Whistler Critical Mach Number Concept Revisited
: Balikhin, Michael A.; Agapitov, Oleksiy V.; Krasnoselskikh, Vladimir; Roytershteyn, Vadim; Walker, Simon N.; Gedalin, Michael; Jeba Raj, Immanuel Christopher; Colomban, Lucas
Publisher: American Geophysical Union (AGU)
: 2026
Journal of Geophysical Research: Space Physics
: e2025JA034905
: 131
: 1
: 2169-9380
: 2169-9402
DOI: https://doi.org/10.1029/2025JA034905
: https://doi.org/10.1029/2025ja034905
: https://research.utu.fi/converis/portal/detail/Publication/509013992
The formation of a collisionless shock is the result of a balance between nonlinear steepening and processes that counteract this steepening. Dispersive shocks are shocks in which dispersive processes counterbalance the front steepening and are formed when the dispersive spatial scale exceeds scales associated with resistive processes. Oblique dispersive shocks are characterized by a phase standing wave precursor adjacent to the magnetic ramp. The whistler critical Mach number is defined as the maximum Mach number for which a linear whistler wave can phase stand upstream of the shock front. It was widely accepted that if the Mach number exceeds , linear whistler waves propagating along the shock normal are not able to "phase stand" in the upstream flow, and "& mldr;the shock will be initiated by a monotonic ramp." (Kennel et al., 1985, https://doi.org/10.1029/gm034p0001). In this study, we present results of numerical simulations and observations of shocks with that reveal the occurrence of an alternative scenario. For both the shock resulting from kinetic particle-in-cell simulations and that observed by MMS, the propagation direction of the precursor deviates from the shock normal direction. As a result, the velocity of the surface of constant phase along the shock normal exceeds the phase speed of these waves. It is shown that the propagation of the surface of constant phase along the shock normal occurs at a velocity that is nearly equal to the shock speed. Hence, these waves are "phase standing along the shock normal" in spite of .
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The authors acknowledge support from the International Space Science Institute, Bern, Switzerland. The simulations were performed using computational resources provided by the Texas Advanced Computing Center (TACC) at The University of Texas at Austin. MAB and SW were supported by the Science and Technology Facilities Council [ST/Y001575/1]. OVA, VK, and LC were supported by NASA Grants 80NSSC20K0697 and 80NSSC21K1770. OVA and LC were partially supported by NASA's Living with a Star (LWS) program (contract 80NSSC20K0218), and NASA Grants contracts 80NSSC22K0433 and 80NSSC22K0522. The work of VR was supported by NASA Grant 80NSSC21K1680. I.C.J. acknowledges support from the Research Council of Finland (X-Scale, Grant 371569).