**Supernova explosion**: fast; ejecta with speed v ~ 10^{4}km/s.**Free expansion**: hundred of years; ejecta mass > swept up mass.**Adiabatic or Sedov:**10,000-20,000 years; swept-up mass > eject mass.**Snow-plow or Cooling**: Few 100,000 years; shock front cools, interior also cools.**Disappearence**: Up to millions of years; remnant slows to speed of the random velocities in the surrounding medium, merges with ISM.

At time t=0, a mass m_{0} of gas is ejected with velocity v_{0} and total kinetic energy E_{0}.

This interacts with surrounding interstellar material (ISM) with density ρ_{0} and low T.

The shell velocity much higher than the sound speed in ISM, so a shock front of radius R forms.

The shell of swept-up material in front of shock does not represent a significant increase in mass of the system.

The ISM mass previously within the swept-up sphere of radius R is still small compared to the ejecta mass:

- Since momentum is conserved:

- As long as swept-up mass << ejecta mass, the velocity of the shock front remains constant and R
_{s}(t) ~ v_{0}t

- The temperature decreases can be calculated assuming adiabatic expansion, given the relatively short duration of this phase compared to other characteristic thermal timescales:

The dynamics can be described by location of shock front versus time.

Without discussing all the details of the Sedov soulution let’s just look for a self-similar solution, in which the dynamics can be reduced to one variable = Rtl.

Note that dynamics are determined by initial energy of explosion, E, and the density of ISM, ρ_{0}.

Consider quantity E/ρ_{0}. It has units of (length)^{5}(time)^{-2}.

Therefore, (E/ρ_{0})(t^{2}/R^{5}) is a dimensionless quantity which describes the dynamics of the expansion.

The solution requires R(t) = k(E/ρ_{0})^{1/5} t^{2/5} and v(t) = 2R/5t.

This solution describes the expansion of SNR pretty well.

- Mass flux:
*ρ*_{1}ν_{1}= ρ_{0}ν_{0} - Momentum flux:

*P _{1 }+ *

- Energy flux:

*½**ρ _{1}ν_{1}^{3}*+

where *ρ* is density, *P* is pressure, *γ* is the adiabatic index.

Introduce the Mach number *M = v _{0}/c_{0} where c_{0} = sqrt(γP_{0}/ρ_{0}) *is the sound speed upstream, and find in the limit of large

*ρ _{1}*/

For *γ** = 5/3, find **ρ _{1}*/

Get large increase in temperature for large* M*.

In Sedov solution, find for downstream material:

pressure = (3/4) *ρ _{0}*

temperature = (3

Temperature ~ (10 K)*v*^{2} for *v* in km/s,

For *v* ~ 1000 km/s, have *T* ~ 10^{7} K which means gas is heated to X-ray producing temperatures.

The precursor to this supernova is thought to have been 25 times the mass of our Sun.

This region measures 50 light years across. The SN is located in the Large Magellanic Cloud, 170,000 light years away.

Stellar material is moving out at velocities of about 2,000 km/s, creating shock fronts.

Shock fronts from the original SN have been reflected from dense ISM clouds. As the stellar material passes through in filaments, they glow. The dense ISM clouds have been heated and crushed by the SN shocks.

Gas is heated by shock to X-ray emitting temperatures.

Although gas glows in X-rays, the loss of energy due to radiation is relatively unimportant to the dynamics of the expansion, i.e. cooling time is longer than age of SNR.

Eventually, the shock slows down. We can define the end of adiabatic phase as when half of energy has been radiated away.

Typically, at this stage the shock speed is about 200 km/s (with dependence on initial energy and ISM density).

Without the high temperature behind the shock, there is no high pressure to drive it forward through the ISM. The shock front is now `coasting’ with constant radial momentum, ie. All the material in the shell moves outwards with total momentum given by the equation shown.

Most of the swept-up material is compressed into a dense, relatively cool shell (a temperature of approx. 10^{4} K).

There is some X-ray emission from the residual gas in the interior, but this is much weaker than before.

When shock velocity drop to ~20 km/s, the expansion becomes subsonic and the SNR merges with the ISM.

However, this is an oversimplification since the ISM has magnetic fields and may present inhomogeneities. Moreover, the pressure of cosmic rays must be taken into account. Both of these factors affect the expansion of the SNR.

The magnetic field may help the coupling of the ejected matter with the ISM so that a shock wave can develop. Inhomogeneities of the ISM are also important, since the shock velocity and radiation intensity are both a function of density; as the shock enters a dense cloud, the velocity decreases and the radiation increases.

*2*. Absorption and scattering processes – Part I

*3*. Absorption and scattering processes – Part II

*4*. Emission processes – Part I

*5*. Emission processes – Part II

*6*. Instruments for X-ray and γ-ray Astrophysics – Part I

*7*. Instruments for X-ray and γ-ray Astrophysics – Part II

*8*. X-rays from the solar system

*9*. X-rays from low-mass and PMS stars

*12*. Evolution of Shell-type Supernova remnants

*13*. X-ray binaries

*14*. X-ray emission in normal galaxies

*15*. Active Galactic Nuclei – part I

*16*. Active Galactic Nuclei – Part II

*17*. Active Galactic Nuclei – Part III

*18*. Clusters of Galaxies – Part I

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