7
Black Holes Cannot Blow Jets
Wolfgang Kundt
Argelander Institute of Bonn University, Auf dem H¨ugel 71, D-53121 Bonn, Germany
Summary. Both Jet Sources (or Bipolar Flows), and Gamma-Ray Bursts, have been known for roughly forty years, and there are various, mutually inconsistent descriptions in the wide literature. Their high energies, and large spatial ranges manifest that they are generated by powerful engines, almost comparable with human high-tech equipment, so that a thorough understanding of their functioning will help us understand the most efficient engines of dead matter. An important detail of these lectures will be the insight that black holes fail to be members of their toolbox; they just cannot do it.
1 Introduction
In military language, jet sources are fantastic weapons: they can fire extremely relativistic (microscopic) bullets through distances exceeding megaparsecs with an opening angle of the order of one percent, steadily throughout 108 years, with total powers ranging up to 1048erg/s, and with only minor transport losses during their Myr-long flights. We now know that individual electrons in the dumping sites of the jets can reach Lorentz factors of (even!) 109 – both electrons and positrons – as upper limits to their power-law distributions at ejection. Such feats require long-lived engines, whose foundations must be safely protected against the swallowing habit of black holes (BHs). And even the tiniest among the jet set, newly born brown 2 3 dwarfs with masses 10 MJUP , realize jet lengths of several 10 astronomical units [Whelan et al 2009]. Jet sources have been discovered in the sky, and mapped for more than 30 years, beginning at radio frequencies, closely followed by optical frequencies, then X-rays and γ-rays up to GeV energies, and recently even up to TeV energies, or even PeV energies! Whilst more and more morphological and temporal details have been elaborated, the modes of their generation, propagation, termination, and evolution have found unacceptably diverging treatments in the extended literature. This decades-long stagnation of insight, it appears to me, is predominantly due to the black-hole dictatorship in present-day astrophysics: Black Holes lack persistent, time-varying magnetic fields (for pair formation, and for their post-acceleration via an outgoing strong wave), and lack quasi-static (high-density) deLaval nozzles for the formation of a pair of supersonic antipodal jets, as opposed to fast-rotating magnetized stars inside shearing accretion disks, or differentially rotating magnetized coronas of central galactic disks which have been the preferred jet sources in Kundt & Gopal-Krishna [1980, 2004] as well as in Blome & Kundt [1988], and in Kundt [1989, 1996, 2001a,b, 2002, 2005, 2009a,b]. In my mother language: Schwarze L¨ocher schlucken,siespucken nicht. This compact review of jet formation will begin with a listing of the wide range of observed jet sources, or ‘bipolar flows’, grouping them into a 4-headed family according to their different central engines: (a) newborn stars, (b) forming white dwarfs, (c) middle-aged binary neutron stars, and (d) nuclear-burning centers of galactic disks. Note that these four source types are all expected to anchor a rapidly corotating transverse magnetic moment, whilst the often proposed (stellar-mass) ‘BH-Candidates’ may have been mistaken for neutron stars inside of massive accretion disks, and the ‘supermassive BHs’ at the centers of galaxies mistaken for nuclear-Burning central galactic Disks (BDs). Next, in the section ‘necessary properties’, I will collect a number of plausible constraints on jet sources to function, and sort between viable and non-viable mechanisms for their realisation. The quasi-unique analytical class of jet solutions found in [Kundt & Krishna 2004] will then be reviewed, and subsequently contrasted to the 2 Wolfgang Kundt sources of the GRBs, which are emitted without any jets (in my understanding). Quite similar approaches to jet sources have been taken by Phil Morrison [1981], and by Peter Scheuer [1996], who are both, unfortunately, no longer with us.
2 The Bipolar-Flow Family
Even though the astrophysical jet sources range through huge factors in {size, age, power, mass(CE)}, CE ::= central engine, viz. range through respective factors {108,107,109,109}, they appear astonishingly similar in their essential properties such as the jets’ opening angle Θ, the jet/core power ratio, maximal speed, morphology, stability, spectrum, and variability. They tend to be divided into ‘micro-quasars’ and ‘quasars’ – the prefix “micro” alluding to a typical discriminating factor of 106 in their listed properties – a classification which essentially agrees with ‘stellar’ and ‘galactic’ CEs. Here is a table of the complete family of Jet Sources, or Bipolar Flows (BFs):
Newborn Stars (YSOs) Forming White Dwarfs (inside PNe) Elderly Binary Neutron Stars Centers of Galactic Disks (AGN)
For an easier comparison of the subsequent modeling with the best-studied astronomical jet sources, let us look at a few outstanding representatives of the four classes: (a) Newborn stars, or young stellar objects (YSOs), tend to emit predominantly thermal spectra, hence they look often rather different from their more powerful and larger relatives of the BF family. Yet as already stressed in earlier publications, a few exceptions exist which look exactly like miniature copies of their larger relatives, e.g. like fast expanding radio triples, of age 103yr, see Blome & Kundt [1988], or Kundt [1996, 2001, 2002, 2005]. Surprising was last year’s discovery by Whelan et al [2009] of half a dozen brown dwarfs with jets: Even such YSOs, of subsolar mass, have strong enough magnetospheres in fast enough corotation to blow (feeble) jets, of lengths 1016.5cm. And yet newer are the properties of the massive protostellar jet HH 80-81 found by Carrasco-Gonzalez et al [2010] which highlights the similarity of the four classes. (b) Forming white dwarfs,insideplanetary nebulae (PNe), have various morphologies, but at least some of them show clear evidences of feeble jets near their symmetry axes, see [Kundt 1996], and indications of two antipodal elongated lobes, and their various morphologies cannot be understood without multiple plasma components of strongly differing densities in extended interaction. An increasing number of cataclysmic variables appear to join the jet set. (c)Thisclass,ofBFspoweredbyelderly neutron stars, is likewise known for more than 30 years, with SS 433 as its most powerful, and most exotic representative: SS 433 is particularly famous for its multiple, transrelativistic and almost periodic optical and X-ray emission lines – reminiscent of the broad emission lines of the quasars – which I understand as multiply excited recombination lines from dragged-along channel- wall material of the innermost parts of its precessing jets [Kundt 1996, 1998, 2001, 2005]. The channel-wall material may well stem from the wind of its (ordinary) stellar companion. Just recently, Pakull et al [2010] have discovered a 20 times older brother of its kind, ‘nebula’ S26in the outskirts of the Sculptor galaxy NGC 7793, which is similarly impressive even if somewhat fainter than SS 433. The authors may have overestimated its mechanical power by assuming that its lobes radiated preferentially (optically) from a skin-like radiative shock at their periphery, rather than from small-filling-factor filamentary inclusions, at about 103times higher densities, by 103times less matter, and therefore with 103times less mechanical power than stated. By taking care of a filling factor f ≈10−3 of the optical source in its lobes, the properties of S 26 conform nicely with those of all the other class-(c) sources. With the probable exception of our Galactic center, neutron stars are the only jet class with central engines which have shown (≥ eight cases of) emission of the 511 keV e±-pair annihilation line, redshifted by some 7% [Kaiser & Hannikainen 2002], an indication of significant local pair excess. There is also unredshifted emission of the 511 keV line from a vicinity of Felix Mirabel’s ‘great annihilator’ [1992]. Interesting, and still poorly understood are the frequently reported time-periodic motions of X-ray spectra of class-(c)-sources in the intensity-vs-hardness plane, and of their correlations with radio outbursts, and with flaring jet formation, on varying time scales between weeks and years, which take the shape of a repeatedly Black Holes Cannot Blow Jets 3 traversed turkey head,[K¨ording et al 2006]. They should eventually allow us to get a deeper insight into the quasi-periodic physical processes taking place near the jets’ CE. Similar quasi-periodicities take place in the AGN sources, though on distinctly longer time scales, and detected in different frequency ranges [K¨ording et al 2008]. (d) Many new discoveries have been made relating to those luminous ‘unresolved massive objects’ (UMOs) at the centers of massive galaxies often called ‘supermassive black holes’, or simply ‘active galactic nuclei’ (AGN), which may instead be the dense, nuclear-burning centers of their massive disks. Their best known representative is the source SgrA* at our own Galactic center, whose supposed BH nature has received another seven severe blows during the past four years. Serious doubts on its BH interpretation were already expressed in [Kundt 1990, 2001b], among others because of its strong wind, mapped in the Brackett α and γ lines, of −2.5 3 mass rate 10 M /yr, speed 10 km/s, which is seen to blow off tails from windzones of 8 stars within 1 lyr of SgrA*. These doubts were enhanced when a thin, lower-hemisphere jet was mapped with CHANDRA at X-rays by Baganoff et al [2003], between 0.5 and 1 pc from Sgr A*, and further when Aharonian et al [2004] detected SgrA* in emission at TeV energies, because the temperature of an accreting BH (of mass 1/4 M) is predicted to be below 1 keV(M /M) , controlled by the Eddington limit on its luminosity. Then came the news from Frank Eisenhauer, in his 16 Nov. 2007 Bonn colloquium, that the 16 yr-Kepler ellipse of the star S2 (around SgrA*) did not close, by some 3 degrees, some 102.2 times larger than the general- relativistic periastron precession rate, cf. [Gualandris et al 2010]: Did the non-pointlike gravity of a massive central disk make itself felt? Such a high-density, flat central mass array had already indicated its presence by a monotonicly increasing estimated mass of SgrA*, between 2003 and 2007, during increasing approach, 6.41 6.58 6.63 from 10 to 10 M ,orevento10 M , as well as by an increasing estimated distance d of SgrA*, towards 8.33 kpc, in mild conflict with other, independent distance estimates, of d 8.1 kpc; (d allows the conversion of angular velocities into linear transverse velocities of a test star). A fourth, and fifth orbital anomaly of star S2 were reported by Gillessen et al [2009]: When approaching its peri-astron in 2002, S2 flared by half a magnitude, and six successive position measurements were shifted by 10 mas towards NE, 12 −3 reminiscent of an IR fata morgana caused by a discal medium of (high) number density ne ≈ 10 cm . Finally, there is the sub-event-horizon VLBI morphology of SgrA* at 1.3 cm wavelength, with structure down 12.6 to the scale of 4 RS =10 cm, reported in Nature on 4 September 2008, plus the concern of Hagai B. Perets and Alessia Gualandris that star formation between 0.01pc and 0.5 pc separation from SgrA* would have been prevented by tidal forces if the mass of SgrA* was distributed only of BH extent. All these ten facts are inconsistent with a BH interpretation of SgrA*. Proceeding towards more distant AGN, there is the recent news by Cheung et al [2010] that Cen A is a ‘γ-ray galaxy’ rather than a ‘radio galaxy’, its lobes emitting more than ten times its radio power near MeV energies. Being the nearest of its kind, we may speculate that the lobes of most radio galaxies are dominant emitters at VHE energies, often reaching TeV, or even PeV energies. Consistent with this expectation are the highest-resolution messages on the nearest cD galaxy M87 by Kovalev et al [2007] and by Hada et al [2011], further the broadband variability data on the quasar PKS 1510-089 by Marscher et al [2010], and on quasar 3C 454.3 by Jorstad et al [2010], and also the news on γ-ray flaring of the blazar 3C 279,with strong, monotonic variation of its linear optical polarization reported in [Abdo et al 2010]. Note that this last-mentioned, rapidly varying source with its (large) redshift z = 0.536 has a marginally harder spectrum than expected, due to inverse-Compton propagation losses on the cosmic radiation background. And there is the unforgotten optical quasar 3C 273 of extreme sidedness, of redshift z = 0.158, with a softening spectrum towards its approaching head [Kundt & Krishna 1986]. According to the long list of arguments collected in [Kundt 2009a,b], none of the above UMOs qualifies as a candidate for a BH. This long list should be extended by the non-correlations of SBH masses with galaxy-disk and halo masses found recently by Kormendy et al [2011]. If so, the rare, huge, very-soft X-ray flares detected by ROSAT in the centers of ≥seven galaxies – by factors between 102 and 104,reaching transient powers of 1044erg/s, with short rise times, and longer decline times (as t−5/3) between months and years – which have been reported by Stefanie Komossa [2005], and recently by Burrows et al [2011] and Zauderer et al [2011], cannot be explained as tidal disruptions of stars by a central SBH. They should rather be re-interpreted as rare plunges of stars deflected into strongly inclined orbits, into the dense innermost disk of that galaxy. There is yet another argument against BH engines. Scientists studying gravitational collapse have found in recent years that cosmic censorship was too early an assumption by Roger Penrose. Formation of naked singularities appears to be the rule rather than the exception during gravitational collapse. Black-Hole 4 Wolfgang Kundt formation is restricted to a tiny subclass of collapses, of high spatial symmetry [Joshi 2009, Quevedo 2010, Kov´acs & Harko 2010].
3 Necessary Properties of the Astrophysical Jet Sources
In this section, a number of plausible constraints on a jet source to function will be presented. In line with common wisdom, let us assume that all the jets are blown by some material, leptonic, hadronic, or of multiple composition, whose motion is supersonic at least in some neighbourhood of the central engine where the jets’ opening angles are narrow (1%). Moreover, jets have never been seen to split, or branch, or disappear without flaring (like in the terminal ‘hot spots’, or ‘heads’), except in the rare Cen A-type case of ‘inner radio lobes’ (where a plasma sheath acts as a beam splitter). We then have the following more restrictive further constraints: (1) For the longest known BFs (of length several Mpc), the CE must supply the (abundant!) jet material 7 10.5 9 continuously for at least 10 yr, equal to 10 (10 M /MBH ) infall times into a supermassive BH (whose 9 mass enters in units of 10 M )! As one consequence, the CE cannot be a BH. Note that many further reasons against BH CEs have been given in [Kundt 2001, 2002, 2009a,b]. (2) The spectra of BFs range from low radio frequencies all the way up into the hard γ-ray regime, to TeV, or even PeV energies (corresponding to frequencies of 1030Hz). Individual charges must therefore have kinetic energies reaching TeV, or even PeV energies. For electrons, this constraint implies Lorentz factors γ reaching 106,oreven109. If instead, the emission came from relativistic protons, the protons would have to be 1013 times more numerous in the emission volume than their accompanying electrons of at least the same 2γ2 2 ∼ −4 energy, because the radiated electromagnetic power scales as (e /m) m0 with the particles’ charge e, Lorentz factor γ, and (relativistic) mass m = γ m0. This rules against hadronic radiation. (3) The often extreme sidedness of the mapped jets, and the frequent superluminal propagation of radiating 2 knots in the jets argue in favour of extremely relativistic bulk Lorentz factors γbulk (> 10 ) of the jet substance. (4) The narrowness of the beams (1%), with occasional refocussing,almostnosplitting, and considerable bending (for their power) speak in favour of low inertia, i.e. prefer leptonic jets over hadronic ones. (5) The extremely low synchrotron losses of the beams, on supersonic propagation scales reaching Mpc distances, require E x B-drifting pair plasma: relativistic electrons and positrons coasting at equal speeds. Their only losses are inverse-Compton radiation on the background radiations. Often quoted in situ post- accelerations have been shown to be in conflict with the Second Law of thermodynamics [Kundt 1984]. They would, moreover, ask for unrealistically large magnetic field strengths of their booster, most notably at the high-energy end of the beam-particle spectrum. (6) The high observed jet-formation efficiency, a lobe/core power ratio of 10−2±2, requires a suitable (universal) functioning of the CE. I like to think of reconnecting magnetic fields of the central rotating magnet, followed by buoyancy in its deep gravitational potential well plus post-acceleration by its outgoing strong low-frequency waves. (7) The comparatively slow propagation speeds of the heads of the flows (for their power), determined by β 2 1/2 −2.7 1/2 ram pressure balance, argue against hadronic beam loading: head =(2kT/mH c ) =10 T7 holds for 7 pure pair plasma running into hydrogen, where T7 := T/10 K. From these seven constraints I conclude that every jet engine requires a heavy, rotating magnet at its center which provides the allimportant (highly relativistic) pair plasma, via shearing friction on a surrounding disk, leading to permanent magnetic reconnections. We see this process at work at the surface of our Sun. All sources discussed in the past section are of this type, whilst BHs cannot possibly do it. An estimate of the Lorentz factors γ of the newly formed pairs can be gleaned from the energy integral ΔW, via γ = 106(ΔW/TeV):
ΔW=e (E + β x B) · dx ≈ TeV β−3 B6 Δx6.5 ,(1) in which ΔW has been coarsely evaluated in the comoving system with vanishing electric field E, for β =v/c =10−3,B=106G, and Δx=106.5cm. −8.3 The newly formed pair plasma is practically weightless compared with thermal matter (10 T4), hence escapes by buoyancy, at right angles to the central disk. It thereby blows the broad-line region (BLR), in which it is post-accelerated by the outgoing strong, low-frequency waves of the central magnetized rotator, but at the same time is decelerated by inverse-Compton losses on the ambient photon bath. Part of the Black Holes Cannot Blow Jets 5 dense, warm ambient plasma is pushed aside by the buoyant pair plasma, into the shape of Blandford & Rees’s deLaval nozzle, beyond which it turns supersonic, i.e. escapes faster than at (2/3)c, with frozen-in transverse toroidal magnetic fields, and self-generated radial electric Hall fields, in the form of an almost charge-neutral, highly ordered, monoenergetic beam of E x B-drifting charges, as will be detailed in the next section. Small deviations from charge-neutrality, of order 10−9, are automatically imposed by Maxwell’s equations, through the constraint of equipartition between electromagnetic fields and their anchoring charge and current densities, which accompany the flow. Such a highly structured charged pair-plasma flow forms automatically, so I claim, under the prescribed conditions, and satisfies all the preceding seven constraints, including a comoving voltage Φ of strength eΦ ≈ e π /c 1/2 19.5 1/2 ( L ) =10 eV L44 (2) for a beam power L in units of 1044erg/s. No stochastic post acceleration in the beam is required to guarantee radiating electrons at the termination hotspot up to PeV energies, where the comoving voltage redistributes the energies of the relativistically streaming leptonic charges from monoenergetic into a broad, almost white 2 −ε power law: E dNE ˜E with ε 0.
4 Our Semi-Analytical Model
This section presents a short review of our preferred semi-analytical jet model [Kundt & Krishna 2004, Kundt 2005], whose main characteristics have already been sketched in the preceding section. It treats a bipolar flow as a composite of three successive stages: (i) the formation of relativistic jets around a magnetized rotator, (ii) the electromagnetic structure of a leptonic beam, approximated cylindrically, and (iii) the discharging of a jet, on running into an extended, heavy conductor. Whilst stages (i) and (iii) can only be coarsely described, by pointing out analogies to better known, simpler scenarios, stage (ii) allows the presentation of a complete set of solutions whose simplified cylindrical geometry can be easily reshaped into a more realistic conical geometry. · 2 (i) In order to blow a relativistic twin jet of power L, one needs a heavy generator of N =L/2γ mec = 45.7 −1 4 10 s L44/γ4 electron-positron pairs per second, of mean Lorentz factor γ of order 10 , which we conceive of as a rotating magnetosphere rubbing (shearing) against the inner edge of a surrounding gaseous accretion disk, but the precise mode of magnetic reconnection should not matter, cf. [Kundt 1996, 2001, 2002]. In the case of our present Sun, pair formation at its surface may rather be due to reconnections of excess magnetic flux dragged out of its convection zone by the escaping solar wind, but only at a low rate N˙ , insufficient for jet formation. At the same time, we have learned from pulsars that a rotating magnetosphere of angular velocity ω emits strong, low-frequency spherical waves of (large) strength parameter f:
14.2 f := eB/me cω=10 B3/ω−4 (3)
3 −4 −1 for a typical coronal field of strength B measured in kG, with B3 := B/10 G, ω−4 := ω/10 s ,which 2/3 9.5 2/3 post-accelerates charges of either sign to an asymptotic Lorentz factor γ of order f =10 (B3/ω−4) ,in the absence of damping [Kulsrud et al 1972]. Some such damping is expected to occur via scattering on the ambient photon bath, whose main effect will be to narrow the energy distribution of the escaping charges, as is known from laboratory experiments where atomic beams are routinely cooled via scattering on laser light. On the other hand, only 10% of all AGN have low enough inverse-Compton losses to blow jets, the rest of them is radio quiet, or even radio silent, through exactly such collisional losses on the photon bath of the BLR. Taken together, the newly created pair plasma is post accelerated both by buoyancy and by the outgoing strong low-frequency (LF) waves, as sketched in Fig.1. Both the outgoing LF waves and the more isotropic high-frequency (HF) background radiation tend to narrow the energy distribution of the escaping relativistic electrons (of the radio-loud subpopulation) towards a relativistic Maxwellian, whereupon their subsequent funneling into two antipodal jets – by the heavy thermal deLaval nozzles – has been shown in [Kundt & Krishna 2004] to further narrow it into a mono-energetic (delta) flow: E x B-drifting rearranges the speeds of the charges until they are uniform across the beam. (Remember that the radio spectrum of SgrA* is consistent 6 Wolfgang Kundt
Fig. 1 Sketch of a plausible Central Engine: Coronal magnetic reconnections create e±-pairs, the warm central (star and/or) disk emits high-frequency (HF) photons, low-frequency waves (LFW) post-accelerate the escaping e±, and the latter boost the HF photons to HE γ-rays. An ambient thermal bulge serves as the deLaval nozzles from which a twin jet emerges, along the spin axis of the central rotator. In galactic-center sources, this region is observed as the BLR. with monoenergetic synchrotron radiation, with γ =104). In this way, their propagation is loss-free, apart from inverse-Compton losses on the background radiations. (ii) Beyond a deLaval nozzle, the relativistic charges – of bulk Lorentz factor γ 104 – rearrange their velocities orderly as E x B-drifters, β = E x B /B2, whereby in a cylindical section of a beam, the toroidal B-fields and radial electric Hall fields imply unique charge- and current-densities {ρ, j}, smoothly distributed throughout the beam, whose lowest-order Fourier components are indicated in Fig. 2 and read:
Es = Bϕ = C sin(πs/R) /s , Bz = const (4)
ρ = jz/c =(πC/R)cos(πs/R) /s
−1 in cylindrical coordinates {s, ϕ,z}, with R := cylinder radius; βϕ turns out to be small, of order γ , unrelated to observed spiral patterns. Note that such beams have vanishing net charges and currents, and that their charge amplitudes are of order 10−9 of those of the convected charges. Fields and charges are in equipartition, and determined by the power L of a beam and its cross section A via:
2 2 2 2 ne γme c ≈ L/A c ≈ (E + B )/8π ≈ B /4π (5) for a pair-plasma number density ne. Note that these field strengths correspond to (huge) convected electric potentials Φ given in (2) above, which guarantee electron energies up into the PeV range in the ultimate power-law distribution of the charges, once they have been stalled by a heavy obstacle. No stochastic (in situ) acceleration is required anywhere in the beams. · Note also that the E x B-drifting leptons described by equations (4) and by c(γβ) =(e/me)(E + β x B) have their dominating losses through inverse Compton collisions on the 2.73 K background radiation, with a (large) degradation e-folding length ldeg given by Black Holes Cannot Blow Jets 7
Fig. 2 Cross section through (the ground mode of) a cylindrical beam segment, showing the radial depen- dences (∼s/R) of ρ,j,Es,Bϕ, R := beam radius.