Model Atmospheres for Irradiated Giant Stars: Implications for the Galactic Center

0.29 MB·English

by  Raul Jimenez

Draftversion February5,2008
PreprinttypesetusingLATEXstyleemulateapjv.6/22/04
MODEL ATMOSPHERES FOR IRRADIATED GIANT STARS: IMPLICATIONS FOR THE GALACTIC
CENTER
Raul Jimenez,1 Juliana P. da Silva,2,4 S. Peng Oh,3 Uffe G. Jørgensen,4 David Merritt5
Draft versionFebruary 5, 2008
ABSTRACT
Irradiation of a stellar atmosphere by an external source (e.g. an AGN) changes its structure
andthereforeitsspectrum. Usingastate-of-the-artstellaratmospherecode,wecalculatethe infrared
spectraofsuchirradiatedandtransformedstars. Weshowthattheoriginalspectrumofthestar,which
6
isdominatedbymolecularbands,changesdramaticallywhenirradiatedevenbyalow-luminosityAGN
0 (L = 1033 erg s−1), becoming dominated by atomic lines in absorption. We study the changes in
0 X
the spectrum of low-mass carbon- and oxygen-rich giant stars as they are irradiated by a modest
2
AGN, similar to the one at the Galactic center (GC). The resulting spectra are similar to those of

n the faintest S-cluster stars observedin the GC. The spectrum of a star irradiatedby a much brighter
a
AGN, like that powered by a tidally disrupted star, is very different from that of any star currently
J
observedneartheGC.Forthefirsttimewehavediscoveredthatthestructureoftheatmosphereofan
7 irradiatedgiant changes dramatically and induces a double inversionlayer. We show that irradiation
2
at the current level can explain the observed trend of CO band intensities decreasing as a function
of increasing proximity to Sg A∗. This may indicate that (contrary to previous claims) there is no
2
paucity of old giants in the GC, which coexist simultaneously with young massive stars.
v
7 Subject headings: stars: winds - Galaxy: centre
2
5
1 1. INTRODUCTION andmolecularlinesthatdominatetheinfrared(IR)spec-
0 The fact that UV radiation and X-rays can al- trum. Our computational approach is general, but we
6 focushereonthespectrumofastarthatisirradiatedby
ter the atmospheres of stars has been recognized for
0 a source at the Galactic center (GC). We are motivated
more than thirty years (Davidson & Ostriker 1973;
/ bytherecentdiscovery(Revnivtsev et al.2004)thatthe
h Basko & Sunyaev 1973; Arons 1973; Basko et al. 1974;
GC may have been a low-luminosity AGN (L ≈ 1039
p Fabian1979). Irradiationbyasourcelikeanactivegalac-
- tic nucleus (AGN) will produce an increase in the atmo- erg s−1) as recently as a couple of hundred years ago.
o In addition, recent estimates of the rate of stellar tidal
spheric temperature and in the mass loss rate (Edwards
r disruptions by the GC supermassive black hole (SBH)
t 1980; Voit & Shull 1988; Chiu & Draine 1998). Even a
s (Wang & Merritt 2004; Merritt & Szell 2005) suggest a
modest level of irradiation from a low-luminosity AGN,
a rateoforderoneeventper104yrorhigherforsolar-mass
: liketheonecurrentlyatthecenteroftheMilkyWay,can
v stars. Tidal disruption of a star by a SBH is expected
be sufficient to destroy molecules formed in the atmo-
i to produce an extremely luminous event, L ≈ 1044 erg
X sphere of cool giant stars, thus transforming their spec-
s−1, with a duration of weeks or months (e.g. Komossa
trum without inducing significant mass loss. Recently,
r (2002)).
a Barman et al. (2004) carried out detailed computations
The GC SBH was recently found to be surrounded by
of the atmospheric structure of an M dwarf irradiated
a cluster of apparently young stars. For one of these
by a hot stellar companion (a pre-cataclysmic variable).
stars, S0-2, an IR spectrum showed no CO absorption,
However, up to now, and despite recent advances in the
andpossibleHeI(2.1µm)absorption(Ghez et al.2003).
calculation of molecular opacities (Jørgensen 2005) and
The latter indicates that the star cannot have an effec-
instellarmodelingalgorithms,nodetailedcomputations
tivetemperaturelessthanabout15,000K(Hanson et al.
of the atmosphere of a cool giant star that is irradiated
1996). The orbit of S0-2 has a pericenter distance of
by an external source have been performed.
∼100AUandanapocenterdistance of∼1000AU.The
Inthispaper,forthefirsttime,wecomputethestellar
presence of the HeI line and the absence of CO point
spectrum and atmospheric structure of a cool (∼ 4000
to S0-2 being young, with spectral class in the domain
K)giant(both carbonandoxygenrich) starin the pres-
O and B. The case for hot stars so close to the GC
ence of an AGN. Our stellar atmosphere code includes a
has been further reinforced by Eisenhauer et al. (2005)
complete frequency dependent description of the atomic
whoobtainedhighS/Nspectraof17S-clusterstars. For
1DepartmentofPhysicsandAstronomy,UniversityofPennsyl- the brightest stars in this sample, spectra clearly show
vania,Philadelphia,PA19104, USA;[email protected] the presence of the HeI line at 2.1127µm. However for
2DepartmentofPhysics,UniversidadeFederaldeMinasGerais, stars with K > 15 the line is not present. Hence, the
Brasil;[email protected]
spectral properties of the S-cluster stars are not uni-
3 Department of Physics, University of California, Santa Bar-
bara,CA93106,USA;[email protected] form. If these stars are actually young (a few Myr),
4 Niels Bohr Institute, Copenhagen, DK-2100, Denmark; uf- their formation so close to GC SBH is a serious theo-
[email protected] retical challenge (Phinney 1989). One possibility is that
5 Department of Physics, Rochester Institute of Technology,
these stars are not young but old, and that their at-
Rochester,NY,USA;[email protected]
2
mospheres have been modified by some physical mech- However, in order to compare with the observa-
anism: stellar collisions, tidal stripping or external ra- tions of Eisenhauer et al. (2005), we are interested in
diation (e.g. Genzel et al. (2003); Alexander & Morris computing detailed spectra of irradiated stars. For
(2003); Hansen & Milosavljevi´c (2003), see also the re- this purpose we have used a stellar atmosphere code
view by Alexander (2005) and references therein). Jorgensenet al. (1992), which is based on the MARCS
In this work, we compute the detailed spectrum of gi- code(Gustafsson et al.1975). Themodelsarecomputed
ant stars irradiated by an AGN in the luminosity range inhydrostaticequilibrium,withradiativeandconvective
1033 − 1044 erg s−1 integrated over the range 2 − 200 energy transport included. Plane parallel and spherical
keV(hereafter wedenote the luminosity inthis rangeby geometry are considered where appropriate. The radia-
L . In particular, we show how these old giants are af- tivetransferincludesneutralandonetimeionizedatomic
X
fected by low-luminosity AGN (L ≈ 1039erg s−1) like lines from the VALD data base and molecular opacities
X
the one that mayhavebeen presentatthe GC inthe re- fromCO,C2,CN,CS,HCN,C2H2,C3,SiO,TiO,H2O,
centpast,andalsobythehighluminosity(L ≈1044erg and several diatomic hydrates (Jørgensen (2003, 2005)
X
s−1) that is believed to accompany the tidal disruption and references therein). All opacities are treated by the
of a star by the SBH. We find that the spectrum of an opacity sampling technique (Helling & Jorgensen 1998).
irradiated old giant star is similar to that of the faintest Theatmosphericstructureandthespectraarecomputed
S-cluster stars (K > 15) observed by Eisenhauer et al. separately (in order to allow studies of the contribution
(2005). However,weareunabletotransformthespectra ofvariousspeciestothespectraindividually),butconsis-
ofcoolgiantssuchthattheyresemblethoseofthebright- tently and based on the same linelists. A new feature of
est S-cluster stars for a low luminosity AGN (L <1039 the version of the code used for the present paper is the
X
erg s−1). Higher luminosities though, as the one from a treatment of external illumination, which we have based
tidally disrupted star are sufficient to heat up the stel- on the inclusion of an improved version of the subrou-
lar atmosphere above 15,000 K, and therefore produce tines developed and described by Alencar et al. (1999);
theHeIline. However,thetotaldestructionofmolecular Nordlund & Vaz (1990); Vaz & Nordlund (1985).
linesinthespectraofthesegiantsseemstopointoutthat For reference, we first compute the spectra of non-
the deficiency of giants in the GC (Sellgren et al. 1990) irradiated oxygen-rich (C/O= 0.0, T = 4000 K, log
eff
might not be such. We show that, within our model, ir- g=2.0, Z = Z⊙) and carbon-rich (C/O> 1) stars. We
radiation explains the decreasing CO band intensity ob- then consider an irradiated star. The irradiation source
served as a function of radius from Sgr A∗. The other is taken to be the GC with an AGN spectral shape as
main result of our study is that we find a double layer given by Sazonov et al. (2004). In particular, we use
inversion in the atmospheres of irradiated giants for ir- their eq. 14 for the energy range 1eV < E < 2keV
radiation fluxes f > 102 erg s−1 cm−2 on the surface of and their eq. 8 for E > 2 keV and 23 for E < 1 eV.
the star. The total flux for Sgr A∗, assuming a mass of 3.7×106
WedemonstratethateveniftheAGNwasshiningator M⊙ is L = 5.0×1039(fEDD/10−4) erg s−1 (Ghez et al.
near the Eddington luminosity for 106 years, due to the 2005). Although the Sazonov et al. (2004) spectral en-
higheccentricityoftheS-clusterstarsorbits,theamount ergy distribution is for typical QSO’s we use it here as
ofirradiationismostlikelynotsufficienttomaketheHeI a good approximation to describe the AGN at the GC.
line appear. On the other hand, stars on more circular Ourresultsarenotsensitiveto moderatechangesonthe
orbitscouldpotentiallybesufficientlytransformedtore- parametersthatdescribethespectralenergydistribution
producethespectralpropertiesofthe brightestS-cluster of QSO’s in Sazonov et al. (2004). For f =10−4 the
EDD
stars (including the HeI line). luminosity of the AGN at the GC corresponds roughly
to the estimate by Revnivtsev et al. (2004) for the lumi-
2. IRRADIATIONOF STELLAR ATMOSPHERES:THE
nosity of the GC a few hundred years ago.
IR SPECTRUM
TheIRspectrum(2−2.4µ)forthenon-irradiatedcase
If the atmosphere of the star is sufficiently irradiated, is shown in Fig. 1 for the oxygen-rich model. The top
the energy deposited in the atmosphere will heat up the panel shows the atomic lines, the second panel the CO
outer layers and produce a wind. bands, the third panel other molecular bands and the
Basko & Sunyaev (1973) constructed a semi-analytic bottom panel is the total spectrum. Clearly, the IR
model to account for the effects of irradiation on a stel- spectrum of an oxygen-rich giant is dominated mainly
lar atmosphere. The most obvious consequence of irra- by molecular bands but also shows some atomic lines.
diation is that the temperature of the area of the star The most prominent of these atomic lines is the Brγ
facing the AGN increases by T /T ∼ (1+F /F )(1/4). line at 2.1661µ. Note that there are no emission lines.
s i x i
At the microscopic level the X-rays photo-ionize He It is also worth mentioning that there are no CO lines
I, He II and O, C, Ne, N, Fe and its ions. Below in the 2−2.3µ range; they appear only at wavelengths
5000 K the main source of opacity is due to photo- beyond 2.3µ. Therefore, these strong bands would not
detachmentofH−,whileabovethistemperatureopacity be observed in the spectra of Ghez et al. (2003) or
is dominated by photo-ionization of oxygen and carbon. Eisenhauer et al. (2005). While the molecular bands are
Basko & Sunyaev (1973) find that in their models the somewhat stronger than those observed in the faintest
envelope develops a significant wind, although most of S-clusterstars,the spectrumofanon-irradiatedoxygen-
the energy is re-radiated. By integrating the hydrody- rich giant is not too dissimilar from the ones observed
namicequations,Voit & Shull(1988)calculatedtherate for the faint stars in the S-cluster sample (see Fig. 1
at which mass is lost from the envelope of red super- in Ghez et al. (2003) and Fig. 5 in Eisenhauer et al.
giants. We use their work to estimate the mass loss rate (2005)). Fig. 2 shows the non-irradiated spectrum for
from giant atmospheres in §3. a carbon-rich star. Note the absence of CO lines be-
3
Fig. 1.— Theoretical IR spectrum of an oxygen-rich star at an Fig. 2.— SameasFig.1butforacarbon-richgiant. Notethat
effectivetemperatureof4000K.Theupperpanelshowstheatomic CO lines are only present beyond 2.3µ, whilethe other molecules
lines,thesecondpaneltheCOlines,thethirdpanelothermolecules getconsiderablystrongerthanforanoxygen-richstar.
while the bottom panel shows the total spectrum. Note that the
strong CO bands start at about 2.3µ, usually beyond the range
observedbyGhezetal.(2003)andEisenhaueretal.(2005). Note
alsothepresenceinthetotal spectrum ofmolecular-bandabsorp-
tionlinesbutalsooftheBrγ atomiclineat2.1661µ. ThefirstthingtonotefromFig.3isthedecreaseinthe
strengthofthemolecularlinesevenforf =f . Notealso
o
the reduction of the CO band intensity. If we examine
low 2.3µ (they are very strong CO bands beyond this the spectrum of the star for f = 102f , (Fig. 4), we
wavelength)andtheincreaseinthestrengthoftheother o
notice even more significant changes. As expected, all
molecular bands. Clearly, the non-irradiated spectrum
the molecular bands are gone, including the CO bands.
of a C-rich giant does not resemble at all any of the ob-
However, now some of the atomic lines are in emission
served S-cluster stars.
due to the stronger irradiation. In particular, the Brγ
We then irradiate the star as described above, assum-
lineat2.1661µisnowinemission. Atthissmalldistance,
ing different incident fluxes. Fig. 3 assumes an orbit av-
irradiation results in a rise in the temperature of the
eraged flux: atmosphere at τ = 10−4.9 from 2500 K to 8000 K.
ROSS
L f r erg However, the HeI line at 2.11 µ is clearly not present,
supp min
fo =2 1033ergs−1 0.6 100A.U. scm2 (1) and more importantly, no other line in the irradiated
(cid:18) (cid:19)(cid:18) (cid:19)(cid:16) (cid:17) star appears at the same wavelength.
where rmin is the pericenter distance. See Eq. 6 and ItisclearthatS-clusterstarsirradiatedattheirpresent
Fig. 7 for a definition of fsup. On the other hand, Fig. 4 orbits (5 × 10−4 to 5 × 10−3 pc) by a low-luminosity
assumes a flux of f = 102f , corresponding to a star AGN a few hundredyears agodo not resemble the spec-
o
illuminated by Sg A∗ during a more active state when tra of any of the observed S-cluster stars seen today
L ≈ 1035ergs−1, still smaller than the luminosity esti- (Ghez et al. 2003; Eisenhauer et al. 2005). Their spec-
mated by Revnivtsev et al. (2004) for the luminosity of tra would be totally dominated by emission lines. On
the GC a few hundredyearsago. Ourilluminated atmo- the other hand, if we look at Fig. 3, which is equivalent
sphericmodelsarestaticandwearenotabletocompute to a star irradiated at a distance of a few hundred AU
models with larger illumination fluxes that f = 102f . but with a luminosity of L ∼ 1033 erg s−1 the similar-
o X
For this dynamic models arerequired,which we are cur- itywith the fainteststarsofthe Eisenhauer et al.(2005)
rently constructing. However, even for f = 102f the sample is striking. In this case, the HeI line is absent
o
transformation of the spectrum is significant. and the deepest absorption feature in the spectrum is
4
Fig. 3.— IR spectrum of an irradiated oxygen-rich star illumi- Fig. 4.—SameasFig.3butforastarwithanilluminationflux
natedwithafluxf =fo. Theupperpanelshowstheatomiclines, f =100fo. Notetheextremetransformationofthespectrumwith
the second panel the CO lines, the third panel other molecules nowonlyatomiclinesinemissionandnomolecules,includingCO.
while the bottom panel shows the total spectrum. Note the de-
crease in the strength of the molecular lines with respect to the
non-irradiatedspectrumofFig.1. 10000
8000
dominated by the Brγ line.
It is clear that after the level of irradiation suggested
bdinyowaRnfeevwanniydvetarseresavd(eajutssastol.too(n2i0at0ss4tp)hreheavtesiomcuepsaesereqadut,uiltrihbeeriisustlmoawrswietniulolauctigoohonl, mperature[K] 6000
Te 4000
about2000K,moleculeswillformimmediatelyonatime
scale of seconds). However, the presence of illumination
will stop convection on the atmosphere. It takes of the
2000
orderofafewhundredyearsforconvectiontoberestored
and therefore the temperature in the outer layers to de-
crease enough for molecules to be allow to reform. This 0
−2 −1 0 1 2 3 4 5
argumentalsoassuresthatthetime-scaleofmoleculefor- log(Pgas[dyn/cm2])
mationislongerthanthe rotationtime-scaleofthestars Fig. 5.— Plot of the T −Pgas structure of the relevant model
assuringthatmoleculeswillbe wipedoutoverthe whole atmospheres: solidlineisfor f =0, dashed lineisforf =fo and
surfaceofthestar. NotehoweverthatthepresentX-ray dottedlineisforf =100fo. Notetheinversiontemperature layer
flux from the GC is sufficient to destroy molecules, as thattakes placesatilluminationfluxesoff =100fo
shown in Fig. 3.
Figure 5 shows the temperature versus gas pressure
modelstructure fora oxygen-richgiantfor f =0,f and sphere. As a result, the model structure resembles a
o
102f . In the moderately irradiated model f = f from photospheric-chromospheric atmosphere with a slowly
o o
the GC (as well as in the non-irradiatedmodel), the up- rising, almost flat, chromospheric temperature distribu-
per layers are relatively dense (P ≈ 100 dyn/cm2). tion. The inner part of the atmosphere is almost unaf-
gas
Therefore the absorption of radiation from the SBH at fected by the illumination at f = f . For f = 102f
o o
the GC is substantial already in the top of the atmo- the radiation is strong enough that the atmosphere is
5
envelopes off stars near the GC. If the effective temper-
1 f=0 1
Total free electrons 0000 ....02468 f=10f=0ff00 Ionization Fractions − C I 0000 ....02468 f=10ff=0=ff000 aitcpcshloteuueurhssarniteegtteuhrimfrsoeesorsntodaonwtiruhfilsiygel,elhdrnthahtuasioomvstuaeepbdrgrslehiortfdecosotoutifucamaelbrsdestotsauhewrwtesxihptToohilbebcaffhsishneeirear≈gvvdrheeeedd1trt5hoH(e0oese0ffeIose0ehbclieoKstnqiervert.)ev(,tweotdth2ehaimecSicnhn---
−4 −3 −2 −1 0 1 2 −4 −3 −2 −1 0 1 2
log tross log tross Goodman & Paczynski (2005)). Note that stripping the
0.5 envelopeis adifferentmechanismthanthe oneproposed
PE/PG 0000 ....01234 f=10ff=0=ff000 Ionization Fractions − C II 0000 ....012468 f=10ff=0=ff000 iantsnhctaeuattnrithoaeeknroeipowferptitethshvheeitoorhsuuetetesilmsslstaeeanrclsoltasaiotrslmonoasusotsrms.ocpfeIohttseohpirsfihesthehwwreieaasotsrhciknrooagntwi.ssahteIanednndredtttuhithleheleuetsmostttrieainimlprlaupptwmiienoirilng--l
−0.1 cool down to a new equilibrium configuration.
−4 −3 −2 −1 0 1 2 −4 −3 −2 −1 0 1 2
log tross log tross Regardless, it is still interesting to explore the conse-
Fig. 6.—Theplotshowsthevalueoftheionizationfractionsof quences of the mass loss as it will be a useful marker
CI and CII (right panels) and electron pressure over gas pressure of the past activity of Sgr A∗. This mechanism will
(bottom-left panel) and total density of free electrons (upper left clearly predict a characteristic dependence of the num-
panel)fornon-irradiatedandirradiatedmodels.
ber of ”hot” stars on pericentric radius. Stripping the
envelope off a star exposes its hotter core, and thus in-
creases its effective temperature. However, the luminos-
heated at all optical depths in the atmospheric model, ity of the star will be unaffected, since the conditions in
and the chromospheric temperature rise is substantial. the stellar core are effectively decoupled from the con-
As a result, the degree of ionization increases, making ditions in the envelope. With numerical stellar models
thecontinuousopacityincrease,wherebytheatmosphere (Jimenez et al. 2004), we compute the effective temper-
expands(considerably). Figure6showstherelativefrac- ature Teff of the stripped star, and its new radius R∗,
tion of neutral (Ci) and one time ionized (Cii) carbon assuming L=4πR2σT4 =const.
∗ eff
(the two right panels) for the three models in Fig. 5. Can the entire envelope be stripped due to a close en-
Otheratoms,includingH,N,O,Al,Si,S,Ca,andNi,be- counter with an AGN? Voit & Shull (1988) consider the
have qualitatively similarly (whereas Ca, Mg, Cr and Fe X-rayinducedmasslossfromstarsnearAGN.Theycon-
aresubstantiallydoubleionizedinthetop-layers,andHe sider mass loss due to two mechanisms: thermal winds
is neutral throughout the atmosphere). The main con- driven by X-ray heating, and stellar ablation by radia-
tributeroffreeelectronsishydrogen,andthetotalabun- tion pressure. For thermally driven winds, they directly
danceandpressureofelectronsareshowninthe twoleft integratethe hydrodynamicequations,andfindthat the
panels. It is seen that the degree of ionization (and the formula:
abundance of free electrons) increases rapidly outward
fromlogτROSS ≈0to −2. Thisisthe regionoftempera- M˙thermal =5.0×10−6M⊙yr−1L402.9Rd−,11.58R∗2,100 (2)
ture rise in the strongly irradiated model (logP from
gas
reproduces their results very well, as well as the pre-
≈ 3 to 0). From logτ = −2 and outward hydro-
ROSS
vious analytic results of Basko et al. (1977). Here
gen is fully ionized, and the electron density and pres-
L ≡ L/(1042ergs−1) is the AGN luminosity, R ≡
sure therefore now again decreases outward. As a con- 42 d,18
sequence the opacity decreases in the outermost layers, Rd/1018cm is the distance of the star from the AGN,
and the energy deposition due to external illumination and R∗,100 ≡ R∗/100R⊙ is the stellar radius. Note
also decreases outwards from log P =0 onwards. The that this calculation assumes that emission line cooling
gas
temperature thereforedecreasestowardthe surface from is quenched in the wind, and is therefore potentially an
this point onwards, just like in a normal photospheric overestimate. They find that ablative mass loss (which
model. This feature is not seen in any chromospheric is independent of emission line cooling), is
model heated from below. It is particular to strongly
irradiated atmospheres. M˙abl ≈3.8×10−6M⊙yr−1L42Rd−,215M∗−1/2R∗5,/1200 (3)
3. MASS LOSSFROM AGN IRRADIATION for R<Rabl, where
In this section, we consider whether the heat input Rabl =6.3×1015 cm M∗1/2L142/2R100. (4)
from AGN irradiation is sufficient to evaporate the stel-
lar envelope of a star, causing an observable change in We will approximate the suppression for R > Rabl via
its spectrum. We consider much larger AGN luminosi- M˙ → M˙ exp(−R/R )2. Since the orbital distance
abl abl abl
ties than in the previous section, up to ∼ 0.5%LEdd. Rd,15, the stellar mass M∗ and the stellar radius R∗,100
This assumption is motivated by the very high lumi- arealltime-dependent, wefindthe totalmasslossbyin-
nosities believed to accompany stellar tidal disruptions tegratingequations (2) or (4) numerically. For the AGN
(Komossa 2002), and the estimated high rate of such luminosityassumed,L42 ∼5×10−3LEddfora3×106M⊙
events(Wang & Merritt2004;Merritt & Szell2005),one SBH,the stellarenvelopewillbe strippedfromastaraf-
per 103−104 yr or so. ter∼10%ofitsmainsequencelifetime,or∼105years,if
This is a radiative rather than a gravitational (e.g., thestarremainsat∼100A.U.fromtheSBHthroughout
Davies & King (2005)) mechanism for stripping stellar this time.
6
TABLE 1
Massloss andstellareffectivetemperaturesfor
measuredorbits. Theorbitalparametersarefromthe
fitsof Eisenhaueretal(2005). We assumetheAGNshines
with a luminosity L=1043ergs−1 for∼106yrs. Thefirst
set of columnsis fora 1M⊙ starwith an initial
Teff =3000K, R∗,100=1,thesecond setof columnsis fora
2M⊙ starwith aninitial Teff =4000K, R∗,100=1.23.
rmin/AU e ∆M/M⊙ Teff/K ∆M/M⊙ Teff/K
S2 120 0.87 0.31 6400 0.47 7900
S12 220 0.73 0.18 5300 0.22 6300
S14 100 0.97 0.29 6200 0.51 8100
S1 2020 0.62 0.35 3900 0.07 4900
S8 180 0.98 0.15 5100 0.30 6900
S13 1000 0.47 0.09 4400 0.14 5600
Fig. 7.— The flux weighted fraction of time an object spends
close to pericenter, as given by equation (6), as a function of the
eccentricity e. This gives the relative reduction in flux compared
toacircularorbitatpericenterdistance.
PropermotionobservationsofGCstarshavemanaged
to pin down their orbital parameters: specifically, their
eccentricityeandpericenterdistancer (Scho¨del et al.
min
2003; Eisenhauer et al. 2005). The orbits are all highly
eccentric; typically e ≈ 0.8−0.9, while pericenter dis-
tances are of order ∼ 100−1000 A.U. Given these pa-
rameters, we can solve for the orbit R(t) implicitly: Fig. 8.— Predicted strength of CO (solid line)as a function of
distancefromtheGCformodelsirradiatedbyanAGNofluminos-
r= rmin(1+e) (5) ity LX = 1033 erg s−1. Overplotted are CO measurements from
Sellgrenetal.(1990).
(1+ecosθ)
2πt
=ψ−esinψ
τ
4. THELACK OFGIANTS NEAR THEGALACTIC
1/2
θ 1+e ψ
CENTER
tan =tan tan
2 1−e 2
(cid:18) (cid:19) "(cid:18) (cid:19) # Given the strong transformation in the atmosphere of
whereτ = 4π2a3/(GM ) 1/2 istheKeplerianorbital old giant stars due to irradiation, it is worth exploring
AGN howtheCOabundancecorrelateswithdistancefromthe
period, and the semi-major axis a = rmin/(1−e). In GC. CO observations have been obtained for a dozen
(cid:2) (cid:3)
Table 1, we show the results for a 1M⊙ and 2M⊙ gi- starsfrom0.2pcupto3.6pcfromtheGC(Sellgren et al.
ant undergoing mass loss for ∼ 106 years, assuming the 1990). They show a cleardecrease in the strength of the
observed orbital parameters. CObandatdistancesofabout0.5pcfromtheGC.From
Themasslosscanbe asignificantamountofthestar’s our numerical experiments we can measure the strength
mass, but is still insufficient to boost the effective tem- of the CO absorption as a function of distance from the
peratures to sufficiently high values. This is because the GC.Todothiswehaveirradiatedthestarwiththesame
orbits are highly eccentric, andspend most of their time parametersasin§2atdifferentdistancesfortheluminos-
at largeradii, far frompericenter rmin. We can compute ityoftheAGNattheGCtoday(LX =1033 ergs−1). As
the suppression factor compared to a purely circular or- can be seen from Fig. 3, the irradiated star with f =f
o
bit by considering the flux-weighted fraction of time an still contains CO.
object spends close to pericenter in a single orbit: Fig. 8 shows our prediction (solid line) and the
r2 τ dt Sellgren et al. (1990) data. To compute our predic-
fsupp(e)= mτin R2(e,t). (6) tions we have chosen an average value of the eccentric-
Z0 ity e = 0.77 from Table 1 and applied the correspond-
(it is acceptable to average over a single orbit since the ing suppression(0.2) factor fromFig.7 to the irradiated
typicalorbitalperiodτ ∼100yearsismuchlessthanthe flux today. Although our model is not a perfect fit, the
mainsequencelifetime;weareestimatingthecumulative agreement is good and the general trend is reproduced,
mass loss over many orbits). This is shown in Fig 7. namely, a decrease in CO absorption band strength the
7
closer the star is to the GC. This indicates that AGN observationsbySellgren et al.(1990). Thissuggeststhat
irradiationisproducingtherightfluxofphotonstostart contrary to previous claims, there is no dearth of old gi-
COdestructionatadistanceof∼1pc. Thisimpliesthat ants near the galactic center; their molecular signatures
theremightnotbealackofgiantsneartheGCandthat have simply been wiped out by the radiation field from
the only thing we might be seeing is a transformationof SgA∗. However,someoftheobservedS-clusterstarshave
the spectrum of the star due to irradiation by the low- astrongHeIlineintheirspectra. Wehavenotbeenable
luminosity AGN. toreproducethislineforirradiatedlow-massstarsforre-
alistic values of the GC luminosity, suggesting that that
5. DISCUSSIONANDCONCLUSIONS someothermechanism(perhaps recentstarformationof
It has been argued in the literature (e.g. Ghez et al. massive star) is responsible for their presence.
(2003)) that the observed spectra of the S-cluster stars, Our illuminated atmospheric code is static. In fact
areinagreementwithstandardspectraoftypeB8orear- we have only been able to obtain converged models for
lier,indicatingthatthestarsareyoung,whichisapuzzle values of f < 100fo. We have not been able with the
because at such distances the tidal force by the central present static code to predict the structure and spec-
BH is far to great to be overcome by densities in nor- trum of a star illuminated with f > 100fo. For doing
mal molecular clouds. However, effects of the radiation this a dynamic model is needed. It is not inconceivable
field due to Sg A∗ on stellar atmospheres has hitherto that when dynamics effects are included and models are
not been taken into account. The upper layers of stars converged for f > 100fo, the spectra of these irradiated
at the distance of the S-cluster will be strongly affected stars will look even more extreme than the models pre-
by this irradiation. We have therefore computed fully sented in this work. In particular it will be interesting
self-consistentstellar atmospheres where this irradiation to investigate if the HeI line can be obtained at higher
is take into account. The result is a substantial heating illuminations for dynamical models.
oftheupperatmosphere. Theheatingoftheupperlayers
of the atmosphere reduce the intensity of the CO bands
ACKNOWLEDGMENTS
aswellasallothermolecularbands,herebymakingeven
starsofquitelatetypelookfairlymuchliketheobserved The research of RJ is partially supported by NSF
S-cluster stars. grants AST-0408698, AST-0420920, AST-0437519 and
In particular, in the spectra from our model atmo- PIRE-0507768andbyNASAgrantNNG05GG01G.SPO
spheres of irradiated giant stars with T ≈ 4000K, the is supportedby NSF AST-0407084. DMis supportedby
eff
intensityoftheCObandsisdecreasingwhenthedistance grants AST-0420920 from the NSF and NNG04GJ48G
to Sgr A is decreased, in qualitative agreement with the from NASA. JPS acknowledges support from ITA.
REFERENCES
Alencar,S.H.P.,Vaz,L.P.R.,&Nordlund,˚A.1999,A&A,346, Hanson,M.M.,Conti,P.S.,&Rieke,M.J.1996,ApJS,107,281
556 Helling,C.,&Jorgensen, U.G.1998,A&A,337,477
Alexander,T.2005,Phys.Rep.,419,65 Jimenez,R.,MacDonald,J.,Dunlop,J.S.,Padoan,P.,&Peacock,
Alexander,T.,&Morris,M.2003,ApJ,590,L25 J.A.2004, MNRAS,349,240
Arons,J.1973,ApJ,184,539 Jørgensen,U.G.2003,inASPConf.Ser.288:StellarAtmosphere
Barman,T.S.,Hauschildt,P.H.,&Allard,F.2004,ApJ,614,338 Modeling,303
Basko,M.M.,&Sunyaev, R.A.1973,Ap&SS,23,71 Jørgensen,U.G.2005,inASPConf.Ser.336:CosmicAbundances
Basko, M. M., Sunyaev, R. A., Hatchett, S., & McCray, R. 1977, asRecordsofStellarEvolutionandNucleosynthesis, 269
ApJ,215,276 Jorgensen,U.G.,Johnson,H.R.,&Nordlund,A.1992,A&A,261,
Basko,M.M.,Sunyaev,R.A.,&Titarchuk,L.G.1974,A&A,31, 263
249
Komossa, S. 2002, in Lighthouses of the Universe: The Most
Chiu,W.A.,&Draine,B.T.1998,ArXivAstrophysicse-prints
Luminous Celestial Objects and Their Use for Cosmology
Davidson,K.,&Ostriker,J.P.1973,ApJ,179,585
Proceedings oftheMPA/ESO/,p.436,436
Davies,M.B.,&King,A.2005,ApJL,624,L25
Merritt,D.,&Szell,A.2005, ArXivAstrophysicse-prints
Edwards,A.C.1980,MNRAS,190,757
Nordlund,A.,&Vaz,L.P.R.1990,A&A,228,231
Eisenhaueretal.,F.2005,ApJ,628,246
Phinney,E.S.1989,inNATOASICProc.290:TheoryofAccretion
Fabian,A.C.1979,RoyalSocietyofLondonProceedingsSeriesA,
Disks,457
366,449
Revnivtsev, M. G., Churazov, E. M., Sazonov, S. Y., Sunyaev,
Genzel, R., Scho¨del, R., Ott, T., Eisenhauer, F., Hofmann, R.,
R. A., Lutovinov, A. A., Gilfanov, M. R., Vikhlinin, A. A.,
Lehnert, M., Eckart, A., Alexander, T., Sternberg, A., Lenzen,
Shtykovsky, P.E.,&Pavlinsky,M.N.2004, A&A,425,L49
R.,Cl´enet,Y.,Lacombe,F.,Rouan,D.,Renzini,A.,&Tacconi-
Sazonov, S. Y., Ostriker, J. P., & Sunyaev, R. A. 2004, MNRAS,
Garman,L.E.2003, ApJ,594,812
347,144
Ghez,A.M.,Duchˆene,G.,Matthews,K.,Hornstein,S.D.,Tanner,
Scho¨del, R., Ott, T., Genzel, R., Eckart, A., Mouawad, N., &
A.,Larkin,J., Morris,M.,Becklin, E.E.,Salim,S.,Kremenek,
Alexander,T.2003,ApJ,596,1015
T.,Thompson,D.,Soifer,B.T.,Neugebauer, G.,&McLean, I.
Sellgren, K., McGinn, M. T., Becklin, E. E., & Hall, D. N. 1990,
2003, ApJL,586,L127
ApJ,359,112
Ghez, A. M., Salim, S., Hornstein, S. D., Tanner, A., Lu, J. R.,
Vaz,L.P.R.,&Nordlund,A.1985,A&A,147,281
Morris,M.,Becklin,E.E.,&Duchˆene, G.2005,ApJ,620,744
Voit,G.M.,&Shull,J.M.1988, ApJ,331,197
Goodman,J.,&Paczynski,B.2005,ArXivAstrophysicse-prints
Wang,J.,&Merritt,D.2004,ApJ,600,149
Gustafsson, B., Bell, R. A., Eriksson, K., & Nordlund, A. 1975,
A&A,42,407
Hansen,B.M.S.,&Milosavljevi´c,M.2003,ApJ,593,L77