Analytical approximation of the exterior gravitational field of rotating neutron stars

It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior vacuum region of numerically calculated neutron stars. Therefore we study how an Ernst potential given on the rotation axis and containing an arbitrary number of constants can be used to determine the metric everywhere. Then we review two methods to determine those constants from a numerically calculated solution. Finally, we compare the metric and physical properties of our analytic solution with the numerical data and find excellent agreement even for a small number of parameters.Comment: 9 pages, 10 figures, 3 table

Collapse in the nonlocal nonlinear Schr\"odinger equation

We discuss spatial dynamics and collapse scenarios of localized waves governed by the nonlinear Schr\"{o}dinger equation with nonlocal nonlinearity. Firstly, we prove that for arbitrary nonsingular attractive nonlocal nonlinear interaction in arbitrary dimension collapse does not occur. Then we study in detail the effect of singular nonlocal kernels in arbitrary dimension using both, Lyapunoff's method and virial identities. We find that for for a one-dimensional case, i.e. for $n=1$, collapse cannot happen for nonlocal nonlinearity. On the other hand, for spatial dimension $n\geq2$ and singular kernel $\sim 1/r^\alpha$, no collapse takes place if $\alpha<2$, whereas collapse is possible if $\alpha\ge2$. Self-similar solutions allow us to find an expression for the critical distance (or time) at which collapse should occur in the particular case of $\sim 1/r^2$ kernels. Moreover, different evolution scenarios for the three dimensional physically relevant case of Bose Einstein condensate are studied numerically for both, the ground state and a higher order toroidal state with and without an additional local repulsive nonlinear interaction. In particular, we show that presence of an additional local repulsive term can prevent collapse in those cases

Validation and data characteristics of methane and nitrous oxide profiles observed by MIPAS and processed with Version 4.61 algorithm

The ENVISAT validation programme for the atmospheric instruments MIPAS, SCIAMACHY and GOMOS is based on a number of balloon-borne, aircraft, satellite and ground-based correlative measurements. In particular the activities of validation scientists were coordinated by ESA within the ENVISAT Stratospheric Aircraft and Balloon Campaign or ESABC. As part of a series of similar papers on other species [this issue] and in parallel to the contribution of the individual validation teams, the present paper provides a synthesis of comparisons performed between MIPAS CH4 and N2O profiles produced by the current ESA operational software (Instrument Processing Facility version 4.61 or IPF v4.61, full resolution MIPAS data covering the period 9 July 2002 to 26 March 2004) and correlative measurements obtained from balloon and aircraft experiments as well as from satellite sensors or from ground-based instruments. In the middle stratosphere, no significant bias is observed between MIPAS and correlative measurements, and MIPAS is providing a very consistent and global picture of the distribution of CH4 and N2O in this region. In average, the MIPAS CH4 values show a small positive bias in the lower stratosphere of about 5%. A similar situation is observed for N2O with a positive bias of 4%. In the lower stratosphere/upper troposphere (UT/LS) the individual used MIPAS data version 4.61 still exhibits some unphysical oscillations in individual CH4 and N2O profiles caused by the processing algorithm (with almost no regularization). Taking these problems into account, the MIPAS CH4 and N2O profiles are behaving as expected from the internal error estimation of IPF v4.61 and the estimated errors of the correlative measurements

CCl 4 distribution derived from MIPAS ESA v7 data: intercomparisons, trend, and lifetime estimation

Abstract. Atmospheric emissions of carbon tetrachloride (CCl4) are regulated by the Montreal Protocol due to its role as a strong ozone-depleting substance. The molecule has been the subject of recent increased interest as a consequence of the so-called mystery of CCl4, the discrepancy between atmospheric observations and reported production and consumption. Surface measurements of CCl4 atmospheric concentrations have declined at a rate almost 3 times lower than its lifetime-limited rate, suggesting persistent atmospheric emissions despite the ban. In this paper, we study CCl4 vertical and zonal distributions in the upper troposphere and lower stratosphere (including the photolytic loss region, 70–20 hPa), its trend, and its stratospheric lifetime using measurements from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS), which operated onboard the ENVISAT satellite from 2002 to 2012. Specifically, we use the MIPAS data product generated with Version 7 of the Level 2 algorithm operated by the European Space Agency.The CCl4 zonal means show features typical of long-lived species of anthropogenic origin that are destroyed primarily in the stratosphere, with larger quantities in the troposphere and a monotonic decrease with increasing altitude in the stratosphere. MIPAS CCl4 measurements have been compared with independent measurements from other satellite and balloon-borne remote sounders, showing a good agreement between the different datasets.CCl4 trends are calculated as a function of both latitude and altitude. Negative trends of about −10 to −15 pptv decade−1 (−10 to −30 % decade−1) are found at all latitudes in the upper troposphere–lower stratosphere region, apart from a region in the southern midlatitudes between 50 and 10 hPa where the trend is positive with values around 5–10 pptv decade−1 (15–20 % decade−1). At the lowest altitudes sounded by MIPAS, we find trends consistent with those determined on the basis of long-term ground-based measurements (−10 to −13 pptv decade−1). For higher altitudes, the trend shows a pronounced asymmetry between the Northern and Southern hemispheres, and the magnitude of the decline rate increases with altitude. We use a simplified model assuming tracer–tracer linear correlations to determine CCl4 lifetime in the lower stratosphere. The calculation provides a global average lifetime of 47 (39–61) years, considering CFC-11 as the reference tracer. This value is consistent with the most recent literature result of 44 (36–58) years

Tracking azimuthons in nonlocal nonlinear media

We study the formation of azimuthons, i.e., rotating spatial solitons, in media with nonlocal focusing nonlinearity. We show that whole families of these solutions can be found by considering internal modes of classical non-rotating stationary solutions, namely vortex solitons. This offers an exhaustive method to identify azimuthons in a given nonlocal medium. We demonstrate formation of azimuthons of different vorticities and explain their properties by considering the strongly nonlocal limit of accessible solitons.Comment: 11 pages, 7 figure

Mechanostimulation of Medicago truncatula leads to enhanced levels of jasmonic acid

Wounding of plants leads to endogenous rise of jasmonic acid (JA) accompanied with the expression of a distinct set of genes. Among them are those coding for the allene oxide cyclase (AOC) that catalyses a regulatory step in JA biosynthesis, and for 1-deoxy-D-xylulose 5-phosphate synthase 2 (DXS2), an enzyme involved in isoprenoid biosynthesis. To address the question how roots and shoots of Medicago truncatula respond to mechanostimulation and wounding, M. truncatula plants were analysed in respect to JA levels as well as MtAOC1 and MtDXS2-1 transcript accumulation. Harvest-caused mechanostimulation resulted in a strong, but transient increase in JA level in roots and shoots followed by a transient increase in MtAOC1 transcript accumulation. Additional wounding of either shoots or roots led to further increased JA and MtAOC1 transcript levels in shoots, but not in roots. In situ hybridization revealed a cell-specific transcript accumulation of MtAOC1 after mechanostimulation in companion cells of the vascular tissue of the stem. AOC protein, however, was found to occur constitutively in vascular bundles. Further, transcript accumulation of MtDXS2-1 was similar to that of MtAOC1 in shoots, but its transcript levels were not enhanced in roots. Repeated touching of shoots increased MtAOC1 transcript levels and led to significantly shorter shoots and increased biomass. In conclusion, M. truncatula plants respond very sensitively to mechanostimulation with enhanced JA levels and altered transcript accumulation, which might contribute to the altered phenotype after repeated touching of plants

Validation of MIPAS-ENVISAT NO2 operational data

The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) instrument was launched aboard the environmental satellite ENVISAT into its sun-synchronous orbit on 1 March 2002. The short-lived species NO₂ is one of the key target products of MIPAS that are operationally retrieved from limb emission spectra measured in the stratosphere and mesosphere. Within the MIPAS validation activities, a large number of independent observations from balloons, satellites and ground-based stations have been compared to European Space Agency (ESA) version 4.61 operational NO₂ data comprising the time period from July 2002 until March 2004 where MIPAS measured with full spectral resolution. Comparisons between MIPAS and balloon-borne observations carried out in 2002 and 2003 in the Arctic, at mid-latitudes, and in the tropics show a very good agreement below 40 km altitude with a mean deviation of roughly 3%, virtually without any significant bias. The comparison to ACE satellite observations exhibits only a small negative bias of MIPAS which appears not to be significant. The independent satellite instruments HALOE, SAGE II, and POAM III confirm in common for the spring-summer time period a negative bias of MIPAS in the Arctic and a positive bias in the Antarctic middle and upper stratosphere exceeding frequently the combined systematic error limits. In contrast to the ESA operational processor, the IMK/IAA retrieval code allows accurate inference of NO₂ volume mixing ratios under consideration of all important non-LTE processes. Large differences between both retrieval results appear especially at higher altitudes, above about 50 to 55 km. These differences might be explained at least partly by non-LTE under polar winter conditions but not at mid-latitudes. Below this altitude region mean differences between both processors remain within 5% (during night) and up to 10% (during day) under undisturbed (September 2002) conditions and up to 40% under perturbed polar night conditions (February and March 2004). The intercomparison of ground-based NDACC observations shows no significant bias between the FTIR measurements in Kiruna (68&deg; N) and MIPAS in summer 2003 but larger deviations in autumn and winter. The mean deviation over the whole comparison period remains within 10%. A mean negative bias of 15% for MIPAS daytime and 8% for nighttime observations has been determined for UV-vis comparisons over Harestua (60&deg; N). Results of a pole-to-pole comparison of ground-based DOAS/UV-visible sunrise and MIPAS mid-morning column data has shown that the mean agreement in 2003 falls within the accuracy limit of the comparison method. Altogether, it can be indicated that MIPAS NO₂ profiles yield valuable information on the vertical distribution of NO₂ in the lower and middle stratosphere (below about 45 km) during day and night with an overall accuracy of about 10&ndash;20% and a precision of typically 5&ndash;15% such that the data are useful for scientific studies. In cases where extremely high NO₂ occurs in the mesosphere (polar winter) retrieval results in the lower and middle stratosphere are less accurate than under undisturbed atmospheric conditions

Validation of first chemistry mode retrieval results from new limb-imaging FTS GLORIA with correlative MIPAS-STR observations

We report first chemistry mode retrieval results from the new airborne limb-imaging infrared FTS (Fourier transform spectrometer) GLORIA (Gimballed Limb Observer for Radiance Imaging of the Atmosphere) and comparisons with observations by the conventional airborne limb-scanning infrared FTS MIPAS-STR (Michelson Interferometer for Passive Atmospheric Sounding - STRatospheric aircraft). For GLORIA, the flights aboard the high-altitude research aircraft M55 Geophysica during the ESSenCe campaign (ESa Sounder Campaign 2011) were the very first in field deployment after several years of development. The simultaneous observations of GLORIA and MIPAS-STR during the flight on 16 December 2011 inside the polar vortex and under conditions of optically partially transparent polar stratospheric clouds (PSCs) provided us the first opportunity to compare the observations by two different infrared FTS generations directly. We validate the GLORIA results with MIPAS-STR based on the lower vertical resolution of MIPAS-STR and compare the vertical resolutions of the instruments derived from their averaging kernels. The retrieval results of temperature, HNO3, O3, H2O, CFC-11 and CFC-12 show reasonable agreement of GLORIA with MIPAS-STR and collocated in situ observations. For the horizontally binned hyperspectral limb images, the GLORIA sampling outnumbered the horizontal cross-track sampling of MIPAS-STR by up to 1 order of magnitude. Depending on the target parameter, typical vertical resolutions of 0.5 to 2.0 km were obtained for GLORIA and are typically a factor of 2 to 4 better compared to MIPAS-STR. While the improvement of the performance, characterization and data processing of GLORIA are the subject of ongoing work, the presented first results already demonstrate the considerable gain in sampling and vertical resolution achieved with GLORIA

Validation of first chemistry mode retrieval results from the new limb-imaging FTS GLORIA with correlative MIPAS-STR observations

We report first chemistry mode retrieval results from the new airborne limb-imaging infrared FTS (Fourier transform spectrometer) GLORIA (Gimballed Limb Observer for Radiance Imaging of the Atmosphere) and comparisons with observations by the conventional airborne limb-scanning infrared FTS MIPAS-STR (Michelson Interferometer for Passive Atmospheric Sounding – STRatospheric aircraft). For GLORIA, the flights aboard the high-altitude research aircraft M55 Geophysica during the ESSenCe campaign (ESa Sounder Campaign 2011) were the very first in field deployment after several years of development. The simultaneous observations of GLORIA and MIPAS-STR during the flight on 16 December 2011 inside the polar vortex and under conditions of optically partially transparent polar stratospheric clouds (PSCs) provided us the first opportunity to compare the observations by two different infrared FTS generations directly. We validate the GLORIA results with MIPAS-STR based on the lower vertical resolution of MIPAS-STR and compare the vertical resolutions of the instruments derived from their averaging kernels. The retrieval results of temperature, HNO3, O3, H2O, CFC-11 and CFC-12 show reasonable agreement of GLORIA with MIPAS-STR and collocated in situ observations. For the horizontally binned hyperspectral limb images, the GLORIA sampling outnumbered the horizontal cross-track sampling of MIPAS-STR by up to 1 order of magnitude. Depending on the target parameter, typical vertical resolutions of 0.5 to 2.0 km were obtained for GLORIA and are typically a factor of 2 to 4 better compared to MIPAS-STR. While the improvement of the performance, characterization and data processing of GLORIA are the subject of ongoing work, the presented first results already demonstrate the considerable gain in sampling and vertical resolution achieved with GLORIA