A mystery solved: the mass ratio of the dwarf nova EM Cygni

We have discovered that the spectrum of the well-known dwarf nova EM Cyg is contaminated by light from a K25V star (in addition to the K-type mass donor star). The K25V star contributes approximately 16 per cent of the light from the system and if not taken into account has a considerable effect upon radial velocity measurements of the mass donor star. We obtain a new radial velocity amplitude for the mass donor star of K ₂=202±3 km s¹, compared with the value of K ₂=135±3 km s¹ obtained in Stover, Robinson & Nather's classic study of EM Cyg. The revised value of the amplitude, combined with a measurement of rotational broadening of the mass donor, v  sin  i =140±6 km s¹, leads to a new mass ratio of q M ₂ M ₁=0.88±0.05. This solves a long-standing problem with EM Cyg, because Stover et al.'s measurements indicated a mass ratio q >1, a value that should have led to dynamically unstable mass transfer for the secondary mass deduced by Stover et al. The revised value of the mass ratio, combined with the orbital inclination i =67±2°, leads to masses of 0.99±0.12 M and 1.12±0.08 M for the mass donor and white dwarf respectively. The mass donor is evolved, because it has a later spectral type (K3) than its mass would imply.
We discuss whether the K star could be physically associated with EM Cyg or not, and present the results of the spectroscopic study.     

The mass of the white dwarf in the recurrent nova U Scorpii

We present spectroscopy of the eclipsing recurrent nova U Sco. The radial velocity semi-amplitude of the primary star was found to be     from the motion of the wings of the He  ii λ 4686-Å emission line. By detecting weak absorption features from the secondary star, we find its radial velocity semi-amplitude to be     . From these parameters, we obtain a mass of     for the white dwarf primary star and a mass of     for the secondary star. The radius of the secondary is calculated to be     , confirming that it is evolved. The inclination of the system is calculated to be     , consistent with the deep eclipse seen in the light-curves. The helium emission lines are double-peaked, with the blueshifted regions of the disc being eclipsed prior to the redshifted regions, clearly indicating the presence of an accretion disc. The high mass of the white dwarf is consistent with the thermonuclear runaway model of recurrent nova outbursts, and confirms that U Sco is the best Type Ia supernova progenitor currently known. We predict that U Sco is likely to explode within ∼700 000 yr.     

SY Cnc, a case for unstable mass transfer?

Intermediate-resolution (0.5–1 Å) optical spectroscopy of the cataclysmic variable (CV) SY Cnc reveals the spectrum of the donor star. Our data enable us to resolve the orbital motion of the donor and provide a new orbital solution, binary mass ratio and spectral classification. We find that the donor star has spectral-type G8 ± 2 V and orbits the white dwarf with   P = 0.382 3753 ± 0.000 0003  d,   K ₂= 88.0 ± 2.9  km s⁻¹ and   V sin  i = 75.5 ± 6.5  km s⁻¹. Our values are significantly different from previous works and lead to   q = M ₂/ M ₁= 1.18 ± 0.14  . This is one of the highest mass ratios known in a CV and is very robust, because it is based on resolving the rotational broadening over a large number of metallic absorption lines. The donor could be a slightly evolved main sequence or descendant from a massive star which underwent an episode of thermal time-scale mass transfer.     

The component masses of the cataclysmic variable V347 Puppis

We present time-resolved spectroscopy and photometry of the double-lined eclipsing cataclysmic variable V347 Pup (=LB 1800). There is evidence of irradiation on the inner hemisphere of the secondary star, which we correct for using a model to give a secondary-star radial velocity of   K _R= 198 ± 5 km s⁻¹  . The rotational velocity of the secondary star in V347 Pup is found to be   v sin  i = 131 ± 5 km s⁻¹  and the system inclination is   i = 840 ± 23  . From these parameters we obtain masses of   M ₁= 0.63 ± 0.04 M_⊙  for the white dwarf primary and   M ₂= 0.52 ± 0.06 M_⊙  for the M0.5V secondary star, giving a mass ratio of   q = 0.83 ± 0.05  . On the basis of the component masses, and the spectral type and radius of the secondary star in V347 Pup, we find tentative evidence for an evolved companion. V347 Pup shows many of the characteristics of the SW Sex stars, exhibiting single-peaked emission lines, high-velocity S-wave components and phase-offsets in the radial velocity curve. We find spiral arms in the accretion disc of V347 Pup and measure the disc radius to be close to the maximum allowed in a pressureless disc.     

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.     

SPH simulations of negative (nodal) superhumps: a parametric study

Negative superhumps in cataclysmic variable systems result when the accretion disc is tilted with respect to the orbital plane. The line of nodes of the tilted disc precesses slowly in the retrograde direction, resulting in a photometric signal with a period slightly less than the orbital period. We use the method of smoothed particle hydrodynamics to simulate a series of models of differing mass ratio and effective viscosity to determine the retrograde precession period and superhump period deficit  ɛ₋  as a function of system mass ratio q . We tabulate our results and present fits to both  ɛ₋  and  ɛ₊  versus q , as well as compare the numerical results with those compiled from the literature of negative superhump observations. One surprising result is that while we find negative superhumps most clearly in simulations with an accretion stream present, we also find evidence for negative superhumps in simulations in which we shut off the mass transfer stream completely, indicating that the origin of the photometric signal is more complicated than previously believed.     

Optical spectroscopy and Doppler tomography of Cygnus X-2

We present phase resolved optical spectroscopy and Doppler tomography of V1341 Cygni, the optical counterpart to the neutron star low-mass X-ray binary (LMXB) Cygnus X-2 (Cyg X-2). We derive a radial velocity (RV) curve for the secondary star, finding a projected RV semi-amplitude of   K ₂= 79 ± 3 km s⁻¹  , leading to a mass function of  0.51 ± 0.06 M_⊙, ∼30  per cent lower than the previous estimate. We tentatively attribute the lower value of K ₂ (compared to that obtained by other authors) to variations in the X-ray irradiation of the secondary star at different epochs of observations. The limited phase coverage and/or longer timebase of previous observations may also contribute to the difference in K ₂. Our value for the mass function implies a primary mass of  1.5 ± 0.3 M_⊙  , somewhat lower than previous dynamical estimates, but consistent with the value found by analysis of type-I X-ray bursts from this system. Our Doppler tomography of the broad He  ii λ4686 line reveals that most of the emission from this line is produced on the irradiated face of the donor star, with little emission from the accretion disc. In contrast, the Doppler tomogram of the N  iii λ4640.64 Bowen blend line shows bright emission from near the gas stream/accretion disc impact region, with fainter emission from the gas stream and secondary star. This is the first LMXB for which the Bowen blend is dominated by emission from the gas stream/accretion disc impact region, without comparable emission from the secondary star. This has implications for the interpretation of Bowen blend Doppler tomograms of other LMXBs for which the ephemeris may not be accurately known.     

Analysing the atolls: X-ray spectral transitions of accreting neutron stars

We systematically analyse all the available X-ray spectra of disc accreting neutron stars (atolls and millisecond pulsars) from the RXTE data base. We show that while all these have similar spectral evolution as a function of mass accretion rate, there are also subtle differences. There are two different types of hard/soft transition, those where the spectrum softens at all energies, leading to a diagonal track on a colour–colour diagram, and those where only the higher energy spectrum softens, giving a vertical track. The luminosity at which the transition occurs is correlated with this spectral behaviour, with the vertical transition at   L / L _Edd∼ 0.02  while the diagonal one is at ∼0.1. Superimposed on this is the well-known hysteresis effect, but we show that classic, large-scale hysteresis occurs only in the outbursting sources, indicating that its origin is in the dramatic rate of change of mass accretion rate during the disc instability. We show that the long-term mass accretion rate correlates with the transition behaviour, and speculate that this is due to the magnetic field being able to emerge from the neutron star surface for low average mass accretion rates. While this is not strong enough to collimate the flow except in the millisecond pulsars, its presence may affect the inner accretion flow by changing the properties of the jet.     

Atlas of tilted accretion discs and source to negative superhumps

Using smoothed particle hydrodynamics, we numerically simulate steady-state accretion discs for cataclysmic variable dwarf novae systems that have a secondary-to-primary mass ratio  0.35 ≤ q ≤ 0.55  . After these accretion discs have come to quasi-equilibrium, we rotate each disc out of the orbital plane by  δ= (1, 2, 3, 4, 5 or 20)°  to induce negative superhumps. For accretion discs tilted  5°  , we generate light curves and associated Fourier transforms for an atlas on negative superhumps and retrograde precession. Our simulation results suggest that accretion discs need to be tilted more than 3° for negative superhumps to be statistically significant. We also show that if the disc is tilted enough such that the gas stream strikes a disc face, then a dense cooling ring is generated near the radius of impact.
In addition to the atlas, we study these artificially tilted accretion discs to find the source to negative superhumps. Our results suggest that the source is additional light from innermost disc annuli, and this additional light waxes and wanes with the amount of gas stream overflow received as the secondary orbits. The nodes, where the gas stream transitions from flowing over to under the disc rim (and vice versa), precess in the retrograde direction.     

Black hole mergers: can gas discs solve the 'final parsec' problem?

We compute the effect of an orbiting gas disc in promoting the coalescence of a central supermassive black hole binary. Unlike earlier studies, we consider a finite mass of gas with explicit time dependence: we do not assume that the gas necessarily adopts a steady state or a spatially constant accretion rate, i.e. that the merging black hole was somehow inserted into a pre-existing accretion disc. We consider the tidal torque of the binary on the disc, and the binary's gravitational radiation. We study the effects of star formation in the gas disc in a simple energy feedback framework.
The disc spectrum differs in detail from that found before. In particular, tidal torques from the secondary black hole heat the edges of the gap, creating bright rims around the secondary. These rims do not in practice have uniform brightness either in azimuth or time, but can on average account for as much as 50 per cent of the integrated light from the disc. This may lead to detectable high-photon-energy variability on the relatively long orbital time-scale of the secondary black hole, and thus offer a prospective signature of a coalescing black hole binary.
We also find that the disc can drive the binary to merger on a reasonable time-scale only if its mass is at least comparable with that of the secondary black hole, and if the initial binary separation is relatively small, i.e.   a ₀≲ 0.05  pc. Star formation complicates the merger further by removing mass from the disc. In the feedback model we consider, this sets an effective limit to the disc mass. As a result, binary merging is unlikely unless the black hole mass ratio is ≲0.001. Gas discs thus appear not to be an effective solution to the 'last parsec' problem for a significant class of mergers.     

Optical photometry and spectroscopy of the accretion-powered millisecond pulsar HETE J1900.1 − 2455

We present phase resolved optical photometry and spectroscopy of the accreting millisecond pulsar HETE J1900.1−2455. Our R -band light curves exhibit a sinusoidal modulation, at close to the orbital period, which we initially attributed to X-ray heating of the irradiated face of the secondary star. However, further analysis reveals that the source of the modulation is more likely due to superhumps caused by a precessing accretion disc. Doppler tomography of a broad Hα emission line reveals an emission ring, consistent with that expected from an accretion disc. Using the velocity of the emission ring as an estimate for the projected outer disc velocity, we constrain the maximum projected velocity of the secondary to be 200 km s⁻¹, placing a lower limit of  0.05 M_⊙  on the secondary mass. For a  1.4 M_⊙  primary, this implies that the orbital inclination is low, ≲20°. Utilizing the observed relationship between the secondary mass and the orbital period in short-period cataclysmic variables, we estimate the secondary mass to be ∼0.085  M_⊙  , which implies an upper limit of  ∼2.4 M_⊙  for the primary mass.     

The stellar mass ratio of GK Persei

We study the absorption lines present in the spectra of the long-period cataclysmic variable GK Per during its quiescent state, which are associated with the secondary star. By comparing quiescent data with outburst spectra we infer that the donor star appears identical during the two states and the inner face of the secondary star is not noticeably irradiated by flux from the accreting regions. We obtain new values for the radial velocity semi-amplitude of the secondary star,     , a projected rotational velocity,     and consequently a measurement of the stellar mass ratio of GK Per,     . The inferred white dwarf radial velocities are greater than those measured traditionally using the wings of Doppler-broadened emission lines suspected to originate in an accretion disc, highlighting the unsuitability of emission lines for mass determinations in cataclysmic variables. We determine mass limits for both components in the binary,     and     .     

Optical spectroscopy of the low-mass X-ray binary GX 9+9

Phase-resolved medium-resolution VLT spectroscopy of the low-mass X-ray binary GX 9+9 has revealed narrow C  iii emission lines that move in phase relative to our new estimate of the ephemeris, and show a velocity amplitude of 230 ± 35 km s⁻¹. We identify the origin of these lines as coming from the surface of the donor star, thereby providing the first estimate of the mass function of   f ( M ₁) ≥ 0.22 M_⊙  . Rotational broadening estimates together with assumptions for the mass donor give  0.07 ≤ q ≤ 0.35  and  182 ≤ K ₂≤ 406 km s⁻¹  . Despite a low-mass ratio, there is no evidence for a superhump in our data set. Doppler maps of GX 9+9 show the presence of a stream overflow, either in the form of material flowing downward along the accretion disc rim or in a similar fashion as occurs in high mass transfer rate cataclysmic variables known as the SW Sex stars. Finally, we note that the Bowen region in GX 9+9 is dominated by C  iii instead of N  iii emission as has been the case for most other X-ray binaries.     

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.     

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.     

A TiO study of the black hole binary GRO J0422+32 in a very low state

We present 53 simultaneous photometric ( I band) and spectroscopic (69009500 Å) observations of GRO J0422+32, taken during 1997 December. From these we determine that J0422+32 was in its lowest state yet observed, at I =20.44±0.08. Using relative spectrophotometry, we show that it is possible to correct very accurately for telluric absorption. Following this, we use the TiO bands at 7055 and 7589 Å for a radial velocity study and thereby obtain a semi-amplitude of 378±16 km s¹, which yields f ( M )=1.191±0.021 M and consistent with previous observations. We further demonstrate that this little-explored method is very powerful for such systems. We also determine a new orbital ephemeris of HJD=245 0274.4156±0.0009+0.212 1600±0.000 0002 E .
We see some evidence for an ellipsoidal modulation, from which we determine the orbital inclination of J0422+32 to be less than 45°. We therefore calculate a minimum mass for the primary of 2.22 M, consistent with a black hole, but not necessarily the supermassive one proposed recently (1997) by Beekman et al. We obtain an M45 spectral type for the secondary star, and determine that the secondary contributes 38±2 per cent of the flux that we observe from J0422+32 over the range 69508400 Å. From this we calculate the distance to the system to be 1.39±0.15 kpc.     

The quiescent light curve and the evolutionary state of GRO J1655–40

We present ellipsoidal light-curve fits to the quiescent B , V , R and I light curves of GRO J1655–40 (Nova Scorpii 1994). The fits are based on a simple model consisting of a Roche-lobe-filling secondary and an accretion disc around the black hole primary. Unlike previous studies, no assumptions are made concerning the interstellar extinction or the distance to the source; instead these are determined self-consistently from the observed light curves. In order to obtain tighter limits on the model parameters, we used the distance determination from the kinematics of the radio jet as an additional constraint. We obtain a value for the extinction that is lower than was assumed previously; this leads to lower masses for both the black hole and the secondary star of  5.4±0.3  and  1.45±0.35 M_⊙  , respectively. The errors in the determination of the model parameters are dominated by systematic errors, in particular arising from uncertainties in the modelling of the disc structure and uncertainties in the atmosphere model for the chemically anomalous secondary in the system. A lower mass of the secondary naturally explains the transient nature of the system if it is in either a late case A or early case B mass-transfer phase.     

Eccentric discs in binaries with intermediate mass ratios: superhumps in the VY Sculptoris stars

We investigate the role of the eccentric disc resonance in systems with mass ratios q ≳1/4, and demonstrate the effects that changes in the mass flux from the secondary star have upon the disc radius and structure. The addition of material with low specific angular momentum to the outer edge of a disc restricts that disc radially. Should the mass flux from the secondary be reduced, it is possible for the disc in a system with mass ratio as large as 1/3 to expand to the 3:1 eccentric inner Lindblad resonance and for superhumps to be excited.     

High-frequency X-ray variability as a mass estimator of stellar and supermassive black holes

There is increasing evidence that supermassive black holes in active galactic nuclei (AGN) are scaled-up versions of Galactic black holes. We show that the amplitude of high-frequency X-ray variability in the hard spectral state is inversely proportional to the black hole mass over eight orders of magnitude. We have analysed all available hard-state data from RXTE of seven Galactic black holes. Their power density spectra change dramatically from observation to observation, except for the high-frequency (≳10 Hz) tail, which seems to have a universal shape, roughly represented by a power law of index −2. The amplitude of the tail,   C _M   (extrapolated to 1 Hz), remains approximately constant for a given source, regardless of the luminosity, unlike the break or quasi-periodic oscillation frequencies, which are usually strongly correlated with luminosity. Comparison with a moderate-luminosity sample of AGN shows that the amplitude of the tail is a simple function of black hole mass,   C _M = C / M   , where   C ≈ 1.25 M_⊙ Hz⁻¹  . This makes   C _M   a robust estimator of the black hole mass which is easy to apply to low- to moderate-luminosity supermassive black holes. The high-frequency tail with its universal shape is an invariant feature of a black hole and, possibly, an imprint of the last stable orbit.     

High-resolution simulations of clump–clump collisions using SPH with particle splitting

We investigate, by means of numerical simulations, the phenomenology of star formation triggered by low-velocity collisions between low-mass molecular clumps. The simulations are performed using a smoothed particle hydrodynamics code which satisfies the Jeans condition by invoking on-the-fly particle splitting.
Clumps are modelled as stable truncated (non-singular) isothermal, i.e. Bonnor–Ebert, spheres. Collisions are characterized by M ₀ (clump mass), b (offset parameter, i.e. ratio of impact parameter to clump radius) and     (Mach number, i.e. ratio of collision velocity to effective post-shock sound speed). The gas subscribes to a barotropic equation of state, which is intended to capture (i) the scaling of pre-collision internal velocity dispersion with clump mass, (ii) post-shock radiative cooling and (iii) adiabatic heating in optically thick protostellar fragments.
The efficiency of star formation is found to vary between 10 and 30 per cent in the different collisions studied and it appears to increase with decreasing M ₀, and/or decreasing b , and/or increasing     . For   b < 0.5  collisions produce shock-compressed layers which fragment into filaments. Protostellar objects then condense out of the filaments and accrete from them. The resulting accretion rates are high,     , for the first     . The densities in the filaments,     , are sufficient that they could be mapped in NH₃ or CS line radiation, in nearby star formation regions.