þÿ<HTML><TITLE>Dark Matter/Dark E nergy </TITLE> <head> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <META NAME="generator" CONTENT="BBEdit 5.0"> <LINK REL="stylesheet" REV="alternate" HREF="../Physics_Style.css" TYPE="text/css"> </HEAD> <H1>Dark Matter and Dark Energy</H1> <P>or <H2>What you can't see can't hurt you</H2> <OL> <LI>A quick tour of the universe <LI>Why does the density of the Universe matter? <LI>Why must it be Dark Matter? <LI>What is the Dark Matter? <LI>Why is the Dark Matter? <li>Why is there Dark Energy? <LI> What is the dark energy? </OL> <P>Notes are (will be) on <ADDRESS>http://www.physics.carleton.ca/~watson </ADDRESS> </ol><P class = "quote"> Space is big. Really big. You won't believe how vastly, hugely, mind-bogglingly big it is. </b> <p></P> <P><i>Hitchhiker's guide to the Galaxy.</i></P> <P> How big? Could it be infinite? </P> <P> Firstly, a quick look at the skies:<TABLE BORDER="1" frame="box" rules="all" > <TR> <TD><BR CLEAR="all"> This shows a region in Andromeda: &upsilon; And. is a star believed to have 3 planets. Note M31, M33 and a small cluster of stars: everything else are just Milky Way stars.</TD> <TD><IMG SRC="Astro_Pics/upsand_credner.jpg" ALT="" WIDTH="681" HEIGHT="419">.</TD> </TR> </TABLE> <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD> The best known cluster is the Pleaides: (Seven Sisters except we can only see 6 now)</TD> <TD><IMG SRC="Astro_Pics/pleiadesCal_dd.gif" ALT="" WIDTH="579" HEIGHT="369"></TD> </TR> <TR> <TD>A closer look: the Pleiades are a very young group of stars, about 10<SUP>7</SUP> years old, and very close: about 40 light-years, so light takes 40 years to travel from them. </TD> <TD><IMG SRC="Astro_Pics/pleiades_uks_big.gif" ALT="" WIDTH="497" HEIGHT="396"></TD> </TR> </TABLE> <BR CLEAR="all"> <P> <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>M31 is a massive spiral galaxy, rather like the Milky Way with about 10<sup>10</sup> stars</P></TD> <TD><IMG SRC="Astro_Pics/m31_oregon.gif" ALT="" WIDTH="580" HEIGHT="351"></TD> </TR> </TABLE> <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>M33 is a slightly smaller galaxy, rather further away</TD> <TD><img src="Gifs/M33" width="530" height="751"></TD> </TR> <TR> <TD>M74 is another spiral</TD> <TD><img src="Gifs/M74.gif" align=Bottom alt=""></TD> </TR> <TR> <TD>This is M87 (a giant elliptical galaxy) in Virgo. Almost perfectly spherical: about 10<sup>11</sup> stars</TD> <TD><img src="Gifs/M87.gif" align=Bottom alt=""></TD> </TR> <TR> <TD>A very pretty spiral (ESO 269), Note the very distant galaxies in the background!</TD> <TD><IMG SRC="Astro_Pics/eso269_vlt.jpg" ALT="" WIDTH="609" HEIGHT="457"></TD> </TR> </TABLE> <P> <P> We have found about 10<SUP>8</SUP> galaxies. <P>Galaxies form clusters: <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>The Hickson cluster is a very small compact one</TD> <TD><IMG SRC="Astro_Pics/hickson40_subaru.jpg" ALT="" WIDTH="488" HEIGHT="367"></TD> </TR> <TR> <TD>Virgo cluster is closest large one with about 1000 galaxies in it </TD> <TD><img src="Gifs/Virgo.gif" width="340" height="274"></TD> </TR> <TR> <TD>Coma cluster contains at least 10<sup>4 </sup>galaxies</TD> <TD><img src="Gifs/coma.jpeg" width="512" height="512"></TD> </TR> </TABLE> </P> <P>But this is only the beginning: We have measured the position of at least 10 million galaxies.......</P> <P><img src="Gifs/Hubble_deep.jpeg" width="800" height="840">and we can go deeper <P>And further: this is a cluster of galaxies at a redshift of .5</P> <P><img src="Gifs/clusmedz.jpg" width="600" height="740"></P> <P>and further: this is a cluster of galaxies which is fairly close, but there the most distant galaxy known is buried in the picture</P> <P><img src="Gifs/cl1358.jpg" width="640" height="583"></P> <h2>So how did it all begin?</H2><P> <P><h2>Redshift</H2><P> Slipher-Hubble-Humason found light from most galaxies is redshifted: i.e. light which is emitted at one wavelength is observed at a longer one. This tells us that they are moving away from us<P> Doppler effect gives <P> <PRE> z = <U>&#955;-&#955;</U><SUB>0</SUB> = <U>&delta;&lambda;</U> &#955; &#955; </PRE> <p>Measurement of Distance. Popular one is the light year: distance traveled by light in 1 yr ~ 10<SUP>16</SUP>m. Astronomers usually use the "parsec": 1pc = 3*10<SUP>16</SUP> m. Closest star (&#945; Centauri) is at a distance of ~1.3 pc. Sirius is at about 5 pc, M31 at 1.5 Mpc. <P> <p>Vel. of recession <P> <pre> v = zc = c<u>&#948;&#955;</u> &#955;<sub>0</sub> </pre> <p></P> <P> <P> This formula isn't quite right: we can have z &gt; 1: in fact the furthest known galaxy has z = 4.9. We have to use a relativistic formula in that case. <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>Hubble found vel. of recession &#8733; distance <PRE> zc = Hd = v </PRE> <PRE> H ~ 65kms<sup>-1</sup>/Mpc </PRE> <P>1 Mpc (megaparsec) = 3x10<sup>22</sup> m </TD> <TD><img src="Gifs/Hubbleplot.gif" align=Bottom alt=""></TD> </TR> </TABLE> <h2>Big Bang (once over lightly) </h2> <P>RULE 1 in Physics 100: Never mix your units!) </P><TABLE BORDER="1" frame="box" rules="all" > <TR> <TD><pre> H= <u>65x10</u><sup>3</sup>= 1.8x10<sup>-19</sup> (m s<sup>-1</sup>)/m 3.10<sup>22</sup> </pre> <P>We can invert this to give<PRE> H<sup>-1</sup>= 5.4x10<sup>17</sup> s =1.7x10<sup>10</sup> yr. </PRE> </P> <P>What does this time represent?</TD> <TD><img src="Gifs/Hubble1.gif" align=Bottom alt=""> </TD> </TR> <TR> <TD><P>Must be age of universe: if expansion does not change</P> <P>i.e. 17x10<sup>9</sup> yr ago, all the galaxies were in the same place. Universe had a beginning, implied by the big bang. Can run Hubble expansion back: we would like to use this to predict what will happen in the end</TD> <TD><img src="Gifs/Big_Bang1.gif" align=Bottom alt=""></TD> </TR> </TABLE> <P> Where was the Big Bang?<P><P><P><P> </P> <P><img src="Gifs/Everywhere.gif" align=middle alt=""> <P>A 2-D analog is the surface of a balloon: it has no centre in 2-D space. Deflating it reduces it to zero size</P> <P>At the moment of the big bang, not only matter was created, but also space and time </P> <P><a name="What's going to happen in the end"> <h2>What's going to happen in the end?</H2><P> </a><p></P> <P class = "quote">The sky becomes black, Earth sinks into the sea From Heaven fall the bright stars The sea ascends in storm to Heaven It swallows the Earth, the air becomes sterile</b></P> <P><i>From the Hyndluljod (Iceland)</i></P> <P> How can we tell if the universe will expand forever?</P> <P></P> <P> <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>As a model, consider this as an escape velocity problem. How hard do we need to throw a galaxy on the "outside" so that it escapes? Note: our calculation had better not depend on r! <pre> <u>1</u> mv<sup>2</sup> - <u>GMm</u> = 0 2 r </pre>but<PRE> v = Hr </PRE> <P> and the total mass of the universe inside <P> <PRE> M = <sup>4&pi;</sup>/<sub>3</sub> &#961; r<sup>3</sup> </PRE> </TD> <TD><img src="Gifs/Galaxy_escape.gif" align=Bottom alt=""></TD> </TR> </TABLE> <p></P> <P> <P> so...</P> <P><PRE> H<sup>2</sup>r<sup>2</sup> = 2G<sup>4&pi;</sup>/<sub>3</sub> &#961; r<sup>2</sup> </PRE> <P> (we got lucky: the r cancels out!). We can turn this round and write it as an equation for &#961;</P> <P> <pre> &#961;<sub>0</sub> = <u>3 H</u><sup>2</sup> 8&#960; G </pre> <p></P> <P> Hence the critical density </P> <P>&#961;<SUB>0</SUB> ~ 6 x 10<sup>-27</sup> kg m<sup>-3</sup> ~ 3.6 Hydrogen Atoms m<sup>-3</sup> (Number is flaky:we'll use 3). Also use <PRE> &Omega; = <U>&#961;</U> &#961;<sub>0</sub> </PRE> <P>because some errors cancel out. </P> <P>The entire future of the universe is given by this one number!!!!!!!!!</P> <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD><P>So if <ul> <li>&Omega; > 1 Universe come to nasty end in ~ 50 x 10<sup>9</sup> yr. </li> <li>&Omega; = 1 Universe expansion slows down asymptotically : &quot;critical universe&quot;</li> <li>&Omega; < 1<sub>0</sub> Universe expands forever</li> </ul><P> <p></P> <P> More important:we live forever if &Omega; &le; 1, (well maybe). </TD> <TD><img src="Gifs/closed_open_crit.gif" align=Bottom alt=""></TD> </TR> </TABLE> <P>So how do we weigh the universe?</P> <P>a) First Guess</P> <P>Count number of galaxies in a region of space, assume they consist of stars much like the sun <PRE> <U>M</U> = <U>M</U><sub>0</sub> ~ 5x10 <sup>5</sup> kg W<SUP>-1</sup> L L<sub>0</sub> </PRE> <P>(say 1&#956;W/kg) <FONT FACE="Symbol">ÿý</FONT> Density <PRE> &#937; = <U>&#961;</U> ~ .01 &#961;<SUB>0</SUB> </PRE> <P>Note all these numbers are uncertain to <FONT FACE="Symbol">&#177;</FONT> 50%!) Obviously must average over large enough volume such that universe is smooth R > 100 Mpc, and the universe is a very lumpy place!<img src="Astro_Pics/2dFzcone_main.gif" alt="" width="720" height="431"> <P class = "Warning"> We live forever (Hooray!) <P>But wait a moment... <P><h2>There is still a big dark mystery out there</a></H2><P> <p Class = "quote">There is only a single God, Mixcoatl, whose image they possess, but they believe in another, invisible, god, not represented by any image, called Yoalli Ehecatl, That is to say, God Invisible, Impalpable, Beneficent, Protector, Omnipotent by whose strength alone ... rules all things</b></P> <P><i>Nahuatlan Myth</i> <H2>So how do we weigh the universe?</H2><P>Can only see luminous matter: how much Dark Matter is there?</P> <OL> <LI>First Guess: Density of dark matter <PRE> &#961;<SUB>dm</SUB> ~ 0 <FONT COLOR="#000000">so</FONT> <U>M</U> = <U>M</U><sub>0</sub> L L<SUB>0</SUB> </PRE> <LI> 0th order estimate: based on lose estimates of dark nebulae, obscuration of light and dust seen in other galaxies <PRE> <U>&#961;<SUB>dm</SUB></U> ~ 1 <FONT COLOR="#000000">so</FONT> <U>M</U> ~ 2<U>M</U><sub>0</sub> &#961;<SUB>lum</SUB> L L<SUB>0</SUB> </PRE> <LI>Local Dynamics: Can get estimate of local density by motion of stars <PRE> <U>&#961;<SUB>dm</SUB></U> ~ 2 <FONT COLOR="#000000">so</FONT> <U>M</U> ~ 3<U>M</U><sub>0</sub> &#961;<SUB>lum</SUB> L L<SUB>0</SUB> </PRE> </PRE> <P> (first direct evidence for D.M.) <LI> Spiral galaxies <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>Measurement of velocities of individual stars or measurement of hydrogen via 21cm line &rArr;rotation curves</TD> <TD><img src="Gifs/m81_Doppler.gif" align=BOTTOM alt=""></TD> </TR> </TABLE> <P></P> <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>Luminosity of galaxy should reflect mass</P> <P>Typical Spiral R ~ 20 kpc but outer parts are just seen as H gas. Should be able to calculate rotational speed, since most of the light is fairly concentrated, so this should be good approx to the mass. <P>These should show rotation curves that drop as expected. Can fix this by saying that galaxy has halo of dark matter around it. <P>Halo + core add together to give correct curve</TD> <TD><img src="Gifs/NGC3198_luminosity.gif" align=BOTTOM alt=""><P><img src="Gifs/NGC3198.gif" align=BOTTOM alt=""><P><img src="Gifs/NGC3198_Rotation.gif" align=BOTTOM alt=""></TD> </TR> </TABLE> <P></P> <P></P> <P>Note this is not unique to NGC 3198: all measured spirals show same. (Have to have spiral that is not "flat on", since no Doppler, or "side on" since cannot separate different parts)</P> <img src="Gifs/Several_Galaxy_Rotation.gif" align=BOTTOM alt=""> <P> For spirals <PRE> 10<U>M</U><sub>0</sub> &lt; <U>M</U> &lt; 40<U>M</U><sub>0</sub> L<SUB>0</SUB> L L<SUB>0</SUB> </PRE> <LI><P>Large clusters of galaxies: By measuring vel. cpt. in line of sight (via Doppler) can get estimate of M <PRE> &lt;K.E.&gt; = -<SUP>1</SUP>/<SUB>2</SUB>&lt;P.E.&gt; </PRE> <P>(Just like measuring mass of a planet via orbits of its moons)<PRE> <U>M</U> ~ 100<U>M</U><sub>0</sub> L L<SUB>0</SUB> </PRE> <P>This gives much higher masses than individual spirals. A check: large clusters contain a lot of hot gas, which is strong X-ray source</P> <P>X-ray pictures measure density and temp: </P> <IMG SRC="Gifs/coma.GIF" ALT="" WIDTH="256" HEIGHT="256"><img src="Gifs/Coma_X-ray.gif" align=BOTTOM alt=""><P> Also large clusters show gravitational lensing, can get quantitative estimate <IMG SRC="Gifs/Grav_lensing.gif" ALT="" WIDTH="660" HEIGHT="800"> <LI> <P>Finally IR sky surveys suggest that the total mass may be much higher </OL> <P> Note that the larger the object, the more massive (proportionately) that it is. <img src="Gifs/Mass_light_ratios.gif" align=BOTTOM alt=""></P> <P Class = "warning">a) What the hell? i.e. what is the dark matter? <P Class = "Warning">b) Why the hell? i.e. why is &#937;~1 (after all it could be anything?) </P> <P>Actually, there is a limit <PRE> &Omega;</FONT> &lt; 3 </PRE> </P> <P>otherwise the universe would be younger than the earth (wouldn't that make the creationists happy!!) </P> <P>What the hell:</P> <P> <ol> <li>Brown dwarfs </li> <li>Hydrogen gas </li> <li>Jupiters </li> <li>Hydrogen rain </li> <li>Low surface brightness galaxies </li> <li>Maxi Black holes</li> <li>Mini Black holes</li> <li>Neutrinos </li> <li>He H <SUP>+</SUP> </li> <li>Modified 1/r<SUP>2</SUP> law </li> <li>Axions </li> <li>Weakly Interacting Massive Particles (WIMPS)</li> <li>Magnetic Monopoles </li> <LI> Majorons <LI>Photinos <li>E<sub>8</sub> shadow matter</li> <LI> Cosmic Strings </ol><P> <P>Which is it? We don't know! However, all of the above have problems. <P>The Generic Candidates for Dark Matter : <OL> <LI>Baryonic (BDM) ordinary matter, but maybe in some odd form e.g. rocks <LI>Hot (HDM) particles which were relativistic at time of BB e.g. &#957;'s <LI>Cold (CDM): heavy (usually) particles e.g. WIMPs <LI>Mixed (MDM) e.g. 70% WIMPs, 30% &#957;'s <LI>Decaying Dark Matter (DDM) </OL> Why can't it be all BDM (wouldn't it be a lot easier?). <a href="BDM.html">It isn't!</a> <P><TABLE BORDER="1" frame="box" rules="all" > <TR> <TD> <H2>No-Nameons: CDM candidates</H2> <P><UL> <LI>Axions <LI> Majorons <LI> Weakly Interacting Massive Particles <LI> Photinos <LI> LSP's (Lightest supersymmetric particles) <LI> Magnetic Monopoles <LI> E<sub>8</sub> shadow matter </UL> </P> <P>....and there is a tooth fairy</P> <P>Although these are similar cosmologically, they are very different from the point of view of detection. A lot can be ruled out by "in vitro" experiments (e.g. OPAL at CERN puts limits on LSP's</P> <P></P> <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>Generic WIMPS can be seen "in vivo" via a variety of low temp. expts.: e.g. Queens expt, U de Montreal expt. <P>Nucleus will recoil and transfer energy to lattice, flipping superconductor or sending off ballisitic phonons. So far, no results!</TD> <TD><img src="Gifs/WIMP_detector.gif" align=BOTTOM alt=""> </TD> </TR> </TABLE> <P> <H2>Neutrinos</H2> <P>Best bet: we know they must be there, and SNO/Kamioka experiments show they have some mass. Need M<SUB>&#957;</SUB> &le;30eV if they were the only ingredients</P> <H2>Why the Hell?</H2> <P>Why is &#937; = 1 so important?</P> <img src="Gifs/omega_fixed_point.gif" align=BOTTOM alt=""> <P>Since we now measure &#937; ~ 0.1, this means that at the time of the BB it must have been ~ 1 - 10<sup>-60</sup></P> <P>i.e. &#937; = 1 is an unstable critical point</P> <H2>Dark Energy</H2> <P> Dark Matter is bad enough, but now there is an extra problem. <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>If we buy the BB, the expansion of the universe should be slowing down, or at worst constant. We measure this by the "deceleration" parameter q<SUB>0</SUB>, which should be &ge; 0. To get at this we need to go to very large distances, which are automatically shaky.</TD> <TD><IMG SRC="Gifs/Q0_plot.gif" ALT="" WIDTH="371" HEIGHT="321"></TD> </TR> </TABLE> <P> LBL & Harvard have been measuring the distance more accurately than ever before by looking at <A HREF="Astro_Pics/saul_sm.qt"> supernovae</A> (Sn1a: all have the same light curve). <P>The implication is that the expansion of the universe is accelerating: q<SUB>0</SUB>,&lt; 0(!) <TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>Confirmed by observations of radio-galaxies: size allows distance to be estimated.</TD> <TD><img src="Astro_Pics/3c175_vla.jpg" alt="" width="625" height="414">.</TD> </TR> </TABLE> <a href="Astro_Pics/SCP2003SNeCMBClust.pdf"></a><P><BR><HR><TABLE BORDER="1" frame="box" rules="all" > <TR> <TD>Combining this with data from WMAP gives <ul type="circle"> <li>&Omega;<sub>&Lambda;</sub> = .7 <li>&Omega;<sub>CDM</sub> = .3 </ul>This gives a "best guess" due to Michael Turner</TD> <TD><IMG SRC="Gifs/Matter_energy.gif" ALT="" WIDTH="559" HEIGHT="180"></TD> </TR> </TABLE> <P> Implies a very different picture for the <a href="Astro_Pics/expansionhistoryphystoday.pdf">expansion of the universe</a> <P> What can dark energy be? We can parametrise the expansion <pre> <u>R</u><font face="Lucida Grande"><FONT SIZE="+1">&#775;</font></font>=-<sup>4&pi;</sup>/<sub>3</sub>G&rho;(1+3w) R</P> </pre> where w = P/&rho; is the "equation of state parameter". if w&lt;-1/3 we get a positive energy density, but (effectively) a negative pressure which overcomes gravitational attraction at very large distances. <ul type="circle"> <li>BDM,CDM w &sim; 0 <li>HDM (&gamma;'s and &nu;'s) w = 1/3 <li>&Lambda w = -1 </ul> <P>This implies a cosmological constant &Lambda (Einstein's "fudge factor") <a href="Astro_Pics/HubbleDiagramPhysicsToday.pdf">Hubble Diagram</a><P> <P> <p class="warning">We don't know (although there are models..................). Note that w need not even be constant with time <P> However, there are major problems (what, more?). Dark energy implies that the vacuum has an energy density: &rho;<sub>&Lambda;</sub>. Can write baryon energy density (units are c=&#295;=1) <pre> &rho;<sub>BDM</sub>&cong;10<sup>-13</sup> eV<sup>4</sup>. </pre><P> We can understand &rho;<sub>&Lambda;</sub> &equiv; 0. : The only working theory for particles (the standard model) gives <pre> &rho;<sub>&Lambda;</sub> &cong; 10<sup>100</sup> eV<sup>4</sup> - V<sub>0</sub> </pre> <P> where V<sub>0</sub> is a (unknown) correction. in fact <pre> &rho;<sub>&Lambda;</sub> &cong; 10<sup>-8</sup> eV<sup>4</sup>., </pre> <P>so we need cancelation to 110 places of decimals. Secondly, &rho;<sub>&Lambda;</sub> and &rho;<sub>Matter</sub> are almost equal at present. In the past they would have differed by 10<sup>40</sup> If w(t) is increasingly negative (whihc is best fit) universe will accelerate out of control &rArr; Big Rip in &sim; 35 *10<sup>9</sup> years <P></P><P>A final aspect of this: there have been 3 scientific revolutions, all devastating for man's dignity.</P> <P> <ol> <li><i>Copernicus:</i> <b>We are not the centre of the universe</b></li> <li><i>Darwin </i><b>We are no different from the animals </b></li> <li><i>Dark Matter:</i> <b>We are not even made of what most of the universe is made of! (but that means we are special!)</b></li> </ol><P><IMG SRC="Gifs/Calvin%26Hobbes.gif" ALT="" WIDTH="592" HEIGHT="211"> <P>Some references <UL> <LI>Notes are (will be) on <ADDRESS>http://www.physics.carleton.ca/~watson </ADDRESS> <LI>Some pictures from <a href="http://antwrp.gsfc.nasa.gov/apod/archivepix.html">Astro-photo of the day archive </A> <LI><A HREF="http://www-supernova.lbl.gov">Supernova pics from LBL</A> <LI><P> Two excellent semi-popular books: "The First Three Minutes", Steven Weinberg <LI><P> "Gravitation and Cosmology" M. F. Berry </UL> </body> </html>