Most recent edit on 2009-03-29 04:08:39 by CharlesFrancis
Additions:
The simulation uses orbits with random eccentricities between 0.10 and 0.18, corresponding to observations of local stars in the Milky Way. The pattern created is a grand-design two-armed spiral. To see an orbit, follow the path of one of the giant stars. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits. If one were to scale this galaxy to the Milky Way, with the bar taking up the central section, the Solar orbit would be about midway in the spiral. The diameter of the galaxy would be about 130,000 light years. The Sun has been moving down a spiral arm for about 150 million years, and is now crossing outwards through this arm, prior to leaving the arm, crossing the other arm, and rejoining the original arm. The time for the animation is about 200 million years.
<a href=images/spiralmotions/gss.avi>Longer, 85 MB simulation with more stars and a bar.</a><br><br>
Deletions:
The simulation uses orbits with random eccentricities between 0.10 and 0.18, corresponding to observations of local stars in the Milky Way. The pattern created is a grand-design two-armed spiral. To see an orbit, follow the path of one of the giant stars. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits.
<a href=images/spiralmotions/galaxy.avi>70 MB simulation with more stars and a bar.</a><br><br>
Edited on 2009-03-25 01:54:29 by CharlesFrancis
Additions:
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and in the halo. Rosettes are aligned because of mutual gravity. The gravity of the arm causes stars to follow the arm during the ingoing part of their orbit.
<a href=images/spiralmotions/galaxy.avi>70 MB simulation with more stars and a bar.</a><br><br>
Under gravity, gas clouds follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. Gas in the arm is in turbulent motion, as gas clouds seek to cross in the arm and gain velocity as they approach pericentre. As shown in the simulation, stars rarely collide because of their small size compared to space between them. Stars pass outwards towards apocentre through the arm, but when outgoing gas from one arm meets ingoing gas in another arm, collisions between gas clouds create regions of higher pressure, and greater turbulence. Pockets of extreme pressure due to turbulence generate the molecular clouds» in which new stars» form.
Deletions:
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and in the halo. In this model, rosettes are aligned because of mutual gravity between stars.
<a href=images/spiralmotions/gss.avi>82 MB simulation with more stars and a bar.</a><br><br>
Under gravity, gas clouds follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. Gas in the arm is in turbulent motion, as gas clouds cross the arm and gain velocity as they approach pericentre. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas from one arm meets ingoing gas in another arm, collisions between gas clouds create regions of higher pressure, and greater turbulence. Pockets of extreme pressure due to turbulence generate the molecular clouds» in which new stars» form.
Edited on 2009-03-24 01:15:39 by CharlesFrancis
Additions:
<a href=images/spiralmotions/gss.avi>82 MB simulation with more stars and a bar.</a><br><br>
Deletions:
<a href=images/spiralmotions/gss.avi>70 MB simulation with more stars and a bar.</a><br><br>
Edited on 2009-03-24 01:15:21 by CharlesFrancis
Additions:
<a href=images/spiralmotions/gss.avi>70 MB simulation with more stars and a bar.</a><br><br>
Deletions:
<a href=images/spiralmotions/galaxy.avi>70 MB simulation with more stars and a bar.</a><br><br>
Edited on 2009-03-22 13:30:51 by CharlesFrancis
No differences.
Edited on 2009-03-22 13:29:40 by CharlesFrancis
Additions:
<img border="0" src="images/spiralmotions/galaxy.gif" width=450 height=440 align="right">
These movies may be freely distributed, provided that a credit is given to Charles Francis and Erik Anderson as authors of the model and the animation. Please cite <a href=http://arxiv.org/abs/0901.3503>arXiv:0901.3503<sup>»</sup></a>». The relationships between speed of rotation of the bar (bar pattern speed) the speed of rotation of the spiral (spiral pattern speed) and orbital velocities depend on the mass distribution of the Galaxy and are not known. </td>
</table>
====<a name="GalacticOrbits"></a>""Galactic Orbits
Deletions:
<img border="0" src="images/spiralmotions/galaxy.gif" width=450 height=440 align="right"></p>
I</table>
These movies may be freely distributed, provided that a credit is given to Charles Francis and Erik Anderson as authors of the model and the animation. Please cite <a href=http://arxiv.org/abs/0901.3503>arXiv:0901.3503<sup>»</sup></a>». The relationships between speed of rotation of the bar (bar pattern speed) the speed of rotation of the spiral (spiral pattern speed) and orbital velocities depend on the mass distribution of the Galaxy and are not known. <p> </td>
</table>====<a name="GalacticOrbits"></a>""Galactic Orbits
Edited on 2009-03-22 13:27:09 by CharlesFrancis
Additions:
← The Anatomy of Spiral Arms ↑ →
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and in the halo. In this model, rosettes are aligned because of mutual gravity between stars.
<br><br>
The simulation uses orbits with random eccentricities between 0.10 and 0.18, corresponding to observations of local stars in the Milky Way. The pattern created is a grand-design two-armed spiral. To see an orbit, follow the path of one of the giant stars. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits.
<br><br>
</table>====<a name="GalacticOrbits"></a>Galactic Orbits====
In a spiral galaxy», mass is distributed thoughout the disc and also in the halo». As a star moves towards pericentre, the gravitational mass drawing it towards the galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse, and the orbit opens out into a rosette.
In each part of the orbit, the motion is approximated by elliptical motion. It is still meaningful to define the eccentricity vector. The eccentricity vector is seen to regress; it rotates backwards with respect to orbital motion. It also changes in magnitude; eccentricity is less near to pericentre (change in magnitude will not concern us in this analysis). If we imagine looking at the motion from above from a platform rotating with the eccentricity vector, the orbit will once again appear closed — the orbit will be approximately elliptical with the galactic centre at the focus, as in the previous image.
====<a name="OrbitalAlignment"></a>Orbital Alignment====
Now let us assume that orbits precess at the same rate at any orbital radius. Use coordinates rotating with the eccentricity vectors. In these coordinates orbits are approximate to ellipses aligned at a focus. If the major axis is rotated for larger orbits, they can be aligned in such a way that more than half of each orbit lies on an equiangular spiral».
In practice, regions of higher density exert more gravity, and attract more stars. The gravity of the arm ensures that stars rejoin the arm near apocentre, where they move more slowly. Thus gravity of the arm maintains the required orbital alignment to preserve the spiral pattern, and ensures that orbits do precess at the same rate, the rate of spiral pattern speed.
The pitch angle of a given spiral galaxy is directly related to the orbital eccentricities of stars in that galaxy. Higher eccentricity orbits fit spirals with higher pitch angles. The pitch angle of this arm is 11°. Orbits have eccentricity 0.3. Eccentricities in the range ˜0.25 to ˜0.35 can be fitted to an arm with this pitch angle.
====<a name="FlocculentSpirals"></a>Flocculent Spirals====
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. In this way, flocculent galaxies form. Focculence consists of spiral segments, formed out of alignments in orbital rosettes. This will tend to happen more on the outer part of stellar orbits, where orbital velocity is less and stars spend more time. In consequence, trailing spirals are found in galaxies.
NGC 4414 as observed by the Hubble Space Telescope». Credit: HST/NASA/ESA
====<a name="Multi-armedSpirals"></a>Multi-armed Spirals====
As a galaxy evolves, the gravity of larger spiral segments in a flocculent galaxy attract increasing numbers of stars, and spiral segments join up to form arms.
The Pinwheel Galaxy, M101, as observed by the Hubble Space Telescope». Credit: HST/NASA/ESA
====<a name="StarFormation"></a>Star Formation====
Under gravity, gas clouds follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. Gas in the arm is in turbulent motion, as gas clouds cross the arm and gain velocity as they approach pericentre. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas from one arm meets ingoing gas in another arm, collisions between gas clouds create regions of higher pressure, and greater turbulence. Pockets of extreme pressure due to turbulence generate the [[http://en.wikipedia.org/wiki/Molecular_clouds molecular clouds]] in which [[http://en.wikipedia.org/wiki/Protostar new stars]] form.
====<a name="BisymmetricSpirals"></a>""Bisymmetric Spirals
<img border="0" width=450 height=440 src="images/spiralmotions/gas.gif" align="right"></td>
In a multi-arm spiral, outgoing gas meeting an arm would outweigh ingoing gas in the arm. This would tend to remove gas from the arm. In a two armed spiral, the gas in the arm has greater mass. Thus, a two-armed gaseous spiral can be stable, whereas multiarmed gaseous spirals cannot.
<br><br>
Outgoing gas applies pressure to the trailing edge of a spiral arm with an inverse proportionality to radius. If one gaseous arm advances compared to the bisymmetric position, the pressure due to gas from the other arm will be reduced. At the same time, pressure on the retarded arm due to outgoing gas from the advanced arm will be increased. Thus gas motions preserve the symmetry of two-armed spirals.
<br><br>
In a flocculent galaxy, gas will also be attracted into spiral segments. When gas clouds meet they combine to form larger clouds, adding more quickly to the mass of the segment. An underlying bisymmetric structure is observed, even in flocculent spirals, due to the formation of gaseous arms (containing gas as well as stars). Because of the pressure on the trailing edge of a gaseous arm, it will regress more slowly than a non-gaseous arm. Thus non gaseous arms are absorbed into a gaseous arm and multi-armed spirals evolve into bisymmetric spirals.
The Anatomy of Spiral Arms ↑ The Velocity Distribution of Local Stars →
Deletions:
← Spiral Arms Unravelled ↑ →
Our paper, Galactic Spiral Structure, arXiv:0901.3503», shows how galaxies naturally evolve to form grand-design two-arm spirals. Here we give a brief description of the workings of Spiral arms.
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and the halo. To see an orbit, follow the path of one of the giant stars. In our model, rosettes are aligned because of mutual gravity between stars. The pattern created is a grand-design two-armed spiral, with a pitch angle close to that of the Milky Way. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits. <br><br>
</table>""
Galactic Orbits
<img border="0" width=450 height=440 src="images/spiralmotions/rosette.gif">
In a <a href=http://en.wikipedia.org/wiki/Spiral_galaxy>spiral» galaxy<sup>»</sup></a>, mass is distributed thoughout the disc and also in the <a href=http://en.wikipedia.org/wiki/Galactic_spheroid#Galactic_spheroid>halo<sup>»</sup></a>». As a star moves towards pericentre, the gravitational mass drawing it towards <a href=http://en.wikipedia.org/wiki/Sgr_A*>Sgr» A*</a> at the Galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse and the orbit opens out into a rosette. <br><br>
In each part of the orbit, the motion is approximated by elliptical motion, and it is still meaningful to define the eccentricity vector. The eccentricity vector is seen to regress; it rotates backwards with respect to orbital motion. It also changes in magnitude; eccentricity is less near to pericentre, but the change in magnitude will not concern us in this analysis. If we imagine looking at the motion from above from a platform rotating with the eccentricity vector, the orbit will once again appear closed — the orbit will be approximately elliptical with Sgr A* at the focus, as in the previous image.
Orbital Alignment
<img border="0" width=450 height=440 src="images/spiralmotions/arm.png" align="right"></td>
Now let us assume that orbits precess at the same rate at any orbital radius, and that they are aligned at the focus. Use coordinates rotating with the eccentricity vectors. If the major axis is rotated as the orbits grow larger, it is possible to align them in such a way that more than half of each orbit lies on an equiangular spiral. The pitch angle of this arm is 11° and orbits have eccentricity 0.3. Lower eccentricity orbits fit better with lower pitch angles. Eccentricities in the range ˜0.25 to ˜0.35 can be fitted to an arm with this pitch angle.
Flocculent Spirals
<img border="0" width=450 height=440 src="images/spiralmotions/flocculentgalaxy.jpg" align="right"></td>
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. This will tend to happen more on to outer part of stellar orbits, where orbital velocity is less and stars spend more time. In this way flocculent galaxies can be formed. The flocculence consists of spiral segments, formed out of alignments in orbital rosettes
Multi-armed Spirals
<img border="0" width=450 height=440 src="images/spiralmotions/multiarmgalaxy.jpg" align="right"></td>
As a galaxy evolves, the gravity of the spiral segments in a flocculent galaxy attract increasing numbers of stars, and the spiral segments join up to form arms.
Star Formation
Gas will also be attracted into spiral segments. When gas clouds meet they combine to form larger clouds, and add more quickly to the mass of the segment, so that the process of reducing flocculent spiral segments to a small number of arms is faster for gaseous galaxies. Under gravity, gas clouds will follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas meets ingoing gas in another arm, the collision creates regions of high pressure and turbulence in which new stars can form.
Bisymmetric Spirals
<img border="0" width=450 height=440 src="images/spiralmotions/gas.png" align="right"></td>
In a multi-arm spiral, outgoing gas meeting an arm would outweigh ingoing gas in the arm. This would tend to remove gas from the arm. In a two armed spiral, the gas in the arm has greater mass. Thus a two-armed gaseous spiral can be stable, whereas multiarmed gaseous spirals cannot.
Outgoing gas applies pressure to the inside of a spiral arm with an inverse proportionality to radius. If one gaseous arm advances compared to the bisymmetric position, the pressure due to gas from the other arm will be reduced. At the same time, pressure on the retarded arm due to outgoing gas from the advanced arm will be increased. Thus gas motions provide a mechanism to maintain the symmetry of two-armed spirals.
An underlying bisymmetric structure is observed, even in flocculent spirals, due to the formation of gaseous arms (containing gas as well as stars). Because of the pressure on the trailing edge of a gaseous arm, it will regress more slowly than a non-gaseous arm. Thus a non gaseous arms are absorbed into a gaseous arm and multi-armed spirals evolve into bisymmetric spirals
Spiral Arms Unravelled ↑ The Velocity Distribution of Local Stars →
Edited on 2009-03-22 13:23:34 by CharlesFrancis
Additions:
← Spiral Arms Unravelled ↑ →
Our paper, Galactic Spiral Structure, arXiv:0901.3503», shows how galaxies naturally evolve to form grand-design two-arm spirals. Here we give a brief description of the workings of Spiral arms.
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and the halo. To see an orbit, follow the path of one of the giant stars. In our model, rosettes are aligned because of mutual gravity between stars. The pattern created is a grand-design two-armed spiral, with a pitch angle close to that of the Milky Way. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits. <br><br>
</table>""
Galactic Orbits
<img border="0" width=450 height=440 src="images/spiralmotions/rosette.gif">
In a <a href=http://en.wikipedia.org/wiki/Spiral_galaxy>spiral» galaxy<sup>»</sup></a>, mass is distributed thoughout the disc and also in the <a href=http://en.wikipedia.org/wiki/Galactic_spheroid#Galactic_spheroid>halo<sup>»</sup></a>». As a star moves towards pericentre, the gravitational mass drawing it towards <a href=http://en.wikipedia.org/wiki/Sgr_A*>Sgr» A*</a> at the Galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse and the orbit opens out into a rosette. <br><br>
In each part of the orbit, the motion is approximated by elliptical motion, and it is still meaningful to define the eccentricity vector. The eccentricity vector is seen to regress; it rotates backwards with respect to orbital motion. It also changes in magnitude; eccentricity is less near to pericentre, but the change in magnitude will not concern us in this analysis. If we imagine looking at the motion from above from a platform rotating with the eccentricity vector, the orbit will once again appear closed — the orbit will be approximately elliptical with Sgr A* at the focus, as in the previous image.
Orbital Alignment
<img border="0" width=450 height=440 src="images/spiralmotions/arm.png" align="right"></td>
Now let us assume that orbits precess at the same rate at any orbital radius, and that they are aligned at the focus. Use coordinates rotating with the eccentricity vectors. If the major axis is rotated as the orbits grow larger, it is possible to align them in such a way that more than half of each orbit lies on an equiangular spiral. The pitch angle of this arm is 11° and orbits have eccentricity 0.3. Lower eccentricity orbits fit better with lower pitch angles. Eccentricities in the range ˜0.25 to ˜0.35 can be fitted to an arm with this pitch angle.
Flocculent Spirals
<img border="0" width=450 height=440 src="images/spiralmotions/flocculentgalaxy.jpg" align="right"></td>
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. This will tend to happen more on to outer part of stellar orbits, where orbital velocity is less and stars spend more time. In this way flocculent galaxies can be formed. The flocculence consists of spiral segments, formed out of alignments in orbital rosettes
Multi-armed Spirals
<img border="0" width=450 height=440 src="images/spiralmotions/multiarmgalaxy.jpg" align="right"></td>
As a galaxy evolves, the gravity of the spiral segments in a flocculent galaxy attract increasing numbers of stars, and the spiral segments join up to form arms.
Star Formation
Gas will also be attracted into spiral segments. When gas clouds meet they combine to form larger clouds, and add more quickly to the mass of the segment, so that the process of reducing flocculent spiral segments to a small number of arms is faster for gaseous galaxies. Under gravity, gas clouds will follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas meets ingoing gas in another arm, the collision creates regions of high pressure and turbulence in which new stars can form.
Bisymmetric Spirals
<img border="0" width=450 height=440 src="images/spiralmotions/gas.png" align="right"></td>
In a multi-arm spiral, outgoing gas meeting an arm would outweigh ingoing gas in the arm. This would tend to remove gas from the arm. In a two armed spiral, the gas in the arm has greater mass. Thus a two-armed gaseous spiral can be stable, whereas multiarmed gaseous spirals cannot.
Outgoing gas applies pressure to the inside of a spiral arm with an inverse proportionality to radius. If one gaseous arm advances compared to the bisymmetric position, the pressure due to gas from the other arm will be reduced. At the same time, pressure on the retarded arm due to outgoing gas from the advanced arm will be increased. Thus gas motions provide a mechanism to maintain the symmetry of two-armed spirals.
An underlying bisymmetric structure is observed, even in flocculent spirals, due to the formation of gaseous arms (containing gas as well as stars). Because of the pressure on the trailing edge of a gaseous arm, it will regress more slowly than a non-gaseous arm. Thus a non gaseous arms are absorbed into a gaseous arm and multi-armed spirals evolve into bisymmetric spirals
Spiral Arms Unravelled ↑ The Velocity Distribution of Local Stars →
Deletions:
← The Anatomy of Spiral Arms ↑ →
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and in the halo. In this model, rosettes are aligned because of mutual gravity between stars.
<br><br>
The simulation uses orbits with random eccentricities between 0.10 and 0.18, corresponding to observations of local stars in the Milky Way. The pattern created is a grand-design two-armed spiral. To see an orbit, follow the path of one of the giant stars. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits.
<br><br>
</table>====<a name="GalacticOrbits"></a>Galactic Orbits====
In a spiral galaxy», mass is distributed thoughout the disc and also in the halo». As a star moves towards pericentre, the gravitational mass drawing it towards the galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse, and the orbit opens out into a rosette.
In each part of the orbit, the motion is approximated by elliptical motion. It is still meaningful to define the eccentricity vector. The eccentricity vector is seen to regress; it rotates backwards with respect to orbital motion. It also changes in magnitude; eccentricity is less near to pericentre (change in magnitude will not concern us in this analysis). If we imagine looking at the motion from above from a platform rotating with the eccentricity vector, the orbit will once again appear closed — the orbit will be approximately elliptical with the galactic centre at the focus, as in the previous image.
====<a name="OrbitalAlignment"></a>Orbital Alignment====
Now let us assume that orbits precess at the same rate at any orbital radius. Use coordinates rotating with the eccentricity vectors. In these coordinates orbits are approximate to ellipses aligned at a focus. If the major axis is rotated for larger orbits, they can be aligned in such a way that more than half of each orbit lies on an equiangular spiral».
In practice, regions of higher density exert more gravity, and attract more stars. The gravity of the arm ensures that stars rejoin the arm near apocentre, where they move more slowly. Thus gravity of the arm maintains the required orbital alignment to preserve the spiral pattern, and ensures that orbits do precess at the same rate, the rate of spiral pattern speed.
The pitch angle of a given spiral galaxy is directly related to the orbital eccentricities of stars in that galaxy. Higher eccentricity orbits fit spirals with higher pitch angles. The pitch angle of this arm is 11°. Orbits have eccentricity 0.3. Eccentricities in the range ˜0.25 to ˜0.35 can be fitted to an arm with this pitch angle.
====<a name="FlocculentSpirals"></a>Flocculent Spirals====
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. In this way, flocculent galaxies form. Focculence consists of spiral segments, formed out of alignments in orbital rosettes. This will tend to happen more on the outer part of stellar orbits, where orbital velocity is less and stars spend more time. In consequence, trailing spirals are found in galaxies.
NGC 4414 as observed by the Hubble Space Telescope» Credit: HST/NASA/ESA
====<a name="Multi-armedSpirals"></a>Multi-armed Spirals====
As a galaxy evolves, the gravity of larger spiral segments in a flocculent galaxy attract increasing numbers of stars, and spiral segments join up to form arms.
The Pinwheel Galaxy, M101, as observed by the Hubble Space Telescope» Credit: HST/NASA/ESA
====<a name="StarFormation"></a>Star Formation====
Under gravity, gas clouds follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. Gas in the arm is in turbulent motion, as gas clouds cross the arm and gain velocity as they approach pericentre. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas from one arm meets ingoing gas in another arm, collisions between gas clouds create regions of higher pressure, and greater turbulence. Pockets of extreme pressure due to turbulence generate the [[http://en.wikipedia.org/wiki/Molecular_clouds molecular clouds]] in which [[http://en.wikipedia.org/wiki/Protostar new stars]] form.
====<a name="BisymmetricSpirals"></a>""Bisymmetric Spirals
<img border="0" width=450 height=440 src="images/spiralmotions/gas.gif" align="right"></td>
In a multi-arm spiral, outgoing gas meeting an arm would outweigh ingoing gas in the arm. This would tend to remove gas from the arm. In a two armed spiral, the gas in the arm has greater mass. Thus, a two-armed gaseous spiral can be stable, whereas multiarmed gaseous spirals cannot.
<br><br>
Outgoing gas applies pressure to the trailing edge of a spiral arm with an inverse proportionality to radius. If one gaseous arm advances compared to the bisymmetric position, the pressure due to gas from the other arm will be reduced. At the same time, pressure on the retarded arm due to outgoing gas from the advanced arm will be increased. Thus gas motions preserve the symmetry of two-armed spirals.
<br><br>
In a flocculent galaxy, gas will also be attracted into spiral segments. When gas clouds meet they combine to form larger clouds, adding more quickly to the mass of the segment. An underlying bisymmetric structure is observed, even in flocculent spirals, due to the formation of gaseous arms (containing gas as well as stars). Because of the pressure on the trailing edge of a gaseous arm, it will regress more slowly than a non-gaseous arm. Thus non gaseous arms are absorbed into a gaseous arm and multi-armed spirals evolve into bisymmetric spirals.
The Anatomy of Spiral Arms ↑ The Velocity Distribution of Local Stars →
Edited on 2009-03-22 12:30:19 by CharlesFrancis
Additions:
<a target="_blank" href="http://en.wikipedia.org/wiki/NGC_4414"><img» border="0" src="images/spiralmotions/ngc4414.jpg" ></a>
NGC 4414 as observed by the <a href=http://en.wikipedia.org/wiki/Hubble_Space_Telescope>Hubble» Space Telescope<sup>»</sup></a> Credit: HST/NASA/ESA
<img border="0" src="images/spiralmotions/m101.jpg" ></a></td>
The Pinwheel Galaxy, M101, as observed by the <a href=http://en.wikipedia.org/wiki/Hubble_Space_Telescope>Hubble» Space Telescope<sup>»</sup></a> Credit: HST/NASA/ESA
Deletions:
<a target="_blank" href="http://en.wikipedia.org/wiki/NGC_4414"><img» border="0" src="images/spiralmotions/ngc4414.jpg" </a>
<img border="0" src="images/spiralmotions/m101.jpg" </a></td>
Edited on 2009-03-22 12:23:09 by CharlesFrancis
Additions:
<a target="_blank" href="http://en.wikipedia.org/wiki/NGC_4414"><img» border="0" src="images/spiralmotions/ngc4414.jpg" </a>
<a href="http://en.wikipedia.org/wiki/Messier_101»" target="_blank">
<img border="0" src="images/spiralmotions/m101.jpg" </a></td>
Deletions:
<img border="0" src="images/spiralmotions/ngc4414.jpg" align="right"></td>
<img border="0" src="images/spiralmotions/m101.jpg" align="right"></td>
Edited on 2009-03-22 12:13:32 by CharlesFrancis
Additions:
<img border="0" src="images/spiralmotions/m101.jpg" align="right"></td>
Deletions:
<img border="0" src="images/spiralmotions/M101.jpg" align="right"></td>
Edited on 2009-03-22 12:11:57 by CharlesFrancis
Additions:
Our paper, Galactic Spiral Structure, arXiv:0901.3503», shows how galaxies naturally evolve to form grand-design two-arm spirals. Here we give a brief description of the workings of spiral arms.
<img border="0" src="images/spiralmotions/ngc4414.jpg" align="right"></td>
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. In this way, flocculent galaxies form. Focculence consists of spiral segments, formed out of alignments in orbital rosettes. This will tend to happen more on the outer part of stellar orbits, where orbital velocity is less and stars spend more time. In consequence, trailing spirals are found in galaxies.
<img border="0" src="images/spiralmotions/M101.jpg" align="right"></td>
Deletions:
Our paper, Galactic Spiral Structure, arXiv:0901.3503», shows how galaxies naturally evolve to form grand-design two-arm spirals. Here we give a brief description of the workings of Spiral arms.
<img border="0" width=450 height=440 src="images/spiralmotions/flocculentgalaxy.jpg" align="right"></td>
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. This will tend to happen more on to outer part of stellar orbits, where orbital velocity is less and stars spend more time. In this way flocculent galaxies form. Focculence consists of spiral segments, formed out of alignments in orbital rosettes
<img border="0" width=450 height=440 src="images/spiralmotions/multiarmgalaxy.jpg" align="right"></td>
Edited on 2009-03-22 04:48:45 by CharlesFrancis
Additions:
As shown by Newton, orbits about a massive body are ellipses, aligned with the massive body at a focus. The <a href=http://en.wikipedia.org/wiki/Eccentricity_vector>eccentricity» vector<sup>»</sup></a> (or, equivalently, the <a href=http://en.wikipedia.org/wiki/Laplace-Runge-Lenz_vector>Laplace–Runge–Lenz» vector<sup>»</sup></a>) is defined pointing in the direction from apocentre toward pericentre, and with magnitude equal to the eccentricity of the ellipse.
In a <a href=http://en.wikipedia.org/wiki/Spiral_galaxy>spiral» galaxy<sup>»</sup></a>, mass is distributed thoughout the disc and also in the <a href=http://en.wikipedia.org/wiki/Galactic_spheroid#Galactic_spheroid>halo<sup>»</sup></a>». As a star moves towards pericentre, the gravitational mass drawing it towards the galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse, and the orbit opens out into a rosette.
Now let us assume that orbits precess at the same rate at any orbital radius. Use coordinates rotating with the eccentricity vectors. In these coordinates orbits are approximate to ellipses aligned at a focus. If the major axis is rotated for larger orbits, they can be aligned in such a way that more than half of each orbit lies on an <a href=http://en.wikipedia.org/wiki/Logarithmic_spiral>equiangular» spiral<sup>»</sup></a>.
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. This will tend to happen more on to outer part of stellar orbits, where orbital velocity is less and stars spend more time. In this way flocculent galaxies form. Focculence consists of spiral segments, formed out of alignments in orbital rosettes
Under gravity, gas clouds follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. Gas in the arm is in turbulent motion, as gas clouds cross the arm and gain velocity as they approach pericentre. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas from one arm meets ingoing gas in another arm, collisions between gas clouds create regions of higher pressure, and greater turbulence. Pockets of extreme pressure due to turbulence generate the molecular clouds» in which new stars» form.
In a multi-arm spiral, outgoing gas meeting an arm would outweigh ingoing gas in the arm. This would tend to remove gas from the arm. In a two armed spiral, the gas in the arm has greater mass. Thus, a two-armed gaseous spiral can be stable, whereas multiarmed gaseous spirals cannot.
Deletions:
As shown by Newton, orbits about a massive body are ellipses, aligned with the massive body at a focus. The <a href=http://en.wikipedia.org/wiki/Eccentricity_vector>eccentricity» vector</a><sup>»</sup> (or, equivalently, the <a href=http://en.wikipedia.org/wiki/Laplace-Runge-Lenz_vector>Laplace–Runge–Lenz» vector</a><sup>»</sup>) is defined pointing in the direction from apocentre toward pericentre, and with magnitude equal to the eccentricity of the ellipse.
In a <a href=http://en.wikipedia.org/wiki/Spiral_galaxy>spiral» galaxy</a><sup>»</sup>, mass is distributed thoughout the disc and also in the <a href=http://en.wikipedia.org/wiki/Galactic_spheroid#Galactic_spheroid>halo</a><sup>»</sup>». As a star moves towards pericentre, the gravitational mass drawing it towards the galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse, and the orbit opens out into a rosette.
Now let us assume that orbits precess at the same rate at any orbital radius. Use coordinates rotating with the eccentricity vectors. In these coordinates orbits are approximate to ellipses aligned at a focus. If the major axis is rotated for larger orbits, they can be aligned in such a way that more than half of each orbit lies on an equiangular spiral.
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. This will tend to happen more on to outer part of stellar orbits, where orbital velocity is less and stars spend more time. In this way flocculent galaxies canform. Focculence consists of spiral segments, formed out of alignments in orbital rosettes
Under gravity, gas clouds follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. Gas in the arm is in turbulent motion, as gas clouds cross the arm and gain velocity as they approach pericentre. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas from one arm meets ingoing gas in another arm, collisions between gas clouds create regions of higher pressure, and greater turbulence. Pockets of extreme pressure due to turbulence generate the molecular clouds in which new stars can form.
In a multi-arm spiral, outgoing gas meeting an arm would outweigh ingoing gas in the arm. This would tend to remove gas from the arm. In a two armed spiral, the gas in the arm has greater mass. Thus a two-armed gaseous spiral can be stable, whereas multiarmed gaseous spirals cannot.
Edited on 2009-03-22 04:29:40 by CharlesFrancis
Additions:
← The Anatomy of Spiral Arms ↑ →
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and in the halo. In this model, rosettes are aligned because of mutual gravity between stars.
<br><br>
The simulation uses orbits with random eccentricities between 0.10 and 0.18, corresponding to observations of local stars in the Milky Way. The pattern created is a grand-design two-armed spiral. To see an orbit, follow the path of one of the giant stars. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits.
<br><br>
</table>====<a name="GalacticOrbits"></a>""Galactic Orbits
In a <a href=http://en.wikipedia.org/wiki/Spiral_galaxy>spiral» galaxy</a><sup>»</sup>, mass is distributed thoughout the disc and also in the <a href=http://en.wikipedia.org/wiki/Galactic_spheroid#Galactic_spheroid>halo</a><sup>»</sup>». As a star moves towards pericentre, the gravitational mass drawing it towards the galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse, and the orbit opens out into a rosette.
In each part of the orbit, the motion is approximated by elliptical motion. It is still meaningful to define the eccentricity vector. The eccentricity vector is seen to regress; it rotates backwards with respect to orbital motion. It also changes in magnitude; eccentricity is less near to pericentre (change in magnitude will not concern us in this analysis). If we imagine looking at the motion from above from a platform rotating with the eccentricity vector, the orbit will once again appear closed — the orbit will be approximately elliptical with the galactic centre at the focus, as in the previous image.
In practice, regions of higher density exert more gravity, and attract more stars. The gravity of the arm ensures that stars rejoin the arm near apocentre, where they move more slowly. Thus gravity of the arm maintains the required orbital alignment to preserve the spiral pattern, and ensures that orbits do precess at the same rate, the rate of spiral pattern speed.
Under gravity, gas clouds follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. Gas in the arm is in turbulent motion, as gas clouds cross the arm and gain velocity as they approach pericentre. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas from one arm meets ingoing gas in another arm, collisions between gas clouds create regions of higher pressure, and greater turbulence. Pockets of extreme pressure due to turbulence generate the molecular clouds in which new stars can form.
<img border="0" width=450 height=440 src="images/spiralmotions/gas.gif" align="right"></td>
In a flocculent galaxy, gas will also be attracted into spiral segments. When gas clouds meet they combine to form larger clouds, adding more quickly to the mass of the segment. An underlying bisymmetric structure is observed, even in flocculent spirals, due to the formation of gaseous arms (containing gas as well as stars). Because of the pressure on the trailing edge of a gaseous arm, it will regress more slowly than a non-gaseous arm. Thus non gaseous arms are absorbed into a gaseous arm and multi-armed spirals evolve into bisymmetric spirals.
The Anatomy of Spiral Arms ↑ The Velocity Distribution of Local Stars →
Deletions:
← Spiral Arms Unravelled ↑ →
Our paper, Galactic Spiral Structure, arXiv:0901.3503», shows how galaxies naturally evolve to form grand-design two-arm spirals. Here we give a brief description of the workings of Spiral arms.
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and in the halo. In this model, rosettes are aligned because of mutual gravity between stars. The simulation uses orbits with random eccentricities between 0.10 and 0.18, corresponding to observations of local stars in the Milky Way. The pattern created is a grand-design two-armed spiral. To see an orbit, follow the path of one of the giant stars. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits. <br><br>
</table>
====<a name="GalacticOrbits"></a>""Galactic Orbits
In a <a href=http://en.wikipedia.org/wiki/Spiral_galaxy>spiral» galaxy</a><sup>»</sup>, mass is distributed thoughout the disc and also in the <a href=http://en.wikipedia.org/wiki/Galactic_spheroid#Galactic_spheroid>halo</a><sup>»</sup>». As a star moves towards pericentre, the gravitational mass drawing it towards <a href=http://en.wikipedia.org/wiki/Sgr_A*>Sgr» A*</a> at the Galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse and the orbit opens out into a rosette.
In each part of the orbit, the motion is approximated by elliptical motion, and it is still meaningful to define the eccentricity vector. The eccentricity vector is seen to regress; it rotates backwards with respect to orbital motion. It also changes in magnitude; eccentricity is less near to pericentre (change in magnitude will not concern us in this analysis). If we imagine looking at the motion from above from a platform rotating with the eccentricity vector, the orbit will once again appear closed — the orbit will be approximately elliptical with Sgr A* at the focus, as in the previous image.
In practice, regions of higher density exert more gravity, and attract more stars. The gravity of the arm ensures that stars rejoin the arm near apocentre, where they move more slowly. Thus gravity of the arm maintains the required orbital alignment to preserve the spiral pattern, ensuring that orbits do precess at the same rate, the rate of spiral pattern speed.
Gas will also be attracted into spiral segments. When gas clouds meet they combine to form larger clouds, adding more quickly to the mass of the segment. Thus, the process of reducing flocculent spiral segments to a small number of arms is faster for gaseous galaxies. Under gravity, gas clouds follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. Gas in the arm is in turbulent motion, as gas clouds cross the arm and gain velocity as they approach pericentre. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas from one arm meets ingoing gas in another arm, collisions between gas clouds create regions of higher pressure, and greater turbulence. Pockets of extreme pressure due to turbulence generate the molecular clouds in which new stars can form.
<img border="0" width=450 height=440 src="images/spiralmotions/gas.png" align="right"></td>
An underlying bisymmetric structure is observed, even in flocculent spirals, due to the formation of gaseous arms (containing gas as well as stars). Because of the pressure on the trailing edge of a gaseous arm, it will regress more slowly than a non-gaseous arm. Thus a non gaseous arms are absorbed into a gaseous arm and multi-armed spirals evolve into bisymmetric spirals
Spiral Arms Unravelled ↑ The Velocity Distribution of Local Stars →
Edited on 2009-03-22 03:38:49 by CharlesFrancis
Additions:
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and in the halo. In this model, rosettes are aligned because of mutual gravity between stars. The simulation uses orbits with random eccentricities between 0.10 and 0.18, corresponding to observations of local stars in the Milky Way. The pattern created is a grand-design two-armed spiral. To see an orbit, follow the path of one of the giant stars. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits. <br><br>
Galactic Orbits
In a <a href=http://en.wikipedia.org/wiki/Spiral_galaxy>spiral» galaxy</a><sup>»</sup>, mass is distributed thoughout the disc and also in the <a href=http://en.wikipedia.org/wiki/Galactic_spheroid#Galactic_spheroid>halo</a><sup>»</sup>». As a star moves towards pericentre, the gravitational mass drawing it towards <a href=http://en.wikipedia.org/wiki/Sgr_A*>Sgr» A*</a> at the Galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse and the orbit opens out into a rosette.
<br><br>
In each part of the orbit, the motion is approximated by elliptical motion, and it is still meaningful to define the eccentricity vector. The eccentricity vector is seen to regress; it rotates backwards with respect to orbital motion. It also changes in magnitude; eccentricity is less near to pericentre (change in magnitude will not concern us in this analysis). If we imagine looking at the motion from above from a platform rotating with the eccentricity vector, the orbit will once again appear closed — the orbit will be approximately elliptical with Sgr A* at the focus, as in the previous image.
Orbital Alignment
<td background="images/spiralmotions/gumballs_bg.gif" valign="top">
<img border="0" src="images/spiralmotions/gumballsframes.gif" align="right">
Now let us assume that orbits precess at the same rate at any orbital radius. Use coordinates rotating with the eccentricity vectors. In these coordinates orbits are approximate to ellipses aligned at a focus. If the major axis is rotated for larger orbits, they can be aligned in such a way that more than half of each orbit lies on an equiangular spiral.
<br><br>
In practice, regions of higher density exert more gravity, and attract more stars. The gravity of the arm ensures that stars rejoin the arm near apocentre, where they move more slowly. Thus gravity of the arm maintains the required orbital alignment to preserve the spiral pattern, ensuring that orbits do precess at the same rate, the rate of spiral pattern speed.
<br><br>
The pitch angle of a given spiral galaxy is directly related to the orbital eccentricities of stars in that galaxy. Higher eccentricity orbits fit spirals with higher pitch angles. The pitch angle of this arm is 11°. Orbits have eccentricity 0.3. Eccentricities in the range ˜0.25 to ˜0.35 can be fitted to an arm with this pitch angle.
Flocculent Spirals
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. This will tend to happen more on to outer part of stellar orbits, where orbital velocity is less and stars spend more time. In this way flocculent galaxies canform. Focculence consists of spiral segments, formed out of alignments in orbital rosettes
Multi-armed Spirals
As a galaxy evolves, the gravity of larger spiral segments in a flocculent galaxy attract increasing numbers of stars, and spiral segments join up to form arms.
Star Formation
Gas will also be attracted into spiral segments. When gas clouds meet they combine to form larger clouds, adding more quickly to the mass of the segment. Thus, the process of reducing flocculent spiral segments to a small number of arms is faster for gaseous galaxies. Under gravity, gas clouds follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. Gas in the arm is in turbulent motion, as gas clouds cross the arm and gain velocity as they approach pericentre. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas from one arm meets ingoing gas in another arm, collisions between gas clouds create regions of higher pressure, and greater turbulence. Pockets of extreme pressure due to turbulence generate the molecular clouds in which new stars can form.
Bisymmetric Spirals
<img border="0" width=450 height=440 src="images/spiralmotions/gas.png" align="right"></td>
Outgoing gas applies pressure to the trailing edge of a spiral arm with an inverse proportionality to radius. If one gaseous arm advances compared to the bisymmetric position, the pressure due to gas from the other arm will be reduced. At the same time, pressure on the retarded arm due to outgoing gas from the advanced arm will be increased. Thus gas motions preserve the symmetry of two-armed spirals.
<br><br>
Deletions:
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and the halo. To see an orbit, follow the path of one of the giant stars. In our model, rosettes are aligned because of mutual gravity between stars. The pattern created is a grand-design two-armed spiral, with a pitch angle close to that of the Milky Way. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits. <br><br>
Galactic Orbits
In a <a href=http://en.wikipedia.org/wiki/Spiral_galaxy>spiral» galaxy</a><sup>»</sup>, mass is distributed thoughout the disc and also in the <a href=http://en.wikipedia.org/wiki/Galactic_spheroid#Galactic_spheroid>halo</a><sup>»</sup>». As a star moves towards pericentre, the gravitational mass drawing it towards <a href=http://en.wikipedia.org/wiki/Sgr_A*>Sgr» A*</a> at the Galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse and the orbit opens out into a rosette. <br><br>
In each part of the orbit, the motion is approximated by elliptical motion, and it is still meaningful to define the eccentricity vector. The eccentricity vector is seen to regress; it rotates backwards with respect to orbital motion. It also changes in magnitude; eccentricity is less near to pericentre, but the change in magnitude will not concern us in this analysis. If we imagine looking at the motion from above from a platform rotating with the eccentricity vector, the orbit will once again appear closed — the orbit will be approximately elliptical with Sgr A* at the focus, as in the previous image.
Orbital Alignment
<img border="0" width=450 height=440 src="images/spiralmotions/arm.png" align="right"></td>
Now let us assume that orbits precess at the same rate at any orbital radius, and that they are aligned at the focus. Use coordinates rotating with the eccentricity vectors. If the major axis is rotated as the orbits grow larger, it is possible to align them in such a way that more than half of each orbit lies on an equiangular spiral. The pitch angle of this arm is 11° and orbits have eccentricity 0.3. Lower eccentricity orbits fit better with lower pitch angles. Eccentricities in the range ˜0.25 to ˜0.35 can be fitted to an arm with this pitch angle.
Flocculent Spirals
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. This will tend to happen more on to outer part of stellar orbits, where orbital velocity is less and stars spend more time. In this way flocculent galaxies can be formed. The flocculence consists of spiral segments, formed out of alignments in orbital rosettes
Multi-armed Spirals
As a galaxy evolves, the gravity of the spiral segments in a flocculent galaxy attract increasing numbers of stars, and the spiral segments join up to form arms.
Star Formation
Gas will also be attracted into spiral segments. When gas clouds meet they combine to form larger clouds, and add more quickly to the mass of the segment, so that the process of reducing flocculent spiral segments to a small number of arms is faster for gaseous galaxies. Under gravity, gas clouds will follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas meets ingoing gas in another arm, the collision creates regions of high pressure and turbulence in which new stars can form.
Bisymmetric Spirals
<img border="0" width=450 height=440 src="images/spiralmotions/gas.gif" align="right"></td>
Outgoing gas applies pressure to the inside of a spiral arm with an inverse proportionality to radius. If one gaseous arm advances compared to the bisymmetric position, the pressure due to gas from the other arm will be reduced. At the same time, pressure on the retarded arm due to outgoing gas from the advanced arm will be increased. Thus gas motions provide a mechanism to maintain the symmetry of two-armed spirals.
Edited on 2009-03-21 17:47:43 by CharlesFrancis
Additions:
<img border="0" width=450 height=440 src="images/spiralmotions/gas.gif" align="right"></td>
Deletions:
<img border="0" width=450 height=440 src="images/spiralmotions/gas.png" align="right"></td>
Edited on 2009-03-21 14:39:37 by CharlesFrancis
Additions:
← Spiral Arms Unravelled ↑ →
In this simulation with 2 010 stars, each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and the halo. To see an orbit, follow the path of one of the giant stars. In our model, rosettes are aligned because of mutual gravity between stars. The pattern created is a grand-design two-armed spiral, with a pitch angle close to that of the Milky Way. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits. <br><br>
<img border="0" src="images/spiralmotions/rosetteframes.gif">
Deletions:
In this simulation with 2 010 stars each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and the halo. To see an orbit, follow the path of one of the giant stars. In our model, rosettes are aligned because of mutual gravity between stars. The pattern created is a grand-design two-armed spiral, with a pitch angle close to that of the Milky Way. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits. <br><br>
<img border="0" width=450 height=440 src="images/spiralmotions/rosette.gif">
Oldest known version of this page was edited on 2009-03-21 10:50:59 by CharlesFrancis []
Page view:
Our paper,
Galactic Spiral Structure,
arXiv:0901.3503», shows how galaxies naturally evolve to form grand-design two-arm spirals. Here we give a brief description of the workings of Spiral arms.
Simulation
| |
I |
In this simulation with 2 010 stars each star follows a rosette. This is the form of orbits predicted under Newtonian gravity for mass distributed symmetrically in the galactic plane and the halo. To see an orbit, follow the path of one of the giant stars. In our model, rosettes are aligned because of mutual gravity between stars. The pattern created is a grand-design two-armed spiral, with a pitch angle close to that of the Milky Way. The spiral pattern seems to shrink, but really it is rotating slowly backwards compared to stellar orbits.
70 MB simulation with more stars and a bar.
These movies may be freely distributed, provided that a credit is given to Charles Francis and Erik Anderson as authors of the model and the animation. Please cite arXiv:0901.3503». The relationships between speed of rotation of the bar (bar pattern speed) the speed of rotation of the spiral (spiral pattern speed) and orbital velocities depend on the mass distribution of the Galaxy and are not known.
Galactic Orbits
|
As shown by Newton, orbits about a massive body are ellipses, aligned with the massive body at a focus. The eccentricity vector» (or, equivalently, the Laplace–Runge–Lenz vector») is defined pointing in the direction from apocentre toward pericentre, and with magnitude equal to the eccentricity of the ellipse.
|
In a spiral galaxy», mass is distributed thoughout the disc and also in the halo». As a star moves towards pericentre, the gravitational mass drawing it towards Sgr A* at the Galactic centre is less than it would be if all the mass of the galaxy was concentrated at one central point. As a result the orbit of the star is less curved at pericentre than an ellipse and the orbit opens out into a rosette.
In each part of the orbit, the motion is approximated by elliptical motion, and it is still meaningful to define the eccentricity vector. The eccentricity vector is seen to regress; it rotates backwards with respect to orbital motion. It also changes in magnitude; eccentricity is less near to pericentre, but the change in magnitude will not concern us in this analysis. If we imagine looking at the motion from above from a platform rotating with the eccentricity vector, the orbit will once again appear closed — the orbit will be approximately elliptical with Sgr A* at the focus, as in the previous image.
|
Orbital Alignment
|
Now let us assume that orbits precess at the same rate at any orbital radius, and that they are aligned at the focus. Use coordinates rotating with the eccentricity vectors. If the major axis is rotated as the orbits grow larger, it is possible to align them in such a way that more than half of each orbit lies on an equiangular spiral. The pitch angle of this arm is 11° and orbits have eccentricity 0.3. Lower eccentricity orbits fit better with lower pitch angles. Eccentricities in the range ˜0.25 to ˜0.35 can be fitted to an arm with this pitch angle.
|
Flocculent Spirals
|
As stars follow orbits of different sizes and at different rates, accidental alignments lead to regions of greater mass, which attract more stars. This will tend to happen more on to outer part of stellar orbits, where orbital velocity is less and stars spend more time. In this way flocculent galaxies can be formed. The flocculence consists of spiral segments, formed out of alignments in orbital rosettes
|
Multi-armed Spirals
|
As a galaxy evolves, the gravity of the spiral segments in a flocculent galaxy attract increasing numbers of stars, and the spiral segments join up to form arms.
|
Star Formation
Gas will also be attracted into spiral segments. When gas clouds meet they combine to form larger clouds, and add more quickly to the mass of the segment, so that the process of reducing flocculent spiral segments to a small number of arms is faster for gaseous galaxies. Under gravity, gas clouds will follow similar motion to stars, going in towards pericentre along the arm, and coming away from pericentre in a diffused manner. As shown in the simulation, stars simply pass outwards towards apocentre through the arm, but when outgoing gas meets ingoing gas in another arm, the collision creates regions of high pressure and turbulence in which new stars can form.
Bisymmetric Spirals
|
In a multi-arm spiral, outgoing gas meeting an arm would outweigh ingoing gas in the arm. This would tend to remove gas from the arm. In a two armed spiral, the gas in the arm has greater mass. Thus a two-armed gaseous spiral can be stable, whereas multiarmed gaseous spirals cannot.
Outgoing gas applies pressure to the inside of a spiral arm with an inverse proportionality to radius. If one gaseous arm advances compared to the bisymmetric position, the pressure due to gas from the other arm will be reduced. At the same time, pressure on the retarded arm due to outgoing gas from the advanced arm will be increased. Thus gas motions provide a mechanism to maintain the symmetry of two-armed spirals.
An underlying bisymmetric structure is observed, even in flocculent spirals, due to the formation of gaseous arms (containing gas as well as stars). Because of the pressure on the trailing edge of a gaseous arm, it will regress more slowly than a non-gaseous arm. Thus a non gaseous arms are absorbed into a gaseous arm and multi-armed spirals evolve into bisymmetric spirals
|
Spiral Arms Unravelled ↑ The Velocity Distribution of Local Stars →
