A simple model for lensing by black holes in galactic nuclei

The lensing properties of the Plummer model with a central point mass and external shear are derived, including the image multiplicities, critical curves and caustics. This provides a simple model for a flattened galaxy with a central supermassive black hole. For the Plummer model with black hole, the maximum number of images is four, provided the black hole mass is less than an upper bound which is calculated analytically. This introduces a method to constrain black hole masses by counting images, thus applicable at cosmological distance. With shear, the maximum number of images is six and we illustrate the occurrence of an astroid caustic and two metamorphoses.     

Reconstruction of palaeosalinity using carbon isotopes and benthic associations: a comparison

Carbon and oxygen isotopes were determined on 40 recrystallized shells of Late Jurassic bivalves from the Lusitanian Basin of Portugal. In contrast with the oxygen isotopes, which exhibited considerable diagenetic distortion, the carbon isotopes are thought to preserve a record of the salinity of the Jurassic marginal marine seas in which these bivalves lived. The reconstructed palaeosalinities range from 35%o (euhaline) to 5% (oligohaline). Comparing these values with the palaeosalinity reconstructed from a palaeoecological analysis of 17 stratigraphic levels within the basin, the independently derived values agree in most cases. Strongly differing values are explained as being due to biotic factors and to diagenetic distortion of the isotopic signal; they are less likely to be due to smallscale time-averaging or insufficient microstratigraphic sampling. On the whole, the carbon isotope analyses are thought to produce reasonable palaeosalinity values, although data from infaunal, originally aragonitic bivalves appear to be less reliable than those from epifaunal bivalves with a predominantly or exclusively calcitic shell. As diagenetic alteration of the carbon isotope signal is, however, unpredictable and biotic effects on the isotopic composition are insufficiently known, palaeosalinity reconstructions based on stable isotope data should be supported by palaeoecological data.     

Intercalibration of Solar Soft X-Ray Broad Band Measurements from SOLRAD 9 through GOES-12

The two-band soft X-ray observations of solar flares made by the Naval Research Laboratory’s (NRL) SOLar RADiation (SOLRAD) satellites and by the Geostationary Orbiting Environmental Satellites (GOES) operated by the National Oceanic and Atmospheric Administration’s (NOAA) Space Weather Prediction Center have produced a nearly continuous record of solar flare observations over a period of more than forty years (1969 – 2011). However, early GOES observations (i.e., GOES-2) and later (GOES-8 and subsequent missions) are not directly comparable due to changes in the conversion of measured currents to integrated fluxes in the two spectral bands that were adopted: 0.05 – 0.3 (or 0.4) nm, which we refer to as XS and 0.1 – 0.8 nm (XL). Furthermore, additional flux adjustments, using overlapping data sets, were imposed to provide consistency of flare-flux levels from mission to mission. This article evaluates the results of these changes and compares experimental GOES-8/GOES-2 results with changes predicted from modeled flare spectra. The factors by which recent GOES observations can be matched to GOES-2 are then optimized by adapting a technique first used to extrapolate GOES X-ray fluxes above saturation using ionospheric VLF radio phase enhancements. A nearly 20% increase in published GOES-8 XL data would be required to match to GOES-2 XL fluxes, which were based on observed flare spectra. On the other hand, a factor of 1.07 would match GOES-8 and later flat-spectrum 0.1 – 0.8 nm fluxes to GOES-2 XL if the latter data were converted to a flat-spectrum basis. Finally, GOES-8 observations are compared to solar soft X-ray estimates made concurrently with other techniques. Published GOES-8 0.1 – 0.8 nm fluxes are found to be 0.59 of the mean of these other determinations. Rescaling GOES to a realistic flare spectrum and removing a 30% downward adjustment applied to the GOES-8 measurements during initial data processing would place GOES-8 and later GOES XL fluxes at 0.94 of this XL mean. GOES-2 on the same scale would lie at about 0.70 of this mean. Significant uncertainties in the absolute levels of broad band soft X-ray fluxes still remain, however.     

Über Den Aufbau Der Stern- Und Galaxienhaufen

In star clusters and in galaxy clusters the exponentn of the generalized law of Schuster statistically decreases with increasing masses of the clusters or increasing numbersL of their members. In most casesn(gal. cl.) is smaller thann(st. cl.). It is confirmed, that in larger galaxy clusters the brighter members are somewhat more concentrated at the center than the fainter members.

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Mitteilungen Serie A.     

Science-based approach for credible accounting of mitigation in managed forests

Background

The credibility and effectiveness of country climate targets under the Paris Agreement requires that, in all greenhouse gas (GHG) sectors, the accounted mitigation outcomes reflect genuine deviations from the type and magnitude of activities generating emissions in the base year or baseline. This is challenging for the forestry sector, as the future net emissions can change irrespective of actual management activities, because of age-related stand dynamics resulting from past management and natural disturbances. The solution implemented under the Kyoto Protocol (2013–2020) was accounting mitigation as deviation from a projected (forward-looking) “forest reference level”, which considered the age-related dynamics but also allowed including the assumed future implementation of approved policies. This caused controversies, as unverifiable counterfactual scenarios with inflated future harvest could lead to credits where no change in management has actually occurred, or conversely, failing to reflect in the accounts a policy-driven increase in net emissions. Instead, here we describe an approach to set reference levels based on the projected continuation of documented historical forest management practice, i.e. reflecting age-related dynamics but not the future impact of policies. We illustrate a possible method to implement this approach at the level of the European Union (EU) using the Carbon Budget Model.

Results

Using EU country data, we show that forest sinks between 2013 and 2016 were greater than that assumed in the 2013–2020 EU reference level under the Kyoto Protocol, which would lead to credits of 110–120 Mt CO₂/year (capped at 70–80 Mt CO₂/year, equivalent to 1.3% of 1990 EU total emissions). By modelling the continuation of management practice documented historically (2000–2009), we show that these credits are mostly due to the inclusion in the reference levels of policy-assumed harvest increases that never materialized. With our proposed approach, harvest is expected to increase (12% in 2030 at EU-level, relative to 2000–2009), but more slowly than in current forest reference levels, and only because of age-related dynamics, i.e. increased growing stocks in maturing forests.

Conclusions

Our science-based approach, compatible with the EU post-2020 climate legislation, helps to ensure that only genuine deviations from the continuation of historically documented forest management practices are accounted toward climate targets, therefore enhancing the consistency and comparability across GHG sectors. It provides flexibility for countries to increase harvest in future reference levels when justified by age-related dynamics. It offers a policy-neutral solution to the polarized debate on forest accounting (especially on bioenergy) and supports the credibility of forest sector mitigation under the Paris Agreement.

     

Die Kupferlagerstätte von Trattenbach (Niederösterreich)

Zusammenfassung Aus dem nördlichen Teil der Wechselserie wird die Kupferlagerstätte von Trattenbach in Niederösterreich beschrieben. Nach einem kurzen Überblick über die Erzparagenese wird ausführlich auf die Gangarten eingegangen. Die Mineralvergesellschaftung liegt heute in umgeprägter Form vor, die Lagerstätte wurde metamorph, doch sind die ursprünglichen Bildungen noch in Relikten vorhanden. Abschließend wird die Lagerstätte von Trattenbach mit stofflich ähnlichen Vorkommen dieses Gebietes verglichen. Es wird dabei auf die Schwierigkeiten eingegangen, die sich nach den neuen Untersuchungen beim Versuch ergeben, die Vererzung von Trattenbach in das in der Literatur gegebene System der ostalpinen Vererzung einzuoronen.

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Summary The copper deposit at Trattenbach (Lower Austria) in the Wechselserie is described. An informative and short review of the ore paragenesis is given, and the gangue is described in detail. The deposit has been metamorphosed, but in addition to the present mineral association, there are relicts of the original one. Finally, the Trattenbach deposit is compared with similar ones from this region, and the difficulties in fitting the results of the new investigations from this deposit into the system of ore genesis in the Eastern Alps used in the literature is discussed.

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Mit 32 Textabbildungen und 1 Karte     

Coherence analysis of granular intensity

A high resolution spectrogram of the Mg b₂ line from the quiet Sun disc centre is subjected to a coherence analysis. We find that the coherence between intensity fluctuations in the continuum and the wings of the line breaks down at a distance = 0.35 Å from line centre. From this and the r.m.s. intensity contrast as a function of we are led to the following simple model of temperature fluctuation T in the solar photosphere: A lower part (below 50 km, or ₅₀₀₀ > 0.25) with strongly inward increasing T and an upper part (above 50 km) with constant T = 75 K. The two parts are supposed to fluctuate incoherently.Mitteilungen aus dem Kiepenheuer Institut Nr. 166.     

Mutual Potential of Homogeneous Polyhedra

The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O(6 ⁿ ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.