A&A 438, 11-21 (2005)

DOI: 10.1051/0004-6361:20042260

## The shocking properties of supersonic flows: Dependence of the thermal
overstability on **M**, , and **T**
/**T**

**M**

**T**

**T**

**J. M. Pittard**

^{1}, M. S. Dobson^{1}, R. H. Durisen^{2}, J. E. Dyson^{1}, T. W. Hartquist^{1}and J. T. O'Brien^{1}^{1}School of Physics and Astronomy, The University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK

e-mail: jmp@ast.leeds.ac.uk

^{2}Department of Astronomy, Indiana University, Swain Hall West 319, 727 East 3rd St., Bloomington 47405, USA

(Received 27 October 2004 / Accepted 8 April 2005 )

** Abstract **

We present hydrodynamical calculations of radiative shocks
with low Mach numbers and find that the well-known global
overstability can occur if the temperature exponent () of the
cooling is sufficiently negative. We find that the stability of
radiative shocks increases with decreasing Mach number, with the
result that *M*=2 shocks require
in order to be
overstable. Such values occur within a limited temperature range of
many cooling curves. We observe that Mach numbers of order 100 are
needed before the strong shock limit of
is reached, and we discover that the frequency of oscillation of the
fundamental mode also has a strong Mach number dependence. We find
that feedback between the cooling region and the cold dense layer (CDL)
further downstream is a function of Mach number, with stronger
feedback and oscillation of the boundary between the CDL
and the cooling region occuring at lower Mach numbers. This feedback
can be quantified in terms of the reflection coefficient of sound
waves, and in those cases where the cooling layer completely
disappears at the end of each oscillation cycle, the initial velocity
of the waves driven into the upstream pre-shock flow and into the
downstream CDL, and the velocity of the the boundary between the CDL and
the cooling layer, can be understood in terms of the solution to the
Riemann problem. An interesting finding is that the stability properties
of low Mach number shocks can be dramatically altered if the shocked gas is
able to cool to temperatures less than the pre-shock value (i.e. when
, where is the ratio of the temperature of the cold
dense layer to the pre-shock temperature). In such circumstances, low
Mach number shocks have values of
which are
comparable to values obtained for higher Mach number shocks when . For instance,
when *M*=2 and ,
comparable to that when *M*=10 and . Thus, it is probable
that low Mach number astrophysical shocks will be overstable in a
variety of situations. We also explore the effect of different
assumptions for the initial hydrodynamic set up and the type of
boundary condition imposed downstream, and find that the properties of
low Mach number shocks are relatively insensitive to these issues.
The results of this work are relevant to astrophysical shocks with low
Mach numbers, such as supernova remnants (SNRs) immersed in a hot
interstellar medium (e.g., within a starburst region), and shocks in
molecular clouds, where time-dependent chemistry can lead to
overstability.

**Key words:**hydrodynamics

**--**shock waves

**--**instabilities

**--**ISM: kinematics and dynamics

**--**ISM: supernova remnants

**--**stars: winds, outflows

SIMBAD Objects

**©**

*ESO 2005*