Planetary bow shocks: Gasdynamic analytic approach

Веригин, М. И.; Slavin, J. A.; Szabó, Á.; Gombosi, T. I.; Котова, Г. А.; Plochova, O.; Szegö, K.; Tátrallyay, M.; Кабин, К.; Shugaev, F. V.

doi:10.1029/2002ja009711

Cited by 38 publications

(34 citation statements)

References 34 publications

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“…related (at least in an isothermal atmosphere), causing underestimation/overestimation of the Mach number from the value of ∆/R assuming the reference model (e.g. Verigin et al 2003). Moreover, we see that the combination of the two effects produces an even larger deviation than the linear sum of the deviations expected from each effect separately.…”

Section: Acceleration/deceleration Plus Density (Pressure) Gradientsmentioning

confidence: 74%

“…The theory of bow shocks driven by blunt bodies has been extensively studied theoretically and experimentally, including space physics applications (e.g. Van Dyke 1958;Farris & Russell 1994;Fairfield et al 2001;Petrinec 2002;Verigin et al 2003;Keshet & Naor 2016). The standoff distance ∆ is defined as the distance between the stagnation point of the body and the closest point on the shock front (see Fig.…”

Section: Introductionmentioning

confidence: 99%

“…1a). In this work, we use the results of Verigin et al (2003) as a baseline model for the standoff distance (hereafter, ∆V ) for a moving sphere with a radius R (see equation A4). The normalized standoff distance ∆V /R is a monotonically decreasing function of the Mach number Ms = Mg (particularly sensitive to Ms when Ms 3, see Fig.…”

Section: Introductionmentioning

confidence: 99%

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Standoff distance of bow shocks in galaxy clusters as proxy for Mach number

Zhang

Churazov

Forman

et al. 2018

Monthly Notices of the Royal Astronomical Society

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X-ray observations of merging clusters provide many examples of bow shocks leading merging subclusters. While the Mach number of a shock can be estimated from the observed density jump using Rankine-Hugoniot condition, it reflects only the velocity of the shock itself and is generally not equal to the velocity of the infalling subcluster dark matter halo or to the velocity of the contact discontinuity separating gaseous atmospheres of the two subclusters. Here we systematically analyze additional information that can be obtained by measuring the standoff distance, i.e. the distance between the leading edge of the shock and the contact discontinuity that drives this shock. The standoff distance is influenced by a number of additional effects, e.g. (1) the gravitational pull of the main cluster (causing acceleration/deceleration of the infalling subcluster), (2) the density and pressure gradients of the atmosphere in the main cluster, (3) the non-spherical shape of the subcluster, and (4) projection effects. The first two effects tend to bias the standoff distance in the same direction, pushing the bow shock closer to (farther away from) the subcluster during the pre-(post-)merger stages. Particularly, in the post-merger stage, the shock could be much farther away from the subcluster than predicted by a model of a body moving at a constant speed in a uniform medium. This implies that a combination of the standoff distance with measurements of the Mach number from density/temperature jumps can provide important information on the merger, e.g. differentiating between the pre-and post-merger stages.

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Section: Acceleration/deceleration Plus Density (Pressure) Gradientsmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

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Standoff distance of bow shocks in galaxy clusters as proxy for Mach number

Zhang

Churazov

Forman

et al. 2018

Monthly Notices of the Royal Astronomical Society

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“…It is a highly dynamic boundary, controlled by temporal variations in solar wind characteristics. The general shape of the shock has been investigated with empirical models [e.g., Fairfield, 1971;Slavin and Holzer, 1981], gas dynamic flow models [e.g., Slavin et al, 1983a;Verigin et al, 2003a], and magnetohydrodynamic models [e.g., Chapman and Cairns, 2003] and is well described by a conic section. Formisano et al [1971] found that the subsolar bow shock position moves outward during conditions of low Alfvén Mach number (M A ).…”

Section: Introductionmentioning

confidence: 99%

Mercury's magnetopause and bow shock from MESSENGER Magnetometer observations

et al. 2013

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[1] We have established the average shape and location of Mercury's magnetopause and bow shock from orbital observations by the MESSENGER Magnetometer. We fit empirical models to midpoints of boundary crossings and probability density maps of the magnetopause and bow shock positions. The magnetopause was fit by a surface for which the position R from the planetary dipole varies as [1 + cos(θ)]Àa , where θ is the angle between R and the dipole-Sun line, the subsolar standoff distance R ss is 1.45 R M (where R M is Mercury's radius), and the flaring parameter a = 0.5. The average magnetopause shape and location were determined under a mean solar wind ram pressure P Ram of 14.3 nPa. The best fit bow shock shape established under an average Alfvén Mach number (M A ) of 6.6 is described by a hyperboloid having R ss = 1.96 R M and an eccentricity of 1.02. These boundaries move as P Ram and M A vary, but their shapes remain unchanged. The magnetopause R ss varies from 1.55 to 1.35 R M for P Ram in the range of 8.8-21.6 nPa. The bow shock R ss varies from 2.29 to 1.89 R M for M A in the range of 4.12-11.8. The boundaries are well approximated by figures of revolution. Additional quantifiable effects of the interplanetary magnetic field are masked by the large dynamic variability of these boundaries. The magnetotail surface is nearly cylindrical, with a radius of~2.7 R M at a distance of 3 R M downstream of Mercury. By comparison, Earth's magnetotail flaring continues until a downstream distance of~10 R ss .

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“…Maloney & Gallagher (2011) examined whether normalized stand-off distance ratios, which are defined as Δ CME divided by either the CME radius (R CME ) or the radius of curvature at the nose of a CME front ( ) R C CME , are in agreement with those from bow shock relationships based on gasdynamic (GD) theories (Seiff 1962;Spreiter et al 1966;Farris & Russell 1994). For this, they analyzed the CME-driven shock observed on 2008 April 5 by COR2 and the Heliospheric Imager 1 (H1) of the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI; Howard et al 2008) on board the Solar TErrestrial Relations Observatory (STEREO) A and B, and determined the normalized stand-off distance ratios by using the tie-point method (Temmer et al 2009;Byrne et al 2010;Mierla et al 2010) and the analytical bow shock model (Verigin et al 2003). They found that stand-off distance ratios D ( ) R CME CME show better agreements with the relationships using the ratio of specific heat (γ) of 5/3 than normalized stand-off distances Using bow shock relationships under magnetohydrodynamic (MHD) theories (Cairns & Lyon 1995, 1996Merka et al 2003) and the relationships under GD theories, several researchers made an observational test as to which bow shock relationship is better suited for predicting Earth's bow shock locations (Fairfield et al 2001;Merka et al 2003).…”

Section: Introductionmentioning

confidence: 99%

Which Bow Shock Theory, Gasdynamic or Magnetohydrodynamic, Better Explains CME Stand-off Distance Ratios from LASCO-C2 Observations ?

Lee

Moon

Lee

et al. 2017

ApJ

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It is generally believed that fast coronal mass ejections (CMEs) can generate their associated shocks, which are characterized by faint structures ahead of CMEs in white-light coronagraph images. In this study, we examine whether the observational stand-off distance ratio, defined as the CME stand-off distance divided by its radius, can be explained by bow shock theories. Of 535 SOHO/LASCO CMEs (from 1996 to 2015) with speeds greater than 1000 km s −1 and angular widths wider than 60°, we select 18 limb CMEs with the following conditions: (1) their Alfvénic Mach numbers are greater than one under Mann's magnetic field and Saito's density distributions; and (2) the shock structures ahead of the CMEs are well identified. We determine observational CME stand-off distance ratios by using brightness profiles from LASCO-C2 observations. We compare our estimates with theoretical stand-off distance ratios from gasdynamic (GD) and magnetohydrodynamic (MHD) theories. The main results are as follows. Under the GD theory, 39% (7/18) of the CMEs are explained in the acceptable ranges of adiabatic gamma (γ) and CME geometry. Under the MHD theory, all the events are well explained when we consider quasiparallel MHD shocks with γ=5/3. When we use polarized brightness (pB) measurements for coronal density distributions, we also find similar results: 8% (1/12) under GD theory and 100% (12/12) under MHD theory. Our results demonstrate that the bow shock relationships based on MHD theory are more suitable than those based on GD theory for analyzing CME-driven shock signatures.

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Planetary bow shocks: Gasdynamic analytic approach

Cited by 38 publications

References 34 publications

Standoff distance of bow shocks in galaxy clusters as proxy for Mach number

Standoff distance of bow shocks in galaxy clusters as proxy for Mach number

Mercury's magnetopause and bow shock from MESSENGER Magnetometer observations

Which Bow Shock Theory, Gasdynamic or Magnetohydrodynamic, Better Explains CME Stand-off Distance Ratios from LASCO-C2 Observations ?

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