Astron. Nachr. / AN 329, No. 9/10, 940 – 943 (2008) / DOI 10.1002/asna.200811052

The orbital structure of the massive elliptical galaxy NGC 5846

P. Das1,�, O. Gerhard1, L. Coccato1, E. Churazov2,3, W. Forman4, A. Finoguenov1, H. Bohringer1, M.Arnaboldi5,6, M. Capaccioli7,8, A. Cortesi9, F. de Lorenzi1, N. G. Douglas10, K. C. Freeman11,K. Kuijken12, M. R. Merrifield9, N. R. Napolitano13, E. Noordermeer9, and A. J. Romanowsky14

1 Max-Planck-Institut fur extraterrestrische Physik, Giessenbachstr., 85748, Garching bei Munchen, Germany2 Max-Planck-Institut fur Astrophysik, Karl-Schwarzschild-Str. 1, 85741, Garching bei Munchen, Germany3 Space Research Institute (IKI), Profsoyuznaya 84/32, Moscow 117997, Russia4 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA5 European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748, Garching bei Munchen, Germany6 INAF, Osservatorio Astronomico di Pino Torinese, I-10025 Pino Torinese, Italy7 Dipartimento di Scienze Fisiche, Universita Federico II, Via Cinthia, 80126, Naples, Italy8 INAF - VSTceN, Salita Moiariello, 16, 80131, Naples, Italy9 School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

10 Kapteyn Astronomical Institute, Postbus 800, 9700 AV Groningen, The Netherlands11 Research School of Astronomy & Astrophysics, ANU, Canberra, Australia12 Leiden Observatory, Leiden University, PO Box 9513, 2300RA Leiden, The Netherlands13 INAF-Observatory of Capodimonte, Salita Moiariello, 16, 80131, Naples, Italy14 UCO/Lick Observatory, University of California, Santa Cruz, CA 95064, USA

Received 2008 Sep 18, accepted 2008 Sep 19Published online 2008 Nov 20

Key words celestial mechanics, stellar dynamics – dark matter – galaxies: elliptical and lenticular, cD – galaxies: halos– galaxies: individual (NGC 5846) – planetary nebulae: general – X-rays: galaxies

We use density and temperature profiles obtained from XMM-Newton observations to derive a potential of NGC 5846 outto 11Re, thus probing the mass distribution deep into the halo. The inferred circular velocity is significantly higher thanthe extrapolation of dynamical models implying a halo, more massive than previously thought. Using an I-band surface-brightness profile and a projected velocity dispersion profile consisting of long-slit kinematic measurements and planetarynebulae (PNe) velocity dispersions, we solve the Jeans equations, assuming a non-rotating spherical system. The solutionssuggest a highly radially anisotropic galaxy outside 0.7Re with β ∼ 0.75.

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1 Introduction

Knowledge of the three-dimensional orbital structure of agalaxy is invaluable as it serves as a relic of its formationpath. To obtain such an insight from observations of two-dimensional projected properties, one has to create dynam-ical models. These are usually constructed in an assumedpotential by superposing a library of orbits (Schwarzschild1979; Thomas et al. 2005; van den Bosch et al. 2008) ordistribution functions (e.g., Gerhard et al. 1998), or by con-structing a system of particles (NMAGIC, de Lorenzi et al.2007) that reproduces the observed surface brightness andkinematics. The degeneracy existing between the mass dis-tribution, orbital structure and shape, is mitigated by fittingto higher-order moments of the LOSVD (Gerhard 1993).

Kronawitter et al. (2000) constructed spherical dynam-ical models of round elliptical galaxies using datawithin ∼1Re, and found an isotropic to slightly radiallyanisotropic orbital structure. More recently de Lorenzi etal. (2008a,b) created NMAGIC models of the intermediate-luminosity elliptical galaxies, NGC 4697 and NGC 3379,

� Corresponding author: pdas@mpe.mpg.de

incorporating integral-field data and PNe velocity disper-sions extending out to 5 and 7Re respectively. Thesemeasurements probe the outer halo of these galaxies,where dynamical timescales are longer and relics ofthe formation mechanism better preserved. They founda range of spherical and axisymmetric models consis-tent with the data, ranging from almost isotropic sys-tems with diffuse dark matter haloes to highly ra-dially anisotropic systems, accommodating moderatelymassive dark matter haloes.

To obtain more stringent constraints on the orbital struc-ture in elliptical galaxies it would be conducive to derive thepotential of the galaxy independently, to eliminate the de-generacy between mass and orbital structure. Massive ellip-ticals harbour a hot (T ∼ 1 keV) interstellar medium (ISM)in the form of a low density (n < 0.1 cm−3) plasma trappedin the galaxy’s gravitational potential. In massive ellipti-cals, the observed X-ray spectrum is dominated by emissionfrom the ISM primarily via thermal bremsstrahlung and X-ray lines of heavy elements (Forman et al. 1985). In quies-cent galaxies, where the gas is not significantly distorted byinteractions with companion galaxies, one can assume hy-

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Astron. Nachr. / AN (2008) 941

Fig. 1 (online colour at: www.an-journal.org) (a) Potential of NGC 5846: The blue dots refer to the potential derived from XMM-Newton observations and the dashed-dotted pink line shows the best-fit cubic spline. For comparison, the potential derived from Chandraobservations (red dots) and the potential corresponding to the best dynamical model of Kronawitter et al. (2000) (solid black line) arealso shown. (b) Circular velocity curve of NGC 5846: The solid black line corresponds to the circular velocity curve of Kronawitter etal. (2000) over the range of their data and the dashed black line shows its extrapolation. The black dotted lines show the 95% confidencerange. The dashed-dotted pink line shows the differential of the best-fit cubic-spline to the potential derived from the XMM-Newtonobservations.

drostatic equilibrium and use the temperature and densityprofiles derived from X-ray spectra to obtain a mass profile(e.g., Fukazawa et al. 2006).

In a non-rotating spherical system, if the potential isknown a priori then Binney & Mamon (1982) showed thatthe second-order Jeans equation for the intrinsic second-order velocity moments can be inverted using photomet-ric observations and measurements of the projected second-order velocity moments. Simpler solutions were found byTonry (1983) and Dejonghe & Merritt (1992), who also gen-eralise their solution for all intrinsic velocity moments.

We apply the algorithm of Dejonghe & Merritt (1992)to NGC 5846. This is a massive, nearby elliptical galaxylocated at the centre of a group of galaxies. It is an idealgalaxy to test the feasibility of using the potential derivedfrom X-ray observations in which to invert the Jeans equa-tions, as ample amounts of data already exist in the litera-ture across the X-ray and optical wavelengths. In addition,its optical and X-ray images are near-circular justifying aspherical model, and the rotation measured by the Plane-tary Nebula Spectrograph (PN.S) is negligible (Coccato etal. 2008). We adopt a distance of 24.2 Mpc and an effec-tive radius Re = 81′′ = 9.5 kpc (Cappellari et al. 2006 andreferences therein).

We shall discuss the derivation of the potential of NGC5846 from X-ray observations in Sect. 2. We present the so-lution to the second-order Jeans equation for a non-rotatingspherical system and its application to NGC 5846 to deriveits orbital structure in Sect. 3.

2 Derivation of potential

The X-ray observations consist of temperature and densityprofiles derived by Finoguenov et al. (2006) from archivalXMM-Newton observations, extending to almost 11Re,therefore enabling us to probe the potential deep into thehalo of the galaxy.

We assume that the ISM surrounding NGC 5846 is com-posed of an ideal gas in hydrostatic equilibrium and spher-ically distributed. Following the robust algorithm presentedin Churazov et al. (2008), we proceed by calculating thechange in potential ΔΦ between consecutive shells posi-tioned at the radii of the derived temperature and pressurevalues. We estimate the errors using Monte Carlo simula-tions. Then we calculate the absolute potential profile bynormalising to the potential calculated from the circular ve-locity curve of Kronawitter et al. (2000) for NGC 5846. Fig-ure 1 (a) shows the potential we derive from XMM-Newtondata. For comparison we also overplot the potential derivedfrom Chandra observations using an analogous method, andthe potential we calculated from the dynamical models ofKronawitter et al. (2000). In general the potentials seem toagree with each other. In the central 0.04Re the Chandrapotential shows larger scatter than that derived from the dy-namical models, perhaps due to central AGN activity. Be-tween 0.3–1.1Re, the slope of the XMM-Newton potentialis slightly flatter than that from Chandra and the dynamicalmodels.

We fit a smooth cubic spline through the XMM-Newtonpotential and differentiate to obtain Vc(r)2 = r dΦ/dr, thecircular velocity required for the Jeans equations. This isshown in Fig. 1 (b) along with the circular velocity curveof Kronawitter et al. (2000). Taking the derivative accentu-ates any differences and this is especially apparent in thisplot. It appears that in the central 1Re the spatial informa-tion in the XMM-Newton observations is unable to repro-duce the circular velocity curve to the same detail as thedynamical models. Outside this region, the XMM-Newtoncircular velocity curve rises steadily to a constant value ofabout 400–420 km/s between ∼2–11Re, which is consider-ably higher than the extrapolation of the dynamical modelsof Kronawitter et al. (2000).

Due to the possible uncertainties associated with theXMM-Newton circular velocity curve in the central Re, we

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942 P. Das et al.: The orbital structure of NGC 5846

consider two different circular velocity curves for our Jeansmodels:

1. Total circular velocity as determined from the XMM-Newton observations.

2. Total circular velocity curve as determined from the dy-namical models of Kronawitter et al. (2000) until 1.2Re

followed by that from the XMM-Newton observations.

3 Derivation of orbital structure

3.1 Inversion of the Jeans equations

The dynamics of a non-rotating spherical system of starswith density, j(r), moving in a potential with a circular ve-locity curve, Vc(r), is governed by the second-order Jeansequation

ddr

(jσ2r ) +

2β

rjσ2

r +jV 2

c

r= 0 , (1)

where σr(r) is the intrinsic velocity dispersion and β(r) =1 − σ2

θ(r)/σ2r (r)) quantifies the orbital structure.

In reality, we only have access to projected quantitiesfrom observations. The observed surface brightness profile,I(R), can be deprojected to give the intrinsic luminositydensity, j(r), and the observed projected velocity disper-sion, σP(R), is related to the intrinsic radial velocity dis-persion, σr(r), through:

σ2P =

2I

∫ ∞

R

jσ2r

(1 − β

R2

r2

)r

(r2 − R2)1/2dr, (2)

Once j(r) has been derived, Eqs. (1) and (2) can be solvedto give σ2

r(r) and β(r), done most simply by Dejonghe &Merritt (1992):

σ2r = − 2

πr3j

∫ ∞

r

[cos−1

( r

R

)+

r

(R2 − r2)1/2

]Iσ2

P RdR

+2

3r3j

∫ ∞

r

(r′3 +

r3

2

)j(r′)Vc(r′)2

r′dr′, (3)

Then β(r) is obtained by rearranging Eq. (1):

β(r) = − V 2c

2σ2r

− 12

d ln(jσ2r)

d ln r, (4)

which expresses the derivative in log-log space, where it isalmost linear.

3.2 Tests

We tested the implementation of this solution using self-consistent galaxy models described by a γ-model potential-density pair (Dehnen, 1993) and both a constant and the ra-dially varying Osipkov-Merritt anisotropy profile (Osipkov1979; Merritt 1985a,b).

The intrinsic luminosity density of a γ-model is

j(r) =(3 − γ)aL

4πrγ(r + a)4−γ, (5)

Fig. 2 (online colour at: www.an-journal.org) Black stars showthe velocity dispersions of the stars, derived from the stellar kine-matic data of Kronawitter et al. (2000). Black dots show the PNevelocity dispersions. The red line illustrates the best-fit profilefrom the adopted parameterisation.

where a is a scale radius, L is the total luminosity and γis a constant. The gravitational potential generated by thisdensity results in a circular velocity curve given by

Vc(r) =[

GMr2−γ

(r + a)3−γ

]1/2

, (6)

where M = ΓL is the total luminous mass in M� and Γ isthe mass-to-light ratio in M�/L�.

The Osipkov-Merritt anisotropy profile is given by

β(r) =r2

r2 + r2a

, (7)

where ra is a scale radius, often called the anisotropy ra-dius. For small r, this profile is isotropic. The model be-comes increasingly radially anisotropic approaching 1 asr → ∞. The transition is quite rapid and occurs at aroundthe anisotropy radius. We carried out tests for

1. γ = 1.0, β = 0;2. γ = 1.0, β = 0.5;3. γ = 1.0, ra = 2.41a;4. γ = 1.5, ra = 2.41a.

For the first two cases the intrinsic and projected veloc-ity dispersion profiles can be expressed analytically and inthe latter two, they can be evaluated numerically from theknown distribution function. In all four cases, the algorithmwas able to reproduce the known intrinsic and projected ve-locity dispersion profiles to within 1%.

3.3 Application to NGC 5846

Cappellari et al. (2006) obtained a surface-brightness pro-file for NGC 5846 in the I-band and found that a de Vau-couleurs profile is able to reproduce it well, outside a radiusof 10′′. They obtained an effective radius of Re = 9.5 kpcand an I-band surface-brightness at the effective radius ofIe,I = 23.3 L� kpc−2. For the intrinsic luminosity density,j(r), we adopt the analytical approximation of Prugniel &Simien (1997) to the deprojection of de Vaucouleurs law.

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Astron. Nachr. / AN (2008) 943

Fig. 3 (online colour at: www.an-journal.org) Plots showing the(a) intrinsic radial velocity dispersion; (b) anisotropy and; (c) re-projected velocity dispersion profiles for the two adopted circularvelocity curves, 1. (red dashed line), and 2. (black dashed line),described in Sect. 2. The black crosses in the third plot are ex-tracted from the input parameterisation for the projected velocitydispersion profile.

We use the long-slit kinematics of Kronawitter et al.(2000), extending to about 1.2Re, and PNe velocity dis-persions as measured by the PN.S (Coccato et al., 2008),extending to almost 4Re. The long-slit kinematics were ex-tracted along a major axis slit and a slit parallel to the minoraxis, on both sides of the galaxy. As we are constructinga non-rotating spherical model of NGC 5846, we take theodd moments of the LOSVD (V and h3) to be zero, andfold the σ and h4 profiles symmetrically about the centrefor the major axis, and about the major axis for measure-ments parallel to the minor axis. We also assign to eachof the kinematic data points a radius equal to the distancefrom the centre of the galaxy. As these moments are de-rived from fitting a Gaussian to the LOSVD, σ differs fromthe true second-order projected moment by approximatelyσP = σ(1 +

√6)h4. Errors are assigned to σP by applying

the error propagation formula to the measured errors in σand h4.

The PNe velocity dispersions were calculated by bin-ning their individual velocities into four circular annuli,with 35 PNe in the first three rings and 41 in the outermostring, amounting to 146 PNe in total.

The total projected velocity dispersion profile, σP(R),is shown in Fig. 2 along with the adopted parameterisation.Within the central 0.1Re, the projected velocity dispersionis approximately constant at just above 250 km/s and then

decreases almost linearly in the logarithmic radius scale toa value of almost 180 km/s at about 4Re.

Figure 3 shows the intrinsic radial velocity dispersion,anisotropy and reprojected velocity dispersion profiles weobtain from applying the algorithm to NGC 5846 in thetwo circular velocity curves described in Sect. 2. They areshown only outside 0.4Re due to uncertainties in the XMM-Newton circular velocity curve in that region and also dueto diverging solutions to the Jeans equation when the inputprofiles are not exactly in virial equilibrium with each other(Dejonghe & Merritt 1992). Beyond 0.7Re the three profilesagree almost exactly and show an anisotropy of β ∼ 0.75 inthe massive halo, implying the dominance of highly radialorbits in this region. We also constructed constant β mod-els in the XMM-Newton potential and found β = 0.8 be-yond 0.8Re. These results are reminiscent of the numericalsimulations of Abadi et al. (2006), who find that the orbitalstructure of the stellar component of galaxies becomes in-creasingly radially anisotropic up to β ∼ 0.8 at the virialradius.Acknowledgements. PD was supported by the DFG Cluster of Ex-cellence “Origin and Structure of the Universe”.

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