An analysis of the turbulence in the central region of M 42 through structure functions

Añorve-Zeferino, G. A.

doi:10.1093/mnras/sty3035

Cited by 5 publications

(1 citation statement)

References 33 publications

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“…A popular diagnostic tool in the field of astrophysical turbulence (e.g. Lis et al 1998;Esquivel et al 2007;Anorve-Zeferino 2019) is the two-dimensional structure function, loosely speaking a 2-d correlation function analysis of the line centroid shift map. Obtaining analytical expressions of the sample variance of these estimators requires the formalism above to be extended and to account for the 3-dimensional structure of the velocity field and the emissivity field.…”

Section: Two-dimensional Characterisation Of the Velocity Fieldmentioning

confidence: 99%

Towards mapping turbulence in the intra-cluster medium -- I. Sample variance in spatially-resolved X-ray line diagnostics

Clerc,

Cucchetti,

Pointecouteau

et al. 2019

Preprint

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Context. X-ray observations of galaxy clusters provide insights on the nature of gaseous turbulent motions, their physical scales and on the fundamental processes they are related to. Spatially-resolved, high-resolution spectral measurements of X-ray emission lines provide diagnostics on the nature of turbulent motions in emitting atmospheres. Since they are acting on scales comparable to the size of the objects, the uncertainty on these physical parameters is limited by the number of observational measurements, through sample variance.Aims. We propose a different and complementary approach for the computation of sample variance to repeating numerical simulations (i.e. Monte-Carlo sampling) by introducing new analytical developments for lines diagnosis. Methods. We consider the model of a "turbulent gas cloud", consisting in isotropic and uniform turbulence described by a universal Kolmogorov power-spectrum with random amplitudes and phases in an optically thin medium. Following a simple prescription for the 4-term correlation of Fourier coefficients, we derive generic expressions for the sample mean and variance of line centroid shift, line broadening and projected velocity structure function. We perform a numerical validation based on Monte-Carlo simulations for two popular models of gas emissivity based on the β-model. Results. Generic expressions for the sample variance of line centroid shifts and broadening in arbitrary apertures are derived and match the simulations within their range of applicability. Generic expressions for the mean and variance of the structure function are provided and verified against simulations. An application to the Athena/X-IFU (Advanced Telescope for High-ENergy Astrophysics/X-ray Integral Field Unit) and XRISM /Resolve (X-ray Imaging and Spectroscopy Mission) instruments forecasts the potential of sensitive, spatially-resolved spectroscopy to probe the inertial range of turbulent velocity cascades in a Coma-like galaxy cluster. Conclusions. The formulas provided are of generic relevance and can be implemented in forecasts for upcoming or current X-ray instrumentation and observing programs.

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Section: Two-dimensional Characterisation Of the Velocity Fieldmentioning

confidence: 99%

Towards mapping turbulence in the intra-cluster medium -- I. Sample variance in spatially-resolved X-ray line diagnostics

Clerc,

Cucchetti,

Pointecouteau

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

Towards mapping turbulence in the intra-cluster medium

Clerc

Cucchetti

Pointecouteau

et al. 2019

A&A

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Context. X-ray observations of galaxy clusters provide insights into the nature of gaseous turbulent motions, their physical scales, and the fundamental processes to which they are related. Spatially-resolved, high-resolution spectral measurements of X-ray emission lines provide diagnostics on the nature of turbulent motions in emitting atmospheres. Since they are acting on scales comparable to the size of the objects, the uncertainty on these physical parameters is limited by the number of observational measurements, through sample variance. Aims. We propose a different and complementary approach to repeating numerical simulations for the computation of sample variance (i.e. Monte-Carlo sampling) by introducing new analytical developments for lines diagnosis. Methods. We considered the model of a “turbulent gas cloud”, consisting in isotropic and uniform turbulence described by a universal Kolmogorov power-spectrum with random amplitudes and phases in an optically thin medium. Following a simple prescription for the four-term correlation of Fourier coefficients, we derived generic expressions for the sample mean and variance of line centroid shift, line broadening, and projected velocity structure function. We performed a numerical validation based on Monte-Carlo simulations for two popular models of gas emissivity based on the β-model. Results. Generic expressions for the sample variance of line centroid shifts and broadening in arbitrary apertures are derived and match the simulations within their range of applicability. Generic expressions for the mean and variance of the structure function are provided and verified against simulations. An application to the Athena/X-IFU (Advanced Telescope for High-ENergy Astrophysics/X-ray Integral Field Unit) and XRISM/Resolve (X-ray Imaging and Spectroscopy Mission) instruments forecasts the potential of sensitive, spatially-resolved spectroscopy to probe the inertial range of turbulent velocity cascades in a Coma-like galaxy cluster. Conclusions. The formulas provided are of generic relevance and can be implemented in forecasts for upcoming or current X-ray instrumentation and observing programmes.

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Empirical constraints on the turbulence in QSO host nebulae from velocity structure function measurements

Chen

Rauch

et al. 2022

Monthly Notices of the Royal Astronomical Society

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We present the first empirical constraints on the turbulent velocity field of the diffuse circumgalactic medium around four luminous QSOs at z ≈ 0.5–1.1. Spatially extended nebulae of ≈50–100 physical kpc in diameter centered on the QSOs are revealed in [O ii] λλ 3727, 3729 and/or [O iii] λ 5008 emission lines in integral field spectroscopic observations obtained using MUSE on the VLT. We measure the second- and third-order velocity structure functions (VSFs) over a range of scales, from ≲ 5 kpc to ≈20–50 kpc, to quantify the turbulent energy transfer between different scales in these nebulae. While no constraints on the energy injection and dissipation scales can be obtained from the current data, we show that robust constraints on the power-law slope of the VSFs can be determined after accounting for the effects of atmospheric seeing, spatial smoothing, and large-scale bulk flows. Out of the four QSO nebulae studied, one exhibits VSFs in spectacular agreement with the Kolmogorov law, expected for isotropic, homogeneous, and incompressible turbulent flows. The other three fields exhibit a shallower decline in the VSFs from large to small scales. However, with a limited dynamic range in the spatial scales in seeing-limited data, no constraints can be obtained for the VSF slopes of these three nebulae. For the QSO nebula consistent with the Kolmogorov law, we determine a turbulence energy cascade rate of ≈0.2 cm2 s−3. We discuss the implication of the observed VSFs in the context of QSO feeding and feedback in the circumgalactic medium.

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An analysis of the turbulence in the central region of M 42 through structure functions

Cited by 5 publications

References 33 publications

Towards mapping turbulence in the intra-cluster medium -- I. Sample variance in spatially-resolved X-ray line diagnostics

Towards mapping turbulence in the intra-cluster medium -- I. Sample variance in spatially-resolved X-ray line diagnostics

Towards mapping turbulence in the intra-cluster medium

Empirical constraints on the turbulence in QSO host nebulae from velocity structure function measurements

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