Cosmologia AA 2017/2018Prof. Alessandro Marconi

Dipartimento di Fisica e AstronomiaUniversità di Firenze

INAF - Osservatorio Astrofisico di Arcetri

Contatti, Bibliografia e LezioniProf. Alessandro Marconi

Dipartimento di Fisica e Astronomia, stanza 254 (2o piano)Via G. Sansone 1, 50019, Sesto Fiorentino (Firenze), Italiaemail: alessandro.marconi@unifi.ittel: 055 457 2069 (Dip.) - 055 2752 239 (Oss.)

Bibliografia Malcolm Longair, Galaxy FormationSpringerHoujun Mo, Frank van den Bosch, Simon White, Galaxy Formation and EvolutionCambridge UPBarbara Ryden, Introduction to CosmologyCambridge UPDove trovare le lezioni

MOODLE Corso “B016319 (B058) - Cosmologia 2017-2018” http://www.arcetri.astro.it/~marconi → ”Didattica”

Argomenti del corsoBasi osservative: radiazione cosmica di fondo, struttura a larga scala, legge di Hubble

Basi teoriche: curvatura dello spazio e la metrica, equazioni di Friedmann e loro caratteristiche, i parametri cosmologici

La storia termica dell'universo

La nucleosintesi

Lo sviluppo e l'evoluzione delle fluttuazioni primordiali

L'importanza della materia oscura

La ricombinazione: il fondo cosmico a microonde e le sue fluttuazioni

L'epoca successiva alla ricombinazione (→Cosmologia II)

Il mezzo intergalattico (→Cosmologia II)

La formazione delle prime stelle (→Cosmologia II)

Modelli di formazione ed evoluzione delle galassie (→Cosmologia II)

Osservazioni Fondamentali

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La radiazione di fondo cosmica

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Spettro della CMB osservato e fit; le incertezze corrispondono a 400 σ (Fixsen et al. 1996).

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La radiazione di fondo cosmica

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Mappa della temperatura della radiazione di fondo su tutto il piano del cielo (risoluzione spaziale 7o).

2.1 The Spectrum and Isotropy of the Cosmic Microwave Background Radiation 31

Fig. 2.2a–c. Maps of the whole sky in galactic coordinates as observed at a wavelength of5.7 mm (53 GHz) by the COBE satellite at different sensitivity levels. a The distribution of totalintensity over the sky. b Once the uniform component was removed, the dipole componentassociated with the motion of the Earth through the background radiation was observed, aswell as a weak signal from the Galactic plane. c Once the dipole component was removed,radiation from the plane of the Galaxy was seen as a bright band across the centre of thepicture. The fluctuations seen at high galactic latitudes were a combination of noise fromthe telescope and the instruments and a genuine cosmological signal. The rms value of thefluctuations at each point away from the Galactic equator amounted to 36 µK. When averagedstatistically over the whole sky at high latitudes, an excess sky noise signal of cosmologicalorigin of 30 ± 5 µK was detected (Bennett et al., 1996)

smoothed to 10 angular scale. These values were found to be frequency independentfor the three COBE frequency channels at 31.5, 53 and 90 GHz. The detection ofthese fluctuations is a crucial result for understanding the origin of the large-scalestructure of the Universe. The COBE observations allow information to be obtainedabout the angular spectrum of the intensity fluctuations on all scales θ ≥ 7. InChap. 15, we will deal with the important cosmological information which can be

A. Marconi Cosmologia (2016/2017)

La radiazione di fondo cosmica

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Mappa della temperatura della radiazione di fondo su tutto il piano del cielo (risoluzione spaziale 7o).

Mappa dopo la sottrazione del valore medio della temperatura.

2.1 The Spectrum and Isotropy of the Cosmic Microwave Background Radiation 31

Fig. 2.2a–c. Maps of the whole sky in galactic coordinates as observed at a wavelength of5.7 mm (53 GHz) by the COBE satellite at different sensitivity levels. a The distribution of totalintensity over the sky. b Once the uniform component was removed, the dipole componentassociated with the motion of the Earth through the background radiation was observed, aswell as a weak signal from the Galactic plane. c Once the dipole component was removed,radiation from the plane of the Galaxy was seen as a bright band across the centre of thepicture. The fluctuations seen at high galactic latitudes were a combination of noise fromthe telescope and the instruments and a genuine cosmological signal. The rms value of thefluctuations at each point away from the Galactic equator amounted to 36 µK. When averagedstatistically over the whole sky at high latitudes, an excess sky noise signal of cosmologicalorigin of 30 ± 5 µK was detected (Bennett et al., 1996)

smoothed to 10 angular scale. These values were found to be frequency independentfor the three COBE frequency channels at 31.5, 53 and 90 GHz. The detection ofthese fluctuations is a crucial result for understanding the origin of the large-scalestructure of the Universe. The COBE observations allow information to be obtainedabout the angular spectrum of the intensity fluctuations on all scales θ ≥ 7. InChap. 15, we will deal with the important cosmological information which can be

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La radiazione di fondo cosmica

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Mappa della temperatura della radiazione di fondo su tutto il piano del cielo (risoluzione spaziale 7o).

Mappa dopo la sottrazione del valore medio della temperatura.

Mappa dopo la sottrazione del termine di dipolo.

Bennett et al. 1996

2.1 The Spectrum and Isotropy of the Cosmic Microwave Background Radiation 31

Fig. 2.2a–c. Maps of the whole sky in galactic coordinates as observed at a wavelength of5.7 mm (53 GHz) by the COBE satellite at different sensitivity levels. a The distribution of totalintensity over the sky. b Once the uniform component was removed, the dipole componentassociated with the motion of the Earth through the background radiation was observed, aswell as a weak signal from the Galactic plane. c Once the dipole component was removed,radiation from the plane of the Galaxy was seen as a bright band across the centre of thepicture. The fluctuations seen at high galactic latitudes were a combination of noise fromthe telescope and the instruments and a genuine cosmological signal. The rms value of thefluctuations at each point away from the Galactic equator amounted to 36 µK. When averagedstatistically over the whole sky at high latitudes, an excess sky noise signal of cosmologicalorigin of 30 ± 5 µK was detected (Bennett et al., 1996)

smoothed to 10 angular scale. These values were found to be frequency independentfor the three COBE frequency channels at 31.5, 53 and 90 GHz. The detection ofthese fluctuations is a crucial result for understanding the origin of the large-scalestructure of the Universe. The COBE observations allow information to be obtainedabout the angular spectrum of the intensity fluctuations on all scales θ ≥ 7. InChap. 15, we will deal with the important cosmological information which can be

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La radiazione di fondo cosmica

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Mappa delle fluttuazioni di temperatura ottenuta dal satellite WMAP dopo aver sottratto termine costante, di dipolo ed emissione galattica. La risoluzione angolare è ~1/20 delle immagini precedenti (20 arcmin).

Bennett et al. 2003

32 2 The Large-Scale Structure of the Universe

Fig. 2.3. A map of the whole sky in galactic coordinates as observed by the WMAP satelliteat millimetre wavelengths (Bennett et al., 2003). The angular resolution of the map is about20 times higher than that of Fig. 2.2c. The emissions due to Galactic dust and synchrotronradiation have been subtracted from this map

derived from observations of temperature fluctuations in the Cosmic MicrowaveBackground Radiation on smaller angular scales.

It is interesting to compare the COBE map (Fig. 2.2c) with the more recentWMAP observations of 2003 made with about 20 times higher angular resolution(Bennett et al., 2003) (Fig. 2.3). It can be seen that the same large scale featuresare present on both maps. In particular, regions of strong positive and negativefluctuations agree rather well. We will have a lot more to say about Fig. 2.3 in duecourse.

The COBE observations are crucial for cosmology. From the point of view ofthe structure of the Universe on the very largest angular scales, they show thatthe Cosmic Microwave Background Radiation is isotropic to better than one partin 100,000. Whatever its origin, this observation in itself shows that the Universemust be extraordinarily isotropic on the large scale. As we will show, it is whollyconvincing that this radiation is the cooled remnant of the very hot early phases ofthe Big Bang.

How is the distribution of radiation related to the distribution of matter in theUniverse? We will take up this topic in much more detail in Chap. 9, but it is useful tooutline here how they are related. In the standard Big Bang picture, when the Universewas squashed to only about one thousandth of its present size, the temperature ofthe Cosmic Microwave Background Radiation was about one thousand times greaterthan it is now. The temperature of the background radiation varies with redshift zas Tr = 2.728(1 + z) K and so, at a redshift z = 1500, the temperature of theradiation field was about 4000 K. At this temperature, there were sufficient Lymancontinuum photons in the Wien region of the background spectrum to photoioniseall the neutral hydrogen in the Universe. At this early epoch, known as the epoch

La radiazione di fondo cosmica

Mappa delle fluttuazioni di temperatura ottenuta nel 2013 dal satellite Planck (ESA).

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Distribuzione delle galassie

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34 2 The Large-Scale Structure of the Universe

Fig. 2.4. The distribution of galaxies with 17 ≤ bj ≤ 20.5 shown in an equal area projectioncentred on the South Galactic pole. This image was reconstructed from machine scans of 185UK Schmidt plates by the Cambridge APM measuring machine. There are over two milliongalaxies in this image. The small empty patches in the map are regions that have been excludedabout bright stars, nearby dwarf galaxies, globular clusters and step wedges (Maddox et al.,1990)

apparent magnitudes in the range 17 ≤ bj ≤ 20.5 and so represents the distributionof galaxies on the sky on the grandest scale.

It is apparent that, although one bit of Fig. 2.4 does not look too different fromanother on a large enough scale, the distribution of galaxies is far from uniform ona small scale. There appear to be clumps of galaxies, stringy structures and holes but,of course, the eye is expert at finding such structures in random data. Despite thisconcern, much of the obvious clumping, the clusters, holes and stringy structuresare real features of our Universe. To demonstrate the reality of these features, thethree-dimensional distribution of galaxies needs to be determined and so distanceshave to be measured for very large samples of galaxies. Although this is a reallyhuge task, this has now been achieved thanks to the efforts of many astronomers.

2.2.1 Two-Point Correlation Functions

We need statistical methods appropriate for describing the clustering properties ofgalaxies on a wide range of scales and the simplest approach is to use two-pointcorrelation functions. In the cosmological case, these can be described either interms of the distribution of galaxies on the sky, or in terms of spatial two-pointcorrelation functions in three dimensions. On the sky, we define the angular two-point correlation function, w(θ), by

N(θ) dΩ = ng[1 + w(θ)]dΩ , (2.4)

Distribuzione delle galassie (17 < bj < 10.5) su grande scala. Scansione di 185 lastre del telescopio UK Schmidt con macchina APM con oltre 2 milioni di galassie.

Maddox et al. 1990

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36 2 The Large-Scale Structure of the Universe

Fig. 2.5a,b. The two-point correlation function for galaxies over a wide range of angularscales. a The scaling test for the homogeneity of the distribution of galaxies can be performedusing the correlation functions for galaxies derived from the APM surveys at increasinglimiting apparent magnitudes in the range 17.5 < m < 20.5. The correlation functions aredisplayed in intervals of 0.5 magnitudes. b The two-point correlation functions scaled to thecorrelation function derived from the Lick counts of galaxies (Maddox et al., 1990)

Fig. 2.6a,b. The two-point correlation function for galaxies determined from the Sloan DigitalSky Survey (SDSS) (Connolly et al., 2002; Scranton et al., 2002). a The angular two-pointcorrelation function determined in a preliminary analysis of 2% of the galaxy data containedin the Sloan Digital Sky Survey. b Comparison of the scaled angular two-point correlationfunctions found by Maddox and his colleagues from the APM galaxy survey (solid line) withthat found from the SDSS analysis

Funzione di correlazione a due punti w(θ) per galassie con diverse magnitudini (step di 0.5 mag tra 17.5 < m < 20.5).Le stesse funzioni sono state poi riscalate ai conteggi di galassie locali. mostrando che la struttura non cambia.

Maddox et al. 1990

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Distribuzione delle galassie

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Funzione di correlazione a due punti dalla Sloan Digital Sky Survey (SDSS) ed il paragone con i risultati ottenuti dalla survey APM.

36 2 The Large-Scale Structure of the Universe

Fig. 2.5a,b. The two-point correlation function for galaxies over a wide range of angularscales. a The scaling test for the homogeneity of the distribution of galaxies can be performedusing the correlation functions for galaxies derived from the APM surveys at increasinglimiting apparent magnitudes in the range 17.5 < m < 20.5. The correlation functions aredisplayed in intervals of 0.5 magnitudes. b The two-point correlation functions scaled to thecorrelation function derived from the Lick counts of galaxies (Maddox et al., 1990)

Fig. 2.6a,b. The two-point correlation function for galaxies determined from the Sloan DigitalSky Survey (SDSS) (Connolly et al., 2002; Scranton et al., 2002). a The angular two-pointcorrelation function determined in a preliminary analysis of 2% of the galaxy data containedin the Sloan Digital Sky Survey. b Comparison of the scaled angular two-point correlationfunctions found by Maddox and his colleagues from the APM galaxy survey (solid line) withthat found from the SDSS analysis

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Distribuzione delle galassie

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Distribuzione di ~14000 galassie con v< 15000 km/s dalla survey del CfA.Le galassie sono state ottenute per declinazioni +8.5°, +44.5° e propiettate su coordinate polari nel piano con distanza (r) e RA (ϑ),La nostra Galassia è al centro, il raggio massimo è 150/h Mpc.

Geller & Huchra 1989

2.2 The Large-Scale Distribution of Galaxies 39

Fig. 2.7. The distribution of galaxies in the nearby Universe as derived from the Harvard–Smithsonian Center for Astrophysics survey of galaxies. The map contains over 14,000galaxies which form a complete statistical sample around the sky between declinationsδ = 8.5 and 44.5. All the galaxies have recession velocities less than 15,000 km s−1.Our Galaxy is located at the centre of the map and the radius of the bounding circle is150h−1 Mpc. The galaxies within this slice have been projected onto a plane to show thelarge-scale features in the distribution of galaxies. Rich clusters of galaxies which aregravitationally bound systems with internal velocity dispersions of about 103 km s−1 appearas ‘fingers’ pointing radially towards our Galaxy at the centre of the diagram. The distributionof galaxies is highly irregular with huge holes, filaments and clusters of galaxies throughoutthe local Universe (Geller and Huchra, 1989)

about half-way to the limit of the survey. There are a number of ‘streaks’ or ‘fingers’pointing towards our own Galaxy and these correspond to clusters of galaxies, thelengths of the ‘streaks’ corresponding to the components of the velocity dispersionof the galaxies in the clusters along the line of sight.

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Distribuzione delle galassie

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Distribuzione di galassie dalle survey 2dF e SDSS fino a z~0.25 che mostra la struttura cellulare (filamentare).

40 2 The Large-Scale Structure of the Universe

Fig. 2.8a,b. The spatial distribution of galaxies on a large-scale. In both diagrams, the dis-tribution extends to a redshift z ≈ 0.25. a A slice through the Anglo-Australian Telescope2dF Galaxy Survey (Colless et al., 2001) showing the pronounced ‘cellular’ structure of thedistribution of galaxies on the large scale (image courtesy of the 2dFGRS Team). b Thedistribution of galaxies in the Sloan Digital Sky Survey, showing the same ‘cellular’ structureobserved in the AAT 2dF survey (Stoughton et al., 2002)

40 2 The Large-Scale Structure of the Universe

Fig. 2.8a,b. The spatial distribution of galaxies on a large-scale. In both diagrams, the dis-tribution extends to a redshift z ≈ 0.25. a A slice through the Anglo-Australian Telescope2dF Galaxy Survey (Colless et al., 2001) showing the pronounced ‘cellular’ structure of thedistribution of galaxies on the large scale (image courtesy of the 2dFGRS Team). b Thedistribution of galaxies in the Sloan Digital Sky Survey, showing the same ‘cellular’ structureobserved in the AAT 2dF survey (Stoughton et al., 2002)

SDSS

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La Legge di Hubble

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SDSS

Legge di Hubble per le “brightest cluster galaxies” (BCG) in ammassi ricchi (Sandage 1968)

2.3 Hubble’s Law and the Expansion of the Universe 45

Fig. 2.11. A modern version of the velocity–distance relation for galaxies for the brightestgalaxies in rich clusters of galaxies. This correlation indicates that the brightest galaxies inclusters have remarkably standard properties and that their velocities of recession from ourown Galaxy are proportional to their distances (Sandage, 1968)

This was the approach adopted by Hubble and Humason in their pioneering analysisof 1934 (Hubble and Humason, 1934) – they assumed that the 5th brightest galaxyin a cluster would have more or less the same intrinsic luminosity (Fig. 1.5b). InFig. 2.11, the corrected apparent magnitude in the V waveband is plotted againstthe logarithm of the redshift of the brightest galaxies in a number of rich clustersof galaxies which span a wide range of redshifts. The redshift z is defined by theformula

z = λobs − λem

λem, (2.13)

where λem is the emitted wavelength of some spectral feature and λobs is the wave-length at which is it observed. In the limit of small velocities, v ≪ c, if the redshiftis interpreted in terms of a recessional velocity v of the galaxy, v = cz and thisis the type of velocity plotted in the velocity–distance relation. It is an unfortunatetradition in optical astronomy that the splendidly dimensionless quantity, the redshiftz, is converted into a velocity by multiplying it by the speed of light. As we will seebelow, interpreting the redshift in terms of a recessional velocity leads to confusionand misunderstanding of its real meaning in cosmology. It is best if all mention ofrecessional velocities are expunged in developing the framework of cosmologicalmodels.

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SDSS

Legge di Hubble per le “brightest cluster galaxies” (BCG) in ammassi

Present Epoch Brightest Cluster Galaxies 5

10

12

14

16

5,000 10,000 20,000cz (km/s)

Figure 3. The Hubble diagram derived from the present 24K sample, showing BCG apparent metric luminosity as a function of clusterredshift (CMB frame). The red line is the mean theoretical Hubble relationship assuming m = 0.3, and = 0.7. The inset shows thebinned residuals about relation in shells of 4000 km s1 starting at 4000 km s1

, expressed as H/H0. The largest deviation in a shell isH/H0 = 0.022, but none is significantly di↵erent from zero.

pleteness is lower at lower richness, higher redshift, andlower galactic latitude. More specifically, Postman et al.(2002) show that the detection eciency as a function ofrichness class in the Abell catalog is 55% for RC = 0,75% for RC = 1 and is essentially 100% for RC 2.The richness class distribution in the current 24K sam-ple is 55% RC=0, 35% RC=1, and 10% RC 2. Ourstudy here is immune to the known completeness trendsso long as the properties of the BCG in the detectedAbell clusters are representative of those in the clustersthat were missed during the construction of the northernand southern Abell catalogs.

2.1.1. A BCG Hubble Diagram

As a further illustration of the sample geometry andits utility as a probe of the Hubble flow within the lo-cal volume, we show a Hubble diagram derived from ourBCG sample in Figure 3. The details of the sample selec-tion, reduction, and analysis of the photometry neededto generate this figure are the subject of much of the

rest of this paper. For now, the relevant details are thatthe velocities are mean cluster velocities in the cosmicmicrowave background (CMB) frame, and the photome-try is the apparent metric luminosity, Rm, of the BCGs,but with extinction and k-corrections applied. The pho-tometry has also been corrected to ↵ = 0.5 using therelationship (equation 8) between metric luminosity andlog↵, a parameter measuring the slope of the photomet-ric curve-of-growth at the metric radius, rm.

The Hubble diagram shows that the number of galax-ies per velocity interval, rises with distance as D

2,

as expected for a survey with a roughly constant clus-ter density with redshift. The sharp cut-o↵ at the 24Kvelocity limit is also evident. The rms scatter aboutthe nominal theoretical relation specified by m = 0.3,and = 0.7 is 0.271 mag. We can constrain any de-partures from the expected Hubble flow as a functionof redshift by binning the residuals about the Hubblerelation. Since our sample is full sky, this e↵ectivelytests for monopole variations in the Hubble flow with

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6/6/16$

6$

1929: Hubble shows that galaxies have a measured redshift proportional to estimated distance.

Hubble 1929 Freedman et al. 2001

Hubble’s Law:

cz = H0r

H0 = ‘Hubble constant’ = 68 ± 2 km s-1 Mpc-1

1/H0 = ‘Hubble time’ = 14.4 ± 0.4 Gyr

c/H0 = ‘Hubble distance’ = 4400 ± 100 Mpc

La Legge di Hubble

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SDSS

Legge di Hubble per galassie locali utilizzando le variabili Cefeidi

La Legge di HubbleCome l’espansione uniforme dell’universo dà origine alla legge di Hubble