Magnetic Penrose Process and Blanford-Zanejk mechanism: A clarification
aa r X i v : . [ a s t r o - ph . H E ] O c t Magnetic Penrose Process and Blanford-Zanejkmechanism: A clarification
Naresh DadhichCentre for Theoretical Physics, Jamia Millia Islamia, New Delhi 110 025 & IUCAA, Post Bag 4, Ganeshkhind, Pune 411 007, India [email protected]
PACS numbers :04.20.-q, 04.70-s, 04.70.Dy, 95.30.Sf
Abstract
The Penrose process (PP) is an ingenious mechanism of extracting rotational energy from a rotatingblack hole, however it was soon realized that it was not very efficient for its astrophysical applications forpowering the central engine of quasars and AGNs. The situation however changed dramatically in thepresence of magnetic field produced by the accretion disk surrounding the hole in the equatorial plane. In1985, Wagh, Dhurandhar and Dadhich [1] had for the first time considered the magnetic Penrose process(MPP) in which the magnetic field could now provide the energy required for a fragment to ride on negativeenergy orbit thereby overcoming the stringent velocity constraint of the original PP. Thus MPP turnedvery efficient and so much so that efficiency could now even exceed percent. They had in principleestablished revival of PP for astrophysical applications in powering the high energy sources. MPP ishowever similar to the earlier discovered and well known Blandford-Znajeck (BZ) mechanism in which therotational energy of the hole is extracted out through a purely electromagnetic process. Though both theprocesses use magnetic field as a device to extract rotational energy from the hole, yet their kernel is quitedifferent in spirit. For the former magnetic field provides the threshold energy for particle to get ontonegative energy orbit so that the other fragment goes out with enhanced energy while for the latter itgenerates an electric potential difference between the equatorial plane and the polar region, and it is thedischarge of which that drives the energy flux out of the hole. In other words, MPP is still rooted in thespacetime geometry while BZ is essentially driven by electromagnetic interaction. Introduction
The Penrose process [2] is an ingenious mechanism of extracting rotational energy from a rotatingblack hole which was entirely driven by the spacetime geometry. In the neighborhood of black holeevent horizon, there occurs a region called ergosphere, which is bounded by the static limit on oneside and the horizon on the other, where there exist timelike particle orbits with negative totalenergy relative to infinity. Penrose exploited this property for extraction of the hole’s rotationalenergy. It was envisioned that a particle falling from infinity on to the hole splits into two in theergosphere, the one of which rides on the negative energy orbit and falls into the hole while theother escapes out with energy larger than the incident particle. This is how the rotational energyof the black hole can be extracted out. This is what is known as the Penrose process (PP). Theessential requirement for it is existence of the ergosphere, where negative energy orbits can occur,and it is purely a geometric construct caused by rotation of the hole. It cannot work for a nonrotating black hole from which no energy could be extracted out by this process simply becausethere can occur no negative energy orbits in its neighborhood.It came at the very right time in 1969, just when the quasars, which were discovered a littleearlier, and AGNs were asking for the energy source for their central engine. Here was a processprovided by the spacetime geometry itself and hence it created a good bit of excitement. It wasenvisaged that a star like object grazing a super massive rotating black hole tidally or otherwisesplits into fragments in the ergoshere, some of which fall into the hole with negative energy whilethe others come out accelerated with large energy. However it was soon realized that for a frag-ment to ride on the negative energy orbit, it should instantly be accelerated to velocity > c/ [3, 4]. This was however astrophysically unsustainable as there could be no conceivable processthat could accelerate the fragments to such a high velocity instantaneously. In other words, PPwould have a very low efficiency of energy extraction and hence it is novel but not astrophysicallyviable. Thus the excitement generated in 1969 died out by 1974. Since then some variants of itlike the collisional PP were considered without much improving the situation [5, 6].Then in 1977 came the celebrated Blandford-Zanejk (BZ) mechanism [7] of the electromag-netic extraction of the rotational energy of a rotating black hole. Here it is envisioned thatmagnetic field produced by the accretion disk threads the black hole horizon and if the field isstrong enough, vacuum would be unstable to cascade production of electron-positron pairs andthereby establishing a force free magnetosphere. Thus an electric potential difference would begenerated between the equatorial plane and the polar region and when it is discharged, therewould be energy flux out of the hole. This is how the rotational energy of the hole would beextracted out by purely an electromagnetic process. This was indeed one of the most promising2strophysically viable mechanisms for powering the central engine in quasars and AGNs.In 1985 Wagh, Dhurandhar and Dadhich [1] argued that a rotating black hole does not sitin isolation but is always surrounded by an accretion disk which could produce a magnetic fieldthreading the black hole horizon. It would therefore be pertinent to consider PP in presence ofelectromagnetic field (magnetic field anchored on the inherent rotation in the ergosphere wouldalso develop a quadrupole electric component). Now the fragments in the ergosphere could becharged and they could therefore derive energy from electromagnetic field to get onto the negativeenergy orbit thereby overcoming the stringent velocity constraint of the original PP. The processcould thus be highly efficient and hence it could be revived for astrophysical applications. Thiswas what was exactly claimed in [1], and this was the first explicit consideration of the magneticPenrose process (MPP). It was first presented in [8, 9] as electromagnetic revival of PP as en-ergy source for prime movers in high energy sources. The authors carried out a comprehensivestudy of the process establishing that efficiency could even exceed percent in realistic settings[10, 11, 12]. It was concluded in writing a review on the energetics of black holes in electromagneticfields by the Penrose process [13]. The viability of MPP was established in principle for a discreteparticle accretion and it had remained so until recently [14, 15]. This is indeed very gratifying tosee that MPP is now considered to be the most pertinent process for powering the central enginein quasars and AGNs. It is however thought that MPP is the same as BZ mechanism [16], andthat is what I take up next. It is generally believed that the two processes are similar and it would be hard to find a signatureto distinguish between them. As mentioned earlier, for both magnetic field plays the catalytic rolefor mining the rotational energy of the hole. MPP is rooted in the existence of negative energyorbits which are caused by the coupling of particle angular momentum with the hole’s angularmomentum and in that magnetic field adds its own contribution to effective angular momentumof the particle. It is that which facilitates particles of Newtonian orbits get onto negative energyorbits. The magnetic field contribution thus favorably affects the particle energetics for MPP towork with very high efficiency. On the other hand BZ is essentially an electromagnetic processwith force free magnetosphere produced by cascade of electron-positron pairs, and development ofa potential difference between equatorial plane and polar region. Then the completion of electriccircuit by discharge of the potential difference that drives the (negative) energy flux into the holeand enhanced flux out to infinity. Here it is the electromagnetic interaction which is at the core ofthis process. Since it takes place in the background geometry of a rotating black hole which has3nherent and irresistable rotation in the ergosphere, magnetic field lines are wound and anchoredon the horizon. Spacetime geometry thus plays a passive role in this case in contrast to MPPwhere it is an active driving element. This is how their kernel is quite different in spirit buteffectively both require very high magnetic field for the energy extraction to be efficient enough toserve as a viable source for the high energy sources. Note that efficiency of MPP was shown to begreater than percent [10] which augurs very well with the current investigations [16, 14, 15].As a matter of fact efficiency exceeding percent could be considered as the distinguishingfeature of MPP.The distinction between the two could arise in the limiting case of magnetic field tending tozero. In that case MPP would go to PP, though inefficient yet there is some possibility of energyextraction while for BZ there would be the null result. In the pertinent case of strong magneticfield, one can perhaps take it as MPP or BZ, and it is simply a matter of taste whether one wouldprefer gravity/geometry or electromagnetic field plays the active role. We could as well considera synthesis of the two where one complements the other. For MPP, it is envisaged that thereis accreting matter from the disk on the hole that could provide fragments which could ride onnegative energy orbits and fall into the hole while others come out accelerated with large energy.The vacuum polarization of BZ could serve as a good viable source for fragments in the ergosphererequired for MPP to work. For BZ, the inherent irresistable rotation in the ergosphere plays arole in enhancing the magnetic field strength and creating the magnetosphere. It would thereforebe appropriate and pertinent to consider the synthesis of the two mechanisms, and the energyextraction could be looked upon as MPP or BZ, the two equivalent processes for strong magneticfield regime. We would just like to point out that MPP may be the same as BZ mechanism, itwas however as such first considered by us in [1] as revival of PP for astrophysical applications.It is both heartening and gratifying to see that it is now the most favored mechanism for primemover in the high energy sources [16, 14, 15, 17].
Acknowledgements
It is a plesaure to thank S Wagh, S Dhurandhar, S Parthasarthy and M Bhat, who formed acohesive team that investigated various aspects of MPP, for successful collaboration. I wouldalso like to thank several colleagues at various institutes and universities for discussions of thisinteresting phenomenon at the time of its discovery in mid to late 1980s. I am grateful to RameshNarayan for referring to our work in his plenary lecture at the Relativity and Gravitation: 100years after Einstein in Prague, June 25-29, 2012.4 eferences [1] S. M. Wagh, S. V. Dhurandhar and N. Dadhich, Astrophys. J. (1985) 12; Erratum,Astrophys. J. (1986) 1018.[2] R. Penrose, Riv. Nuovo Cimento bf1 (1969) 252.[3] J. M. Bardeem, W. Press and S. Teukolsky, Astrophys. J. (1972) 347.[4] R. M. Wald, Astrophys. J. (1974) 231.[5] T. Piran, J. Shaham and J. Katz, Nature (1975) 112.[6] T. Piran and J. Shaham, Astrophys. J. (1977) 268.[7] R. D. Blandford and R. L. Znajek, Mom. Not. R. Astron. Soc. (1977) 433.[8] S. M. Wagh and N. Dadhich, in Quasars, Proc. Of IAU Symposium 119 (Bangalore, 1985)eds. G. Swarup and V. K. Kapahi (Reidel, Dordrecht, 1986).[9] N. Dadhich, in Highlights in gravitation and cosmology, eds. B. R. Iyer, A. K. Kembhavi, J.V. Narlikar and C. V. Vishveshwara (Cambridge Univ. Press, Cambridge, 1989).[10] S. Parthasarthy, S. M. Wagh, S. V. Dhurandhar and N. Dadhich, Astrophys. J. (1986)38.[11] M. Bhat, S. V. Dhurandhar and N. Dadhich, J. Astrophys. Astron. (1985) 85.[12] S. M. Wagh, Ph. D. thesis, (University of Poona, 1987).[13] S. M. Wagh and N. Dadhich, Physics Reports (1989) 137-192.[14] A. Techekhovskoy, R. Narayan and J. C. McKinney, Mon. Not. R. Astron. Soc. (2011)L79.[15] R. Narayan and J. E. McClintock, Mon. Not. R. Astron. Soc.419