<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <G0wfjFFvYIkAFwYT@clef.demon.co.uk>,\nCharles Francis <charles@clef.demon.co.uk> wrote:\n\n>You gave a figure for energy in neutrinos, which I assume was based on\n>the neutrino having zero mass, but do we have any idea how much missing\n>matter there may be in cold neutrinos if neutrinos have mass?\n\nYou\'re right: the number I quoted was assuming massless neutrinos.\nTheoretically, the story should go like this.\n\nIf neutrinos are massless, they should have a thermal distribution\nwith a temperature of about 2 K today. That corresponds to\nan energy of kT = 0.2 meV. So any neutrino species with a mass\nmuch less than that is effectively massless.\n\nWhat about neutrino species with masses more than that? They were\nstill ultrarelativistic (so effectively massless) in the early Universe\nwhen the neutrino background formed, so the number density of such\nneutrinos (averaged over the whole Universe) should be the same\nas in the massless case. That number density works out to be something\nlike 100 particles / cm^3 in each species. (That\'s just an order\nof magnitude. Kolb & Turner\'s "The Early Universe," among others,\nwould give the exact figure.) Any neutrino species with a mass\nabove an meV or so would be nonrelativistic today, so its energy\nwould essentially just be its rest energy.\n\nSo if you have a favorite value for the mass of a neutrino species,\njust multiply that by about 100 / cm^3 to get the density in those\nparticles. If you want to convert that to an Omega, divide by\nthe critical density, which is about 10^4 eV/cm^3.\n\nIncidentally, if neutrinos are massive enough to be nonrelativistic,\nthen they clump gravitationally. So the density of such particles\nin our galaxy would be more than that average value over the whole\nUniverse.\n\n-Ted\n\n\n--\n[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <G0wfjFFvYIkAFwYT@clef.demon.co.uk>,
Charles Francis <charles@clef.demon.co.uk> wrote:
>You gave a figure for energy in neutrinos, which I assume was based on
>the neutrino having zero mass, but do we have any idea how much missing
>matter there may be in cold neutrinos if neutrinos have mass?
You're right: the number I quoted was assuming massless neutrinos.
Theoretically, the story should go like this.
If neutrinos are massless, they should have a thermal distribution
with a temperature of about 2 K today. That corresponds to
an energy of [itex]kT =[/itex] .2 meV. So any neutrino species with a mass
much less than that is effectively massless.
What about neutrino species with masses more than that? They were
still ultrarelativistic (so effectively massless) in the early Universe
when the neutrino background formed, so the number density of such
neutrinos (averaged over the whole Universe) should be the same
as in the massless case. That number density works out to be something
like 100 particles [itex]/ cm^3[/itex] in each species. (That's just an order
of magnitude. Kolb & Turner's "The Early Universe," among others,
would give the exact figure.) Any neutrino species with a mass
above an meV or so would be nonrelativistic today, so its energy
would essentially just be its rest energy.
So if you have a favorite value for the mass of a neutrino species,
just multiply that by about 100 [itex]/ cm^3[/itex] to get the density in those
particles. If you want to convert that to an [itex]\Omega,[/itex] divide by
the critical density, which is about [itex]10^4 eV/cm^3[/itex].
Incidentally, if neutrinos are massive enough to be nonrelativistic,
then they clump gravitationally. So the density of such particles
in our galaxy would be more than that average value over the whole
Universe.
[tex]-Ted[/tex]
--
[E-mail me at
name@domain.edu, as opposed to
name@machine.domain.edu.]