A spectroscopic study of IRAS F10214 + 4724

The z  = 2.286  IRAS galaxy F10214 + 4724 remains one of the most luminous galaxies in the Universe, despite its gravitational lens magnification. We present optical and near-infrared spectra of F10214 + 4724, with clear evidence for three distinct components: lines of width ∼ 1000 km s⁻¹ from a Seyfert 2 nucleus; ≲ 200 km s⁻¹ lines which are likely to be associated with star formation; and a broad (∼ 4000 km s⁻¹) C  III ] 1909-Å emission line which is blueshifted by ∼ 1000 km s⁻¹ with respect to the Seyfert 2 lines. Our study of the Seyfert 2 component leads to several new results. (i) From the double-peaked structure in the Lyα line, and the lack of Lyβ, we argue that the Lyα photons have emerged through a neutral column of N _H ∼ 2.5 × 10²⁵ m⁻², possibly located within the AGN narrow-line region, as proposed for several high-redshift radio galaxies. (ii) The resonant O  VI 1032, 1036-Å doublet (previously identified as Lyβ) is in an optically thick (1:1) ratio. At face value this implies an extreme density ( n _e ∼ 10¹⁷ m⁻³) more typical of broad-line region clouds. However, we attribute this instead to the damping wings of Lyβ from the resonant absorption. (iii) A tentative detection of He  II 1086 suggests little extinction in the rest frame ultraviolet.     

ASCA observations of deep ROSAT fields — III. The discovery of an obscured Type 2 AGN at z = 0.67

We report on the discovery of a narrow-emission-line object at z  = 0.672 detected in a deep ASCA survey. The object, AXJ 0341.4–4453, has a flux in the 2–10 keV band of 1.1 ± 0.27 × 10⁻¹³ erg s⁻¹ cm⁻², corresponding to a luminosity of 1.8 × 10⁴⁴ erg s⁻¹ ( q ₀ = 0.5, H ₀ = 50 km s⁻¹ Mpc⁻¹). It is also marginally detected in the ROSAT 0.5–2 keV band with a flux 5.8 × 10⁻¹⁵ erg s⁻¹ cm⁻². Both the ASCA data alone and the combined ROSAT/ASCA data show a very hard X-ray spectrum, consistent with either a flat power law (α < 0.1) or photoelectric absorption with a column of n _H > 4 × 10²² cm⁻² (α = 1). The optical spectrum shows the high-ionization, narrow emission lines typical of a Seyfert 2 galaxy. We suggest that this object may be typical of the hard sources required to explain the remainder of the X-ray background at hard energies.     

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.     

Additional ultra-high-resolution observations of Ca+ ions in the local interstellar medium

We present ultra-high-resolution (0.35 km s⁻¹ FWHM) observations of the interstellar Ca K line towards seven nearby stars. The spectral resolution was sufficient to resolve the line profiles fully, thereby enabling us to detect hitherto unresolved velocity components, and to obtain accurate measurements of the velocity dispersions ( b values). Absorption components with velocities similar to those expected for the Local Interstellar Cloud (LIC) and the closely associated 'G cloud' were identified towards six of the seven stars. However, in most cases the b values deduced for these components were significantly larger than the b  ≈ 2.2 km s⁻¹ (i.e. T _k ≈ 7000 K, v _t ≈ 1 km s⁻¹) expected for the LIC, and it is argued that this results from the presence of additional, spectrally unresolved, components having similar velocities and physical conditions. For two stars (δ Vel and α Pav) we detect interstellar components with much smaller b values (1.1 ± 0.3 and 0.8 ± 0.1 km s⁻¹, respectively) than are expected for low-density clouds within the Local Bubble. In the case of the narrow α Pav component, we also find an anomalously large Na  i /Ca  ii column density ratio, which is indicative of a relatively high density. Thus it is possible that, in addition to LIC-type clouds, the local interstellar medium contains a population of previously undetected cooler and denser interstellar clouds.     

Rotation and activity in the solar-type stars of NGC 2547

We present high-resolution spectroscopy of a sample of 24 solar-type stars in the young (15–40 Myr), open cluster NGC 2547. We use our spectra to confirm cluster membership in 23 of these stars, to determine projected equatorial velocities and chromospheric activity, and to search for the presence of accretion discs. We find examples of both fast ( v _e sin  i >50 km s⁻¹) and slow ( v _e sin  i <10 km s⁻¹) rotators, but no evidence for active accretion in any of the sample. The distribution of projected rotation velocities is indistinguishable from the slightly older IC 2391 and IC 2602 clusters, implying similar initial angular momentum distributions and circumstellar disc lifetimes. The presence of very slow rotators indicates either that long (10–40 Myr) disc lifetimes or internal differential rotation are needed, or that NGC 2547 (and IC 2391/2602) were born with more slowly rotating stars than are presently seen in even younger clusters and associations. The solar-type stars in NGC 2547 follow a similar rotation–activity relationship to that seen in older clusters. X-ray activity increases until a saturation level is reached for v _e sin  i >15–20 km s⁻¹. We are unable to explain why this saturation level, of log( L _x L _bol)≃−3.3, is a factor of 2 lower than in other clusters, but rule out anomalously slow rotation rates or uncertainties in X-ray flux calculations.     

HST and ground-based eclipse observations of V2051 Ophiuchi: binary parameters

We report on high-speed eclipse photometry of the dwarf nova V2051 Oph while it was in a low brightness state, at B  ≃ 16.2 mag. In comparison with the average IUE spectra, the ultraviolet continuum and emission lines appear reduced by factors of, respectively, ≃ 4 and ≃ 5. Flickering activity is mostly suppressed and the light curve shows the eclipse of a compact white dwarf at the disc centre which contributes ≃ 60 per cent of the total light at 3900–4300 Å. We use measurements of contact phases in the eclipse light curve to derive the binary geometry and to estimate masses and relevant dimensions. We find a mass ratio of q  = 0.19 ± 0.03 and an inclination of i  = 83 ± 2°. The masses of the component stars are M ₁ = 0.78 ± 0.06 M⊙ and M ₂ = 0.15 ± 0.03 M⊙. Our photometric model predicts K ₁ = 83 ± 12 km s⁻¹ and K ₂ = 436 ± 11 km s⁻¹. The predicted value of K₁ is in accordance with the velocity amplitude obtained from the emission lines after a correction for asymmetric line emission in the disc is made. The secondary of V2051 Oph is significantly more massive than the secondaries of the other ultrashort period dwarf novae. V2051 Oph is probably a relatively young system, with a secondary star that has not had enough time to evolve out of thermal equilibrium.     

The circumstellar material around SN IIn 1997eg: another detection of a very narrow P Cygni profile

We report the detection of a very narrow P Cygni profile on top of the broad emission H α and H β lines of the Type IIn Supernova 1997eg. A similar feature has been detected in SN 1997ab, SN 1998S and SN 1995G . The detection of the narrow P Cygni profile indicates the existence of a dense circumstellar material (CSM), into which the ejecta of the supernova is expanding. From the analysis of the spectra of SN 1997eg we deduce (i) that such CSM is very dense  ( n ≳5×10⁷ cm^-3)  , (ii) that it has a low expanding velocity of about 160 km s⁻¹. The origin of such dense CSM can be either a very dense progenitor wind  ( M˙ ∼10^-2 M_⊙ yr^-1)  or a circumstellar shell product of the progenitor wind expanding into a high-pressure environment.     

The circumstellar medium of the peculiar supernova SN1997ab

We report the detection of the slow-moving wind into which the compact supernova remnant SN 1997ab is expanding. Echelle spectroscopy provides clear evidence for a well-resolved narrow (full width at zero intensity, FWZI ∼180 km s⁻¹) P Cygni profile, both in Hα and Hβ, superimposed on the broad emission lines of this compact supernova remnant. From theoretical arguments we know that the broad and strong emission lines imply a circumstellar density ( n  ≥ 10⁷ cm⁻³). This, together with our detection, implies a massive and slow stellar wind experienced by the progenitor star shortly prior to the explosion.     

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.     

Comparison of the SFI peculiar velocities with the IRAS 1.2-Jy gravity field

We present a comparison between the peculiar velocity fields measured from a recently completed l -band Tully–Fisher survey of field spirals (SFI) and that derived from the IRAS 1.2-Jy redshift survey galaxy distribution. The analysis is based on the expansion of these data in redshift space using smooth orthonormal functions, and is performed using low- and high-resolution expansions, with an effective smoothing scale which increases almost linearly with redshift. The effective smoothing scales at 3000 km s⁻¹ are 1500 and 1000 km s⁻¹ for the low- and high-resolution filters. The agreement between the high- and low-resolution SFI velocity maps is excellent. The general features in the filtered SFI and IRAS velocity fields agree remarkably well within 6000 km s⁻¹. This good agreement between the fields allows us to determine the parameter β = Ω^0.6 / b , where Ω is the cosmological density parameter, and b is the linear biasing factor. From a likelihood analysis on the SFI and IRAS modes we find that β = 0.6 ± 0.1, independently of the resolution of the modal expansion. For this value of β, the residual fields for the two filters show no systematic variations within 6000 km s⁻¹. Most remarkable is the lack of any coherent, redshift-dependent dipole flow in the residual field.     

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.     

Interaction between the north-eastern boundary of Sgr A East and giant molecular clouds

We have detected the   v = 1 → 0 S(1) (λ= 2.1218 μm)  and   v = 2 → 1 S(1) (λ= 2.2477 μm)  lines of H₂ in the Galactic Centre, in a  90 × 27 arcsec²  region between the north-eastern boundary of the non-thermal source Sgr A East, and the giant molecular cloud (GMC)  M−0.02 − 0.07  . The detected  H₂ v = 1 → 0  S(1) emission has an intensity of  1.6–21 × 10⁻¹⁸ W m⁻² arcsec⁻²  and is present over most of the region. Along with the high intensity, the large linewidths  (FWHM = 40–70 km s⁻¹)  and the  H₂ v = 2 → 1 S(1)  to   v = 1 → 0 S(1)  line ratios (0.3–0.5) can be best explained by a combination of C-type shocks and fluorescence. The detection of shocked H₂ is clear evidence that Sgr A East is driving material into the surrounding adjacent cool molecular gas. The H₂ emission lines have two velocity components at ∼+50 and  ∼0 km s⁻¹  , which are also present in the NH₃(3, 3) emission mapped by McGary, Coil & Ho. This two-velocity structure can be explained if Sgr A East is driving C-type shocks into both the  GMC M−0.02 − 0.07  and the northern ridge of McGary et al.     

The black hole mass–stellar velocity dispersion correlation: bulges versus pseudo-bulges

We investigate the correlation between the supermassive black holes (SMBHs) mass ( M _bh) and the stellar velocity dispersion  (σ_*)  in two types of host galaxies: the early-type bulges (disc galaxies with classical bulges or elliptical galaxies) and pseudo-bulges. In the form  log ( M _bh/M_⊙) =α+β log (σ_*/200 km s⁻¹)  , the best-fitting results for the 39 early-type bulges are the slope  β= 4.06 ± 0.28  and the normalization  α= 8.28 ± 0.05  ; the best-fitting results for the nine pseudo-bulges are  β= 4.5 ± 1.3  and  α= 7.50 ± 0.18  . Both relations have intrinsic scatter in  log  M _bh  of ≲0.27 dex. The   M _bh–σ_*  relation for pseudo-bulges is different from the relation in the early-type bulges over the 3σ significance level. The contrasting relations indicate the formation and growth histories of SMBHs depend on their host type. The discrepancy between the slope of the   M _bh–σ_*  relations using different definition of velocity dispersion vanishes in our sample, a uniform slope will constrain the coevolution theories of the SMBHs and their host galaxies more effectively. We also find the slope for the 'core' elliptical galaxies at the high-mass range of the relation appears steeper  (β≃ 5–6)  , which may be the imprint of their origin of dissipationless mergers.     

The mass of the white dwarf in the old nova BT Mon

We present spectrophotometry of the eclipsing old nova BT Mon (Nova Mon 1939). By detecting weak absorption features from the secondary star, we find its radial velocity semi-amplitude to be K _R = 205 ± 5 km s⁻¹ and its rotational velocity to be v  sin  i  = 138 ± 5 km s⁻¹. We also measure the radial velocity semi-amplitude of the primary star to be K _R = 170 ± 10 km s⁻¹. From these parameters we obtain a mass of 1.04 ± 0.06 M⊙ for the white dwarf primary star and a mass of 0.87 ⊙ 0.06 M⊙ for the G8 V secondary star. The inclination of the system is found to be 82^°_.2 ± 32^°_.2 and we estimate that the system lies at a distance of 1700 ± 300 pc. The high mass of the white dwarf and our finding that BT Mon was probably a fast nova together constitute a new piece of evidence in favour of the thermonuclear runaway model of classical nova outbursts. The emission lines are single-peaked throughout the orbital cycle, showing absorption around phase 0.5, high-velocity S-wave components and large phase offsets in their radial velocity curves. In each of these respects, BT Mon is similar to the SW Sex stars. We also find quasi-periodic flaring in the trailed spectra, which makes BT Mon a candidate intermediate polar.     

BF Eridani: a cataclysmic variable with a massive white dwarf and an evolved secondary

We present high- and medium-resolution spectroscopic observations of the cataclysmic variable BF Eridani (BF Eri) during its low and bright states. The orbital period of this system was found to be 0.270881(3) d. The secondary star is clearly visible in the spectra through the absorption lines of the neutral metals Mg  i , Fe  i and Ca  i . Its spectral type was found to be K3±0.5. A radial velocity study of the secondary yielded a semi-amplitude of   K ₂= 182.5 ± 0.9 km s⁻¹  . The radial velocity semi-amplitude of the white dwarf was found to be   K ₁= 74 ± 3 km s⁻¹  from the motion of the wings of the Hα and Hβ emission lines. From these parameters, we have obtained that the secondary in BF Eri is an evolved star with a mass of  0.50–0.59 M_⊙  , whose size is about 30 per cent larger than a zero-age main-sequence single star of the same mass. We also show that BF Eri contains a massive white dwarf  ( M ₁≥ 1.2 M_⊙)  , which allows us to consider the system as a Type Ia supernova progenitor. BF Eri also shows a high γ-velocity  (γ=−94 km s⁻¹)  and substantial proper motion. With our estimation of the distance to the system  ( d ≈ 700 ± 200 pc)  , this corresponds to a space velocity of ∼350 km s⁻¹ with respect to the dynamical local standard of rest. The cumulative effect of repeated nova eruptions with asymmetric envelope ejection might explain the high space velocity of the system. We analyse the outburst behaviour of BF Eri and question the current classification of the system as a dwarf nova. We propose that BF Eri might be an old nova exhibiting 'stunted' outbursts.     

ASCA observations of two steep soft X-ray quasars

Steep soft X-ray (0.1–2 keV) quasars share several unusual properties: narrow Balmer lines, strong Fe  II emission, large and fast X-ray variability, and a rather steep 2–10 keV spectrum. These intriguing objects have been suggested to be the analogues of Galactic black hole candidates in the high, soft state. We present here results from ASCA observations for two of these quasars: NAB 0205 + 024 and PG 1244 + 026.   Both objects show similar variations (factor of ∼ 2 in 10 ks), despite a factor of ∼ 10 difference in the 0.5–10 keV luminosity (7.3 × 10⁴³ erg s⁻¹ for PG 1244 + 026 and 6.4 × 10⁴⁴ erg s⁻¹ for NAB 0205 + 024, assuming isotropic emission, H ₀ = 50.0 and q ₀ = 0.0).   The X-ray continuum of the two quasars flattens by 0.5–1 going from the 0.1–2 keV band towards higher energies, strengthening recent results on another half-dozen steep soft X-ray active galactic nuclei.   PG 1244 + 026 shows a significant feature in the '1-keV' region, which can be described either as a broad emission line centred at 0.95 keV (quasar frame) or as edge or line absorption at 1.17 (1.22) keV. The line emission could be a result of reflection from a highly ionized accretion disc, in line with the view that steep soft X-ray quasars are emitting close to the Eddington luminosity. Photoelectric edge absorption or resonant line absorption could be produced by gas outflowing at a large velocity (0.3–0.6 c ).     

A numerical simulation of a wind/molecular clump interaction

It has been pointed out in the past that it is impossible to accelerate molecular material to velocities ≥ 25 km s⁻¹ with gasdynamic shocks without dissociating the gas. Because of this, it has been argued that observations of molecular emission with radial velocities ∼ 20–100 km s⁻¹ imply the presence of 'C-shocks' (which have much lower post-shock temperatures, and therefore do not dissociate the gas) and the existence of strong (∼ 10–100 μG) magnetic fields.   In this paper, we discuss an alternative mechanism for accelerating molecular material to high velocities: a high-velocity, low-density wind drives a non-dissociative shock (with shock velocity v _cs ≤ 25 km s⁻¹) into a high-density, molecular clump. Once this shock wave has gone through the clump, the molecular material is moving at a velocity ∼  v _cs and has a gas pressure approximately equal to the ram pressure of the impinging wind. The compressed molecular clump can now be accelerated directly by the ram pressure of the wind (without the passage of further shocks through the molecular material), and will eventually move at the wind velocity.   This mechanism has been previously invoked to explain high-velocity molecular emission. However, numerical simulations have shown that a wind/clump interaction leads to the fragmentation of the clump before it can be accelerated to large velocities. In our numerical simulation (which includes an approximate treatment of the relevant microphysics) we find that the fragments that are produced are still largely molecular, and that they are rapidly accelerated to velocities comparable to the wind velocity. We therefore conclude that a wind/molecular clump interaction is indeed a valid mechanism for producing high-velocity molecular features.     

A Herbig–Haro object associated with GGD30 and its exciting source

GGD30 has been suggested to be either a small reflection nebulosity or a Herbig–Haro (HH) object formed in the outflow from a nearby obscured star. Observations to date have not been able to distinguish between these two scenarios. In addition, there are conflicting proposals for the location of the exciting source for GGD30. To resolve these questions, we have carried out optical spectroscopy and near-infrared ( J , K and 3.6-μm) imaging of GGD30. Taken together, these observations reveal that the bright optical knot in GGD30 must be a HH object, excited by the outflow from an optically obscured pre-main-sequence (PMS) star located ∼3 arcsec to the southwest. Based on mid-infrared fluxes from the Mid-course Space Experiment ( MSX ) satellite, we estimate the luminosity of this PMS star to be  ∼12.5 L_⊙  which suggests it is an intermediate-mass object rather than low-mass as previously proposed. The optical spectroscopy indicates projected velocities of  ∼−270 km s⁻¹  associated with the HH object. The fact that these velocities are blueshifted and relatively high compared to the velocities typical of HH flows suggests that the outflow from the PMS star must be almost aligned with the line of sight. There is an additional low-velocity  (∼−70 km s⁻¹) Hα  component but its origin is not clear.     

On the motion of the Local Group and its substructures

We consider the problem of the relative motion both of the substructures of the Local Group of galaxies (revealed via the S-tree method), and of the velocity of the Local Group itself. The existence of statistically significant bulk flow of the Milky Way subsystem is shown via a 3D reconstruction procedure, which uses information on the radial velocities of the galaxies but does not take account of their distances. Once the bulk motion of the substructures is estimated we also consider, in combination with the observed cosmic microwave background (CMB) dipole, the mean velocity of the Local Group itself. Assigning to the Local Group the mean motion of its main substructures, we evaluate its peculiar velocity in Milky Way frame V _LG→MW = (−7 ± 303, −15 ± 155, +177 ± 144) or 178 km s⁻¹ toward galactic coordinates l  = 245 and b  = +85. Combined with the CMB dipole V _MW→CMB, we obtain a Local Group velocity in CMB frame: V _LG→CMB = (−41 ± 303, −497 ± 155, 445 ± 144) or 668 km s⁻¹ towards l  = 265 and b  = 42. This estimation is in good agreement, within the 1 σ level, with the estimation of Yahil et al.     

Spectroscopy of the optical Einstein ring 0047 – 2808

We present optical and near-infrared spectroscopic observations of the optical Einstein ring 0047 – 2808. We detect both [O III ] lines λλ4959, 5007 near ∼ 2.3 μm, confirming the redshift of the lensed source as z  = 3.595. The Lyα line is redshifted relative to the [O III ] line by 140 ± 20 km s⁻¹. Similar velocity shifts have been seen in nearby starburst galaxies. The [O III ] line is very narrow, 130 km s⁻¹ FWHM. If the ring is the image of the centre of a galaxy, the one-dimensional stellar velocity dispersion σ = 55 km s⁻¹ is considerably smaller than the value predicted by Baugh et al. for the somewhat brighter Lyman-break galaxies. The Lyα line is significantly broader than the [O III ] line, probably due to resonant scattering. The stellar central velocity dispersion of the early-type deflector galaxy at z  = 0.485 is 250 ± 30 km s⁻¹. This value is in good agreement both with the value predicted from the radius of the Einstein ring (and a singular isothermal sphere model for the deflector), and with the value estimated from the D _n −σ relation.