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  1. #21
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    For 400 years, since Galileo, human "space eyes" have steadily improved, and have steadily revealed "more-and-fainter" space objects. This centuries-spanning track-record has shattered Geo-centrism, Helio-centrism, and even Galacto-centrism (e.g., Edwin Hubble). And, even today, when human astronomers extrapolate, from the "tip-of-the-obvious-ice-berg" that they do see, to what looks likely to lie "below-the-murky-water-line", their best-fit formulae -- for astronomical objects ranging from stars, to galaxies -- mathematically imply, an infinitely large population of as-yet-un-human-observed, low mass, low luminosity, "dim (normal) matter" objects, still to-be-seen in space:

    star Initial Mass Function (IMF) implies infinite 'low-mass limit'

    The well-known IMF, for stars, has the form:

    N(M) ~ M^(-7/3)

    This function can be plotted online, and clearly "blows up at the origin", as M -> 0. To wit, the best fit, for current human observations, of stars, is that the as-yet-human-un-observed population, of low-mass-and-so-low-luminosity stars, is "immeasurably large".


    Galactic Luminosity Function (GLF) implies infinite 'low-luminosity limit'

    The best-fit-to-observations GLF, proposed by "P. Schechter and others, in surveys of galaxies in our local region", and proposed by "G.R. Burbidge and [J.V. Narlikar] in 1981 AD" in calculations considering "farther & farther regions", has the following form (Narlikar. Intro. to Cosmology, p.364):

    f(Lgal) ~ l^(-5/4) * exp(-l), where l = Lgal/L*, and L* ~ 20e9 Lsol ~ LMW, LAnd
    (Note that this function is quite close to e^(-l) / l, the "exponentially-quenched power law", where, again, galaxy luminosities are measured in "Milky Way / Andromeda units".) This function can be plotted online, and clearly "blows up at the origin", as Lgal -> 0. To wit, the best fit, for current human observations, of galaxies, is that the as-yet-human-un-observed population, of low-luminosity-limit galaxies, is "immeasurably large".

  2. #22
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    Quote Originally Posted by Widdekind View Post
    That is clear, cogent, & concise, and is the first I have heard that explanation -- so, neutrinos indirectly "smooth out matter fluctuations", at +400 Kyr, by "smoothing out the space-time fabric", which then affects other matter particles. To wit, neutrinos do not produce a "wind" which smooths out other particles, by direct collisional interactions, but by first affecting space-time itself.

    That explanation is quite clear, and so I accept it. Would you please tell me where you learned that from ? I read allot, and every source I've seen always has said "neutrinos interacted w/ matter to smooth the CMB", and none said "neutrinos smoothed SPACE-TIME"... (or so I interpreted them to say)... such is an important distinction, what source could I consult that is that clear on the concept??
    I don't want to say "smoothed spacetime" because I am not sure that we all agree on what that term means. But I will be happy to give you an excellent reference:

    Particle Dark Matter: Evidence, Candidates and Constraints

    This is an excellent (but long) review paper that very effectively covers the current state of knowledge about Dark Matter. Skip over to page 31, section 3, "Candidates". This section briefly discusses every dark matter candidate based on particles. The very first candidate discussed is "Standard Model Neutrinos", in other words, the neutrinos that we know about. Skip over to the very last paragraph. That's the one that has the information you are looking for. I quote it here:

    Being relativistic collisionless particles, neutrinos erase (moving from high
    to low density regions) fluctuations below a scale of ∼ 40 Mpc (mν /30 eV),
    called the free-streaming length [122]. This would imply a top-down forma-
    tion history of structure in the Universe, where big structures form first.
    The fact that our galaxy appears to be older than the Local Group [413],
    and the discrepancy between the predicted late formation of galaxies, at
    redshift z < 1, against observations of galaxies around z > 4 [123], is a
    further argument against neutrinos as a viable dark matter candidate.

    The paper itself has references that you can follow to explore this further. Anyway, in this paragraph you can see the key points you are interested in:

    * Neutrinos move very fast ("relativistic").

    * Since they don't collide or feel pressure, they move freely. Just by moving in random directions they will tend to move from regions where they are heavily concentrated (i.e. higher density) to regions where they are less concentrated (i.e. lower density).

    * In doing so, purely by gravity, they tend to tug and pull other matter along with them. Thus, they tend to erase density fluctuations smaller than a certain length scale.

    * Given their high speed, that length scale works out to ~40 Mpc.

    That is how neutrinos "interact with matter to smooth the CMB". This also one of the reasons why neutrinos are no longer a top candidate for dark matter. They tend to get in the way of galaxy formation, so having a lot of them would be a problem.
    Astronomer. Lund Observatory

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  4. #23
    Widdekind's Avatar
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    neutrinos not DM

    Neutrinos come in three types, as defined by their rest-mass energies. These "energy eigenstates" -- labelled v1, v2, v3 -- are combined, in varying quantum-mechanical super-positions, into the three "flavors" of neutrinos, that are actually created or absorbed, in actual nuclear interactions, with electrons / muons / taons. Thus, any actual neutrino particle, is a QM combo, of all three neutrino mass eigenstates. And, so, its physical mass, is seemingly some "average" of those neutrino eigenstate masses, m1, m2, m3.

    Now, Neutrino Oscillation provide information, about the mass differences, if not the absolute masses themselves, of those eigenstates. Specifically,

    m2^2 - m1^2 ~ 0.01 eV

    m3^2 - m2^2 ~ 0.05 eV
    And, "the simplest interpretation, is that the first neutrino is much lighter than the second [and] that the second one is much lighter than the third, implying m3 ~ 0.05 eV... and then the second will have a mass" m2 ~ 0.01 eV (Oxford Companion to Cosmology, p.212). Judging by the apparent pattern, of decreasing mass, both of the neutrino mass eigenstates specifically, and of all fundamental particles in the Standard Model, the first neutrino eigenstate, then, probably masses m1 << 0.01 eV. And, since an actual physical neutrino particle, is some QM super-position of those states, actual neutrinos might mass some sort of QM 'average' of those values, say ~0.02 eV.

    Now, recalling discussions, in PPs above, about the 'Bullet Cluster', DM appears to behave like, equivalently, astronomical (pressure-less) "dust"; "MACHOs"; and/or "stars". In no way, could a "blizzard of ultra-light neutrinos" match those observations -- such ultra-light neutrinos would be "sloshed out" of cluster gravity wells, by energetic mergers... even if such ultra-light neutrinos could even be confined within those gravity potentials, in the first place.

    Therefore, it does seem doubtful, that neutrinos could account, for the persistently concentrated DM, inferred to reside, in galactic & super-galactic objects, even through major mergers.



    MACHOs might be DM

    In contrast to neutrinos, observation, of gravity micro-lensing events -- on ~12 million sight-lines, to stars, in the LMC, observed by the Great Melbourne Telescope in Canberra Australia, until it was burned & destroyed in 2003 AD -- already indicate, that up to "50% of the mass of the [Milky Way] halo consists of MACHOs, with individual MACHO masses in the range of 15-90% of the mass of the Sun [that] may be white dwarves" (Oxford Companion to Cosmology, p.197). Perhaps future, space-based observations, above earth's interfering atmosphere, could detect additional events? The fact remains, current observations of MACHOs already can account for a major amount of the DM. And, their low masses, are also completely consistent, with the "diverging to infinity" low-mass-and-luminosity base, of the stellar IMF ('Brown Dwarves'), which observers have long inferred to exist, by observations of "tip-of-the-iceberg" brighter objects, of the same (stellar) class, of astronomical object ("another indication of dim matter").

    So, it certainly seems possible, if currently, to "hold out hope", for MACHOs conceivably accounting, for DM. If so, then DM is "dim-but-normal" matter. Clutching Occam's Razor, and with an admitted desire to minimize "strangenesses in astronomy", this writer will, if currently, "root" for MACHOs, as a "dim matter" candidate, for DM.

  5. #24
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    MACHOs would have spatial density of 1 per 10 light-years cubed

    According to Bertone 2004, DM's inferred density is typically 0.2-0.8 GeV / cm3. Now, for MACHOs, observed to have masses ranging from 0.15-0.9 Msol, that density corresponds to one such average MACHO, per 10 light-years cubed -- a perfectly plausible stellar sort of density.

    If halo MACHOs co-rotate, with the galactic disk, then sight-lines towards the LMC look "straight into the motion" of most MACHOs:

    As such, there would be allot less relative "crossways" motion, cutting across LOSs, and so LMC-derived MACHO observations, might underestimate, the total number of such halo objects.
    Last edited by Widdekind; 07-26-2011 at 01:24 AM.

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    Quote Originally Posted by DanielC View Post
    Being relativistic collisionless particles, neutrinos erase (moving from high to low density regions) fluctuations below a scale of ∼ 40 Mpc (mν /30 eV), called the free-streaming length [122]...[/CENTER]
    Is that perhaps a typo (original to the paper), for 40 Mpc / (mv / 30 eV) ? For, does not the Jeans Length decrease, for increasing particle mass (heavier particles, gravitationally cluster more readily) ?? If so, for mv ~ 0.02 eV, that corresponds to spatial size-scales >100 Gly, larger than that, of our entire current Hubble Volume.

    (Here is a link, to the original cited article.)
    Last edited by Widdekind; 07-26-2011 at 01:17 AM.

 

 
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