The flat synchrotron spectra of partially self-absorbed jets revisited

Flat radio spectra with large brightness temperatures at the core of active galactic nuclei and X-ray binaries are usually interpreted as the partially self-absorbed bases of jet flows emitting synchrotron radiation. Here we extend previous models of jets propagating at large angles to our line of sight to self-consistently include the effects of energy losses of the relativistic electrons due to the synchrotron process itself and the adiabatic expansion of the jet flow. We also take into account energy gains through self-absorption. Two model classes are presented. The ballistic jet flows, with the jet material travelling along straight trajectories, and adiabatic jets. Despite the energy losses, both scenarios can result in flat emission spectra; however, the adiabatic jets require a specific geometry. No re-acceleration process along the jet is needed for the electrons. We apply the models to observational data of the X-ray binary Cygnus X-1. Both models can be made consistent with the observations. The resulting ballistic jet is extremely narrow with a jet opening angle of only 5 arcsec. Its energy transport rate is small compared to the time-averaged jet power and therefore suggests the presence of non-radiating protons in the jet flow. The adiabatic jets require a strong departure from energy equipartition between the magnetic field and the relativistic electrons. These models also imply a jet power of two orders of magnitude higher than the Eddington limiting luminosity of a  10-M_⊙  black hole. The models put strong constraints on the physical conditions in the jet flows on scales well below achievable resolution limits.     

On the evolution of the cosmic supernova rates

The Galactic radio-emitting X-ray binary Cygnus X-3 is known to be a source of large-scale radio jets associated with periods of intense radio flaring. These jets have been found to have an expansion velocity of ∼0.3 c and are believed (on kinematic grounds) to lie close to the plane of the sky. We present new observations of Cygnus X-3 using the VLBA at 15 GHz. These observations, which included the detection of two small flares, show an additional kind of behaviour with apparent superluminal expansion along both major and minor axes. Evidence for superluminal activity has been found in a number of X-ray binary systems such as GRS 1915+105 and GRO J1655−40 with their superluminal radio jets. Apparently similar morphologies of the Galactic and extragalactic jet sources have led to the X-ray binaries being described as 'micro-quasars'. The superluminal expansion seen in our results appears to be different in nature from these other two sources, and a number of mechanisms are presented and discussed.     

Bulk motion of ultrarelativistic conical blazar jets

Allowing for the conical shape of ultrarelativistic blazar jets with opening angles of a few degrees on parsec-scales, we show that their bulk Lorentz factors and viewing angles can be much larger than the values usually inferred by combining their flux-variability and proper-motion measurements. This is in accord with our earlier finding that such ultrarelativistic (Lorentz factor,  Γ > 30  ) conical jets can reconcile the relatively slow apparent motions of Very Long Baseline Interferometry (VLBI) knots in TeV blazars with the extremely fast flows implied by their rapid γ-ray variability. This jet geometry also implies that de-projected jet opening angles will typically be significantly underestimated from VLBI measurements. In addition, de-projected jet lengths will be considerably overestimated if high Lorentz factors and significant opening angles are not taken into account.     

The very flat radio–millimetre spectrum of Cygnus X-1

We present almost-simultaneous detections of Cygnus X-1 in the radio and mm regimes, obtained during the low/hard X-ray state. The source displays a flat spectrum between 2 and 220 GHz, with a spectral index | α |0.15 (3 σ ). There is no evidence for either a low- or high-frequency cut-off, but in the mid-infrared (∼30 μm) thermal emission from the OB-type companion star becomes dominant. The integrated luminosity of this flat-spectrum emission in quiescence is 2×10³¹ erg s⁻¹ (2×10²⁴ W). Assuming the emission originates in a jet for which non-radiative (e.g. adiabatic expansion) losses dominate, this is a very conservative lower limit on the power required to maintain the jet. A comparison with Cyg X-3 and GRS 1915+105, the other X-ray binaries for which a flat spectrum at shorter than cm wavelengths has been observed, shows that the jet in Cyg X-1 is significantly less luminous and less variable, and is probably our best example to date of a continuous, steady, outflow from an X-ray binary. The emissive mechanism responsible for such a flat spectral component remains uncertain. Specifically, we note that the radio–mm spectra observed from these X-ray binaries are much flatter than those of the 'flat-spectrum' AGN, and that existing models of synchrotron emission from partially self-absorbed radio cores, which predict a high-frequency cut-off in the mm regime, are not directly applicable.     

Energization of interstellar media and cosmic ray production by jets from X-ray binaries

Drawing on recent estimates of the power of jets from X-ray binary systems as a function of X-ray luminosity, combined with improved estimates of the relevant  log( N )–log( L _X)  luminosity functions, we calculate the total energy input to the interstellar medium (ISM) from these objects. The input of kinetic energy to the ISM via jets is dominated by those of the black hole systems, in contrast to the radiative input, which is dominated by accreting neutron stars. Summing the energy input from black hole jets L _J in the Milky Way, we find that it is likely to correspond to ≥1 per cent of L _SNe, the time-averaged kinetic luminosity of supernovae, and ≥5 per cent of L _CR, the cosmic ray luminosity. Given uncertainties in jet power estimates, significantly larger contributions are possible. Furthermore, in elliptical galaxies with comparable distributions of low mass X-ray binaries, but far fewer supernovae, the ratio   L _J/ L _SNe  is likely to be larger by a factor of ∼5. We conclude that jets from X-ray binaries may be an important, distributed, source of kinetic energy for the ISM in the form of relativistic shocks, and as a result are likely to be a major source of cosmic rays.     

The large-scale structure of FR-II radio sources

The large-scale flow produced by classical and relativistic jets in a uniform external medium is explored using a combination of general arguments and numerical simulations. We find that in both cases, jets with finite initial opening angles are recollimated by the high pressure in the cocoon and that the outer flow becomes approximately self-similar at large times. However, if the opening angle is significantly less than 20°, then there is an intermediate stage during which the working surface propagates at a constant speed, which is of the same order as that in the jet. The behaviour of the relativistic and classical jets is very similar, except that the relativistic jets generate lighter cocoons. Application of the model to Cygnus A gives estimates of the source age and advance speed which agree very well with spectral ageing observations. Quantitative estimates and general arguments suggest that the regularly spaced knots in the Cygnus A jet can be interpreted as shocks associated with reconfinement of an initially free jet, knot 3 of the Cygnus A jet being identified with the reflection point of the reconfinement shock. However, the model predicts too large an initial opening angle for the Cygnus A jets. It is possible that this discrepancy is due to our imposition of axisymmetry which allows the numerical jets to become much better collimated after the reconfinement than they would be in the three-dimensional case. Further study is needed to test this idea.     

A transient relativistic radio jet from Cygnus X-1

We report the first observation of a transient relativistic jet from the canonical black hole candidate, Cygnus X-1, obtained with the Multi-Element Radio-Linked Interferometer Network (MERLIN). The jet was observed in only one of six epochs of MERLIN imaging of the source during a phase of repeated X-ray spectral transitions in 2004 Jan–Feb, and this epoch corresponded to the softest 1.5–12 keV X-ray spectrum. With only a single epoch revealing the jet, we cannot formally constrain its velocity. Nevertheless, several lines of reasoning suggest that the jet was probably launched 0.5–4.0 d before this brightening, corresponding to projected velocities of  0.2 c ≲ v _app≲ 1.6 c   , and an intrinsic velocity of  ≳0.3 c   . We also report the occurrence of a major radio flare from Cyg X-1, reaching a flux density of ∼120 mJy at 15 GHz, and yet not associated with any resolvable radio emission, despite a concerted effort with MERLIN. We discuss the resolved jet in terms of the recently proposed 'unified model' for the disc–jet coupling in black hole X-ray binaries, and tentatively identify the 'jet line' for Cyg X-1. The source is consistent with the model in the sense that a steady jet appears to persist initially when the X-ray spectrum starts softening, and that once the spectral softening is complete the core radio emission is suppressed and transient ejecta/shock observed. However, there are some anomalies, and Cyg X-1 clearly does not behave like a normal black hole transient in progressing to the canonical soft/thermal state once the ejection event has happened.     

The violent past of Cygnus X-2

Cygnus X-2 appears to be the descendant of an intermediate-mass X-ray binary (IMXB). Using Mazzitelli's stellar code we compute detailed evolutionary sequences for the system and find that its prehistory is sensitive to stellar input parameters, in particular the amount of core overshooting during the main-sequence phase. With standard assumptions for convective overshooting a case B mass transfer starting with a 3.5-M_⊙ donor star is the most likely evolutionary solution for Cygnus X-2. This makes the currently observed state rather short-lived, of order 3 Myr, and requires a formation rate > 10⁻⁷–10⁻⁶ yr⁻¹ of such systems in the Galaxy. Our calculations show that neutron star IMXBs with initially more massive donors (≳4 M_⊙) encounter a delayed dynamical instability; they are unlikely to survive this rapid mass transfer phase. We determine limits for the age and initial parameters of Cygnus X-2 and calculate possible dynamical orbits of the system in a realistic Galactic potential, given its observed radial velocity. We find trajectories which are consistent with a progenitor binary on a circular orbit in the Galactic plane inside the solar circle that received a kick velocity ≤200 km s⁻¹ at the birth of the neutron star. The simulations suggest that about 7 per cent of IMXBs receiving an arbitrary kick velocity from a standard kick velocity spectrum would end up in an orbit similar to Cygnus X-2, while about 10 per cent of them reach yet larger Galactocentric distances.     

Evidence for a jet contribution to the optical/infrared light of neutron star X-ray binaries

Optical/near-infrared (optical/NIR, OIR) light from low-mass neutron star X-ray binaries (NSXBs) in outburst is traditionally thought to be thermal emission from the accretion disc. Here we present a comprehensive collection of quasi-simultaneous OIR and X-ray data from 19 low magnetic field NSXBs, including new observations of three sources: 4U 0614+09, LMC X−2 and GX 349+2. The average radio–OIR spectrum for NSXBs is  α≈+ 0.2  (where   L _ν∝ν^α  ) at least at high luminosities when the radio jet is detected. This is comparable to, but slightly more inverted than the  α≈ 0.0  found for black hole X-ray binaries. The OIR spectra and relations between OIR and X-ray fluxes are compared to those expected if the OIR emission is dominated by thermal emission from an X-ray or viscously heated disc, or synchrotron emission from the inner regions of the jets. We find that thermal emission due to X-ray reprocessing can explain all the data except at high luminosities for some NSXBs, namely, the atolls and millisecond X-ray pulsars. Optically thin synchrotron emission from the jets (with an observed OIR spectral index of  α_thin < 0  ) dominate the NIR light above     and the optical above     in these systems. For NSXB Z-sources, the OIR observations can be explained by X-ray reprocessing alone, although synchrotron emission may make a low-level contribution to the NIR, and could dominate the OIR in one or two cases.     

Jet disc coupling in black hole binaries

In the last decade multi-wavelength observations have demonstrated the importance of jets in the energy output of accreting black hole binaries. The observed correlations between the presence of a jet and the state of the accretion flow provide important information on the coupling between accretion and ejection processes. After a brief review of the properties of black hole binaries, I illustrate the connection between accretion and ejection through two particularly interesting examples. First, an INTEGRAL observation of Cygnus X-1 during a ‘mini-’ state transition reveals disc jet coupling on time scales of orders of hours. Second, the black hole XTEJ1118+480 shows complex correlations between the X-ray and optical emission. Those correlations are interpreted in terms of coupling between disc and jet on time scales of seconds or less. Those observations are discussed in the framework of current models.     

High resolution images of Cygnus X-1

The classic black hole candidate Cygnus X-1 exhibits many similarities to Galactic jet sources (micro-quasars) in soft gamma and hard X-ray rays. This has fuelled suspicions that radio jets also may be present in Cygnus X-1. The lack of radio flaring in Cygnus X-1 has been associated with the presence of continuous jets rather than multiple plasmon ejection however no evidence for this has been observed with the VLA, or with MERLIN. Recent VLBA observations at 15 GHz have detected extended emission and further multi frequency observations are required to confirm the presence of jets on a milliarcsecond level.     

Normal-branch quasi-periodic oscillations during the high-intensity state of Cygnus X-2

Using data obtained with the Rossi X-ray Timing Explorer , we report the detection of a 5-Hz quasi-periodic oscillation (QPO) in the bright low-mass X-ray binary and Z source Cygnus X-2 during high overall intensities (the high-intensity state). This QPO was detected on the so-called normal-branch and can be identified with the normal-branch QPO or NBO. Our detection of the NBO is the first one during times when Cygnus X-2 was in the high-intensity state. The rms amplitude of this QPO decreased from 2.8 per cent between 2 and 3.1 keV to <1.9 per cent between 5.0 and 6.5 keV. Above 6.5 keV, its amplitude rapidly increased to ∼12 per cent rms above 16 keV. The time lags of the QPO were consistent with being zero below 5 keV (compared with the 2–3.1 keV band), but they rapidly increased to ∼70 ms (140°) around 10 keV, above which the time lags remained approximately constant near 70 ms. The photon energy dependences of the rms amplitude and the time lags are very similar to those observed for the NBO with other satellites ( Ginga , EXOSAT ) at different (i.e. lower) intensity states.     

The orbital period of HDE 226868/Cyg X-1

We present epoch 1996, high-quality radial velocity data for HDE 226868, the optical counterpart of Cygnus X-1. Combining our results with all published historical data, we have derived a new ephemeris for the system of HJD 245 0235.29 + n  × 5.5998, which allows accurate orbital phase calculations to be made for any X-ray observations over the last 30 years. We find no evidence for any period change such as that suggested by Ninkov, Walker &38; Yang. We discuss the shortcomings of previous work in establishing the period and orbital elements.     

Bayesian inference of jet bulk-flow speeds in Fanaroff–Riley type II radio sources

Radio jet and core data for a complete sample of 98 Fanaroff–Riley type II sources with   z < 1  are analysed with a Markov Chain Monte Carlo model fitting method to obtain constraints on bulk-flow speeds in the beam. The Bayesian parameter-inference method is described and demonstrated to be capable of providing meaningful constraints on the Lorentz factor at both kpc and parsec scales. For both jets and cores, we show that models in which some intrinsic dispersion is present in the features' intrinsic prominence, bulk-flow speeds or both provide the best fit to the data. The constraints on the Lorentz factor on parsec scales are found to be consistent with the expected values given very long baseline interferometry observations and other evidence, with     . On kpc scales, the Lorentz factor is found to be ≈1.18–1.49, in agreement with the results of previous analyses of radio jet data. These values are clearly not consistent with the  γ≈ 10  speeds required by beamed inverse-Compton models of X-ray emission from quasar jets; our results therefore support models that require velocity structure in powerful jets.     

On the formation and evolution of black hole binaries

We present the results of a systematic study of the formation and evolution of binaries containing black holes and normal-star companions with a wide range of masses. We first reexamine the standard formation scenario for close black hole binaries, where the progenitor system, a binary with at least one massive component, experienced a common-envelope phase and where the spiral-in of the companion in the envelope of the massive star caused the ejection of the envelope. We estimate the formation rates for different companion masses and different assumptions about the common-envelope structure and other model parameters. We find that black hole binaries with intermediate- and high-mass secondaries can form for a wide range of assumptions, while black hole binaries with low-mass secondaries can only form with apparently unrealistic assumptions (in agreement with previous studies).
We then present detailed binary evolution sequences for black hole binaries with secondaries of 2 to 17 M_⊙ and demonstrate that in these systems the black hole can accrete appreciably even if accretion is Eddington-limited (up to 7 M_⊙ for an initial black hole mass of 10 M_⊙) and that the black holes can be spun up significantly in the process. We discuss the implications of these calculations for well-studied black hole binaries (in particular GRS 1915+105) and ultraluminous X-ray sources of which GRS 1915+105 appears to represent a typical Galactic counterpart. We also present a detailed evolutionary model for Cygnus X-1, a massive black hole binary, which suggests that at present the system is most likely in a wind mass-transfer phase following an earlier Roche-lobe overflow phase. Finally, we discuss how some of the assumptions in the standard model could be relaxed to allow the formation of low-mass, short-period black hole binaries, which appear to be very abundant in nature.     

The search for hot spots associated with the Cygnus X-3 relativistic jet

We report and shortly discuss here the observational work carried out in order to test the possibility that two previously detected radio sources, in the vicinity of the well known microquasar Cygnus X-3, could be hot spot tracers of interaction between its relativistic jet and the interstellar medium (ISM). The motivation behind this search is in part justified considering recent theoretical models of high energy γ-ray emission which strongly rely on the interaction sites of galactic relativistic jets with nearby ISM clouds. The results presented in this paper include an improved radio exploration of the several arc-minute field around Cygnus X-3 using the Very Large Array (VLA), as well as deep near infrared (NIR) imaging with the Calar Alto 3.5 m telescope. We anticipate here that our observations do not appear to support the initial hot spot hypothesis. Instead, the resulting images suggest that the two radio sources, originally believed to be hot spot candidates, are most likely background or foreground objects.     

Evidence for deceleration in the radio jets of GRS 1915+105?

There is currently a clear discrepancy in the proper motions measured on different angular scales in the approaching radio jets of the black hole X-ray binary GRS 1915+105. Lower velocities were measured with the Very Large Array (VLA) prior to 1996 than were subsequently found from higher resolution observations made with the Very Long Baseline Array and the Multi-Element Radio Linked Interferometer Network. We initiated an observing campaign to use all three arrays to attempt to track the motion of the jet knots from the 2006 February outburst of the source, giving us unprecedented simultaneous coverage of all angular scales, from milliarcsecond scales out to arcsecond scales. The derived proper motion, which was dominated by the VLA measurements, was found to be 17.0 mas d⁻¹, demonstrating that there has been no significant permanent change in the properties of the jets since 1994. We find no conclusive evidence for deceleration of the jet knots, unless this occurs within 70 mas of the core. We discuss possible causes for the varying proper motions recorded in the literature.     

Relativistic large-scale jets and minimum power requirements

The recent discovery, by the Chandra satellite, that jets of blazars are strong X-ray emitters at large scales     , lends support to the hypothesis that emitting plasma is still moving at highly relativistic speeds on these scales. In this case in fact the emission via inverse Compton scattering off cosmic background photons is enhanced and the resulting predicted X-ray spectrum accounts well for the otherwise puzzling observations. Here we point out another reason to favour relativistic large-scale jets, based on a minimum power argument: by estimating the Poynting flux and bulk kinetic powers corresponding to, at least, the relativistic particles and magnetic field responsible for the emission, one can derive the value of the bulk Lorentz factor for which the total power is minimized. It is found that both the inner and extended parts of the jet of PKS     satisfy such a condition.     

Stellar contributors to the hard X-ray background?

We use simple energetic arguments to estimate the contribution of massive X-ray binaries and supernova remnants to the cosmic X-ray background (XRB) at energies in excess of 2 keV. Recent surveys have shown that active galactic nuclei (AGN) probably account for most of the hard XRB ( E >2 keV), but there have been many suggestions that star-forming galaxies could emerge at fainter fluxes and perhaps account for a significant fraction of the soft and hard X-ray energy density. Assuming that the formation rate of massive X-ray binaries (MXRBs) traces the global star-formation rate, we find that their integrated contribution to the hard XRB can be estimated and is shown to be small (at less than the 1 per cent level). Similarly, the integrated flux of supernovae (SN) is also shown to be insignificant, or at most comparable to MXRBs. AGN therefore remain the most viable candidates for producing the hard XRB, unless additional processes can be shown to dominate the global hard X-ray emission in distant starburst galaxies.     

The first light-curve analysis of eclipsing binaries observed by the INTEGRAL/OMC

Three Algol-type binaries in Cygnus constellation were selected for an analysis from a huge database of observations made by the INTEGRAL/OMC camera. These data were processed and analyzed, resulting in a first light-curve study of these neglected eclipsing binaries. The temperatures of the primary components range from 9500 K to 10,500 K and the inclinations are circa 73° (for PV Cyg and V1011 Cyg), while almost 90° for V822 Cyg. All of them seem to be main-sequence stars, well within their critical Roche lobes. Nevertheless, further detailed analyses are still needed.