Research

Shocks

Astrophysical shock waves (or shocks) are produced by supersonic motions that are ubiquitous in the universe. Supernovae, stellar and galactic jets, solar flares, accretion flows, galaxy-galaxy collisions, and many other astrophysical phenomena produce shocks. Shocks are an important dissipation process in the thermodynamic balance of the interstellar medium. The impact of shocks may also induce the collapse of clouds and trigger star-formation, or disrupt clouds and suppress star-formation.

Shock emission

Shocked gas emits radiation at all wavelengths, including the radio, optical, UV, and X-rays. The study of many astrophysical objects, in particular supernova remnants, involves the analysis of shock emission, which offers insights into the properties, e.g. the composition, of the interstellar medium. We also learn about emission processes and the plasma physics that mediate shocks. We differentiate two types of shocks: when a shock retains most of its internal energy, it is called an "adiabatic shock". When it radiates away most of its internal energy so that the shocked gas becomes cold and dense, it is called a "radiative shock".

Cosmic ray acceleration in shocks

Shocks also accelerate particles (electrons and ions) by a process known as first order Fermi acceleration. Beyond a certain energy, these particles form a distinct non-thermal phase in the interstellar medium called "cosmic rays". In our Galaxy, the cosmic rays have, on average, an energy density comparable to that of the thermal interstellar gas, the radiation field, the turbulence, and the magnetic fields. Cosmic rays are partly responsible for launching the Galactic wind, and for triggering the chemistry inside molecular clouds.

When cosmic rays are accelerated in shocks, they gain energy and modify the shock structure through their back reaction on the magnetic fields they scatter against. In particular a cosmic-ray precursor develops, a region in front of the shock into which cosmic-rays diffuse and smoothly decelerate and heat the thermal gas. Cosmic-ray modification of adiabatic shocks has been extensively studied since the early 1980s (e.g. Drury & Volk 1981; the complete solution space was first solved analytically by Becker & Kazanas 2001), but cosmic-ray modification of radiative shocks and the effects on the emission from shocks have not been studied much. This then became the topic of my doctoral thesis.

Hydrodynamic models of cosmic-ray modified shocks

A convenient way to study the effect of cosmic rays on the shock structure is to, just as with the thermal gas particles, treat them as a fluid. The cosmic rays are thus coupled in a two-fluid system with the thermal gas according to the following equations:

The equations represent the evolution of the thermal and cosmic-ray fluids with time and space, and contain a number of additional physics, are contained in the exchange source terms $S_g$ and $S_g$ (see Wagner et al 2009 for their form and for explanation of other symbols, pdf | NASA ADS):

• Acoustic instability (Drury & Falle 1986): An instability in the precursor by which sound waves grow in amplitude. Damping of the sound waves transfers energy from the cosmic-rays to the thermal gas.
• Cosmic-ray injection (Malkov & Volk 1995): Thermal gas particles transitioning to the non-thermal phase and participating the acceleration mechanism.

Given a set of initial conditions, e.g. a shock not yet modified by cosmic rays, the equations can be solved with a hydrodynamic simulation code.

Thermal stability of a cosmic-ray modified radiative medium

It is informative to perform a linear stability analysis of the above equations for a homogeneous radiative medium under small adiabatic or isobaric perturbations. Due to the strong dependence of the cooling function on temperature, the interstellar medium tends to be unstable against small changes on the cooling rate due to these perturbations. The results are in my first paper (Wagner et al 2005, pdf | NASA ADS).

The analysis shows that the thermal stability of the two-fluid medium against isobaric perturbations is unchanged in the presence of cosmic rays. Cosmic rays, however, stabilize the medium if the cosmic ray pressure is larger than the thermal pressure and if the diffusion length is large compared to the cooling length and the wavelength of the perturbation. These conditions may be satisfied in astrophysical shocks.

Cosmic-ray modified radiative shocks

Radiative shocks may exhibit a structural instability closely related to the thermal instability, in which the cooling layer periodically contracts and expands, creating a turbulent postshock flow. The "radiative overstability" was discovered by Langer et al (1981).

Shock structures of cosmic-ray modified radiative shocks including the effects of an acoustic instability for various damping timescales of the acoustic instability with respect for the cosmic ray diffusion timescale. The shocks are Mach 5 shocks and a power-law cooling function was used.

When cosmic rays are accelerated in radiative shocks, they gain energy both across the shock and in the cooling region (Wagner et al 2006, pdf | NASA ADS). In fact, cosmic ray acceleration in radiative shocks is so efficient, that, if the diffusion length of cosmic rays is comparable or larger than the cooling length, the cosmic rays easily suppress the thermal overstability.

Time-space diagram of the radiative overstability which, in this case, is damped by cosmic rays. The light-grey region is the upstream flow, the oscillating grey region is the cooling region, and the black region is the cold dense layer.

Time-space diagram of the radiative overstability which, in this case, is enhanced by cosmic rays. Whether cosmic rays damp or enhance the acoustic instability depends on the ratio of the cooling length to the diffusion length and the ratio of the acoustic instability timescale to the diffusion timescale.

Since the energy gain of cosmic rays dominates radiative energy losses behind the shock, the shock structure does not exhibit a cold dense layer and, instead, has a maximum compression ratio of 7 and is nearly isothermal everywhere. The steady-state versions of the two-fluid equations can be easily integrated for the case for which the diffusion length is much larger than the cooling length can be easily numerically integrated.

Isothermal shocks are not realistic models for shocks in supernova remnants, in which emission from an extended cooling region is observed. Reconciliation with observations may be achieved by including the effects of the acoustic instability, which transfers energy back from the cosmic rays to the thermal gas, and thereby partly restores the cooling region and cold dense layer (Wagner et al 2007, pdf | NASA ADS). This results in shock structures that have an overall compression ratio anywhere between that of a cosmic-ray dominated shock and that of an unmodified radiative shock. Such models can explain shocks observed in supernova remnants that appear to have compression ratios intermediate to adiabatic shocks and radiative shocks.

A cosmic-ray explanation for the preheating in Balmer-dominated shocks

Balmer-dominated shocks are fast, adiabatic shock that primarily emit a hydrogen Balmer line with a peculiar profile consisting of a narrow and a broad component (and likely an intermediate component). Detailed analysis of the line profiles suggests that the preshock medium in most Balmer-dominated shocks is preheated to a few times the undisturbed ambient ISM. Cosmic-ray modified shocks offer an explanation, because at high Mach numbers and reasonable values for the cosmic ray diffusion coefficient and acoustic instability damping rate, there exists a branch of solutions for which cosmic ray acceleration is very inefficient resulting only in mild precursor heating and hardly any flow deceleration, in agreement with observations. In our paper (Wagner et al 2009, pdf | NASA ADS), we suggest that this branch of solutions can explain the natural weak broadening of the narrow component Hα line profile seen in almost all Balmer-dominated filaments.

A Balmer-dominated shock in Tycho's supernova remnant

A full Chandra X-ray view of the Tycho SNR with knot g indicated. (Credit: NASA/CXC/Chinese Academy of Sciences/F. Lu et al.)

Shock profile of the model that fits the Hα emission in knot G in Tycho's supernova remnant. The gas subshock is located at $x=0$.

The bright Balmer-dominated shock in Tycho's SNR remnant at knot G is observed to have assocaited faint Hα emission ahead of the shock, possibly coming from a cosmic ray precursor (Lee et al. 2010). If this is true, this the first direct observation of a cosmic-ray precursor in a supernova remnant, and direct proof of cosmic ray acceleration in supernova remnant shocks. We test a cosmic-ray modified shock model using the Hα flux profile across the shock front as a diagnostic to constrain shock and cosmic-ray parameters (Wagner et al 2009).

The particular model that fits the data includes (and requires) the effects particle injection and of the acoustic instability. The following table summarizes the shock and cosmic-ray parameters determined from the model.