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 (α) 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 α≲-1.2 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 α_{cr}≃0.4 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 χ<1, where χ 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 α_{cr} which are comparable to values obtained for higher Mach number shocks when χ=1. For instance, α_{cr}=-0.1 when M=2 and χ=0.1, comparable to that when M=10 and χ=1. 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.
(Ref) Object type as listed in the reference "Ref"
(acronym) Object type linked to the acronym according to the original reference
() Anterior to 2007, before we can link the objet type to a reference, or given by the CDS team in some particular cases
Other object types:
SNR
(Ref,AJG,...),
X
(1E,1ES,...),
Rad
(GRS),
UV
(2RE),
gam
(1FGL)
Syntax of coordinates is : "ra dec (wtype) [error ellipse] quality bibcode" :
ra dec : right ascension and declination (unit and frame defined according to your Output Options)
Grey values are increasing the original precision due to the computation of frame transformations
(wtype) : wavelength class for the origin of the coordinates (Rad, mm, IR, Optical, UV, Xray, Gam)
[error ellipse] : measurement uncertainty, on (ra,dec) if the positional angle is 90 degrees, on (majaxis,minaxis) otherwise (in mas at defined epoch in the original catalogue),
position angle (in degrees North celestial pole to East)
Syntax of coordinates is : "ra dec (wtype) [error ellipse] quality bibcode" :
ra dec : right ascension and declination (unit and frame defined according to your Output Options)
Grey values are increasing the original precision due to the computation of frame transformations
(wtype) : wavelength class for the origin of the coordinates (Rad, mm, IR, Optical, UV, Xray, Gam)
[error ellipse] : measurement uncertainty, on (ra,dec) if the positional angle is 90 degrees, on (majaxis,minaxis) otherwise (in mas at defined epoch in the original catalogue),
position angle (in degrees North celestial pole to East)
quality : flag of quality
E ≥ 10"
D : 1-10" (and some old data)
C : 0.1-1"
B : 0.01-0.1" + 2MASS, Tyc
A : VLBI, Hipparcos
bibcode : bibcode of the coordinates reference
FK4
coord.
(ep=B1950 eq=1950) :
08 32 20.1 -45 39 39
[
]
Syntax of coordinates is : "ra dec (wtype) [error ellipse] quality bibcode" :
ra dec : right ascension and declination (unit and frame defined according to your Output Options)
Grey values are increasing the original precision due to the computation of frame transformations
(wtype) : wavelength class for the origin of the coordinates (Rad, mm, IR, Optical, UV, Xray, Gam)
[error ellipse] : measurement uncertainty, on (ra,dec) if the positional angle is 90 degrees, on (majaxis,minaxis) otherwise (in mas at defined epoch in the original catalogue),
position angle (in degrees North celestial pole to East)
quality : flag of quality
E ≥ 10"
D : 1-10" (and some old data)
C : 0.1-1"
B : 0.01-0.1" + 2MASS, Tyc
A : VLBI, Hipparcos
bibcode : bibcode of the coordinates reference
Gal
coord.
(ep=J2000) :
263.9390 -03.3683
[
]
Syntax of angular size is : "maj-axis min-axis angle (wtype) quality bibcode"
maj-axis : major axis size (arc minutes)
min-axis : minor axis size (arc minutes)
angle : orientation angle (in degrees)
(incl) : inclination (in units of 15° from 0 to 7)
(wtype) : wavelength class for the origin of the angular size (Rad, mm, IR, Opt, UV, Xray, Gam)
quality : flag of quality of the angular size values ( A=best quality -> E=worst quality, {� } =unknown quality)
References (1091 between 1850 and 2020) (Total 1091)
Simbad bibliographic survey began in 1850 for stars (at least bright stars) and in 1983 for all other objects (outside the solar system).
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