Acceleration of particles in the vicinity of a massive black hole

Recent results of the gamma-ray Cherenkov astronomy definitely prove the existence of fast variability in the very high energy (V.H.E.) gamma-ray flux of some active galactic nuclei. The BL Lac PKS 2155-304 for instance showed variations down to a few minutes time scale. From standard light travel time argument, these variations put extremely strong constraints on the size of the TeV emitting zone, which has to be of the order of a few Schwarzschild radius, even for high values of the relativistic Doppler factor of the emitting jets. Such discovery is a challenge for particle acceleration scenarios, which have to imagine efficient acceleration processes at work in a very compact zone. Eventually, the immediate vicinity of the central black hole appears as the most conservative choice for the location of the TeV emission region of active galactic nuclei. In this paper, we propose a two-step mechanism for charged particle acceleration in the magnetosphere of a massive black hole surrounded by an accretion disk. Particles first gain energy by a stochastic process during the accretion phase. It is shown that effective proton acceleration up to energies 10¹⁷–10¹⁹ eV is possible in a low-luminosity magnetized accretion disk with 2D turbulent motion. The distribution function of energetic protons over energies is a power law function with typical index ≃−1. Here electrons are not very efficiently accelerated because of their drastic losses by synchrotron radiation. In a second time, part of the fast particles escape from the disk and are then entrained by the magnetic structure above the disk, in the rotating black hole magnetosphere. They thus gain additional energy by direct centrifugal mechanism, up to about 10²⁰ eV for the protons and to 10–100 TeV for the electrons when they cross the light cylinder surface. Such energetic particles can further radiate in the TeV spectral range observed by Cherenkov experiments as HESS, MAGIC and VERITAS. Energetic protons can produce γ-radiation in the energy band 1 GeV–100 TeV and above mainly by nuclei collisions with the disk matter, clouds, or ambient low energy photons. Energetic electrons can also reach the required spectral range by inverse Compton emission. However their acceleration is less efficient due to heavy radiation losses, and only gained by centrifugal process during the second phase of the whole mechanism we describe. Our present analysis would therefore favor hadronic scenarios for TeV emission of active galactic nuclei. It is tempting to relate long term variability over years of TeV active galactic nuclei to the first stochastic acceleration phase, which also provides the needed power law particle distributions, while short term variability over minutes is more likely due to perturbations of the second fast direct acceleration phase.     

High-energy gamma-ray emission from the inner jet of LS I +61 303: the hadronic contribution revisited

LS I +61 303 has been detected by the Cherenkov telescope MAGIC at very high energies, presenting a variable flux along the orbital motion with a maximum clearly separated from the periastron passage. In the light of the new observational constraints, we revisit the discussion of the production of high-energy gamma rays from particle interactions in the inner jet of this system. The hadronic contribution could represent a major fraction of the TeV emission detected from this source. The spectral energy distribution resulting from pp interactions is recalculated. Opacity effects introduced by the photon fields of the primary star and the stellar decretion disk are shown to be essential in shaping the high-energy gamma-ray light curve at energies close to 200 GeV. We also present results of Monte Carlo simulations of the electromagnetic cascades developed very close to the periastron passage. We conclude that a hadronic microquasar model for the gamma-ray emission in LS I +61 303 can reproduce the main features of its observed high-energy γ-ray flux.      

Models of Very-High-Energy Gamma-Ray Emission from the Jets of Microquasars: Orbital Modulation

The recent detection of very-high-energy (GeV – TeV) γ-ray emission from the Galactic black-hole candidate and microquasar LS 5039 has sparked renewed interest in jet models for the high-energy emission in those objects. In this work, we have focused on models in which the high-energy emission results from synchrotron and Compton emission by relativistic electrons in the jet (leptonic jet models). Particular attention has been paid to a possible orbital modulation of the high-energy emission due to azimuthal asymmetries caused by the presence of the companion star. Both orbital-phase dependentγγ absorption and Compton scattering of optical/UV photons from the companion star may lead to an orbital modulation of the gamma-ray emission. We make specific predictions which should be testable with refined data from HESS and the upcoming GLAST mission.     

Radio-to-TeV γ-ray emission from PSR B1259–63

We discuss the implications of the recent X-ray and TeV γ-ray observations of the PSR B1259–63 system (a young rotation powered pulsar orbiting a Be star) for the theoretical models of interaction of pulsar and stellar winds. We show that previously considered models have problems to account for the observed behaviour of the system. We develop a model in which the broad band emission from the binary system is produced in result of collisions of GeV–TeV energy protons accelerated by the pulsar wind and interacting with the stellar disk. In this model the high energy γ-rays are produced in the decays of secondary neutral pions, while radio and X-ray emission are synchrotron and inverse Compton emission produced by low-energy (≤100 MeV) electrons from the decays of secondary charged π ^± mesons. This model can explain not only the observed energy spectra, but also the correlations between TeV, X-ray and radio emission components.      

Modeling the emission processes in blazars

Blazars are the most violent steady/recurrent sources of high-energy gamma-ray emission in the known Universe. They are prominent emitters of electromagnetic radiation throughout the entire electromagnetic spectrum. The observable radiation most likely originates in a relativistic jet oriented at a small angle with respect to the line of sight. This review starts out with a general overview of the phenomenology of blazars, including results from a recent multiwavelength observing campaign on 3C279. Subsequently, issues of modeling broadband spectra will be discussed. Spectral information alone is not sufficient to distinguish between competing models and to constrain essential parameters, in particular related to the primary particle acceleration and radiation mechanisms in the jet. Short-term spectral variability information may help to break such model degeneracies, which will require snap-shot spectral information on intraday time scales, which may soon be achievable for many blazars even in the gamma-ray regime with the upcoming GLAST mission and current advances in Atmospheric Cherenkov Telescope technology. In addition to pure leptonic and hadronic models of gamma-ray emission from blazars, leptonic/hadronic hybrid models are reviewed, and the recently developed hadronic synchrotron mirror model for TeV γ-ray flares which are not accompanied by simultaneous X-ray flares (“orphan TeV flares”) is revisited. The U.S. Government’s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

The Converter Mechanism of Particle Acceleration and Its Applications to the Unidentified Egret Sources

We discuss the properties of gamma-ray radiation accompanying the acceleration of cosmic rays via the converter mechanism. The mechanism exploits multiple photon-induced conversions of high-energy particles from charged into neutral state (namely, protons to neutrons and electrons to photons) and back. Because a particle in the neutral state can freely cross the magnetic field lines, this allows to avoid both particle losses downstream and reduction in the energy gain factor, which normally takes place due to highly collimated distribution of accelerated particles. The converter mechanism efficiently operates in relativistic outflows under the conditions typical for Active Galactic Nuclei, Gamma-Ray Bursts, and microquasars, where it outperforms the standard diffusive shock acceleration. The accompanying radiation has a number of distinctive features, such as an increase of the maximum energy of synchrotron photons and peculiar radiation beam-pattern, whose opening angle is much wider at larger photon energies. This provides an opportunity to observe off-axis relativistic jets in GeV–TeV energy range. One of the implications is the possibility to explain high-latitude unidentified EGRET sources as off-axis but otherwise typical relativistic-jet sources, such as blazars.     

Timing and spectral properties of the X-ray emission from the blazar 1ES 1426+428

Most of the extragalactic sources from which very-high-energy (VHE, E > 10¹¹ eV) gamma-ray fluxes have been detected belong to the category of high-energy peaked BL Lacertae objects (HBLs)—the sources in which the synchrotron radiation peaks in the UV or X-ray band. They often have higher X-ray luminosities than the VHE gamma-ray energy output, which makes them the most valuable objects for studying the characteristic spectral and temporal variations in the region of the synchrotron peak of the spectral energy distribution. The blazar 1ES 1426+428 belonging to this category is a target of many multiwavelength studies, both orbital and ground-based ones. The properties of its X-ray emission have also been investigated using RXTE/PCA, XMM-Newton, and SWIFT observations. Archival PCA/RXTE data with a total exposure time in 2002 and 2004 of ≈120^h and the most recent available background and calibration files have been used. The extracted light curves of 1ES 1426+428 in the 2.9–24 keV energy band have shown an intense flaring activity on various time scales. Analysis of the observational data has also confirmed the spectral hardening with increasing X-ray intensity typical of blazars. The flaring state of the object is also characterized by a flat spectrum, which steepens with decreasing flux. The previously detected evidence of a spectral hysteresis in a separate flare has also been confirmed. Observations of 1ES 1426+428 with the SWIFT/XRT telescope and the EPIC instrument onboard XMM-Newton have revealed several intermediate-intensity flares in the 1.5–12 keV energy band with flux variations reaching a factor of 2, while analysis of the light curves has revealed a correlation between two components of the X-ray emission from the object.     

INTEGRAL serendipitous detection of the gamma-ray microquasar LS 5039

LS 5039 is the only X-ray binary persistently detected at TeV energies by the Cherenkov HESS telescope. It is moreover a γ-ray emitter in the GeV and possibly MeV energy ranges. To understand important aspects of jet physics, like the magnetic field content or particle acceleration, and emission processes, such as synchrotron and inverse Compton (IC), a complete modeling of the multiwavelength data is necessary. LS 5039 has been detected along almost all the electromagnetic spectrum thanks to several radio, infrared, optical and soft X-ray detections. However, hard X-ray detections above 20 keV have been so far elusive and/or doubtful, partly due to source confusion for the poor spatial resolution of hard X-ray instruments. We report here on deep (∼300 ks) serendipitous INTEGRAL hard X-ray observations of LS 5039, coupled with simultaneous VLA radio observations. We obtain a 20–40 keV flux of 1.1±0.3 mCrab (5.9 (±1.6) ×10⁻¹² erg cm⁻² s⁻¹), a 40–100 keV upper limit of 1.5 mCrab (9.5×10⁻¹² erg cm⁻² s⁻¹), and typical radio flux densities of ∼25 mJy at 5 GHz. These hard X-ray fluxes are significantly lower than previous estimates obtained with BATSE in the same energy range but, in the lower interval, agree with extrapolation of previous RXTE measurements. The INTEGRAL observations also hint to a break in the spectral behavior at hard X-rays. A more sensitive characterization of the hard X-ray spectrum of LS 5039 from 20 to 100 keV could therefore constrain key aspects of the jet physics, like the relativistic particle spectrum and the magnetic field strength. Future multiwavelength observations would allow to establish whether such hard X-ray synchrotron emission is produced by the same population of relativistic electrons as those presumably producing TeV emission through IC.     

Diffusion of cosmic rays in a multiphase interstellar medium swept-up by a supernova remnant blast wave

Supernova remnants (SNRs) are one of the most energetic astrophysical events and are thought to be the dominant source of Galactic cosmic rays (CRs). A recent report on observations from the Fermi satellite has shown a signature of pion decay in the gamma-ray spectra of SNRs. This provides strong evidence that high-energy protons are accelerated in SNRs. The actual gamma-ray emission from pion decay should depend on the diffusion of CRs in the interstellar medium. In order to quantitatively analyse the diffusion of high-energy CRs from acceleration sites, we have performed test particle numerical simulations of CR protons using a three-dimensional magnetohydrodynamics (MHD) simulation of an interstellar medium swept-up by a blast wave. We analyse the diffusion of CRs at a length scale of order a few pc in our simulated SNR, and find the diffusion of CRs is precisely described by a Bohm diffusion, which is required for efficient acceleration at least for particles with energies above 30 TeV for a realistic interstellar medium. Although we find the possibility of a superdiffusive process (travel distance ∝ t^0.75) in our simulations, its effect on CR diffusion at the length scale of the turbulence in the SNR is limited.     

The Galactic Center: a laboratory for AGN?

Summary. This paper reviews the physical state of stars and Interstellar Matter in the Galactic Bulge (radius kpc from the dynamical center of the Galaxy), in the Nuclear Bulge (kpc) and in the Sgr A Radio and GMC Complex, i.e. the central \,pc of our Galaxy. The Galactic Bulge is devoid of cold Interstellar Matter and consists mainly of old stars, while the Nuclear Bulge accounts for of the mass of all of the Interstellar Matter in the Galaxy. A similar ratio holds for the formation rate of medium and high mass stars in Bulge and Disk. The metal abundance of the Interstellar Matter in the Galactic Bulge is found to be . The H-to-CO conversion factors to be applied to molecular gas in the Central Region are by factors 3 (Arimoto et al. 1996) to 10 (Sodroski et al. 1995) lower than in the solar vicinity. Hence, most H masses derived for the Central Region appear to be considerably overestimated. The Nuclear Bulge is pervaded by a thermal plasma (K) which is responsible for the diffuse free-free emission. Lyman continuum photon and dust IR luminosity of the Nuclear Bulge again account for of the respective total luminosities of the Galaxy. Magnetic fields in the Nuclear Bulge are strong (up to mG) as compared with the Galactic Disk (a few tens of G). The field lines are oriented parallel to the galactic plane inside giant molecular clouds and perpendicular to the plane in the intercloud medium. The compact source Sgr A* is close to or at the dynamical center of the Galaxy. Its radio spectrum with a high frequency cut-off at GHz, a low frequency turnover at GHz and a flux density dependence in between can be explained by synchrotron emission from quasi-monoenergetic relativistic electrons. Due to an extinction between Sun and Galactic Center corresponding to , an intrinsic weakness of this source in the near infrared, and a strong background emission from warm dust there are only upper limits available for the flux density of Sgr A* in the far, mid and near infrared and X-ray regime. The size of Sgr A* in the radio regime is cm, its dereddened K-band flux density is mJy, its luminosity has upper limits of (if radiation comes from an Accretion Disk) and (if black-body radiation from an object with a single temperature of K is assumed). If anyone of the soft X-ray sources detected by ROSAT actually coincides with Sgr A*, its X-ray luminosity would be less than a few . With a dark mass of Sgr A* is the best candidate for a starving black hole, although there are no observational indications for the presence of a (Standard) Accretion Disk. While the radio/IR spectrum of Sgr A* is purely nonthermal, the spectrum integrated over the central parsec resembles that of a Seyfert galaxy. Sgr A* is embedded in the Hii region Sgr A West with part of the ionized gas forming a minispiral. Sgr A West is surrounded by the Circum Nuclear Disk, an irregular shaped assembly of molecular gas which extends from pc and rotates around the Galactic Center with an estimated dynamical time scale of \,yr. The total luminosity of of the central parsec is due to the radiation of early-type stars of which have now been directly identified as luminous blue supergiants. It is still debated, however, if these stars can also account for all of the ionization of Sgr A West. In addition, the central parsec contains red giants, AGB stars, and a few super giants of which the brightest are now identified by direct imaging. These stars – together with a few million low mass main sequence stars – account for the bulk of the 2.2\,m emission. The spatial distributions of the three stellar populations in the central pc are remarkably different. Sgr A* is – along the line-of-sight – presumably located close to the center of the Hii region Sgr A West, which in turn is located in front of the extended (pc) synchrotron source Sgr A East, which appears to be the remnant of a gigantic explosion (of the order of the energy of a single supernova explosion) which took place yr ago inside the GMC Sgr A East Core. X-ray observations show within pc a pervasive hot (keV) plasma of expansion age of yr. Both phenomena – as well as the formation of the Circum Nuclear Disk – may have the same origin. Influx of material is observed within the Nuclear Bulge on all distance scales. In the Nuclear Bulge (pc) as well as in the Circum Nuclear Disk (pc) inflow towards the Galactic Center occurs primarily in the galactic plane and amounts to a few . The accretion rate into the central Black Hole, deduced from the luminosity of Sgr A*, however, appears to be lower by at least five orders of magnitude (assuming standard disk accretion). But in an equilibrium state only part of the infalling mass which is not accreted by the Black Hole can be consumed by star formation. A mass inflow rate varying with time is a more natural explanation. Comparing the physical state of the Center of our Galaxy with that of Active Galactic Nuclei derived from observations and modelling, we find that most of the basic characteristics of an AGN are also present in the Galactic Center. Lacking are, however, both the evidence for a standard Accretion Disk and a hard UV spectrum with accompanying high excitation emission lines in the Galactic Center which are characteristic for AGN. The luminosity of the central parsec, , amounts to only of the total luminosity of the Galaxy of . Seen from a distance of M31 (kpc) with an angular resolution of (corresponding to a linear size of pc) the Center of our Galaxy would appear as a mildly active nucleus with some starburst activity and would probably be classified as a weak Seyfert galaxy. The synchrotron spectrum of Sgr A*, however, would be completely masked by reprocessed stellar light (i.e. free-free and dust emission). Received: October 21, 1996     

Nucleonic gamma-ray production in pulsar wind nebulae

Observations of the inner radian of the Galactic disk at very high energy (VHE) gamma-rays have revealed at least 16 new sources. Besides shell type super-nova remnants, pulsar wind nebulae (PWN) appear to be a dominant source population in the catalogue of VHE gamma-ray sources. Except for the Crab nebula, the newly discovered PWN are resolved at VHE gamma-rays to be spatially extended (5–20 pc). Currently, at least 3 middle aged (t>10 kyrs) PWN (Vela X, G18.0-0.7, and G313.3+0.6 in the “Kookaburra” region) and 1 young PWN MSH 15-52 (t=1.55 kyrs) have been identified to be VHE emitting PWN (sometimes called “TeV Plerions”). Two more candidate “TeV Plerions” have been identified and have been reported at this conference (Carrigan, These proceedings, in preparation). In this contribution, the gamma-ray emission from Vela X is explained by a nucleonic component in the pulsar wind. The measured broad band spectral energy distribution is compared with the expected X-ray emission from primary and secondary electrons. The observed X-ray emission and TeV emission from the three middle aged PWN are compared with each other.     

High energy neutrinos from the TeV Blazar 1ES 1959 + 650

The AMANDA neutrino telescope has recently reported the detection of high-energy neutrinos spatially and temporally coincident with the flaring of the TeV blazar 1ES 1959 + 650. If high-energy neutrinos are in fact generated by this blazar, it would be the first strong evidence for the hadronic acceleration of cosmic rays. At present, the statistical significance of this observation cannot be reliably assessed, however. In this letter, we investigate whether circumstances exist where the source can produce the flux implied by the coincident events. We show that if the TeV gamma-ray emission observed from 1ES 1959 + 650 or other nearby TeV blazars is the result of accelerated protons interacting with nucleons, it is reasonable that AMANDA could detect several events during a flaring period. Such rates require that the spectral index of the source be rather high (for instance ∼2.8 for 1ES 1959 + 650) and that the Lorentz factor of the jet be fairly small (Γ ∼ 1).     

Detection potential of the KM3NeT detector for high-energy neutrinos from the Fermi bubbles

A recent analysis of the Fermi Large Area Telescope data provided evidence for a high-intensity emission of high-energy gamma rays with a E⁻² spectrum from two large areas, spanning 50° above and below the Galactic centre (the “Fermi bubbles”). A hadronic mechanism was proposed for this gamma-ray emission making the Fermi bubbles promising source candidates of high-energy neutrino emission. In this work Monte Carlo simulations regarding the detectability of high-energy neutrinos from the Fermi bubbles with the future multi-km³ neutrino telescope KM3NeT in the Mediterranean Sea are presented. Under the hypothesis that the gamma-ray emission is completely due to hadronic processes, the results indicate that neutrinos from the bubbles could be discovered in about one year of operation, for a neutrino spectrum with a cutoff at 100 TeV and a detector with about 6 km³ of instrumented volume. The effect of a possible lower cutoff is also considered.     

INTEGRAL observations of TeV plerions

Amongst the sources seen in very high gamma-rays several are associated with Pulsar Wind Nebulae (“TeV plerions”). The study of hard X-ray/soft gamma-ray emission is providing an important insight into the energetic particle population present in these objects. The unpulsed emission from pulsar/pulsar wind nebula systems in the energy range accessible to the INTEGRAL satellite is mainly synchrotron emission from energetic and fast cooling electrons close to their acceleration site. Our analyses of public INTEGRAL data of known TeV plerions detected by ground based Cherenkov telescopes indicate a deeper link between these TeV plerions and INTEGRAL detected pulsar wind nebulae. The newly discovered TeV plerion in the northern wing of the Kookaburra region (G313.3+0.6 powered by the middle aged PSR J1420-6048) is found to have a previously unknown INTEGRAL counterpart which is besides the Vela pulsar the only middle aged pulsar detected with INTEGRAL. We do not find an INTEGRAL counterpart of the TeV plerion associated with the X-ray PWN “Rabbit” G313.3+0.1 which is possibly powered by a young pulsar.     

Gamma-Ray Line Observations of the 2000 July 14 Flare and SEP Impact on the Earth

The HXS and GRS detectors on Yohkoh observed the 14 July 2000, X5.7 flare, beginning at ∼ 10:20 UT, ∼ 4 min before the peak in soft X-rays. The hard X-rays and γ-rays peaked ∼ 3 min later at ∼ 10:27 UT. Solar γ-ray emission lasted until ∼ 10:40 UT. Impact of high-energy ions at the Sun is revealed by the γ-ray lines from neutron capture, annihilation radiation and de-excitation that are visible above the bremsstrahlung continuum. From measurement of these lines we find that the flare-averaged spectrum of accelerated protons is consistent with a power law ge10 MeV with index 3.14±0.15 and flux 1.1×10³² protons MeV⁻¹ at 10 MeV. We estimate that there were ∼1.5×10³⁰ erg in accelerated ions if the power law extended without a break down to 1 MeV; this is about 1% of the energy in electrons > 20 keV from measurements of the hard X-rays. We find no evidence for spectral hardening in the hard X-rays that has been suggested as a predictor for the occurrence of solar energetic particle (SEP) events. This was the third largest proton event above 10 MeV since 1976. The GRS and HXS also observed γ-ray lines and continuum produced by the impact of SEP on the Earth's atmosphere beginning about 13 UT on 14 July. These measurements show that the SEP spectrum softened considerably over the next 24 hours. We compare these measurements with proton measurements in space.     

Search for ultrahigh-energy cosmic gamma-ray bursts on the Baksan underground scintillation telescope

Based on data from the Baksan underground scintillation telescope (BUST) for the period 2001–2004, we searched for cosmic gamma-ray bursts (GRBs) at primary photon energies of 0.5 TeV or higher. We obtained constraints on the rate of bursts with durations of 1–10 s for fluences within the range 4.6 × 10⁻³-1.8 × 10⁻² erg cm⁻² in the declination band 30° ≤ δ ≤ 80°. We searched for ultrahigh-energy gamma rays from GRBs detected on spacecraft during and within ±2 h of the burst. No statistically significant excesses above the background of random coincidences were found. The derived constraints on the ultrahigh-energy gamma-ray fluence during GRBs lie within the range 4.6 × 10⁻³-3.7 × 10⁻² erg cm⁻².     

Gamma-ray bursts, ultra-high-energy cosmic rays, and cosmic gamma-ray background

We argue that gamma-ray bursts (GRBs) may be the origin of the cosmic gamma-ray background radiation observed in the GeV range. It has theoretically been discussed that protons may carry a much larger amount of energy than electrons in GRBs, and this large energy can be radiated in the TeV range by synchrotron radiation of ultra-high-energy protons ( 10²⁰ eV). The possible detection of GRBs above 10 TeV suggested by the Tibet and HEGRA groups also supports this idea. If this is the case, most of TeV gamma-rays from GRBs are absorbed in intergalactic fields and eventually form GeV gamma-ray background, whose flux is in good agreement with the recent observation.     

High energy neutrinos from the TeV Blazar 1ES 1959 + 650

The AMANDA neutrino telescope has recently reported the detection of high-energy neutrinos spatially and temporally coincident with the flaring of the TeV blazar 1ES 1959 + 650. If high-energy neutrinos are in fact generated by this blazar, it would be the first strong evidence for the hadronic acceleration of cosmic rays. At present, the statistical significance of this observation cannot be reliably assessed, however. In this letter, we investigate whether circumstances exist where the source can produce the flux implied by the coincident events. We show that if the TeV gamma-ray emission observed from 1ES 1959 + 650 or other nearby TeV blazars is the result of accelerated protons interacting with nucleons, it is reasonable that AMANDA could detect several events during a flaring period. Such rates require that the spectral index of the source be rather high (for instance 2.8 for 1ES 1959 + 650) and that the Lorentz factor of the jet be fairly small (Γ  1).     

Is there a limit on solar flare proton fluxes?

We explore the possibility that solar flare proton fluxes are limited in magnitude by saturation effects inherent to the acceleration mechanism. If cyclotron damping of Alfvén waves acts to accelerate protons, the criterion that the damping time is comparable to the acceleration time provides a fast particle number density at which protons load the wave spectrum. The limiting flux J ^*at 1 AU is obtained by a volume integration over the acceleration region and redistribution into an interplanetary emission cone. A simplified explosion model permits a delineation between volume and surface acceleration mechanisms in terms of a temporal parameter, the effective duration of acceleration. We conclude that J ^*may be a realistic concept, but that further investigation is warranted to sharpen the criterion.