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Home , Baryonic dark matter, Dark matter, Matter

Dark and the Topic 4 Hunting for Baryonic Black Holes, Dead , & the Primordial Soup Why is the dark matter not ordinary matter we can not see? Contents of Topic 4 In this Topic we move to consider the possible Baryonic candidates for dark matter, their and the arguments that eventually lead to the conclusion that dark matter can not be composed of hidden . We cover: ‣ , , rocks and smaller material as dark matter ‣ Massive Astronomical Compact Halo Objects (MACHOs), Brown Dwarfs, Dead Stars and Stellar Remnants ‣ Hunting for MACHOs with Gravitational Microlensing ‣ Microlensing theory, Amplification Factor and Einstein ‣ Very Massive Objects (VMOs), Black Holes, & Stars ‣ Nucleosynthesis, the CMBR and ΩB ‣ The death of ‣ First ideas on dark matter - and Neutrinos Baryonic Dark Matter Candidates ‣ It is clear from the evidence shown that there are copious amounts of Missing Matter or Dark Matter in the Universe. ‣ Whatever this material is it must not give off or interact with light, otherwise we would see it! ‣ A first step to unravelling this huge mystery, investigated by the first involved, is to consider objects or classes of ordinary material, i.e. Baryonic Material, that are known to exist but that might be hidden from us. An example is Gas: ‣ The term basically refers to and . Strewn throughout the Universe are "trees" of H gas that absorb light from distant objects. For instance they leave absorption lines in distant 's spectra. Baryonic Dark Matter Candidates ‣ A more complete list of possible Baryonic Candidates, roughly in order of , is as follows: (1) Gas - hot and cold gas, hydrogen and (2) Snowballs - of frozen gas (3) Dust - particles that include heavier elements like Si (4) Rocks and Small - including asteroid size objects (5) Dim Stars - including Brown Dwarfs and Black Dwarfs (6) Neutron Stars - remnants of supernovae (7) Black Holes - remnants of bigger supernovae ‣ Candidates labelled (5) have been the subject of intense searches in the halo of our . They are often called: Massive Astronomical Compact Halo Objects (MACHOs) ‣ Candidates (6) and (7) come under the heading Very Massive Object (VMO) Gas, Dust and Smaller Material ‣ This type of material is actually hard to hide in the Universe. It can produce spectral lines if hot or absorption lines due to background stars. Gas as Baryonic Dark Matter ‣ A first obvious Baryonic Candidate might be objects made of hydrogen or helium gas, the most abundant elements in the Universe. But each class of this has a problem:

(1)so called “Snowballs” (small lumps of frozen hydrogen) – it turns out that these would be expected to evaporate.

(2)Hot Gas - this is expected to emit x-rays, but very little such is seen.

(3)Cool Neutral Hydrogen Gas – this should absorb background light from distant objects like , but not much of this absorption is seen either. Dust, Rocks and Small Planets ‣ So what about material with elements more complex than hydrogen, forming dust, rocks, asteroids or even small planets. It certainly exists, here is an example Porous Chondrite interplanetary dust particle. ‣ But if the Universe is filled with a lot of this stuff then stars should be contaminated with significant abundance of “Metals”. This is not seen. We see mainly hydrogen again. ‣ Also rocks and dust can be observed by obscuration of background light. It is actually hard to hide in the Universe. It can produce spectral lines if hot or absorption lines due to background stars. Not enough of this phenomena is seen. None of this can explain the dark matter problem. MACHOs ‣ MACHOs are another possibility, basically Very Low Luminosity Stars, sometimes called Dead Stars or Stellar Remnants, stars known as Brown Dwarfs and Jupiter-like Objects. These objects would have < ~0.08 M⦿. ‣ Below this mass they never attain a high enough central for the fusion reactions that convert H into He normal in larger mass stars to start and produce high luminosity. ‣ The only they can radiate comes from Gravitational Energy as they slowly contract to a final dense state. There is an initial fairly fast contraction which can cause significant luminosity but it does not last long. Hunting for MACHOs ‣ So MACHOs can not be seen with but it is possible to use so-called Gravitational Microlensing (GM). This exciting method to search for faint stars in the halo of our galaxy was first proposed by Bohdan Paczynski in 1986. ‣ GM is a variant of the lensing described earlier but here the lens is a MACHO in the halo of our galaxy (a much smaller object than considered before) and the source is a in a nearby galaxy, usually the Large Magellanic (LMC).

Bohdan MACHO Paczynski Star in nearby galaxy Gravitational Microlensing Theory ‣ We can use the same equations for GM as previously used for Gravitational Lensing. However, in Microlensing there are a few interesting differences to what is happening: (1)For a small lens like a we might expect an or Multiple Images, but in practice the light bending is too small for this to be resolved in a on Earth. Instead we see a general brightening resulting from the multiple images superposed on each other. MOVING MACHO (2)Another vital difference is that STAR IN OBSERVER we expect the MACHO to be LMC ON EARTH moving in the halo such that the alignment between Observer, MACHO and Lens that produces this brightening will only occur for a timescale of ~days to months. Microlensing Example ‣ The image here shows an actual example candidate MACHO Event. We see a sequence of pictures of a small section of a star field taken over a period of a few weeks. Note how one of the stars in the centre gets brighter and then dims. ‣ A plot of the brightness vs. time gives us a characteristic Light Curve for the event as opposite. We see a Transient Brightening of the background star as the MACHO passes by. Microlensing Theory? ‣ We can use the same equations to describe Microlensing as we examined for general lensing previously.

r here is distance of the MACHO from the line-of-sight r source observer MACHO (lens) ‣ The MACHO moves across the line-of-sight so r changes with time, i.e. r(t). We can call it the angular separation of the lens from the observer-source line-of-sight vs. time. ‣ The Impact Parameter b, as defined previously, is effectively the instantaneous value of r. The Amplification Factor ‣ The source brightness is amplified by an Amplification Factor A that depends only on how close the alignment, r(t), is between observer, lens, and source. It is given by:

here u(t) is defined in terms of r(t), the angular separation of the lens from the observer-source line-of-sight, divided by the Einstein Radius θE and is given by:

where t0 is the time at Peak Brightness and u0 = u(t = t0). τE is the Einstein Time, the time taken by the lens to travel the angular distance θE. u = 0 corresponds to perfect alignment. The Amplification Factor ‣ So when t = t0, we have Peak Brightness. ‣ The smaller u becomes, the bigger the amplitude A, and also the smaller the value for u0 = u(t = t0), the bigger is the value that the Amplification Factor A can achieve. ‣ In the extreme case that u0 = 0, which corresponds to a situation where we get perfect alignment of source, lens and observer at t = t0, then A would become infinite.

‣ Here is an example light curve u0 for a point like MACHO for different values of u0 vs. time. ‣ The vertical axis is logarithmic multiplied with 2.5 to obtain the astronomical logarithmic brightness measure Magnitude. How to Identify a MACHO ‣ Microlensing differs from Macrolensing (the Strong and Weak Lensing with ) in that the value of u changes significantly in a short period of time, ~days to months. ‣ Note also that observation of a MACHO Event can allow us to determine a value for the Einstein Time τE, but this is not sufficient to allow the MACHO mass to be determined because we also need to know the distance D and the of the MACHO vM.

‣ In other words the main observable, the Einstein Time, is a degenerate function of the lens mass, distance and velocity. We can not determine them from a single event. ‣ So in practice to get at the we need multiple events and estimates of the distances and . How to Identify a MACHO ‣ Another issue is that many stars naturally have variability. It is important to distinguish such stars from MACHO Events. ‣ This can be done because MACHOs have three particular characteristics: (1) A MACHO Event should never repeat (they are too rare). (2) The Light Curve for a MACHO should be symmetric in time, i.e. rising and falling with the same shape. (3)The magnitude of the Light Amplification should be the same in all wavelengths e.g. the blue and red wavebands as typically measured in astronomical observations. ‣ This difference arises because the change in light for a MACHO concerns purely gravitational effects, whereas in a variable star, such as a Ceyfert Variable, the changes are due to processes to do with the star itself. MACHOs Found! or Not ‣ Several extensive searches have been undertaken for MACHOs in the halo of our galaxy by observing many stars in the LMC over several years. ‣ The most important work has been by the EROS, OGLE and MACHO collaborations. ‣ Here are examples for the first few candidate events seen by the MACHO Collaboration. Red and blue light curves of the first three microlensing candidates of the MACHO collaboration.

THE ASTROPHYSICAL JOURNAL 479, 119 È146 (1997) MACHOs Found! or Not ‣ The MACHO Collaboration identified about 45 lensing candidates towards the bulge of our own galaxy and 4 lensing candidates towards the Large Magellanic Cloud. OGLE identified about 500 events in the Galactic Bulge. ‣ As mentioned there are difficulties with interpretation. It is difficult to tell exactly where along the line-of-sight the lens is located, e.g. the LMC events could also perhaps be in our own or an intervening . Candidates in our own bulge are less convincing due to th known populations of dim stars there. ‣ Nevertheless the number of events observed can be used to infer the fraction of dark matter in galactic halos. ‣ Unfortunately, it turns out to be like enough to solve the dark matter problem as explained next: MACHOs Found! or Not ‣ Here are results from the EROS team, given as an Exclusion Plot of the fraction of our halo that could be made of MACHOs vs. mass. The curves refer to different observations. Regions above the curves are excluded at 95% confidence. The full black line is the sum of all results. ‣ The conclusion here is that MACHOs can at most make about 15% of the halo. ‣ As we will see, there are theoretical reasons to believe the fraction to be much less. It is hard to create enough baryons in the early Universe to make the number of MACHOs needed for DM. Direct Observation of Brown Dwarfs ‣ Microlensing provides a powerful tool for searching for MACHOs but there are other techniques that have been used, for instance to look for Brown Dwarfs, seen as the most likely candidate object in the class of MACHOs. ‣ Do Brown Dwarfs at least exist? A few appear to have been detected but the evidence is not clear. They are very dim <10-4 L⊙ so can easily be confused with distant bright stars and they will only ever be seen nearby. Several techniques exist: ‣ One possibility is to use their Proper . i.e. there should be candidates near to us so these will have a motion against the background sky over a few years. ‣ An example is Epsilon Indi B - a Brown Dwarf object less than 12 light-years from the Sun, discovered from the comparatively rapid motion across the sky. Direct Observation of Brown Dwarfs ‣ Probably most Brown Dwarfs are in Binary Systems like most stars. However, usually the pair of stars in binaries are found to have similar masses, so this might be true for Brown Dwarfs as well, making them difficult to see. Nevertheless there are two techniques with binaries: (1) Look for Irregularity in the motion of the companion star (2) Direct Observation ‣ For (2) the companion must not be too bright. We look for Infrared Emission, where BDs emit most strongly. ‣ However, note that even if Brown Dwarfs are seen in binaries, and even if every star had a Brown Dwarf companion, there would still not be enough to form all the Dark Matter. ‣ i.e. if Brown Dwarfs are the Dark Matter they must be mainly single stars and in large numbers. Direct Observation of Brown Dwarfs ‣ Here is one example of Brown Dwarf found in a Binary System.

These two false-colour telescope images show the first unambiguous detection of a Brown Dwarf, called GL229B. It is in orbit around the Red Dwarf star Gliese 229, located approximately 18 light-years away in the constellation Lepus. The Brown Dwarf is about 20-50 the mass of Jupiter, but is so dense it is about the same diameter as Jupiter. Very Massive Objects (VMOs) ‣ Another potential Baryonic Candidate are so-called Very Massive Objects (VMOs) - the remnants of a hypothetical population of very heavy stars that formed in early Galactic history - predicted to have masses of 103 - 106 M⊙. ‣ Such objects might lead to a large population now of: (1) Neutron Stars (2) Massive Black Holes Neutron Stars (NS) as Dark Matter ‣ Neutron Stars usually result from Supernovae. So if these are the Dark Matter then a most of the present mass of the galaxy would have had to go through a Supernovae Stage.

visualisation of a

Supernova remnant N49 shown in x-ray and optical together ‣ This seems very implausible because Supernovae produce Heavy Elements and so there should be lots of heavy elements around in the Universe. But this is not seen. ‣ Also a conventional Neutron Star ends up with mass <2 M⊙, so there would need to be a huge number of them. ‣ These factors rule out Neutron Stars as the Dark Matter. Black Holes (BH) as Dark Matter ‣ Stars larger than ~50M⊙ likely collapse into a with almost all mass going to form Black Hole (unlike the Neutron Star case where there is a ejecting material into ). This is all unlikely but not completely ruled out. There are three ways to search for Black Holes: (1) Direct Detection of Black Holes - most likely the BHs would have to be single to account for the dark matter. They might be detected because of gas and dust would cause emission lines as the gas collide with each other. (2) Disruption of Binaries - if there are a large number of BHs they would be expected to gravitationally disrupt Wide Binaries. i.e. we would not expect there to be many “loose” or wide ordinary binary systems. So finding lots of wide binaries would be a clear sign of the non- of large BHs. (3) Quasar Microlensing - described as follows: Detection of BH by Quasar Microlensing ‣ Black Holes might be detectable also by Gravitational Microlensing. BUT if they make a large fraction of the halo then because their mass is so high it means: (i) the lensing will be infrequent, and (ii) the lensing time will be very long, proportional to M1/2. Remember the Opening Angle of the Einstein Ring: ‣ For a given lensing angle so the Cross Section for lensing or a given mass , goes UP with D. So in principle if we look for lensing of halo objects in a distant galaxy by an even more distant quasar we would expect a much higher probability of lensing ‣ However, note that here the timescale for events is years or decades. ‣ There is little evidence that such Quasar Lensing exists. Conclusion so far on Baryons ‣ So observation of spectral emission and absorption rules out Gas, Dust and Smaller Candidates as the Dark Matter. ‣ Microlensing and the other observations essentially rule out MACHOs (massively compact halo objects), including Brown Dwarfs, as being a dominant Dark Matter component. ‣ The various calculations and observations above seem to indicate that the total contribution from VMO objects, Neutron Stars and Black Holes gives Ωo < ~0.03. So direct searches conclude that normal baryons do not appear to account for the dark matter ‣ But this conclusion is made far stronger by two further pieces of evidence from studies of the “Primordial Soup”: (1) from (BBNS) (2) from the Cosmic Microwave Background (CMBR) Big Bang Nucleosynthesis (BBNS) ‣ BBNS is the process by which the Light Elements (H, D, He, Li etc) get formed in the Early Universe. Calculations of this can also tell us the total number of baryons expected in the Universe, or rather the , ΩB.

‣ By comparing the value of ΩB we get from BBNS with our measurements of Ω0 we can tell what fraction of the Universe we expect to be Baryons. ‣ The nuclear reactions that occur in the early Universe are very interesting. It is covered more fully in other courses. Here we just show the main reaction equations (opposite) and give the most important details: Big Bang Nucleosynthesis (BBNS) ‣ Nucleosynthesis, by which the protons and neutrons (the Baryons) formed in the Big Bang start to do the reactions shown, begins when the Universe is about 1 minute old. ‣ The details of how the reactions work out, depend critically on the total Density of Baryons B, the ratio of the number of neutrons to protons, the p-n Ratio, and the Neutron Lifetime. It is these factors that determine the eventual Relative Abundances of the light elements. ‣ If we were confident of the in the early Universe then we could fully predict both B and the p-n Ratio. Instead we look at the effect on abundances of changing the Baryon Number and p-n Ratio and compare this with astronomical observation of the abundances now. ‣ The relative abundances are very sensitive to Baryon Density. BBNS vs. Time ‣ This plot shows how the abundances might evolve with time (or temperature) for one particular set of assumptions for B. The abundance (y-axis) is given relative to hydrogen: Abundances vs. ΩB ‣ Based on such data we can plot the Relative Abundances vs. the He-4 Baryon Density now, because we know how the D Universe expands (obviously the density will be less now than it was). the circles He-3 We can do this in terms of indicate the ‣ values ΩB, the contribution to the measured total density of the Li-7 Universe, noting that if ΩB = 1 then all the matter in the Universe would be Baryonic. BBNS and ΩB ‣ The plot shows us how the Light Elements Abundances depend on the value ΩB. Measuring those abundances thus provides a powerful means to find the real value of ΩB. ‣ The circles in the plot indicate typical values found for 4He, D, 3He and 7Li. They line up as indicated on the grey band.

‣ Amazingly the result is Ωb = 0.044 ± 0.004, in other words: The data are consistent with only about 4% of the matter density of the Universe being baryonic! ‣ So BBNS, based on simple and observation of the Light Element Abundances, tells us we should expect only 4% of the Universe to be ordinary matter. ‣ This is a startling result, but it is in clear agreement with the previous conclusions on searches for Baryonic Objects in the Universe, like MACHOs etc. CMBR and ΩB ‣ Studies of the Cosmic Microwave Background Radiation (CMBR), thanks to the satellite missions COBE, WMAP and , have revolutionised in recent decades. In particular, this has also provided further independent measurements of the Baryon Density ΩB. ‣ As indicated in Topic 1, the CMBR is a smooth radiation we seen now at 2.7K, arising from the time of “” in the early Universe when matter ceased to be ionised and were thus first free to travel. ‣ But taking a closer look we find fluctuations at about one part in 10,000. A plot from Planck showing the Universe in Galactic coordinates. Colours show the temperature with blue being the coldest. CMBR and ΩB ‣ It turns out that the size of the temperature fluctuations depends on what Angular Scale you look at on the plot, the biggest being at a scale of ~1 degree. This “Power Spectrum” is shown here: ‣ There is huge cosmology information in this plot but most importantly we see a characteristic Acoustic Oscillation due to conflict in the -Baryon at the time. The size and shape of this is very sensitive to the mixture of material and energy in the early Universe (baryons, neutrinos, dark matter). This is because photon tends to erase anisotropies while Baryon gravitational attraction tends to enhance them. CMBR and ΩB ‣ The beautiful data on the plot well fits the theoretical derived black curve and yields the following results:

Hubble constant:

Matter abundance:

Baryon abundance

Age of universe:

Age of microwave background: ‣ Here again we see the startling result that ΩB ~4% ‣ We also see for the first time a conclusion that the total matter content, ΩM is ~30%. Matter is missing! Summary on Baryons so far ‣ What we conclude from this astonishing set of data, spanning many different, independent, techniques is: We do not see enough baryonic matter as gas or dust to account for the missing matter There are nothing like enough MACHOs, VMOs or any other types of baryonic candidate Big Bang Nucleosynthesis predicts that we should anyway not expect more than 4% as baryons CMBR measurements also tells us that we don’t expect more than 4% as baryons ‣ We are starting to run out of any explanations that involve “normal” matter. However, there are perhaps two remaining possibilities we should examine before moving on to more exotic possibilities, these are: ANTIMATTER NEUTRINOS Why Not Antimatter? ‣ We know at least that Antimatter and Neutrinos exist. So could these explain the Dark Matter? ‣ Every type of particle has a corresponding , Antimatter feels like matter, and it definitely exists. ‣ Particle and antiparticle pairs have the same and mass but are opposite in all other ways (charge, colour charge, numbers). So when they collide, given that charge, energy & are conserved, they must Annihilate leaving something neutral and energetic, like Gamma Rays, /Antiquark or /Antineutrino Pairs. ‣ But we do not see enough of this . In fact it is a great mystery in why matter dominates. ‣ And anyway Antimatter still counts as part of the atomic Universe, part of the ~4% baryons. So even if it existed much in nature it could at most explain half of that. Neutrinos as Dark Matter ‣ What about Neutrinos as the Dark Matter? They at least exist!. They feel gravity and the Weak Force. ‣ They don’t actually count as an atomic component because neutrino reactions have stopped before Nucleosynthesis occurs, so they don’t influence the atomic abundance. ‣ Hot Big-Bang Theory also tells us that we expect a lot of neutrinos in the Universe, about as many cosmic ”Black- Body Neutrinos” as there are microwave photons. So if neutrinos have even a small mass they can contribute to the dark matter. The density of neutrinos is given by:

3 sum extends over the masses of all ρ = n m v 11 γ ∑ υ the neutrino flavours present-day density in microwave background photons ‣ We now know there are 3 neutrino flavours so . € Neutrinos as Dark Matter ‣ From this we can estimate the actual number density of neutrinos now from the energy in radiation in today's Universe using the Stefan-Boltzmann Law, considering that the Universe is filled with blackbody radiation at 2.7 K. ‣ The in this equilibrium radiation is given by: u(T) = const × T 4 const ~ 7.56 x 10-15 erg cm-3 k-4 ‣ From this the Number Density of Photons expect is: u(T) n = ~ 1080 cm-3 so: cm-3 γ kT € ‣ Allowing for possible errors in the Hubble Constant and for the possibility that neutrinos might contribute anything from some of the Dark Matter to all of it, we predict a reasonable € range of mass for the neutrino as: 4eV ≤ mν ≤ 40eV ‣ Note the point here that if the neutrino mass is too large then we might “Over-Close” the Universe.

€ Dark Matter and Neutrino Mass ‣ We do not yet know the mass of neutrinos but the Ray Davis experiment that first observed neutrinos from the Sun, subsequently confirmed by many others, eventually showed that Neutrinos Oscillate between their 3 flavours and so do have mass. ‣ These result plus cosmology data indicate that the combined mass must be <1 eV. ‣ So neutrinos are simply too light and at most add to 0.5% of the mass in the Universe. ‣ Note that this is about the same amount as all the stars in the Universe! an amazing conclusion in itself.. ‣ As we will see in Topic 5 there are many other reasons to disfavour neutrinos as dark matter. We reach a final overall conclusion here: Dark Matter is highly likely to be NON-BARYONIC and furthermore probably new physics Summary of Topic 4 A guide for the exam ‣ A first explanation for dark matter is that it is hidden baryonic material - understand the various possible candidates and the arguments that make each one unlikely to be correct. ‣ Understand MACHOs and the basic equations that govern Microlensing searches for them in our galaxy. Know about searches for Brown Dwarfs, VMOs and other candidates. ‣ Big Bang Nucleosynthesis theory and observation of the Cosmic Microwave Background Radiation provides important evidence for the lack of baryons in the Universe - understand the arguments that lead us to believe ΩB ~0.04. ‣ We are forced to conclude that normal baryonic matter can not explain the dark matter - know the arguments about antimatter and neutrinos that lead us to believe also that no known subatomic particles can be the explanation either. Terms to know from Topic 4 A guide for the exam ‣ Baryons, Baryonic Materials, Interstellar Gas, Snowballs, Dust, Rocks ‣ Dim Stars, Brown Dwarfs, Stellar Remnants, Dead Stars, MACHOs ‣ Cool Neutral Hydrogen Gas, Hot Gas, Jupiter-like Objects ‣ Gravitational Microlensig, LMC, Light Curve, Transient Brightening ‣ Amplification Factor, Einstein Radius, Einstein Time, Peak Brightness ‣OGLE, EROS, MACHO Collaborations, Halo Fraction, Exclusion Plot ‣ Proper Motion, Binary Systems, VMO, Neutron Star, Black Hole ‣ Quasar Microlensing, Wide Binary, Big Bang Nucleosynthesis, BBNS ‣ Baryon Number Density, ΩB, p-n Ratio, Light Element Abundances, ‣ Cosmic Microwave Background Radiation, CMBR, Angular Scale ‣ Power Spectrum, Acoustic Oscillation, Photon-Baryon Plasma ‣ Antimatter, Neutrino Mass, Stefan-Boltzmann, Universe Over-Closure Questions on Topic 4 to help with exam revision ‣ Use the gravitational lensing equations to show that we do not expect to be able to resolve an Einstein Ring in the case of a MACHO event. ‣ What three characteristics of a MACHO event allow it to be distinguished from a variable star. ‣ Why is antimatter not the solution to the dark matter problem? ‣ How does the Einstein Time of a MACHO event depend on the MACHOs velocity and mass. ‣ What is the theoretical value for the Amplification Factor A in gravitational microlensing when there is perfect alignment? ‣ Explain how Brown Dwarfs might be observable, other than by microlensing. ‣ How much more 6Li would there need to be than is observed to make us believe that the Universe had enough baryons for closure? ‣ What is the peak angular scale seen in the CMBR? ‣ What mass would neutrinos need to have to explain all the dark matter? Equations from Topic 4 Equation reminders for the exam

u(T) n = γ kT 3 ρ = n m v 11 γ ∑ υ € u(T) u(T) = const × T 4 n = γ kT €

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