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Estimation of Dark Matter Mass from Galaxy Rotation Curves

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Estimation of Dark Matter Mass from Galaxy Rotation Curves An Introduction to Galaxies and the Interstellar Medium IIA Summer School Instructor : Mousumi Das, [email protected] July 2021 !opics that "e plan to co#er ... ● What are Galaxies? ● Spirals and ellipticals ==> the 2 main types of galaxies. ● The main components of spiral and elliptical galaxies. ● Our Galaxy : the Mil!y Way and the interstellar medium ● The morphological classes ==> the Hu##le Se$uence. ● Galaxy clustering : galaxy pairs, groups, clusters and the large scale structure of our uni&erse. ● Our galaxy neigh#ourhood. ● Galaxy interactions. ● Galaxy e&olution and the color-magnitude plot. ● Galaxy rotation and dark matter. !he Mil$y %ay in the ni&ht s$y ● The ilky Way ( W) appears in the night s!y as a stream of diffuse emission. This term +as coined #y the Gree!s and it means ,ri&er of milk-. ● Galileo in ./.0 o#ser&ed it +ith his telescope and found it to #e composed of stars. "ence the W +as con1rmed to #e a stellar system. ● The W is actually the plane of our o+n galaxy. Our galaxy is called the W and is al+ays denoted #y Galaxy i.e. +ith a capital G. ● We can see the plane of our Galaxy #ecause the solar system is tilted out of the Galactic plane. Galactic Plane and Island Universes ● Immanuel Kant (in approx 1787) was the first to give a theory of the sun and solar system moving under their mutual gravitational field. ● He also explained the formation of the galactic plane and hence the origin of the MW in the sky. ● He also explained that the fuzzy patches in the sky may other galaxies or “island universes”. ● Comet hunter Charles Messier catalogued may more fainter nebulae (both stellar and planetary nebulae). His catalogue is the Messier catalogue. ● William and Caroline Herschel (1800's) also compiled a list. Dreyer (1895) compiled the New General Catalogue (NGC). Photographic plates : revolutionized astronomy ● With the advent of photography, astronomers were able to record spectra of stars and images of the night sky. ● Kapetyn used stellar spectra to build a model of our Galaxy, called the Kapteyn Universe. However, he did not correct for interstellar extinction. Hence his model put our solar system too close to the galaxy center. Barnard Cloud and and a nearby star forming region Ad#ent o' radioastronomy ● In 1932 Karl Jansky discovered that our universe emits in a broad range of radio waves. ● van der Hulst (1944) predicted that we should be able to detect 21cm radio emission from neutral hydrogen (HI) from galaxies and the MW. ● Detection (approx 1950) was done by several scientists e.g. Oort and Muller (Netherlands), Ewan and Purcell (Harvard), Christiansen (Australia). ● Stellar and radio observations helped us understand how stars and gas rotate in the disks of galaxies (e.g. Lindblad, Oort). In Pune, India "e ha#e one o' the lar&est arrays of radio telescopes in the world called the Giant Meter"a#e radio telescope (GMR!+ which is used for doin& low fre,uency radioastronomy. Multi"a#elen&th Approach to Astronomy ● Research in astronomy is now done at a variety of wavelengths. The different wavelengths enable us to study different physical processes in space. ● Both space based and ground based observatories are used to study galactic and extragalactic sources. ImagingImaging ofof galaxiesgalaxies :: studyingstudying galaxiesgalaxies atat differentdifferent wa&elengthswa&elengths %e obser#e galaxies at different "a#elen&ths. It helps us understand the different processes taking place in &alaxies. --ray : ROSA! Ultraviolet : GA12- 3isible : DSS Radio : 5ear-infrared : IRAS Mid-infrared : 7ar.infrared : SPI!62* IS/ Effelsber& Stars : the basic buildin& bloc$s o' galaxies 3 ain se$uence type star. assi&e and has a high temperature The star cluster .04. 5ote the reddish stars. 3 molecular cloud +ith ne+ly formed stars. The stars are formed as a cluster and ha&e &arying masses. The stellar +inds can dri&e the gas a+ay. %hat%hat areare galaxiesgalaxies andand thethe 22 mainmain typestypes ● Galaxies are collections of stars (106 to 1011 in number). The smallest galaxies may have even 105 number of stars. ● Galaxies are mainly of 2 types : elliptical or spiral depending on their morphology. Spiral galaxies have a disk of stars that are rotating in a plane whereas elliptical galaxies are ellipsoid in shape. There are also irregular and peculiar shaped galaxies. An elliptical galaxy : ellipsoidal in shape A spiral Galaxy : has a disky shape Image Credit HST : Above is the Hubble Deep Field showing different types of galaxies. What are galaxies made of9 A typical spiral or disk galaxy is made up of stars, interstellar gas (both ionized and neutral gas (mainly hydrogen denoted by HI and ionized H gas by HII), interstellar dust and dark matter. A typical elliptical galaxy is mainly composed of stars, hot ionized gas and dark matter. The gas is mainly neutral hydrogen (called HI), molecular hydrogen and ionized gas. The stars can vary from the most massive O and A types in the star forming disks to the really old stars in globular clusters. An elliptical galaxy: NGC 4458 The spiral Galaxy M101 2mage 6redit : en.+ikipedia.com Image Credit : Hu##lesite.org Important distance scales : The fundamental distance unit in astronomy is the parsec (pc) scale. 2t is defined as the distance at which a star has a parallax of .-. 7arallax is the angular shift in the s!y of a star o&er a period of / months . pc = 20/ 2/8 39 = 4.0:/ x .0.: cm = 4.2/ light years (Where . 3U = earth ; sun distance approx = .<=%8=>%:>. km . light year = distance light tra&els in one year ) Important distance scales for galaxies : ?iloparsec (!pc) : example, our galaxy has a radius of at least .8 kpc Megaparsec ( pc) : example, near#y large galaxies are a fe+ Mpc a+ay. The differences bet"een spirals and ellipticals KinematicKinematic DifferenceDifference bet"eenbet"een 2llipticals2llipticals andand SpiralsSpirals ● Spirals are rotating disks of stars and gas and dark matter, where the support against gravity is due to rotation. This is similar to the satellite problem that you may have studied in high school. GM(r)/r2 = v2/r ● In an elliptical galaxy the gravitational support is due to the random motion of the stars. So we have to use the virial equation 2T + V =0 2 Σm v = Σ Gm m /r i i i j ij Or σ2 = GM/R TheThe MassMass inin aa @isk@isk galaxygalaxy ● A disk galaxy has a rotation velocity of 220 km/s at a radius of 8.5 kpc from the galaxy center. Calculate the mass within that radius. What is the mass in solar mass units where 33 21 M = 2x10 gm and 1kpc=3x10 cm sun ● Answer : M = v2xR/G = (220x105)2 x (8.5x3x1021 cm)/6.67x10-8 39 8 = 1850x10 gm = 6.16 x 10 M sun TheThe MassMass ofof anan EllipticalElliptical galaxygalaxy ● An elliptical galaxy has a mean velocity dispersion of 100 km/s and a radius of 20 kpc. Calculate the mass of the elliptical galaxy in solar mass units where 33 M = 2x10 gm sun SpiralSpiral GalaxiesGalaxies :: dis!sdis!s embeddedembedded inin haloshalos ● The stars in spiral galaxies are in disks and are supported by rotational motion about their galaxy centers. ● It is composed of a disk of stars and gas that are embedded in a very massive dark matter halo. There maybe a bulge in the center of the disk and an elongated feature called a bar. ● There are compact old, star clusters called globular clusters in the halo. ● The name `spiral' comes from the spiral features seen in the disks. Our Galaxy Structure Image credit : astronomyonline.org 2lliptical2lliptical GalaxiesGalaxies :: SupportedSupported byby randomrandom motionmotion oror non-circularnon-circular orbitsorbits ofof starsstars ● They are ellipsoidal in shape and M87 Galaxy supported #y the the motion of the stars that are in &arious non'circular or#its (loop or#its% #oxy or#its% etc) . ● They often appear fairly featureless in optical images. Their stars are old and generally no ongoing star formation is seen. ● The most massi&e #lac! holes are found in the centers of elliptical galaxies. They usually sho+ strong nuclear acti&ity Image Credit : APOD, star.ucl.uk 2lliptical Galaxies : their halos ● The stars are embedded in a very massive dark matter halo. There may small nuclear disks of dust and gas, possibly due to mergers. ● They are often surrounded by massive halos of hot gas emitting in X-rays. The gas is a remnant from early star formation. NGC6482 : 2MASS image K band NGC6482 : Xray halo (image credit image (2MASS survey) Chandra/NASA) 2lliptical Galaxies : nuclear acti#ity ● They have the most massive nuclear black holes (107 to 1010 solar mass) in the Universe. A good example is M87, the nearest elliptical galaxy. The recent Event Horizon Telescope (EVT) detection of a SMBH “shadow” in a nearby galaxy was from M87. ● They show the high nuclear activity due to accretion onto the supermassive black holes (SMBHs). Quasar host galaxies are ellipticals. They often have radio jets. They show emission in the highest frequencies – gamma rays and X-rays. Centaurus Galaxy (with jets overlaid) Image credit : apod.nasa.gov Differences between spiral (or disk) and elliptical galaxies ● They are rotationally supported ● Supported by velocity dispersion of against gravity. Disky shapes. stars. Ellipsoidal shapes. ● Contain an interstellar gas in the ● Usually do not contain interstellar form of molecular hydrogen gas neutral hydrogen or molecular (H ) and neutral hydrogen (HI) gas. 2 hydrogen gas. ● Made up of a mixture of old and ● They are made up of old stars and do young stars.
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