Time-series Paschen-β spectroscopy of SU Aurigae

We present time-series echelle spectra of the Paβ line of the T Tauri star SU Aur, observed over three consecutive nights. The line shows strong variability (∼10 per cent) over the velocity range 100–420 km s⁻¹ in the red broad absorption component, and weaker variability (∼2 per cent) over the velocity range  −200–0 km s⁻¹  in the blue wing. The variability in the velocity range  −200–0 km s⁻¹  is correlated with that in  200–400 km s⁻¹  , and the variability in these velocity ranges anticorrelates with that in  0–100 km s⁻¹  . The mean spectrum from the second night shows the suggestion of a blueshifted absorption component at about  −150 km s⁻¹  , similar to that found in the Hα and Hβ lines. We find the position of the subpeak in the red absorption component changes steadily with time, and its motion modulates at half the rotational period. We also find that the modulation of the line equivalent width is possibly associated with a half and a third of the rotational period, which is consistent with the surface Doppler images of SU Aur. Radiative transfer models of a rotationally modulated Paβ line, produced in the shock-heated magnetospheric accretion flow, are also presented. Models with a magnetic dipole offset reproduce the overall characteristics of the observed line variability, including the line equivalent width and the motion of the subpeak in the red absorption trough.     

The high-velocity molecular stream in W51B: a ring structure with compact H ii regions

We present ¹³ CO J  = 1 − 0 line observations of the H  ii region complex W51B located in the high-velocity (HV) stream. These observations reveal a filamentary and clumpy structure in the molecular gas. The mean local standard of rest (LSR) velocity ∼ + 65 km s⁻¹ of the molecular gas in this region is greater than the maximum velocities allowed by kinematic Galactic rotation curves. The size and mass of the molecular clouds are ∼ 48 × 17 pc² and ∼ 2.4 × 10⁵ M⊙ respectively. In a position–velocity diagram, molecular gas in the southern part comprises a redshifted ring structure with v _LSR=+ 60 to +73 km s⁻¹. The velocity gradient of this ring is ∼ 0.5 km s⁻¹ pc⁻¹, and the mass is ∼ 6.2 × 10⁴ M⊙. If we assume that the ring is expanding with a uniform velocity, the expansion velocity, radius and kinetic energy are ∼ 7 km s⁻¹, ∼ 13 pc and ∼ 3.0 × 10 ⁴⁹ erg respectively. The kinetic energy and mass spectrum of the ring could be explained by an expanding cylindrical cloud with a centrally condensed mass distribution. The locations of two compact H  ii regions, G49.0−0.3 and G48.9−0.3, coincide with the two molecular clumps in this ring. We discuss star formation, and the mechanism that produced the ring structure.     

Iron line profiles including emission from within the innermost stable orbit of a black hole accretion disc

We propose a model for the source of the X-ray background (XRB) in which low-luminosity active nuclei ( L  ∼ 10⁴³ erg s⁻¹) are obscured ( N  ∼ 10²³ cm⁻²) by nuclear starbursts within the inner ∼ 100 pc. The obscuring material covers most of the sky as seen from the central source, rather than being distributed in a toroidal structure, and hardens the averaged X-ray spectrum by photoelectric absorption. The gas is turbulent with velocity dispersion ∼ few × 100 km s⁻¹ and cloud–cloud collisions lead to copious star formation. Although supernovae tend to produce outflows, most of the gas is trapped in the gravity field of the star-forming cluster itself and the central black hole. A hot ( T  ∼ 10⁶ − 10⁷ K) virialized phase of this gas, comprising a few per cent of the total obscuring material, feeds the central engine of ∼ 10⁷ M⊙ through Bondi accretion, at a sub-Eddington rate appropriate for the luminosity of these objects. If starburst-obscured objects give rise to the residual XRB, then only 10 per cent of the accretion in active galaxies occurs close to the Eddington limit in unabsorbed objects.     

A sample of galaxies near the South Celestial Pole

This paper reports the results of a modest redshift survey carried out, at generally low Galactic latitudes, in the vicinity of the South Celestial Pole. Target galaxies were selected as a 'representative' sample of underlying large-scale structures. Dimensions, approximate magnitudes and radial velocity measurements, are reported for 336 galaxies. Two obvious Seyfert 1 galaxies, one probably Seyfert 1 and three Seyfert 2 galaxies have been discovered. The redshifts are used to supplement existing data and serve to map southern voids and features out to 25 000 km s⁻¹ in the region  270° < l < 330°, 0° > b > −45°  . Three distinct superclusters and twenty apparent voids are tentatively identified. One Void, at   l = 300°, b =−20°, cz = 16 000 km s⁻¹  , with a diameter of 6000 km s⁻¹, is as large as any yet mapped. It appears as part of a general underdense region.     

Distant field blue horizontal branch stars – III. Identification of a probable outer halo stream at Galactocentric distance r= 70 kpc

We present FOcal Reducer/low dispersion Spectrograph-1 spectra (from the European Southern Observatory's Very Large Telescope) of a sample of 34 faint  20.0 < g * < 21.1  A-type stars selected from the Sloan Digital Sky Survey Early Data Release, with the goal of measuring the velocity dispersion of blue horizontal branch (BHB) stars in the remote Galactic halo,   R ∼ 80 kpc  . We show that colour selection with  1.08 < u *− g * < 1.40  and  −0.2 < g *− r * < −0.04  minimizes contamination of the sample by less luminous blue stragglers. In classifying the stars we confine our attention to the 20 stars with spectra of signal-to-noise ratio >15 Å⁻¹. Classification produces a sample of eight BHB stars at distances  65–102 kpc  from the Sun (mean 80 kpc), which represents the most distant sample of Galactic stars with measured radial velocities. The dispersion of the measured radial component of the velocity with respect to the centre of the Galaxy is  58 ± 15 km s⁻¹  . This value is anomalously low in comparison with measured values for stars at smaller distances, as well as for satellites at similar distances. Seeking an explanation for the low measured velocity dispersion, further analysis reveals that six of the eight remote BHB stars are plausibly associated with a single orbit. Three previously known outer halo carbon stars also appear to belong to this stream. The velocity dispersion of all nine stars relative to the orbit is only  15 ± 4 km s⁻¹  . Further observations along the orbit are required to trace the full extent of this structure on the sky.     

The interstellar medium in the Upper Cepheus-Cassiopeia region

We have studied the kinematics and spatial distribution of the interstellar gas in the sky region  110°≤ l ≤ 135°, 10°≤ b ≤ 20°  , using the extensive Leiden–Dwingeloo Survey of H  i emission and the Columbia Survey of CO emission. The spectra show two main velocity components, namely feature A that has a mean local standard of rest (LSR) velocity of  ∼0  km s⁻¹  and is due to the Lindblad ring of the Gould belt, and feature C that has a mean LSR velocity of  ∼−11  km s⁻¹  and is associated to the local arm or Orion arm. The H  i and CO distributions of feature A in the region trace a large complex of gas and dust known as the Cepheus Flare, which lies at a distance of 300 pc. The spectral line profiles of feature A, which are rather broad and often double-peaked, reveal that the Cepheus Flare forms part of a big expanding shell of interstellar matter that encloses an old supernova remnant associated with a void inside the Cepheus Flare. On the other hand, by analysing the distribution and velocity structure of feature C, we have detected a second large expanding shell in the region, located at a distance of 800 pc in the local arm. This shell surrounds the stellar association Cepheus OB4 and was probably generated by stellar winds and supernovae of Cepheus OB4. The radii, expansion velocities and H  i masses of the two shells are approximately 50 pc, 4  km s⁻¹ and  1.3 × 10⁴ M_⊙  for the Cepheus Flare shell and 100 pc, 4 km s⁻¹ and  9.9 × 10⁴ M_⊙  for the Cepheus OB4 shell. Both shells have similar ages of the order of a few 10⁶ yr.     

The Norma cluster (ACO 3627) – I. A dynamical analysis of the most massive cluster in the Great Attractor

A detailed dynamical analysis of the nearby rich Norma cluster (ACO 3627) is presented. From radial velocities of 296 cluster members, we find a mean velocity of 4871 ± 54 km s⁻¹ and a velocity dispersion of 925 km s⁻¹. The mean velocity of the E/S0 population (4979 ± 85 km s⁻¹) is offset with respect to that of the S/Irr population (4812 ± 70 km s⁻¹) by  Δ v = 164 km s⁻¹  in the cluster rest frame. This offset increases towards the core of the cluster. The E/S0 population is free of any detectable substructure and appears relaxed. Its shape is clearly elongated with a position angle that is aligned along the dominant large-scale structures in this region, the so-called Norma wall. The central cD galaxy has a very large peculiar velocity of 561 km s⁻¹ which is most probably related to an ongoing merger at the core of the cluster. The spiral/irregular galaxies reveal a large amount of substructure; two dynamically distinct subgroups within the overall spiral population have been identified, located along the Norma wall elongation. The dynamical mass of the Norma cluster within its Abell radius is  1–1.1 × 10¹⁵  h ⁻¹₇₃ M_⊙  . One of the cluster members, the spiral galaxy WKK 6176 which recently was observed to have a 70 kpc X-ray tail, reveals numerous striking low-brightness filaments pointing away from the cluster centre suggesting strong interaction with the intracluster medium.     

The formation of the black hole in the X-ray binary system V404 Cyg

Using new and archival radio data, we have measured the proper motion of the black hole X-ray binary V404 Cyg to be  9.2 ± 0.3 mas yr⁻¹  . Combined with the systemic radial velocity from the literature, we derive the full three-dimensional heliocentric space velocity of the system, which we use to calculate a peculiar velocity in the range 47–102 km s⁻¹, with a best-fitting value of 64 km s⁻¹. We consider possible explanations for the observed peculiar velocity and find that the black hole cannot have formed via direct collapse. A natal supernova is required, in which either significant mass  (∼11 M_⊙)  was lost, giving rise to a symmetric Blaauw kick of up to ∼65 km s⁻¹, or, more probably, asymmetries in the supernova led to an additional kick out of the orbital plane of the binary system. In the case of a purely symmetric kick, the black hole must have been formed with a mass  ∼9 M_⊙  , since when it has accreted  0.5–1.5 M_⊙  from its companion.     

Neutral gas and dust in the central region of the ultraluminous infrared galaxy Mrk 273

We have used MERLIN to observe neutral hydrogen absorption against the central region of the ultraluminous infrared galaxy (ULIRG) galaxy Mrk 273 with an angular resolution of 0.2 arcsec. This represents a factor of 5 increase in resolution compared with previous work. Absorption has been resolved against two of three radio continuum components. A Hubble Space Telescope ( HST ) image reveals a complex central region composed of clumpy emission obscured by dust lanes. We find that the northern and south-eastern radio components are associated with two optical components. The alignment supports the idea that Mrk 273 has a double nucleus due to a recent galactic merger event.
Broad, strong and spatially varying absorption is seen against the northern radio component with a velocity gradient of 1990±50 km s⁻¹ kpc⁻¹. The absorption resolves into six discrete components with an average column density of 1.7×10²² atom cm⁻². We propose that the absorption is due to a clumpy ring or disc of neutral gas of radius ∼250 pc rotating around a central starburst. In addition to the broad component, narrow absorption (<100 km s⁻¹) is detected against the northern and south-eastern components. Absorption is not detected against the weak (2 mJy) south-western component. We propose that the narrow absorption is due to quiescent gas in a large-scale dust lane that coincides with these regions of narrow absorption.     

Modelling the bar in the centre of the starburst galaxy M82

We present VLA A-array 21-cm atomic hydrogen (H  i ) absorption observed against the central region of the starburst galaxy M82 with an angular resolution of ∼1.3 arcsec (≃20 pc). These observations, together with MERLIN H  i absorption measurements, are compared with the molecular (CO) and ionized ([Ne  ii ]) gas distributions and are used to constrain the dynamics and structure of the ionized, neutral and molecular gas in this starburst.
A position–velocity diagram of the H  i distribution reveals an unusual 'hole' feature which, when previously observed in CO, has been interpreted as an expanding superbubble contained within a ring of gas in solid body rotation. However, we interpret this feature as a signature of a nearly edge-on barred galaxy. In addition, we note that the CO, H  i and [Ne  ii ] position–velocity diagrams reveal two main velocity gradients, and we interpret these as gas moving on x₁- and x₂-orbits within a bar potential. We find the best fit to the data to be produced using a bar potential with a flat rotation curve velocity v _b=140 km s⁻¹ and a total length of 1 kpc, a non-axisymmetry parameter q =0.9, an angular velocity of the bar Ω_b=217 km s⁻¹ arcsec⁻¹, a core radius R _c=25 pc, an inclination angle i =80° and a projected angle between the bar and the major axis of the galaxy φ '=4°. We also discuss the orientation of the disc and bar in M82.     

The local star formation rate and radio luminosity density

We present a new determination of the local volume-averaged star formation rate from the 1.4-GHz luminosity function of star forming galaxies. Our sample, taken from the   B ≤12  Revised Shapley–Ames catalogue (231 normal spiral galaxies over an effective area of 7.1 sr) has ≃100 per cent complete radio detections and is insensitive to dust obscuration and cirrus contamination. After removal of known active galaxies, the best-fitting Schechter function has a faint-end slope of  −1.27±0.07  in agreement with the local H α luminosity function, characteristic luminosity   L ∗=(2.6±0.7)×10²² W Hz⁻¹  and density   φ ∗=(4.8±1.1)×10⁻⁴ Mpc⁻³.  The inferred local radio luminosity density of  (1.73±0.37±0.03)×10¹⁹ W Hz⁻¹ Mpc⁻³  (Poisson noise, large-scale structure fluctuations) implies a volume-averaged star formation rate ∼2 times larger than the Gallego et al. H α estimate, i.e.   ρ _1.4 GHz=(2.10±0.45±0.04)×10⁻² M_⊙ yr⁻¹ Mpc⁻³  for a Salpeter initial mass function from  0.1–125 M_⊙  and Hubble constant of 50 km s⁻¹ Mpc⁻¹. We demonstrate that the Balmer decrement is a highly unreliable extinction estimator, and argue that optical–ultraviolet (UV) star formation rates (SFRs) are easily underestimated, particularly at high redshift.     

Kinematics of massive stars in the Small Magellanic Cloud

We present radial velocities for 2045 stars in the Small Magellanic Cloud (SMC), obtained from the 2dF survey by Evans et al. The great majority of these stars are of OBA type, tracing the dynamics of the young stellar population. Dividing the sample into ad hoc 'bar' and 'wing' samples (north and south, respectively, of the line:  δ=−77°50'+[4α]'  , where α is the right ascension in minutes of time) we find that the velocities in the SMC bar show a gradient of 26.3 ± 1.6 km s⁻¹ deg⁻¹ at a position angle of 126°± 4°. The derived gradient in the bar is robust to the adopted line of demarcation between the two samples. The largest redshifts are found in the SMC wing, in which the velocity distribution appears distinct from that in the bar, most probably a consequence of the interaction between the Magellanic Clouds that is predicted to have occurred 0.2 Gyr ago. The mean velocity for all stars in the sample is +172.0 ± 0.2 km s⁻¹ (redshifted by ∼20 km s⁻¹ when compared to published results for older populations), with a velocity dispersion of 30 km s⁻¹.     

Structures in the Great Attractor region

To further our understanding of the Great Attractor (GA), we have undertaken a redshift survey using the 2-degree Field (2dF) instrument on the Anglo-Australian Telescope (AAT). Clusters and filaments in the GA region were targeted with 25 separate pointings resulting in approximately 2600 new redshifts. Targets included poorly studied X-ray clusters from the Clusters in the Zone of Avoidance (CIZA) Catalogue as well as the Cen–Crux and PKS 1343−601 clusters, both of which lie close to the classic GA centre. For nine clusters in the region, we report velocity distributions as well as virial and projected mass estimates. The virial mass of CIZA J1324.7−5736, now identified as a separate structure from the Cen–Crux cluster, is found to be  ∼3 × 10¹⁴ M_⊙  , in good agreement with the X-ray inferred mass. In the PKS 1343−601 field, five redshifts are measured of which four are new. An analysis of redshifts from this survey, in combination with those from the literature, reveals the dominant structure in the GA region to be a large filament, which appears to extend from Abell S0639  ( l = 281°, b =+11°)  to  ( l ∼ 5°, b ∼−50°)  , encompassing the Cen–Crux, CIZA J1324.7−5736, Norma and Pavo II clusters. Behind the Norma cluster at   cz ∼ 15 000 km s⁻¹  , the masses of four rich clusters are calculated. These clusters (Triangulum Australis, Ara, CIZA J1514.6−4558 and CIZA J1410.4−4246) may contribute to a continued large-scale flow beyond the GA. The results of these observations will be incorporated into a subsequent analysis of the GA flow.     

Large-scale galactic turbulence: can self-gravity drive the observed H i velocity dispersions?

Observations of turbulent velocity dispersions in the H  i component of galactic discs show a characteristic floor in galaxies with low star formation rates and within individual galaxies the dispersion profiles decline with radius. We carry out several high-resolution adaptive mesh simulations of gaseous discs embedded within dark matter haloes to explore the roles of cooling, star formation, feedback, shearing motions and baryon fraction in driving turbulent motions. In all simulations the disc slowly cools until gravitational and thermal instabilities give rise to a multiphase medium in which a large population of dense self-gravitating cold clouds are embedded within a warm gaseous phase that forms through shock heating. The diffuse gas is highly turbulent and is an outcome of large-scale driving of global non-axisymmetric modes as well as cloud–cloud tidal interactions and merging. At low star formation rates these processes alone can explain the observed H  i velocity dispersion profiles and the characteristic value of  ∼10 km s⁻¹  observed within a wide range of disc galaxies. Supernovae feedback creates a significant hot gaseous phase and is an important driver of turbulence in galaxies with a star formation rate per unit area  ≳10⁻³ M_⊙ yr⁻¹ kpc⁻²  .     

A statistical study of 233 pulsar proper motions

We present and analyse a catalogue of 233 pulsars with proper motion measurements. The sample contains a wide variety of pulsars including recycled objects and those associated with globular clusters or supernova remnants. After taking the most precise proper motions for those pulsars for which multiple measurements are available, the majority of the proper motions (58 per cent) are derived from pulsar timing methods, 41 per cent using interferometers and the remaining 1 per cent using optical telescopes. Many of the one-dimensional (1D) and two-dimensional (2D) speeds (referring to speeds measured in one coordinate only and the magnitudes of the transverse velocities, respectively) derived from these measurements are somewhat lower than earlier estimates because of the use of the most recent electron density model in determining pulsar distances. The mean 1D speeds for the normal and recycled pulsars are 152(10) and 54(6) km s⁻¹, respectively. The corresponding mean 2D speeds are 246(22) and 87(13) km s⁻¹. PSRs B2011+38 and B2224+64 have the highest inferred 2D speeds of  ∼1600 km s⁻¹  . We study the mean speeds for different subsamples and find that, in general, they agree with previous results. Applying a novel deconvolution technique to the sample of 73 pulsars with characteristic ages less than 3 Myr, we find the mean three-dimensional (3D) pulsar birth velocity to be 400(40) km s⁻¹. The distribution of velocities is well described by a Maxwellian distribution with  1D rms σ= 265 km s⁻¹  . There is no evidence for a bimodal velocity distribution. The proper motions for PSRs B1830−08 and B2334+61 are consistent with their proposed associations with the supernova remnants W41 and G114.3+0.3, respectively.     

Global velocity field and bubbles in the blue compact dwarf galaxy Mrk 86

We have studied the velocity field of the blue compact dwarf galaxy Mrk 86 (NGC 2537) using data provided by 14 long-slit optical spectra obtained in 10 different orientations and positions. This kinematical information is complemented with narrow-band ([O  iii ]5007 Å and H α ) and broad-band ( B , V , Gunn r and K ) imaging. The analysis of the galaxy global velocity field suggests that the ionized gas could be distributed in a rotating inclined disc, with projected central angular velocity of Ω=34 km s⁻¹ kpc⁻¹. The comparison between the stellar, H  i and modelled dark matter density profile indicates that the total mass within its optical radius is dominated by the stellar component. Peculiarities observed in its velocity field can be explained by irregularities in the ionized gas distribution or local motions induced by star formation.
Kinematical evidences for two expanding bubbles, Mrk 86–B and Mrk 86–C, are given. They show expanding velocities of 34 and 17 km s⁻¹, H α luminosities of 3×10³⁸ and 1.7×10³⁹ erg s⁻¹, and physical radii of 374 and 120 pc, respectively. The change in the [S  ii ]/H α , [N  ii ]/H α , [O  ii ]/[O  iii ] and [O  iii ]/H β line ratios with the distance to the bubble precursor suggests a diminution in the ionization parameter and, in the case of Mrk 86–B, an enhancement of the shock-excited gas emission. The optical–near-infrared colours of the bubble precursors are characteristic of low‐metallicity star‐forming regions (∼0.2 Z_⊙) with burst strengths of about 1 per cent in mass.     

Optical spectroscopy and photometry of SAX J1808.4−3658 in outburst

We present phase resolved optical spectroscopy and photometry of V4580 Sagittarii, the optical counterpart to the accretion powered millisecond pulsar SAX J1808.4−3658, obtained during the 2008 September/October outburst. Doppler tomography of the N  iii λ4640.64 Bowen blend emission line reveals a focused spot of emission at a location consistent with the secondary star. The velocity of this emission occurs at  324 ± 15 km s⁻¹  ; applying a ' K -correction', we find the velocity of the secondary star projected on to the line of sight to be  370 ± 40 km s⁻¹  . Based on existing pulse timing measurements, this constrains the mass ratio of the system to be  0.044^+0.005_−0.004  , and the mass function for the pulsar to be  0.44^+0.16_−0.13 M_⊙  . Combining this mass function with various inclination estimates from other authors, we find no evidence to suggest that the neutron star in SAX J1808.4−3658 is more massive than the canonical value of  1.4 M_⊙  . Our optical light curves exhibit a possible superhump modulation, expected for a system with such a low mass ratio. The equivalent width of the Ca  ii H and K interstellar absorption lines suggest that the distance to the source is ∼2.5 kpc. This is consistent with previous distance estimates based on type-I X-ray bursts which assume cosmic abundances of hydrogen, but lower than more recent estimates which assume helium-rich bursts.     

The kinematics and zero-point of the log P–〈MK〉 relation for Galactic RR Lyrae variables via statistical parallax

We use accurate absolute proper motions and Two-Micron All-Sky Survey   K_s   -band apparent magnitudes for 364 Galactic RR Lyrae variables to determine the kinematical parameters of the Galactic RR Lyrae population and constrain the zero-point of the   K_s   -band period–luminosity relation for these stars via statistical parallax. We find the mean velocities of the halo- and thick-disc RR Lyrae populations in the solar neighbourhood to be  [ U ₀(Halo), V ₀(Halo), W ₀(Halo)]= (−12 ± 10, −217 ± 9, −6 ± 6) km s⁻¹  and  [ U ₀(Disc), V ₀(Disc), W ₀(Disc)]= (−15 ± 7, −44 ± 7, −25 ± 5) km s⁻¹  , respectively, and the corresponding components of the velocity-dispersion ellipsoids,  [σ V_R (Halo), σ V _θ(Halo), σ W (Halo)]= (167 ± 9, 86 ± 6, 78 ± 5) km s⁻¹  and  [σ V_R (Disc), σ V _θ(Disc), σ W (Disc)]= (55 ± 7, 44 ± 6, 30 ± 4) km s⁻¹  , respectively. The fraction of thick-disc stars is estimated at  0.25 ± 0.03  . The corrected infrared period–luminosity relation is     , implying a Large Magellanic Cloud (LMC) distance modulus of  18.27 ± 0.08  and a solar Galactocentric distance of  7.58 ± 0.40 kpc  . Our results suggest no or slightly prograde rotation for the population of halo RR Lyraes in the Milky Way.     

The 1997 periastron passage of the binary pulsar PSR B1259−63

We report here on multifrequency radio observations of the pulsed emission from PSR B1259−63 around the time of the closest approach (periastron) to its B2e companion star. There was a general increase in the dispersion measure (DM) and scatter-broadening of the pulsar, and a decrease in the flux density towards periastron although fluctuation in these parameters were seen on time-scales as short as minutes. The pulsed emission disappeared 16 d prior to periastron and remained undetectable until 16 d after periastron.
The observations are used to determine the parameters of the wind from the Be star. We show that a simple model, in which the wind density varies with radius as r ⁻², provides a good fit to the data. The wind is highly turbulent with an outer scale of ≤10¹⁰ cm and an inner scale perhaps as small as 10⁴ cm, a mean density of ∼10⁶ cm⁻³ and a velocity of ∼2000 km s⁻¹ at a distance of ∼50 stellar radii. We find a correlation between DM variations and the pulse scattering times, suggesting that the same electrons are responsible for both effects.     

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.