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ABSTRACT We present the results from an analysis of deep Herschel far-infrared (far-IR) observations of the edge-on disc galaxy NGC 3079. The point spread function-cleaned Photodetector Array Camera and Spectrometer (PACS) images at 100 and 160 µm display a 25 × 25 kpc2 X-shape structure centred on the nucleus that is similar in extent and orientation to that seen in H α, X-rays, and the far-ultraviolet. One of the dusty filaments making up this structure is detected in the Spectral and Photometric Imaging Receiver 250 µm map out to ∼25 kpc from the nucleus. The match between the far-IR filaments and those detected at other wavelengths suggests that the dusty material has been lifted out of the disc by the same large-scale galactic wind that has produced the other structures in this object. A closer look at the central 10 × 10 kpc2 region provides additional support for this scenario. The dust temperatures traced by the 100–160 µm flux ratios in this region are enhanced within a biconical region centred on the active galactic nucleus, aligned along the minor axis of the galaxy, and coincident with the well-known double-lobed cm-wave radio structure and H α–X-ray nuclear superbubbles. PACS imaging spectroscopy of the inner 6 kpc region reveals broad [C ii] 158 µm emission line profiles and OH 79 µm absorption features along the minor axis of the galaxy with widths well in excess of those expected from beam smearing of the disc rotational motion. This provides compelling evidence that the cool material traced by the [C ii] and OH features directly interacts with the nuclear ionized and relativistic outflows traced by the H α, X-ray, and radio emission.
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On the Increasing Tritronquée Solutions of the Painlevé-II Equation
The increasing tritronquée solutions of the Painlevé-II equation with parameter α exhibit square-root asymptotics in the maximally-large sector |arg(x)| < 2π and have recently appeared in applications where it is necessary to understand the behavior of these solutions for complex values of α. Here these solutions are investigated from the point of view of a Riemann–Hilbert representation related to the Lax pair of Jimbo and Miwa, which naturally arises in the analysis of rogue waves of infinite order. We show that for generic complex α, all such solutions are asymptotically pole-free along the bisecting ray of the complementary sector |arg(−x)| < 1π that contains the poles far from the origin. This allows the definition of a total integral of the solution along the axis containing the bisecting ray, in which certain algebraic terms are subtracted at infinity and the poles are dealt with in the principal-value sense. We compute the value of this integral for all such solutions. We also prove that if the Painlevé-II parameter α is of the form α = ±1 + ip, p ∈ R \ {0}, one of the increasing tritronquée solutions has no poles or zeros whatsoever along the bisecting axis.
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- Award ID(s):
- 1812625
- PAR ID:
- 10093608
- Date Published:
- Journal Name:
- Symmetry, integrability and geometry: methods and applications
- Volume:
- 14
- ISSN:
- 1815-0659
- Page Range / eLocation ID:
- 125, 38 pages
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/doi.org/10.3842/SIGMA.2018.125
