Physics Reports 442 (2007) 1–4www.elsevier.com/locate/physrep

Introduction: Hans Bethe Centennial Volume

Hans Bethe worked right up until the end of his life on astrophysics. In fact, Gerry Brown phoned him the morningof his death March 6, 2005 to discuss the manuscript Evolution and Merging of Binaries with Compact Objects, whichis included in this volume, although updated to include developments since Hans’ death. Gerry also told Hans that C.N.Yang had agreed to write an article on the Bethe Ansatz, named Bethe’s Hypothesis with Mo-lin Ge in the biographicalvolume Hans Bethe and His Physics1 which Hans had asked Gerry to write. Hans’ voice was clear and strong andGerry thought that Hans would live to see his own Centennial volume published. Hans had earlier expressed his viewson authors and possible subjects so his spirit is represented in this volume.

Hans’ work in astrophysics can be broken down into three main parts, although he separately carried on other relatedwork, such as his work on neutrino mixing, partly in collaboration with John Bahcall, and on dense matter in neutronstars, while working on other problems at the same time.

(1) In 1938 George Gamow and Edward Teller invited Hans to a small conference in Washington on the energyproduction in stars. The conference turned out to have one really important piece of information. Bengt Strömgrenreported that the central temperature of the sun was estimated as 15 million degrees, not Eddington’s 40. The changecame as a result of assuming that the sun was predominantly hydrogen with approximately 25% helium, rather thanassuming it had about the same chemical composition as the earth. The lower atomic weight of the revised mix loweredthe temperature.

The lower temperature meant that the reactions calculated in Hans’ paper with Critchfield [1] correctly predicted theluminosity of the sun.

That left unsolved the question of energy production in larger stars. From observations one could show that coretemperatures increase slowly with increasing mass, but luminosity increases very rapidly. The proton–proton reactionscould not predict this, as the rate of the reaction increases fairly slowly as the core temperature rises.

The necessary nuclear reactions had all been measured, mostly by Willy Fowler’s group at Caltech. In a few weeksHans had put together the carbon cycle, which begins with the reaction 12C + H ⇒ 13N + � and ends with 15N + H ⇒12C + 4He. Thus, the carbon acts as a catalyst.

(2) In 1978, after he had retired, Hans went to Copenhagen to work with Gerry Brown. Their work on effectiveinteractions in nuclear matter and in nuclei had brought them together earlier, and Gerry had worked in Birmingham,England, 1950–1960 with Rudi Peierls, Hans’ closest friend. (They were students of Sommerfeld’s together.) Hansasked, “What should we work on?” Gerry replied, “Let’s work on the collapse of large stars.” The result was “Babble”[2]. As Gerry came in the first morning, April, 2, 1978, after having left a computer output on Hans’ desk the eveningbefore, Hans remarked “The entropy is low.” “So what?” Gerry asked: “That means that the Fe nuclei will collapseall the way to nuclear matter density and then merge, rather than breaking up, because there’s not enough entropy forthem to break up.” (In units of Boltzmann’s constant, the entropy in Woosley’s output was about unity per nucleonin the Fe. This would be increased by about ln 56, the logarithm of the number of particles in the iron atom, were itto break up.) Of course, there is considerable increase in entropy with the increase in temperature in the collapse, butMazurek et al. [3] had already shown that including the many excited states in nuclei during the collapse could soakup the energy, and therefore the entropy, very effectively without increasing the pressure. The paper by Bethe et al.

1 Edited by Gerald E Brown and Chang-Hwan Lee, World Scientific Publishing Co. (2006).

0370-1573/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.physrep.2007.02.007

2 G. Brown et al. / Physics Reports 442 (2007) 1–4

[2] (BABL or “Babble” in Willy Fowler’s terminology) not only settled the problems of the collapse of large stars, butunleashed the amazing abilities and experience of Hans Bethe onto current astrophysics.

The supernova calculations did not, however, end up in successful explosions. For a while Hans, together with JimWilson, thought that a small part of the ∼ 1053 erg energy lost in neutrinos, could be coupled back in some way to givethe ∼ 1051 erg shock wave that would produce a successful supernova explosion. Seemingly successful explosionswere produced, but then when better neutrino diffusion was put into the computer codes, the explosions no longerworked. In this volume, the Report by Adam Burrows and collaborators suggests a promising new approach in termsof channeling acoustic power into the explosion. This scenario seems to be robust, in the sense that a lot of acousticpower is provided by the accretion of matter onto the core of the exploding star, and the accretion goes on until thestar explodes. The authors of the paper are properly conservative in their claims and say that there is much more to bedone.

Hans Bethe and Gerry Brown got together every January to do research somewhere on the west coast, Santa Barbara,Santa Cruz and Caltech, chiefly at the latter. The relevant University gave them a condominium for their stay. RoseBethe stayed at home, because she had old parents to look after, and Betty Brown stayed at home because of youngchildren. Gerry did the cooking because Hans liked a home life with home cooking. The most essential part of thecondominium was a large bathtub for Hans, because he did his best thinking in the morning while taking a long bath.In 1987, Bethe and Brown found they could do no more on the theory of supernovas without more data and beganworking on the relativistic heavy ion collisions in preparation for the Brookhaven heavy ion collider. As Gerry wenthome, he shook hands with Hans and said, “Now it’s time for a supernova explosion.” One came February 23 of thatyear. The explosion lasted, however, only about 12 s, as measured both in Kamiokande in Japan and in the PittsburghPlate Glass Mine, by detecting the neutrinos.

Madappa Prakash had an explanation for the short neutrino emission lifetime of SN 1987A. In the usual equationsof state, when the neutrinos, which are highly degenerate when trapped in the collapse of a large star, and thereforecontribute quite a lot of pressure, leave the star, the pressure is lessened. However, as the star neutronizes the strongrepulsions between the neutrons predominate over the softening by neutrino losses and the proto neutron star willremain stable. However, if there is a condensate of negatively charged hyperons, such as the �−, then there will haveto be more protons to render the hadrons electrically neutral. Because the neutron–proton interaction is much moreattractive than the neutron–neutron one, the nuclear equation of state is not so repulsive when the neutrinos leave, andthe neutron star will drop into a black hole.

Bethe and Brown were interested in a K− condensate which would require protons to neutralize the charge.Hans once in a walk outside of Santa Barbara asked, “You mean, you want to squeeze electrons into K−mesons?”The K− meson is composed of a u antiquark and a strange quark s. The u antiquark experiences the attractionwith the nucleons resulting from exchange of the vector mesons � and �. This attraction brings down the massof the K− meson from its free-particle value of 494 MeV. The electron chemical potential �e in a neutron star isgenerally found to be about half of this free-particle K−mass, at nuclear densities of 3 n0, where n0 is the den-sity of nuclear matter. Once the in-medium K−*-mass (the star denotes in-medium) is brought down to the �−

e

the electrons will change into a Bose condensate of K−–mesons, with all mesons in the (same) ground state. Thepressure is decreased considerably by the change of degenerate relativistic electrons (fermions with a high chem-ical potential �e) into the K− Bose condensate, so the neutron star evolves (in a light-crossing time) into a blackhole.

Although this scenario seems exotic, it occupied in various forms, a lot of the Bethe, Brown and Lee SelectedPapers with Commentary [4]. They believed that SN 1987A had gone, through kaon condensation, into a black hole.Calculations by several groups had found compact object masses of ∼ 1.5 M� for the ZAMS ∼ 20 M� progenitor of1987A (actually, more precisely ∼ 18 M�) Bethe and Brown [5], working from the 0.075 M� amount of 56Ni producedin SN 1987A obtained 1.56 M� as upper limit on the compact object mass, which they believed to be a (low-mass)black hole. (In stars with ZAMS mass > ∼ 20 M� the 12C produced by the triple-alpha process is removed by the12C(�, �)16O reaction as quickly as it is produced. The absence of 12C, the burning of which would bring the entropydown a lot, is responsible for stars with ZAMS mass > 20 M� to evolve into black holes [6].)

The most serious observational challenge to the Bethe–Brown limit on the maximum neutron star mass is the measureof 2.1 +.2

−.2 M� for the neutron star mass in the white dwarf binary J0751+1807 [7] and the 1.86+.16−.16 M� mass of Vela

X-1 [8]. These are discussed in the Report of Bethe, Brown and Lee in this volume. Gerry Brown can be criticizedfor hanging on to the low mass of Mmax(NS) = 1.5 M� but Hans was confident of the determination of 1.56 M� from

G. Brown et al. / Physics Reports 442 (2007) 1–4 3

1987A. Certainly a measurement of a mass above 1.56 M� with a significance level of at least 3-sigma would be desiredto really establish that neutron stars with higher masses exist.

Marten van Kerkwijk, who participated in the experiment to determine the mass of Vela X-1 to be 1.86+.16−.16 M�

continually asks Gerry Brown if he still stands by ∼ 1.5 M� as maximum mass, and is delighted that the theory getsbetter and better for the latter. Observers like nothing better than to challenge theory, although it must be conceded thatnot many theorists support the Bethe–Brown limit. Still, it adds the challenge of a neatly definitive measurement.

Bethe and Brown also quantified the process of hypercritical accretion onto compact objects in common envelopesallowing for accretion at rates higher than 104 Eddington. This involved directly and indirectly the co-editors VickyKalogera and Ed van den Heuvel, of this volume.

In the autumn of 1994, Gerry Brown attended a meeting on relativistic heavy ion physics at the Institute for TheoreticalPhysics in Santa Barbara. Usually two different programs went on at the same time. The other one, Dense StellarSystems, was very interesting for Gerry. Providentially, his office was just across the hall from that of Fred Rasio (nowthe husband of Vicky Kalogera). Fred captured Gerry’s imagination by telling him about common envelope evolution,which is used in the evolution of compact binaries. Chevalier [9] had estimated that when a neutron star went intocommon envelope evolution with a red giant companion, the neutron star would accrete enough matter to evolve intoa black hole. Gerry checked this and estimated that there was enough accretion to do this. But we know that thereare binary neutron stars, so if they do not evolve through the first-born neutron star, the pulsar, surviving commonenvelope evolution with the companion giant, then there had to be an alternative. He found that if the two progenitorgiants burned helium at the same time, they could avoid common envelope evolution. In order to burn He at the sametime they could differ up to only 4% in mass. Bethe, Brown and Lee show that the two stars in double neutron starswith accurately measured masses do show evidence of this, in their contribution in this volume. Vicky Kalogera—whobecame interested in this after discussing it with Hans while visiting Cornell in November 1998—also discusses thischannel in the double neutron star evolution in her Report in this volume. Gerry talked about his paper in 1995 at Edvan den Heuvel’s Institute in Amsterdam. After his talk, Ed said politely that he had to disagree with him, and overthe years we have continued this disagreement, Ed saying that since we see so many neutron stars, we should seea black-hole, neutron-star binary if the main channel produced these. However, more recently Belczynski et al. [10]showed that in their model with hypercritical accretion binaries with a black hole and a neutron star still form at a ratethat is consistent with the lack of any binary pulsar with a black hole, given the radio pulsar selection effects and thecurrent sample of binary pulsars with neutron star companions [11]. Ed also has said, “There is always room for newideas,” and has welcomed them. But he wants to see them in observation, and it must be admitted that Hans and Gerrychiefly made predictions about the future, hoping to see them fulfilled.

In any case, Gerry returned to the U.S. loaded down by Ed’s Saas-Fe Lectures [12] and he already had in hand thePhysics Report by Ed and Bhattacharya [13]. This was enough material to get into binary evolution.

(3) The last day Hans and Gerry were in were in Caltech, in 1996 when Hans was 90, Kip Thorne came into theiroffice and said, “You guys seem to be better than other people in working out things we don’t see. Could you workout the merging of black-hole neutron-star binaries for LIGO? Gerry said to Hans, “OK, we can begin that next year.”Hans said, “No, I want to begin it right now. Could you send me a review?”

Gerry sent him a copy of the Meurs and van den Heuvel [14] which estimated that there are (1–2) ×104 potentialB-emission / X-ray binaries in the galaxy. As these systems are expected to live for ∼ 107 years, one expects, if 10percent of them produce close binary pulsars, that the Galactic formation rate of close binary pulsars is ∼ (1–2) ×10−4

yr−1. Hans forged ahead on a population synthesis calculation which became Evolution of Binary Compact Objectsthat Merge [15]. The referee of this paper was Peter Eggleton, the dean of British stellar modelers. He wrote “This is aninteresting paper, making a useful point in an unusually simple and elegant manner. I recommend that it be published,but I would like to make a couple of points which the authors might be able to incorporate. . .” Bethe and Brown foundthat the ∼ (1–2) ×10−4 yr−1 rate kept coming back at them over and over for the Galactic2 rate in about everythingthey did, except that because of their “special channel” necessary to make binary neutron stars, the division betweendouble neutron star and low-mass black-hole, neutron-star binaries changed with the new developments as discussedin the Bethe, Brown and Lee paper in this volume.

The common envelope problem has a lot in common with the nuclear stopping power problem [16] solved by Hans.He sat down one morning to solve it analytically. In [15] one can read that he did this using the laws of gravitational

2 Because of enhanced star formation at earlier times, the rate was higher then.

4 G. Brown et al. / Physics Reports 442 (2007) 1–4

attraction for stars, Newton’s and Kepler’s laws and drag coefficient Cd that had been evaluated by some Japaneseastronautical engineers. Hans saw that he had two more variables than equations. The smallest mass was the compactobject mass M�. He approximated by setting M� = 0. As luck would have it, two of his variables disappeared, andwith the above approximations he could solve the common envelope problem analytically. Later Belczynski et al. [10]solved the hyper-critical accretion in common envelope problem by solving the set of ordinary differential equationsnumerically and found that Hans’ approximations had overestimated the accretion by a factor ∼ 4/3; i.e., the correctamount was ∼ 3/4 of that in Bethe and Brown [15].

Hans Bethe had an insatiable interest in how the universe, both big and small, worked. In his Januaries at Caltechhe would sit down, with Gerry Brown, at one of the professors’ tables at the Athenaeum. Almost invariably, one of theprofessors next to him had used one of Hans’ papers in an important part of his research.

In astrophysics Hans lived to learn why Ray Davis had found only a fraction of the neutrinos Hans predicted in hisbig tank of cleaning fluid down in the Homestake gold mine. His office at home had folders and folders of his attemptsto make the supernova explode. He had an abiding interest in the r-process and there were many papers attemptingto make it work, each set accompanied by a letter from Stan Woosley showing why it would not work. UndoubtedlyHans’ interest was to find out how uranium was made.

In this volume of Physics Reports written by his friends, each an expert in what they write about, we see what Hanscontributed to science, particularly to astrophysics.

References

[1] M.A. Bethe, C.L. Critchfield, Phys. Rev. 54 (1938) 248.[2] H.A. Bethe, G.E. Brown, J. Applegate, J. Lattimer, Nucl. Phys. A 324 (1978) 487.[3] T.J. Mazurek, J.M. Lattimer, G.E. Brown, Astrophys. J. 229, 713.[4] H.A. Bethe, G.E. Brown, C.H. Lee, (Eds.), Formation and Evolution of Black Holes in the Galaxy, Selected Papers with Commentary, World

Scientific Publ., Singapore, 2003.[5] H.A. Bethe, G.E. Brown, Astrophys. J. 445 (1995) L129–L132.[6] G.E. Brown, A. Heger, N. Langer, C.H. Lee, S. Wellstein, H.A. Bethe, The effect of the skipping of convective carbon burning here is an update

of the discussions by S. Woosley in a number of earlier papers, as well as with A. Heger in this volume.[7] D.J. Nice, et al., Astrophys. J. 634 (2005) 1242.[8] O. Barziv, et al., Astron. Astrophys. 377 (2001) 925.[9] R.A. Chevalier, Astrophys. J. 411 (1993) L33.

[10] K. Belczynski, V. Kalogera, T. Bulik, Astrophys. J. 572 (2002) 407.[11] C.-L. Kim, 2006, Ph.D. Thesis, 〈http://www.astro.northwestern.edu/∼ciel/ckim_thesis.pdf〉.[12] E.P.J. Van den Heuvel, Interacting binaries, in: H., Nussbaumer, A. Orr. (Eds.), Lecture Notes of the 22nd Advanced Course of the Swiss Society

for Astronomy and Astrophysics (SSAA) held at Sans-Fe, Switzerland, 1992, Berlin, Springer, 1994.[13] D. Bhattacharya, E.P.J. van den Heuvel, Phys. Rep. 203 (1991) 1.[14] E. Meurs, E.P.J. van den Heuvel, Astron. Astrophys. 226 (1989) 88.[15] H.A. Bethe, G.E. Brown, Astrophys. J. 506 (1998) 780.[16] H.A. Bethe, Ann. Phys. 5 (5) (1930) 325.

Gerry BrownVicky Kalogera

Ed van den HeuvelState University of New York Institute for Theoretical Physics,

Stony Brook, Ny 11974, USAE-mail address: gerald.brown@sunysb.edu (G. Brown)