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Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches

The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within ΛCDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observations nearly cover the full sky. The most generic signature of cosmic topology in the microwave background is pairs of circles with matching temperature and polarization patterns. No such circle pairs have been seen above noise in the WMAP or Planck temperature data, implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface. We translate this generic constraint into limits on the parameters that characterize manifolds with each of the nine possible non-trivial orientable Euclidean topologies, and provide a code which computes these constraints. In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6. Further, this result implies that a broader range of manifolds is observationally allowed than widely appreciated. Probing these manifolds will require more subtle statistical signatures than matched circles, such as off-diagonal correlations of harmonic coefficients.

79 ASTRONOMY AND ASTROPHYSICS↗

Emission Patterns of Solar Type III Radio Bursts: Stereoscopic Observations

Simultaneous observations of solar type III radio bursts obtained by the STEREO A, B, and WIND spacecraft at low frequencies from different vantage points in the ecliptic plane are used to determine their directivity. The heliolongitudes of the sources of these bursts, estimated at different frequencies by assuming that they are located on the Parker spiral magnetic field lines emerging from the associated active regions into the spherically symmetric solar atmosphere, and the heliolongitudes of the spacecraft are used to estimate the viewing angle, which is the angle between the direction of the magnetic field at the source and the line connecting the source to the spacecraft. The normalized peak intensities at each spacecraft Rj = Ij /[Sigma]Ij (the subscript j corresponds to the spacecraft STEREO A, B, and WIND), which are defined as the directivity factors are determined using the time profiles of the type III bursts. It is shown that the distribution of the viewing angles divides the type III bursts into: (1) bursts emitting into a very narrow cone centered around the tangent to the magnetic field with angular width of approximately 2 deg and (2) bursts emitting into a wider cone with angular width spanning from [approx] -100 deg to approximately 100 deg. The plots of the directivity factors versus the viewing angles of the sources from all three spacecraft indicate that the type III emissions are very intense along the tangent to the spiral magnetic field lines at the source, and steadily fall as the viewing angles increase to higher values. The comparison of these emission patterns with the computed distributions of the ray trajectories indicate that the intense bursts visible in a narrow range of angles around the magnetic field directions probably are emitted in the fundamental mode, whereas the relatively weaker bursts visible to a wide range of angles are probably emitted in the harmonic mode.

Thejappa, G.↗

Antarctic Circumpolar Current Transport Variability during 2003-05 from GRACE

Gravity Recovery and Climate Experiment (GRACE) gravity data spanning January 2003-November 2005 are used as proxies for ocean bottom pressure (BP) averaged over 1 month, spherical Gaussian caps 500 km in radius, and along paths bracketing the Antarctic Circumpolar Current's various fronts. The GRACE BP signals are compared with those derived from the Estimating the Circulation and Climate of the Ocean (ECCO) ocean modeling-assimilation system, and to a non-Boussinesq version of the Regional Ocean Model System (ROMS). The discrepancy found between GRACE and the models is 1.7 cm H2O (1 cm H2O approx. 1 hPa), slightly lower than the 1.9 cmH2O estimated by the authors independently from propagation of GRACE errors. The northern signals are weak and uncorrelated among basins. The southern signals are strong, with a common seasonality. The seasonal cycle GRACE data observed in the Pacific and Indian Ocean sectors of the ACC are consistent, with annual and semiannual amplitudes of 3.6 and 0.6 cmH2O (1.1 and 0.6 cm H2O with ECCO), the average over the full southern path peaks (stronger ACC) in the southern winter, on days of year 197 and 97 for the annual and semiannual components, respectively; the Atlantic Ocean annual peak is 20 days earlier. An approximate conversion factor of 3.1 Sv (Sv equiv 10(exp 6)cu m/s) of barotropic transport variability per cm H2O of BP change is estimated. Wind stress data time series from the Quick Scatterometer (QuikSCAT), averaged monthly, zonally, and over the latitude band 40(deg)- 65(deg)S, are also constructed and subsampled at the same months as with the GRACE data. The annual and semiannual harmonics of the wind stress peak on days 198 and 82, respectively. A decreasing trend over the 3 yr is observed in the three data types.

Gravity Recovery and Climate Experiment (GRACE)↗

Antarctic Circumpolar Current Transport Variability during 2003-05 from GRACE

Gravity Recovery and Climate Experiment (GRACE) gravity data spanning January 2003 - November 2005 are used as proxies for ocean bottom pressure (BP) averaged over 1 month, spherical Gaussian caps 500 km in radius, and along paths bracketing the Antarctic Circumpolar Current's various fronts. The GRACE BP signals are compared with those derived from the Estimating the Circulation and Climate of the Ocean (ECCO) ocean modeling-assimilation system, and to a non-Boussinesq version of the Regional Ocean Model System (ROMS). The discrepancy found between GRACE and the models is 1.7 cm(sub H2O) (1 cm(sub H2O) similar to 1 hPa), slightly lower than the 1.9 cm(sub H2O) estimated by the authors independently from propagation of GRACE errors. The northern signals are weak and uncorrelated among basins. The southern signals are strong, with a common seasonality. The seasonal cycle GRACE data observed in the Pacific and Indian Ocean sectors of the ACC are consistent, with annual and semiannual amplitudes of 3.6 and 0.6 cm(sub H2O) (1.1 and 0.6 cm(sub H2O) with ECCO), the average over the full southern path peaks (stronger ACC) in the southern winter, on days of year 197 and 97 for the annual and semiannual components, respectively; the Atlantic Ocean annual peak is 20 days earlier. An approximate conversion factor of 3.1 Sv ( Sv equivalent to 10(exp 6) m(exp 3) s(exp -1)) of barotropic transport variability per cm(sub H2O) of BP change is estimated. Wind stress data time series from the Quick Scatterometer (QuikSCAT), averaged monthly, zonally, and over the latitude band 40 de - 65 deg S, are also constructed and subsampled at the same months as with the GRACE data. The annual and semiannual harmonics of the wind stress peak on days 198 and 82, respectively. A decreasing trend over the 3 yr is observed in the three data types.

oceanographic regions↗