Probing the thermal character of analogue Hawking radiation for shallow water waves?

We study and numerically compute the scattering coefficients of shallow water waves blocked by a stationary counterflow. When the flow is transcritical, the coefficients closely follow Hawking's prediction according to which black holes should emit a thermal spectrum. We study how the spectrum deviates from thermality when reducing the maximal flow velocity, with a particular attention to subcritical flows since these have been recently used to test Hawking's prediction. For such flows, we show that the emission spectrum is strongly suppressed, and that its Planckian character is completely lost. For low frequencies, we also show that the scattering coefficients are dominated by elastic hydrodynamical channels. Our numerical results reproduce rather well the observations made by S. Weinfurtner {\it et al.} in the Vancouver experiment. Nevertheless, we propose a new interpretation of what has been observed, as well as new experimental tests.Comment: 23 pages, 14 figures, 2 figures updated to match the PRD version, final version published in Physical Review

Mode mixing in sub- and trans-critical flows over an obstacle: When should Hawking's predictions be recovered?

We reexamine the scattering coefficients of shallow water waves blocked by a stationary counter current over an obstacle. By considering series of background flows, we show that the most relevant parameter is $F_{\rm max}$, the maximal value of the ratio of the flow velocity over the speed of low frequency waves. For subcritical flows, i.e., $F_{\rm max} < 1$, there is no analogue Killing horizon and the mode amplification is strongly suppressed. Instead, when $F_{\rm max} \gtrsim 1.1$, the amplification is enhanced at low frequency and the spectrum closely follows Hawking's prediction. We further study subcritical flows close to that used in the Vancouver experiment. Our numerical analysis suggests that their observation of the "thermal nature of the mode conversion" is due to the relatively steep slope on the upstream side and the narrowness of the obstacle.Comment: 11 pages, 6 figure

The incorrect rotation curve of the Milky Way

In the fundamental quest of the rotation curve of the Milky Way, the tangent-point (TP) method has long been the simplest way to infer velocities for the inner, low latitude regions of the Galactic disk from observations of the gas component. We test the validity of the method on realistic gas distribution and kinematics of the Milky Way, using a numerical simulation of the Galaxy. We show that the resulting velocity profile strongly deviates from the true rotation curve of the simulation, as it overstimates it in the central regions, and underestimates it around the bar corotation. Also, its shape strongly depends on the orientation of the stellar bar. The discrepancies are caused by highly non-uniform azimuthal velocities, and the systematic selection by the TP method of high-velocity gas along the bar and spiral arms, or low-velocity gas in less dense regions. The velocity profile is in good agreement with the rotation curve only beyond corotation, far from massive asymmetric structures. Therefore the observed velocity profile of the Milky Way inferred by the TP method is expected to be very close to the true Galactic rotation curve for 4.5<R<8 kpc. Another consequence is that the Galactic velocity profile for R<4-4.5 kpc is very likely flawed by the non-uniform azimuthal velocities, and does not represent the true Galactic rotation curve, but instead local motions. The real shape of the innermost rotation curve is probably shallower than previously thought. Using a wrong rotation curve has a dramatic impact on the modelling of the mass distribution, in particular for the bulge component of which derived enclosed mass within the central kpc and scale radius are, respectively, twice and half of the actual values. We thus strongly argue against using terminal velocities or the velocity curve from the TP method for modelling the mass distribution of the Milky Way. (abridged)Comment: Accepted for publication in Astronomy & Astrophysics, 8 pages, 10 figures, revised version after A&A language editin

A flexible method to evolve collisional systems and their tidal debris in external potentials

We introduce a numerical method to integrate tidal effects on collisional systems, using any definition of the external potential as a function of space and time. Rather than using a linearisation of the tidal field, this new method follows a differential technique to numerically evaluate the tidal acceleration and its time derivative. Theses are then used to integrate the motions of the components of the collisional systems, like stars in star clusters, using a predictor-corrector scheme. The versatility of this approach allows the study of star clusters, including their tidal tails, in complex, multi-components, time-evolving external potentials. The method is implemented in the code nbody6 (Aarseth 2003).Comment: MNRAS accepted. Code available here: http://personal.ph.surrey.ac.uk/~fr0005/nbody6tt.ph

No hair theorems for analogue black holes

We show that transonic one dimensional flows which are analogous to black holes obey no-hair theorems both at the level of linear perturbations and in non-linear regimes. Considering solutions of the Gross-Pitaevskii (or Korteweg-de Vries) equation, we show that stationary flows which are asymptotically uniform on both sides of the horizon are stable and act as attractors. Using Whitham's modulation theory, we analytically characterize the emitted waves when starting from uniform perturbations. Numerical simulations confirm the validity of this approximation and extend the results to more general perturbations and to the (non-integrable) cubic-quintic Gross-Pitaevskii equation. When considering time reversed flows that correspond to white holes, the asymptotically uniform flows are unstable to sufficiently large perturbations and emit either a macroscopic undulation in the supersonic side, or a non-linear superposition of soliton trains.Comment: Final version published in PRD; a new figure illustrates the link with the relativistic regime, and another the stability of the results when considering larger non-linear perturbations; a few typos fixe

Dynamical instabilities and quasi-normal modes, a spectral analysis with applications to black-hole physics

Black hole dynamical instabilities have been mostly studied in specific models. We here study the general properties of the complex-frequency modes responsible for such instabilities, guided by the example of a charged scalar field in an electrostatic potential. We show that these modes are square integrable, have a vanishing conserved norm, and appear in mode doublets or quartets. We also study how they appear in the spectrum and how their complex frequencies subsequently evolve when varying some external parameter. When working on an infinite domain, they appear from the reservoir of quasi-normal modes obeying outgoing boundary conditions. This is illustrated by generalizing, in a non-positive definite Krein space, a solvable model (Friedrichs model) which originally describes the appearance of a resonance when coupling an isolated system to a mode continuum. In a finite spatial domain instead, they arise from the fusion of two real frequency modes with opposite norms, through a process that closely resembles avoided crossing.Comment: 31 pages, 13 figures. Small clarifications, title changed, matches published versio

The origin of the Milky Way globular clusters

We present a cosmological zoom-in simulation of a Milky Way-like galaxy used to explore the formation and evolution of star clusters. We investigate in particular the origin of the bimodality observed in the colour and metallicity of globular clusters, and the environmental evolution through cosmic times in the form of tidal tensors. Our results self-consistently confirm previous findings that the blue, metal-poor clusters form in satellite galaxies which are accreted onto the Milky Way, while the red, metal-rich clusters form mostly in situ or, to a lower extent in massive, self-enriched galaxies merging with the Milky Way. By monitoring the tidal fields these populations experience, we find that clusters formed in situ (generally centrally concentrated) feel significantly stronger tides than the accreted ones, both in the present-day, and when averaged over their entire life. Furthermore, we note that the tidal field experienced by Milky Way clusters is significantly weaker in the past than at present-day, confirming that it is unlikely that a power-law cluster initial mass function like that of young massive clusters, is transformed into the observed peaked distribution in the Milky Way with relaxation-driven evaporation in a tidal field.Comment: MNRAS accepte