Ay 20 - Fall 2004 - Lecture 18Dark MatterSpiral StructureBasic Galaxy MorphologyDisk Galaxy Rotation Curves:Mass Component ContributionsgasstarsdarkhalototalDark Matterdominates atlarge radii.It cannot beconcentratedin the disk, asit would makethe velocitydispersion ofstars too high.Mass Budget of the Universe~ 70% “dark energy” (aka quintessence, cosmologicalconstant, vacuum energy …)~ 30% matter, of which~ 5% baryonic (from cosmic nucleosynthesis and CMBR)of which~ 0.5% visible (stars, gas)Since 5% < 30%, there is non-baryonic dark matterSince 0.5% < 5%, there is baryonic dark matterIn addition to dynamical measurements (e.g., rotation curves)there is a more comprehensive evidence for the existence ofdark matter. Modern cosmological experiments give thefollowing breakdown of the mass/energy budget:Possibilities for dark matter include:• molecular hydrogen gas clouds• very low mass stars / brown dwarfs• stellar remnants: white dwarfs, neutron stars, black holesbaryonic darkmatter - made (originally) fromordinary gas• primordial black holes• elementary particles, probably currently unknown- non-baryonic dark matterThe Milky Way halo probably contains some baryonic dark matter - brown dwarfs + stellar remnants accompanying theknown population of low mass stars.This uncontroversial component of dark matter is not enough -is the remainder baryonic or non-baryonic?(From P. Armitage)Non-Baryonic DM Candidates• Massive neutrinos– Known to exist and to have mass, but how much?• Weakly Interacting Massive Particles (WIMPs)– Not known to exist, but possible– A generic category, e.g., the neutralino = the least massiveSUSY particle– Thermal relics from the Big Bang– Possible masses > 10 GeV• Axions– Predicted in some versions of quantum chromodynamics– Originate in non-thermal processes– Could interact electromagnetically• Many other speculative possibilities …LaboratoryDetection ofDark MatterParticles?Baryonic DM Candidates• MAssive Compact Halo Objects (MACHOs)– Very low mass stars, white dwarfs, neutron stars, black holes(produced post-nucleosynthesis, from baryons), browndwarfs, interstellar comets, slushballs…• Cold molecular (H2) gas clouds– Would have to be compact, dense, low volume fill factor– Very hard to detect!• Warm/hot gas, bound to galaxy groups– Leftover gas from IGM, never collapsed to galaxies– Virial temperatures ~ 105 - 106 K, corresponding to thevelocity dispersions ~ 300 km/s– Very hard to detect! (ISM opaque to FUV/soft-X)Gravitational Lensing as a Tool toStudy Dark Matter• Mass (visible or not) deflects light, in an achromaticfashion:• Background image is magnified by the lens (e.g., aMACHO). If the lens moves, the background sourcewill brighten and then fadeExpectedGravitationalMicrolensingLightcurves:The peak magnificationdepends on the lensalignment (impactparameter).The event durationdepends on the lensvelocity.How can we see MACHOs ?• Problem: a probability of a distant star beinglensed is maybe ~ 10-7 per year• Solution: monitor ~ 107 stars simultaneouslyMicrolensing experimentsSeveral experiments have searched for microlensing events:• toward the Galactic Bulge (lensesare disk or bulge stars)• toward the Magellanic Clouds(lenses could be stars in the LMC / SMC, or halo objects)MACHO (Massive Compact Halo Object):• observed 11.9 million stars in the Large Magellanic Cloudfor a total of 5.7 years.OGLE (Optical Gravitational Lensing Experiment):• ongoing experiment• presently monitor 33 millions stars in the LMC, plus 170 million stars in the Galactic Bulge.(From P. Armitage)Microlensing observables:Suppose that between us and the Magellanic Clouds there are a large number of dark, compact objects.Source starsin the LMCUnseen lenses in the Galactic haloAt any one time, we will see a clear lensing event (i.e. thebackground star will be magnified) if the line of sight passesthrough the Einstein ring of one of the lenses.Previously derived the angular radius of the Einstein ring on thesky !E. Area is "!E2.(From P. Armitage)! "E=2cGMdLSdLdSSingle lens of mass M, at distance dL. Observer - source distance is dS, lens - source distance is dLS (=dS-dL)Probability that this lens will magnify a given source is:! P "#E2"dLSdLdS$ % & ' ( ) * Mdirectly proportional to the mass of the lensSame is obviously true for a population of lenses, with totalmass Mpop - just add up the individual probabilities. Conclude:• measuring the fraction of stars that are being lensed atany one time measures the total mass in lenses,independent of their individual masses• geometric factors remain - we need to know where thelenses are to get the right mass estimate.(From P. Armitage)No way to determine from a single image whether a givenstar is being magnified by lensing. Need a series of imagesto see star brighten then fade as the alignment changes:Line of sightPosition of Einstein ring when eventstars…when event endsMotion of lensLensing time scale: equals the physical distance across theEinstein ring divided by the relative velocity of the lens:! "=2 dL#EvL(From P. Armitage)! "=4vLcGMdLdLSdSTime scale is proportional to the squareroot of the individual lens masses.Put in numbers appropriate for disk stars lensing stars in theGalactic bulge:• dS = 8 kpc, dL = dLS = 4 kpc• M = 0.3 Msun• vL = 200 km s-1! "# 40M0.3Msun daysWeak dependence on mass is very convenient observationally,if we observe every night can detect:• events with # ~ 1 day: M < Jupiter mass (10-3 Msun)• events with # ~ 1 year: M ~ 25 Solar masses (e.g. stellarmass black holes)• + everything in between…(From P. Armitage)The First MACHOEvent Seen in theLMC Experiment:To date, several tens(or more) microlensingevents have beendetected by variousgroups.For each event, there are only two observables:• duration # - if we know the location of the lens along theline of sight this gives the lens mass directly• peak amplification A: this is related to how close the lineof sight passes to the center of the Einstein ringb! Define u =bdL"EA =u2+ 2u u2+ 4Note: amplification tells us nothing useful about the lens.Additionally, observing many events gives an estimate of theprobability that a given source star will be lenses at any one time (often called the optical depth to microlensing). This measures the total mass of all the lenses, if their location isknown.(From P. Armitage)What AreMACHOs?Analysis of the LMCmicrolensing