Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class

Harju, Antti J.; Mickelsson, Jouko

doi:10.1017/is014007001jkt274

Cited by 12 publications

(49 citation statements)

References 11 publications

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“…As discussed in Sect. 1, the latter position is close to one of the positions observed in o-H 2 D + by Harju et al (2006;10 ′′ . 4 offset from their source Ori B9 N).…”

Section: Orion B9 In a Wider Context Of H 2 D + Studies Of Star-formisupporting

confidence: 81%

“…Caselli et al (2008) also searched for o-H 2 D + (1 1, 0 − 1 1, 1 ) emission towards a position near (10 ′′ . 4 offset) to one of those observed by Harju et al (2006), but no line was detected.…”

Section: Introductionmentioning

confidence: 52%

“…We note that Harju et al (2006) already used APEX to search for o-H 2 D + (1 1, 0 −1 1, 1 ) emission towards three selected positions near and around IRAS 05405 (the N 2 H + (1 − 0) peaks found by Caselli & Myers (1994)), but the target positions were offset from the submillimetre dust continuum peaks that we later uncovered, rendering the line detections fairly weak ( 3.7σ). Caselli et al (2008) also searched for o-H 2 D + (1 1, 0 − 1 1, 1 ) emission towards a position near (10 ′′ .…”

Section: Introductionmentioning

confidence: 64%

“…We also note that Ori B9 is often considered to be a massive dense core in the literature (e.g. Harju et al 2006;Caselli et al 2008;Pillai et al 2012), but the source is composed of a system of low-mass dense cores. Caselli et al (2008) used a somewhat different method to calculate the o-H 2 D + column densities (e.g.…”

Section: Orion B9 In a Wider Context Of H 2 D + Studies Of Star-formimentioning

confidence: 94%

“…The o-H 2 D + line widths derived by Caselli et al (2008) for their starless and protostellar cores are 0.33 − 0.73 km s −1 and 0.51 − 1.49 km s −1 (the authors adopted a line width of 0.42 km s −1 for Ori B9 from Harju et al (2006), but that value refers to the starless source Ori B9 N, and is hence neglected from the latter range). The corresponding averages are 0.47 km s −1 and 0.93 km s −1 .…”

Section: Orion B9 In a Wider Context Of H 2 D + Studies Of Star-formimentioning

confidence: 99%

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APEX observations of ortho-H₂D⁺ towards dense cores in the Orion B9 filament

Miettinen

2020

A&A

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Context. Initial conditions and very early stages of star formation can be probed through spectroscopic observations of deuterated molecular species. Aims. We aim to determine the ortho-H 2 D + properties (e.g. column density and fractional abundance with respect to H 2 ) in a sample of dense cores in the Orion B9 star-forming filament, and to compare those with the previously determined source characteristics, in particular with the gas kinetic temperature, [N 2 D + ]/[N 2 H + ] deuterium fractionation, and level of CO depletion. Methods. We used the Atacama Pathfinder EXperiment (APEX) telescope to observe the 372 GHz o-H 2 D + (J Ka, Kc = 1 1, 0 − 1 1, 1 ) line towards three prestellar cores and three protostellar cores in Orion B9. We also employed our previous APEX observations of C 17 O, C 18 O, N 2 H + , and N 2 D + line emission, and 870 µm dust continuum emission towards the target sources.Results. The o-H 2 D + (1 1, 0 − 1 1, 1 ) line was detected in all three prestellar cores, but in only one of the protostellar cores. The corresponding o-H 2 D + abundances were derived to be ∼ (12 − 30) × 10 −11 and ∼ 6 × 10 −11 . Two additional spectral lines, DCO + (5 − 4) and N 2 H + (4 − 3), were detected in the observed frequency bands with high detection rates of 100% and 83%, respectively. We did not find any significant correlations among the explored parameters, although our results are mostly consistent with theoretical expectations. Also, the Orion B9 cores were found to be consistent with the relationship between the o-H 2 D + abundance and gas temperature obeyed by other low-mass dense cores. The o-H 2 D + abundance was found to decrease as the core evolves. Conclusions. The o-H 2 D + abundances in the Orion B9 cores are in line with those found in other low-mass dense cores and larger than derived for high-mass star-forming regions. The higher o-H 2 D + abundance in prestellar cores compared to that in cores hosting protostars is to be expected from chemical reactions where higher concentrations of gas-phase CO and elevated gas temperature accelerate the destruction of H 2 D + . The validity of using the [o-H 2 D + ]/[N 2 D + ] abundance ratio as an evolutionary indicator, which has been proposed for massive clumps, remains to be determined when applied to these target cores. Similarly, the behaviour of the [o-H 2 D + ]/[DCO + ] ratio as the source evolves was found to be ambiguous. Still larger samples and observations of additional deuterated species are needed to explore these potential evolutionary indicators further. The low radial velocity of the line emission from one of the targeted prestellar cores, SMM 7 (∼ 3.6 km s −1 versus the systemic Orion B9 velocity of ∼ 9 km s −1 ), suggests that it is a chance superposition seen towards Orion B9. Overall, as located in a dynamic environment of the Orion B molecular cloud, the Orion B9 filament provides an interesting target system to investigate the deuterium-based chemistry, and further observations of species like para-H 2 D + and D 2 H + would be of...

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“…As discussed in Sect. 1, the latter position is close to one of the positions observed in o-H 2 D + by Harju et al (2006;10 ′′ . 4 offset from their source Ori B9 N).…”

Section: Orion B9 In a Wider Context Of H 2 D + Studies Of Star-formisupporting

confidence: 81%

Section: Introductionmentioning

confidence: 52%

Section: Introductionmentioning

confidence: 64%

Section: Orion B9 In a Wider Context Of H 2 D + Studies Of Star-formimentioning

confidence: 94%

Section: Orion B9 In a Wider Context Of H 2 D + Studies Of Star-formimentioning

confidence: 99%

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APEX observations of ortho-H₂D⁺ towards dense cores in the Orion B9 filament

Miettinen

2020

A&A

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Twisted K-theory constructions in the case of a decomposable Dixmier–Douady class II: Topological and equivariant models

Harju

2014

Journal of Geometry and Physics

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bstract This is a study of twisted K-theory on a product space TˆM . The twisting comes from a decomposable cup product class which applies the 1-cohomology of T and the 2-cohomology of M . In the case of a topological product, we give a concrete realization for the gerbe associated to a cup product characteristic class and use this to realize twisted K 1 -theory elements in terms of supercharge sections in a Fredholm bundle. The nontriviality of this construction is proved. Equivariant twisted K-theory and gerbes are studied in the product case as well. This part applies Lie groupoid theory. Superconnection formalism is used to provide a construction for characteristic polynomials which are used to extract information from the twisted K-theory classes.MSC: 19L50, 53C08, 22A22.

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Extensions of lattice groups, gerbes and chiral fermions on a torus

Mickelsson

2017

Journal of Geometry and Physics

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Motivated by the topological classification of hamiltonians in condensed matter physics (topological insulators) we study the relations between chiral Dirac operators coupled to an abelian vector potential on a torus in 3 and 1 space dimensions. We find that a large class of these hamiltonians in three dimensions is equivalent, in K theory, to a family of hamiltonians in just one space dimension but with a different abelian gauge group.The moduli space of U(1) gauge connections over a torus with a fixed Chern class is again a torus up to a homotopy. Gerbes over a n-torus can be realized in terms of extensions of the lattice group acting in a real vector space. The extension comes from the action of the lattice group (thought of as "large" gauge transformations, homomorphisms from the torus to U(1)) in the Fock space of chiral fermions. Interestingly, the K theoretic classification of Dirac operators coupled to vector potentials in this setting in 3 dimensions can be related to families of Dirac operators on a circle with gauge group the 3-torus.

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Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class

Cited by 12 publications

References 11 publications

APEX observations of ortho-H₂D⁺ towards dense cores in the Orion B9 filament

APEX observations of ortho-H₂D⁺ towards dense cores in the Orion B9 filament

Twisted K-theory constructions in the case of a decomposable Dixmier–Douady class II: Topological and equivariant models

Extensions of lattice groups, gerbes and chiral fermions on a torus

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Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class

Cited by 12 publications

References 11 publications

APEX observations of ortho-H2D+ towards dense cores in the Orion B9 filament

APEX observations of ortho-H2D+ towards dense cores in the Orion B9 filament

Twisted K-theory constructions in the case of a decomposable Dixmier–Douady class II: Topological and equivariant models

Extensions of lattice groups, gerbes and chiral fermions on a torus

Contact Info

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APEX observations of ortho-H₂D⁺ towards dense cores in the Orion B9 filament

APEX observations of ortho-H₂D⁺ towards dense cores in the Orion B9 filament