Effects of Lower Boundary Conditions on the Stability of Radiative Shocks

Saxton, C. J.

doi:10.1071/as02004

Cited by 11 publications

(13 citation statements)

References 27 publications

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“…(6), for different white dwarf masses. We note that the dependency ofṀ with B derived here from Saxton (1999) is significantly different from the one shown by Lamb & Master (1979), who used different prescriptions to compute the bremsstrahlung and cyclotron cooling times.…”

Section: The Qpo Regimecontrasting

confidence: 41%

“…The condition s 1 will indicate a bremsstrahlung dominated shock favouring QPOs, while s > 1 indicates a cyclotron-dominated shock with an expected damping of the QPOs. Following Saxton (1999), s can be expressed as a function of relevant parameters of the system, V ff the free-fall velocity, ρ the flow density above the shock, B the magnetic field, and A the cylindrical column cross-section as…”

Section: The Qpo Regimementioning

confidence: 99%

“…These instabilities have been studied theoretically in more detail by considering different processes and modelisations, such as cyclotron emission (Chanmugam et al 1985), parametric cooling function (Chevalier & Imamura 1982;Mignone 2005), gravitational potential , unequal ionelectron temperatures (Imamura et al 1987;Saxton & Wu 1999), different boundary conditions (Saxton 2002;Mignone 2005) and noise-driven excitation (Wood et al 1992;Wu et al 1992).…”

Section: Introductionmentioning

confidence: 99%

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Quasi-periodic oscillations in accreting magnetic white dwarfs

Bonnet‐Bidaud

Mouchet

Busschaert

et al. 2015

A&A

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Quasi-periodic oscillations (QPOs) are observed in the optical flux of some polars with typical periods of 1 to 3 s but none have been observed yet in X-rays where a significant part of the accreting energy is released. QPOs are expected and predicted from shock oscillations. Most of the polars have been observed by the XMM-Newton satellite. We made use of the homogeneous set of observations of the polars by XMM-Newton to search for the presence of QPOs in the (0.5-10 keV) energy range and to set significant upper limits for the brightest X-ray polars. We extracted high time-resolution X-ray light curves by taking advantage of the 0.07 s resolution of the EPIC-PN camera. Among the 65 polars observed with XMM-Newton from 1998 to 2012, a sample of 24 sources was selected on the basis of their counting rate in the PN instrument to secure significant limits. We searched for QPOs using Fast Fourier Transform (FFT) methods and defined limits of detection using statistical tools. Among the sample surveyed, none shows QPOs at a significant level. Upper limits to the fractional flux in QPOs range from 7% to 71%. These negative results are compared to the detailed theoretical predictions of numerical simulations based on a 2D hydrodynamical code presented in Paper II. Cooling instabilities in the accretion column are expected to produce shock quasi-oscillations with a maximum amplitude reaching ∼40% in the bremsstrahlung (0.5-10 keV) X-ray emission and ∼20% in the optical cyclotron emission. The absence of X-ray QPOs imposes an upper limit of ∼(5-10) g cm −2 s −1 on the specific accretion rate but this condition is found inconsistent with the value required to account for the amplitudes and frequencies of the observed optical QPOs. This contradiction outlines probable shortcomings with the shock instability model.

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Section: The Qpo Regimecontrasting

confidence: 41%

Section: The Qpo Regimementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quasi-periodic oscillations in accreting magnetic white dwarfs

Bonnet‐Bidaud

Mouchet

Busschaert

et al. 2015

A&A

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“…Since the boundary conditions imposed in numerical models of radiative shocks can also affect their stability (Strickland & Blondin 1995;Saxton 2002), we investigate the nature of the instability as the boundary conditions and initial conditions are varied. In Sect.…”

Section: Introductionmentioning

confidence: 99%

The shocking properties of supersonic flows: Dependence of the thermal overstability on M, α, and T$\mathsf{_{c}}\,$/ T$\mathsf{_{0}}$

Pittard

Dobson

Durisen

et al. 2005

A&A

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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 (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.

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“…Stability properties of radiative shocks with unequal ion and electron temperatures were investigated by Imamura et al (1996), while flows with multiple cooling functions (i.e., bremsstrahlung and cyclotron) were examined in both the singleand two-temperature regimes by Saxton et al (1997Saxton et al ( , 1998, Saxton (1999Saxton ( , 2002, and Saxton & Wu (1999. Additional references can be found in the review by Wu (2000).…”

Section: Introductionmentioning

confidence: 99%

The Dynamics of Radiative Shock Waves: Linear and Nonlinear Evolution

Mignone

2005

ApJ

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The stability properties of one-dimensional radiative shocks with a power-law cooling function of the form Ã / 2 T are the main subject of this work. The linear analysis originally presented by Chevalier & Imamura is thoroughly reviewed for several values of the cooling index and higher overtone modes. Consistently with previous results, it is shown that the spectrum of the linear operator consists of a series of modes with increasing oscillation frequency. For each mode a critical value of the cooling index, c , can be defined so that modes with < c are unstable while modes with > c are stable. The perturbative analysis is complemented by several numerical simulations to follow the time-dependent evolution of the system for different values of . Particular attention is given to the comparison between numerical and analytical results (during the early phases of the evolution) and to the role played by different boundary conditions. It is shown that an appropriate treatment of the lower boundary yields results that closely follow the predicted linear behavior. During the nonlinear regime, the shock oscillations saturate at a finite amplitude and tend to a quasi-periodic cycle. The modes of oscillations during this phase do not necessarily coincide with those predicted by linear theory but may be accounted for by modemode coupling.

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Effects of Lower Boundary Conditions on the Stability of Radiative Shocks

Cited by 11 publications

References 27 publications

Quasi-periodic oscillations in accreting magnetic white dwarfs

Quasi-periodic oscillations in accreting magnetic white dwarfs

The shocking properties of supersonic flows: Dependence of the thermal overstability on M, α, and T$\mathsf{_{c}}\,$/ T$\mathsf{_{0}}$

The Dynamics of Radiative Shock Waves: Linear and Nonlinear Evolution

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