Astronomy Without A Telescope – SLoWPoKES

Article written: 14 May , 2011
Updated: 24 Dec , 2015
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The Sloan Low-mass Wide Pairs of Kinematically Equivalent Stars (SLoWPoKES) catalog was recently announced, containing 1,342 common proper motion pairs (i.e. binaries) – which are all low mass stars in the mid-K and mid-M stellar classes – in other words, orange and red dwarves.

These low mass pairs are all at least 500 astronomical units distance from each other – at which point the mutual gravitation between the two objects gets pretty tenuous – or so Newton would have it. Such a context provides a test-bed for something that lies in the realms of ‘fringe science’ – that is, Modified Newtonian Dynamics, or MoND.

The origin of MoND theory is generally attributed to a paper by Milgrom in 1981, which proposed MoND as an alternative way to account for the dynamics of disk galaxies and galactic clusters. Such structures can’t obviously hold together, with the rotational velocities they possess, without the addition of ‘invisible mass’ – or what these days we call dark matter.

MoND seeks to challenge a fundamental assumption built into both Newton’s and Einstein’s theories of gravity – where the gravitational force (or the space-time curvature) exerted by a massive object recedes by the inverse square of the distance from it. Both theories assume this relationship is universal – it doesn’t matter what the mass is or what the distance is, this relationship should always hold.

In a roundabout way, MoND proposes a modification to Newton’s Second Law of Motion – where Force equals mass times acceleration (F=ma) – although in this context, a is actually representing gravitational force (which is expressed as an acceleration).

If a expresses gravitational force, then F expresses the principle of weight. So for example, you can easily exert a sufficient force to lift a brick off the surface of the Earth, but it’s unlikely that you will be able to lift a brick, with the same mass, off the surface of a neutron star.

Anyhow, the idea of MoND is that by allowing F=ma to have a non-linear relationship at low values of a, a very tenuous gravitational force acting across a great distance might still be able to hold something in a loose orbit around a galaxy, despite the principle of a linear F=ma relationship predicting that this shouldn’t happen.

Left image: The unusual flat curve (B) of velocities of objects in disk galaxies versus what would be expected by a naive application of Kepler's Third Law (A). Right image: A scatter plot of selected binaries from the SLoWPoKE catalogue (blue) plotted against the trend expected by Kepler's Third Law (red). Credit: Hernandez et al. (Author's note - Kepler's Third Law of Planetary Motion fits the context of the solar system where 99% of the mass is contained in the Sun. Its applicability to the motion of stars in a galactic disk, with a much more even mass distribution, is uncertain)

MoND is fringe science, an extraordinary claim requiring extraordinary evidence, since if Newton’s or Einstein’s theories of gravity cannot be assumed to universal, a whole bunch of other physical, astrophysical and cosmological principles start to unravel.

Also, MoND doesn’t really account for other observational evidence of dark matter – notably the gravitational lensing seen in different galaxies and galactic clusters – a degree of lensing that exceeds what is expected from the amount of visible mass that they contain.

In any case, Hernandez et al have presented a data analysis drawn from the SLoWPoKES database of widely spread low-mass binaries, suggestive that MoND might actually work at scales of around 7000 astronomical units. Now, since this hasn’t yet been picked up by Nature, Sci. Am. or anyone else of note – and since some hack writer at Universe Today is just giving it a ‘balanced’ review here, it may be premature to consider that a major paradigm of physics has been overturned.

Nonetheless, the concept of ‘missing mass’ and dark matter has been kicked around for close on 90 years now – with no-one seemingly any closer to determining what the heck this stuff is. On this basis, it is reasonable to at least entertain some alternate views.

Further reading:
Dhital et al Sloan Low-mass Wide Pairs of Kinematically Equivalent Stars (SLoWPoKES): A Catalog of Very Wide, Low-mass Pairs (note that this paper makes no reference to the issue of MoND).

Hernandez et al The Breakdown of Classical Gravity?



31 Responses

  1. Anonymous says

    ” 1,342 common proper motion pairs (i.e. binaries)”

    This is actually incorrect. Common proper motion pairs could be just moving together in space. In theory, their origins are thought to be old open star clusters or stellar associations, which travel through space in one common direction. Over time these clusters or grouping fall apart, therefore spreading over many 100s of parsecs. Each of these stars can therefore look like they are attached because of the common proper motion, but are too far apart to make any orbit around their common centre of gravity.

    As for MoND here, it would be fairly hard to prove if only because of the inordinate time a 7000AU binary would need to show it is indeed in orbit; then you would have to prove on top of that, that the gravitational orbits do not apply to Newtonian physics.

    Thanks for the article, Steve.

    • Anonymous says

      Well I plan to be there still when the orbits converge so as to check them.

      Mary

    • Member
      Steve_Nerlich says

      Well, it is a correct (pretty much verbatim) description of the SLoWPoKES catalog entry criteria. The catalog only includes pairs where the calculated probability of chance alignment is less than 0.05.

      Agree MOND is on shaky ground. Thanks.

  2. Anonymous says

    As a comment, there are two other possibilities for common proper motion pairs. This is that they are so-called temporary binaries or that the orbits are not elliptical orbits but are hyperbolic orbits.
    Briefly, temporary binaries would have weak attachments compared to the gravitation influenced by the surrounding nearby stars. A close approach by either component are sufficient to brake the system apart. Dissolution of such stars are more rapid due to significant perturbations influenced from nearby stars.
    General theory proposes that most of the field stars visible in the night time sky have been temporary binaries. They are mostly considered systems having a separations great than about 4,000 Astronomical Units (A.U.) or c. 0.2 parsecs.
    For hyperbolic or (parabolic) orbits, the motion is only caused by the proximity of the stars, that looks like binary motion, but is not. The stars show independent velocities exceeding that of a velocity required for Kepler’s laws of motion to be valid in some formal binary star. Note: The orbital eccentricity exceeds 1.00, a value often labelled as ‘q’. Eccentricity is between 0 (circular) and <1 (elliptical)

    Both temporary binaries and hyperbolic (or parabolic) orbits have been considered for more than a century, but are near impossible to prove.

    • Member
      Steve_Nerlich says

      Good points – though I understand these issues were considered in putting together the SLoWPoKES catalog. They included some wide binaries that were probably evolving towards becoming two separate entities, but only after a long period of binary-ness. I don’t think this is the same as a so-called temporary binary.

  3. Anonymous says

    The MOND theory suffers from a number of irregularities. It can be made in part to fit with the dark matter predicted orbits of stars in galaxies. The problem has been that because different galaxies have different halos and distribution of dark matter in them it is hard to get a modified F = ma, to work uniformly.

    It is possible that such systems could exhibit departures in 1/r^2 dynamics because of dark matter which induces a small r^2 force in addition. The reason for this r^2 force is that the orbiting system is immersed in the dark matter, rather than the dark matter acting as a radially dependent force.

    LC

    • Anonymous says

      Perfectly true. However, the essential point is that, galaxies are a different proposition in these circumstance than stars. MoND is this case is mostly insignificant compared to the gravitational forces by stars surrounding these wide common proper motion systems. Dynamics here are grossly effected by local environment which changes significantly in time as stars orbit within the galaxy. I.e. Stellar density per unit space. Due to this, talking in terms of F=ma is mostly fiction. It should be in terms of gravitational potentials. I.e. The interesting paper Eric Poisson’s “Post-Newtonian theory for the common reader : Lecture notes (July 2007).” (See Chapter 5) [Not for novices!!]

      • Anonymous says

        The paper by Poisson is pretty massive. The primary difficulty with using planetary or double star systems to test for dark matter is that the amount of DM is the volume of integration which contains the orbit is very small. By the same surname as the paper author, Poisson tells us that

        nabla^2U = nabla*F = 4piGrho.

        For a homogeneous DM distribution rho, the mass density, is constant. Integration over the volume and Stokes law gives the force as

        4pi r^2F = (4pi)^2/3 Grho r^3

        and so F is

        (4piGrho/3)r.

        The smallness of the volume means that the distance, here r, that the system “probes” DM distribution is very small compared to galactic dimensions. The mass density is around 10^{-28}g/cm^3 and so a large distance r is needed to really “probe” for the occurrence of DM.

        LC

      • Anonymous says

        Err, there is a negative sign error in the first equation — sorry

      • Torbjörn Larsson says

        FWIW, Disqus gives me a permanent edit facility of own comments.

  4. Member
    IVAN3MAN_AT_LARGE says

    I think that the proponents of Modified Newtonian Dynamics (MoND) are ignoring that big cosmic elephant in the room known as the Bullet cluster (1E 0657-56), which provides the best current evidence for the nature of dark matter as well as providing evidence against some of the more popular versions of MoND when applied to large galactic clusters.

    (Just my two pennies’ worth before I go to bed.)

  5. Torbjörn Larsson says

    I think it is worse for MOND than that.

    Inclusion of DM predicts all large scale gravitational systems up to and including the standard cosmology.

    MOND fails for clusters (even GR modifications need a different parameter set for each cluster according to Starting With A Bang), and is _only_ better on galactic disks. In that sense it is an isolated ad hoc. Which of course can be made better than a general predictive theory at any given time once you give up the pretense of testable “theory” and go for an adjustable model.

    Nonetheless, the concept of ‘missing mass’ and dark matter has been kicked around for close on 90 years now – with no-one seemingly any closer to determining what the heck this stuff is. On this basis, it is reasonable to at least entertain some alternate views.

    Personally I don’t agree with this judgment, acknowledging it is personal judgment..

    DM has become more predictive (encompasses more systems) and more tested as time passes. Meanwhile alternatives like MOND have failed more and more, in the sense of theory as per above.

    I think it is unreasonable to entertain or even expect alternates on such a basis, the likelihoods trends in the wrong direction. It is, for my 2 $s, only reasonable to acknowledge that DM has to pass more tests and can still fail.

    Historically dark matter is at the stage atomic theory was at before Rutherford’s experiments showed that atoms were localized objects.* The cluster models are akin to Einstein’s Brownian motion models.

    Looking at it this way it is unfair to ask for more direct observations of DM at once.

    Atoms were only observed on an individual basis in the 90s, as light emitters in ion traps or hillocks in AFM images. But we didn’t wait until the last decade and “direct observation”** to declare atoms as fact.

    Something similar happened with exoplanets I believe, they were accepted before imaged.

    * Which may be taken as a determination of what the heck atoms really are.

    ** An oxymoron if there ever was one. You can perhaps quantify directness; interesting that no one ever does but instead insists on recognizing it when they see it.

    Tune in next week when we discuss “common sense” and how that too muddles analysis in a similar manner.

    Nitpick:

    Newton’s Second Law of Motion is that the net force on a body is equal to the rate of change of its momentum. I think you would have problems explaining rockets otherwise. =D

  6. Torbjörn Larsson says

    I think it is worse for MOND than that.

    Inclusion of DM predicts all large scale gravitational systems up to and including the standard cosmology.

    MOND fails for clusters (even GR modifications need a different parameter set for each cluster according to Starting With A Bang), and is _only_ better on galactic disks. In that sense it is an isolated ad hoc. Which of course can be made better than a general predictive theory at any given time once you give up the pretense of testable “theory” and go for an adjustable model.

    Nonetheless, the concept of ‘missing mass’ and dark matter has been kicked around for close on 90 years now – with no-one seemingly any closer to determining what the heck this stuff is. On this basis, it is reasonable to at least entertain some alternate views.

    Personally I don’t agree with this judgment, acknowledging it is personal judgment..

    DM has become more predictive (encompasses more systems) and more tested as time passes. Meanwhile alternatives like MOND have failed more and more, in the sense of theory as per above.

    I think it is unreasonable to entertain or even expect alternates on such a basis, the likelihoods trends in the wrong direction. It is, for my 2 $s, only reasonable to acknowledge that DM has to pass more tests and can still fail.

    Historically dark matter is at the stage atomic theory was at before Rutherford’s experiments showed that atoms were localized objects.* The cluster models are akin to Einstein’s Brownian motion models.

    Looking at it this way it is unfair to ask for more direct observations of DM at once.

    Atoms were only observed on an individual basis in the 90s, as light emitters in ion traps or hillocks in AFM images. But we didn’t wait until the last decade and “direct observation”** to declare atoms as fact.

    Something similar happened with exoplanets I believe, they were accepted before imaged.

    * Which may be taken as a determination of what the heck atoms really are.

    ** An oxymoron if there ever was one. You can perhaps quantify directness; interesting that no one ever does but instead insists on recognizing it when they see it.

    Tune in next week when we discuss “common sense” and how that too muddles analysis in a similar manner.

    Nitpick:

    Newton’s Second Law of Motion is that the net force on a body is equal to the rate of change of its momentum. I think you would have problems explaining rockets otherwise. =D

    • Member
      Steve_Nerlich says

      This is all fine – I was seeking to communicate the Hernandez et al argument which did seek to dismiss dark matter entirely and is all about motion at extreme levels of a (from F=ma). To their credit, they do show their hand – with some seemingly convincing data analysis. I don’t have the expertise to determine whether there are holes in the math. I am assuming it may not be bullet-proof given no-one else has obviously picked it up.

    • Anonymous says

      I don’t think you properly understand what is meant by “Dark Matter” (or “Dark Energy” for that matter). It isn’t necessarily real matter. Scientists do not know what exactly is missing from their calculations that cause them to differ from observations … that difference is what is referred to as Dark Matter.

      Including an unknown, Dark Matter, cannot accurately predict anything because even if the prediction is found to be true, you still don’t know WHY (because it is based on an unknown).

      • Anonymous says

        As IVAN3MAN_AT_LARGE says the Bullet Cluster observation tells us that dark matter does exist. It is true that we have no data which tells us just what dark matter is. The best theoretical model is that it is the neutralino, a condensate state of supersymmetric partners of some known particles.

        History illustrates many examples of where something is known to exist, but its nature is unknown. Rutherford showed the atom has a small central mass, but its nature was not known until several decades later. The neutrino has a similar story.

        LC

      • Anonymous says

        As IVAN3MAN_AT_LARGE says the Bullet Cluster observation tells us that dark matter does exist. It is true that we have no data which tells us just what dark matter is. The best theoretical model is that it is the neutralino, a condensate state of supersymmetric partners of some known particles.

        History illustrates many examples of where something is known to exist, but its nature is unknown. Rutherford showed the atom has a small central mass, but its nature was not known until several decades later. The neutrino has a similar story.

        LC

  7. Torbjörn Larsson says

    Slightly OT, but I feel I must parse my previous comment on what I personally believe is reasonable in science and place it in context.

    Given that it is unreasonable to expect alternates to a seemingly successful but yet not finalized theory that dominates the field, what are the ramifications?

    I don’t think it is “reasonable” to ask for abandonment of fringe science alternates. (On what grounds, really!?)

    – If the main stream theory fails, it is good to pick up immediately. Fresh insight may be valuable, but then again even if the fringe has been laboring in unhealthy circumstances (shrinking relative success) they may still have something of value. If they go, in practice the alternates often go with them AFAIK.

    – One may entertain that having a fringe and discussing it once in a while shows health of science at large. I dunno if that is wishful thinking or if there is something in it.

    • Member
      Jon Voisey says

      I agree with this. I quite like the idea of MOND conceptually. We’ve had trouble getting gravity to work on quantum scales, so why should we inherently assume it works the exact same on the grandest of scales. In science, we often assume something to be true and operate as if it were until doing so proves to be inconsistent with the evidence. I respect MOND for being willing to explore these other options and provide numerical models against which we can test predictions. MOND hasn’t worked well in the vast majority of cases, but at least the scientists working on it fairly acknowledge its shortcomings (such as were previously mentioned), which is far more than I can say for the EU crowd.

      • Anonymous says

        To be honest I find MoND to be butt faced ugly. The problem is that on a Newtonian level it would mean that gravity is not a force that obeys Gauss’ law. The gravity acceleration

        a = -GMm/r^2

        means that the integration of this force over a 2-dimensional sphere of area 4pi r^2 gives

        int a*d(area) = (GMm/r^2)( 4pi r^2) = 4piGM.

        The MoND modification means that for small accelerations this does not hold. This could be interpreted as meaning the gravitational mass and inertial mass are different for weak gravity. To be honest I hope this is not how nature works.

        MoND has a sort of phenomenological use in working out the distribution of DM. So there is a possible utility to it. However, I would be unhappy if it emerged as a fundamental theory.

        LC

  8. Damian says

    What came first, the universe or our theory of it?
    Somehow, I think even 10 thousand years of observation and debate will still leave mysteries to argue about. Isn’t it great. 🙂

  9. I believe that moving charged ionized plasma particles connect together these slowpoke binary stars, and that gravitational forces are weaker then electro-magnetic forces in outer space zero gravity plasma binary stars. Heliosphere Plasma physics forces are overwhelming responsible for maintaining the inertial angular orbital momentum of slowpoke stars. Observational evidence includes Protostars forming and having strong magnetic fields where filaments are found.

  10. Sean Leslie says

    There is a point that I would like to raise in regards to MoND. To the best of my recollection, Milgrom himself has said that it wasn’t actually the intention of MoND to do away with dark matter entirely, and I’m equally certain that Milgrom has also aknowledged that MoND can’t work without dark matter. The formulation of MoND, to the best of my recollection, was only ever supposed to reduce the amount of dark matter in the universe. This seems to be a common misconception among proponents and opponents alike.

    (The poster formerly known as Trippy).

    • Sean Leslie says

      Specifically – I came across a lecture by Milgrom in which he discusses, among other things, a 1998 paper (I think) and essentially states that MoND can account for the mass anomaly at the Galactic scale, and at large scales in galaxy clusters, but, curiously, fails to account for the cores of galaxy clusters – apparently under those conditions, even MoND predicts there should be more mass than is actually visible, however, he attributes the missing mass to baryonic dark matter (MoND seemingly reduces the amount of dark matter required to make this viable).

      (The poster formerly known as Trippy)

    • Sean Leslie says

      Specifically – I came across a lecture by Milgrom in which he discusses, among other things, a 1998 paper (I think) and essentially states that MoND can account for the mass anomaly at the Galactic scale, and at large scales in galaxy clusters, but, curiously, fails to account for the cores of galaxy clusters – apparently under those conditions, even MoND predicts there should be more mass than is actually visible, however, he attributes the missing mass to baryonic dark matter (MoND seemingly reduces the amount of dark matter required to make this viable).

      (The poster formerly known as Trippy)

  11. Can gravity just be cumulative weak gravity? Can weak gravity just be electromagnetic attraction of energy? My math and physics are weak, but I’ve often thought of gravity as an intricate lattice of aligned electromagnetic forces that follows the scales of energy from the subatomic to the universal.

    On the biggest scale, I’m curious what cumulative gravity the entire universe would exert on space beyond the universe. What’s out there beyond say 30 billion light years, and how would it respond to inter-universal space? If the big bang did indeed happen, would it act sort of like a star forming in a nearby nebula? There could be stuff out there, or there could be… Nothing. 😉

    If there was nothing, it would make sense that we should expand in an unlimited sort of way – the expansion of the universe would never encounter that surrounding nebula and never interact with it. I’m curious what this math would say about both scenarios.

  12. Anonymous says

    Nice little story, but what has this to do with this one?
    Yes. Electromagnetic forces exist in the universe, but their role in star formation is fairly minor. Also such forces are not scaleable in very large scales. Nebulae are fairly small compared to galaxies and on huge scales like the big bang.

  13. Member
    Anonymous says

    Thanks for the clear explanation of the MoND concept Steve… good job~

    About the gravitational lensing seen in different galaxies and galactic clusters that exceed the amount of visible mass that they contain…. Wouldn’t a change in acceleration or ‘a’ values account for that with the increased influence of gravity over distance?

  14. Member
    Dale M. Jacobs says

    Interesting comments!

  15. Anonymous says

    All observations have shown that the universe is infinite. What you are thinking about is the cosmological horizon (the farthest point high energy particles have reached us since the Big Bang). There is likely no “space outside the universe.” The big bang has no singular starting point in space. It happened everywhere.

    Gravity is a force independent of electromagnetism. Electromagnetism is a weak force in comparison.

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