Disk Instability Model Research Articles

Revisiting a fundamental test of the disc instability model for X-ray binaries

We revisit a core prediction of the disc instability model (DIM) applied to X-ray binaries. The model predicts the existence of a critical mass transfer rate, which depends on disc size, separating transient and persistent systems. We therefore selected a sample of 52 persistent and transient neutron star and black hole X-ray binaries and verified if observed persistent (transient) systems do lie in the appropriate stable (unstable) region of parameter space predicted by the model. We find that, despite the significant uncertainties inherent to these kinds of studies, the data are in very good agreement with the theoretical expectations. We then discuss some individual cases that do not clearly fit into this main conclusion. Finally, we introduce the transientness parameter as a measure of the activity of a source and show a clear trend of the average outburst recurrence time to decrease with transientness in agreement with the DIM predictions. We therefore conclude that, despite difficulties in reproducing the complex details of the lightcurves, the DIM succeeds to explain the global behaviour of X-ray binaries averaged over a long enough period of time.

Inside-out outbursts in the thermally unstable accretion disk of the neutron star microquasar Aquila X-1

The observed features of typical, symmetric outbursts in the neutron star X-ray transient Aquila X-1 such as the rise, the plateau in the maximum, and the decay, are reproduced with a timedependent disk instability model. No external effect such as irradiation is necessary to account for the observation. In the model, a truncated inner disk radius that is more than ten times larger than the magnetically truncated one and that is plausibly appropriate to the scale proposed by hot flow models must be adopted. The model shows that such symmetric outbursts in Aql X-1 may be inside-out outbursts, while outside-in outbursts have been conjectured based on observations. The implication of the presented model, with observations, is discussed together.

The universal nature of accretion-induced variability: the rms-flux relation in an accreting white dwarf

We report the discovery of a linear relationship between the root-mean-square (rms) variability amplitude and the mean flux in the accreting white dwarf binary system MV Lyrae. Our lightcurve, obtained with the Kepler satellite, spans 633 days with quasi-continuous 58.8 second cadence resolution. We show, for the first time, how this cataclysmic variable displays linear rms-flux relations similar to those observed in many other black hole binaries, neutron star binaries and Active Galactic Nuclei. The phenomenological similarity between the rms-flux relation observed here and in other X-ray binaries suggests a common physical origin for the broad-band variability, independent of source type, mass or size of the compact accretor. Furthermore, we infer the viscosity parameter, alpha, and disk scale height, H/R, using two independent methods. In both cases, both values are found to be uncomfortably high to be accommodated by the disk instability model.

A flickering study of nova-like systems KR Aur and UU Aqr

We present a study of the flickering activity in two nova-like systems, KR Aur and UU Aqr. We applied a statistical model of flickering simulations in accretion discs based on turbulent angular momentum transport between two adjacent rings with an exponential distribution of the turbulence dimension scale. The model is based on a steady-state disc model, which is satisfied in the case of hot ionized discs of nova-like cataclysmic variables. Our model successfully fits the observed power-density spectrum of KR Aur with the disc parameter α= 0.10–0.40 and an inner-disc truncation radius in the range Rin= 0.88–1.67 × 109 cm. The exact values depend on the mass-transfer rate in the sense that α decreases and Rin increases with mass-transfer rate. In any case, the inner-disc radius found for KR Aur is considerably smaller than those for quiescent dwarf novae, as predicted by the disc instability model. On the other hand, our simulations fail to reproduce the power-density spectrum of UU Aqr. A tantalizing explanation involves the possible presence of spiral waves, which are expected in UU Aqr because of its low mass ratio but not in KR Aur. In general our model predicts the observed concentration of flickering in the central disc. We explain this by the radial dependence of the angular-momentum gradient.

MULTIWAVELENGTH OBSERVATIONS OF A0620-00 IN QUIESCENCE

[Abridged.] We present multiwavelength observations of the black hole binary system, A0620-00. Using the Cosmic Origins Spectrograph on the Hubble Space Telescope, we have obtained the first FUV spectrum of A0620-00. The observed spectrum is flat in the FUV and very faint (with continuum fluxes \simeq 1e - 17 ergs/cm^2/s/A). We compiled the dereddened, broadband spectral energy distribution of A0620-00 and compared it to previous SEDs as well as theoretical models. The SEDs show that the source varies at all wavelengths for which we have multiple samples. Contrary to previous observations, the optical-UV spectrum does not continue to drop to shorter wavelengths, but instead shows a recovery and an increasingly blue spectrum in the FUV. We created an optical-UV spectrum of A0620-00 with the donor star contribution removed. The non-stellar spectrum peaks at \simeq3000 {\deg}A. The peak can be fit with a T=10,000 K blackbody with a small emitting area, probably originating in the hot spot where the accretion stream impacts the outer disk. However, one or more components in addition to the blackbody are needed to fit the FUV upturn and the red optical fluxes in the optical-UV spectrum. By comparing the mass accretion rate determined from the hot spot luminosity to the mean accretion rate inferred from the outburst history, we find that the latter is an order of magnitude smaller than the former, indicating that \sim90% of the accreted mass must be lost from the system if the predictions of the disk instability model and the estimated interoutburst interval are correct. The mass accretion rate at the hot spot is 10^5 the accretion rate at the black hole inferred from the X-ray luminosity. To reconcile these requires that outflows carry away virtually all of the accreted mass, a very low rate of mass transfer from the outer cold disk into the inner hot region, and/or radiatively inefficient accretion.

Exoplanets

Exoplanets

THE ORIGIN OF VARIABILITY OF THE INTERMEDIATE-MASS BLACK-HOLE ULX SYSTEM HLX-1 IN ESO 243-49

The ultra-luminous intermediate-mass black-hole system HLX-1 in the ESO 243-49 galaxy exhibits variability with a possible recurrence time of a few hundred days. Finding the origin of this variability would constrain the still largely unknown properties of this extraordinary object. Since it exhibits an intensity-hardness behavior characteristic of black-hole X-ray transients, we have analyzed the variability of HLX-1 in the framework of the disk instability model that explains outbursts of such systems. We find that the long-term variability of HLX-1 is unlikely to be explained by a model in which outbursts are triggered by thermal-viscous instabilities in an accretion disc. Possible alternatives include the instability in a radiation-pressure dominated disk but we argue that a more likely explanation is a modulated mass-transfer due to tidal stripping of a star on an eccentric orbit around the intermediate-mass black hole. We consider an evolutionary scenario leading to the creation of such a system and estimate the probability of its observation. We conclude, using a simplified dynamical model of the post-collapse cluster, that no more than 1/100 to 1/10 of Mbh < 10^4 Msun IMBHs - formed by run-away stellar mergers in the dense collapsed cores of young clusters - could have a few times 1 Msun Main-Sequence star evolve to an AGB on an orbit eccentric enough for mass transfer at periapse, while avoiding collisional destruction or being scattered into the IMBH by 2-body encounters. The finite but low probability of this configuration is consistent with the uniqueness of HLX-1. We note, however, that the actual response of a standard accretion disk to bursts of mass transfer may be too slow to explain the observations unless the orbit is close to parabolic (and hence even rarer) and/or additional heating, presumably linked to the highly time-dependent gravitational potential, are invoked.

Spectral and timing properties of the accreting X-ray millisecond pulsar IGR J17511–3057

IGR J17511-3057 is the second X-ray transient accreting millisecond pulsar discovered by INTEGRAL. It was in outburst for about a month from September 13, 2009. The broad-band average spectrum is well described by thermal Comptonization with an electron temperature of kT_e ~ 25 keV, soft seed photons of kT_bb ~ 0.6 keV, and Thomson optical depth \tau_T ~ 2 in a slab geometry. During the outburst the spectrum stays remarkably stable with plasma and soft seed photon temperatures and scattering optical depth being constant within errors. We fitted the outburst profile with the exponential model, and using the disk instability model we inferred the outer disk radius to be (4.8 - 5.4) \times 1010 cm. The INTEGRAL and RXTE data reveal the X-ray pulsation at a period of 4.08 milliseconds up to ~ 120 keV. The pulsed fraction is shown to decrease from ~22% at 3 keV to a constant pulsed fraction of ~17-18% between 7-30 keV, and then to decrease again down to ~13% at 60 keV. The nearly sinusoidal pulses show soft lags monotonically increasing with energy to about 0.2 ms at 10-20 keV similar to those observed in other accreting pulsars. The short burst profiles indicate hydrogen-poor material at ignition, which suggests either that the accreted material is hydrogen-deficient, or that the CNO metallicity is up to a factor of 2 times solar. However, the variation of burst recurrence time as a function of m (inferred from the X-ray flux) is much smaller than predicted by helium-ignition models.

A DOUBLE OUTBURST FROM IGR J00291+5934: IMPLICATIONS FOR ACCRETION DISK INSTABILITY THEORY

The accretion-powered millisecond pulsar IGR J00291+5934 underwent two ~10 d long outbursts during 2008, separated by 30 d in quiescence. Such a short quiescent period between outbursts has never been seen before from a neutron star X-ray transient. X-ray pulsations at the 599 Hz spin frequency are detected throughout both outbursts. For the first time, we derive a pulse phase model that connects two outbursts, providing a long baseline for spin frequency measurement. Comparison with the frequency measured during the 2004 outburst of this source gives a spin-down during quiescence of -4(1)x10^-15 Hz/s, approximately an order of magnitude larger than the long-term spin-down observed in the 401 Hz accretion-powered pulsar SAX J1808.4-3658. If this spin-down is due to magnetic dipole radiation, it requires a 2x10^8 G field strength, and its high spin-down luminosity may be detectable with the Fermi Large Area Telescope. Alternatively, this large spin-down could be produced by gravitational wave emission from a fractional mass quadrupole moment of Q/I = 1x10^{-9}. The rapid succession of the outbursts also provides a unique test of models for accretion in low-mass X-ray binaries. Disk instability models generally predict that an outburst will leave the accretion disk too depleted to fuel a second outburst after such a brief quiescence. We suggest a modification in which the outburst is shut off by the onset of a propeller effect before the disk is depleted. This model can explain the short quiescence and the unusually slow rise of the light curve of the second 2008 outburst.

Accretion-disc model spectra for dwarf-nova stars

Radiation from accretion discs in cataclysmic variable stars (CVs) provides fundamental information about the properties of these close binary systems and about the physics of accretion in general. The detailed diagnostics of accretion disc structure can be achieved by including in its description all the relevant heating and cooling physical mechanism, in particular the convective energy transport that, although dominant at temperatures less than about 10 000 K, is usually not taken into account when calculating spectra of accretion discs. We constructed a radiative transfer code coupled with a code determining the disc's hydrostatic vertical structure. We have obtained for the first time model spectra of cold, convective accretion discs. As expected, these spectra are mostly flat in the optical wavelengths with no contribution from the UV, which in quiescence must be emitted by the white dwarf. The disc structures obtained with our radiative-transfer code compare well with the solutions of equations used to describe the dwarf-nova outburst cycle according to the thermal-viscous disc instability model thus allowing the two to be combined. Our code allows calculating the spectral evolution of dwarf nova stars through their whole outburst cycle, providing a new tool for testing models of accretion discs in cataclysmic variables. We show that convection plays an important role in determining the vertical disc structure and substantially affects emitted spectra when, as often the case, it is effective at optical depths tau ~ 1. The emergent spectrum is independent of the parameters of the convection model.(Abstract shortened)

DYNAMICAL CONSTRAINTS ON THE ORIGIN OF THE YOUNG B-STARS IN THE GALACTIC CENTER

Regular star formation is thought to be inhibited close to the massive black hole (MBH) in the Galactic center. Nevertheless, tens of young main sequence B stars have been observed in an isotropic distribution close to it. Various models have been suggested for the formation of the B-stars closest to the MBH (<0.05 pc; the S-stars), typically involving the migration of these stars from their original birthplace to their currently observed position. Here we explore the orbital phase space distribution of the B-stars throughout the central pc expected from the various suggested models for the origin of the B-stars. We find that most of these models have difficulties in explaining, by themselves, both the population of the S-stars (<0.05 pc), and the population of the young B-stars further away (up to 0.5 pc). Most models grossly over-predict the number of B-stars up to 0.5 pc, given the observed number of S-stars. Such models include the intermediate-mass black hole assisted cluster inspiral scenario, Kozai-like perturbations by two disks, spiral density waves migration in a gaseous disk, and some of the eccentric disk instability models. We focus on one of the other models, the massive perturber induced binary disruption, which is consistent with both the S-stars and the extended population of B-stars further away. For this model we use analytical arguments and N-body simulations to provide further observational predictions. These could be compared with future observations to further support this model, constrain it or refute it. These predictions include the radial distribution of the young B-stars, their eccentricity distribution and its dependence on distance from the MBH (higher eccentricities at larger distances from the MBH), as well as less specific expectations regarding their mass function.

Multiwavelength observations of the helium dwarf nova KL Dra through its outburst cycle

We present multi-wavelength observations of the helium-dominated accreting binary KL Dra which has an orbital period of 25 mins. Our ground-based optical monitoring programme using the Liverpool Telescope has revealed KL Dra to show frequent outbursts. Although our coverage is not uniform, our observations are consistent with the outbursts recurring on a timescale of ~60 days. Observations made using Swift show that the outbursts occur with a similar amplitude at both UV and optical energies and a duration of 2 weeks. Although KL Dra is a weak X-ray source we find no significant evidence that the X-ray flux varies over the course of an outburst cycle. We can reproduce the main features of the 60 day outburst cycle using the Disc Instability Model and a helium-dominated accretion flow. Although the outbursts of KL Dra are very similar to those of the hydrogen accreting dwarf novae, we cannot exclude that they are the AM CVn equivalent of WZ Sge type outbursts. With outbursts occurring every ~2 months, KL Dra is an excellent target to study helium-dominated accretion flows in general.

X-ray observations of SU UMa throughout six outbursts

We present RXTE observations covering six normal outbursts of the dwarf nova SU UMa, the prototype of its class. The outbursts showed consistent X-ray behaviour with the X-ray count rate dropping suddenly by a factor of our, and with evidence for a half day delay between the optical rise and the X-ray suppression. In contrast to SS Cyg, an X-ray flux increase at the beginning of outburst was not observed, although it is expected from boundary layer models. The X-ray flux was high and decreasing during quiescence, in conflict with the disc instability model. The X-ray spectrum of SU UMa was softer in outburst than during quiescence, and it was consistent with constant reflection.

Restless quiescence: thermonuclear flashes between transient X-ray outbursts

For thermonuclear flashes to occur on neutron-star surfaces, fuel must have been accreted from a donor star. However, sometimes flashes are seen from transient binary systems when they are thought to be in their quiescent phase, during which no accretion, or relatively little, is expected to occur. We investigate the accretion luminosity during several such flashes, including the first-ever and brightest detected flash from Cen X-4 in 1969. We infer from observations and theory that immediately prior to these flashes the accretion rate must have been between about 0.001 and 0.01 times the equivalent of the Eddington limit, which is roughly 2 orders of magnitude less than the peak accretion rates seen in these transients during an X-ray outburst and 3-4 orders of magnitude more than the lowest measured values in quiescence. Furthermore, three such flashes, including the one from Cen X-4, occurred within 2 to 7 days followed by an X-ray outburst. A long-term episode of enhanced, but low-level, accretion is predicted near the end of the quiescent phase by the disk-instability model, and may thus have provided the right conditions for these flashes to occur. We discuss the possibility of whether these flashes acted as triggers of the outbursts, signifying a dramatic increase in the accretion rate. Although it is difficult to rule out, we find it unlikely that the irradiance by these flashes is sufficient to change the state of the accretion disk in such a dramatic way.

HEAVY-ELEMENT ENRICHMENT OF A JUPITER-MASS PROTOPLANET AS A FUNCTION OF ORBITAL LOCATION

We calculate heavy element enrichment in a Jupiter-mass protoplanet formed by disk instability at various radial distances from the star, considering different disk masses and surface density distributions. Although the available mass for accretion increases with radial distance (a) for disk solid surface density (sigma) functions sigma=sigma_0*a^(-alpha) with alpha < 2, the accretion timescale is significantly longer at larger radial distances. Efficient accretion is limited to the first ~ 1E5 years of planetary evolution, when the planet is extended and before gap opening and type II migration take place. The accreted mass is calculated for disk masses of 0.01, 0.05 and 0.1 M_sun with alpha = 1/2, 1, and 3/2. We show that a Jupiter-mass protoplanet can accrete 1 to 110 M_earth of heavy elements, depending on the disk properties. Our results explain the large variation in heavy element enrichment found in extra-solar giant planets. Since higher disk surface density is found to lead to larger heavy element enrichment, our model results are consistent with the correlation between heavy element enrichment and stellar metallicity. Our calculations also suggest that Jupiter could have formed at a larger radial distance than its current location while still accreting the mass of heavy elements predicted by interior models. We conclude that in the disk instability model the final composition of a giant planet is strongly determined by its formation environment. The heavy element abundance of a giant planet does not discriminate between its origin by either disk instability or core accretion.

AN ACCURATE DETERMINATION OF THE OPTICAL PERIODIC MODULATION IN THE X-RAY BINARY SAX J1808.4–3658

We report on optical imaging of the X-ray binary SAX J1808.4-3658 with the 8-m Gemini South Telescope. The binary, containing an accretion-powered millisecond pulsar, appears to have a large periodic modulation in its quiescent optical emission. In order to clarify the origin of this modulation, we obtained three time-resolved $r'$-band light curves (LCs) of the source in five days. The LCs can be described by a sinusoid, and the long time-span between them allows us to determine optical period P=7251.9 s and phase 0.671 at MJD 54599.0 (TDB; phase 0.0 corresponds to the ascending node of the pulsar orbit), with uncertainties of 2.8 s and 0.008 (90 % confidence), respectively. This periodicity is highly consistent with the X-ray orbital ephemeris. By considering this consistency and the sinusoidal shape of the LCs, we rule out the possibility of the modulation arising from the accretion disk. Our study supports the previous suggestion that the X-ray pulsar becomes rotationally powered in quiescence, with its energy output irradiating the companion star, causing the optical modulation. While it has also been suggested that the accretion disk would be evaporated by the pulsar, we argue that the disk exists and gives rise to the persistent optical emission. The existence of the disk can be verified by long-term, multi-wavelength optical monitoring of the source in quiescence, as an increasing flux and spectral changes from the source would be expected based on the standard disk instability model.

The thermal-viscous disk instability model in the AGN context

Accretion disks in AGN should be subject to the same type of instability as in cataclysmic variables (CVs) or in low-mass X-ray binaries (LMXBs), which leads to dwarf nova and soft X-ray transient outbursts. It has been suggested that this thermal/viscous instability can account for the long term variability of AGNs. We test this assertion by presenting a systematic study of the application of the disk instability model (DIM) to AGNs. We are using the adaptative grid numerical code we have developed in the context of CVs, enabling us to fully resolve the radial structure of the disk. We show that, because in AGN disks the Mach numbers are very large, the heating and cooling fronts are so narrow that they cannot be resolved by the numerical codes that have been used until now. In addition, these fronts propagate on time scales much shorter than the viscous time. As a result, a sequence of heating and cooling fronts propagate back and forth in the disk, leading only to small variations of the accretion rate onto the black hole, with short quiescent states occurring for very low mass transfer rates only. Truncation of the inner part of the disk by e.g. an ADAF does not alter this result, but enables longer quiescent states. Finally we discuss the effects of irradiation by the central X-ray source, and show that, even for extremely high irradiation efficiencies, outbursts are not a natural outcome of the model.

Core formation in giant gaseous protoplanets

Sedimentation rates of silicate grains in gas giant protoplanets formed by disk instability are calculated for protoplanetary masses between 1 M Saturn to 10 M Jupiter . Giant protoplanets with masses of 5 M Jupiter or larger are found to be too hot for grain sedimentation to form a silicate core. Smaller protoplanets are cold enough to allow grain settling and core formation. Grain sedimentation and core formation occur in the low mass protoplanets because of their slow contraction rate and low internal temperature. It is predicted that massive giant planets will not have cores, while smaller planets will have small rocky cores whose masses depend on the planetary mass, the amount of solids within the body, and the disk environment. The protoplanets are found to be too hot to allow the existence of icy grains, and therefore the cores are predicted not to contain any ices. It is suggested that the atmospheres of low mass giant planets are depleted in refractory elements compared with the atmospheres of more massive planets. These predictions provide a test of the disk instability model of gas giant planet formation. The core masses of Jupiter and Saturn were found to be ∼ 0.25 M ⊕ and ∼ 0.5 M ⊕ , respectively. The core masses of Jupiter and Saturn can be substantially larger if planetesimal accretion is included. The final core mass will depend on planetesimal size, the time at which planetesimals are formed, and the size distribution of the material added to the protoplanet. Jupiter's core mass can vary from 2 to 12 M ⊕ . Saturn's core mass is found to be ∼ 8 M ⊕ .

Mass transfer variation in the outburst model of dwarf novae and soft X-ray transients

Context. In the standard formulation of the disc instability model for soft X-ray transient and dwarf nova outbursts, the mass transfer rate from the secondary is assumed to be constant. This may seem natural since the L1 point remains shielded from the accretion luminosity by the accretion disc. However an indirect heating could take place and could lead to an enhancement of the mass transfer rate. It is still debated whether such an enhancement of the mass transfer rate during outbursts is a missing ingredient of the current model. Aims. We discuss two mechanisms that could result in an enhancement of the mass transfer rate during outbursts: the hot outer disc rim itself could significantly heat the L1 point; scattered radiation by optically thin outflowing matter could also heat L1 significantly. We determine quantitatively the increase of the mass transfer rate resulting from an extra heating. Methods. We estimate the heating of the L1 point by the disc rim by analytical and numerical arguments. The fraction of the luminosity scattered by matter above the disc, here modeled as a spherically symmetric outflow, is determined analytically. We finally solve in a numerical way the vertical structure equations for the secondary star and calculate the mass transfer enhancement. Results. During outbursts, the temperature at the outer edge of the disc reaches 10 4 K. The disc edge heats up the upper layer of the secondary with a flux of the order of the intrinsic stellar flux. This probably has no large effect on the mass transfer rate. In soft X-ray transients, the environing medium of the disc (corona+wind) could back-scatter a certain fraction of the accretion luminosity toward L1. In dwarf novae, the same effect could be due to the wind present during outburst. Since soft X-ray transients reach high luminosities, even a low efficiency of this effect could yield a significant heating of L1, whereas we show that in dwarf novae this effect is negligible. Initially the incoming radiation does not penetrate below the photosphere of the secondary. Depending on the heating efficiency, which has to be determined, the mass transfer rate could be significantly increased.

Stability of helium accretion discs in ultracompact binaries

Context. Stellar companions of accreting neutron stars in ultra compact X-ray binaries (UCXBs) are hydrogen-deficient. Their helium or C/O accretion discs are strongly X-ray irradiated. Both the chemical composition and irradiation determine the disc stability with respect to thermal and viscous perturbations. At shorter periods, UCXBs are persistent, whereas longer-period systems are mostly transient. Aims. To understand this behaviour one has to derive the stability criteria for X-ray irradiated hydrogen-poor accretion discs. Methods. We use a modified and updated version of the Dubus et al. code describing time-dependent irradiated accretion discs around compact objects. Results. We obtained the relevant stability criteria and compared the results to observed properties of UCXBs Conclusions. Although the general trend in the stability behaviour of UCXBs is consistent with the prediction of the disc instability model, in a few cases the inconsistency of theoretical predictions with the system observed properties is weak enough to be attributed to observational and/or theoretical uncertainties. Two systems might require the presence of some amount of hydrogen in the donor star.