English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Detailed studies of the shape of dust emission spectra are possible thanks tothe current instruments capable of observations in several sub-millimetre bands(e.g., Herschel and Planck). However, some controversy remains even on thebasic effects resulting from the mixing of temperatures along theline-of-sight.  Studies have suggested either a positive or a negative correlation betweenthe colour temperature T_C and the observed spectral index beta_Obs. Our aim isto show that both cases are possible and to determine the factors leading toeither behaviour. We start by studying the sum of two or three modified blackbodies of different temperature. With radiative transfer modelling, we examinethe probability distributions of the dust mass as a function of the physicaldust temperature. With these results as a guideline, we examine the (T_C,beta_Obs) relations for different sets of clouds.  Even in the case of modified blackbodies at temperatures T_0 and T_0+ DeltaT_0, the correlation between T_C and beta_Obs can be either positive ornegative. If one compares models where Delta T_0 is varied, the correlation isnegative. If the models differ in their mean temperature T_0 rather than inDelta T_0, the correlation remains positive. Radiative transfer models showthat externally heated clouds have different mean temperatures but the widthsof their temperature distributions are rather similar. Thus, the correlationbetween T_C and beta_Obs is expected to be positive. The same result applies toclouds illuminated by external radiation fields of different intensity. Forinternally heated clouds a negative correlation is the more likely alternative.  If the signal-to-noise ratio is high, the observed negative correlation couldbe explained by the temperature dependence of the dust optical properties butthat intrinsic dependence could be even steeper than the observed one.

The effect of temperature mixing on the observable (T,beta)-relation of interstellar dust clouds