Shocks and Cavities from Multiple Outbursts in the Galaxy Group NGC 5813: A Window to AGN Feedback

Abstract

We present results from new Chandra, GMRT, and SOAR observations of NGC 5813, the dominant central galaxy in a nearby galaxy group. The system shows three pairs of collinear cavities at 1 kpc, 8 kpc, and 20 kpc from the central source, from three distinct outbursts of the central AGN, which occurred 3x10^6, 2x10^7, and 9x10^7 yr ago. The H-alpha and X-ray observations reveal filaments of cool gas that has been uplifted by the X-ray cavities. The inner two cavity pairs are filled with radio emitting plasma, and each pair is associated with an elliptical surface brightness edge, which we unambiguously identify as shocks (with measured temperature jumps) with Mach numbers of M~1.7 and M~1.5 for the inner and outer shocks, respectively. Such clear signatures from three distinct AGN outbursts in an otherwise dynamically relaxed system provide a unique opportunity to study AGN feedback and outburst history. The mean power of the two most recent outbursts differs by a factor of six, from 1.5--10x10^42 erg/s, indicating that the mean jet power changes significantly over long (~10^7 yr) timescales. The total energy output of the most recent outburst is also more than an order of magnitude less than the total energy of the previous outburst (1.5x10^56 erg versus 4x10^57 erg), which may be a result of the lower mean power, or may indicate that the most recent outburst is ongoing. The outburst interval implied by both the shock and cavity ages (~10^7 yr) indicates that, in this system, shock heating alone is sufficient to balance radiative cooling close to the central AGN, which is the relevant region for regulating feedback between the ICM and the central SMBH. Comment: Replaced with version submitted to ApJ. Some reorganization of the text, and typos corrected in Tables 1 & 2

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Preprint typeset using LATEX style emulateapj v. 11/10/09
SHOCKS AND CAVITIES FROM MULTIPLE OUTBURSTS IN THE GALAXY GROUP NGC 5813: A
WINDOW TO AGN FEEDBACK
S. W. Randall1, W. R. Forman1, S. Giacintucci1,2, P. E. J. Nulsen1, M. Sun3, C. Jones1, E. Churazov4,5, L. P.
David1, R. Kraft1, M. Donahue6, E. L. Blanton7, A. Simionescu8, N. Werner8
ABSTRACT
We present results from new Chandra, GMRT, and SOAR observations of NGC 5813, the dominant
central galaxy in a nearby galaxy group. The system shows three pairs of collinear cavities at 1 kpc,
8 kpc, and 20 kpc from the central source, from three distinct outbursts of the central AGN, which
occurred 3 × 106, 2 × 107, and 9 × 107yr ago. The Hα and X-ray observations reveal filaments
of cool gas that has been uplifted by the X-ray cavities. The inner two cavity pairs are filled with
radio emitting plasma, and each pair is associated with an elliptical surface brightness edge, which we
unambiguously identify as shocks (with measured temperature jumps) with Mach numbers of M ≈ 1.7
and M ≈ 1.5 for the inner and outer shocks, respectively. Such clear signatures from three distinct
AGN outbursts in an otherwise dynamically relaxed system provide a unique opportunity to study
AGN feedback and outburst history. The mean power of the two most recent outbursts differs by
a factor of six, from 1.5–10×1042erg s−1, indicating that the mean jet power changes significantly
over long (∼ 107yr) timescales. The total energy output of the most recent outburst is also more
than an order of magnitude less than the total energy of the previous outburst (1.5 × 1056erg versus
4 × 1057erg ), which may be a result of the lower mean power, or may indicate that the most recent
outburst is ongoing. The outburst interval implied by both the shock and cavity ages (∼ 107yr)
indicates that, in this system, shock heating alone is sufficient to balance radiative cooling close to the
central AGN, which is the relevant region for regulating feedback between the ICM and the central
SMBH.
Subject headings: galaxies: active — galaxies: clusters: general — galaxies: groups: individual
(NGC5813) — galaxies: individual (NGC5813) — X-rays: galaxies
1. INTRODUCTION
A major result from early Chandra and XMM-Newton
observations was that the amount of gas in cool core clus-
ters that cools to low temperatures is less than predicted
by classical radiative cooling models (David et al. 2001;
Peterson et al. 2001; Peterson & Fabian 2006). The im-
plication is that the central gas must be re-heated. The
source of this heating, and understanding when and how
it takes place, has recently been a major topic of study. A
promising candidate is feedback from energy injection by
the central AGN of the cD galaxy (e.g., Churazov et al.
2001; Churazov et al. 2002; for a review see McNamara
& Nulsen 2007). However, the details of this interaction,
and how the energy is transferred from the jets to the
ambient ICM, are poorly understood.
provide an excellent opportunity to study heating and
other non-gravitational processes in the ICM. Although
Galaxy groups
1Harvard-Smithsonian Center for Astrophysics, 60 Garden
St., Cambridge, MA 02138, USA; srandall@cfa.harvard.edu
2INAF/IRA, via Gobetti 101, I-40129 Bologna, Italy
3Department of Astronomy, University of Virginia, P.O. Box
400325, Charlottesville, VA 22901, USA
4Max-Planck-Institut f¨ ur Astrophysik, Karl-Schwarzschild-
Strasse 1, 85741 Garching, Germany
5Space ResearchInstitute
Moscow 117810, Russia
6Physics & Astronomy Department, Michigan State Univer-
sity, East Lansing, MI 48824-2320, USA
7Institute for Astrophysical Research and Astronomy Depart-
ment, Boston University, 725 Commonwealth Avenue, Boston,
MA 02215, USA
8KIPAC, Stanford University, 452 Lomita Mall, Stanford, CA
94305, USA
(IKI), Profsoyuznaya84/32,
not as X-ray luminous as clusters, the effects of heating
are more readily apparent in groups, due to their lower
gas temperatures, masses, and central densities. For ex-
ample, the gas to total mass fraction in groups ranges
from 0.02–0.07, with a scatter of ∼ 2 at a fixed tem-
perature within r2500. The scatter is tightly correlated
with the central entropy (Gastaldello et al. 2007; Sun et
al. 2009), reflecting the greater role of non-gravitational
processes in the centers of groups as compared to clus-
ters.
In this paper, we report on Chandra observations of
NGC 5813 (UGC 09655), a bright (MV = −22.01, Lauer
et al. 2007) E1 galaxy. It is the central dominant mem-
ber of a subgroup (which we shall call the NGC 5813
galaxy group) in the NGC 5846 galaxy group (Mahdavi
et al. 2005). NGC 5846 and NGC 5813 have a projected
separation of 79.7?(740 kpc). This group is relatively iso-
lated, lying well off the plane of the Local Supercluster.
Both the NGC 5813 and NGC 5846 galaxy groups are
members of the ROSAT-ESO Flux-Limited X-ray (RE-
FLEX) galaxy cluster catalog (B¨ ohringer et al. 2004).
Detailed Hubble Space Telescope (HST) observations re-
veal that NGC 5813 contains a relatively undisturbed
dusty circumnuclear disk (Tran et al. 2001), suggesting
that this galaxy has not recently experienced a major
merger. Emsellem et al. (2007) classify NGC 5813 as a
“slow rotator” galaxy which, they argue, represents the
extreme evolutionary end point reached in deep poten-
tial wells, consistent with this object being a dynam-
ically old galaxy at the center of a galaxy subgroup.
NGC 5813 contains a 2.8 × 108M? supermassive black
arXiv:1006.4379v2 [astro-ph.CO] 26 Jul 2010

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2RANDALL ET AL.
hole (SMBH), and an associated AGN that is a known
radio source (e.g., Balmaverde & Capetti 2006; Maglioc-
chetti & Br¨ uggen 2007).
We report here on a 150 ksec combined observation of
NGC 5813 with the Chandra X-ray Observatory, an anal-
ysis of archival multi-frequency Very Large Array (VLA)
observations, Hα observations with the Southern Astro-
physics Research Telescope (SOAR), and on some initial
results from low frequency Giant Metrewave Radio Tele-
scope (GMRT) radio observations. We focus on three
main results:
1. The ICM in NGC 5813 shows clear signatures from
three distinct AGN outbursts, with three pairs of
roughly collinear cavities and unambiguous shocks
with measured temperature jumps associated with
the inner and intermediate cavities.
2. The mean power of the two most recent outbursts
differs by a factor of six, from 1.5–10×1042erg s−1,
even in this otherwise dynamically relaxed system,
indicating that the mean jet power varies over long
(∼ 107yr) timescales.
3. The heating from shocks alone is sufficient to offset
radiative cooling locally (within at least 10 kpc),
without requiring the internal energy of the X-
ray cavities. The heating is roughly isotropic, and
strongest near the AGN where the shock Mach
numbers are larger, which is the region of inter-
est for regulating feedback between the ICM and
the central SMBH.
We assume an angular diameter distance to NGC 5813
of 32.2 Mpc (Tonry et al. 2001), which gives a scale
of 0.15 kpc/??for Ω0 = 0.3, ΩΛ = 0.7, and H0 =
70 km s−1Mpc−1. All uncertainty ranges are 68% con-
fidence intervals (i.e., 1σ), unless otherwise stated.
2. OBSERVATIONS AND DATA REDUCTION
2.1. Chandra Observations
NGC 5813 was originally observed with Chandra on
April 2, 2005, for 49 ksec (ObsID 5907) with the Chan-
dra CCD Imaging Spectrometer (ACIS), pointed such
that the galaxy was centered on the back-side illuminated
ACIS-S3 CCD (the ACIS-S1 as well as the front-side
illuminated ACIS-I3 and ACIS-S2 CCDs were also ac-
tive). It was subsequently observed for 100 ksec on June
5, 2008 (ObsID 9517) with the same chip configuration.
These data were reduced using the method described in
Randall et al. (2008). All data were reprocessed from
the level 1 event files using the latest calibration files
(as of CIAO4.2). CTI and time-dependent gain cor-
rections were applied. lc clean was used to remove
background flares9. The mean event rate was calculated
from a source free region using time bins within 3σ of
the overall mean, and bins outside a factor of 1.2 of this
mean were discarded. There were no periods of strong
background flares. The resulting cleaned exposure times
were 48.7 and 99.6 ksec, respectively.
Diffuse emission from NGC 5813 fills the image FOV
for each observation. We therefore used the CALDB10
9http://asc.harvard.edu/contrib/maxim/acisbg/
10http://cxc.harvard.edu/caldb/
blank sky background files appropriate for each obser-
vation (including the new “period E” files for the more
recent observation), normalized to our observations in
the 10-12 keV energy band. To generate exposure maps,
we used a MEKAL model with kT = 0.7 keV, Galac-
tic absorption, and abundance of 30% solar at a redshift
z = 0.006578, which is consistent with typical results
for the extended emission from detailed spectral fits (see
§ 4).
The exposure corrected, background subtracted, 0.3–
2 keV Chandra image is shown in Figure 1. To enhance
the visibility of the diffuse emission, bright point sources
were removed, and the regions containing point sources
were “filled in” using a Poisson distribution whose mean
was equal to that of a local annular background region.
A close-up of the core in Figure 2 shows small-scale struc-
ture in the center, while the more heavily smoothed im-
age in Figure 3 shows structure in the fainter outer re-
gions. We discuss the main features in these images in
§ 3.
All X-ray spectra were fitted in the 0.6–3.0 keV band
and grouped to a minimum of 40 counts per spectral
bin. The absorption was fixed to the Galactic value of
NH = 4.37 × 1020cm−2(Kalberla et al. 2005). Vary-
ing the absorption from the Galactic value did not sig-
nificantly improve the fit.
abundance ratios were assumed throughout, unless oth-
erwise stated. Temperature maps were derived using the
method of Randall et al. (2008). For each temperature
map pixel, we extracted a spectrum from a circular re-
gion containing a minimum number of net counts (af-
ter subtracting the blank sky background) in the 0.6 –
3.0 keV band. The resulting spectrum was fitted with an
absorbed apec model using xspec, with the abundance
allowed to vary.
Anders & Grevesse (1989)
2.2. Radio Observations
NGC 5813 was observed with the GMRT at 235 MHz,
as part of a larger, ongoing project (Giacintucci et al.
2009; Giacintucci et al. 2010). The observations were
carried out in August 2008 for a total of 100 minutes on
source. The NRAO Astronomical Image Processing Sys-
tem (AIPS) package was used for the data reduction and
analysis. The visibilities were inspected and edited to
identify and remove bad data. After the initial calibra-
tion, phase-only self-calibration was applied to remove
residual phase variations. Multi-field imaging was im-
plemented in each step of the data reduction. The rms
noise level (1σ) achieved in the image is 0.3 mJy/beam.
We refer to Giacintucci et al. (2010) for a detailed de-
scription of the data reduction and analysis.
We also include results from an analysis of archival
VLA observations at multiple frequencies. Data calibra-
tion and imaging were carried out in AIPS following the
standard procedure (Fourier-transform, Clean and Re-
store). Phase-only self-calibration was applied to remove
residual phase variations and improve the quality of the
image. The properties of the VLA and GMRT radio ob-
servations are summarized in Table 1.
2.3. Hα Observations
Narrow-band Hα imaging observations were made with
the SOAR Optical Imager (SOI) on July 6, 2008 (UT).

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N5813 FROM CHANDRA3
The night was clear and photometric.
narrow-band filters were used, 660075-4 for the Hα+[NII]
lines and 6129/140 for the continuum. Three 15-minute
exposures were taken with the 660075-4 filter and three
12-minute exposures were taken with the 6129/140 filter.
Spectroscopic standard stars were EG274 and LTT7987.
More detail on the SOI data reduction can be found in
Sun et al. (2007).
Two CTIO
3. X-RAY CAVITIES AND SHOCKS
As we discuss in detail in this paper, the X-ray im-
ages show signatures from three episodes of AGN ac-
tivity. There are two clear pairs of cavities distributed
collinearly (in a direction roughly parallel to the minor
axis of the elliptical optical isophotes) and symmetri-
cally about the galaxy center, each pair associated with
a shock. In addition, we argue for a third pair of cavi-
ties at larger radii (along roughly the same line) and an
associated third surface brightness edge, which may be a
weak shock. In detail, we see the following:
1. A pair of inner cavities at ∼ 1.4 kpc, inflated by
the most recent AGN outburst about 3 × 106yr
ago (Figure 2). The cavities are surrounded by
bright rims of emission, similar to what is seen in
other systems (e.g., the Perseus Cluster Fabian et
al. 2003, M87 Forman et al. 2007; M84 Finoguenov
et al. 2008, Abell 2052 Blanton et al. 2009; see
Figure 2), though here we find the rims to be hotter
than the ambient gas, whereas in other systems
they are typically cooler. We identify the sharp
edge in the rims, 1.4 kpc southeast of the AGN,
as a shock, which we refer to as the 1.5 kpc shock,
with a Mach number of M = 1.7 (see § 5.1). The
rims overlap to form an indented structure to the
northwest. The northeastern inner cavity has an
irregular morphology, possibly due to the wall of
the cavity being “punched through” by the AGN
jet.
2. A pair of intermediate cavities at ∼ 8 kpc, inflated
by a previous AGN outburst about 2 × 107yr ago
(Figure 1, Figure 4). The southwestern cavity has a
regular morphology, while the northeastern cavity
is more extended in the radial direction and may
be a double “Russian doll” cavity (e.g., as in M84,
Finoguenov et al. 2008). The intermediate cavi-
ties lie just inside a sharp, elliptical edge, which
we identify as a shock (and refer to as the 10 kpc
shock) with M = 1.5 (see § 5.1).
3. A faint pair of outer cavities, at ∼ 20 kpc, inflated
by a previous outburst about 9 × 107yr ago (Fig-
ure 3, Figure 4). The northeastern outer cavity
is surrounded by a rim of brighter emission, while
the southwestern outer cavity is a weaker feature
(see § 5.3). The outer cavities are associated with
a weak outer edge-like feature at ∼ 25 kpc (Fig-
ure 3), just past the outer edges of the cavities.
This feature may represent an old shock, or a tran-
sition region from the galaxy atmosphere to the
extended group atmosphere (see § 5.2).
4. A central point source, offset ∼ 0.5 kpc southeast of
the axis defined by the cavities (Figure 2), with an
X-ray luminosity of LX= 1.6×1039erg s−1in the
0.3 – 12.0 keV rest frame energy band. Although
this source is quite faint, we identify it as the AGN
that has inflated the X-ray cavities and driven the
shocks in the ICM due to its central location and
detection in the radio (see § 4.2.5)
Since it is difficult to show all the cavities simultaneously
in the same image, we divided the X-ray image by a β-
model to better show surface brightness fluctuations over
a wider dynamic range. The resulting image is shown in
Figure 4, with the cavities indicated by overlaid regions
for clarity. The overall morphology of NGC 5813 is re-
markably symmetric and regular, suggesting that AGN
feedback maintains a near “steady state” through regular
outbursts in an otherwise undisturbed system (consistent
with optical studies that also conclude NGC 5813 is dy-
namically old, Tran et al. 2001; Emsellem et al. 2007).
3.1. Radio Emission from the X-ray Cavities
Radio contours from our 235 MHz GMRT observations
(green) and archival 1.36 GHz VLA observations (blue)
are shown overlaid on the Chandra image of the core
in Figure 5. Extended radio emission at 1.36 GHz fills
the inner cavities, while the 235 MHz emission overfills
the cavities, extending along the axis of symmetry of
the cavities (this extension is real, and not due to the
larger beam size at 235 MHz). The intermediate cavi-
ties are filled with 235 MHz radio emission, but show no
emission at 1.36 GHz. The intermediate cavities are also
not detected at 1.4 GHz in the NRAO VLA Sky Survey
(NVSS, which has a beam size of 45??) or at 1.36 GHz in
archival VLA C array configuration observations (see Ta-
ble 1). The outer cavities, which are outside the FOV of
Figure 5, do not show any detected radio emission. The
radio images are therefore qualitatively consistent with
what is expected for intermittent AGN outbursts, where
the electrons contained in the cavities age due to syn-
chrotron, inverse Compton, and adiabatic losses as the
cavities rise buoyantly after the outburst phase. The cen-
tral cavities contain recently accelerated electrons, which
emit at high and low frequencies, while older cavities
contain older electron populations with fewer energetic
particles and weaker high frequency emission.
4. THE THERMAL STRUCTURE OF THE GAS
4.1. Temperature Map
The X-ray image (Figure 1) shows complicated struc-
ture in the ICM, which fills the FOV. To study the ther-
mal structure of the ICM, we generated a temperature
map, requiring 1500 net counts per extraction region.
The resulting temperature map, with the X-ray cavity
regions overlaid, is shown in Figure 6. The corresponding
pseudo-pressure and pseudo-entropy maps are shown in
Figure 7. The extraction radii range from 2.8??(0.4 kpc)
in bright regions near the core to 59??(9 kpc) in faint
outer regions. The temperature uncertainties are be-
tween 2% – 3% across the map.
The temperature map shows that even in the pro-
jected, effectively smoothed map, the hot (0.7–0.75 keV)
10 kpc shocks are visible at the location of the promi-
nent surface brightness edges. The pseudo-pressure map
also shows large jumps across the edges, consistent with

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4 RANDALL ET AL.
these features being shock fronts. There is a trail of cool
0.55 keV gas though the galaxy center, along the line
defined by the X-ray cavities indicated in Figure 1, ter-
minating at the edges of the intermediate cavities (we
discuss this feature further in § 5.4). The kT ∼ 0.65 keV
gas extends to larger radii (out to ∼ 27 kpc) in the east-
northeast, coincident with the extension of diffuse emis-
sion across the outer edge in Figure 3. East of this exten-
sion, the temperature rises rapidly from about 0.65 keV
to 0.75 keV over ∼ 7 kpc.
To study the detailed structure in the core, we made a
higher angular resolution temperature map of the central
region of NGC 5813. In addition to the finer spatial bin-
ning, each extracted spectrum had only 1000 net counts,
giving smaller extraction radii (and thus less smoothing
in the map), ranging from 0.4 kpc to 1.8 kpc. The result-
ing temperature map is shown in Figure 8, and the corre-
sponding pressure and entropy maps in Figure 9, with the
0.3–2.0 keV X-ray surface brightness contours overlaid.
The bright rims surrounding the innermost bubbles are
revealed to contain relatively hot (kT ≈ 0.7 keV), high
pressure gas, in contrast to the cool bubble rims seen in
some other systems (e.g., the Perseus Cluster, Fabian et
al. 2003; M87, Forman et al. 2007; Abell 2052, Blanton
et al. 2009). The gas in the rims has likely been shock
heated by a recent AGN outburst, which has rapidly in-
flated the innermost cavities.
4.2. Detailed Spectral Analysis
4.2.1. Azimuthally Averaged Profiles
We produced projected radial profiles by fitting spec-
tra extracted from concentric annuli, centered on the cen-
troid of the diffuse emission at larger radii. Each annular
bin was fitted with an absorbed apec model, with the
abundance allowed to vary. The resulting temperature
profile is shown in the top panel of Figure 10. There
is a temperature increase of ∼ 0.05 keV at ∼10 kpc,
at the location of the surface brightness edges indicated
in Figure 1, unambiguously identifying these features as
shocks. Additionally, there is an inner temperature jump
of ∼ 0.06 keV at ∼2 kpc, at the location of the bright
rims around the inner bubbles, consistent with the core
temperature map shown in Figure 8. Although the point
source presumed to be the central AGN has been ex-
cluded, the temperature profile shows a strong central
spike. This is because the profile center is in the region
of the hot overlapping rims of the central cavities, shown
in Figure 2.
4.2.2. Deprojection Analysis
To determine the 3D structure of the ICM we per-
formed a deprojection analysis using concentric annuli as
in § 4.2.1, but with bins 2–3 times larger to provide ad-
equate statistics for the deprojection analysis. We used
the “onion peeling” method (employed, e.g., by Fabian
et al. 1981, Blanton et al. 2003) to derive deprojected
profiles. First, the projected temperature, abundance,
and xspec normalization are determined by fitting an
absorbed apec model to the outermost annulus. Fits to
spectra from annuli at smaller radii are then determined
by adding an additional component for each outer annu-
lus, with fixed temperature and abundance, and a nor-
malization scaled to project from the outer to the inner
annulus, assuming spherical symmetry. We note that this
procedure does not correctly account for the uncertain-
ties, since the contributions from outer shells are fixed.
This method was adopted instead of simultaneously fit-
ting spectra in all of the bins (e.g., with the projct
model in xspec) to prevent spectra at small radii, where
the spherical symmetry approximation is less accurate,
influencing the fitting results at large radii. A compari-
son of the two methods shows that while the best-fitting
temperature profile is not significantly affected, the den-
sity profile determined with the projct model differs
somewhat from the profile we present here and shows a
∼50% increase in density with radius between 6–9 kpc
(in the region of the intermediate bubbles and 10 kpc
shock front). Thus, while the azimuthally averaged de-
projected temperature profile is not significantly affected
by the assumption of spherical symmetry, the density
profile is sensitive to this assumption and is therefore
only approximate.
As a further check on the deprojection, we performed
an independent analysis, with the data analyzed as de-
scribed in Vikhlinin et al. (2005) and the deprojection
method described in Churazov et al. (2008, 2010). This
method accounts for emission at large radii by assum-
ing a power law density profile for emission outside of
the FOV and fitting the normalization of this component
along with the fluxes from spherical shells. The derived
temperatures agreed within the 1σ confidence range, and
the temperature jumps were fully consistent within the
uncertainties.
In the case of NGC 5813, measuring the deprojected
abundance profile is extremely difficult. This is because
at these relatively low gas temperatures (0.6–0.7 keV)
the spectral resolution of the ACIS instrument is such
that there is a strong degeneracy between line emission
(which determines the abundance) and continuum emis-
sion (which determines the electron density). When this
effect is accumulated across several shells and projected
onto the inner shells, the inner abundances are essentially
indeterminate, leading to a highly uncertain density pro-
file. Furthermore, determining abundances in multiphase
gas is a known problem (e.g., Buote 1999; Rasia et al.
2008). We therefore fixed the abundance at 50% solar,
which is an average value from the projected profile fits.
The resulting deprojected (red triangles) and projected
(black circles) temperature profiles are shown in the top
panel of Figure 10, alongside the corresponding density,
pressure, and entropy profiles. The entropy is taken to be
S = kTn−2/3
e
and the pressure P = nkT, where neis the
electron density and n = 1.8ne. The most significant ef-
fect of the deprojection on the temperature profile is the
lower temperature of the gas at ∼5 kpc (0.55 keV ver-
sus 0.61 keV) once the projection effects from the outer
shock-heated gas have been removed, as well as a signif-
icant increase in the central temperature (from 0.65 keV
to 0.7 keV). Note that in these plots the shock front
edges are smeared over multiple bins since they are not
spherically symmetric with respect to the galaxy center.
4.2.3. Temperature Profile Across the Shocks
The azimuthally averaged temperature profiles (Fig-
ure 10) and projected temperature (Figure 6) map show
temperature rises at the location of the surface bright-

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N5813 FROM CHANDRA5
ness edges, characteristic of shock fronts. We therefore
extracted spectra in sectors across these edges to bet-
ter characterize the temperature jumps. Each sector was
centered on the center of curvature defined by the cor-
responding edge, which is not coincident with the cen-
tral position used to extract the azimuthally averaged
profiles. The extraction regions were truncated at small
radii to avoid the complex structure in the central re-
gion (additionally, the assumption of spherical symmetry
breaks down at small radii since the centers of curvature
are not coincident with the overall centroid of the diffuse
emission). The projected and deprojected temperature
profiles are shown in Figure 11. The northwestern region
shows higher overall temperatures and a larger temper-
ature jump of ∼ 0.15 keV as compared to ∼ 0.1 keV in
the southeast (where we estimate the size of the jumps
by extrapolating the base-line deprojected temperature
increase on either side of the temperature peak, roughly
from r < 10 kpc and r > 18 kpc). The lower tempera-
tures in the southeast are likely due in part to the east-
northeast extension of cool gas seen in the temperature
map (§ 4.1), which overlaps with the extraction annuli.
4.2.4. Total Diffuse Emission
To accurately determine the weighted average prop-
erties of the diffuse gas, we extracted and fitted spec-
tra for the total diffuse emission within 2.9?(27 kpc).
We initially fitted the spectra with a single apec model.
The resulting model showed residuals near the 1.8 keV
Si and 2.46 keV S lines, possibly indicating non-solar
abundance ratios. We therefore fit the spectra with a
vapec model with the abundances of O, Ne, Mg, Si, S,
and Fe allowed to vary independently (other elements
were not well constrained and were fixed at 1/2 the
solar abundance, except He which was fixed at solar).
The resulting fitted abundance values were 0.8 – 1.0 so-
lar, with Si and S having somewhat larger values than
Ne and Mg, except for O (ZO = 0.35 ± 0.03) and Fe
(ZFe= 0.65±0.03). Since the total diffuse emission is ex-
pected to include emission from gas at multiple tempera-
tures, we added a second vapec component to the model
and tied individual abundances for the two components
together. This model provided a much improved fit, with
abundance values of ZO = 0.13+0.03
ZMg= 0.65 ± 0.04, ZSi= 0.78 ± 0.04, ZS= 0.94 ± 0.08,
and ZFe = 0.53 ± 0.03. The fitted temperatures were
kT1= 0.35+0.03
ing a power-law component in each of the above models,
but in no case did this addition improve the fit (even if
the photon index was fixed at a typical value of 1.5 for
an unresolved LMXBs population) or tightly constrain
the photon index. This suggests that emission from un-
resolved LMXBs is not significant in this energy band.
We note that the above results depend somewhat on the
adopted abundance table. If we adopt the updated abun-
dance table of Grevesse & Sauval (1998), we find that Fe
is no longer under-abundant compared to the other ele-
ments, with ZFe, ZS, and ZSiall roughly 0.7 solar, and
ZNe and ZMg about 0.6 solar. O is still found to be
under-abundant, with ZO = 0.16+0.04
in the fitted value for ZFewas noted previously, e.g., by
Humphrey et al. (2004).
As a further check of this result, we examined data
−0.02, ZNe = 0.59+0.05
−0.04,
−0.01and kT2= 0.671+0.011
−0.007. We tried includ-
−0.03. This difference
from XMM-Newton RGS observations, which has bet-
ter spectral resolution in the region of the O lines. The
processing of the RGS data is described in Werner et
al. (2009). We fitted the spectrum from a 1?wide re-
gion centered on the core of NGC 5813 between 10–25˚ A
with a collisionally ionized plasma (cie) model with two
cooling flow components, one to account for gas cooling
down to 0.4 keV and a second to account for gas cool-
ing to lower temperatures. The abundances were con-
strained to be equal across each model component. We
found best-fitting abundance values of ZFe= 0.60±0.06,
ZO= 0.44±0.06, and ZNe= 0.42±0.06. Although this
gives a higher ZO/ZFeratio (0.7 versus 0.2 from Chan-
dra), O is still found to be under-abundant as compared
to Fe. We conclude that there is evidence for non-solar
abundance ratios in the diffuse ICM, with the most ro-
bust result being a decreased O abundance relative to
solar. Similar sub-solar values for ZO/ZFehave been re-
ported for other galaxy groups, massive elliptical galax-
ies, and clusters of galaxies, and imply a greater rela-
tive enrichment from Type Ia supernovae as compared
to Type II (e.g., Finoguenov et al. 2000; Finoguenov et
al. 2001). However, sub-solar ZO/ZFe values are diffi-
cult to reconcile with the larger ZSi/ZFe and ZS/ZFe
abundance ratios when one tries to apply SN enrich-
ment models to explain the observed ICM abundances
(see Humphrey et al. 2004 and references therein for a
discussion).
4.2.5. The Central Source
NGC 5813 contains a central X-ray point source, vis-
ible in Figure 2. We extracted a spectrum for the cen-
tral source using an aperture with a radius of 1.5??and
a background determined from a local annular region.
The spectrum, which had 550 counts in the 0.6–5.0 keV
band, was fitted with an absorbed power-law, giving a
best-fitting photon index of Γ = 1.5+0.5
X-ray luminosity is LX = 1.6+0.8
the 0.3 – 12.0 keV rest frame energy band (90% con-
fidence ranges). We calculated the radio luminosity be-
tween 10 MHz and 100 GHz using archival VLA A array
configuration observations of the core at 1.49 GHz and
4.86 GHz. This gave a spectral index of αr= 0.35 and
a luminosity of LR= 1 × 1036erg s−1. Even though the
spectral index indicates a relatively flat spectrum for a
core AGN, giving a larger estimate of the broad band lu-
minosity than would a steeper spectrum, the calculated
luminosity is still two orders of magnitude fainter than
the faintest source in the sample of systems containing
X-ray cavities given in Bˆ ırzan et al. (2008). However,
they mainly consider sources at the cores of galaxy clus-
ters, which are higher mass systems than the subgroup
we consider here.
Although the central source is X-ray faint enough to
be classified as an ultraluminous X-ray source (ULX), we
identify it as the AGN that has inflated the X-ray cavi-
ties and driven the shocks in the ICM due to its central
location and detection in the radio (see Figure 5). Its
low luminosity identifies this source as a low luminosity
AGN, which typically have LX< 1×1042erg s−1(Ptak
2001). This suggests that the source is either faint yet
mechanically powerful, in a quiescent state after having
recently had an outburst that inflated the inner X-ray
−0.6. The nuclear
−0.5× 1039erg s−1in

Page 6

6 RANDALL ET AL.
cavities, or heavily obscured (allowing the absorption to
vary gave a value that was 4 times Galactic, although the
fit was not improved and the absorption was consistent
with the Galactic value to within 1σ).
5. DISCUSSION
5.1. Structure of the Shock Fronts
The hard band image, temperature and pressure maps,
and deprojected temperature and pressure profiles iden-
tify the prominent surface brightness edges around the
intermediate cavities as shock fronts. To quantitatively
study the structure of these shocks, we extracted the 0.3-
2.0 keV surface brightness profiles from the sectors used
to derive the temperature profiles shown in Figure 11.
Note that the profiles are defined by the centers of cur-
vature of the 10 kpc shocks, which do not coincide with
the location of the central AGN. The profiles were then
converted to integrated emission measure (IEM) profiles,
using the temperatures from the projected temperature
profile shown in Figure 11, with the abundance fixed at
50% solar (roughly the average from projected profile fits
in this region, see § 4.2.2). The resulting IEM profiles are
shown in Figure 12. Each profile shows a sharp edge at
∼13 kpc. Following our previous work (Vikhlinin et al.
2001; Randall et al. 2009a, 2009b), we fit the profiles
by projecting a 3 dimensional density profile consisting
of two power laws, connected by a discontinuous break,
or “jump”. The free parameters were the normalization,
the inner (α) and outer (β) power law slopes, the position
of the density discontinuity (bbreak), and the amplitude
of the jump (A).The best-fitting model is shown as
the solid lines in Figure 12, with the fitted break radii
indicated by the vertical dashed lines. The best fitting
inner density jumps for the northwest and southeast sec-
tors are Anw = 1.75+0.04
ing the Rankine-Hugoniot shock jump conditions for a
γ = 5/3 gas implies Mach numbers of Mnw= 1.53 and
Mse= 1.48, and temperature jumps by the same factor
as the Mach numbers. The predicted temperature jumps
are greater than the temperature jumps of ∼ 1.2 detected
in the deprojected temperature profiles (Figure 11). We
discuss this discrepancy below.
The core temperature map (Figure 8) and the az-
imuthally averaged temperature profile (Figure 10) show
evidence for shock heated gas in the bright rims sur-
rounding the innermost bubbles, about 1 − 2 kpc from
the central AGN. The X-ray image of the core (Figure 2)
shows a sharp contrast between the bright bubble rims
and the surrounding gas, with the sharpest edge to the
southeast. We extracted the surface brightness profile
in a 52◦wide sector across the southeastern edge, cen-
tered on the AGN, and fit the IEM profile with a broken
power law density model as above. To the northwest,
the morphology is more complicated, with the two rims
meeting to form an indented structure. Since this struc-
ture is not well-modeled by our assumption of spherical
symmetry we did not fit the IEM profile to the north-
west. There were too few counts to accurately measure
the temperature profile across the southeast, so we as-
sumed an isothermal gas with kT = 0.6 keV and 50% so-
lar abundance. The resulting IEM profile, along with the
best fitting model, is shown in Figure 13. The deviant
point at 2 kpc is due to small-scale clumpiness in the
−0.03and Ase = 1.69 ± 0.07. Us-
ICM, visible in the X-ray image. We find a density jump
of 1.97 ± 0.12, which corresponds to a M = 1.71 ± 0.1
shock with a temperature jump of 1.72 ± 0.12. Unfortu-
nately, there are too few counts to derive a deprojected
temperature profile to compare to the inferred temper-
ature jump, although the corresponding inner jump in
the azimuthally averaged temperature profile of about
1.1 (Figure 10) is much smaller than the jump of 1.7 pre-
dicted from the density discontinuity. To better quantify
the temperature jump across the 1.5 kpc shock, we ex-
tracted a spectrum of the total emission from the post-
shock region in the core wedge used to fit the surface
brightness profile, and from a similar sized region in the
same wedge just outside the shock edge. We find that
the (inner) post-shock region is best fit by a two temper-
ature thermal model, with best-fitting temperatures of
kT1= 0.64+0.03
region is adequately described by a single thermal model
with kT = 0.5±0.01. If we assume that the two thermal
components in the post-shock region give the tempera-
tures of the shocked gas and local projected pre-shocked
gas this gives a temperature jump of 1.5 ± 0.3. This is
consistent with a temperature jump of 1.7 as expected
from the Mach number, although the large uncertainties
limit the usefulness of this comparison. The properties of
the 10 kpc and 1.5 kpc shocks are summarized in Table 2.
For both the 1.5 kpc and 10 kpc shocks, the observed
temperature rise is less than what is expected based on
the Mach number, even in the deprojected temperature
profiles. To better estimate the expected measured tem-
perature rise associated with the shocks we ran 1D hydro-
dynamical simulations to fully model their evolution. For
the 10 kpc shocks, the simulations start with an isother-
mal sphere with kT = 0.67 and a power law density pro-
file, in hydrostatic equilibrium. The logarithmic slope of
the density profile was taken to be 1.46, which was deter-
mined by fitting the slope of the surface brightness pro-
file beyond the 10 kpc shocks. The shocks were initiated
by a central point explosion and allowed to propagate
freely. Since the gas is initially isothermal with a power
law density profile, the simulations are scale free, so we
can choose the point of evolution at which the code best
reproduces the observed surface brightness jump at the
shock front and scale accordingly. The resulting Mach
number for the 10 kpc shocks is M = 1.52, in excellent
agreement with what was found above by fitting a discon-
tinuous power law density model to the integrated emis-
sion measure profile. The expected projected tempera-
ture profile is shown in Figure 14. The solid lines show
the emission weighted temperature (with 90% confidence
ranges) and the points show single temperature fits to
more accurately simulated model spectra folded through
the Chandra response (the discrepancy between emission
weighted temperatures and fitted temperatures for multi-
temperature gas has previously been noted by Mazzotta
et al. 2004). The simulations predict a projected temper-
ature rise of ∼ 0.1 keV, consistent with observations (see
Figure 10). Similar simulations fit to the 1.5 kpc shock to
the southeast predict a measured projected temperature
rise of ∼ 30%, consistent with observations (although the
observational uncertainties are large). We conclude that
the projected temperature profiles are consistent with
the calculated Mach numbers (although the temperature
−0.04and kT2= 0.97+0.21
−0.17, while the pre-shock

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N5813 FROM CHANDRA7
structure of the 1.5 kpc shock is poorly constrained).
The deprojected temperature measurements cannot re-
solve the temperature jump due to the narrow width of
the shock and the rarefied cool gas behind the shock (the
temperature of which drops slightly below the ambient
temperature in our isothermal simulations).
5.2. The Outer Edge at 25 kpc
There is a weak surface brightness edge (most clearly
seen in Figure 3) surrounding most of NGC 5813 at a dis-
tance of ∼160??(25 kpc) from the central AGN. To check
the significance of this feature we extracted the surface
brightness profile across this edge in two sectors, one to
the northwest between 12◦- 79◦(measured north from
west, the same angular range spanned by the bright sec-
tion of the elliptical edge to the northwest) and a wider
wedge between 206◦- 320◦to the south. The wedges
were chosen to match the curvature of the outer edge,
so that the profiles were off center from the peak of the
overall diffuse emission. The resulting surface brightness
profiles are shown in Figure 15. Both profiles show a sim-
ilar change in slope at ∼ 170??(26 kpc), at the position
of the outer edge, and the northwestern profile shows a
sharp jump at the same location. We conclude that the
outer edge-like feature indicated in Figure 3 is real, and
corresponds to a change in slope and possibly a discon-
tinuity in the surface brightness profile. The edge lies
just beyond the outer X-ray cavities indicated in Fig-
ure 3, and the association is reminiscent of the 1.5 kpc
and 10 kpc shocks to the inner and intermediate cavities.
The discontinuous jump is also stronger in the northwest
than in the south, consistent with what is seen for the
elliptical 10 kpc shock front edge. It may therefore rep-
resent the weak remnants of a shock associated with this
older outburst.
To determine the nature of this edge, we fit the surface
brightness profile in the wedge to the the south, where
this feature is the sharpest. Although there is a signif-
icant surface brightness discontinuity to the northwest
(see Figure 15), we focus on the wedge to the south, since
we have better statistics in the wider southern wedge,
and since the shape of the northwestern discontinuity
is not well-described by our shock model density pro-
file (compare the profile shapes in Figure 15 and in Fig-
ure 12). The shape of the surface brightness profile is
obviously not well-described by a single power-law, and
modeling this profile with a projected power-law density
model did not provide an acceptable fit. We also fit the
profile with a β-model density profile, which gave a poor
fit with χ2
ν= 13.9/6. The fitted model showed asymmet-
ric residuals in the region of the surface brightness edge,
so we tried fitting the edge with a projected discontin-
uous power-law density model, as in § 5.1. This gave
an improved fit, with χ2
ν= 0.4/4, and a density jump
factor of Aouter = 1.06+0.12
The inner and outer slopes of the density profile were
α = −0.62+0.09
there were inadequate statistics to measure the temper-
ature and abundance profiles across this outer edge and
confirm it as an old shock. In particular, the edge could
in principle be a metallicity edge, or the interface be-
tween the galaxy atmosphere and the extended group
atmosphere (where one would expect to see a change in
−0.13, consistent with no jump.
−0.18and β = −2.30+0.25
−0.32. Unfortunately,
slope of the surface brightness profile). We conclude that,
while the outer edge is consistent with an old shock with
M ≈ 1.1 associated with the outermost X-ray cavities,
the data are also consistent with no density jump and
further observations are needed to determine its nature.
5.3. The X-ray Cavities
The X-ray image shows three pairs of roughly collinear
cavities (Figure 1, Figure 4). Although most of the cav-
ities are clear, the outermost cavities (in particular, the
southwestern outer cavity) are weak features. To check
their significance, we extracted surface brightness profiles
across each outer cavity, centered on the overall diffuse
emission. The resulting profiles are shown in Figure 16.
Each profile shows a significant dip at the location of the
outer cavities. The profile across the northeastern cav-
ity also shows a significant hump just beyond the cavity
dip, corresponding to the bright outer rim seen in the X-
ray images. For the southwestern outer cavity, the rise
just outside the cavity is less pronounced, since it lacks a
bright rim. We conclude that the faint outer southwest-
ern cavity indicated in Figure 3 is likely a real feature
and represents a paired cavity to the outer northeastern
cavity, each initially created by the same AGN outburst
from the central SMBH.
Each of the three pairs of X-ray cavities in NGC 5813
is likely associated with a distinct AGN outburst. Al-
though the position angle of the inner and intermediate
cavity pairs appears to vary slightly, by about 10◦- 15◦,
possibly indicating that the central black hole that has
inflated the cavities is precessing, the cavities are roughly
collinear.The fact that the cavities are regular and
collinear suggest that they have evolved passively, i.e.,
have not been disturbed by gas motions due to sloshing,
turbulence, mergers, etc., consistent with previous con-
clusions on the dynamical state of this system (Tran et
al. 2001; Emsellem et al. 2007). Measuring the proper-
ties of these cavities is therefore of great interest, since
a comparison of the different pairs will provide informa-
tion on how the cavities evolve, and on the outburst his-
tory of the central AGN (in particular, we want to know
whether the outbursts have a similar total energy output
and mean power, as might be expected in a near “steady
state” AGN feedback model, or whether the outbursts
change significantly even in an otherwise apparently re-
laxed system like NGC 5813).
5.3.1. Cavity Ages and Energies
Table 3 summarizes the properties of the X-ray cav-
ities, which are shown as overlaid regions in Figure 4.
We assume that the cavities rise in the plane of the sky,
that the mass of material within the cavities is negligible,
and that each cavity has a spherical or oblate spheroidal
geometry with the minor axis in the plane of the sky.
The former assumption is suggested by the fact that the
cavities are detected in the image, and that the inner
two pairs are near the same projected radii as their as-
sociated shock fronts. If the global gas distribution was
significantly extended along the line of sight, with the
bubbles rising along this extension, they would be diffi-
cult to detect for large inclination angles of the extension
due to the large column of cool gas at smaller radii be-
hind (or in front of) the bubbles (see Bˆ ırzan et al. 2009).

Page 8

8 RANDALL ET AL.
Columns 2 & 3 in Table 3 give the cavity major and mi-
nor axis, respectively, and Column 4 gives the distance
from the AGN to the center of the cavity. The rise time
of the cavities, given in Column 5, is calculated assum-
ing that they rise buoyantly at half the sound speed cs,
similar to what is found from simulations (e.g., 0.6–0.7cs
in Churazov et al. 2001). For a kT = 0.65 keV gas, the
sound speed is cs= 416 km s−1. Note that for the inner-
most cavities, the distance from the AGN is comparable
to the cavity size, suggesting that they are currently be-
ing, or have only recently been, inflated by the AGN.
Therefore the rise times, which are computed using the
distance from the AGN to the cavity center, are not a
reliable estimate of the true age, since early on the cav-
ities are driven by the momentum of the jet (see Bˆ ırzan
et al. 2008).
Finally, the mechanical energy required to inflate the
bubbles is given in Column 6, which we estimate as PV ,
where P is the pressure at the location of the bubble cen-
ter (taken from the azimuthally averaged pressure profile
shown in Figure 10) and V is the cavity volume. The to-
tal internal energy of each cavity is expected to be a few
times the mechanical energy (∼ 3PV for a relativistic
plasma, see McNamara & Nulsen 2007).
The total mechanical energy is about the same for the
southwestern and northeastern cavities for both the in-
nermost (∼ 1.3 × 1055erg) and intermediate (∼ 1.4 ×
1056erg) pairs (taking the sum of the two intermedi-
ate cavities to the northeast), consistent with each pair
having formed in two distinct AGN outbursts.
mechanical energies for the outer cavities differ signifi-
cantly from one another (2.6×1056erg versus 6.0×1055
for the northeastern and southwestern cavities, respec-
tively). We suggest three possibilities to explain this dis-
crepancy. First, the outer southwestern cavity is only
marginally detected, so its measured properties may be
inaccurate. Second, the outer cavities may be in the pro-
cess of breaking apart, as suggested by their significantly
different volumes, and if they are not devoid of X-ray
emitting gas, then the mechanical energy will be incor-
rectly estimated. Finally, Figure 1 shows that the inter-
mediate northeastern cavities may connect to the outer
northeastern cavity. If this is indeed the case, energy may
“leak” from the intermediate to the outer cavity, adding
to its internal energy and inflating it, making it easier to
detect (there is no such connection in the southwest).
A comparison of the ages of the cavities (approximated
by the rise times given in Table 3) and the shocks (ap-
proximated by the travel time given in Table 2) for the
“inner” and “middle” features shows that they are sim-
ilar (∼ 107yr), consistent with the interpretation that
each set of features was formed at the same time by the
same outburst event. The cavity ages are systematically
larger than the shock ages derived from our hydrodynam-
ical simulations (by about a factor of 3). This is likely
due to the cavities being initially driven and inflated at
some significant distance from the central AGN, only to
rise buoyantly after the end of the outburst, so that re-
garding the cavities as buoyantly rising bubbles early in
their lives is not accurate. Thus, using the buoyant rise
velocities of the cavities likely overestimates their ages.
The
5.3.2. Pressure Balance with the ICM
The non-thermal radio pressure in X-ray cavities, un-
der the assumptions of hydrostatic equilibrium and elec-
tron dominated pressure, is commonly found to be less
than the pressure of the surrounding gas derived from
X-ray observations (Bˆ ırzan et al. 2008). To accurately
estimate the radio pressure, flux measurements at mul-
tiple frequencies are required to estimate the spectral
index αrof the radio emission. In NGC 5813, only the
innermost cavities are detected at more than one fre-
quency (see § 3.1). Unfortunately, the large beam size
and contamination from extended emission outside the
cavities at 235 MHz make it difficult to accurately mea-
sure αr. Comparing the total emission in the region of
the inner cavities, including contributions from extended
emission outside of the central cavities at 235 MHz and
1.36 GHz (the latter detected in archival VLA C array
configuration observations) and emission from the core,
gives αr= 0.88. If we assume αr= 0.7 within the inner
cavities, a typical value for young radio lobes (Bˆ ırzan et
al. 2008), we find that the non-thermal pressure in each
cavity is Prad ∼ 2.3 × 10−12erg cm−3(where we have
used the revised equipartition equations of Brunetti et
al. 1997 with a low-energy cut-off of γmin= 100). This
is much less than the X-ray gas pressure outside the cav-
ities Pgas ∼ 10−10erg cm−3(see Figure 10). Balancing
the pressure with low energy electrons alone would re-
quire αr ≈ 2, which is unusually steep for young radio
cavities (Bˆ ırzan et al. 2008). If we assume αr= 0.7 and
vary the ratio of the energy in protons to the energy in
electrons k, we find that k ≈ 2000 is required to balance
the non-thermal and X-ray gas pressures, which is typ-
ical for radio galaxies in cool cores (Bˆ ırzan et al. 2008;
Dunn et al. 2010; Gitti et al. 2010).
We compared the radio and cavity power of the in-
ner cavities with predictions based on the Bˆ ırzan et al.
(2008) sample. The 1.36 GHz radio power for each of
the inner cavities is P1360≈ 1 × 1020W Hz−1. The re-
lation of Bˆ ırzan et al. (2008) then predicts a total cavity
power of Pcav ≈ 9 × 1042erg s−1. Taking the cavity
ages and mechanical energy (PV ) from Table 3 and as-
suming total cavity energies of 3PV gives a power of
Pcav≈ 4×1041erg s−1for the inner cavities, more than
an order of magnitude less than the estimate from Bˆ ırzan
et al. (2008). However, it is within the range of the large
scatter in the Bˆ ırzan et al. (2008) sample (see their Fig-
ure 6). More recently, Cavagnolo et al. (2010) derive a
relation between Pcavand Pradiofor lower mass systems
and find a steeper slope than Bˆ ırzan et al. (2008). Their
sample includes results from the Chandra observations of
NGC 5813 we consider here, so that NGC 5813 is con-
sistent with their derived relation.
5.4. Buoyantly Lifted Gas
The temperature map (Figure 6) shows an extension
of cool gas along the line defined by the X-ray cavities,
offset ∼ 3 kpc to the southeast. This cool gas extends
11 kpc to the inner edges of the intermediate cavities.
The most natural interpretation of this feature is cool
gas that has been buoyantly lifted by the intermediate
X-ray cavities, as seen in other systems (Forman et al.
2007; Simionescu et al. 2008; Kirkpatrick et al. 2009;
Simionescu et al. 2009; Randall et al. 2010; Werner et al.
2010). The Hα image, taken with the SOAR telescope

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N5813 FROM CHANDRA9
(Donahue et al. 2007), with the X-ray surface bright-
ness contours overlaid, as well as the temperature map
with the Hα contours overlaid, are shown in Figure 17.
The Hα filaments are co-spatial with the trail of cool
gas seen in the X-ray temperature map, as seen in many
other systems (e.g., Sanders et al. 2007, 2009), confirm-
ing the presence of cool gas.
N[II]λ6583/Hα = 1 and N[II]λ6548/Hα = 0.35, the total
Hα flux is FHα= 9.2 × 10−14erg s−1cm−2(assuming
no intrinsic absorption). The Kennicutt relation for the
star formation rate
Assuming line ratios of
SFR(M?/yr) = 7.9 × 10−42LHα(erg s−1)
(Kennicutt 1998) then gives SFR = 0.09M?yr−1. This
assumes that the Hα emission is completely driven by
UV radiation from young stars, which may not be the
case (e.g., Ferland et al. 2009), and that there is no in-
trinsic absorption. A violation of the former assump-
tion would give an overestimate of the SFR, while a vi-
olation of the latter would give an underestimate. We
compared the derived SFR to the mass cooling rate es-
timated from the X-ray observations by fitting the spec-
trum of the cool filament with a vapec plus a cooling
flow vmcflow model, with the abundances fixed at the
best fitting values for the total diffuse emission given
in § 4.2.4.
of 0.41 ± 0.07M?yr−1. One concern with this result is
that fitting a multi-temperature gas with a single cooling
flow component may boost the inferred mass accretion
rate. Unfortunately, we were unable to obtain a fit with
reasonable parameter constraints from the Chandra data
using a model combining an apec and two vmcflow
components. We therefore consider the mass accretion
rate inferred from the fit to XMM-Newton RGS data de-
scribed in § 4.2.4. From the two cooling flow compo-
nents, we infer upper limits on the mass accretion rate
of < 0.45M? yr−1and < 0.25M? yr−1for gas cool-
ing above and below 0.4 keV, respectively (these are 2σ
upper limits). Therefore, we conclude that the upper
limit on the mass accretion rate from X-ray observations
(< 0.25M? yr−1) and the star formation rate implied
by Hα observations (SFR = 0.09M?yr−1) are consistent
with star formation being fueled by gas cooling down
from X-ray temperatures.
For the cool gas to be buoyantly lifted by the X-ray
cavities, its total mass must be less than the mass of
gas displaced by the cavities. In particular, simulations
indicate that the mass of gas buoyantly lifted by an
AGN-blown bubble is about half the mass displaced by
the bubble (Pope et al. 2010). We estimated the gas
mass in the southern filament by fitting the spectra in
this region with an apec model and assuming that the
cool gas is contained in a cylinder of radius 3.5 kpc and
length 9.2 kpc, with the axis in the plane of the sky.
The emission is dominated by the cool gas in this region,
and accounting for the projected hot gas did not signif-
icantly change our results. We find a total gas mass of
Mfil = 1.5 × 108M?. A similar fit to an annulus sur-
rounding the southwestern intermediate cavity gives an
average electron density of ne = 0.022 cm−3, giving a
total mass of displaced gas Mdisp= 1.6×108M?, similar
to the mass of gas in the filament. Thus, Mfilis larger
than the value predicted by simulations (∼ 0.5Mdisp)
(1)
This gives a mass cooling rate in the gas
by a factor of two. We note that deep observations of
the buoyantly lifted filaments in M87 reveal that they
have a fine filamentary structure (Forman et al. 2007),
in contrast with the solid cylindrical geometry we have
assumed above (Werner et al. 2010 argue that the filling
factor in M87 is of order unity in most regions, although
they find a filling factor less than unity in some regions
where there is fine filamentary structure). If the filling
factor is less than unity then Mfilwill be smaller by the
same fraction. We conclude that the gas mass of the
cool filament to the south is consistent with having been
buoyantly lifted by the intermediate southwestern cavity,
and is consistent with simulations if the filling factor is on
the order of ∼ 0.5. We also note that if the filament has
indeed been buoyantly lifted by the intermediate cavity
then the filament, and hence the trajectory of the inter-
mediate cavity, cannot lie far from the plane of the sky
without assuming a small filling factor, since the length
of the filament (and hence the volume it occupies) grows
with inclination angle.
5.5. The Offset of the Central AGN
As noted in § 3, the central AGN is offset
southeast of the line defined by the X-ray cavities (see
Figure 2). It is also offset from the center points of the
elliptical edges defined by both the 1.5 kpc and 10 kpc
shock fronts (which are each roughly coincident with the
line defined by their respective cavity pairs), by about
2.3??(400 pc) for the 1.5 kpc shock and 7.5??(1.15 kpc)
for the 10 kpc shock.A comparison of the Chandra
image with the optical Sloan Digital Sky Survey image
(Adelman-McCarthy et al. 2008) shows that the centroid
of the optical emission is coincident with the AGN, and
is separated from the center points of the elliptical X-
ray shock fronts. This suggests that the cD galaxy has
some peculiar velocity relative to the ICM, and that the
AGN has moved since first inflating the X-ray cavities.
The initial outburst that inflated the inner cavities oc-
curred about 3 × 106yr ago (see Table 2). Since then,
the AGN has traveled about 400 pc in projection. This
requires a relative velocity between the galaxy and the
ICM of at least ∼ 130 km s−1(this is a lower limit since
we measure the projected velocity). Similarly, the 10 kpc
shock implies a relative velocity of ∼ 100 km s−1. This is
smaller than the host group’s (NGC 5846) velocity dis-
persion (322 km s−1, Mahdavi et al. 2005), and the rel-
ative radial velocity between NGC 5813 and NGC 5846
(∼ 260 km s−1), and is therefore a reasonable peculiar
velocity for the cD galaxy relative to the group mean
(or for the flow velocity of the ICM gas). We suggest
that during the last ∼ 2 × 107yr there has been a rela-
tive motion between the NGC 5813 galaxy and its ICM,
from northwest to southeast, in projection, with the cen-
tral AGN driving outbursts (i.e., inflating cavities into
the ICM) at two locations (the outer cavities and edge
are too poorly resolved to accurately measure the loca-
tion of the associated outburst). The relative velocity
may be due to the peculiar velocity of the cD relative to
the group mean, or to bulk gas motions or gas sloshing
of the ICM, or both. We note that once the outburst
begins and the cavities are initially inflated, the location
at which the energy is injected into the cavities is unim-
portant. The AGN may continue to move off of the axis
∼ 0.5 kpc

Page 10

10 RANDALL ET AL.
of symmetry of a pair of cavities while still depositing en-
ergy into them, driving their expansion and the resulting
shocks.
5.6. Outburst Energy
During an AGN outburst, the jets inflate cavities in
the ICM, which do work on the surrounding gas and
drive shocks. It is convenient to regard the work done
by the expanding lobes as “shock energy”, in which case
the outburst energy that is available to heat the ICM
is deposited to the ICM in two forms: the internal en-
ergy of the X-ray cavities and the shock energy. Since
NGC 5813 shows both cavities and shocks from two dis-
tinct outbursts, we can compare the total energy, mean
power, and the energy budget between shocks and cavi-
ties for each outburst. The shock energy can be roughly
estimated from the pressure increase across the shock
front. If a total energy E is added to a gas of volume
V the pressure increase is roughly ∆P ∼ E/V . For a
shock with a known Mach number, the ratio of the post-
and pre-shock pressure fP = (P + ∆P)/P is given by
the Rankine-Hugoniot shock jump conditions. The total
shock energy is therefore
E ≈ PV (fP− 1). (2)
As a consistency check, we compare the estimated shock
age, total energy, and mean power with results from our
hydrodynamical model in Table 2. The shock age tage,est
is estimated as the travel time from the current position
of the shock front to the center point of the elliptical
shock edge, assuming a constant Mach number and a
sound speed of cs = 416 km s−1for a kT = 0.65 keV
gas. The shock energy Esh,est is estimated using equa-
tion 2, assuming a prolate ellipsoidal geometry for the
volume contained within the shock front with semi-major
and -minor axes of 1.44?(13.5 kpc) and 1.13?(10.5 kpc)
for the 10 kpc shocks and 17.6??(2.7 kpc) and 11.7??
(1.8 kpc) for the 1.5 kpc shocks. Pressures were taken
from the azimuthal pressure profile shown in Figure 10.
Although the energies we give from the hydrodynami-
cal model represent the total outburst energy, the point
explosion model minimizes the internal energy in cavi-
ties, such that the energy in the central cavity is only a
few percent of the total outburst energy. The model en-
ergy is therefore a very good approximation of the shock
energy, and we refer to it as such. The model shock en-
ergies Esh,modelwere scaled to account for the difference
in total volume for the spherically symmetric model as
compared to the observed elliptical edges, and for the
lower average pressure along the elliptical shock fronts,
which cover a range in radii, assuming the shock energy
scales as in equation 2 (these effects somewhat balance
each other, as the volume correction increases the total
energy, while the pressure correction decreases it). The
correction factors are between 15–40%. The estimated
and model shock energies and mean powers agree rea-
sonably well, within factors of a few, demonstrating the
consistency between rough estimates and results from our
point explosion hydrodynamical model.
Table 2 indicates that the shock energy for the cur-
rent outburst is more than an order of magnitude smaller
than for the previous outburst. The mean power of the
current outburst is also less than that of the previous
outburst, by about a factor of six (1.5×1042erg s−1ver-
sus 1.0×1043erg s−1, where we take the mean outburst
power to be the sum of the shock energy and the 3PV in-
ternal energy of the cavities divided by the shock model
ages). The lower shock energy of the most recent out-
burst may indicate that it is ongoing, having only de-
posited ∼1/40 of its expected total energy output into
the observed shocks (assuming that the current outburst
is similar to the previous one). However, the lower shock
energy may simply be a result of the lower mean power
of the current outburst. We note that from X-ray ob-
servations of elliptical galaxies Allen et al. (2006) find
evidence that accretion flows around central AGN are
stable over a few million years, whereas we find that the
mean jet power varies on time scales of ∼ 107yr (the
time between outbursts).
We wish to compare the energy in shocks to the en-
ergy in the X-ray cavities for each outburst. The to-
tal internal energy of the cavities is roughly 3 times the
mechanical energy (PV ) required to inflate the cavities
(McNamara & Nulsen 2007), which is given in Table 3.
We find total cavity internal energies of 8.6 × 1056erg
and 7.8 × 1055erg for the outbursts that produced the
intermediate and inner cavities, respectively. Thus, the
total internal energy in cavities is roughly 30% of the
shock energy for the previous outburst and 1.3 times the
shock energy for the current outburst. This is consistent
with the current outburst being young, with the jets ac-
tively inflating the inner cavities and driving the 1.5 kpc
shock, whereas for the previous outburst the shock has
detached from the cavities, which rise buoyantly and lose
energy as they age. We note that while our point explo-
sion shock model is only approximate, so that the shock
energies are somewhat uncertain, the relative sense of the
energies is correct. Therefore, the larger fraction of total
energy in cavities in the current outburst (as compared
to the previous one) is a robust result.
For the outermost pair of cavities, the total internal
energy in the cavities is ∼ 9.6×1056erg, on the order of
the total energy of the intermediate cavities. However,
80% of this energy is contained in the northeastern cavity.
While it is in principle possible for the mechanical energy
to differ between paired cavities from the same outburst,
the measurements for the southwestern cavity are uncer-
tain since it is only marginally detected. Furthermore,
such a large difference is not seen in the inner and in-
termediate cavity pairs. As discussed in § 5.3, the outer
cavities may be in the process of breaking apart, and the
outer northeastern cavity may have been re-energized by
the intermediate cavity, making the measured mechani-
cal energy (and hence the internal energy) uncertain.
We conclude that the lower total energy of the most
recent outburst, as compared to the previous outburst,
suggests that the outburst is ongoing, though this may
simply be an effect of the lower mean power. Although
the luminosity of the central source is low (see § 4.2.5),
it may be in a short term quiescent state or heavily
obscured, and does not rule out an ongoing outburst.
AGN luminosities are known to vary by several orders
of magnitude over very short time scales (e.g., Harris et
al. 2009). Results from our 1D hydrodynamical simula-
tions suggest that the mean power over longer timescales
(∼ 107yr) can also vary significantly between outbursts,

Page 11

N5813 FROM CHANDRA11
even in an otherwise relaxed system like NGC 5813.
5.7. The Balance Between Heating and Cooling in the
ICM
As noted in § 5.6, the total mechanical energy output
of the AGN that is available to heat the ICM is primar-
ily in two forms: the internal energy of X-ray cavities,
which rise buoyantly after being inflated by jets from the
AGN, and the “shock energy”, from shocks driven by the
rapid inflation of the cavities. When and where the in-
ternal energy of the X-ray cavities gets transferred to the
ICM is not well understood. In contrast, the local heat
input at the shock front can be calculated directly from
the Mach number. Furthermore, shock heating has two
desirable features. First, the gas is more strongly heated
in the core where Mach numbers are larger, close to the
central AGN, which is the region of interest for regulat-
ing feedback between the ICM and the central SMBH.
Second, the heating is roughly isotropic (as opposed to
heating with jets or with the internal energy of the X-ray
cavities). We therefore consider the energy input due to
shocks, which, as we show in § 5.6, contain 40–80% of the
total outburst energy in NGC 5813 (for a detailed dis-
cussion of heating with AGN outburst shocks see David
et al. 2001).
To balance radiative cooling with AGN feedback
shocks, the average outburst power must be on the order
of or larger than the rate of radiative cooling. We esti-
mated the radiative cooling rate as the X-ray luminosity,
which we obtained by fitting the spectrum from the total
emission within 170??(26.3 kpc) with an absorbed apec
model (using a vapec or two apec model did not sig-
nificantly change the resulting luminosity). The derived
X-ray luminosity of LX= 5.4×1041erg s−1within 26 kpc
implies a mean cooling time of tcool= 1.0 Gyr (where we
take the cooling time to be the time it would take to
radiate away all of the internal energy of the gas at the
current luminosity). For the 10 kpc shocks, we calculate
the total shock energy to be ∼ 3 × 1057erg (see § 5.6).
Therefore, only 6 such outbursts are needed per cooling
time to provide enough energy to completely offset ra-
diative cooling with shocks alone within 26 kpc. The
time between outbursts given by both the buoyant rise
times of the cavities (Table 3) and, more reliably, from
hydrodynamical simulations of the shocks (Table 2) is on
the order of 107yr, allowing 100 shocks per cooling time,
more than is needed to provide the necessary energy.
While results from the 10 kpc shocks indicate that
there is sufficient energy in shocks alone to offset radia-
tive cooling, there are two points that must be consid-
ered. First, as discussed in § 5.6, the observed shocks
suggest that the current and previous outburst shock en-
ergies differ in strength by more than an order of mag-
nitude (although the most recent outburst may be ongo-
ing). Furthermore, only some fraction of the total shock
energy will go into heating the gas within the cooling ra-
dius, and for weak shocks this fraction is relatively small
(? 10%). We therefore consider the local balance of shock
heating and radiative cooling for each shock. The pri-
mary effect of radiative cooling is to reduce the entropy
of the gas. To offset cooling, the heating mechanism is
required to increase the entropy by at least this amount.
Shocks will also affect the kinetic, thermal, and potential
energy of the gas, but these effects are transient, and for
heating it is the change in entropy of the gas that is rele-
vant. Hence, the entropy increase ∆S caused by a weak
shock can offset a radiative heat loss of ∆Q ? T ∆S,
where T is the gas temperature. Expressed as a fraction
of the gas thermal energy, the effective heat input from
one shock is therefore (T ∆S)/E = ∆ln(P/ργ), where
E is the thermal energy and γ is the adiabatic index.
For the 10 kpc shocks, the Mach numbers given in Ta-
ble 2 imply a change in ln(P/ργ) across the shock front of
∼ 5%. Therefore, to balance the total entropy decrease
of the gas about 1/0.05 = 20 outbursts are needed per
local cooling time to completely offset cooling with shock
heating. By the same argument, 10 outbursts per cooling
time are needed to replace the thermal energy of the gas
at the 1.5 kpc shock. The cooling time of the pre-shock
gas just outside the 10 kpc shock edge is 9 × 108yr, so
an outburst interval of 107yr gives 90 shocks per local
cooling time. For the 1.5 kpc shock, the pre-shock gas
cooling time is 2 × 108yr, giving 20 shocks per cool-
ing time. Thus, we conclude that shock heating alone is
sufficient to offset radiative cooling of the gas within the
1.5 kpc and 10 kpc shock fronts, consistent with previous
suggestions that shocks can offset cooling close to central
AGN (Nulsen et al. 2007). The X-ray cavities rise buoy-
antly, and release their internal energy to heat the ICM
gas at larger radii. Although previous studies have found
other systems where there is enough total shock energy
to offset radiative cooling (e.g., M87 Forman et al. 2005,
with M87 also showing concentric shock fronts from mul-
tiple AGN outbursts; Hydra A Nulsen et al. 2005), here
we explicitly show that the fraction of shock energy that
goes into heating the gas (5–10%) is sufficient to balance
radiative cooling locally at the shock fronts. The out-
burst interval is short enough for such shocks to offset
cooling over much longer timescales. This demonstrates
that AGN feedback can operate to heat the gas within
galaxies, as well as the more extended ICM in clusters,
as required by some galaxy formation models (e.g., Kor-
mendy et al. 2009).
6. SUMMARY
We have presented results based on Chandra, VLA,
GMRT, and SOAR observations of NGC 5813, the dom-
inant member of a galaxy group.
clear signatures from three distinct AGN outbursts
in an otherwise relaxed system (including two shocks
with detectable temperature jumps), making this object
uniquely well-suited to the study of AGN feedback. We
find the following:
The ICM shows
1. Three pairs of collinear cavities, where each pair
is associated with a distinct AGN outburst. The
inner two pairs are associated with unambiguous
shocks (with Mach numbers Mi= 1.7, Mo= 1.5),
with clear temperature rises, that can be directly
detected from the X-ray data. The outermost cav-
ity pair also has an associated surface brightness
edge. The properties of this edge are consistent
with an old shock associated with the outermost
cavities, although the current data do not rule out
other interpretations (e.g., a transition region from
the galactic atmosphere to the extended group at-
mosphere). The locations of the cavities and the

Page 12

12 RANDALL ET AL.
shocks indicate an outburst interval of ∼ 107yrs.
2. Diffuse radio emission, filling the inner cavities at
1.36 GHz and 235 MHz and the intermediate cav-
ities at 235 MHz. Radio emission from the outer
cavities is not detected. This reflects the greater
age of the relativistic particles in more distant cav-
ities.
3. A cool trail of gas that has been buoyantly lifted
by the intermediate cavities. The gas is co-spatial
with filaments seen in Hα observations.
4. The mean power of the current outburst is six times
less than that of the previous outburst, indicating
that the average jet power can vary significantly be-
tween outbursts, even in near “steady state” AGN
feedback with regular outbursts in an otherwise dy-
namically relaxed system.
5. The total heat energy input from shocks alone is
sufficient to balance radiative cooling locally. This
heating takes place in the core, close to the central
AGN, which is the region of interest for regulating
feedback between the ICM and the central SMBH.
Thus, for the first time, we explicitly show a sys-
tem where shock heating alone can locally balance
radiative cooling and regulate AGN feedback.
The financial support for this work was partially pro-
vided for by the Chandra X-ray Center through NASA
contract NAS8-03060, and the Smithsonian Institution.
We thank the staff of the GMRT for their help during
the observations. GMRT is run by the National Centre
for Radio Astrophysics of the Tata Institute of Funda-
mental Research. The SOAR Telescope is a joint project
of Conselho Nacional des Pesquisas Cientficas e Tecno-
logicas CNPq-Brazil, The University of North Carolina
Chapel Hill, Michigan State University, and the National
Optical Astronomy Observatory. AS and NW are sup-
ported by the National Aeronautics and Space Adminis-
tration through Chandra/Einstein Postdoctoral Fellow-
ship Award Numbers PF9-00070 and PF8-90056 issued
by the Chandra X-ray Observatory Center, which is op-
erated by the Smithsonian Astrophysical Observatory for
and on behalf of the National Aeronautics and Space Ad-
ministration under contract NAS8-03060.
REFERENCES
Adelman-McCarthy, J. et al. 2008, ApJS, 175, 297
Allen, S. W., Dunn, R. J. H., Fabian, A. C., Taylor, G. B., &
Reynolds, C. S. 2006, MNRAS, 372, 21
Anders, E., & Grevesse, N. 1989, Geochimica et Cosmochimica
Acta, 53, 197
Balmaverde, B. & Capetti, A. 2006, A&A, 447, 97
Bˆ ırzan, L., McNamara, B. R., Nulsen, P. E. J., Carilli, C. L., &
Wise, M. W. 2008, ApJ, 686, 859
Bˆ ırzan, L., McNamara, B. R., Nulsen, P. E. J., & Wise, M. W.
2009, pre-print (arXiv:0909.0397)
Blanton, E. L., Randall, S. W., Douglass, E. M., Sarazin, C. L.,
Clarke, T. E., & McNamara, B. R. 2009, ApJL, 697, 95
Blanton, E. L., Sarazin, C. L., McNamara, B. R. 2003, ApJ, 585,
227
B¨ ohringer, H. et al. 2004, A&A, 425, 367
Brunetti, G., Setti, G., & Comastri, A. 1997, A&A, 325, 898
Buote, D. 1999, MNRAS, 309, 685
Cavagnolo, K. W., McNamara, B. R., Nulsen, P. E. J., Carilli, C.
L., Jones, C., & Bˆ ırzan, L. 2010, (in prep.)
Churazov, E., Br¨ uggen, M., Kaiser, C. R., B¨ ohringer, H., &
Forman, W. 2001, 554, 261
Churazov, E., Forman, W., Vikhlinin, A., Tremaine, S., Gerhard,
O., & Jones, C. 2008, MNRAS, 388, 1062
Churazov, E., Sunyaev, R., Forman, W., & B¨ ohringer, H. 2002,
MNRAS, 332, 729
Churazov, E., Tremaine, S., Forman, W., Gerhard, O., Das, P.,
Vikhlinin, A., Jones, C., B¨ ohringer, H., & Gebhardt, K. 2010,
MNRAS, 404, 1165
David, L. P., Nulsen, P. E. J., McNamara, B. R., Forman, W.,
Jones, C., Ponman, T., Robertson, B., & Wise, M. 2001, ApJ,
557, 546
Donahue, M., Sun, M., O’Dea, C. P.. Voit, G. M., & Cavagnolo,
K. W. 2007, AJ, 134, 14
Dunn, R. J. H., Allen, S. W., Taylor, G. B., Shurkin, K. F., Gentile,
G., Fabian, A. C., & Reynolds, C. S. 2010, MNRAS, 404, 180
Emsellem, E. et al. 2007, MNRAS, 379, 401
Fabian, A. C., Hu, E. M., Cowie, L. L., & Grindlay, J. 1981, ApJ,
248, 47
Fabian, A. C., Sanders, J. S., Crawford, C. S., Conselice, C. J.,
Gallagher, J. S., & Wyse, R. F. G. 2003, MNRAS, 344, 48
Fabian, A. C., Sanders, J. S., Taylor, G. B., Allen, S. W., Crawford,
C. S., Johnstone, R. M., & Iwasawa, K. 2006, MNRAS, 366, 417
Ferland, G. J., Fabian, A. C., Hatch, N. A., Johnstone, R. M.,
Porter, R. L., van Hoof, P. A. M., & Williams, R. J. R. 2009,
MNRAS, 392, 1475
Finoguenov, A., David, L. & Ponman, T. 2000, ApJ, 188, 203
Finoguenov, A., Reiprich, T. & B¨ ohringer, H. 2001, A&A, 368, 749
Finoguenov,A., Ruszkowski,
Vikhlinin, A., Mandel, E. 2008, ApJ, 686, 911
Forman, W., et al. 2007, ApJ, 665, 1057
Forman, W., Nulsen, P., Heinz, S., Owen, F., Eilek, J., Vikhlinin,
A., Markevitch, M., Kraft, R., Churazov, E., & Jones, C. 2005,
ApJ, 635, 894
Gastaldello, F., Buote, D. A., Humphrey, P. J., Zappacosta, L.,
Bullock, J. S., Brighenti, F., & Mathews, W. G. 2007, ApJ, 669,
158
Giacintucci, S., Vrtilek, J. M., O’Sullivan, E., Raychaudhury, S.,
David, L. P., Venturi, T., Athreya, R., & Gitti, M. 2009,
Proceedings of the conference ”The Monster’s Fiery Breath:
Feedback in Galaxies, Groups, and Clusters”, June 2009,
Madison, Wisconsin, pre-print (arXiv:0909.0291)
Giacintucci, S., et al. 2010, ApJ (in prep.)
Gitti, M., O’Sullivan, E., Giacintucci, S., David, L. P., Vrtilek, J.,
Raychaudhury, S., Nulsen, P. E. J. 2010, ApJ, 714, 758
Graham, J., Fabian, A. C., & Sanders, J. S. 2008, MNRAS, 386,
278
Grevesse, N., & Sauval, A. J. 1998, Space Sci. Rev., 85, 161
Harris, D. E., Cheung, C. C., Stawarz, Lukasz, Biretta, J. A., &
Perlman, E. S. 2009, ApJ, 699, 305
Humphrey, P. J., Buote, D. A., & Canizares, C. R. 2004, ApJ, 617,
1047
Kalberla, P. M. W., Burton, W. B., Hartmann, D., Arnal, E. M.,
Bajaja, E., Morras, R., P¨ oppel, W. G. L. 2005, A&A, 440, 775
Kennicutt, R. C. 1998, ARA&A, 36, 189
Kirkpatrick, C. C., Gitti, M., Cavagnolo, K. W., McNamara, B.
R., David, L. P., Nulsen, P. E. J., & Wise, M. W. 2009, ApJL,
707, 69
Kormendy, J., Fisher, D. B., Cornell, M. E., & Bender, R. 2009,
ApJS, 182, 216
Lauer, T. R. et al. 2007, ApJ, 664, 226
Magliocchetti, M. & Br¨ uggen, M. 2007, 379, 260
Mahdavi, A., Trentham, N., & Tully, R. B. 2005, 130, 1502
Mazzotta, P., Rasia, E., Moscardini, L., & Tormen, G. 2004,
MNRAS, 354, 10
McNamara, B. & Nulsen, P. J. E. 2007, ARA&A, 45, 117
Nulsen, P. E. J., Hambrick, D. C., McNamara, B. R., Rafferty, D.,
Bˆ ırzan, L., Wise, M. W., & David, L. P. 2005, ApJ, 625, 9
Nulsen, P. J. E., Jones, C., Forman, W. R., David, L. P.,
McNamara, B. R., Rafferty, D. A., Bˆ ırzan, L., & Wise, M.
W. 2007, Heating versus Cooling in Galaxies and Clusters of
Galaxies, ed. H. B¨ ohringer, G. W. Pratt, A. Finoguenov, & P.
Schuecker (Berlin: Springer), 210
M., Jones,C., Br¨ uggen, M.,

Page 13

N5813 FROM CHANDRA13
Peterson, J. R., & Fabian, A. C. 2006, PhR, 427, 1
Peterson, J. R., Paerels, F. B. S., Kaastra, J. S., Arnaud, M.,
Reiprich, T. H., Fabian, A. C., Mushotzky, R. F., Jernigan, J.
G., & Sakelliou, I. 2001, A&A, 365L, 104
Pope, E. C. D., Babul, A., Pavlovski, G., Bower, R. G., & Dotter,
A. 2010, pre-print (arXiv:1004.2050v2)
Ptak, A. 2001, AIPC, 599, 326
Randall, S. W., Clarke, T. E., Nulsen, P. J. E., Owers, M. S.,
Sarazin, C. L. , Forman, W. R., & Murray, S. S. 2010, ApJ,
(submitted)
Randall, S. W., Jones, C., Kraft, R., Forman, W. R., & O’Sullivan,
E. 2009a, ApJ, 696, 1431
Randall, S. W., Jones, C., Markevitch, M., Blanton, E. L., Nulsen,
P. E. J., & Forman, W. R. 2009b, ApJ, 700, 1404
Randall, S., Nulsen, P., Forman, W., Jones, C., Machacek, M.,
Murray, S., & Maughan, B. 2008, ApJ, 688, 208
Rasia, E., Mazzotta, P., Bourdin, H., Borgani, S., Tornatore, L.,
Ettori, S., Dolag, K. & Moscardini, L. 2008, ApJ, 674, 728
Sanders, J. S. & Fabian, A. C. 2007, MNRAS, 381, 1381
Sanders, J. S., & Fabian, A. C., & Taylor, G. B. 2009, MNRAS,
396, 1449
Simionescu, A., Werner, N., B¨ ohringer, H., Kaastra, J. S.,
Finoguenov, A., Br¨ uggen, M., & Nulsen, P. E. J. 2009, A&A,
493, 409
Simionescu, A., Werner, N., Finoguenov, A., B¨ ohringer, H., &
Br¨ uggen, M. 2008, A&A, 482, 97
Sun, M., Donahue, M., & Voit, G. M. 2007, ApJ, 671, 190
Sun, M., Voit, G. M., Donahue, M., Jones, C., Forman, W., &
Vikhlinin, A. 2009, ApJ, 693, 1142
Tonry, J. L., Dressler, A., Blakeslee, J. P, Ajhar, E. A., Fletcher,
A. B., Luppino, G. A., Metzger, M. R., & Moore, C. B. 2001,
ApJ, 546, 681
Tran, H. D., Tsvetanov, Z., Ford, H. C., Davies, J., Jaffe, W., van
den Bosch, F. C., & Rest, A. 2001, AJ, 121, 2928
Vikhlinin, A., Markevitch, M., Murray, S. S., Jones, C., Forman,
W., & Van Speybroeck, L. 2005, ApJ, 628, 655
Vikhlinin, A., Markevitch, M., & Murray, S. S. 2001, ApJ, 551, 160
Werner, N., et al. 2010, pre-print (arXiv:1003.5334)
Werner, N., Zhuravleva, I., Churazov, E., Simionescu, A., Allen,
S. W., Forman, W., Jones, C., & Kaastra, J. S. 2009, MNRAS,
398, 23

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14 RANDALL ET AL.
TABLE 1
Summary of the Radio Observations
Radio
telescope
Project Observation
date
Array Frequency
(MHz)
Bandwidth
(MHz)
Integration
time (min)
HPBW, PA
(??×??,◦)
16.5 × 15.1,74
1.3 × 1.2,28
4.9 × 4.7,−84
27.4 × 16.8,53
5.0 × 4.5,−4
rms
(µJy b−1)
GMRT
VLA
VLA
VLA
VLA
14SGA01
AF0188
AW0202
AC0488
AW0112
Aug 2008
Apr 1990
Jan 1988
Sept 1997
Jun 1984
full
A
B
C
C
235
1490
1360
1360
4860
8 100
45
30
6
8
300
22
20
30
25
50
50
50
50
TABLE 2
Properties of the Shocks
IDra
∆ρb
Mc
tage,modeld
(107yr)
Esh,modele
(1057erg)
Wmodelf
(1042erg s−1)
Maccg
(103M?)
0.3
8.2
22.4
tage,esth
(107yr)
Esh,esti
(1057erg)
Westj
(kpc)(1042erg s−1)
Inner, SE
Middle, SE
Middle, NW
1.4
9.9
11.5
1.97+0.12
−0.12
1.69+0.07
−0.07
1.75+0.04
−0.03
1.71
1.48
1.53
0.3
1.4
1.3
0.06
2.2
3.3
0.6
5.0
8.0
0.2
1.6
1.6
0.2
3.0
3.0
2.7
5.9
5.9
aDistance from the AGN to the shock front.
bDensity jump at shock front.
cMach number.
dShock age, from the hydrodynamical model. The point explosion approximation gives large Mach numbers at early times, so the shock
ages are underestimated.
eShock energy, from the hydrodynamical model.
fMean shock power, from the hydrodynamical model.
gMinimum accreted mass needed to power the model outburst (assuming 100% efficiency).
hShock age, estimated as the travel time from the current position to the center point of the elliptical shock edge. Since the current Mach
number is used to give a constant velocity, the shock ages are overestimated.
iShock energy, estimated using Equation 2.
jEstimated mean shock power.
TABLE 3
Properties of the X-ray Cavities
IDaa
bb
rc
trised
(107yr)
Emeche
(1055erg) (kpc) (kpc)(kpc)
Inner, SW
Inner, NE
Middle, SW
Middle-1g, NE
Middle-2g, NE
Outerh, SW
Outer, NE
0.95
1.03
3.9
2.9
2.8
5.2
8.0
0.95
0.93
3.9
2.2
2.4
3.0
4.4
1.3
1.4
7.7
4.9
9.3
22.2
18.0
0.6f
0.7f
3.6
2.3
4.4
10.4
8.5
1.1
1.5
15.3
9.3
4.1
6.0
26.0
aSemi-major axis.
bSemi-minor axis.
cDistance from central AGN.
dLower limit on the bubble rise time, assuming that each bubble rises at half the sound speed for a 0.65 keV gas.
ePV mechanical energy required to inflate the cavity.
fThe cavity size is on the order of the distance to the AGN, and these cavities are likely still being or have only recently been inflated by
the AGN, so the computed rise time is not a reliable estimate of the cavity age.
gPart of a “split” or “Russian doll” cavity.
hCavity is only marginally detected, tabulated properties may not be reliable.

Page 15

N5813 FROM CHANDRA 15
225.360225.340225.320 225.300225.280225.260
1.740
1.730
1.720
1.710
1.700
1.690
1.680
1.670
10 kpc
Outer Cavity
Middle Cavity
Middle Cavity
Inner Cavities
Edge
Edge
Fig. 1.— Exposure corrected, background subtracted 0.3–2 keV Chandra image of NGC 5813. The image has been smoothed with a 1.5??
radius Gaussian and point sources have been filled-in by randomly drawing from a Poisson distribution fit to a local background annular
region. The image shows two pairs of cavities, plus an outer cavity to the northeast, two sharp edges to the northwest and southeast, and
bright rims around the pair of inner cavities.