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Thread: Sidereal, anomalistic and draconic periods of Sun in Milky Way

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    Sidereal, anomalistic and draconic periods of Sun in Milky Way

    What are the observed values and observational error bars for these values and their ratios? And what do they reveal about mass distribution in Milky Way?
    I gather that the present estimates for the values are 230, 150 and 60 million years respectively.

    Sun has anomalistic orbital period shorter than sidereal, because the mass distribution of Milky Way crosses Sunīs orbit. The anomalistic period of Sun must be shorter than 230 million years, but also necessarily longer than 115 million years. Guestimates are around 150 million years, but not sure what the observational bounds are. If Milky Way were spherical then there might be no disc, but you could still define draconic period relative to any arbitrarily chosen plane. And the draconic period would then be equal to sidereal - even if the anomalistic period is much shorter. Actually, the same would happen if the disc were plainly marked, but the bulk of Milky Way mass were in spherical dark matter crown and also spherical bulge of old, relatively dim stars, with the disc being a bright but low mass wisp of gas and young bright stars - the draconic period should be close to sidereal, while anomalistic would be much shorter. That it is the opposite - the draconic period at 60 million years is the much shorter one - suggests that either the disc is massive compared to dark matter crown, or else the dark matter is also a disc and not a sphere.

    How is the draconic period of Sun measured?

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    If I understand correctly, none of these periods can be measured, for the simple reason that we would have to be around for hundreds of millions of years to observe a complete cycle. The best we can do is to estimate what they would be based on our estimates of the galaxy's mass distribution and the known current velocity of the Sun.

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    Addendum: The more accurately we estimate the mass distribution by whatever means, the more accurately we can calculate the orbital elements by means of numerical integration.

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    Quote Originally Posted by Hornblower View Post
    If I understand correctly, none of these periods can be measured, for the simple reason that we would have to be around for hundreds of millions of years to observe a complete cycle. The best we can do is to estimate what they would be based on our estimates of the galaxy's mass distribution and the known current velocity of the Sun.
    How can we estimate Milky Wayīs mass distribution, then?

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    Quote Originally Posted by chornedsnorkack View Post
    How can we estimate Milky Wayīs mass distribution, then?
    If I am not mistaken, it is done by observing the radial velocities of stars and nebulae all over the galaxy, and following up with appropriate statistical analysis. Information on the transverse velocities, as indicated by proper motion, would be a huge help, and perhaps GAIA will provide some useful data for remote objects for which proper motion is unobservable by prior methods. We would need some input from experts in celestial mechanics to go into any more detail.

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    What is the definition of "local standard of rest"?

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    This might help:

    http://adsabs.harvard.edu/abs/2015MNRAS.449..162H

    The basic idea is to pick a sample of objects which you think are in a nice, circular orbit in the plane of the Milky Way -- so, either clouds of gas or very young stars -- and do your best to measure their properties.

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    Is "local standard of rest" defined by reference to circular orbit, or by reference to average over objects?
    Note that Solar Neighbourhood contains stars at various tangential speeds. A star with no radial speed may be on a circular orbit (in that case at the tangential speed of circular orbit), or at periapse of an eccentric one (in that case at faster tangential speed) or at apoapse (in that case at slower tangential speed). Solar Neighbourhood also holds stars with radial speed, on inbound or outbound legs of eccentric orbits. On average, their tangential speeds should be slower than the speed of circular orbit.
    "Rotation curve" is the average over all these groups of stars. So appreciably different from the speed of the tangential speed of circular orbit.
    Or is the rotation curve of true circular orbit speeds also observed?

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    Quote Originally Posted by chornedsnorkack View Post
    Is "local standard of rest" defined by reference to circular orbit, or by reference to average over objects?
    Note that Solar Neighbourhood contains stars at various tangential speeds. A star with no radial speed may be on a circular orbit (in that case at the tangential speed of circular orbit), or at periapse of an eccentric one (in that case at faster tangential speed) or at apoapse (in that case at slower tangential speed). Solar Neighbourhood also holds stars with radial speed, on inbound or outbound legs of eccentric orbits. On average, their tangential speeds should be slower than the speed of circular orbit.
    "Rotation curve" is the average over all these groups of stars. So appreciably different from the speed of the tangential speed of circular orbit.
    Or is the rotation curve of true circular orbit speeds also observed?
    My bold. It is my understanding, from numerous sources, that "rotation curve" is a common expression for a graph of the average orbital speeds of groups of stars at various distances from the center of the galaxy as a function of the respective distances. I don't see this as a factor in determining a local standard of rest.

    If I am not mistaken, a local standard of rest is a local frame of reference chosen to make the average value of the observed local velocities come out to zero. A star that is reckoned as stationary in that frame may or may not be in a circular orbit around the center of the galaxy. I see some disagreement about that detail in various online sources, so caveat lector.

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    My bold.
    Quote Originally Posted by Hornblower View Post
    It is my understanding, from numerous sources, that "rotation curve" is a common expression for a graph of the average orbital speeds of groups of stars at various distances from the center of the galaxy as a function of the respective distances. I don't see this as a factor in determining a local standard of rest.

    If I am not mistaken, a local standard of rest is a local frame of reference chosen to make the average value of the observed local velocities come out to zero. A star that is reckoned as stationary in that frame may or may not be in a circular orbit around the center of the galaxy.
    You just defined both through average of stars present of a location. What is the difference between these two?

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    Quote Originally Posted by chornedsnorkack View Post
    My bold.
    You just defined both through average of stars present of a location. What is the difference between these two?
    Please bear with me as I try again. I will concede the possibility that my technical writing is not always as good as I think it is.

    1. Local standard of rest: We examine a small portion of the galaxy within a few hundred light years of the Sun, where we can get good parallax, proper motion and radial velocity information for the stars in close to us. We will find that the velocities of the stars relative to the Sun are all over the place, but they average out to about 12 miles per second away from Hercules. We then invent a local frame of reference whose origin is moving at the same speed and direction. This sample of stars now averages out as stationary with respect to that frame, which we call "local standard of rest," with the Sun moving at 12 miles per second toward Hercules. Please note that this is a kinematic statistical exercise that tells us nothing about the Sun's orbital motion around the center of the galaxy. To determine that we need radial velocity data for much more remote objects all over the sky.

    2. Suppose we have inferred our orbital velocity around the center of the galaxy. Now we look at appropriate samples of stars and determine their respective orbital motions by whatever means. At any given radius we will find scatter in the velocities, depending on the orbital elements of the individual objects, so we calculate the mean values we find at each radius. When we plot these velocities as a function of the radius from the center, we get a graph commonly called a "rotation curve". Not my preferred term, as many people misinterpret a flat curve as if the galaxy is rotating like a rigid disk, which it is not. I would prefer "orbital velocity curve" at the cost of one more word.

    Clear as mud?

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    Quote Originally Posted by Hornblower View Post
    Please bear with me as I try again. I will concede the possibility that my technical writing is not always as good as I think it is.

    1. Local standard of rest: We examine a small portion of the galaxy within a few hundred light years of the Sun, where we can get good parallax, proper motion and radial velocity information for the stars in close to us. We will find that the velocities of the stars relative to the Sun are all over the place, but they average out to about 12 miles per second away from Hercules. We then invent a local frame of reference whose origin is moving at the same speed and direction. This sample of stars now averages out as stationary with respect to that frame, which we call "local standard of rest," with the Sun moving at 12 miles per second toward Hercules.
    Following so far...
    Quote Originally Posted by Hornblower View Post
    Please note that this is a kinematic statistical exercise that tells us nothing about the Sun's orbital motion around the center of the galaxy. To determine that we need radial velocity data for much more remote objects all over the sky.
    How could we predict orbital motion from velocity data?
    Quote Originally Posted by Hornblower View Post
    2. Suppose we have inferred our orbital velocity around the center of the galaxy. Now we look at appropriate samples of stars and determine their respective orbital motions by whatever means. At any given radius we will find scatter in the velocities, depending on the orbital elements of the individual objects, so we calculate the mean values we find at each radius.
    Is that exercise any different from what we did in 1) for solar neighbourhood?
    Quote Originally Posted by Hornblower View Post
    When we plot these velocities as a function of the radius from the center, we get a graph commonly called a "rotation curve". Not my preferred term, as many people misinterpret a flat curve as if the galaxy is rotating like a rigid disk, which it is not. I would prefer "orbital velocity curve" at the cost of one more word.
    But radial velocity is also a part of orbital velocity, yet not of rotation.

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    Quote Originally Posted by chornedsnorkack
    How could we predict orbital motion from velocity data?
    That is a very good question, and I do not know how the celestial mechanics people do it from radial velocity without observable transverse velocity to go with it. The extreme case would be for stars along the circle that is approximated by our own galactic orbit. Since they are all going about the same speed that we are, there would be virtually no radial velocity no matter how fast we and they are going. At other orbital radii we would see some radial velocity in certain directions, but I can imagine a range of possible solutions. I must yield to real experts for answers. We could get a rough idea from radial velocities of other galaxies relative to us if we could somehow allow for their individual motions.

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    Quote Originally Posted by Hornblower
    1. Local standard of rest: We examine a small portion of the galaxy within a few hundred light years of the Sun, where we can get good parallax, proper motion and radial velocity information for the stars in close to us. We will find that the velocities of the stars relative to the Sun are all over the place, but they average out to about 12 miles per second away from Hercules. We then invent a local frame of reference whose origin is moving at the same speed and direction. This sample of stars now averages out as stationary with respect to that frame, which we call "local standard of rest," with the Sun moving at 12 miles per second toward Hercules.
    2. Suppose we have inferred our orbital velocity around the center of the galaxy. Now we look at appropriate samples of stars and determine their respective orbital motions by whatever means. At any given radius we will find scatter in the velocities, depending on the orbital elements of the individual objects, so we calculate the mean values we find at each radius.
    Quote Originally Posted by chornedsnorkack
    Is that exercise any different from what we did in 1) for solar neighbourhood?
    No, if I am not mistaken.
    But radial velocity is also a part of orbital velocity, yet not of rotation.
    I don't understand what you mean by that. When we speak of rotation of a disk galaxy, we are referring to the collective orbital motion of the stars in the disk. Are you thinking of rotation in some sense that is different from stellar orbital motion?

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    Quote Originally Posted by Hornblower View Post
    I don't understand what you mean by that. When we speak of rotation of a disk galaxy, we are referring to the collective orbital motion of the stars in the disk. Are you thinking of rotation in some sense that is different from stellar orbital motion?
    My point is that "collective orbital motion" and individual orbital motion are different things.
    Individual stars possess both tangential velocity and also a radial velocity on inward or outward legs of eccentric orbits in galaxy.
    In Solar Neighbourhood, assuming that there are roughly equal number of stars on inward and outward legs present, the radial velocities would average to zero. The tangential velocities do not average to zero in Solar Neighbourhood.
    Yet although radial velocities cancel out for "collective motion", they are highly relevant for individual orbital motion.

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    Quote Originally Posted by chornedsnorkack View Post
    My point is that "collective orbital motion" and individual orbital motion are different things.
    Individual stars possess both tangential velocity and also a radial velocity on inward or outward legs of eccentric orbits in galaxy.
    In Solar Neighbourhood, assuming that there are roughly equal number of stars on inward and outward legs present, the radial velocities would average to zero. The tangential velocities do not average to zero in Solar Neighbourhood.
    You appear to be referring to the tangential and radial components of the orbital motions with respect to the center of the galaxy, as reckoned in an inertial frame of reference. The invented frame of reference called "local standard of rest" is moving in such a way that the average of both components zeros out as reckoned in that moving frame. It is useful for statistical studies of the deviations of the motions of individual stars from the overall mean motion.
    Yet although radial velocities cancel out for "collective motion", they are highly relevant for individual orbital motion.
    I don't think I ever said otherwise. If you think I did, please point it out. I am here to learn how to improve my technical writing as well as to comment.

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    In support of my earlier brief statement that the "local standard of rest" refers to a hypothetical circular orbit, not a real one, I present a portion of the introduction to "The asymmetric drift, the local standard of rest, and implications from RAVE data"

    http://adsabs.harvard.edu/abs/2013A%26A...557A..92G


    The asymmetric drift of a stellar population is defined as the
    difference between the velocity of a hypothetical set of stars
    possessing perfectly circular orbits and the mean rotation
    velocity of the population under consideration. The velocity
    of the former is called the standard of rest. If the measurements
    are made at the solar Galactocentric radius, it is the local
    standard of rest, or LSR.

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    Quote Originally Posted by StupendousMan View Post
    In support of my earlier brief statement that the "local standard of rest" refers to a hypothetical circular orbit, not a real one, I present a portion of the introduction to "The asymmetric drift, the local standard of rest, and implications from RAVE data"
    So, the point
    that the speed of circular orbit and the average speed of stars present at a region, are two very different things
    is agreed with.
    "Local standard of rest" is suggested to refer to the circular orbit speed;
    the difference is termed as "asymmetric drift".
    Correct?

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    What is the number of Milky Way arms that intersect a circle centered on Milky Way centre and passing through the present position of Sun?

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    Depends a little on how you count, but I think the consensus at this point is four.
    Conserve energy. Commute with the Hamiltonian.

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    What is the radial group velocity of the spiral arms, and what is its direction?
    Like, if you followed a star at present position of Sun, but at a circular orbit, what would be the period between the arm density waves passing such a corotating spot?

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    Just from a quick search, here's what looks like a rough answer:
    Quote Originally Posted by Karen Masters
    We pass through a major spiral arm about every 100 million years, taking about 10 million years to go through.
    Conserve energy. Commute with the Hamiltonian.

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    What is the direction of arm propagation relative to the constituent stars? Inwards or outwards?

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    Quote Originally Posted by chornedsnorkack View Post
    What is the direction of arm propagation relative to the constituent stars? Inwards or outwards?
    The arms are trailing (here's a diagram). I believe that most spiral galaxies where we can tell the direction of rotation have trailing arms, but there are cases where it's the other way. And of course there are many cases where we see spirals edge on and can't tell for sure which way the arms wind.
    Conserve energy. Commute with the Hamiltonian.

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    Quote Originally Posted by Grey View Post
    The arms are trailing (here's a diagram).
    But thatīs just the shape of the pattern. My question was about the motion of the pattern.
    Does the pattern move faster than the stars in the pattern, or slower?

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    If I am not mistaken the spiral pattern is nearly stationary, with stars bunching up a bit as they pass through it.

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    The pattern velocity was determined to be about 25km/s/kpc back in 2005 - I suppose estimates may have changed since then.
    Interestingly, this put the corotation radius close to the Sun's distance from the galactic centre. Stars significantly closer to the centre will overtake the spiral arms; stars farther out will be overtaken by the spiral arms.

    Grant Hutchison

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    Quote Originally Posted by Hornblower View Post
    If I am not mistaken the spiral pattern is nearly stationary, with stars bunching up a bit as they pass through it.
    The pattern velocity was determined to be about 25km/s/kpc back in 2005 - I suppose estimates may have changed since then.
    Interestingly, this put the corotation radius close to the Sun's distance from the galactic centre. Stars significantly closer to the centre will overtake the spiral arms; stars farther out will be overtaken by the spiral arms.

    Grant Hutchison
    I guess I misremembered or misinterpreted something in the past. Good catch, Grant.

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    Quote Originally Posted by chornedsnorkack View Post
    But thatīs just the shape of the pattern. My question was about the motion of the pattern.
    Does the pattern move faster than the stars in the pattern, or slower?
    Ah, my apologies for misunderstanding what you were asking. I see that grant gave you the answer you were looking for, though.
    Conserve energy. Commute with the Hamiltonian.

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    Thanks! So within the margin of error the local standard of rest is corotating - Perseus Arm is always 2000 pc outwards and Sagittarius Arm always 1000 pc inwards.
    How far from Sun, in radial direction, are Sunīs periapse and apoapse?

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