 Spiral structure draws orbits into eccentricities dictated by the pitch angle of the arms. As a result, very few stars are found on circular orbits, leading to a minimum in the velocity distribution at the local standard of rest. In Calculation of the Local Standard of Rest from 20 574 Local Stars in the New Hipparcos Reduction with Known Radial Velocities, Erik Anderson and I used this minimum to find the LSR, obtaining (U0, V0, W0) = (7.5 ± 1.0, 13.5 ± 0.3, 6.8 ± 0.1 ) km s−1.
"" where v is the velocity vector, r is the radial vector, and μ = GM is the standard gravitational parameter for an orbit about a mass M. For a Keplerian orbit the eccentricity vector is a constant of the motion. Stellar orbits are not strictly elliptical, but the orbit will approximate an ellipse at each part of its motion, and the eccentricity vector remains a useful measure (the Laplace-Runge-Lenz vector, which is the same up to a multiplicative factor, is also used to describe perturbations to elliptical orbits). We smoothed the eccentricity distribution by replacing each discrete point with a two dimensional Gaussian function and finding the sum. Standard deviation is used as a smoothing parameter. A standard deviation of 0.005 gave a clear contour plot. In a well-mixed population, eccentricity vectors will be spread smoothly in all directions, with an overdensity at apocentre and underdensity at pericentre, because of the increased orbital velocity at pericentre and because stars at apocentre come from a denser population nearer the galactic centre. This is not seen in the plot. The distribution is concentrated at particular values, corresponding to stream motions. |
""
"" Eccentricity distribution for the entire population, for stars closer to apocentre (green) and stars closer to pericentre (red), as defined by position with respect to the semi-latus rectum. The bulk of local stars have eccentricities in the range 0.07 to 0.2 |
""
""The modal value of eccentricity in the Milky Way is a little above 0.1. This indicates a much lower pitch angle than is used in four armed spirals. We fitted a symmetric double spiral with a pitch angle 4.92° and 8.2 kpc bar to the hydrogen maps of Oort, Kerr and Westerhout and those of Levine, Blitz and Heiles (2006). There is a subjective element in the quality of such a fit, but the two-armed spiral seems to us to better follow the line of the hydrogen clouds, while the more open four armed spirals appear to follow clouds bridging the true line of the arms.
The top plot shows density, the second shows height.
""""
"" It is found from isochrone aging (the position of stars on a Hertzsprung-Russell diagram that the Hercules stream, and the high eccentricity stars in the Alpha Ceti stream consist of old stars, with ages predominantly greater than about 9 Gyrs. Eccentricities are too high for normal spiral arm motion. Orbits with the right eccentricity (~0.29) can be aligned to spiral structure spanning both arms, as in the diagram. The stability of these of configurations shows that the Milky Way has been a grand-design two-armed spiral for about 9 Gyrs. |
""
Deletions:
"" Spiral structure draws orbits into eccentricities dictated by the pitch angle of the arms. As a result, very few stars are found on circular orbits, leading to a minimum in the velocity distribution at the local standard of rest. In Calculation of the Local Standard of Rest from 20 574 Local Stars in the New Hipparcos Reduction with Known Radial Velocities, Erik Anderson and I used this minimum to find the LSR, obtaining (U0, V0, W0) = (7.5 ± 1.0, 13.5 ± 0.3, 6.8 ± 0.1 ) km s−1.
"" where v is the velocity vector, r is the radial vector, and μ = GM is the standard gravitational parameter for an orbit about a mass M. For a Keplerian orbit the eccentricity vector is a constant of the motion. Stellar orbits are not strictly elliptical, but the orbit will approximate an ellipse at each part of its motion, and the eccentricity vector remains a useful measure (the Laplace-Runge-Lenz vector, which is the same up to a multiplicative factor, is also used to describe perturbations to elliptical orbits). We smoothed the eccentricity distribution by replacing each discrete point with a two dimensional Gaussian function and finding the sum. Standard deviation is used as a smoothing parameter. A standard deviation of 0.005 gave a clear contour plot. In a well-mixed population, eccentricity vectors will be spread smoothly in all directions, with an overdensity at apocentre and underdensity at pericentre, because of the increased orbital velocity at pericentre and because stars at apocentre come from a denser population nearer the galactic centre. This is not seen in the plot. The distribution is concentrated at particular values, corresponding to stream motions. |
""
"" Eccentricity distribution for the entire population, for stars closer to apocentre (green) and stars closer to pericentre (red), as defined by position with respect to the semi-latus rectum. The bulk of local stars have eccentricities in the range 0.07 to 0.2 |
""
""The modal value of eccentricity in the Milky Way is a little above 0.1. This indicates a much lower pitch angle than is used in four armed spirals. We fitted a symmetric double spiral with a pitch angle 4.92° and 8.2 kpc bar to the hydrogen maps of Oort, Kerr and Westerhout and those of Levine, Blitz and Heiles (2006). There is a subjective element in the quality of such a fit, but the two-armed spiral seems to us to better follow the line of the hydrogen clouds, while the more open four armed spirals appear to follow clouds bridging the true line of the arms.
The top plot shows density, the second shows height.
""""
"" It is found from isochrone aging (the position of stars on a Hertzsprung-Russell diagram that the Hercules stream, and the high eccentricity stars in the Alpha Ceti stream consist of old stars, with ages predominantly greater than about 9 Gyrs. Eccentricities are too high for normal spiral arm motion. Orbits with the right eccentricity (~0.29) can be aligned to spiral structure spanning both arms, as in the diagram. The stability of these of configurations shows that the Milky Way has been a grand-design two-armed spiral for about 9 Gyrs. |
""
Additions:
""The modal value of eccentricity in the Milky Way is a little above 0.1. This indicates a much lower pitch angle than is used in four armed spirals. We fitted a symmetric double spiral with a pitch angle 4.92° and 8.2 kpc bar to the hydrogen maps of Oort, Kerr and Westerhout and those of Levine, Blitz and Heiles (2006). There is a subjective element in the quality of such a fit, but the two-armed spiral seems to us to better follow the line of the hydrogen clouds, while the more open four armed spirals appear to follow clouds bridging the true line of the arms.
The top plot shows density, the second shows height.
Deletions:
""The modal value of eccentricity in the Milky Way is a little above 0.1. This indicates a much lower pitch angle than is used in four armed spirals. We fitted a symmetric double spiral with a pitch angle 4.92° and 8.2 kpc bar to the hydrogen maps of Oort, Kerr and Westerhout and those of Levine, Blitz and Heiles (2006). There is a subjective element in the quality of such a fit, but the two-armed spiral seems to us to better follow the line of the hydrogen clouds, while the more open four armed spirals appear to follow clouds bridging the true line of the arms.
The top plot shows density, the second shows height.
Additions:
""The modal value of eccentricity in the Milky Way is a little above 0.1. This indicates a much lower pitch angle than is used in four armed spirals. We fitted a symmetric double spiral with a pitch angle 4.92° and 8.2 kpc bar to the hydrogen maps of Oort, Kerr and Westerhout and those of Levine, Blitz and Heiles (2006). There is a subjective element in the quality of such a fit, but the two-armed spiral seems to us to better follow the line of the hydrogen clouds, while the more open four armed spirals appear to follow clouds bridging the true line of the arms.
The top plot shows density, the second shows height.
Deletions:
""The modal value of eccentricity in the Milky Way is a little above 0.1. This indicates a much lower pitch angle than is used in four armed spirals. We fitted a symmetric double spiral with a pitch angle 4.92° and 8.2 kpc bar to the hydrogen maps of Oort, Kerr and Westerhout and those of Levine, Blitz and Heiles (2006). There is a subjective element in the quality of such a fit, but the two-armed spiral seems to us to better follow the line of the hydrogen clouds, while the more open four armed spirals appear to follow clouds bridging the true line of the arms.
The top plot from shows density, the second shows height.
Additions:
The top plot from shows density, the second shows height.
|
""Deletions:
|
""
Additions:
""The modal value of eccentricity in the Milky Way is a little above 0.1. This indicates a much lower pitch angle than is used in four armed spirals. We fitted a symmetric double spiral with a pitch angle 4.92° and 8.2 kpc bar to the hydrogen maps of Oort, Kerr and Westerhout and those of Levine, Blitz and Heiles (2006). There is a subjective element in the quality of such a fit, but the two-armed spiral seems to us to better follow the line of the hydrogen clouds, while the more open four armed spirals appear to follow clouds bridging the true line of the arms.
It is now possible to understand that the major local stellar streams are not dissolved clusters, but actually show the spiral structure of the Milky Way. The Alpha Ceti stream is large and disperse. It consists of stars, like the Sun, in the Orion arm. As can be seen in the [[rqgravity.net/SpiralStructure#Simulation spiral structure animation]], stars move on the inward part of their orbits along the arm with widely varying velocities. The Hyades stream consists of stars from the Centaurus arm, crossing the Orion arm at the same part of their orbit. The Pleiades stream consists of [[rqgravity.net/SpiralStructure#StarFormation new born stars]], with low eccentricities, created when outgoing gas clouds from the Centaurus arm meet with the Orion Arm. The Sirius stream consists of moderately young stars with relatively high eccentricities, whose orbits have not yet settled into alignment with the arms.
""| It is found from isochrone aging (the position of stars on a Hertzsprung-Russell diagram that the Hercules stream, and the high eccentricity stars in the Alpha Ceti stream consist of old stars, with ages predominantly greater than about 9 Gyrs. Eccentricities are too high for normal spiral arm motion. Orbits with the right eccentricity (~0.29) can be aligned to spiral structure spanning both arms, as in the diagram. The stability of these of configurations shows that the Milky Way has been a grand-design two-armed spiral for about 9 Gyrs. |
""
Deletions:
""The modal value of eccentricity in the Milky Way is a little above 0.1. This indicates a much lower pitch angle than is used in four armed spirals. We fitted a symmetric double spiral with a pitch angle 4.92° and 8.2 kpc bar to the hydrogen maps of Oort, Kerr and Westerhout and those of Levine, Blitz and Heiles (2006). There is a subjective element in the quality of such a fit, but the two-armed spiral seems to us to better follow the line of the hydrogen clouds, while the more open four armed spirals appear to follow clouds bridging the true line of the arms.
It is now possible to understand that the major local stellar streams are not dissolved clusters, but actually show the spiral structure of the Milky Way. The Alpha Ceti stream is large and disperse. It consists of stars, like the Sun, in the Orion arm. As can be seen in [[SpiralStructure#Simulation animation]], stars move on the inward part of their orbits along the arm with widely varying velocities. The Hyades stream consists of stars from the Centaurus arm, crossing the Orion arm at the same part of their orbit. The Pleiades stream consists of [[SpiralStructure#StarFormation new born stars]], with low eccentricities, created when outgoing gas clouds from the Centaurus arm meet with the Orion Arm. The Sirius stream consists of moderately young stars with relatively high eccentricities, whose orbits have not yet settled into alignment with the arms.
"" It is found from isochrone aging (the position of stars on a [[http://en.wikipedia.org/wiki/Hertzsprung-Russell_diagram Hertzsprung-Russell diagram]] that the Hercules stream, and the high eccentricity stars in the Alpha Ceti stream consist of old stars, with ages predominantly greater than about 9Gyrs. Eccentricities are too high for normal spiral arm motion. Orbits with the right eccentricity (~0.29) can be aligned to spiral structure spanning both arms, as in the diagram. The stability of these of configurations shows that the Milky Way has been a grand-design two-armed spiral for about 9 Gyrs. |
""
Additions:
"" ""
""| where v is the velocity vector, r is the radial vector, and μ = GM is the standard gravitational parameter for an orbit about a mass M. For a Keplerian orbit the eccentricity vector is a constant of the motion. Stellar orbits are not strictly elliptical, but the orbit will approximate an ellipse at each part of its motion, and the eccentricity vector remains a useful measure (the Laplace-Runge-Lenz vector, which is the same up to a multiplicative factor, is also used to describe perturbations to elliptical orbits). We smoothed the eccentricity distribution by replacing each discrete point with a two dimensional Gaussian function and finding the sum. Standard deviation is used as a smoothing parameter. A standard deviation of 0.005 gave a clear contour plot. In a well-mixed population, eccentricity vectors will be spread smoothly in all directions, with an overdensity at apocentre and underdensity at pericentre, because of the increased orbital velocity at pericentre and because stars at apocentre come from a denser population nearer the galactic centre. This is not seen in the plot. The distribution is concentrated at particular values, corresponding to stream motions. |
""
====""""The Neutral Hydrogen Distribution====
""The modal value of eccentricity in the Milky Way is a little above 0.1. This indicates a much lower pitch angle than is used in four armed spirals. We fitted a symmetric double spiral with a pitch angle 4.92° and 8.2 kpc bar to the hydrogen maps of Oort, Kerr and Westerhout and those of Levine, Blitz and Heiles (2006). There is a subjective element in the quality of such a fit, but the two-armed spiral seems to us to better follow the line of the hydrogen clouds, while the more open four armed spirals appear to follow clouds bridging the true line of the arms.
|
""
Deletions:
"" ""
""| where v is the velocity vector, r is the radial vector, and μ = GM is the standard gravitational parameter for an orbit about a mass M. For a Keplerian orbit the eccentricity vector is a constant of the motion. Stellar orbits are not strictly elliptical, but the orbit will approximate an ellipse at each part of its motion, and the eccentricity vector remains a useful measure (the Laplace-Runge-Lenz vector, which is the same up to a multiplicative factor, is also used to describe perturbations to elliptical orbits). We smoothed the eccentricity distribution by replacing each discrete point with a two dimensional Gaussian function and finding the sum. Standard deviation is used as a smoothing parameter. A standard deviation of 0.005 gave a clear contour plot. In a well-mixed population, eccentricity vectors will be spread smoothly in all directions, with an overdensity at apocentre and underdensity at pericentre, because of the increased orbital velocity at pericentre and because stars at apocentre come from a denser population nearer the galactic centre. This is not seen in the plot. The distribution is concentrated at particular values, corresponding to stream motions. |
""
The Neutral Hydrogen Distribution
""| The modal value of eccentricity in the Milky Way is a little above 0.1 (Figure ). This indicates a much lower pitch angle than is used in four armed spirals. We fitted a symmetric double spiral with a pitch angle 4.92° and 8.2 kpc bar to the hydrogen maps of [[http://adsabs.harvard.edu/full/1958MNRAS.118..379O Oort, Kerr and Westerhout]] and those of [[http://adsabs.harvard.edu/abs/2006Sci...312.1773L Levine, Blitz and Heiles (2006)]]. There is a subjective element in the quality of such a fit, but the two-armed spiral seems to us to better follow the line of the hydrogen clouds, while the more open four armed spirals appear to follow clouds bridging the true line of the arms. |
""
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