Discovery of new low-excitation planetary nebulae

We report a multi-wavelength study of four new planetary nebula (PN) candidates selected from the INT/WFC Photometric Ha Survey of the Northern Galactic Plane (IPHAS) and Deep Sky Hunter (DSH) catalogues. We present mid-resolution optical spectra of these PNs. The PN status of our sample was confirmed by optical narrow-band images and mid-resolution spectra. Based on the locations of these objects in the log (Ha/[N II]) versus log (Ha/[S II]) diagnostic diagram, we conclude that these sources are evolved lowexcitation PNs. The optical and infrared appearances of these newly discovered PNs are discussed. Three of the new nebulae studied here are detected in infrared and have low infrared-to-radio flux ratios, probably suggesting that they are evolved. Furthermore, we derive the dynamical ages and distances of these nebulae and study the spectral energy distribution for one of them with extensive infrared archival data.Comment: 11 pages, 9 figures, 6 tables, accepted for publication on Astronomy & Astrophysic

Theories of Linear Response in BCS Superfluids and How They Meet Fundamental Constraints

We address the importance of symmetry and symmetry breaking on linear response theories of fermionic BCS superfluids. The linear theory of a noninteracting Fermi gas is reviewed and several consistency constraints are verified. The challenge to formulate linear response theories of BCS superfluids consistent with density and spin conservation laws comes from the presence of a broken U(1)$_{\textrm{EM}}$ symmetry associated with electromagnetism (EM) and we discuss two routes for circumventing this. The first route follows Nambu's integral-equation approach for the EM vertex function, but this method is not specific for BCS superfluids. We focus on the second route based on a consistent-fluctuation-of-the order-parameter (CFOP) approach where the gauge transformation and the fluctuations of the order parameter are treated on equal footing. The CFOP approach allows one to explicitly verify several important constraints: The EM vertex satisfies not only a Ward identity which guarantees charge conservation but also a $Q$-limit Ward identity associated with the compressibility sum rule. In contrast, the spin degrees of freedom associated with another U(1)$_z$ symmetry are not affected by the Cooper-pair condensation that breaks only the U(1)$_{\textrm{EM}}$ symmetry. As a consequence the collective modes from the fluctuations of the order parameter only couple to the density response function but decouple from the spin response function, which reflects the different fates of the two U(1) symmetries in the superfluid phase. Our formulation lays the ground work for application to more general theories of BCS-Bose Einstein Condensation crossover both above and below $T_c$.Comment: Review on gauge invariance and charge-spin difference of BCS theory. 27 pages, 1 figure. Some typos have been correcte