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

Additions:

""

Famaey et al., 2005, described six kinematic groups: three streams, Hyades/Pleiades, Sirius and Hercules, a group of young giants, high velocity stars and a smooth background distribution. Famaey found a total stream membership of over 25%, but using statistical analysis it is only possible to put least bounds on stream membership. After taking into consideration the fact that the velocity distribution is highly structured by colour, one sees that streams represent the bulk of the population.

""
""

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.

""

Deletions:

""

Famaey et al., 2005, described six kinematic groups: three streams, Hyades/Pleiades, Sirius and Hercules, a group of young giants, high velocity stars and a smooth background distribution. Famaey found a total stream membership of over 25%, but using statistical analysis it is only possible to put least bounds on stream membership. After taking into consideration the fact that the velocity distribution is highly structured by colour, one sees that streams represent the bulk of the population.

""
""

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.

""

Additions:

""

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

""

Deletions:

""

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 0.1 to 0.2

""

Additions:

Deletions:

Additions:

Deletions:

Additions:

""

Famaey et al., 2005, described six kinematic groups: three streams, Hyades/Pleiades, Sirius and Hercules, a group of young giants, high velocity stars and a smooth background distribution. Famaey found a total stream membership of over 25%, but using statistical analysis it is only possible to put least bounds on stream membership. After taking into consideration the fact that the velocity distribution is highly structured by colour, one sees that streams represent the bulk of the population.

""
""

Large stars burn faster and hotter. So, blue stars are necessarily young. The bluest stars, with B − V < 0.04 (~B-A0) reflect recent star formation. The Pleiades stream consists largely of new-born stars, originating in our own spiral arm and with low eccentricities and typical orbits near to apocentre. We distinguish it from a stream with orbits close to pericentre which contains young as well as old stars, and which we have called the Alpha Lacertae stream. It appears that Famaey’s young giants belong to the Alpha Lacertae stream. "" For 0.04 ≤ B − V < 0.16 (~A1-A5), the velocity distribution is concentrated in the Pleiades and Sirius streams. ====""""The Local Standard Of Rest==== It is customary in kinematic analyses of the stellar population to denote velocity in the direction of the galactic centre by ""U""., in the direction of rotation by ""V""., and perpendicular to the galactic plane by ""W"". The solar motion relative to the LSR is ""(U0, V0, W0)"". The usual way to calculate the LSR is to calculate the mean velocity of a stellar population, and to correct ""V0"" for asymmetric drift. The method assumes a well-mixed distribution, but the observed kinematic distribution is highly structured, and divides into six populations each with distinct motion and stellar composition. Motions of thin disk stars in the ""W""-direction may be treated as a low amplitude oscillation due to the gravity of the disc, and as independent of orbital motion in the ""U-V plane. It is thus not unreasonable to calculate W0 as the mean motion of a population. However, in the absence of knowledge of the causes for streams, there is no way to relate the statistical properties of their motion to ""U0"" and ""V0"". "" 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. "" Deletions: "" Famaey et al., 2005 described six kinematic groups: three streams, Hyades/Pleiades, Sirius and Hercules, a group of young giants, high velocity stars and a smooth background distribution. Famaey found a total stream membership of over 25%, but it is only using statistical analysis it is only possible to put least bounds on stream membership. After taking into consideration the fact that the velocity distribution is highly structured by colour, one sees that streams represent the bulk of the population. "" "" Large stars burn faster and hotter. So, blue stars are necessarily young. The bluest stars, with B − V < 0.04 (~B-A0) reflect recent star formation. The Pleiades stream consists largely of new-born stars, originating in our own spiral arm and with low eccentricities and typical orbits near to apocentre. We distinguished it from a stream with orbits close to pericentre which contains young as well as old stars. We have called this the Alpha Lacertae stream. It appears that Famaey’s young giants belong to the Alpha Lacertae stream. "" For0.04 ≤ B − V < 0.16 (~A1-A5), the velocity distribution is concentrated in the Pleiades and Sirius streams. ====""""Simulation==== The Local Standard Of Rest It is customary in kinematic analyses of the stellar population to denote velocity in the direction of the galactic centre by U., in the direction of rotation by V., and perpendicular to the galactic plane by W. The solar motion relative to the LSR is (U0, V0, W0). The usual way to calculate the LSR is to calculate the mean velocity of a stellar population, and to correct V0 for asymmetric drift. The method assumes a well-mixed distribution, but the observed kinematic distribution is highly structured, and divides into six populations each with distinct motion and stellar composition. Motions of thin disk stars in the W-direction may be treated as a low amplitude oscillation due to the gravity of the disc, and as independent of orbital motion in the U-V plane. It is thus not unreasonable to calculate W0 as the mean motion of a population. However, in the absence of knowledge of the causes for streams, there is no way to relate the statistical properties of their motion to U0 and V0. "" 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. The Eccentricity Distribution "" 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, s, 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. In practice the distribution is concentrated at particular values, corresponding to stream motions. "" Revision [117] Edited on 2009-04-28 05:24:19 by CharlesFrancis Additions: "" We smoothed the velocity distribution by replacing each discrete point with a two-dimensional Gaussian function and finding the sum. A standard deviation of 1 gave a clear contour plot. We distinguish the Hyades and Pleiades streams, since the velocity distributions shows separate peaks, and because these streams contain different distributions of stellar types and ages. There is a large and well dispersed stream centred at (U, V) ≈ (25, −23) , which we have called the Alpha Ceti stream, after the brightest star we identified with this motion. "" Large stars burn faster and hotter. So, blue stars are necessarily young. The bluest stars, with B − V < 0.04 (~B-A0) reflect recent star formation. The Pleiades stream consists largely of new-born stars, originating in our own spiral arm and with low eccentricities and typical orbits near to apocentre. We distinguished it from a stream with orbits close to pericentre which contains young as well as old stars. We have called this the Alpha Lacertae stream. It appears that Famaey’s young giants belong to the Alpha Lacertae stream. "" For0.04 ≤ B − V < 0.16 (~A1-A5), the velocity distribution is concentrated in the Pleiades and Sirius streams. "" We restricted the population to mature stars, red giants and dwarfs aged over 2Gyrs, The distribution is is markedly different from that of the whole population. There is now no peak for the Pleiades stream, and the Sirius stream is also much less prominent. "" "" 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. "" 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 0.1 to 0.2 "" Deletions: "" We smoothed the velocity distribution by replacing each discrete point with a two-dimensional Gaussian function and finding the sum. A standard deviation of 1 gave a clear contour plot. We distinguish the Hyades and Pleiades streams, since the velocity distributions shows separate peaks, and because these streams contain different distributions of stellar types and ages. There is a large and well dispersed stream centred at (U, V) ≈ (25, −23) "" Large stars burn faster and hotter. So, blue stars are necessarily young. The bluest stars, with B − V < 0.04 (~B-A0) reflect recent star formation. The Pleiades stream consists largely of new-born stars, originating in our own spiral arm and with low eccentricities and typical orbits near to apocentre. We distinguished it from a stream with orbits close to pericentre which contains young as well as old stars. We have called this the Alpha Lacertae stream. It appears that Famaey’s young giants belong to the Alpha Lacertae stream. "" For0.04 ≤ B − V < 0.16 (~A1-A5), the velocity distribution is concentrated in the Pleiades and Sirius streams. "" We restricted the population to mature stars, red giants and dwarfs aged over 2Gyrs, The distribution is is markedly different from that of the whole population. There is now no peak for the Pleiades stream, and the Sirius stream is also much less marked. . "" "" 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. "" Eccentricity distribution (based on the LSR found in this paper) for the entire population, for stars closer to apocentre (dots) and stars closer to pericentre (dashes), as defined by position with respect to the semi-latus rectum. The number of stars closer to apocentre is expected to outweigh the number closer to pericentre, by at most about 20% for , and more for larger eccentricities. "" Revision [116] Edited on 2009-04-28 04:19:33 by CharlesFrancis Additions: "" Famaey et al., 2005 described six kinematic groups: three streams, Hyades/Pleiades, Sirius and Hercules, a group of young giants, high velocity stars and a smooth background distribution. Famaey found a total stream membership of over 25%, but it is only using statistical analysis it is only possible to put least bounds on stream membership. After taking into consideration the fact that the velocity distribution is highly structured by colour, one sees that streams represent the bulk of the population. "" "" We smoothed the velocity distribution by replacing each discrete point with a two-dimensional Gaussian function and finding the sum. A standard deviation of 1 gave a clear contour plot. We distinguish the Hyades and Pleiades streams, since the velocity distributions shows separate peaks, and because these streams contain different distributions of stellar types and ages. There is a large and well dispersed stream centred at (U, V) ≈ (25, −23) "" "" Large stars burn faster and hotter. So, blue stars are necessarily young. The bluest stars, with B − V < 0.04 (~B-A0) reflect recent star formation. The Pleiades stream consists largely of new-born stars, originating in our own spiral arm and with low eccentricities and typical orbits near to apocentre. We distinguished it from a stream with orbits close to pericentre which contains young as well as old stars. We have called this the Alpha Lacertae stream. It appears that Famaey’s young giants belong to the Alpha Lacertae stream. "" "" For0.04 ≤ B − V < 0.16 (~A1-A5), the velocity distribution is concentrated in the Pleiades and Sirius streams. "" "" The Hyades stream becomes more prominent than the Sirius stream for 0.16 ≤ B − V < 0.4 (~A6-A9). "" "" The Hyades stream dominates the velocity distributions (by density, not by total population) for dwarves with 0.4 ≤ B − V < 0.56 (~F) "" "" and 0.56 ≤ B − V < 0.8 (~G). "" "" We restricted the population to mature stars, red giants and dwarfs aged over 2Gyrs, The distribution is is markedly different from that of the whole population. There is now no peak for the Pleiades stream, and the Sirius stream is also much less marked. . "" "" 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, s, 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. In practice the distribution is concentrated at particular values, corresponding to stream motions. "" "" Eccentricity distribution (based on the LSR found in this paper) for the entire population, for stars closer to apocentre (dots) and stars closer to pericentre (dashes), as defined by position with respect to the semi-latus rectum. The number of stars closer to apocentre is expected to outweigh the number closer to pericentre, by at most about 20% for , and more for larger eccentricities. "" Deletions: "" [[http://arxiv.org/abs/astro-ph/0409579 Famaey et al., 2005]] described six kinematic groups: three streams, Hyades/Pleiades, Sirius and Hercules, a group of young giants, high velocity stars and a smooth background distribution. Famaey found a total stream membership of over 25%, but it is only using statistical analysis it is only possible to put least bounds on stream membership. After taking into consideration the fact that the velocity distribution is highly structured by colour, one sees that streams represent the bulk of the population. "" We smoothed the velocity distribution by replacing each discrete point with a two-dimensional Gaussian function and finding the sum. A standard deviation of 1 gave a clear contour plot. We distinguish the Hyades and Pleiades streams, since the velocity distributions shows separate peaks, and because these streams contain different distributions of stellar types and ages. There is a large and well dispersed stream centred at (U, V) ≈ (25, −23) Large stars burn faster and hotter. So, blue stars are necessarily young. The bluest stars, with B − V < 0.04 (~B-A0) reflect recent star formation. The Pleiades stream consists largely of new-born stars, originating in our own spiral arm and with low eccentricities and typical orbits near to apocentre. We distinguished it from a stream with orbits close to pericentre which contains young as well as old stars. We have called this the Alpha Lacertae stream. It appears that Famaey’s young giants belong to the Alpha Lacertae stream. For0.04 ≤ B − V < 0.16 (~A1-A5), the velocity distribution is concentrated in the Pleiades and Sirius streams. The Hyades stream becomes more prominent than the Sirius stream for 0.16 ≤ B − V < 0.4 (~A6-A9). The Hyades stream dominates the velocity distributions (by density, not by total population) for dwarves with 0.4 ≤ B − V < 0.56 (~F) and 0.56 ≤ B − V < 0.8 (~G). We restricted the population to mature stars, red giants and dwarfs aged over 2Gyrs, The distribution is is markedly different from that of the whole population. There is now no peak for the Pleiades stream, and the Sirius stream is also much less marked. . [[SpiralStructure 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 [[VelocityDistribution#LocalStandardOfRest local standard of rest]]. In [[Papers#LSR 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 [[http://en.wikipedia.org/wiki/Standard_gravitational_parameter standard gravitational parameter]] for an orbit about a mass M. For a [[http://en.wikipedia.org/wiki/Keplerian_orbit Keplerian orbit]] the [[http://en.wikipedia.org/wiki/Eccentricity_vector 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 [[http://en.wikipedia.org/wiki/Laplace-Runge-Lenz_vector 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, s, 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 [[http://en.wikipedia.org/wiki/Apocenter apocentre]] and underdensity at [[http://en.wikipedia.org/wiki/Apocenter 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. In practice the distribution is concentrated at particular values, corresponding to stream motions. Eccentricity distribution (based on the LSR found in this paper) for the entire population, for stars closer to apocentre (dots) and stars closer to pericentre (dashes), as defined by position with respect to the semi-latus rectum. The number of stars closer to apocentre is expected to outweigh the number closer to pericentre, by at most about 20% for , and more for larger eccentricities. Revision [115] Edited on 2009-04-28 03:35:22 by CharlesFrancis Additions: "" [[http://arxiv.org/abs/astro-ph/0409579 Famaey et al., 2005]] described six kinematic groups: three streams, Hyades/Pleiades, Sirius and Hercules, a group of young giants, high velocity stars and a smooth background distribution. Famaey found a total stream membership of over 25%, but it is only using statistical analysis it is only possible to put least bounds on stream membership. After taking into consideration the fact that the velocity distribution is highly structured by colour, one sees that streams represent the bulk of the population. "" Deletions: "" [[http://arxiv.org/abs/astro-ph/0409579 Famaey et al., 2005]] described six kinematic groups: three streams, Hyades/Pleiades, Sirius and Hercules, a group of young giants, high velocity stars and a smooth background distribution. Famaey found a total stream membership of over 25%, but it is only using statistical analysis it is only possible to put least bounds on stream membership. After taking into consideration the fact that the velocity distribution is highly structured by colour, one sees that streams represent the bulk of the population. "" Revision [114] The oldest known version of this page was created on 2009-04-28 03:28:45 by CharlesFrancis Page History :: 2010-07-09 03:04:14 :: Owner: CharlesFrancis :: Search: Valid XHTML 1.0 Transitional :: Valid CSS :: Powered by WikkaWiki Page was generated in 0.2653 seconds