Bidiagonalization of (k, k + 1)-tridiagonal matrices

Takahira, Souichi; Sogabe, Tomohiro; Usuda, Tsuyoshi Sasaki

doi:10.1515/spma-2019-0002

Cited by 26 publications

(22 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such interaction (cloud-cloud collisions) should sufficiently compress the clouds and may induce massive star formation. The process of cloud-cloud collisions have been long investigated theoretically (e.g., Scoville et al 1986;Habe & Ohta 1992;Tan 2000;Dobbs 2015;Duarte-Cabral et al 2011;Matsumoto et al 2015;Wu et al 2017aWu et al , 2017bTakahira et al 2018). A clear observational evidence of the actual cloud-cloud collisions was first discovered by Hasegawa et al (1994) toward the Sgr B2 giant molecular cloud.…”

Section: Introductionmentioning

confidence: 99%

Cloud–cloud collision in the DR 21 cloud as a trigger of massive star formation

Dobashi

Shimoikura

Katakura

et al. 2019

Publications of the Astronomical Society of Japan

View full text Add to dashboard Cite

We report on a possible cloud-cloud collision in the DR 21 region, which we found through molecular observations with the Nobeyama 45-m telescope. We mapped an area of ∼ 8 × 12 around the region with twenty molecular lines including the 12 CO(J = 1−0) and 13 CO(J = 1−0) emission lines, and sixteen of them were significantly detected. Based on the 12 CO and 13 CO data, we found five distinct velocity components in the observed region, and we call molecular gas associated with these components "−42","−22", "−3", "9", and "17" km s −1 clouds taking after their typical radial velocities. The −3 km s −1 cloud is the main filamentary cloud (∼ 31,000 M ) associated with young massive stars such as DR21 and DR21(OH), and the 9 km s −1 cloud is a smaller cloud (∼ 3, 400 M ) which may be an extension of the W75 region in the north. The other clouds are much smaller. We found a clear anticorrelation in the distributions of the −3 and 9 km s −1 clouds, and detected faint 12 CO emission having intermediate velocities bridging the two clouds at their intersection. These facts strongly indicate that the two clouds are colliding against each other. In addition, we found that DR21 and DR21(OH) are located in the periphery of the densest part of the 9 km s −1 cloud, which is consistent with results of recent numerical simulations of cloud-cloud collisions. We therefore suggest that the −3 and 9 km s −1 clouds are colliding, and that the collision induced the massive star formation in the DR21 cloud. The interaction of the −3 and 9 km s −1 clouds was previously suggested by Dickel, Dickel, and Wilson (1978), and our results strongly support their hypothesis of the interaction.

show abstract

Section: Introductionmentioning

confidence: 99%

Cloud–cloud collision in the DR 21 cloud as a trigger of massive star formation

Dobashi

Shimoikura

Katakura

et al. 2019

Publications of the Astronomical Society of Japan

View full text Add to dashboard Cite

show abstract

“…The CCC mechanism triggers a massive star formation on the collision surface between two molecular clouds (Habe & Ohta 1992). A collision of two molecular clouds having different velocities makes an intermediate velocity component at the collision surface, which is seen as a broad bridge feature on the positionvelocity map (e.g., Hawarth et al 2015;Takahira et al 2018).…”

Section: Introductionmentioning

confidence: 99%

A systematic study of Galactic infrared bubbles along the Galactic plane with AKARI and Herschel. II. Spatial distributions of dust components around the bubbles

Hanaoka

Kaneda

Suzuki

et al. 2019

Publications of the Astronomical Society of Japan

View full text Add to dashboard Cite

Galactic infrared (IR) bubbles, which can be seen as shell-like structures at mid-IR wavelengths, are known to possess massive stars within their shell boundaries. In our previous study, Hanaoka et al. (2019) expanded the research area to the whole Galactic plane (0 • ≤ l ≤ 360 • , |b|≤ 5 • ) and studied systematic differences in the shell morphology and the IR luminosity of the IR bubbles between inner and outer Galactic regions. In this study, utilizing high spatial-resolution data of AKARI and WISE in the mid-IR and Herschel in the far-IR, we investigate the spatial distributions of dust components around each IR bubble to discuss the relation between the star-formation activity and the dust properties of the IR bubbles. For the 247 IR bubbles studied in Hanaoka et al. (2019), 165 IR bubbles are investigated in this study, which have the Herschel data (|b|≤ 1 • ) and known distances. We created their spectral energy distributions on a pixel-by-pixel basis around each IR bubble, and decomposed them with a dust model consisting of polycyclic aromatic hydrocarbons (PAHs), hot dust, warm dust and cold dust. As a result, we find that the offsets of dust heating sources from the shell centers in inner Galactic regions are systematically larger than those in outer Galactic regions. Many of the broken bubbles in inner Galactic regions show large angles between the offset and the broken shell directions from the center. Moreover, the spatial variations of the PAH intensity and cold dust emissivity around the IR bubbles in inner Galactic regions are larger than those in outer Galactic regions. We discuss these results in light of the interstellar environments and the formation mechanism of the massive stars associated with the IR bubbles.

show abstract

“…Interestingly, one of the motivations for such matrices is precisely the band matrix as A n defined in ; compare equation in the work of Egerváry . Two of the more appealing extensions can be found in other works …”

Section: K‐tridiagonal Matricesmentioning

confidence: 99%

“…2 Two of the more appealing extensions can be found in other works. 3,4 A more detailed account on both eigenvalues and eigenvectors was first established in the work of Losonczi. 5 Basically, the characteristic polynomial P n, (x) ofÃ n , can be factorized as…”

Section: K-tridiagonal Matricesmentioning

confidence: 99%

Eigenpairs of some particular band Toeplitz matrices: A comment

Fonseca

2019

Numerical Linear Algebra App

View full text Add to dashboard Cite

Bidiagonalization of (k, k + 1)-tridiagonal matrices

Cited by 26 publications

References 6 publications

Cloud–cloud collision in the DR 21 cloud as a trigger of massive star formation

Cloud–cloud collision in the DR 21 cloud as a trigger of massive star formation

A systematic study of Galactic infrared bubbles along the Galactic plane with AKARI and Herschel. II. Spatial distributions of dust components around the bubbles

Eigenpairs of some particular band Toeplitz matrices: A comment

Contact Info

Product

Resources

About