The Dark Matter Story

Mount Wilson observatory, built on top of Mount Wilson in Southern California by George Ellery Hale, a prolific astronomer who discovered magnetic field in sunspots, houses the 100 inch telescope, largest from November 2, 1917 to January26, 1949. During early 1930’s, Fritz Zwicky, then associate professor of physics at Caltech, was using this 100 inch telescope to look at galaxies in Coma Cluster- a rich cluster of approximately 1000 galaxies about 330 million light years away. Zwicky gathered light from galaxies through the telescope and obtained spectrum by placing spectrograph at focus of telescope. Spectrograph is a Spectrometer used to obtain spectrum which is a graph showing intensity as function of wavelength. Spectrograph of those days were light tight boxes comprising a prism or diffraction grating plate to which light was let through a narrow opening and a detector placed at appropriate distance and angle to record the spectrum. 

Diffraction Gratings, pioneered by David Rittenhouse in 1785 and furthered by Joseph von Fraunhofer in 1821, are plates with many uniformly spaced, parallel, opaque, grooves per millimeter, engraved upon them. Transparent plates are used for making transmission gratings and metal coated opaque plates are used for reflective gratings. Space between grooves could be of the order of microns. Groovings can be sinusoidal or triangular. Triangular groove gratings are also known as blazed gratings because of higher brightness of the spectra they produce. Grooves do the diffraction. Light falling on gratings diffracts and splits into constituent wavelengths. In most directions, light diffracted from one groove cancels out light diffracted from another, known as destructive interference. In certain number of directions though, constructive interference takes place. These directions correspond to diffraction order ‘m’. Many such orders exist when wavelength of light diffracted is much smaller compared to spacing between adjacent grooves often denoted by ‘d’. Fewer such orders exist in case ‘d’ is comparable to wavelength. Wavelength ‘λ’ of diffracted light depends on angle of incidence w.r.t normal to grating substrate, angle of diffraction w.r.t normal to grating substrate, spacing between consecutive grooves and diffraction order. Gratings can be reflective or transmissive. Reflective gratings are better suited for commercial spectrography. The detector used to be a photographic plate which was glass plate coated with special emulsion. 

mλ = d(sinθ_i + sinθ_r)

Where, θ_i = Angle of incidence measured w.r.t grating normal, anticlockwise

           θ_r = Angle of diffraction measured w.r.t grating normal, clockwise

Zwicky obtained graph of intensity of light as function of wavelength. This was usually done using a Microdensitometer which shines a compact ray of light through the photographic plate to a light sensitive photo multiplier tube. The tube evaluates and registers amount of light at each wavelength as light crosses the photographic plate, usually in form of an intensity amplitude and wavelength graph. Once wavelengths were obtained, Zwicky calculated redshift for each galaxy and then radial velocities and using that velocity dispersion for the cluster. Link between redshift and velocity of galaxies can be expressed as:

z = (λ – λ₀)/λ₀ = v/c = (R_Present/R_Emit)-1

For z << 1.

In much broader sense:

z = {(λ/ λ₀)² – 1}/{(λ/ λ₀)² + 1} = v/c

Here, z = Redshift

         λ = Measured wavelength

         λ₀ = Emitted wavelength

         v = Radial velocity of object

         c = Speed of light

         R_Present = Radius of curvature of Universe at present = 1 (Very-Very close)

         R_Emit = Radius of curvature of Universe when radiation was emitted

Velocity v calculated this way is the radial velocity or line of sight velocity of the object.

V_Radial = V_Recessional ± V_Peculiar

Here, V_Recessional is velocity due to accelerating expansion of spacetime and V_Peculiar or sometimes infall velocity is velocity of object due to net gravitational effect of surrounding objects. For higher radial velocities or large distances, V_Radial can be approximated to V_Recessional. Peculiar velocities and Galactocentric velocity of sun become significant at radial velocities below about 1500km/s or in other words for closer objects. Moreover, several Earth related velocities should also be considered for higher precision. Distance d of object from viewer can be linked to its recessional velocity using the equation:

V_Recessional = H₀ × d

Known as Hubble’s law. Here, H₀ is Hubble constant with current value of 67.8 km/s/Mpc, Mpc stands for megaparsec and equals to 1 million parsecs or 3.262 million light years or 3.086×10¹⁹ km. Hubble constant is speed with which a galaxy at 1 Mpc distance, is moving away from us in any direction, assuming our Universe is homogeneous and isotropic at large scales. Inverse of Hubble constant is called Hubble time T_h.

In his 1933 paper titled ‘The redshift of extragalactic nebulae’ Zwicky considered Coma cluster to be virialized which means the cluster is neither expanding nor collapsing, it has reached a state of dynamic equilibrium. Further, he counted the number of Galaxies in cluster to be approximately 800 each having a mass of the order of 10⁹ Solar masses. He thus calculated the approximate total mass M of cluster.

M ∼ 800 × 10⁹ × 2 × 10³⁰ kg = 1.6 × 10⁴² kg

He then calculated mean potential energy of system using:

P.E_Mean = (P.E_Total)/M ∼ -64 ×10⁸ m²/s²

Where, P.E_Total = -(3/5) × (GM²)/R

R is radius of cluster, about a million light years or 10²² m.

Since cluster is considered virialized, virial theorem can be applied, according to which:

K.E_Mean = -(1/2) × P.E_Mean = 32×10⁸ m²/s²

Also, K.E_Mean = (Mean v²)/2

From this, (Mean v²)^1/2 = 80 km/s

Also, mean v² = 3 × σ², where σ is radial velocity dispersion. From this,

σ = ((Mean v²)^1/2)/√3

Zwicky found a radial velocity dispersion of 1019 ± 360 km/s for Coma cluster which he calculated from observed radial velocity of 8 Galaxies using their spectral redshift, Comparing the two results, Zwicky concluded that average density of Coma cluster must be at least 400 times greater than density due to luminous matter alone, for a velocity dispersion of over 1000 km/s. This directly indicated presence of non luminous matter in the cluster. Zwicky called it Dunkle Materie which is Swiss for dark matter. Since Zwicky considered Hubble parameter H₀ to be 558 km/s/Mpc, his estimates are different than more recent ones, but meaningful nonetheless.

In 1973, Physicist James Peebles and Astronomer Jeremiaha Ostriker were trying to simulate the evolution of Galaxies using N Body Simulation. They programmed 300 mass points to represent stars in a Galaxy rotating about a central point with more mass points towards center and fewer toward boundary. Simulation was based on movement of mass points due to Newtonian gravitational force between them. In less than a rotation period most of the mass points were collapsing into a bar shaped blob near central region. However, they were able to obtain recognizable spiral or elliptical shapes on adding a uniform mass distribution 10 times the size of the 300 mass points. This indicated that Galaxies might be harboring non luminous matter about 10 times the mass of visible matter. They presented their results in 1974 paper titled ‘The size and mass of Galaxies, and the mass of the Universe’. They also gave a criterion known as Ostriker-Peebles criterion, according to which if T is first kinetic energy component and W is total kinetic energy, then, a Galaxy will become barred if T/W > 0.15.

At Carnegie institution in Washington, Astronomer Vera Cooper Rubin was collaborating with instrument maker Kent Ford. Ford had created one of the most sensitive spectrometer of those days. Together they used this spectrometer to obtain reliable spectrum of Hydrogen gas clouds orbiting in different parts of Andromeda, including the boundary regions. They obtained the velocities and plotted a chart. What they obtained was a curve which looked almost flat indicating that the gas near boundary region is orbiting as fast as the gas near central region of Galaxy. They noted an almost constant gas velocity outside visible boundary of Galaxy from their plot. This couldn’t be explained by Newtonian gravity. Gas orbiting that fast near boundary region couldn’t be held by the gravity of luminous mass of Galaxy alone. This indicated presence of non luminous matter in large quantities, about 10 times more than luminous matter according to Rubin’s calculations. Rubin noted that if Andromeda obeyed Newton’s law then it must contain Dark Matter with quantities increasing with increasing distance from its center. Rubin and Ford announced their result first in 1975 at a meeting of the American Astronomical Society. In 1980, Rubin published these results in a widely reviewed paper.

In 2004 NASA’s space based orbiting X-ray observatory recorded an image which came to be known as galaxy cluster 1E 065756 or Bullet Cluster in common usage. A deeper look at object 1E 065756 revealed that it’s in fact two Galaxy clusters that underwent a collision about 100 million years ago. Gas in two clusters underwent friction as the two clusters passed through each other and got superheated emitting X-ray captured by the observatory. Hubble space telescope recorded optical image of the object. Scientists also used gravitational lensing effect of colliding clusters to obtain an image of gravitational mass of object. On combining the three images it was clear that X-ray emitting portion of object is lagging behind mass concentration, indicating that weakly interactive dark matter and heavy compact objects passed right through without colliding but the gas was slowed down.

At end of cosmic inflation, at about 10^-32s after big bang, inflation field decayed into Quark-Gluon plasma. This phenomenon is named Reheating. Between 10^-12s to 10^-6s after big bang, W and Z Bosons and Photons separated and Higgs field manifested and particles interacting with this field acquired mass via Higgs mechanism. Between 10^-6s and 1s after big bang, Universe was cool enough for Quarks to combine using Gluons forming Protons and Neutrons, collectively known as Hadrons. Between 1s and 10s after big bang most of Hadrons and Antihadrons annihilated each other leaving a Universe primarily filled with Leptons and Antileptons. Approximately 10s after, creation of new Lepton-Antilepton pairs stopped as the Universe further expanded and cooled. A small residue of Leptons remained at the end of mutual annihilation. Between 10s and about 380000 years after big bang, Photons kept colliding with charged electrons, protons and nuclei because of low mean free path. Nucleosynthesis took place during this period forming heavier nuclei. 70000 Years after Big Bang, Cold Dark Matter was dominating. Small variations were present in the density of matter and dark matter, owing to quantum mechanical fluctuations. Both normal matter and dark matter were pulled toward higher density regions by gravity making dense regions denser and rare regions rarer. Dark matter kept getting concentrated around center of these quantum mechanical fluctuations without any obstruction as it didn’t interact with Photons, but normal matter while falling in under the effect of gravity was getting hit by Photons causing it to move away. 

When photon pressure was more, normal matter moved away and when gravity was stronger, it fell in creating an oscillating effect known as baryonic acoustic oscillation. When the normal matter fell in it grew denser and therefore hotter and when it was pushed out, it cooled off. Also areas where matter concentrated grew hotter compared to areas from where it moved out giving rise to hotter and colder regions in Universe which we see as hot and cold spots of different sizes in CMB map. About 380000 years after Big Bang, the Universe was so big it became cool enough for electrons and protons to combine to form neutral atoms in a process known as recombination. The process was fast and faster for Helium than for Hydrogen. Due to recombination the mean free path of Photons became infinite and they for the first time were able to travel throughout the Universe. This phenomenon is known as decoupling. The pattern of temperature variation and therefore the baryonic acoustic oscillations and information about fluctuations that rose during inflation was encoded into this light which we today call cosmic microwave background radiation as the wavelength of this primordial light has shifted to microwave band after billions of years of traveling through an expanding Universe. This is why an analysis of cosmic microwave background is sometimes called a baby picture of Universe. It shows the seeds of large scale structures that we find in Universe today. Planck CMB data gives an effective temperature of CMB as 2.7 degree Kelvin with variations of 1 part per 100,000. The angular size of cold and hot spots observed in CMB and extent of temperature variation indicates a dark matter density of 26.8%, normal matter density of 4.9% and a dark energy density of 68.3%.

Efforts are ongoing around world to detect dark matter directly. Scientists have hypothesized a fundamental particle having all known properties of dark matter known as WIMP and are trying to detect it through underground experiments in deep mines such as UK’s Boulby mines. Now,  USA’s large underground xenon or LUX experiment and Europe’s ZonEd proportional scintillation in liquid noble gases or Zeplin experiment are collaborating to combine both experiments to increase sensitivity to WIMPs by more than 100 times. LZ experiment is second generation direct dark matter detection experiment. 7 ton purified liquid xenon at ultra low temperature with an active system to suppress non WIMP signals is used in this experiment to detect faint effect of a WIMP on a Xenon nucleus. The experiment uses high voltage feed through, 120 veto photo multiplier tubes, 488 photo multiplier tubes, additional 180 Xenon skin photomultiplier tubes and Gadolinium loaded liquid scintillator veto.  System is housed inside a water tank shield. The LZ collaboration has 190 scientists in 32 institutions.

Meanwhile scientists working on dark energy survey at Cerro Tololo Inter-American Observatory, in Chilean Andes, are using the 570 megapixel Dark Energy camera or DE cam mounted on Blanco 4 meter telescope there, to create detailed maps of dark matter by utilizing effect of Dark Energy and strong and weak gravitational lensing effect of said dark matter, in order to understand the nature of dark energy through analysis of clumpiness of dark matter in those maps. DE cam has about 3 ft wide mirrors and weighs between 4 to 5 tons. It is the largest digital camera ever built. The survey started on 31 Aug 2013 and will utilize 525 nights of observation till 2018 to record information from 300 million galaxies. It is supposed to create the most detailed dark matter map of Universe. Dark Matter or cold Dark Matter in this case, bends light through its gravitational effect and the bending is directly proportional to strength of gravitational field which is directly proportional to the concentration of dark matter. Therefore a measure of bending in light could be used to create a density map of Dark Matter through careful calculations.

References:
1) http://blair.pha.jhu.edu/spectroscopy/measure.html
2) https://arxiv.org/pdf/astro-ph/9904251.pdf
3) http://adsabs.harvard.edu/full/1999ApJ...525C1223T
4) https://ned.ipac.caltech.edu/level5/Sept03/Einasto/paper.pdf
5) https://www.sciencealert.com/this-timeline-shows-the-entire-history-of-the-universe-and-where-it-s-headed

Image credits goes to respective sources.