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 et al. in the Vancouver experiment. Nevertheless, we propose a new interpretation of what has been observed, as well as new experimental tests.

Note:

23 pages, 14 figures, 2 figures updated to match the PRD version, final version published in Physical Review D

04.60.-m
04.62.+v
04.70.Dy
47.35.Bb
water: wave
radiation: Hawking
spectrum: thermal
flow: velocity
frequency: low
scattering

References(35)

Figures(34)

[1]

Experimental black hole evaporation

W.G. Unruh
(
- British Columbia U.
)

- Phys.Rev.Lett. 46 (1981) 1351-1353
•
DOI:
- 10.1103/PhysRevLett.46.1351

[2]

Particle Creation by Black Holes

S.W. Hawking
(
- Cambridge U., DAMTP and
- Caltech
)

- Commun.Math.Phys. 43 (1975) 199-220,
- Commun.Math.Phys. 46 (1976) 206 (erratum),
•
DOI:
- 10.1007/BF02345020

[3]

Black hole evaporation and ultrashort distances

Theodore Jacobson
(
- Maryland U.
)

- Phys.Rev.D 44 (1991) 1731-1739
•
DOI:
- 10.1103/PhysRevD.44.1731

[4]

Sonic analog of black holes and the effects of high frequencies on black hole evaporation

W.G. Unruh
(
- British Columbia U.
)

- Phys.Rev.D 51 (1995) 2827-2838
•
e-Print:
- gr-qc/9409008
•
DOI:
- 10.1103/PhysRevD.51.2827

[5]

Gravity wave analogs of black holes

- Phys.Rev.D 66 (2002) 044019
•
e-Print:
- gr-qc/0205099
•
DOI:
- 10.1103/PhysRevD.66.044019

[6]

Observation of negative phase velocity waves in a water tank: A classical analogue to the Hawking effect?

Germain Rousseaux
(
- Nice U.
)
,
Christian Mathis
(
- Nice U.
)
,
Philippe Maissa
(
- Nice U.
)
,
Thomas G. Philbin
(
- St. Andrews U., Phys. Astron.
)
,
Ulf Leonhardt
(
- St. Andrews U., Phys. Astron.
)

- New J.Phys. 10 (2008) 053015
•
e-Print:
- 0711.4767
•
DOI:
- 10.1088/1367-2630/10/5/053015

[7]

Measurement of stimulated Hawking emission in an analogue system

- Phys.Rev.Lett. 106 (2011) 021302
•
e-Print:
- 1008.1911
•
DOI:
- 10.1103/PhysRevLett.106.021302

[8]

Hawking radiation without transPlanckian frequencies

R. Brout
(
- Brussels U.
)
,
S. Massar
(
- Brussels U.
)
,
R. Parentani
(
- Ecole Normale Superieure
)
,
P. Spindel
(
- UMH, Mons
)

- Phys.Rev.D 52 (1995) 4559-4568
•
e-Print:
- hep-th/9506121
•
DOI:
- 10.1103/PhysRevD.52.4559

[9]

Hawking spectrum and high frequency dispersion

Steven Corley
(
- Utrecht U. and
- Maryland U.
)
,
Ted Jacobson
(
- Utrecht U. and
- Maryland U.
)

- Phys.Rev.D 54 (1996) 1568-1586
•
e-Print:
- hep-th/9601073
•
DOI:
- 10.1103/PhysRevD.54.1568

[10]

Computing the spectrum of black hole radiation in the presence of high frequency dispersion: An Analytical approach

Steven Corley
(
- Maryland U.
)

- Phys.Rev.D 57 (1998) 6280-6291
•
e-Print:
- hep-th/9710075
•
DOI:
- 10.1103/PhysRevD.57.6280

[11]

0 1 2 3 4 S D 0.02 0.04 0.06 0.08 0.10 T 0 Figure 14. Limit o - 0 of the effective temperature (solid), Hawking temperature (dashed), and steplike result of Eq. (B9) (dotted) as functions of s, for g = J = 1, h0 = 1, and D = 0.2. The dot-dashed line shows the prediction Eq. (B15). Note the very good agreement between the exact numerical calculation and Eq. (B15)