Core-collapse supernovae:
neutrino signals from black hole formation
K. Sumiyoshi,1, 2 S. Yamada,3 H. Suzuki,4 H. Shen,5 and H. Toki6
1Numazu College of Technology, Ooka 3600,Numazu, Shizuoka 410-8501, Japan
E-mail: sumi@numazu-ct.ac.jp

2

National Astronomical Observatory of Japan,

2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
3

Science & Engineering and Advanced Research Institute for Science and Engineering,
Waseda University, Okubo, 3-4-1, Shinjuku, Tokyo 169-8555, Japan
4Faculty of Science and Technology, Tokyo University of Science,
Yamazaki 2641, Noda, Chiba 278-8510, Japan5Department of Physics, Nankai University, Tianjing 300071, China
6

Research Center for Nuclear Physics (RCNP), Osaka University,
Mihogaoka 10-1, Ibaraki, Osaka 567-0047, JapanAbstract
We study the fate of core-collapse supernovae from the massive stars by numerical simulationsof neutrino-radiation hydrodynamics. We follow the long term evolution over 1 sec after the corebounce from the initial gravitational collapse to examine the explosion mechanism and to reveal
the formation of neutron star and black hole. We explore the effects of equation of state (EOS)in these simulations by adopting the two sets of realistic EOS for supernovae. We study the caseof a 40M¯ star and find that the formation of black hole occurs in different timing depending on
the softness of EOS. Resulting properties of emergent neutrinos appear differently from ordinary
supernova neutrinos.

1Core-collapse supernovae originate from the gravitational collapse of massive stars having
more than 10 solar masses (M¯ ). For the massive stars of ∼10–20M¯ , supernova explosions
occur due to the launch of shock wave by the bounce of core at high density, leaving aneutron star. Stars more massive than ∼20M¯ may have different fates since they usually
have large iron cores. They are too massive to have the stellar explosion and the outcome
will be the formation of black hole. Since the detection of neutrinos is clear and unique
identification of such events, it is important to quantitatively predict the neutrino signals
from the compact objects.
In order to to examine the explosion mechanism and to study the formation of neutron starand black hole, we perform numerical simulations of general relativistic neutrino-radiationhydrodynamics [1]. We follow the evolution from the beginning of gravitational core-collapseof massive stars to explore the final outcome. We evaluate the time profile of neutrino burst
and the energy spectrum of neutrinos during the evolution. In order to determine the final
fate, we perform the simulations for a long time scale (∼1 s), which has not been explored
before [1, 2]. For the case of 40M¯ star, it is exciting to find when and how the black holeis formed from the massive star. In order to assess the influence of dense matter, we adopt
two sets of EOS for the numerical simulations. We make comparisons of the evolutions ofcentral core from the initial collapse up to the formation of compact object for the first time.
For the case of 15M¯ star, we refer [1] to see the outcome of propagation of shock wave andthe long term evolution of proto-neutron star.
We perform numerical simulations by solving general relativistic neutrino-radiation hydrodynamics under the spherical symmetry [1]. We solve the Boltzmann equation for neutrinos together with the equations of hydrodynamics simultaneously. The initial models aretaken from the iron core of the presupernova models by Woosley and Weaver [3]. Neutrino
reaction rates are implemented as in the standard rates by Bruenn [4] together with theimproved rates of pair processes and nucleon-nucleon bremsstrahlung.
We adopt two sets of equation of state (EOS) by Lattimer and Swesty (LS-EOS) [5]and by Shen et al. (SH-EOS) [6, 7]. The LS-EOS, which has been used as a standard
in supernova simulations these years, is obtained by the extension of mass formula using
the parameterized function of energy density. The SH-EOS, which is a new complete setof EOS, is constructed by the relativistic mean field (RMF) theory with a local density
approximation. The RMF theory is based on the relativistic Brückner-Hartree-Fock theory
2

50

4040
< Eν > [MeV]< Eν > [MeV]

5030
20
10030
20
10

0.0

0.5

1.0

0

1.5

time after bounce [sec]

0.0

0.5

1.0

1.5

time after bounce [sec]FIG. 1: Average energies of νe (solid), ν̄e (dashed) and νµ/τ (dot-dashed) as a function of timeafter bounce in the cases of LS-EOS (left) and SH-EOS (right).

[8] and is checked by the modern experimental data of neutron-rich unstable nuclei [9]. The
characteristics of the relativistic SH-EOS as compared with the conventional LS-EOS, which
is non-relativistic, appear mainly in the stiffness and the symmetry energy [10].
We report here the numerical results for the case of 40M¯ star. After the core bounce, theshock wave is launched above 100 km and it immediately recedes down due to the dominanceof accretion of material from the outer core of the massive star. The proto-neutron star isformed at center and its mass increases due to the accretion. The density and temperature of
proto-neutron star increase due to the contraction according to the increasing mass. At 1.35
sec after the bounce, the proto-neutron star mass exceeds the maximum mass for hot andlepton-rich configurations determined by SH-EOS. The central part collapses dynamicallyand a black hole is formed.
The timing of the black hole formation is determined by the maximum mass for protoneutron stars and depends substantially on EOS. In the case of LS-EOS, the black holeformation occurs at 0.57 sec, which is earlier than the case of SH-EOS, having the smaller
maximum mass with LS-EOS. During the thermal evolution of proto-neutron star toward
the black hole formation, neutrinos trapped in the central part gradually diffuse outward
and are emitted as supernova neutrinos.
The average energies of neutrinos emitted from the central core in two simulations withLS-EOS and SH-EOS are shown as a function of time after the core bounce in Fig. 1. The rise3

of average energies comes from the temperature increase by the contraction of proto-neutronstars due to the increase of mass. The end points in the figure correspond to the births ofblack hole. It is interesting that the different timing of black hole formation for models
with LS-EOS and SH-EOS is reflected in the different timing of the termination of neutrino
emissions. The LS-EOS is softer than SH-EOS, therefore, it leads to the smaller maximum
mass, the earlier formation of black hole and the shorter neutrino burst. This differencein neutrino signals will provide us with the information on EOS. A terrestrial detection ofneutrino bursts from the black hole formation in future will put a new constraint on theEOS at high density and temperature.
The authors are grateful to K. Oyamatsu, A. Ohnishi, C. Ishizuka and S. Chiba for thecollaborations on the supernova simulations and the table of equation of state. The numericalsimulations were performed at NAO/ADAC (wks06a, wkn10b) and JAERI. This work is
partially supported by the Grants-in-Aid for the Scientific Research (14039210, 14079202,15540243, 15740160, 17540267) of the MOESSC of Japan and for the 21st century COE
program ”Holistic Research and Education Center for Physics of Self-organizing Systems”.

[1] K. Sumiyoshi, S. Yamada, H. Suzuki, H. Shen, S. Chiba, and H. Toki, Astrophys. J. 629, 922(2005).
[2] K. Sumiyoshi, S. Yamada, H. Suzuki, and S. Chiba, Phys. Rev. Lett. (2005), submitted.
[3] S. E. Woosley and T. Weaver, Astrophys. J. Suppl. 101, 181 (1995).
[4] S. W. Bruenn, Astrophys. J. Suppl. 62, 331 (1986).
[5] J. M. Lattimer and F. D. Swesty, Nucl. Phys. A535, 331 (1991).
[6] H. Shen, H. Toki, K. Oyamatsu, and K. Sumiyoshi, Nucl. Phys. A637, 435 (1998).
[7] H. Shen, H. Toki, K. Oyamatsu, and K. Sumiyoshi, Prog. Thoer. Phys. 100, 1013 (1998).
[8] R. Brockmann and R. Machleidt, Phys. Rev. C42, 1965 (1990).
[9] Y. Sugahara and H. Toki, Nucl. Phys. A579, 557 (1994).
[10] K. Sumiyoshi, H. Suzuki, S. Yamada, and H. Toki, Nucl. Phys. A730, 227 (2004).

4