˇadezˇetal.,2008).
Whilemanypapersconceiveofflaresasindependentevents
thatarelimitedin time, otherteamsclaim thatthe IR emission
Fig.1.Chronogramoftheobservations
fromSgrA*ismadeupofpermanentlyfluctuatingemissionthat
couldbedescribedbyrednoisestatistics.Theproponentsofthis
picture considerthe term “flare” as improper(Doetal., 2009).
Thelightcurveswerecreatedwithaperturephotometryinthe
More recently, Dodds-Edenetal. (2011) has resolved the dis-
samewayasinDodds-Edenetal.(2011),usingtwosmallaper-
crepancyinthesetwoviewpoints,findingthattheNIRemission
tures, one centered on Sgr A*, the other centered on the close
hasadualnature,consistingoftwocomponents:thefirstalow-
contaminating star S17. At the time of these observations, Sgr
level,permanentlyfluctuatingcomponent,identifiedastheNIR
A* was confused with the star S17, adding ≈ 3.8 mJy to the
“quiescent”state,thesecondconsistingofadditional,sporadic,
Ks-bandflux(Dodds-Edenetal.,2011),butonlyacontribution
highflux“flare”events.
of ≈ 1 mJy to the L′-bandflux. We subtractedthe contribution
Revealing the enigmatic origin of the flares of Sgr A* is
due to S17 from the lightcurvesshown in Fig. 3. However,we
one of the aims of an ESO large program (LP) of observa-
notethattheremaybeanadditionalcontributionfromfaintstars
tions(ProposalID:179.B-0261,PI:Pr.R.Genzel).Thisproject
(Dodds-Edenetal., 2011), and in L′-band,perhapssome small
combinedall VLT instrumentsavailable forhigh-resolutionin-
contributionfrom the dust cloud Sgr A*-f that is very close to
fraredstudies,aswellassub-mmobservationswiththeAtacama
SgrA*(Cle´netetal.,2005).Weconcentrateonlyonlightcurves
PathfinderEXperiment(APEX),andwaspartofalargeground-
in this paper and leave the polarimetric properties for a future
based and space-based, international multi-wavelength cam-
paper.
paign. Constraining the SED of flares by photometryat a high
The infrared extinction towards the GC has recently been
samplingrateinsub-mm,MIR,andNIRcanconstraintheemis-
investigated in detail by Fritzetal. (2011), who derived an ac-
sion process responsible for the flares. A part of this LP was
curate extinction law from hydrogen lines, calibrated with a
therefore devoted to observing Sgr A* simultaneously in these
(extinction-free)radiomap.WethususedtheFritzetal.(2011)
threewavelengthranges.Throughoutthispaperweuseβforthe
spectralindexthatisdefinedthroughνL ∝ νβ.Forsynchrotron updated extinctions of AL′ = 1.09 and AKs = 2.42 for a red
ν
(comparedtoastellarsource)SgrA*-likesource.
emission this can be related to the particle index, p, of the
synchrotron-emittingelectrondistributiondefinedasn(γ)∝γ−p
throughβ=(3−p)/2.
2.2.MIR
In this paper, we analyze simultaneousobservationsof Sgr
A*atNIR,MIR,andsub-mmwavelengths,carriedoutoverfive MIR observations of Sgr A* at a wavelength of λ = 8.59 µm
consecutivenightsinJuly2007.Webeginwiththeobservations were carried out on 20, 22 and 23 July 2007, using the instru-
anddatareductioninSect.2.InSect.3,wepresentourresults. ment VISIR (Lagageetal., 2004), on UT3 at the VLT. These
Afterdiscussingtheimplicationsonthespectralenergydistribu- observations were taken in parallel with the NIR observations
tion(SED)ofourobservationsinSect.4,weconcludeinSect.5. ina“trigger”mode;i.e.,wheneverincreasedNIRemissionwas
seeninrealtimewithNACO,VISIRbeganimmediatelytoob-
serve Sgr A* to increase the likelihood that a flare would be
2. Observationsanddatareduction detectedinbothspectralbands.OnJuly22forexample,ourfirst
VISIRdatapointonSgrA*wasobtainedaround0:23UT,about
In this section we present simultaneous multi-wavelength ob- 30minafterthefirst(L′-band)peak,andatthebeginningofthe
servations carried out during July 2007 at NIR (2.18 µm and brightest,secondpeak.
3.80 µm),MIR (8.59 µm)andsub-mm(850µm). Aschematic
WeobservedinthePAH1filtercenteredon8.59µm,thefil-
logoftheobservationsispresentedFig.1.
terwith the highesttransmission availableon VISIR according
The July 2007 campaign ran for five nights from 18 July to the user manual 1. At these wavelengths, the thermal back-
2007to23July2007.OnmostnightsNACOoperatedinpolari- ground emission dominates the images. We used the classical
metricimagingmodeinK-band,withsomeshortobservationsat chopping/noddingtechniquewith choppingand noddingthrow
otherwavelengths(H,L′-band),exceptforJuly22whenmostof angles of 10′′. We chose this parameter because we wanted to
the nightwas observedin L′-band.A computercrashat APEX continuouslymonitortheGConthedetectorinordertoincrease
onJuly18stoppedthesub-mmobservationsshortat∼2:00UT. the signal-to-noiseratio andtoavoid gapsin the temporalcov-
On the night of July 21, technical problems with NACO pre- erage. The principle of this chopping/nodding technique is to
ventedusfromobtaininganydata,sothisnightisnotincluded. subtract the high-level sky background (by chopping the sec-
ondary mirror) and correct the differential instrumental back-
ground caused by the chopping (by nodding the telescope, de-
2.1.NIR
tailscanbefoundintheVISIRusermanual).
Herewedescribethe KsandL′-bandimagingobservationsob- VISIRwasusedinBURSTmode(Doucetetal.,2006).The
tainedwithNAOS-CONICAonUT4attheVLT(Lenzenetal., principleoftheBURST modeistotakeshorterexposuresthan
2003;Roussetetal.,2003).Thedatareductionwasthesameas theatmosphericcoherencetime.Themainassetofthistechnique
inDodds-Edenetal.(2009)whenwesubjectedtherawdatatoa is its spatial resolution. In principle, it allows one to reach the
skysubtractioncomputedfromjitteredobjectimages,followed
byflat-fieldingandacorrectionfordead/hotpixels. 1 http://www.eso.org/sci/facilities/paranal/instruments/visir/doc/index.html
2
X.Hauboisetal.:FlaresandvariabilityfromSgrA*:fivenightsofsimultaneousmulti-wavelengthobservations.
diffractionlimitingoodobservingconditions(0.22′′at8.59mi- performs a spiral at constant angular speed at four positions
crons, about three times the pixel scale, with an optical seeing (the raster positions), leading to a fully sampled map over the
<0.5′′),sincetheatmosphericturbulenceisfrozenattherateat full 11′ field of view of LABOCA. The telescope scanning
whichtheimagesarerecorded(anintegrationtimeof20msin speedinthismodeisbetween1′/sand2.5′/s.Eachspiraltakes
ourcase).Thisgaininangularresolutionincreasesthesensitiv- about35syieldingatotalintegrationtimeof140sandatypical
itysincewehaveasharperpointspreadfunction(PSF)thanwith rms noise level of ∼ 60mJy/beam for each map. The Galactic
theusualmode. center observations were followed by observations of G10.62,
In BURST mode, a typical data set is composed of two a standard LABOCA secondary calibrator, and G5.89 2. The
nodding cubes (nodding position A and nodding position B). atmospheric zenith opacity was determined via skydips every
One cube contains 3000 images of the two choppingpositions onetotwohours.
recorded by sequences of 100 frames. The exposure time of
one single frame is 20 milliseconds. Thus, a whole cube spans The data were reduced using the BoA software package 3.
oneminuteintotal.Forreduction,therawframeswerefirstdi- Reduction steps on the bolometer time series include temper-
videdbyaflat-fieldcalibrationimage.Usingtheclassicalchop- ature drift correction based on two “blind” bolometers (whose
ping/noddingcorrection,oneobtainsfourquadrantimageswith hornsweresealedtoblocktheskysignal),flatfielding,calibra-
thetargetappearingasapositivesourceintwoquadrantsanda tion,opacitycorrectionandcorrelatednoiseremovalonthefull
negativesource in the othertwo. However,due to variations in array as well as on groupsof bolometersrelated by the wiring
theatmosphericconditions,theimagequalityvariesfromframe andintheelectronics,flaggingofbadbolometersanddespiking.
to frame anda fractionof them are unusable.We thusselected Eachreducedscanwasthengriddedintoaspatialintensityand
better frames, based on the sharpness of the PSF as estimated weightingmap.ThesereductionsstepwereappliedtotheSgrA*
onIRS21(whichwastheonlyavailablestartodosointhefield andtheG5.89andG10.62scans.Calibrationwasachievedusing
ofviewweobserved).Altogether,85%ofthedataarecombined G10.62whichhasafluxdensityof33.4±2.0JyforLABOCA
inasinglecubetoincreasethesignal-to-noiseratio.Photometric (Siringoetal.,2009).Theabsolutecalibrationaccuracyisabout
calibrationwasperformedusingtheobservationsofseveralstan- 10%. To estimate the relative calibration error we applied the
dardstarsobtainedwithourscientificdataandthestellarfluxes calibrationcurveofG10.62toG5.89anddeterminedthedisper-
fromCohenetal.(1999).Thefinalimagescorrespondtoabout sionofthemeasuredG5.89fluxesovertheobservingperiodof
three minutes of accumulated integration time, and they have 7.5hours.Thisyieldsarelativecalibrationaccuracyof∼2%.
beenco-addedinFig.2toshowthedetectedstructuresbetter. Forthe determinationof the SgrA* lightcurve we first gener-
WeperformedaperturephotometryatthepositionofSgrA* ated a modelof the sub-mm emission in the GC region by co-
on all the images taken during the three VISIR half nights to adding all calibrated, pointing-drift-corrected GC maps. From
search for variability. The position of Sgr A* was determined thishighsignal-to-noisemapthepointsourceSgrA∗ wasfitted
using the positions of the GCIRS stars listed in Paumardetal. by a Gaussian andsubtractedfromthe co-addedmap.We then
(2006)andinOttetal.(1999).We appliedalow-frequencyfil- reducedallGCscansagainandsubtractedthemodelsignalfrom
tertotheselightcurvestodetectvariabilitymoreeasilywithtime thetimeseriesofeachbolometer.Theresultingmapsonlycon-
scales of about five minutes. However, the use of the classical tainthepointsourceSgrA∗.Thelightcurvewasconstructedby
chopping/noddingdata reduction was unsuitable for constrain- fitting a Gaussian to each map. To test the relative calibration
ing the lightcurve of Sgr A*. Indeed, the lightcurves obtained accuracywe also measured the residual peak flux at a position
are different for each quadrant and display a highly noisy pat- nearSgr A∗ located on the GC mini-spiral. The residual varia-
tern because of contamination by field sources (faint stellar or tionswerefoundtobe1.5%comparedtothemodelfluxatthis
extended diffuse objects) and atmospheric turbulence. As a re- position.TheLABOCAlightcurveisshowninFig.3.
sult we did not perform the classical nodding correction, esti-
mating instead the differentialinstrumentemission (introduced
duringthechoppingphase)frombackgroundzonesandsubtract- 3. Results
ingitfromtheSgrA*signal.Inourcase,thistechniquegivesa
3.1.High-qualitymapofGCregionat8.59µm
(sky+instrument)background-correctedfluxestimation,freeof
biasfromcontaminatingsources. The first interesting outcome of these data are the very high-
Forthe8.59µmextinctionweusedA8.59µm =1.6±0.5,from quality images of the GC area at 8.59 microns. In Fig. 2, we
Fritzetal. (2011) computedforthis specific VISIR filter and a see the MIR emission from both the photosphere and the sur-
red(comparedtostars)sourcespectrum. roundingdustshellofthebrightstarsGCIRS21andGCIRS1W.
Also prominentatMIR wavelengthsare the gaseousanddusty
structures such as the Northern and Eastern Arms of the mini-
2.3.Sub-mm
spiral. To see bothSgr A* neighborhoodand brightstellar and
The 870µm data were taken with the Large APEX bolome- gas components, we present the field of view in two different
ter camera, LABOCA (Siringoetal., 2009), located on the images. One of the most striking features in these images is
Atacama Pathfinder EXperiment (APEX) telescope at Llano the presence of elongated filaments in the Northern Arm. A
Chajnantor, Chile. LABOCA is an array of 295 composite proper motion study of these structures in L′-band (3.8 µm) is
bolometers operating in the 345GHz transmission window. Its reported in Muzˇic´etal. (2007). But even more striking is the
bandwidthis∼60GHzandtheFWHMofthePSFat870µmis presenceofastretchedemissionzoneverynearSgrA*inpro-
19′′. The atmospheric precipitable water vapor content (PWV) jection. This structure seems to begin from the Northern Arm
duringtheobservationswasbetween0.6-1.2mmcorresponding (2′′ southeastof SgrA*) and followsan asterism consistingof
toazenithopacityof0.3−0.45fortheLABOCApassband. a few aligned stars leading to the S-star region (those stars are
TheGalacticCenterwasobservedusingtheraster-spiralob- 2 Seehttp://www.apex-telescope.org/bolometer/laboca/calibration/
servingpattern(Siringoetal.,2009).Inthismodethetelescope 3 BoA:http://www.astro.uni-bonn.de/boawiki/Boa
3
X.Hauboisetal.:FlaresandvariabilityfromSgrA*:fivenightsofsimultaneousmulti-wavelengthobservations.
Fig.2.ImageoftheGCzonetakeninthePAH1filterresultingfromtheco-addedimagesof3hoursofobservationon22July2007.
Upperpanel:SgrA*surroundingscompoundofstellarsourcesandgasfilaments.Lowerpanel:close-upontheSgrA*zone.No
extinctioncorrectionwasperformedatthispoint.
detectedinNIRbands).Then,inthemostcentralpart(ataround 3.2.1. NIRvariability
0.5′′ from Sgr A*, see lower panel of Fig.2), it deviates a bit
to the west, then turns back northwest at the Sgr A* position
(Fig.2).Thislastsegmentofthestructureisalsoreportedinpre-
viouspapersasadustridgewhoseemissioncouldcontaminatea
potentialpoint-likeemissionfromSgrA*(Stolovyetal.,1996;
The NIR lightcurves (Fig. 3) display significant variability on
Scho¨deletal., 2007). This elongated structure might be due to
all five observation nights. If translated to Ks-band using a
gaseousmaterialfallingtowardsSgrA*frombothsides(south-
color of F ∝ ν−0.6 (Hornsteinetal., 2007), the L′-band ob-
eastandnorthwest),abridgeofmaterialinprojectionalongthe ν
servations would be fainter by a factor ≈0.7; the H-band ob-
lineofsightoracombinationofforeground/backgroundcompo-
servations would be a factor ≈ 1.2 brighter. For compari-
nentsthatappearasauniqueelementinprojection.Wenotethat
son, we computed some statistical quantities to describe the
theL’-bandsourceSgrA*-f(Cle´netetal.,2005)couldbelongto
variability of the lightcurves in Table 1. The strongest flare
thisfilament,butwecannotconcludeanythingaboutthenature
is seen on July 20 (Ks-band; ≈7 mJy). On July 22 an in-
ofthestructurehere.
teresting variability pattern is seen in the L′-band, with four
clear peaks separated by ∼40 min. This flare was also inves-
tigated previously by Hamausetal. (2009), who derived an
3.2.VariabilityofSgrA* average period of 45 minutes. This is more than twice as
long as the subpeak-to-subpeak timescales observed in previ-
The NIR and sub-mm lightcurves are shown in Fig. 3. In this ousflares(Genzeletal.,2003;Meyeretal.,2006;Eckartetal.,
sectionwediscussthevariabilityintheNIR(Section3.2.1),an 2006b;Trippeetal.,2007;Dodds-Edenetal.,2009).Moreover,
upperlimitfordetectionintheMIR(Section3.2.2),andthenthe wepointoutthatthefluxdropsbetweensubpeaksarealsovery
sub-mmvariabilityanditsrelationshipwiththeNIRvariability deep.AnotherflareisseenintheKs-bandjustafter5:00UTon
forthiscampaign(Section3.2.3). July23.
4
X.Hauboisetal.:FlaresandvariabilityfromSgrA*:fivenightsofsimultaneousmulti-wavelengthobservations.
10
VLT/NACO
8 H,Ks,L−prime
y] 6
mJ
[ν 4
F
2
0
APEX/LABOCA
870µm
3.5
y]
[Jν 3
F
2.5
2
0:00 2:00 4:00 6:00 0:00 2:00 4:00 6:00 0:00 2:00 4:00 6:00 0:00 2:00 4:00 6:00 0:00 2:00 4:00 6:00
UT time on 18/7/07 UT time on 19/7/07 UT time on 20/7/07 UT time on 22/7/07 UT time on 23/7/07
Fig.3. Lightcurves of Sgr A* at NIR and sub-mm wavelengths for five days of the July 2007 campaign. The green, red, and
blue datapoints of the upper panels represent the H, Ks, and L′-band NIR fluxes, respectively. Light red squares show Ks-band
observations for which max(FWHM ,FWHM ) > 15pixels (≈200 mas). The sub-mm lightcurve is shown below in black. One
x y
shouldbearinmindthattheNIRobservationswerenotallmadeinthesamefilter.
Table1.StatisticsoftheNIRlightcurves.
NEAR-INFRARED SUBMM
Night(July2007) 18 19 20 22 23 18 19 20 22 23
Median±Mediandeviation(mJy,Jy) 1.41±0.50 2.96±0.14
Median(mJy,Jy) 0.99 1.15 1.38 1.52 1.35 3.09 2.96 2.75 3.10 2.91
Mediandeviation(mJy,Jy) 0.27 0.61 0.46 0.56 0.67 0.09 0.11 0.15 0.11 0.18
Durationofthesample(min) 338 359 351 344 500 174 422 388 444 506
#peaksabove 1 1 2 2 1 0 0 0 0 0
3-σthresholdofentireobs*
#dipsbelow 0 0 0 0 0 0 0 2 0 0
3-σthresholdofentireobs*
Maximum(mJy,Jy)*avgofthe3highestpoints 3.21 3.85 6.72 5.79 5.21 3.43 3.25 2.98 3.40 3.32
Minimum(mJy,Jy)*avgofthe3lowestpoints - - - - - 2.99 2.71 2.27 2.79 2.40
Averagetimespan - - 120 45 40 - - 120 - -
Betweenpeaks/dips(min)
Notes:Forallnights,theNIRobservationweredoneinthe K-bandexceptforJuly22wheretheL’filterwasused.Wedonotconsiderthe
H-banddatahere.*Apeak/dipisdefinedasasetofmorethan5pointsinarow(3pointsforsub-mmdata)above/belowthe3-σlevel.Flux
unitsareinmJyforNIR,Jyforsub-mm.
3.2.2. MIRupperlimit Wedeterminedanupperlimittothefluxbyinjectinga3×3
pixelsGaussian-shapedsourceofknownintensityintoourMIR
images. For each VISIR observation night we subtracted col-
ThedifficultyofdetectingSgrA*intheMIR(comparedtothe lapsedimagestakenduringintervalsoflowNIRemissionfrom
NIR) comes from to the lower spatial resolution and the dom- collapsedimage fromthe flaringstate intervals(with the artifi-
inating background. Despite the trigger mode used to observe ciallysourceinjected).Thedetectionlimitisthenderivedwhen
withVISIRonlywhenNIRflaresweredetected,wedidnotde- thisartificialpointsourceisdetectedata3-σsignificance.
tect any point-like source at the position of SgrA* at 8.59 µm
inourobservations,norwasthereanysignificantcorrelationbe-
tweenthe NIR andMIR lightcurvesobtainedviaaperturepho- Becauseofthehighqualityofourobservations,weareable
tometry.Uptonow,SgrA*hasneverbeendetectedinMIRand toderiveanespeciallytightupperlimitonatransientsourceat
onlyupperlimitsexist(Telescoetal.,1995;Stolovyetal.,1996; the position of Sgr A* of 22.4 mJy (dereddened, for July 22),
Scho¨deletal.,2007,2011).Thelowestupperlimitat8.59µmto simultaneoustotheL′-bandflare.Thisisthelowestupperlimit
dateintheliteraturegivesameanfluxestimationoftheSgrA* everderivedforaflareat8.59µm.Weemphasizeherethat,com-
emission of 45+/-13 mJy (Scho¨deletal., 2011). Once dered- pared to (Scho¨deletal., 2011) who also used this dataset, the
denedwiththeupdated8.59µmextinctionofA =1.6±0.5 upperlimitreportedhereisduetothespecificityofourmethod,
8.59µm
(Fritzetal., 2011) computed for the VISIR PAH1 filter, this whichconsistsinestimatingthelowestdetectableMIRvariabil-
valuebecomes31+/-9mJyandthus58mJyatthe3-sigmalevel. ityduringanNIRflare.Thisresultthusrepresentsanupperlimit
5
X.Hauboisetal.:FlaresandvariabilityfromSgrA*:fivenightsofsimultaneousmulti-wavelengthobservations.
ontheMIRfluxrelativelytotheNIRfluxduringaflarewhereas up to maximumγ factors of at least γ ≧ 200, and do not
cutoff
theScho¨deletal.oneisanabsoluteMIRupperlimit. allowthe NIR flarestoarise froma purelythermaldistribution
CombinedwiththeNIRmeanfluxinthesametimeinterval, ofelectronspeakinginthesub-mm(θ ∼10).
e
we could also put a lower limit on the spectral index between Moreimportant,mostmeasurementsoftheNIRstellarslope
MIR and the NIR bands. Ifβ is defined through νLν ∼ νβ, the between 3.8µm and 1.65µm have been independent of photo-
bestconstraintisobtainedforthenightofJuly23withalower metric calibration and extinction, since the spectral index was
limitofβ&−0.5(Table2). measured only relative to stellar colors of the close star S2.
This constraintis notas strongas (forexample)derivedby Both Hornsteinetal.(2007) andGillessenetal. (2006), forex-
Dodds-Edenetal.(2009),whoderivedalowerlimitonthespec- ample, foundpositiveslopes of ≈ 0.4±0.2 forhigh fluxesus-
tral index of β > 0.0 from simultaneous NACO (3.8µm) and ingan‘off-state’backgroundsubtractionmethod,whichiscon-
VISIR (11.88µm) observations. The weaker constraint on the sistent with the lower limit on the slope reported here, as well
spectralindexfoundhere,despitethehighsensitivityoftheMIR as thatof Dodds-Edenetal. (2009). At fainterfluxes, however,
upper limit in this paper, is partly due to the relative faintness Eisenhaueretal. (2005) and Gillessenetal. (2006) find a red-
of the flares observed during this observation campaign com- dening of the spectral index, up to β ≈ −3±1 (dependingon
pared to that of Dodds-Edenetal. (2009) and partly due to the the backgroundsubtractionmethod)fordim emission of about
updated extinction law. In fact, the updated extinction also af- 2-3mJy.Ourresultsare,however,inconsistentwithresultswith
fects the lowerlimit of Dodds-Edenetal. (2009), such that the suchsteepspectralindicesatlowfluxes4.Forthethreemethods
constraintshouldbeupdatedtoβ >−0.3.Still,bothlowerlimit of background subtraction presented in Gillessenetal. (2006)
measurementsleaveverylittleroomforanegativeνLνMIR-NIR our results only agree with the “off-state” backgroundsubtrac-
spectralindex. tion method for the dim state, perhaps implying that the other
Acutoffathighenergyintheflarespectralenergydistribu- methodsunderestimatethe spectralindex.However,we cannot
tioncouldbeproducediftheaccelerationprocessisinefficientat compare the results at low fluxes so easily because our flaring
acceleratingelectronstotheseenergies.Iftheaccelerationpro- intervalsincludeamixofbothbrightandfaintNIRemission.
cessshutsoffearly,thenitcanalsobeduetoelectronlossesfrom
synchrotroncooling.Ourmeasurementsclearlyruleoutthatthe
three flares arise from the high-frequency emission of a spec- 3.2.3. Submillimeter&correlationwithNIR
trumfromanelectrondistributionwithanexponentialcutoffat
A striking aspect of the lightcurves presented in Fig.3 is the
sub-mm-emitting energies (i.e. the thermal electrons known to
markedanticorrelationseenonthenightofJuly20,wheretwo
producethesub-mmemission).Whileitishardlydisputedthat
peaksin the NIR emission are coincidentwith the two deepest
theNIR emission(λ < 4µm)fromSgrA*requiresnonthermal
dipsinthesub-mmemission.Inparticularitisnoteworthythat
electrons,itisworthillustratingthepreciserestrictionsourdata
thebrightestNIRpeakofthefivenightsofobservationiscoin-
place on the presence of an exponential cutoff in the electron
cident with the lowest sub-mm flux. Similar behavior (an NIR
distribution. Assuming such an exponential cutoff in the elec-
peakaccompanyingasub-mmdip)isseenonJuly19,aswellas
tronspectrumatanenergyof γ ,withparticleindexbelow
cutoff onthenightofJuly23.
thecutoffof p ,
0 Therearehintsthat,a peakinthe NIRemissionissimulta-
γ neouswitha peakin thesub-mmemissionparticularlyonJuly
n(γ)∼γ−p0 ×exp(− ) (1) 18.Totestwhethertheapparentanticorrelationofsub-mmand
γ
cutoff
NIRemissioninthisdatasetaresignificant,webinnedtheNIR
the particle index, p = −dln(n(γ)) will then be p = p + γ , fluxtothesamplingofthesub-mmlightcurveandcomparedthe
dlnγ 0 γcutoff bins fornon-zerosub-mmand NIR fluxes (Fig. 4). Computing
leadingtoaspectralindexβ=(3−p)/2=1/2×(3−p − γ ).
0 γcutoff the usual(Bravais-Pearson)correlationcoefficientof these two
The energy of NIR-emitting electrons is variables, an anticorrelation with a coefficient of r ≈ −0.5 is
(Rybicki&Lightman,1979): significantforthe Ks-banddataset, witha rejectionprobability
of 6.0× 10−6. The anticorrelation is not significant for the L-
16mc banddataset. Theshape of the correlationplotshown in Fig. 4
γ = v × . (2)
NIR s NIR 3qB is mostly caused by the anticorrelation of the July 20 flare. If
we do not include these data, the correlation is no longer sig-
Thusourmeasurementofβ > −0.5forthenightofthe23rd nificantandraises the possibility thatJuly 20 lightcurvesshow
NIR
implies, anextraordinarybehavior,associatedwithaflareeventand not
characteristicofthequiescentemission.
1 γ
(3−p − NIR )>−0.5, (3) AsimilarrelationshipbetweenNIR/X-rayandlongerwave-
2 0 γ
cutoff length emission was noted by Dodds-Edenetal. (2010) in ob-
servationsfromApril2007,whereadipinmillimeteremission
suchthat,
wasobservedtoaccompanyanNIR/X-rayflare.Inthatcasethe
γ =θ &200( B)−1/2 (4) brightestNIR/X-rayflux of the campaign(which was indeed a
cutoff e 30 very bright flare, brighter than any in our July campaign) was
followed by a ∼200 min dip in the millimeter emission. The
withθ = kT/mc2,forathermaldistribution(p=2andγ =
E cutoff millimeter flux during the dip was the lowest observed during
θ ),or
e
B 4 AlthoughourobservedflaresofJuly20andJuly22hadpeakfluxes
γ &1200( )−1/2 (5)
cutoff comparable with the flare of Gillessenetal. (2006), the interval over
30
whichthespectralindexwasmeasuredhadanaverageNIRfluxofonly
for a more “bottom-heavy” energy distribution below γcutoff 0.1-0.2thefluxofS2(andwouldthuscorrespondtothe“dimstate”of
(p=3). Thus it is clear that our data require electron energies Gillessenetal.,2006).
6
X.Hauboisetal.:FlaresandvariabilityfromSgrA*:fivenightsofsimultaneousmulti-wavelengthobservations.
Table2.UpperlimitsonthedetectionofasyntheticMIRflare,aswellasthecorrespondinglimitsontheMIR-NIRspectralslope
andparticleindex.
Night(July2007) 20 22 23
Onstatetimeinterval/s[UT] 23:07.18to00:13:30, 0:23:12to0:39:48, 5:34:06to5:49:0,
&00:50:54to2:44:54 &1:05:06to1:24:48, &6:04:30to6:19:30
&1:57:00to2:00:00
Offstatetimeinterval/s[UT] 00:17:30to00:35.06 0:41:06to1:03:48, 5:34:06to5:49:06,
&1:26:12to1:55:36, &6:04:30to6:19:30
&2:01:12to2:39:12
Upperlimitfortransientemission 24.2 22.4 31.2
(dereddenedwithA =1.6±0.5)
8.59µm
AverageNIRflux(wavelength) 2.0(Ks) 3.4(L′) 4.1(Ks)
onstatetimeintervals
LowerlimitontheνL spectralindex β>-0.80 β>-1.3 β>-0.46
ν
(νL ∝νβ)
ν
Upperlimitontheparticleindex,p p<4.6 p<5.6 p<4.0
(N(γ)∝γ−p)
4. SEDmodelsforanNIR/X-rayflarewithasub-mm
dip
3.4 VLBI measurements show that the size of Sgr A* decreases
from radio to the sub-mm (e.g. Boweretal., 2004, 2006;
3.2 Doelemanetal., 2008). The sub-mm emission is universally
mJy] 3 pnreormduocsetdreingiomnosdoeflsthbey ahcoctreetlieocntroflnoswo(fclθoese∼to1t0heinlatshtesitna--
ux [ ble orbit), where the electron density is typically ∼ 107cm−3
m fl2.8 andmagneticfieldstrengthisB∼30G(e.g.Markoffetal.,2001;
m Yuanetal., 2003). In the GRMHD simulations of Dexteretal.
b2.6
u (2010) and Mos´cibrodzkaetal. (2009) the mm/sub-mm emis-
s
2.4 sionregionissituatednearthemidplaneofthediskintheinner
few Schwarzschildradii of the accretion flow. Thoughit is not
2.2 at all clear where the NIR flares themselves originate, a dip in
mm/sub-mm emission simultaneous to an NIR flare implies a
2 causalconnectionbetweenthetwo.Inwhatfollows,wediscuss
0 1 2 3 4 5 6 7
a number of possibilities for the relationship between the NIR
NIR flux [mJy]
andsub-mmemissionregion.Weconsiderthatthesub-mmdip
Fig.4.ComparisonofsimultaneousNIRandsub-mmfluxesfor mightoccurdueto:
the July 2007campaign.The graphshowsthe sub-mmvs. Ks-
band(redsquares)or L-band(bluecrosses)NIR flux.TheJuly – ashiftin frequencyofthesub-mmbump,withthesub-mm
20nightdataaremarkedasfilled-inredsquares emission and NIR emission arising from low and high fre-
.TheNIRfluxeswerebinnedtothesamplingofthesub-mm quencysidesofthesub-mmpeak,respectively;
lightcurve(5.6min).TheKs-bandscatterplotsshowsasignificant – adecreaseinthetotalnumberofsub-mmemittingelectrons,
anticorrelationofr≈−0.5,withp-value p=6.0×10−6. throughe.g.heating/acceleration(toproducetheNIR flare)
accompaniedperhapsbycooling/escapeofsomefractionof
theelectrons;
that entire ∼12 day campaign. The explanation put forward in – adecreaseinthesub-mm-emittingelectronsemissivityviaa
Dodds-Edenetal. (2010) was thata dip in millimeteremission decreaseinmagneticfield(Dodds-Edenetal.,2010);
mayoccurduetothelossinemissivityofmm-emittingelectrons – occultationof the quiescentcomponentbythe flaring com-
thatwouldoccurinamagneticreconnectionevent,inwhichsig- ponent(Yusef-Zadehetal.,2010).
nificant magnetic energy is lost in the inner regions of the ac-
cretion flow. Eckartetal. (2008) report a bright NIR flare and We donotconsiderthe expandingblobmodelhere,forthe
a sub-mm signal in which the lowest sub-mm flux is also co- simple reasonthat it does notpredictthatthe highestNIR flux
incident with the highest NIR flux (between 5h and 6h UT). shouldbecoincidentwiththelowestsub-mmflux.Furthermore,
Yusef-Zadehetal.(2010)haverecentlynotedananticorrelation expanding blob models, which are presented elsewhere in the
in NIR/X-ray emission with sub-mm/mm emission, as well in literature, have the following problems: (i) some observations
previouslypublisheddata,extendingthenumberofobservedex- appeartorequirearedderspectralindexintheNIRthanallowed
amplestosix.Thesameexampleswereinmostcasesoriginally byourlowerlimitofβ&−0.5(seee.g.modelsAandBofTable
interpreted as delayed sub-mm flares. This work suggested the 4 in Eckartetal., 2008); the spectral index is given there as α
anticorrelationcouldbeduetoaneclipseofthesteady-stateac- whereS ∝ ν−α,soα = 1−β,(ii)Moreover,theyrequire self-
ν
cretionflowbytheflaringregion. absorbed flare emission in the sub-mm, which can only occur
In the following section, we present different modeling at- for the electron densities and/or magnetic fields that are much
tempts to explain this interesting behavior observed in Sgr A* higherthan the typical values in the accretion flow aroundSgr
emission. A*(Dodds-Edenetal.,2010).
7
X.Hauboisetal.:FlaresandvariabilityfromSgrA*:fivenightsofsimultaneousmulti-wavelengthobservations.
4.2.Lossofelectrons
B or Mdot
2
flare
Another possibility for a decrease in the sub-mm emission is
)
]n thataportionofthesub-mm-electronswereacceleratedtoNIR-
u 1
Ls emitting energies and/orwere lost in an outflow. To determine
[ν howmanyelectronsweneedfortheNIRflare,comparedtohow
ν L 0 many we need to lose for the sub-mm dip, we create toy syn-
( chrotronmodelstomodelboththeNIRflareemissionaswellas
0
g1 jet model, fortheamountof“missing”sub-mmemission.Forthedetailsof
o
l −1 steady state themodelsseeDodds-Edenetal.(2010).Wemodelthemissing
(Falcke+2000) emissionwithathermalelectronpopulationofelectrontemper-
ature θ = 10, magnetic field strength B = 30G, and electron
e
−2
density n in a region of size R. We then model the flare with
10 12 14 e
log (ν [Hz]) the same parameters, but with an accelerated electron distribu-
10 tion, a powerlaw N(γ) ∼ γ−p of γ = 10 and p = 2.2 (since
min
Fig.5. Flare model for Sgr A* from Falcke&Markoff (2000) thenumbersofelectronsdecreasesorapidlywithγ,thevalueof
isplottedinblueandcomparedtothedatafromJuly20(purple γcutoff doesnothaveanyeffectontheelectrondensity,aslong
squarefortheNIRaveragefluxduringtheflaretimeintervaland asitissignificantlyhigherthanγminandhighenoughtoproduce
purplearrowforthe MIR upperlimit;note thatthe MIR upper NIR emission). This choice of particle index both matches the
limitfromtheJuly22waslower).Theredstarspresentthepeak publishedspectralindicesforbrightemission of β = 0.4±0.2
flux of the July 20 flare, together with the simultaneous sub- (Hornsteinetal.,2007;Gillessenetal.,2006),satisfiesourMIR
mm flux. Blue circles show the median fluxes in a non-flaring upper limits, and additionally ensures that the flare itself does
state. The radio-sub-mmSED is shownin black(with squares: notproducetoomuchsub-mmemission(thatwouldresultin a
the compilation of Genzel 2010, diamonds: from Shcherbakov simultaneousflareratherthanasimultaneousdip).
2011. The typical radio-sub-mm variability amplitudes and a
compilation of MIR upper limits are shown in gray and taken
However, we find that the number of electrons required to
from Melia&Falcke (2001). A flare due to a 30% increase in
produce the “missing sub-mm emission” in these models are
B in the jet model is also plotted as a red line. An increase in
greaterthanthenumberrequiredtoproducetheflare,ifthemag-
densityresultingfromatemporaryincreaseintheaccretionrate,
netic field is the same beforeand after acceleration.Only 30%
M˙,hasthesameresult(Markoffetal.,2001).
ofthesesub-mm-emittingelectronsarerequiredtoproduce the
NIRflareundertheconservativeassumptionγ =θ .Thisim-
min E
pliesthatthemissingsub-mmemissioncannotbeexplainedby
theaccelerationofsub-mm-emittingelectronsalone:somefrac-
4.1.Thesub-mmbump
tionmustbecompletelylosttothesystemintheprocess.
A natural origin for an anticorrelation between NIR and sub-
mmfluxisthatbothhighandlowfrequencypartsarisefromthe Given our assumption that electrons are accelerated out of
samecomponent:thesub-mmbump.Onecouldimaginethatif a thermal population, this result is surprisingly robust to the
thepeakofthesub-mmbumpweretovaryinfrequency,e.g.due choice of parameters: i.e. θ , B, for the unaccelerated popula-
E
tounderlyingvariationsindensity(throughtheaccretionrateM˙ tionofelectronsandγ , pfortheacceleratedpopulation.This
min
orthemagneticturbulentasshowninDexteretal.,2010),while is because we are essentially only looking at a relative change
essentially preserving the peak sub-mm bump flux, one would inthe electrondistribution.Boththe missingsub-mmemission
observeanincreaseintheNIRfluxasthesub-mmfluxdecreases andtheflareemission,forexample,aresubjecttothesameBby
(andviceversa). assumption,sochangingBessentiallyonlyrequiresarescaling
Suchasetupis,howeverdifficulttorealizeinpractice.While of the density (which is, however, the same for both unaccel-
an increase in density or magnetic field will increase the fre- erated and accelerated distributions, so a similar fraction must
quencyatwhichthefluxbecomesself-absorbed,italsohasthe still escape). The fraction of escaping electrons is more sensi-
effect of increasing the flux at both sub-mm and NIR frequen- tivetoγ oftheacceleratedpopulation.Alowerγ however
min min
cies.ThisisillustratedinFig.5,whichshowsthequiescentrel- isunrealisticundertheassumptionofelectronacceleration:our
ativistic jet model of Falcke&Markoff (2000) with a 30% in- conditionof γ = θ is already quite conservativesince only
min E
creaseinthemagneticfieldandanincreaseindensityproduced ≈7%ofelectronsactuallyhaveenergieslowerthan θ in arel-
E
byanincreasein M˙ (Markoffetal.,2001).Thismodelwasnot ativistic Maxwellian distribution (the typical energy is, in fact,
createdtofitourflare,butisshownmoreasademonstrationof γ = 2θ ); in otherwords, electronswith γ < θ mightas well
E E
thegeneralbehavioruponincreasing Born inthesteady-state be treated as escaped for the purposes of this paper. A higher
e
models.Therearetwoimportantaspectsthatareinconflictwith γ > θ only decreases the numberof electrons required for
min E
our observations and that disfavor this model: (i) the sub-mm theflare(sincethedensitydependssensitivelyonγ ),thereby
min
flux,asfortheotherfrequencies,increaseswiththeflare,there increasingthefractionthatmustescape.Since it is quitelikely
isnosub-mmdip;(ii)anexponentialcutoffintheflareemission thatγ >θ (Dingetal.,2010),wemightexpectamuchmore
min E
intheNIRisoutofthequestionbecauseoftheMIRupperlimit: significantfractionofelectronstoescape.Theseelectronscould
nonthermalparticleswithatthemost p= 4.6arerequired.This becarriedawayinaveryfastoutflow,forexample,duetotheir
reinforces that acceleration of nonthermal electrons is needed smallnumberproducingverylittleemissionastheyrapidly ex-
toproduceanNIRflare(Markoffetal.,2001;Yuanetal.,2003; pandandcool(adiabaticexpansionDodds-Edenetal.,2010)or
Dodds-Edenetal.,2009). maybeaccretedontothesupermassiveblackhole.
8
X.Hauboisetal.:FlaresandvariabilityfromSgrA*:fivenightsofsimultaneousmulti-wavelengthobservations.
4.3.Decreaseinmagneticfield
2.5
InDodds-Edenetal.(2010),itwassuggestedthatadecreasein
magneticfield(forinstance,thataccompaniesamagneticrecon- 2 flare
nectioneventorduetomagneticturbulenceDexteretal.,2010)
1.5
couldcauseadecreaseinthelongerwavelengthemission.This
could be more efficient at producing a dip in flux than loss of ])n 1
u
electronssincethesynchrotronpoweremittedbyanelectronis Ls
proportionalto B2, while it is only linearly proportionalto the [ν 0.5
L
numberofelectrons. ν 0
(0
Inourtoymodel,wenowholdthetotalnumberofelectrons g1
o −0.5
constant(noescape)betweenthe thermal(θ ∼ 10)andaccel- l
E "missing" submm
eratedpower-lawmodels(γmin = 10, p = 2.2)describedin the −1 flux
last section. The accelerated power-law model, with the same
−1.5
number of electrons as the thermal model and the same mag-
netic field strength, overproducesthe NIR emission. Instead of
−2
decreasingthenumberofelectrons,wefindthatifwedecrease 9 10 11 log12(ν [Hz1]3) 14 15
themagneticfieldfrom B = 30Gto B = 14G,theobservations 10
arewell-matched.ThisflaremodelisshowninFig.6compared
Fig.6. A model for an NIR flare with an accompanying sub-
andcombinedwiththeYuanetal.(2003)modelwhosethermal
mm dip compared to the data from July 20 (see caption of
componentwas scaled down to match the SED in the sub-mm
Fig.5). Compared to the sub-mm-radio SED shown in black
partof the section (in particularourblue “no flare” data point) square/diamonds,itcanbeseenthatthefluxofthesub-mmdip
5. As in the case of electron loss, γ = θ is quite conserva-
min E (redstar)islowerthanthetypicalsub-mmflux.Thedashedlines
tive; if the true γ is higher we would have a higher density
min showatoymodelfortheflare,inred,aswellasforthe“missing”
of high-energyaccelerated electrons, requiring an even greater
sub-mm flux, in blue. The blue solid line shows the quiescent
decreaseinthemagneticfieldtopreventoverproductionofNIR
modelofYuanetal.(2003),andtheredsolidlinerepresentsthe
emission.However,themagneticfieldinarealisticmagneticre-
samemodelbutwiththe”missing”sub-mmfluxsubtractedand
connection event probably also decreases over a larger region
the flare emission added. This particular figure shows the de-
thantheaccelerationsiteitself(Dodds-Edenetal.,2010),which
creasingmagneticfield case:to preventoverproductionofsyn-
wouldproducealargersub-mmdip,whileallowingthefreedom
chrotronemissionfromtheacceleratedpopulationthemagnetic
ofamoremoderatedecreasein B. fielddecreasesfromB=30GtoB=14G.Thespectrumforthe
caseofthelossofelectronsisverysimilar.
4.4.Eclipse
In Yusef-Zadehetal. (2010) it was proposedthat a decrease in
sub-mmemissioncouldoccurviaaneclipseofthesteady-state
emission by the temporary flaring blob. In this section we ex- Moreover, the corresponding flare size would be so small
plore the possibility that occultationis responsiblefor the sub- that it would imply a very high density of nonthermal parti-
mm dips observed in this paper. In this model it is considered cles. Itispossiblethatrelaxingthe assumptionofequipartition
thatthetworegionsareseparate:i.e.acceleratedflareelectrons intheeclipsemodelofYusef-Zadehetal.(2010)mightchange
donotcomefrom(orproduceverylittledisturbanceto)thequi- theseconclusions.Anotherpossibilityis thattheelectronspec-
escentpopulation,and the flaring regionis in frontof, notem- tralindexmightbesteeperthantheassumed p=2ofthemodel
beddedin,thequiescentregioninthelineofsight. (Yusef-Zadehetal.,2010).Althoughasteeperelectronspectrum
can increase the optical depth at low frequencies (and thereby
Figure7showsa plotofthe equationsof Yusef-Zadehetal.
theabsorptionofquiescentemission),italsoincreasesthesub-
(2010)forvariationinsub-mmfluxvs.sizeoftheflaringregion
(R ), fordifferentquiescentregionsizes (R ). Anythinglarger mm emission fromthe flare itself significantly(onthe orderof
F Q
thanR &1R encountersverylittleoccultation.Evidently,both Jy; Dodds-Edenetal.,2010),whichislikelytooverwhelmany
Q S
increasedabsorptionofthequiescentsub-mmemission.
the 850µm and NIR emission regions would have to be very
small (R < 0.6R and R = 0.5-1.0 R ) to produce a dip as Some radio (43 GHz) dips have been reported as well dur-
Q S F Q
largeas0.5Jyinthesub-mmemissionviaoccultation. inganNIRflare(Yusef-Zadehetal.,2010).Wenotethat,forthe
Aquiescentsizeof0.5R ismuchsmallerthanwouldbeex- samemodelingparametersweused,nosignificantdipsinthera-
S
pected. Using the caveat from Marscher (1983) (radius = 0.9* dioareexpectedforanyRF,givena43GHz(λ=7mm)emitting
FWHM) on the FWHM size 3.7RS (37 microarcseconds) at regionsize of RQ = 17RS (Boweretal., 2006). Only a smaller
1.3mm (Doelemanetal., 2008) and extrapolating with the ra- (43 GHz) quiescent region size can produce observable radio
dius∝ λ1.3 wavelengthdependenceBoweretal.(2006),weob- dips due to occultation,for examplefor RQ = 4RS (fourtimes
tain a radius at 870µm of 2.0 R . However, extrapolating the smallerthanobserved)radiodipsofupto∼20%oftheemission
S
size downwardsfrom 1.3 mm to 850 µm could be incorrectas couldbeproducedforflareregionsizesof1−2RS.Yusef-Zadeh
the accretion flow might already become optically thin around etal.arguethata4×smallerquiescentregionsizewasnotneces-
1.3mm.Inthiscasethesizewouldnolongerchange. sarilyinconflictwiththesizeradiomeasurementsasthesource
mightbemuchsmallerinsemi-minoraxis;however,thisinturn
5 WenotethatthenonthermalcomponentofthemodelofYuanetal. imposesincreasinglydifficultconstraintsonboththe geometri-
(2003),with p = 3.5liesclosetothenon-flaring Ks-bandfluxofSgr calshapeoftheflaringregionanditsalignmentwithrespect to
A*,whichisalsosimilartothelong-termmedianofthecontinuously thequiescentregiontoretainahighdegreeofoccultation(given
variableNIRfluxDodds-Edenetal.(2011). thatacoveringfraction(RF/RQ)2ofatleast0.52isrequired).
9
X.Hauboisetal.:FlaresandvariabilityfromSgrA*:fivenightsofsimultaneousmulti-wavelengthobservations.
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Wealsoestimatedthelowestupperlimiteverderivedforaflare
82,3121
at 8.59µm (22.4 mJy with A = 1.6 ± 0.5) and derived
8.59µm Ghez,A.M.,etal.2008,ApJ,689,1044
constraints on the spectral slopes between NIR and MIR. The Ghez, A. M., Salim, S., Hornstein, S. D., Tanner, A., Lu, J. R., Morris, M.,
analysis of the correlation between sub-mm and NIR variabil- Becklin,E.E.,&Ducheˆne,G.2005,ApJ,620,744
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Ghez,A.M.,etal.2003,ApJ,586,L127
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explanationsfor this observational fact. We disfavor variations Gillessen,S.,etal.2006,ApJ,640,L163
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tronloss(>70%forγ =θ ),adecreaseinthemagneticfield Lenzen,R.,etal.2003,Proc.SPIE,4841,944
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Acknowledgements. Thisworkwassupported byagrantfromRe´gionIle-de- Gezari,D.Y.2011,arXiv:1106.5690
France.WealsoreceivedthesupportofPHASE,thehighangularresolutionpart- Scho¨del,R.,Eckart,A.,Muzˇic´,K.,Meyer,L.,Viehmann,T.,&Bower,G.C.
nershipbetweentheONERA,ObservatoiredeParis,CNRS,andParisDiderot 2007,A&A,462,L1
University. Scho¨del,R.,Ott,T.,Genzel,R.,Eckart,A.,Mouawad,N.,&Alexander,T.2003,
ApJ,596,1015
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