Most recent edit on 2009-04-24 13:38:44 by CharlesFrancis
Additions:
 If the total matter distribution in a galaxy is similar to the visible mass distribution, then, under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
 In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
 According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve tends to zero for large distances, but it is not close to zero locally. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
Deletions:
| If the total matter distribution in a galaxy is similar to the visible mass distribution, then, under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
| According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve tends to zero for large distances, but it is not close to zero locally. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
Edited on 2009-03-08 15:17:04 by CharlesFrancis
Additions:
← The Local Slope of the Rotation Curve ↑ →
CDM and
MOND allow flat
galaxy rotation curves, but it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments, and MOND fails in its aim of replacing Newtonian gravity with a law predicting the slope of the rotation curve from visible matter.
The Galaxy Rotation Curve
| If the total matter distribution in a galaxy is similar to the visible mass distribution, then, under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
The Gradient of the Rotation Curve
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
| According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve tends to zero for large distances, but it is not close to zero locally. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
Conflict with CDM and MOND
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and that it contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally. This would imply that CDM must have quite different properties under gravity than ordinary matter. We have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime. This being so, all matter must behave identically under gravity, and the distribution of dark matter in a galaxy should follow that of visible matter. In practice, Wayth et al.» found that the mass distribution of one galaxy, for which good data is available, does follow the visible mass distribution, in direct conflict with the distribution required to produce galactic rotation curves. MOND is also distressed, because instead of being able to predict the rotation curve from visible matter, it becomes necessary to postulate dark matter with a different distribution to account for the Milky Way’s rotation curve.
The Local Slope of the Rotation Curve ↑ Radial Velocity Test →
Deletions:
← Radial Velocity Test ↑ →
Method
We took a population of of 20 574 stars for which there are complete and accurate distance and velocity measurements. The spread of velocities in the local population is much greater than the suggested error in radial velocity which would account for the flattening of rotation curves. A test is required which will not be affected by the structure of the velocity distribution, real velocity gradients, bulk streams and moving groups. To test for a signature in such a noisy distribution we binned the population into 20 bins, each containing around 1 000 stars, and tested the velocity components, U, towards the Galactic centre, V, in the direction of Galactic rotation, and W, perpendicular to the Galactic plane. Testing the component on a particular axis avoids correlations arising from the structure of the velocity distribution.
 We plotted the component of velocity, vaxis, in the direction of the axis, against the cosine of the angle, θ, subtended by the star with that axis. The four quadrants of the plot represent stars positioned in either direction along the axis (quadrants I & IV opposed to quadrants II & III), and stars approaching (quadrants II & IV) and receding (quadrants I & III). Under the null hypothesis, that there is no systematic error in spectrographic measurement of radial velocity, there should be a 50-50 split of plots with absolute component of velocity increasing or decreasing with abs(cos θ). Trials showing increasing abs(vaxis) with abs(cos θ) were designated passes for the alternate hypothesis, radial velocities are overstated. The plot shows four passes in one bin on the W-axis. Correlations are low but the total number of quadrants with absolute value of the component of velocity increasing with the absolute value of the cosine is significant. |
 For stars with equal true velocity and different positions, an error in radial velocity would contribute more to vaxis for stars which subtend a narrow angle with the axis (horizontal), and would tend to generate a correlation between vaxis and cos θ in each of the four quadrants. Separate tests are used in each quadrant. Real velocity gradients and bulk streaming motions would bias particular quadrants towards passes or fails, but would still produce a 50% pass rate under the null hypothesis. |
Test Results
The overall result from 240 quadrants was 140 passes, leading us to reject the null hypothesis with a confidence of 99.4%. Because outliers in regression have a disproportionate effect on results, it is normal to restrict the population to within 3 or fewer standard deviations of the mean. When we restricted to a velocity ellipsoid containing 14 914 stars representing the bulk of thin disc motions, the the number of passes rose to 154, leading to rejection of the null hypothesis with a confidence of 99.9993%. A velocity ellipsoid has no dependency on space coordinates, so does not introduce a bias.
The result on the W-axis is particularly significant because the Sun is close to the Galactic plane, where abs(W) should be at a maximum. We should therefore expect less than a 50% pass rate under the null hypotheses for this axis. In fact there were 60 passes out of 80 tests on this axis, rising to 63 passes out of 80 tests in the velocity ellipsoid, rejecting the null hypothesis with 99.99999% confidence.
The results from 80 tests on each axis show that the components of radial velocity in the V- and W-directions are overstated, but there is no evidence that the component in the U-direction is overstated. In fact there is some indication that the U-component is not overstated. In consequence we may reject the possibility that the results are due to a systematic understatement of Hipparcos parallax distance which would affect the U- V- and W-directions equally.
For the same reason we may reject the possibility that the result is due to truncation bias arising from the fact that measurement errors in radial velocity are slightly larger than those in transverse velocity; the division of the population into stars approaching and stars receding cuts stars which cross the horizontal axis because of measurement errors, and could potentially produce a bias towards passes. Estimates of the magnitude of this bias show that it is greatly outweighed by random factors in the motions of stars, and the reversed correlation on the U-axis shows that this is not the cause of the correlation on the other axes.
Adjusting radial distances by +10% substantially reduces the pass rate, as would be expected, but even with this increase we found 93 successes out of 160 trials on the V- and W-axes for the population in the velocity ellipsoid, rejecting the null hypothesis with a confidence of 97.6%. This shows that the error in radial velocity is of an order greater than 10% and eliminates the possibility that the result could be caused by systematic measurement errors.
Moving groups could potentially affect results. If a group is localised in space, the stars in a given moving group will appear in the same quadrant in each test. Under the null hypothesis, the chance of the gradient in that quadrant being positive or negative is still 50%, but, because group stars are split among the tests, it could potentially be the case that a particular quadrant repeats the same result in several tests because of group stars. Very high results in a particular quadrant would be evidence that the result is due to a moving group, and reduce the significance of the overall result. In fact no quadrants individually show significantly higher results than others. If the result were caused by moving groups, then it would also be dependent on the choice of axis. We rotated the V- and W-axes through 22.5°, 45° and 67.5°, and were able to reject the null hypothesis in each direction. We therefore reject the possibility that the result is due to moving groups.
Implications
Determination of spectral shift is straightforward, well established, and not in itself open to systematic measurement errors of the type seen in the test. The results cannot be accounted through systematic distance adjustments, because there is no observed correlation in the radial direction of the Galaxy. Velocity components are not expected to vary greatly with position over the distances of stars tested and a simple velocity gradient could not be responsible for the results, because this would produce as many fails as passes. If one rejects the notion that the Sun occupies a preferred position in space such that other stars tend to move radially towards and from the Sun, the principle conclusion one can draw is that there is a systematic overstatement in radial velocities.
The cosmological redshift prediction of general relativity based on classical wave motions is clear, but general relativity does not consider the possibility that photons from astronomical objects should be described using quantum theory. In relational quantum gravity, light from distant stars is treated quantum mechanically. As a result spectral shifts have a cosmological component in addition to the accepted Doppler component. To rigorously test this prediction it is necessary to compare astrometric radial velocities with spectrographic radial velocities for individual stars. This will be possible for near, high velocity, stars with Gaia», but cannot be done at current astrometric precision. We do not know of any other cosmological model which modifies spectral shifts without modifying the laws of classical motion in general relativity. The statistical test described here shows, to very high confidence, that spectroscopic radial velocity is overstated, and can be construed as a success for the prediction of relational quantum gravity.
Radial Velocity Test ↑ Solar Motion →
Edited on 2009-03-07 09:48:51 by CharlesFrancis
Additions:
← Radial Velocity Test ↑ →
Method
We took a population of of 20 574 stars for which there are complete and accurate distance and velocity measurements. The spread of velocities in the local population is much greater than the suggested error in radial velocity which would account for the flattening of rotation curves. A test is required which will not be affected by the structure of the velocity distribution, real velocity gradients, bulk streams and moving groups. To test for a signature in such a noisy distribution we binned the population into 20 bins, each containing around 1 000 stars, and tested the velocity components, U, towards the Galactic centre, V, in the direction of Galactic rotation, and W, perpendicular to the Galactic plane. Testing the component on a particular axis avoids correlations arising from the structure of the velocity distribution.
| We plotted the component of velocity, vaxis, in the direction of the axis, against the cosine of the angle, θ, subtended by the star with that axis. The four quadrants of the plot represent stars positioned in either direction along the axis (quadrants I & IV opposed to quadrants II & III), and stars approaching (quadrants II & IV) and receding (quadrants I & III). Under the null hypothesis, that there is no systematic error in spectrographic measurement of radial velocity, there should be a 50-50 split of plots with absolute component of velocity increasing or decreasing with abs(cos θ). Trials showing increasing abs(vaxis) with abs(cos θ) were designated passes for the alternate hypothesis, radial velocities are overstated. The plot shows four passes in one bin on the W-axis. Correlations are low but the total number of quadrants with absolute value of the component of velocity increasing with the absolute value of the cosine is significant. |
| For stars with equal true velocity and different positions, an error in radial velocity would contribute more to vaxis for stars which subtend a narrow angle with the axis (horizontal), and would tend to generate a correlation between vaxis and cos θ in each of the four quadrants. Separate tests are used in each quadrant. Real velocity gradients and bulk streaming motions would bias particular quadrants towards passes or fails, but would still produce a 50% pass rate under the null hypothesis. |
Test Results
The overall result from 240 quadrants was 140 passes, leading us to reject the null hypothesis with a confidence of 99.4%. Because outliers in regression have a disproportionate effect on results, it is normal to restrict the population to within 3 or fewer standard deviations of the mean. When we restricted to a velocity ellipsoid containing 14 914 stars representing the bulk of thin disc motions, the the number of passes rose to 154, leading to rejection of the null hypothesis with a confidence of 99.9993%. A velocity ellipsoid has no dependency on space coordinates, so does not introduce a bias.
The result on the W-axis is particularly significant because the Sun is close to the Galactic plane, where abs(W) should be at a maximum. We should therefore expect less than a 50% pass rate under the null hypotheses for this axis. In fact there were 60 passes out of 80 tests on this axis, rising to 63 passes out of 80 tests in the velocity ellipsoid, rejecting the null hypothesis with 99.99999% confidence.
The results from 80 tests on each axis show that the components of radial velocity in the V- and W-directions are overstated, but there is no evidence that the component in the U-direction is overstated. In fact there is some indication that the U-component is not overstated. In consequence we may reject the possibility that the results are due to a systematic understatement of Hipparcos parallax distance which would affect the U- V- and W-directions equally.
For the same reason we may reject the possibility that the result is due to truncation bias arising from the fact that measurement errors in radial velocity are slightly larger than those in transverse velocity; the division of the population into stars approaching and stars receding cuts stars which cross the horizontal axis because of measurement errors, and could potentially produce a bias towards passes. Estimates of the magnitude of this bias show that it is greatly outweighed by random factors in the motions of stars, and the reversed correlation on the U-axis shows that this is not the cause of the correlation on the other axes.
Adjusting radial distances by +10% substantially reduces the pass rate, as would be expected, but even with this increase we found 93 successes out of 160 trials on the V- and W-axes for the population in the velocity ellipsoid, rejecting the null hypothesis with a confidence of 97.6%. This shows that the error in radial velocity is of an order greater than 10% and eliminates the possibility that the result could be caused by systematic measurement errors.
Moving groups could potentially affect results. If a group is localised in space, the stars in a given moving group will appear in the same quadrant in each test. Under the null hypothesis, the chance of the gradient in that quadrant being positive or negative is still 50%, but, because group stars are split among the tests, it could potentially be the case that a particular quadrant repeats the same result in several tests because of group stars. Very high results in a particular quadrant would be evidence that the result is due to a moving group, and reduce the significance of the overall result. In fact no quadrants individually show significantly higher results than others. If the result were caused by moving groups, then it would also be dependent on the choice of axis. We rotated the V- and W-axes through 22.5°, 45° and 67.5°, and were able to reject the null hypothesis in each direction. We therefore reject the possibility that the result is due to moving groups.
Implications
Determination of spectral shift is straightforward, well established, and not in itself open to systematic measurement errors of the type seen in the test. The results cannot be accounted through systematic distance adjustments, because there is no observed correlation in the radial direction of the Galaxy. Velocity components are not expected to vary greatly with position over the distances of stars tested and a simple velocity gradient could not be responsible for the results, because this would produce as many fails as passes. If one rejects the notion that the Sun occupies a preferred position in space such that other stars tend to move radially towards and from the Sun, the principle conclusion one can draw is that there is a systematic overstatement in radial velocities.
The cosmological redshift prediction of general relativity based on classical wave motions is clear, but general relativity does not consider the possibility that photons from astronomical objects should be described using quantum theory. In relational quantum gravity, light from distant stars is treated quantum mechanically. As a result spectral shifts have a cosmological component in addition to the accepted Doppler component. To rigorously test this prediction it is necessary to compare astrometric radial velocities with spectrographic radial velocities for individual stars. This will be possible for near, high velocity, stars with Gaia», but cannot be done at current astrometric precision. We do not know of any other cosmological model which modifies spectral shifts without modifying the laws of classical motion in general relativity. The statistical test described here shows, to very high confidence, that spectroscopic radial velocity is overstated, and can be construed as a success for the prediction of relational quantum gravity.
Radial Velocity Test ↑ Solar Motion →
Deletions:
← The Local Slope of the Rotation Curve ↑ →
CDM and
MOND allow flat
galaxy rotation curves, but it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments, and MOND fails in its aim of replacing Newtonian gravity with a law predicting the slope of the rotation curve from visible matter.
The Galaxy Rotation Curve
| If the total matter distribution in a galaxy is similar to the visible mass distribution, then, under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
The Gradient of the Rotation Curve
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
| According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve tends to zero for large distances, but it is not close to zero locally. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
Conflict with CDM and MOND
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and that it contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally. This would imply that CDM must have quite different properties under gravity than ordinary matter. We have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime. This being so, all matter must behave identically under gravity, and the distribution of dark matter in a galaxy should follow that of visible matter. In practice, Wayth et al.» found that the mass distribution of one galaxy, for which good data is available, does follow the visible mass distribution, in direct conflict with the distribution required to produce galactic rotation curves. MOND is also distressed, because instead of being able to predict the rotation curve from visible matter, it becomes necessary to postulate dark matter with a different distribution to account for the Milky Way’s rotation curve.
The Local Slope of the Rotation Curve ↑ Radial Velocity Test →
Edited on 2009-03-06 12:30:28 by CharlesFrancis
Additions:
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
Deletions:
| In a study of the velocity distribution of local stars, [[ErikAnderson Erik Anderson]] and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
Edited on 2009-03-06 12:28:17 by CharlesFrancis
Additions:
CDM and MOND allow flat galaxy rotation curves, but it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments, and MOND fails in its aim of replacing Newtonian gravity with a law predicting the slope of the rotation curve from visible matter.
Deletions:
<a href=http://www.teleconnection.info/rqg/GalaxyRotationCurves#CDM>CDM</a»> and MOND allow flat galaxy rotation curves, it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments, and MOND fails in its aim of replacing Newtonian gravity with a law predicting the slope of the rotation curve from visible matter.
Edited on 2009-03-06 12:22:09 by CharlesFrancis
Additions:
<a href=http://www.teleconnection.info/rqg/GalaxyRotationCurves#CDM>CDM</a»> and MOND allow flat galaxy rotation curves, it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments, and MOND fails in its aim of replacing Newtonian gravity with a law predicting the slope of the rotation curve from visible matter.
| If the total matter distribution in a galaxy is similar to the visible mass distribution, then, under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
| In a study of the velocity distribution of local stars, [[ErikAnderson Erik Anderson]] and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
Deletions:
While CDM models of galaxies and MOND predict flat rotation curves, it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments, and MOND fails in its aim of replacing Newtonian gravity with a law predicting the slope of the rotation curve from visible matter.
| If the total matter distribution in a galaxy is similar to the visible mass distribution, then, under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM»), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
Edited on 2009-03-06 10:38:30 by CharlesFrancis
Additions:
| If the total matter distribution in a galaxy is similar to the visible mass distribution, then, under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM»), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
| According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve tends to zero for large distances, but it is not close to zero locally. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
Deletions:
 If the total matter distribution in a galaxy is similar to the visible mass distribution, then, under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM»), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
 In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
 According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve tends to zero for large distances, but it is not close to zero locally. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
Edited on 2009-03-06 04:47:59 by CharlesFrancis
Additions:
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and that it contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally. This would imply that CDM must have quite different properties under gravity than ordinary matter. We have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime. This being so, all matter must behave identically under gravity, and the distribution of dark matter in a galaxy should follow that of visible matter. In practice, Wayth et al.» found that the mass distribution of one galaxy, for which good data is available, does follow the visible mass distribution, in direct conflict with the distribution required to produce galactic rotation curves. MOND is also distressed, because instead of being able to predict the rotation curve from visible matter, it becomes necessary to postulate dark matter with a different distribution to account for the Milky Way’s rotation curve.
Deletions:
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and that it contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally. This would imply that CDM must have quite different properties under gravity than ordinary matter. We have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime. This being so, all matter must behave identically under gravity, and the distribution of dark matter in a galaxy should follow that of visible matter. In practice, Wayth et al.» found that the mass distribution of one galaxy, for which good data is available, does follow the visible mass distribution, in direct conflict with the distribution required to produce galactic rotation curves. MOND is equally distressed, because instead of being able to predict the rotation curve from visible matter, it becomes necessary to postulate dark matter with a different distribution to account for the Milky Way’s rotation curve.
Edited on 2009-03-06 04:47:13 by CharlesFrancis
Additions:
| If the total matter distribution in a galaxy is similar to the visible mass distribution, then, under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM»), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
| According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve tends to zero for large distances, but it is not close to zero locally. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and that it contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally. This would imply that CDM must have quite different properties under gravity than ordinary matter. We have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime. This being so, all matter must behave identically under gravity, and the distribution of dark matter in a galaxy should follow that of visible matter. In practice, Wayth et al.» found that the mass distribution of one galaxy, for which good data is available, does follow the visible mass distribution, in direct conflict with the distribution required to produce galactic rotation curves. MOND is equally distressed, because instead of being able to predict the rotation curve from visible matter, it becomes necessary to postulate dark matter with a different distribution to account for the Milky Way’s rotation curve.
Deletions:
| If the total matter distribution in a galaxy is similar to the visible mass distribution, then under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM»), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
| According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve is close to zero over a wide range of distances. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and that it contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally. This would imply that CDM must have quite different properties under gravity than ordinary matter. We have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime. This being so, all matter must behave identically under gravity, and the distribution of dark matter in a galaxy should follow that of visible matter. In practice, Wayth et al.» found the mass distribution does follow the visible mass distribution, in direct conflict with the distribution required to produce galactic rotation curves. MOND is equally distressed, because instead of being able to predict the rotation curve from visible matter, it becomes necessary to postulate dark matter with a different distribution to account for the Milky Way’s rotation curve.
Edited on 2009-03-06 04:42:15 by CharlesFrancis
Additions:
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With the available stellar data it is only possible to calculate the slope of rotation curve over a short distance. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
Deletions:
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. With the available stellar data it is only calculate the slope of rotation curve over a short distance. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
Edited on 2009-03-06 04:39:57 by CharlesFrancis
No differences.
Edited on 2009-03-06 03:58:54 by CharlesFrancis
Additions:
While CDM models of galaxies and MOND predict flat rotation curves, it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments, and MOND fails in its aim of replacing Newtonian gravity with a law predicting the slope of the rotation curve from visible matter.
Deletions:
While CDM models of galaxies and MOND predict flat rotation curves, it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments, and MOND fails in its aim to replace Newtonian gravity with a law predicting the slope of the rotation curve from visible matter.
Edited on 2009-03-06 03:50:34 by CharlesFrancis
Additions:
While CDM models of galaxies and MOND predict flat rotation curves, it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments, and MOND fails in its aim to replace Newtonian gravity with a law predicting the slope of the rotation curve from visible matter.
Conflict with CDM and MOND
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and that it contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally. This would imply that CDM must have quite different properties under gravity than ordinary matter. We have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime. This being so, all matter must behave identically under gravity, and the distribution of dark matter in a galaxy should follow that of visible matter. In practice, Wayth et al.» found the mass distribution does follow the visible mass distribution, in direct conflict with the distribution required to produce galactic rotation curves. MOND is equally distressed, because instead of being able to predict the rotation curve from visible matter, it becomes necessary to postulate dark matter with a different distribution to account for the Milky Way’s rotation curve.
Deletions:
While CDM models of galaxies and MOND predict flat rotation curves, it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments.
Conflict with CDM
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and that it contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally. This would imply that CDM must have quite different properties under gravity than ordinary matter. We have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime. This being so, all matter must behave identically under gravity, and the distribution of dark matter in a galaxy should follow that of visible matter. In practice, Wayth et al.» found the mass distribution does follow the visible mass distribution, in direct conflict with the distribution required to produce galactic rotation curves.
Edited on 2009-03-06 03:32:21 by CharlesFrancis
Additions:
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. With the available stellar data it is only calculate the slope of rotation curve over a short distance. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic. |
Deletions:
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. |
. With the available stellar data it is only calculate the slope of rotation curve over a short distance. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic.
Edited on 2009-03-06 03:31:26 by CharlesFrancis
Additions:
| If the total matter distribution in a galaxy is similar to the visible mass distribution, then under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The galaxy rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM»), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
The Gradient of the Rotation Curve
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (points at the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. |
. With the available stellar data it is only calculate the slope of rotation curve over a short distance. The method we used will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic.
Conflict with CDM
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and that it contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally. This would imply that CDM must have quite different properties under gravity than ordinary matter. We have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime. This being so, all matter must behave identically under gravity, and the distribution of dark matter in a galaxy should follow that of visible matter. In practice, Wayth et al.» found the mass distribution does follow the visible mass distribution, in direct conflict with the distribution required to produce galactic rotation curves.
Deletions:
| If the total matter distribution in the galaxy is similar to the visible mass distribution, then under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM»), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis»(the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. |
There is some uncertainty in the slope on account of the short distance for which the population is sufficiently dense to find a meaningful minimum in the trough. Moving groups with close to circular motion also increase uncertainty. However, the existence of the trough in the distribution is significant. The method for calculating both the LSR and the circular speed curve will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic.
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally, because this implies means that cold dark matter must have quite different properties under gravity than ordinary matter, yet we have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime, in which case all matter must behave identically under gravity.
Edited on 2009-03-05 13:57:27 by CharlesFrancis
Additions:
| If the total matter distribution in the galaxy is similar to the visible mass distribution, then under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM»), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
| According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve is close to zero over a wide range of distances. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis»(the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. |
Deletions:
| If the total matter distribution in the galaxy is similar to the visible mass distribution, then under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM»), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
| According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve is close to zero over a wide range of distances. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis»(the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. |
Edited on 2009-03-05 13:54:47 by CharlesFrancis
Additions:
| If the total matter distribution in the galaxy is similar to the visible mass distribution, then under Newton’s» inverse square law», matter will orbit more slowly far from the galactic centre. The rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM»), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics. |
| According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve is close to zero over a wide range of distances. The plot shows the Milky Way rotation curve from Combes», with superposed the gradient (dashed) calculated from local stars. |
| In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis»(the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen. |
Deletions:
If the total matter distribution in the galaxy is similar to the visible mass distribution, then under Newton»’s inverse square law», matter will orbit more slowly far from the galactic centre. The rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (CDM), or by modifying gravity (MOND) – both exotic theories for which no explanation is found in fundamental physics.
According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve is close to zero over a wide range of distances. The plot shows the Milky Way rotation curve from , with superposed the gradient (dashed) calculated from local stars.
In a study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to apsis» (the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen.
Oldest known version of this page was edited on 2009-03-05 11:18:04 by CharlesFrancis []
Page view:
← The Local Slope of the Rotation Curve ↑ →
While CDM models of galaxies and MOND predict flat rotation curves, it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments.
The Galaxy Rotation Curve
If the total matter distribution in the galaxy is similar to the visible mass distribution, then under
Newton»’s
inverse square law», matter will orbit more slowly far from the galactic centre. The rotation curve should then slope downwards at large radii. In practice, in observations of many galaxies, we find that the
rotation curve» is approximately flat. This is normally accounted for by hypothesizing a cold dark matter halo (
CDM), or by modifying gravity (
MOND) – both exotic theories for which no explanation is found in fundamental physics.
According to observations of the Doppler shifts of interstellar atomic hydrogen and carbon monoxide, the slope of the Milky Way’s rotation curve is close to zero over a wide range of distances. The plot shows the Milky Way rotation curve from , with superposed the gradient (dashed) calculated from local stars.
In a
study of the velocity distribution of local stars, Erik Anderson and I found that very few stars follow circular orbits. By indentifying stars close to
apsis» (the greatest and least distance of their orbits from the galactic centre) we were able to trace the circular speed curve in the solar neighbourhood. With a little bit of analysis, we found a gradient agreeing with that found from carbon monoxide and atomic hydrogen.
There is some uncertainty in the slope on account of the short distance for which the population is sufficiently dense to find a meaningful minimum in the trough. Moving groups with close to circular motion also increase uncertainty. However, the existence of the trough in the distribution is significant. The method for calculating both the LSR and the circular speed curve will become more valuable when data from Gaia becomes available. It will be potentially be possible to extend the analysis to a much larger region of space, perhaps even to trace the circular speed curve to near the centre of the Galaxy, and a similar distance outward from the Sun where current methods are problematic.
The distribution of matter in the galaxy is determined by gravity. It seems hardly conceivable that the distribution of dark matter should be very different from that of observable matter, and contains just such irregularities so as to cause the slope of the rotation curve to match the Newtonian curve locally, because this implies means that cold dark matter must have quite different properties under gravity than ordinary matter, yet we have seen in the pages on general relativity that the path of matter under gravity is determined by the geometry of spacetime, in which case all matter must behave identically under gravity.
The Local Slope of the Rotation Curve ↑ Radial Velocity Test →
