# Presentation: 806978

## The evolution of supernova remnants in the early universe

**The evolution of supernova remnants in the early universe**

**Takanori Nagakura (Univ. of Tokyo/NAOJ) ,  Collaborators: T. Hosokawa, K.Omukai (NAOJ) **

**1. Physical Model and Numerical Methods:****  **

- 経過時間と時間スケール。
- metal-freeの場合、最大成長の不安定モードが存在しないが、log10(Z/Z☉)~-2の場合には最大最長の不安定モードが存在する。

** ****1.1.1 Cooling processes**
**   ****We include the following cooling ; Compton cooling, bremsstrahlung, **
** ****the collisional ionization, collisional excitation, and recombination cooling of  **
** ****hydrogen and helium atoms (Cen 1992), the ro-vibrational line cooling of molecular  **
** ****hydrogen and HD (Galli & Palla 1998) , the fine structure and meta-stable line  **
** ****cooling of carbon and oxygen (Hollenbach & McKee 1989).** **In the early universe, **
** ****cosmic microwave background (CMB) temperatures are quite as high as several tens **
** ****Kelvins. The CMB radiation prevents gas from cooling down below CMB temperatures **
** ****via radiative processes. We include this effect, but any external heating sources are **
** ****not taken into consideration. **

**1.1 Hydrodynamics**

**ABSTRACT:**
**We investigate the evolution of supernova remnants (SNRs) in the early universe using one-dimensional hydrodynamics with spherical symmetry along with non-equilibrium chemistry. A cooled dense shell, which is formed behind the supernova blastwave during snowplough phase, is thought to be important site where the next generation of stars are born. To elucidate characteristic fragment mass of the shell, we calculate its thermal and chemical evolution in detail. We  show that the shell cools through H****2**** or HD line cooling in the case of the metal-free or extremely low-metallicity environments (Z < 10****-4**** Z****☉****), while that the fine-structure lines of carbon and oxygen dominate the cooling of the shell for more metal abundant environments (Z ****≥**** 10****-3**** Z****☉****). However, the minimum  temperature of the shell is limited by the cosmic microwave background radiation, which leads that the temperature of the shell is less dependent on the metallicity of the gas in our simulated density ranges. The linear stability analysis on the shell coupled with our results suggests that the fragmentation of the shell will strongly depend on the number density of the ambient medium and the supernovae energy but little depend on the metallicity of the gas.**

**1.3 Setup**
**  ****The detailed calculations on the dynamical and thermal evolution of a HII region are required to get realistic initial condition. However, we simply assume, for the first step, that the ambient media around a SN distribute homogeneously and are completely ionized to set the temperature 10****4**** K. This assumption may be justified under the condition that a HII region and a smoothed density region expand as large as our simulation box (****~ ****100 pc). **
**  ****We have start a simulation at z = 15 by putting a SN energy on several fluid elements at the center as a thermal energy and by adding an ejected matter from a SN to the same region. The mass of the ejected matter is assumed to be ten solar masses. The mixing between the ejected material and the ambient media should be considered, but one-dimensional simulations cannot treat exactly how the mixing does proceed. We thus simply assume that the heavy elements such as carbon and oxygen are uniformly distributed. A simulation stops when a velocity of a cooled shell, which is formed behind a shock front, declines to a sound speed of the ambient media.  **
**  ****The parameters we introduce are as follows; a SN energy (E****SN ****= 10****51****,10****52**** ergs), densities of ambient media (n****0**** = 0.1, 1, 10 cm****-3****) , and an elemental abundance of heavy elements (Z/Z****☉**** = 10****-4****,10****-3****,10****-2****). **

**  ****To investigate a dynamical evolution of SNRs, we develop a one-dimensional hydrodynamic code. We assume for simplicity that a supernova and its surrounding media are spherically symmetric. We thus compute only radial structure of SNRs. **
**A set of hydrodynamic equations are written as follows;**

**2. Results:**

**  ****We first show the results for the case of E****SN**** = 10****52**** ergs, n****0**** = 1 cm****-3****, Z/Z****☉**** = 10****-2****. Some snap shots on densities and temperatures are shown in Figure 1. When a cooling time of the post-shock regions becomes smaller than the expansion time, a cooled dense shell forms and is driven by pressures of an inner hot bubble. Figure 2 represents the position of the shell against elapsed time, i.e., expansion law of SNR. Our simulation starts at the end of the free-expansion phase, and hence the expansion during early time is adiabatic. The shell expands as t****2/7**** during the pressure-driven phase, which is consistent with a simple analytic model. **

**  ****The analysis on a gravitational instability of a decelerating and expanding thin shell has been studies by many authors (Elmegreen 1994; Vishniac 1994). We here briefly summarize their studies. An expanding thin shell will sweep up its surrounding media to obtain a huge amount of mass as it moves further distance, which causes its column density to be enhanced. If small density perturbations are given to the shell, they seem to grow owing to their self-gravity. However, in addition to a repulsive thermal pressure, stretching the shell due to expansion prevents them from growing. A gravitational instability of an expanding shell thus depends on a bulk velocity of the shell as well as its column densities and pressures. **
**  ****The detailed linear analysis derived by Elmegreen (1994) shows that the instantaneous maximum growth rate is given by**

**where R, V, Σ****0****, and c****s**** are the radius, velocity, unperturbed column density, and sound speed of the shell. The shell becomes gravitationally unstable if ω****max**** ****>0, or, **

**where t****exp****, t****ff****, and t****cross**** are the expansion, free-fall, and sound crossing time of the shell, respectively. We apply this analysis to our results, and estimate the fragment mass.**
**  ****Figure 7 shows the growing time of density perturbations within the shell in the case of the case of E****SN**** = 10****52**** ergs, n****0**** = 10 cm****-3****, Z/Z****☉**** = 10****-2****.  The shell can fragment at 10 million years after the explosion in this case. We show fragment mass within the shell in Figure 8. In our analysis, the maximum growth mode corresponds to the maximum column density. Thus, the fragment mass is about 6×10****5 ****M****☉****. The next generation of stars will be born in this large clump.**
**  ****We investigate other parameters whether or not the shell can fragment. For low density cases (n****0**** ≤ 0.1 cm****-3****), the column density of the shell is too low to fragment even if a SN energy is high. We find that the shell tends to fragment if a SN energy and ambient density are higher than E****SN****=10****52**** ergs and n****0**** ≥ 1 cm****-3****, respectively. **

**  ****We next show the results for the case of E****SN**** = 10****52**** ergs, n****0**** = 1 cm****-3****, Z/Z****☉**** = 10****-4****. Figure 5, 6 are the same as Figrure 3, 4, respectively, but except for metallicity. In this case, the gas cools via hydrogen deuteride to CMB temperatures. The evolution of the temperatures is similar to the previous case despite of lower metallicity. This is because the gas temperatures are limited by CMB temperatures. **
**  ****We calculate the case of E****SN**** = 10****52**** ergs, n****0**** = 0.1 cm****-3****, Z/Z****☉**** = 10****-2****. In this case, the densities within the shell are too low to form molecular hydrogen effectively, and hence the temperatures do not decline low enough for metallic line cooling to become effective. For the shell to cool down to CMB temperatures, therefore, it is necessary to make the density of the shell high enough.**

**The evolution on temperatures of the shell is depicted in Figure 3. Temperatures around the center of the shell decline below 50 K. Figure 4 shows the evolution of the most dominated cooling agent within the shell. Molecular hydrogen forms at the post-shock regions effectively via H ****–**** channel, and hence the gas within the shell mainly cools via molecular hydrogen at the beginning of the snowplough phase. A large amount of molecular hydrogen cools the gas down to 150 K, and the fine-structure line cooling of [OI] and [CI] becomes dominated the other radiative cooling. The temperatures therefore decrease to CMB temperatures.**

**Summary:**
**We investigate the evolution of SNRs and apply our results to a linear stability analysis on an expanding and decelerating shell.  We find that the temperatures at the center of the shell decline to CMB temperatures via the fine-structure line or HD cooling. The evolution of temperatures within the shell does not strongly depend on the metallicity because gas temperatures are limited by CMB ones. The linear stability analysis coupled with our results show that whether the shell fragment or not depends on an ambient density and a SN energy. **

- Fig.1 Some snap shots on densities (left) and temperatures (right).
- The lines indicate number densities (left) and temperatures (right) against radius when 104, 105, 106, 107  years have passed  from z=15.

- Fig.2 The position of the shell against elapsed time.
- Red line is our numerical result. Green line is a slop of Sedov-Taylor self-similar solution. Blue line is a slop of the solution at pressure-driven snowplough.

- fig.3 The most efficient cooling agent against elapsed time. The longitudinal axis is column density measured from the center. Black lines indicate the boundary of the shell. Orange (green/ red) area represent the area where H2 (OI/CI) cooling is the most efficient.

- fig.4 The contour map of temperatures against elapsed time. The axes are the same as fig.3. Blue, purple, and aqua area represent 50 < T [K] < 100, 100 < T [K] < 150, 150 < T [K] < 200, respectively. The temperatures at the edge of the shell are higher than 200 K.

- fig.5
- Same as fig.3, but except for Z/Z☉=10-4.

- fig.6
- Same as fig.4, but except for Z/Z☉=10-4.

- fig.7 The growth times of density perturbations against elapsed time. The red area means growing times of density perturbations within the shell. The upper side of this area corresponds to the central regions of the shell. Blue line represents the maximum growing mode, which has the shell width.

- fig.8 Fragment mass vs. elapsed time. The red area means fragment mass within the shell. The lower regions correspond to the central regions of the shell. Blue line is the fragment mass at maximum growth rate.