Unresolved emission and ionized gas in the bulge of M31

We study the origin of unresolved X-ray emission from the bulge of M31 based on archival Chandra and XMM–Newton observations. We demonstrate that three different components are present. (i) Broad-band emission from a large number of faint sources – mainly accreting white dwarfs and active binaries, associated with the old stellar population, similar to the Galactic ridge X-ray emission of the Milky Way. The X-ray to K -band luminosity ratios are compatible with those for the Milky Way and for M32; in the 2–10 keV band, the ratio is  (3.6 ± 0.2) × 10²⁷ erg s⁻¹ L⁻¹_⊙  . (ii) Soft emission from ionized gas with a temperature of about ∼300 eV and a mass of  ∼2 × 10⁶ M_⊙  . The gas distribution is significantly extended along the minor axis of the galaxy, suggesting that it may be outflowing in the direction perpendicular to the galactic disc. The mass and energy supply from evolved stars and Type Ia supernovae is sufficient to sustain the outflow. We also detect a shadow cast on the gas emission by spiral arms and the 10-kpc star-forming ring, confirming significant extent of the gas in the 'vertical' direction. (iii) Hard extended emission from spiral arms, most likely associated with young stellar objects and young stars located in the star-forming regions. The   L _X/SFR  (star formation rate) ratio equals  ∼9 × 10³⁸ (erg s⁻¹)(M_⊙ yr⁻¹)⁻¹  , which is about ∼1/3 of the high-mass X-ray binary contribution, determined earlier from Chandra observations of other nearby galaxies.     

Redistributing hot gas around galaxies: do cool clouds signal a solution to the overcooling problem?

We present a pair of high-resolution smoothed particle hydrodynamics simulations that explore the evolution and cooling behaviour of hot gas around Milky Way size galaxies. The simulations contain the same total baryonic mass and are identical other than their initial gas density distributions. The first is initialized with a low-entropy hot gas halo that traces the cuspy profile of the dark matter, and the second is initialized with a high-entropy hot halo with a cored density profile as might be expected in models with pre-heating feedback. Galaxy formation proceeds in dramatically different fashion depending on the initial setup. While the low-entropy halo cools rapidly, primarily from the central region, the high-entropy halo is quasi-stable for  ∼4 Gyr  and eventually cools via the fragmentation and infall of clouds from ∼100 kpc distances. The low-entropy halo's X-ray surface brightness is ∼100 times brighter than current limits and the resultant disc galaxy contains more than half of the system's baryons. The high-entropy halo has an X-ray brightness that is in line with observations, an extended distribution of pressure-confined clouds reminiscent of observed populations and a final disc galaxy that has half the mass and ∼50 per cent more specific angular momentum than the disc formed in the low-entropy simulation. The final high-entropy system retains the majority of its baryons in a low-density hot halo. The hot halo harbours a trace population of cool, mostly ionized, pressure-confined clouds that contain ∼10 per cent of the halo's baryons after 10 Gyr of cooling. The covering fraction for H  i and Mg  ii absorption clouds in the high-entropy halo is ∼0.4 and ∼0.6, respectively, although most of the mass that fuels disc growth is ionized, and hence would be under counted in H  i surveys.     

UBRI photometry of globular clusters in the Leo group galaxy NGC 3379

We present wide-area UBRI photometry for globular clusters around the Leo group galaxy NGC 3379. Globular cluster candidates are selected from their B -band magnitudes and their  ( U − B ) _o   versus  ( B − I ) _o   colours. A colour–colour selection region was defined from photometry of the Milky Way and M31 globular cluster systems. We detect 133 globular cluster candidates, which supports previous claims of a low specific frequency for NGC 3379.
The Milky Way and M31 reveal blue and red subpopulations, with  ( U − B ) _o   and  ( B − I ) _o   colours indicating mean metallicities similar to those expected based on previous spectroscopic work. The stellar population models of Maraston and Brocato et al. are consistent with both subpopulations being old, and with metallicities of  [Fe/H]∼−1.5  and −0.6 for the blue and red subpopulations, respectively. The models of Worthey do not reproduce the  ( U − B ) _o   colours of the red (metal-rich) subpopulation for any modelled age.
For NGC 3379 we detect a blue subpopulation with similar colours, and presumably age/metallicity, to that of the Milky Way and M31 globular cluster systems. The red subpopulation is less well defined, perhaps due to increased photometric errors, but indicates a mean metallicity of [Fe/H]∼−0.6.     

The Milky Way Galaxy as a strong gravitational lens

We study the gravitational lensing effects of spiral galaxies by taking a model of the Milky Way and computing its lensing properties. The model is composed of a spherical Hernquist bulge, a Miyamoto–Nagai disc and an isothermal halo. As a strong lens, a spiral galaxy like the Milky Way can give rise to four different imaging geometries. They are (i) three images on one side of the galaxy centre ('disc triplets'), (ii) three images with one close to the centre ('core triplets'), (iii) five images and (iv) seven images. Neglecting magnification bias, we show that the core triplets, disc triplets and fivefold imaging are roughly equally likely. Even though our models contain edge-on discs, their image multiplicities are not dominated by disc triplets. The halo is included for completeness, but it has a small effect on the caustic structure, the time delays and brightnesses of the images.
The Milky Way model has a maximum disc (i.e. the halo is not dynamically important in the inner parts). Strong lensing by nearly edge-on disc galaxies breaks the degeneracy between the relative contributions of the disc and halo to the overall rotation curve. If a spiral galaxy has a submaximum disc, then the astroid caustic shrinks dramatically in size, whilst the radial caustic shrinks more modestly. This causes changes in the relative likelihood of the image geometries, specifically (i) core triplets are now ∼9/2 times more likely than disc triplets, (ii) the cross-section for threefold imaging is reduced by a factor of ∼2/3, whilst (iii) the cross-section for fivefold imaging is reduced by ∼1/2. Although multiple imaging is less likely (the cross-sections are smaller), the average total magnification is greater. The time delays are smaller, as the total projected lensing mass is reduced.     

Chandra observations of the galaxy cluster Abell 1835

We present the analysis of 30 ks of Chandra observations of the galaxy cluster Abell 1835. Overall, the X-ray image shows a relaxed morphology, although we detect substructure in the inner 30-kpc radius. Spectral analysis shows a steep drop in the X-ray gas temperature from ∼12 keV in the outer regions of the cluster to ∼4 keV in the core. The Chandra data provide tight constraints on the gravitational potential of the cluster which can be parametrized by a Navarro, Frenk & White model. The X-ray data allow us to measure the X-ray gas mass fraction as a function of radius, leading to a determination of the cosmic matter density of
   
. The projected mass within a radius of ∼150 kpc implied by the presence of gravitationally lensed arcs in the cluster is in good agreement with the mass models preferred by the Chandra data. We find a radiative cooling time of the X-ray gas in the centre of Abell 1835 of about
   
. Cooling-flow model fits to the Chandra spectrum and a deprojection analysis of the Chandra image both indicate the presence of a young cooling flow (∼     with an integrated mass deposition rate of     within a radius of 30 kpc. We discuss the implications of our results in the light of recent Reflection Grating Spectrograph (RGS) observations of Abell 1835 with XMM-Newton .     

When is star formation episodic? A delay differential equation 'negative feedback' model

We introduce a differential equation for star formation in galaxies that incorporates negative feedback with a delay. When the feedback is instantaneous, solutions approach a self-limiting equilibrium state. When there is a delay, even though the feedback is negative, the solutions can exhibit cyclic and episodic solutions. We find that periodic or episodic star formation only occurs when two conditions are satisfied. First the delay time-scale must exceed a cloud consumption time-scale. Secondly, the feedback must be strong. This statement is quantitatively equivalent to requiring that the time-scale to approach equilibrium be greater than approximately twice the cloud consumption time-scale. The period of oscillations predicted is approximately four times the delay time-scale. The amplitude of the oscillations increases with both feedback strength and delay time.
We discuss applications of the delay differential equation (DDE) model to star formation in galaxies using the cloud density as a variable. The DDE model is most applicable to systems that recycle gas and only slowly remove gas from the system. We propose likely delay mechanisms based on the requirement that the delay time is related to the observationally estimated time between episodic events. The proposed delay time-scale accounting for episodic star formation in galaxy centres on periods similar to   P ∼ 10 Myr  , irregular galaxies with   P ∼ 100 Myr  , and the Milky Way disc with   P ∼ 2  Gyr, could be that for exciting turbulence following creation of massive stars, that for gas pushed into the halo to return and interact with the disc and that for spiral density wave evolution, respectively.     

Constraining dark matter properties with SPI

Using the high-resolution spectrometer SPI on board the International Gamma-Ray Astrophysics Laboratory ( INTEGRAL ), we search for a spectral line produced by a dark matter (DM) particle with a mass in the range  40 keV < M _DM < 14 MeV  , decaying in the DM halo of the Milky Way. To distinguish the DM decay line from numerous instrumental lines found in the SPI background spectrum, we study the dependence of the intensity of the line signal on the offset of the SPI pointing from the direction toward the Galactic Centre. After a critical analysis of the uncertainties of the DM density profile in the inner Galaxy, we find that the intensity of the DM decay line should decrease by at least a factor of 3 when the offset from the Galactic Centre increases from 0° to 180°. We find that such a pronounced variation of the line flux across the sky is not observed for any line, detected with a significance higher than 3σ in the SPI background spectrum. Possible DM decay origin is not ruled out only for the unidentified spectral lines, having low (∼3σ) significance or coinciding in position with the instrumental ones. In the energy interval from 20 keV to 7 MeV, we derive restrictions on the DM decay line flux, implied by the (non-)detection of the DM decay line. For a particular DM candidate, the sterile neutrino of mass M _DM, we derive a bound on the mixing angle.     

ROSAT ASCA observations of X-ray luminous starburst galaxies: NGC 3310 and 3690

We present ROSAT [High Resolution Imager (HRI) and Position Sensitive Proportional Counter (PSPC)] and ASCA observations of the two luminous ( L _x ∼ 10⁴¹⁻⁴² erg s⁻¹) star-forming galaxies NGC 3310 and 3690. The HRI shows clearly that the sources are extended with the X-ray emission in NGC 3690 coming from at least three regions. The combined 0.1–10 keV spectrum of NGC 3310 can be described by two components, a Raymond–Smith plasma with temperature kT  = 0.81^+0.09_−0.12 keV and a hard power law, Γ = 1.44^−0.20_−0.11 (or alternatively a harder Raymond–Smith plasma with kT  ∼ 15 keV), while there is no substantial excess absorption above the Galactic column value. The soft component emission is probably a super wind while the nature of the hard emission is more uncertain with the likely origins being X-ray binaries, inverse Compton scattering of infrared photons, an active galactic nucleus or a very hot gas component (∼10⁸ K). The spectrum of NGC 3690 is similar, with kT  = 0.83^+0.02_−0.04 keV and Γ = 1.56^+0.11_−0.11. We also employ more complicated models such as a multi-temperature thermal plasma, a non-equilibrium ionization code or the addition of a third softer component, which improve the fit but not at a statistically significant level (2σ). These results are similar to recent results on the archetypal star-forming galaxies M82 and NGC 253.     

Hydrodynamical simulations of Galactic fountains – I. Evolution of single fountains

The ejection of the gas out of the disc in late-type galaxies is related to star formation and is due mainly to Type II supernovae. In this paper, we studied in detail the development of the Galactic fountains in order to understand their dynamical evolution and their influence on the redistribution of the freshly delivered metals over the disc. To this aim, we performed a number of 3D hydrodynamical radiative cooling simulations of the gas in the Milky Way where the whole Galaxy structure, the Galactic differential rotation and the supernova explosions generated by a single OB association are considered. A typical fountain powered by 100 Type II supernovae may eject material up to ∼2 kpc which than collapses back mostly in the form of dense, cold clouds and filaments. The majority of the gas lifted up by the fountains falls back on the disc remaining within a radial distance  Δ R = 0.5 kpc  from the place where the fountain originated. This localized circulation of disc gas does not influence the radial chemical gradients on large scale, as required by the chemical models of the Milky Way which reproduce the metallicity distribution without invoking large fluxes of metals. Simulations of multiple fountains fuelled by Type II supernovae of different OB associations will be presented in a companion paper.     

Shattering and coagulation of dust grains in interstellar turbulence

We investigate shattering and coagulation of dust grains in turbulent interstellar medium (ISM). The typical velocity of dust grain as a function of grain size has been calculated for various ISM phases based on a theory of grain dynamics in compressible magnetohydrodynamic turbulence. In this paper, we develop a scheme of grain shattering and coagulation and apply it to turbulent ISM by using the grain velocities predicted by the above turbulence theory. Since large grains tend to acquire large velocity dispersions as shown by earlier studies, large grains tend to be shattered. Large shattering effects are indeed seen in warm ionized medium within a few Myr for grains with radius   a ≳ 10⁻⁶  cm. We also show that shattering in warm neutral medium can limit the largest grain size in ISM  ( a ∼ 2 × 10⁻⁵ cm)  . On the other hand, coagulation tends to modify small grains since it only occurs when the grain velocity is small enough. Coagulation significantly modifies the grain size distribution in dense clouds (DC), where a large fraction of the grains with   a < 10⁻⁶ cm  coagulate in 10 Myr. In fact, the correlation among   R_V   , the carbon bump strength and the ultraviolet slope in the observed Milky Way extinction curves can be explained by the coagulation in DC. It is possible that the grain size distribution in the Milky Way is determined by a combination of all the above effects of shattering and coagulation. Considering that shattering and coagulation in turbulence are effective if dust-to-gas ratio is typically more than ∼1/10 of the Galactic value, the regulation mechanism of grain size distribution should be different between metal-poor and metal-rich environments.     

Do high-velocity clouds form by thermal instability?

We examine the proposal that the H  i 'high-velocity' clouds (HVCs) surrounding the Milky Way and other disc galaxies form by condensation of the hot galactic corona via thermal instability. Under the assumption that the galactic corona is well represented by a non-rotating, stratified atmosphere, we find that for this formation mechanism to work the corona must have an almost perfectly flat entropy profile. In all other cases, the growth of thermal perturbations is suppressed by a combination of buoyancy and thermal conduction. Even if the entropy profile were nearly flat, cold clouds with sizes smaller than  10 kpc  could form in the corona of the Milky Way only at radii larger than  100 kpc  , in contradiction with the determined distances of the largest HVC complexes. Clouds with sizes of a few kpc can form in the inner halo only in low-mass systems. We conclude that unless even slow rotation qualitatively changes the dynamics of a corona, thermal instability is unlikely to be a viable mechanism for formation of cold clouds around disc galaxies.     

An XMM–Newton observation of the galaxy group MKW 4

We present an X-ray study of the galaxy group or poor cluster MKW 4. Working with XMM–Newton data we examine the distribution and properties of the hot gas which makes up the group halo. The inner halo shows some signs of structure, with circular or elliptical beta models providing a poor fit to the surface brightness profile. This may be evidence of large-scale motion in the inner halo, but we do not find evidence of sharp fronts or edges in the emission. The temperature of the halo declines in the core, with deprojected spectral fits showing a central temperature of ∼1.3 keV compared to ∼3 keV at 100 kpc. In the central ∼30 kpc of the group, multitemperature spectral models are required to fit the data, but they indicate a lack of gas at low temperatures. Steady-state cooling flow models provide poor fits to the inner regions of the group and the estimated cooling time of the gas is long except within the central dominant galaxy, NGC 4073. Abundance profiles show a sharp increase in the core of the group, with mean abundance rising by a factor of 2 in the centre of NGC 4073. Fitting individual elements shows the same trend, with high values of Fe, Si and S in the core. We estimate that ∼50 per cent of the Fe in the central 40 kpc was injected by Type Ia supernovae, in agreement with previous ASCA studies. Using our best-fitting surface brightness and temperature models, we calculate the mass, gas fraction, entropy and mass-to-light ratio of the group. At 100 kpc (∼0.1 virial radius) the total mass and gas entropy of the system (  ∼2 × 10¹³ M_⊙  and ∼300 keV cm²) are quite comparable to those of other systems of similar temperature, but the gas fraction is rather low (∼1 per cent). We conclude that MKW 4 is a fairly relaxed group, which has developed a strong central temperature gradient but not a large-scale cooling flow.     

Astronomical constraints on properties of sterile neutrino dark matter

We consider sterile neutrinos as a component of dark matter in the Milky Way and clusters, and compare their rest mass, decay rate and the mixing angle. A radiative decaying rate of order Γ∼10⁻¹⁹ s⁻¹ for sterile neutrino rest mass m _s =18–19 keV can satisfactorily account for the cooling flow problem and heating source in Milky Way center simultaneously. Also, these ranges of decay rate and rest mass match the prediction of the mixing angle sin ²2θ∼10⁻³ with a low reheating temperature in the inflation model, which enables the sterile-active neutrino oscillation to be visible in future experiments. However, decaying sterile neutrinos have to be ruled out as a major component of dark matter because of the high decay rate.     

Fe K emission in the ultraluminous infrared galaxy Arp 220

Prominent Fe Kα line emission is detected in the XMM–Newton spectrum of the ultraluminous infrared galaxy Arp 220. The centroid of the line is found at an energy of 6.7 keV and the equivalent width of the line is  EW ∼ 1.9 keV  (at 3.5σ significance). A few other spectral features are found at various degrees of significance in the lower energy range on a hard 2.5–10 keV continuum  (Γ∼ 1)  . The large EW of the Fe K line poses a problem with interpreting the hard X-ray emission as integrated X-ray binary emission. A thermal emission spectrum with a temperature of   kT ∼ 7 keV  modified by absorption of   N _H≃ 3 × 10²² cm⁻²  , can describe the 2.5–10 keV continuum shape and the Fe K emission. A hot bubble that is shocked internally in a starburst region would have a similar temperature and gives a good explanation for the observed X-ray properties with a high star formation rate. An ensemble of radio supernovae in a dense environment, as suggested from VLBI imaging, could be another possibility, if such powerful supernovae are produced continuously at a high rate. However, the apparent lack of emission from X-ray binaries is incompatible with the high supernova rate (∼2 SNe yr⁻¹) required by both interpretations. Highly photoionized, low-density gas illuminated by a hidden Compton-thick active galactic nucleus is a possible alternative for the hard X-ray emission, which can be tested by examining whether radiative recombination continua from highly ionized Ca and Fe are present in better quality data from a forthcoming observation.     

A deep X-ray observation of M82 with XMM–Newton

We report on the analysis of a deep (100-ks) observation of the starburst galaxy M82 with the EPIC and RGS instruments onboard the X-ray telescope XMM–Newton . The broad-band (0.5–10 keV) emission is due to at least three spectral components: (i) continuum emission from point sources; (ii) thermal plasma emission from hot gas; and (iii) charge-exchange emission from neutral metals (Mg and Si). The plasma emission has a double-peaked differential emission measure, with the peaks at ∼0.5 and ∼7 keV. Spatially resolved spectroscopy has shown that the chemical absolute abundances are not uniformly distributed in the outflow, but are larger in the outskirts and smaller close to the galaxy centre. The abundance ratios also show spatial variations. The X-ray-derived oxygen abundance is lower than that measured in the atmospheres of red supergiant stars, leading to the hypothesis that a significant fraction of oxygen ions have already cooled off and no longer emit at energies ≳0.5 keV.     

Physics of accretion in the millisecond pulsar XTE J1751 − 305

We have undertaken an extensive study of X-ray data from the accreting millisecond pulsar XTE J1751 − 305 observed by RXTE and XMM–Newton during its 2002 outburst. In all aspects this source is similar to the prototypical millisecond pulsar SAX J1808.4 − 3658, except for the higher peak luminosity of 13 per cent of Eddington, and the optical depth of the hard X-ray source, which is larger by a factor ∼2. Its broad-band X-ray spectrum can be modelled by three components. We interpret the two soft components as thermal emission from a colder  ( kT ∼ 0.6 keV)  accretion disc and a hotter (∼1 keV) spot on the neutron star surface. We interpret the hard component as thermal Comptonization in plasma of temperature ∼40 keV and optical depth ∼1.5 in a slab geometry. The plasma is heated by the accretion shock as the material collimated by the magnetic field impacts on to the surface. The seed photons for Comptonization are provided by the hotspot, not by the disc. The Compton reflection is weak and the disc is probably truncated into an optically thin flow above the magnetospheric radius. Rotation of the emission region with the star creates an almost sinusoidal pulse profile with an rms amplitude of 3.3 per cent. The energy-dependent soft phase lags can be modelled by two pulsating components shifted in phase, which is naturally explained by a different character of emission of the optically thick spot and optically thin shock combined with the action of the Doppler boosting. The observed variability amplitude constrains the hotspot to lie within 3°–4° of the rotational pole. We estimate the inner radius of the optically thick accreting disc to be about 40 km. In that case, the absence of emission from the antipodal spot, which can be blocked by the accretion disc, gives the inclination of the system as ≳70°.     

Infall of substructures on to a Milky Way-like dark halo

We analyse the dynamical properties of substructures in a high-resolution dark matter simulation of the formation of a Milky Way-like halo in a Λcold dark matter cosmology. Our goal is to shed light on the dynamical peculiarities of the Milky Way satellites. Our simulations show that about one-third of the subhaloes have been accreted in groups. We quantify this clustering by measuring the alignment of the angular momentum of subhaloes in a group. We find that this signal is visible even for objects accreted up to z ∼ 1, i.e. 8 Gyr ago, and long after the spatial coherence of the groups has been lost due the host tidal field. This group infall may well explain the ghostly streams proposed by Lynden-Bell & Lynden-Bell to orbit the Milky Way. Our analyses also show that if most satellites originate in a few groups, the disc-like distribution of the Milky Way satellites would be almost inevitable. This non-random assignment of satellites to subhaloes implies an environmental dependence on whether these low-mass objects are able to form stars, possibly related to the nature of reionization in the early Universe. With this picture, both the 'ghostly streams' and the 'disc-like configuration' are manifestations of the same phenomenon: the hierarchical growth of structure down to the smallest scales.     

A model of supernova feedback in galaxy formation

A model of supernova feedback during disc galaxy formation is developed. The model incorporates infall of cooling gas from a halo, and outflow of hot gas from a multiphase interstellar medium (ISM). The star formation rate is determined by balancing the energy dissipated in collisions between cold gas clouds with that supplied by supernovae in a disc marginally unstable to axisymmetric instabilities. Hot gas is created by thermal evaporation of cold gas clouds in supernova remnants, and criteria are derived to estimate the characteristic temperature and density of the hot component and hence the net mass outflow rate. A number of refinements of the model are investigated, including a simple model of a galactic fountain, the response of the cold component to the pressure of the hot gas, pressure-induced star formation and chemical evolution. The main conclusion of this paper is that low rates of star formation can expel a large fraction of the gas from a dwarf galaxy. For example, a galaxy with circular speed 50 km s¹ can expel 6080 per cent of its gas over a time-scale of 1 Gyr, with a star formation rate that never exceeds 0.1 M yr¹. Effective feedback can therefore take place in a quiescent mode and does not require strong bursts of star formation. Even a large galaxy, such as the Milky Way, might have lost as much as 20 per cent of its mass in a supernova-driven wind. The models developed here suggest that dwarf galaxies at high redshifts will have low average star formation rates and may contain extended gaseous discs of largely unprocessed gas. Such extended gaseous discs might explain the numbers, metallicities and metallicity dispersions of damped Lyman systems.     

X-ray emission lines and multiphase gas in elliptical galaxies and galaxy clusters

We examine the K shell emission lines produced by isothermal and simple multiphase models of the hot gas in elliptical galaxies and galaxy clusters to determine the most effective means for constraining the width of the differential emission measure, ( T  ), in these systems which we characterize by a dimensionless parameter, . Comparison of line ratios of two-temperature  ( <1)  and cooling flow  ( 1)  models is presented in detail. We find that a two-temperature model can approximate very accurately a cooling flow spectrum over 0.510 keV.
We re-analyse the ASCA spectra of three of the brightest galaxy clusters to assess the evidence for multiphase gas in their cores: M87 (Virgo), the Centaurus cluster and the Perseus cluster. K emission-line blends of Si, S, Ar, Ca and Fe are detected in each system, as is significant Fe K emission. The Fe K /K ratios are consistent with optically thin plasma models and do not suggest resonance scattering in these systems. Consideration of both the ratios of H-like to He-like K lines and the local continuum temperatures clearly rules out isothermal gas in each case. To obtain more detailed constraints, we fitted plasma models over 1.69 keV where the emission is dominated by these K shell lines and by continuum. In each case the ASCA spectra cannot determine whether the gas emits at only two temperatures or over a continuous range of temperatures as expected for a cooling flow. The metal abundances are near-solar for all of the multiphase models. We discuss the implications of these results and examine the prospects for determining the temperature structure in these systems with upcoming X-ray missions.     

The orbit and mass of the Sagittarius dwarf galaxy

Possible orbital histories of the Sgr dwarf galaxy are explored. A special-purpose N -body code is used to construct the first models of the Milky Way–Sgr dwarf system in which both the Milky Way and the Sgr dwarf are represented by full N -body systems and followed for a Hubble time. These models are used to calibrate a semi-analytic model of the Sgr dwarf's orbit that enables us to explore a wider parameter space than is accessible to the N -body models. We conclude that the extant data on the Sgr dwarf are compatible with a wide range of orbital histories. At one extreme the Sgr dwarf initially possesses ∼10¹¹ M_⊙ and starts from a Galactocentric distance R _D(0)≳200 kpc. At the other extreme the Sgr dwarf starts with ∼10⁹ M_⊙ and R _D(0)∼60 kpc, similar to its present apocentric distance. In all cases the Sgr dwarf is initially dark matter dominated and the current velocity dispersion of the Sgr dwarf's dark matter is tightly constrained to be 21±2 km s⁻¹. This number is probably compatible with the smaller measured dispersion of the Sgr dwarf's stars because of (i) the dynamical difference between dark and luminous matter, and (ii) velocity anisotropy.