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A Simple Predictive Model for the Structure of the Oceanic Pycnocline Anand Gnanadesikan (March 26, 1999) Science 283 (5410), 2077-2079

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A Simple Predictive Model for the Structure of the Oceanic Pycnocline Anand Gnanadesikan (March 26, 1999) Science 283 (5410), 2077-2079 R EPORTS about 1.02, the true spectral resolution is around 9. P. Møller and P. Jakobsen, Astron. Astrophys. 228, 299 16. S. G. Djorgovski et al., GCN Circular 216 (1999). 8 Å, consistent with the measured width of the (1990). 17. J. Hjorth et al., Science 283, 2073 (1999). 18. We thank the NOT director for continued support to our spectral features. The average line profile, con- 10. M. Pettini, D. L. King, L. J. Smith, R. W. Hunstead, Astrophys. J. 478, 536 (1997); M. Pettini, L. J. Smith, GRB programme. This research was supported by the Danish structed from the Fe II lines above 6000 Å, D. L. King, R. W. Hunstead, ibid. 486, 665 (1997). Natural Science Research Council (SNF), the Icelandic Coun- cil of Science and the University of Iceland Research Fund. appears unresolved. This implies that the ab- 11. J. S. Bloom et al., in preparation, preprint available at The Nordic Optical Telescope is operated on the island of La sorbing clouds have a velocity dispersion of http://www.lanl.gov/abs/astro-ph/9902182. 2 Palma jointly by Denmark, Finland, Iceland, Norway, and less than 100 km s 1 in the rest frame. 12. A. S. Fruchter et al., in preparation, preprint available Sweden in the Spanish Observatorio del Roque de los at http://www.lanl.gov/abs/astro-ph/9902236. Muchachos of the Instituto de Astrofı´sica de Canarias. The The observed BATSE gamma-ray fluence of 13. S. Holland and J. Hjorth, Astron. Astrophys., in press, 6 3 –4 –2 data presented here have been taken using ALFOSC, which GRB 990123 is 5.09 0.02 10 erg cm for preprint also available at http://www.lanl.gov/abs/ is owned by the Instituto de Astrofı´sica de Andalucı´a (IAA) energies above 20 keV (14). In Table 2 we give astro-ph/9903175. and operated at the Nordic Optical Telescope under agree- the luminosity distance and the inferred isotropic 14. R. M. Kippen, GCN Circular 224 (1999). ment between IAA and the Astronomical Observatory of the 5 15. See Thermonuclear Supernovae, P. Ruiz-Lapuente, R. University of Copenhagen. energy output in various cosmologies for z Canal, J. Isern, Eds. (Kluwer Academic, Dordrecht, 1.600. A lower limit to the isotropic energy Netherlands, 1997). 23 February 1999; accepted 9 March 1999 release in gamma-rays alone is obtained in an V V 5 Einstein-de Sitter Universe with ( 0 L) (1,0). For a upper limit to the Hubble constant of H , 80 km s–1 Mpc–1 we find a lower limit of A Simple Predictive Model for 0 0.5 times the rest mass of a neutron star (1.4 MJ 5 2.5 3 1054 erg) or ;2.5 times its binding the Structure of the Oceanic energy. For a set of currently observationally V V 5 favored cosmological parameters ( 0 L) 5 21 21 Pycnocline (0.2, 0.8) and H0 65 km s Mpc we derive an energy release in gamma-rays equivalent to Anand Gnanadesikan 1.8 neutron stars. This is 45 times larger than the total energy emitted in all wavelengths by the A simple theory for the large-scale oceanic circulation is developed, relating most luminous Type II supernova, including pycnocline depth, Northern Hemisphere sinking, and low-latitude upwelling to neutrino emission (15). pycnocline diffusivity and Southern Ocean winds and eddies. The results show on October 14, 2016 If the GRB 990123 is located at z . 1.6 our that Southern Ocean processes help maintain the global ocean structure and upper limit on z translates into an upper limit on that pycnocline diffusion controls low-latitude upwelling. 3 55 . the energy release of 1.3 10 erg for H0 50 –1 –1 V V 5 km s Mpc and ( 0 L) (0.2, 0.8). More- The main oceanic pycnocline delineates the sphere (NH) leads to the conversion of light over, if the z 5 1.6 absorption system is associ- boundary between light, low-latitude sur- water to dense water, which flows southward at ated with the main mass component along the face waters and dense, abyssal waters a rate Tn. Some portion of this flux upwells line of sight to GRB 990123, the upper limit on whose properties are set in the high lati- within the Southern Ocean, where precipitation z leads to a required lensing surface mass density tudes (Fig. 1A). The physical properties at causes it to become lighter. This light water is of a factor of about three to four times that in work in the pycnocline and the flows driven then exported to the north at a rate Ts. That normal galaxy lenses. This effectively rules out by the pressure gradients associated with portion of the NH sinking flux that is not bal- the possibility that GRB 990123 was lensed the pycnocline affect the transport of heat, anced by upwelling within the Southern Ocean (multiply imaged) (16) by this mass. salt, and nutrients through the ocean. Here upwells through the low-latitude pycnocline at a http://science.sciencemag.org/ Any of the above numbers indicates a huge I examine the relative importance of sever- rate Tu. I have ignored deep flows associated isotropic energy release which is difficult to al key processes in setting the structure of with the Antarctic Bottom Water (AABW), as- reconcile with current physical theories. In the the pycnocline. These are (i) vertical diffu- suming that they have little direct effect on the absence of lensing one resolution of this energy sion within the pycnocline, (ii) upwelling pycnocline as they are returned at mid-depth (3). problem is that the gamma-ray emission from through the pycnocline in low latitudes, Instead I focus on the effect of Northern and GRB 990123 was not isotropic. This interpre- (iii) the conversion of light to dense water Southern Hemisphere mode waters on the lower tation is consistent with polarimetric observa- associated with the formation of North At- pycnocline. Downloaded from tions (17) and is supported by the breaks ob- lantic Deep Water, (iv) Southern Ocean These fluxes can be connected to the depth served in the light curve (5, 8, 12) which sug- winds, and (v) Southern Ocean eddies. Pre- of the pycnocline, reducing the equations gov- gest that the optical afterglow may have been vious scaling theories of the pycnocline (1) erning the large-scale oceanic circulation to a beamed. have only included the first three processes. single cubic equation in the pycnocline depth D. The western Atlantic Ocean contains a bowl The first step is to derive an expression for Tn, of waters lighter than 1027.5 kg m23 ;1000 m the NH sinking flux. It is common to assume References and Notes deep, with some upward deflection at the equa- that this flow is proportional to the density dif- 1. G. J. Fishman and C. A. Meegan, Annu. Rev. Astron. Astrophys. 33, 415 (1995). tor (2). A tongue of fresh Antarctic Intermediate ference between the light and dense water Dr 2. M. R. Metzger et al., Nature 387, 879 (1997); S. R. Water (AAIW) penetrates northward from the (4). Because northward flow of AAIW and the Kulkarni et al., ibid. 393, 35 (1998); S. G. Djorgovski Southern Ocean and a tongue of salty North southward flow of NADW are essentially pres- et al., Astrophys, J. 507, L25 (1998). 3. J. Heise, in preparation. Atlantic Deep Water (NADW) moves south- sure-driven, there is a level of no motion be- 4. S. C. Odewahn, J. S. Bloom, S. R. Kulkarni, GCN Circular ward. In the conceptual framework I propose tween the two flows at which the velocities and 201 (1999); IAU Circular 7094 (1999). (Fig. 1C), surface cooling in the Northern Hemi- hence the pressure gradients are negligible. The 5. S. R. Kulkarni et al., Nature, in press, preprint mass of water above the level of no motion is also available at http://www.lanl.gov/abs/astro- ph/9902272. thus the same at all latitudes. Because the warm 6. C. W. Akerlof and T. A. McKay, GCN Circular 205 National Oceanic and Atmospheric Administration waters in low latitudes are less dense, they take (1999); IAU Circular 7100 (1999); Nature, in press. (NOAA) Geophysical Fluid Dynamics Laboratory and up more volume and the surface height is higher 7. A more comprehensive analysis of the absorption Atmospheric and Oceanic Sciences Program, Prince- system will be presented in a paper in preparation. ton University, Post Office Box CN710, Princeton, NJ at the equator than in high latitudes. This surface 8. A. J. Castro-Tirado et al., Science 283, 2069 (1999). 08544, USA. E-mail: [email protected] height difference will cause a pressure differ- www.sciencemag.org SCIENCE VOL 283 26 MARCH 1999 2077 R EPORTS ence Dp within the water column Fig. 1. (A) Average po- tential density refer- Dp , DrgD/r 5 g9D (1) enced to 1000 m in the r Atlantic Ocean. (B) Av- 9 erage salinity in the where D is the depth of the light water and g western Atlantic ocean. is the reduced gravity. According to classical (C) Schematic of the boundary layer theory (5) this pressure dif- flows which the simple ference will produce a frictional flow near the theoretical model pre- eastern or western boundary (4, 6) sented here assumes are responsible for the ]2v 1 ]p A V density and salinity 5 3 h Ah ] 2 r ] 2 structure. x y Lm Cg9D 5 1/3b2/3 5 Ah V n (2) Ly where V is the north-south velocity within the 5 b 1/3 boundary layer, Lm (Ah/ ) is the width n of the frictional boundary layer Ly is the north-south distance over which the gradient in layer depth occurs, b is the north-south gradient of the Coriolis parameter, Ah is the eddy viscosity, and C is a constant that incor- porates effects of geometry and boundary layer structure.
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