We present details of the CARMA Large Area Star Formation Survey (CLASSy), while focusing on observations of Barnard 1. CLASSy is a CARMA Key Project that spectrally imaged N2H+, HCO+, and HCN (J=1-0 transitions) across over 800 square arcminutes of
the Perseus and Serpens Molecular Clouds. The observations have angular resolution near 7 and spectral resolution near 0.16 km/s. We imaged ~150 square arcminutes of Barnard 1, focusing on the main core, and the B1 Ridge and clumps to its southwest. N2H+ shows the strongest emission, with morphology similar to cool dust in the region, while HCO+ and HCN trace several molecular outflows from a collection of protostars in the main core. We identify a range of kinematic complexity, with N2H+ velocity dispersions ranging from ~0.05-0.50 km/s across the field. Simultaneous continuum mapping at 3 mm reveals six compact object detections, three of which are new detections. A new non-binary dendrogram algorithm is used to analyze dense gas structures in the N2H+ position-position-velocity (PPV) cube. The projected sizes of dendrogram-identified structures range from about 0.01-0.34 pc. Size-linewidth relations using those structures show that non-thermal line-of-sight velocity dispersion varies weakly with projected size, while rms variation in the centroid velocity rises steeply with projected size. Comparing these relations, we propose that all dense gas structures in Barnard 1 have comparable depths into the sky, around 0.1-0.2 pc; this suggests that over-dense, parsec-scale regions within molecular clouds are better described as flattened structures rather than spherical collections of gas. Science-ready PPV cubes for Barnard 1 molecular emission are available for download.
We present a formalism of the dynamics of internal shocks in relativistic jets where the source has a time-dependent injection velocity and mass-loss rate. The variation of the injection velocity produces a two-shock wave structure, the working surfa
ce, that moves along the jet. This new formalism takes into account the fact that momentum conservation is not valid for relativistic flows where the relativistic mass lost by radiation must be taken into account, in contrast to the classic regime. We find analytic solutions for the working surface velocity and radiated energy for the particular case of a step function variability of the injection parameters. We model two cases: a pulse of fast material and a pulse of slow material (with respect to the mean flow). Applying these models to gamma ray burst light curves, one can determine the ratio of the Lorentz factors gamma_2 / gamma_1 and the ratio of the mass-loss rates dot{m_2} / dot{m_1} of the upstream and downstream flows. As an example, we apply this model to the sources GRB 080413B and GRB 070318 and find the values of these ratios. Assuming a Lorentz factor gamma_1=100, we further estimate jet mass-loss rates between dot{m_1} ~ 10^{-5}-1 Msun.yr^{-1}. We also calculate the fraction of the injected mass lost by radiation. For GRB 070318 this fraction is ~7%. In contrast, for GRB 080413B this fraction is larger than 50%; in this case radiation losses clearly affect the dynamics of the internal shocks.
