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Advection Dominated Accretion Mo del of Sagittarius A
astro-ph/9509140 27 Sep 1995
and Other Accreting Black Holes
Ramesh Narayan Insu Yi and Rohan Mahadevan
Harvard Smithsonian Center for Astrophysics Garden St Cambridge MA USA
Institute for Advanced Study Olden Lane Princeton NJ USA
September
The most imp ortant feature of the new ows is that the Abstract Viscous rotating accretion ows around black
accreting gas is optically thin and has low radiative e holes b ecome advection dominated when the accretion
ciency Therefore the bulk of the energy released through rate M is su ciently low Most of the accretion energy in
viscosity is advected radially inward with the gas as ther such ows is stored within the gas and advected radially
mal energy and only a fraction of the energy is radiated inward The temp erature is therefore very high and much
These advection dominated solutions are very di erent of the radiation comes out in hard X rays and rays We
from the usual co oling dominated solutions considered in have constructed an advection dominated accretion ow
the past where all the released energy is assumed to b e ra mo del for the Galactic Center source Sagittarius A The
diated The solutions are related to the ion torus mo del mo del consists of a M black hole accreting at
developed by Rees et al but are distinct from an M M yr where is the usual viscos
other optically thick branch of advection dominated solu ity parameter The mo del sp ectrum ts the observations
tions discovered by Abramowicz et al from radio to rays quite well and explains the unusually
low luminosity of the source Since the mo del explicitly
The new optically thin advection dominated branch
makes use of a horizon at the inner edge to swallow the
of solutions has several very interesting prop erties which
advected energy the success of the mo del strongly sug
have b een explored in the pap ers listed ab ove Two fea
gests that the central ob ject in Sgr A is a black hole We
tures of particular interest are the following
further show that if is not much smaller than unity
then advection dominated mo dels can b e applied even to
Because all the energy go es into internal energy the
higher luminosity black holes The existence of Low and
gas b ecomes extremely hot Indeed Narayan Yi b
High States in black hole X ray binaries and the abrupt
constructed two temperature mo dels based on the ideas
transition b etween the two states nd a natural explana
of Shapiro Lightman Eardley where the ions
tion The mo dels also explain the close similarity in the
achieve nearly virial temp erature T K r and the
i
hard X ray ray sp ectra of black hole X ray binaries and
electrons are co oler T K for r here r
e
active galactic nuclei
is the radius expressed in Schwarzschild units The nearly
virial ion temp erature causes the accreting gas to rotate
with a sub Keplerian angular velocity and to take up a
nearly spherical morphology rather than a disk like or
toroidal morphology Narayan Yi a The relativis
tic electron temp erature makes it natural for the gas to
radiate a large fraction of its luminosity in soft rays
Introduction
The ow is thermally stable Abramowicz et al
In a series of recent pap ers Narayan Yi a b
Narayan Yi b to lo cal large wavelength p ertur
Abramowicz et al Chen Chen et al a
bations This is an imp ortant feature b ecause prior to
class of accretion ow solutions has b een discussed which
this the only hot accretion ow solution known was the
app ears to b e relevant to accreting black holes and neu
thermally unstable solution discovered by Shapiro Light
tron stars These solutions exist at relatively low mass
man Eardley Kato Abramowicz Chen
accretion rates m where m is expressed in Ed
have recently shown that the new solutions may b e weakly
dington units using a ducial e ciency of and is
unstable to short wavelength thermal p erturbations but the usual viscosity parameter
Narayan Yi Mahadevan
the instability do es not app ear to p ose any danger to the
overall viability of the ows The solutions are also convec
tively unstable Narayan Yi a Igumenshchev
Abramowicz Chen but again this instability do es
not threaten the survival of the ow In fact convection
may help by enhancing turbulent viscosity thereby in
creasing the value of
The high temp erature and thermal stability of the new
solutions make them esp ecially promising for explaining
the hard X ray and soft ray sp ectra of accreting black
hole systems The advection dominated nature of the ow
suggests that the b est applications are likely to b e to low
luminosity systems We describ e one such application in
x and discuss the extension of these mo dels to higher
luminosity systems in x
Application to Sgr A
Fig The solid line shows the sp ectrum of Sgr A corre
We have successfully applied the optically thin advection
sp onding to an advection dominated accretion mo del with a
dominated accretion mo del to several low luminosity sys
black hole mass of M and a mass accretion rate of
tems i the Galactic Center source Sagittarius A Sgr
M M yr The mo del assumes that gas pres
A Narayan Yi Mahadevan ii the nucleus of
sure accounts for of the pressure in the notation
the LINER NGC Lasota et al and iii black
of Narayan Yi b with magnetic pressure accounting for
hole soft X ray transients in quiescence Narayan McClin
the rest The mo del gives a go o d t to measurements over the
to ck Yi Yi et al Here we discuss our mo del
entire sp ectral range from radio to rays see Narayan et al
of Sgr A
for more details on the observational data The dashed
line is a standard thin disk mo del where the black hole mass has
The p eculiar radio source Sgr A at the Galactic Cen
b een kept the same and M has b een reduced to M yr
ter has for many years b een interpreted as a sup ermassive
in order to satisfy the infrared upp er limits This mo del do es
black hole M M based on the dynamics of sur
not t either the radio or the X ray ray data In addition
the M required in this mo del is far lower than the estimated
rounding gas and stars Genzel Townes Genzel
M based on observations of gas in the vicinity of Sgr A
Hollenbach Townes Genzel The source has
a luminosity of ergs s extending in a nearly at
sp ectrum when represented as L vs see Fig from
radio mm through infrared up to hard X rays It is imp os
sible to t the unusual sp ectrum of the source with a stan
the sp ectrum of the optically thin ow by including cyclo
dard thin accretion disk mo del e g see the dashed line in
synchrotron emission Mahadevan Narayan Yi
Fig Furthermore there is evidence for considerable gas
bremsstrahlung and Comptonization As Fig shows the
ows in the vicinity of Sgr A and it is estimated that the
calculated sp ectrum gives quite a go o d t to the observa
mass accretion rate on to the source if it is a sup ermassive
tions The indep endently tted black hole mass falls close
black hole should b e M yr Melia Gen
to the value suggested by the dynamical evidence Genzel
zel et al Such a large M would give an accretion
et al More imp ortantly the mass accretion rate is
luminosity of ergs s if the radiative e ciency is
quite high
as exp ected with a thin disk mo del which is clearly
The last feature is a signi cant improvement over most inconsistent with the observations Various novel mo dels
previous mo dels Given the observed luminosity of the have b een prop osed for Sgr A e g Falcke Mannheim
source a standard co oling dominated mo del would pre Biermann Duschl Lesch Melia but
dict an accretion rate of only M yr which is no mo del has yet b een able to reconcile satisfactorily the
in severe con ict with direct estimates of M The chief requirements of low luminosity at sp ectrum and high
reason our mo del is able to employ a fairly substantial mass accretion rate We have constructed an advection
M and yet explain the very low luminosity of the source dominated mo del of Sgr A in which a M black
is that the mo del is advection dominated Rees In hole accretes at a rate of M yr Narayan
our mo del more than of the viscously dissipated Mahadevan Yi see Rees for a qualitative
energy is advected with the ow and disapp ears through outline of the chief features of the mo del We calculate
Narayan Yi Mahadevan
the horizon of the black hole and less than of the
energy is actually radiated
This brings up the following imp ortant p oint If the
central star in Sgr A were not a black hole but a normal
ob ject with a surface say a M sup ermassive star
then our mo del would fail b ecause the energy would ulti
mately b e re radiated from the stellar surface and would
b e seen somewhere in the sp ectrum The success of our
mo del dep ends critically on the assumption that the cen
tral ob ject p ossesses a horizon The mo del therefore pro
vides strong con rmation that Sgr A is indeed a black
hole as has long b een susp ected but never proved
Application to High Luminosity Sources
The advection dominated nature of the solutions makes
them an obvious choice for mo deling low luminosity
Fig Fig A sequence of mo del sp ectra for a M black
hole with and gas pressure Starting from
sources However the ma jority of black hole X ray binaries
b elow the mo dels have log m log r
tr
XRBs and active galactic nuclei AGNs observed have
and resp ectively Note
luminosities times the Eddington luminosity L
Edd
that the luminosity increases very rapidly with increasing m
Can the same mo dels b e applied also to such sources We
and that for m the sp ectra are quite hard The bumps
nd that we can indeed use our solutions to mo del these
at the left end of the sp ectra are due to blackbo dy radiation
sources provided we take to b e large
from the co ol outer disk Ab ove m an optically th in
advection dominated solution is no longer p ossible and so for
Figure shows a sequence of mo del sp ectra of a M
log m we show the sp ectrum of a standard thin disk
black hole In these mo dels we assume that a standard
extending down to r This sp ectrum is very soft cutting
thin disk extends from a large outer radius r down to
out
o ab ove a few keV
a transition radius r and that the ow then b ecomes
tr
hot and advection dominated from r down to r
tr in
Inside r we assume that the radial velocity b e
in
natural explanation for the Quiescent O State of the comes sup ersonic and the emission is negligible We have
soft X ray transients Narayan McClintock Yi Yi set in the hot inner ow The di erent mo dels shown
et al In our mo del the O State do es not represent in Fig corresp ond to di erent mass accretion rates m
a decrease in m of several orders of magnitude but rather and transition radii r as explained in the gure caption
tr
a decrease of only one or at most two orders of magnitude We see several interesting features The solutions with
relative to the Low State m have very hard sp ectra with photon
indices and with hard X ray soft ray lu
N
We nd that the advection dominated solution ceases
minosities of ergs s The sp ectra have
to exist ab ove a critical m for Narayan
thermal cuto s at photon energies E few keV
Yi b Chen et al Therefore at high m the
These features are very similar to the sp ectra of black hole
only solution we can construct is a thin disk with a soft
XRBs in their so called Low State e g Greb enev et al
sp ectrum see the case corresp onding to log m in
van der Klis and we prop ose that the Low
Fig This naturally explains the sudden app earance in
State corresp onds to such advection dominated ows
luminous black hole systems of the so called High State
with an ultra soft sp ectrum The transition b etween the With decreasing m the luminosity L decreases very
Low State and the High State o ccurs at m in our rapidly roughly as L m This means that relatively
mo dels Translated into luminosity the maximum lumi small changes in m can lead to large variations in L and
nosity we can exp ect in the Low State is L may p erhaps explain the large variability of the hard X
Edd
Since the observed maximum is ab out L ray ux of black hole sources Further we nd that the
Edd
Greb enev et al van der Klis our mo dels need electron temp erature increases with decreasing m which
a large value of to t the observations Even in the is consistent with the indication in some X ray transients
High State black hole XRBs are known to have a low such as GRO J J Kurfess private communica
luminosity hard tail in their sp ectra This is probably due tion Also it is p ossible to achieve extremely low X ray
to a corona ab ove the thin disk which is not included in luminosities at the level of ergs s with only
our mo dels mo derate decrease in m down to This provides a
Narayan Yi Mahadevan
The mo del in its present form cannot explain hard We have compared advection dominated accretion ows
p ower law tails which extend to E MeV Such emis around black holes and neutron stars This is discussed in
sion could arise from a non thermal distribution of elec the accompanying pap er by Yi et al
trons which could in principle b e included as an addi
We nd that the shap es of advection dominated mo del
tional comp onent in the mo del The mo dels developed so
sp ectra are essentially indep endent of the mass of the
far however have considered only purely thermal elec
black hole Figure shows a sequence of mo dels ranging
tron distributions Also the variability prop erties of these
from M M appropriate to XRBs to M M
mo dels have not yet b een considered and it is not clear if
appropriate to the most p owerful AGNs In all cases the
observations like icker and QPO can b e explained natu
sp ectra have with a cuto at few keV This
N
rally
similarity of sp ectra has b een noted in the observations
Acknowledgement This work was supp orted in part by
and is explained naturally by the mo dels
NSF grant AST RN thanks the Inst for Theor
Phys Univ of California for hospitality
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Melia F ApJ
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Narayan R Yi I ApJ L
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Narayan R McClintock J E Yi I ApJ in press
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Rees M J in The Galactic Center eds Riegler Bland
The optically thin advection dominated accretion solution
ford
is a stable and hot accretion ow mo del which naturally
Rees M J Begelman M C Blandford R D Phinney
pro duces sp ectra with substantial luminosity in hard X
E S Nature
rays and soft rays of up to few keV The mo del
Shapiro S L Lightman A P Eardley D M ApJ
is therefore particularly well suited for explaining the ex
tensive observations of accreting black holes b eing carried
van der Klis M ApJS
out with the Compton Gamma Ray Observatory
Yi I Narayan R Barret D McClintock J E this
volume
The solutions work particularly well for low luminosity
sources like Sgr A and quiescent soft X ray transients
This article was pro cessed by the author using Springer Verlag
In addition we nd that the mo dels work well even for
a
L T X A A style le L AA version
E luminous sources provided we set