1

gold.dat• Sul sito del corso 

http://oberon.roma1.infn.it/lezioni/cosmologia_osservativa_specialistica/2015

• È presente il file gold.dat , con una raccolta di dati di SN1a (non è l’ultima, ma è abbastanza ampia)

• 4 colonne, 157 righe :0.04 36.38 0 0.190.05 36.84 0 0.210.0307 35.9 0 0.20.056 37.31 0 0.180.0331 35.54 0 0.20.046 36.35 0 0.210.0265 35.64 0 0.20.101 38.73 0 0.2…. …. …. …. …. ….0.0141 34.13 0 0.25

z              M‐m   dummy    errore

Analisi da fare :• Convertire i moduli di distanza ed i loro errori in distanze e loro errori (facoltativo, si può anche lavorare con i moduli di distanza)

• Usare la routine di calcolo delle distanze di luminosità in funzione dei parametri cosmologici per calcolare il 2 dei dati gold.dat in funzione dei parametri cosmologici Ho, , m:

• Trovare i valori dei parametri minimizzanti il 2. • Graficare il minimo 2 e le curve di livello del 2corrispondenti al 68.3% al 95.5% e al 99.7% di probabilitaà di eccedere nel piano , m. (Ho fissato al best fit).

N

i i

moiThii

mo

HzDDH

12

2

2 ),,,(,,

• Inverse Compton Effect for CMB photons against electrons in the hot gas of clusters

• Cluster optical depth: =nl where l = a few Mpc = 1025 cm, n < 10-3 cm-3 , = 6.65x10-25 cm2

• So =nl = 0.01 : there is a 1% likelihood that a CMB photon crossing the cluster is scattered by an electron

• Eelectron >> Ephoton, so the electron transfers part of his energy to the photon. To first order, the energy gain of the photon is

• The resulting CMB temperature anisotropy is

cluster

01.0500

52

keV

keV

cm

kT

e

e

41001.001.0

T

T Sunyaev R., Zeldovich Y.B., 1972, Comm. Astrophys. Space Phys., 4, 173

Birkinshaw M., 1999, Physics Reports, 310, 97-195

CMB photonsSunyaev-Zeldovich Effect

Bri

ghtn

ess

All photons increase their energy. The result is a

distortion of the spectrum of the CMB in the direction of

rich clusters

A decrement at low frequencies ( <217GHz )

An increment at high frequencies ( > 217GHz )

frequency

Sunyaev-Zeldovich Effect Atmospheric transmission, pwv=0.5mm

ISD emission, 18K6 kJy/sr @ 150 GHz

Thermal SZ

Non-Thermal SZ

Kinematic SZ

Thermal SZ

2

• Photometric observations of the SZ can be significantly biased, when there are

• less spectral channels than free parameters.

• Components, LOS through a rich cluster:

ThSZ

KSZ

CMB

ISD

NThSZ pmin , Amp

Td , d ….()

• Photometric observations of the SZ can be significantly biased, when there are

• less spectral channels than free parameters.

• Components, LOS through a rich cluster:

ThSZ

KSZ

CMB

ISD

NThSZ pmin , Amp

Td , d ….()

At least, 8 independent parameters !

Example : bias in the determination of LOS parameters, for a ground-based telescope with 4 photometric channels( 75-115 ; 125-175 ;200-240 ; 240-300 )

GHz

0001.0nt

Example : bias in the determination of LOS parameters, for a ground-based telescope with 4 photometric channels( 75-115 ; 125-175 ;200-240 ; 240-300 )

GHz

0nt

Example : bias in the determination of LOS parameters, for a ground-based telescope with 4 photometric channels( 75-115 ; 125-175 ;200-240 ; 240-300 )

GHz

Fitting also TCMB : bias removed, but larger errors

The solution: spectroscopic measurements of the SZ

• Requirements:

– Wide spectral coverage (in principle 100 to 1000 GHz)

– Modest spectral resolution ( = 100 to 1000)– Differential input, high rejection of common mode

signal (CMB is common mode and is 2750000 K, cluster signal is differential and can be as low as 10 K).

– Imaging instrument– Wide field of view to image the whole cluster and

have a clean reference area to compare

3

Comparison among Spectrometers solutionsITEM FTS Grating Fabry-

PerotSpectral coverage YES NO: 4 D-G needed NO: 3 F-P

needed

Simultaneous measurements

YES YES NO

Imaging capability YES NO: linear array per pixel

YES

Spectral resolution Variable Fixed Fixed

Differential measurement capability

YES NO NO

Background / noise Large: but relaxes detectors sensitivity and mirrors temperature

Small Small

Technology readiness OK OK OK: but constraint on mirrors planarity and movement

DFTS

• The differential fourier transform spectrometer (DFTS) is the best option.

• We decided to produce a prototype to be used (warm) on the OLIMPO balloon-borne telescope to proof the concept and get preliminary science.

• Scientific targets:– SZ– High redshift galaxies (C+)– Galactic survey (study of CO, also as a contaminant)– Spectral-Spatial anisotropies– ….

• Supponiamo quindi di avere due sorgenti S1 e S’1 , descritte dai vettori di Jones

• Il beam 3, dopo il polarizzatore d’ ingresso (asse principale verticale), sarà

y

x

A

AS1

y

x

B

BS '

1

y

x

rt B

ASPSPS '

113 )0()0(

• Il beam 4 riflesso dal beamsplitter e il beam 4’ trasmesso dal beamsplitter saranno:

yx

yx

y

x

r BA

BA

B

ASPS

2

1

11

11

2

1)4/( 34

yx

yx

y

x

t BA

BA

B

ASPS

2

1

11

11

2

1)4/( 3

'4

• Siccome gli specchi a tetto sono rappresentati da matrici identità, avremo anche

yx

yx

BA

BASS

2

146

iyx

iyx

yx

yx

eBA

eBA

BA

BADDSS

)(

)(

2

1

2

1'4

'6

• Il primo è trasmesso dal beamsplitter, il secondo è riflesso, quindi

'66

'668 11

11

2

1

11

11

2

1)4/3()4/( SSSPSPS rt

• Da cui

)1()1(

)1()1(

2

18

iy

ix

iy

ix

eBeA

eBeAS

0

)1()1(

2

1)0( 89

iy

ix

t

eBeASPS

• Considerando ora il beamsplitter di uscita, ricaviamo i beam che arrivano sui due rivelatori:

'66

'668 11

11

2

1

11

11

2

1)4/3()4/( SSSPSPS rt

)1()1(

0

2

1)0( 8

'9 i

yi

xr eBeA

SPS

4

• Possiamo ora calcolare l’ intensità su ciascuno dei rivelatori in uscita:

cos22

)]cos1()cos1([2

12222

229

yxyxyx

BABABAI

cos22

)]cos1()cos1([2

12222

22'9

yxyxyx

BABABAI

**yyxx EEEEI

• The OLIMPO experiment is a mm-wave balloon-borne telescope, optimized for high-frequency measurements of the Sunyaev-Zeldovich effect. The instrument uses four bolometer arrays, for simultaneous observations at 150, 210, 350, 480 GHz, coupled to a 2.6 m diameter Cassegrain telescope, achieving a resolution of 4,3,2,2 arcmin FWHM respectively.

• OLIMPO is a polar long-duration flight launched from Svalbard islands. The current observation plan includes deep integrations on a selected sample of 40 clusters, plus a wide blind survey of an empty sky area.

• We have recently upgraded the instrument adding spectroscopic capabilities within the 4 bands above, and discuss here the scientific potential of this innovative configuration.

• In fig. 1 we show the OLIMPO balloon payload (Masi et al. 2008), with solar panels, ground shield and sun shield removed.

• Note the tiltable 2.6m primary mirror and the lightweigth secondary.

• Pointing is obtained rotating the payload around an azimuth pivot and changing the elevation of the inner frame, including the telescope, the FTS and the detector’s cryostat

• The total mass of the payload is 1.5 tons.

The Payload

Elevation motor

Azimuth pivot

Cryostat with cold optics and detector arrays

Readout electronics

window

LHe 60 L

LN 60L

Reimaging optics

dichroics

arrays

FTS

Low frequency arrays (TES)• Buffer: Si3N4

• Thermistor: Ti (60nm) + Au (10/20 nm)• Absorber/heater: spiderweb Ti (10 nm) + Au (5 nm), filling factor 5%• NET150GHz=145 µK√s• NET220GHz=275 µK√s• Univ. Of Cardiff (Mauskopf)

Bol. eff [GHz] FWHM [GHz] Res. [‘]19 148.4 21.5 4.2

19 215.4 20.6 2.923 347.7 33.1 1.8

23 482.9 54.2 1.8

High frequency arrays• NbxSi1-x (x=0.085)• SiN 3x3 mm2• Palladium absorber• NET340GHz=430 µK√s• NET450GHz=4300 µK√s• Inst. Neel Grenoble (Camus)

Filters Stacks (Ade, Tucker, Cardiff)

The spectroscopic instrument• SZ studies can benefit significantly from spectroscopic

measurements, which are required to break degeneracies between the parameters describing cluster and foreground emissions along the line of sight (see below).

• In 2008 we have studied for ASI a spectroscopic SZ space-mission (SAGACE, see de Bernardis et al. 2010).

• As a pathfinder, we are building a plug-in Differential FTS for OLIMPO.

• The DFTS configuration offers – an imaging spectrometer with very high throughput,– wide spectral coverage, – medium to high spectral resolution, – rejection of common-mode signals, like instrument emission and most

of the ground pickup.

• The main problem is the high radiative background on the bolometers, which is solved splitting the observed frequency range in several bands with independent detector arrays. In the case of OLIMPO, this was already implemented in the 4-bands photometer.

5

The instrument is based on a double Martin Pupplett Interferometer configuration to avoid the loss of half of the signal.

A wedge mirror splits the sky image in two halves IA and IB, used as input signals for both inputs of the two FTS’s.

Olimpo Telescope

Olimpo Cryostat

0

)2/sin()2/cos( yxFTSII AiBE

)2/sin()2/cos(

0

xy

FTSI

AiBE

outgoing fields : Global design of the optical system

Differential field of view

Optical layout of the doublel Martin-Puplett FTS

Mechanical arrangement of the translation stages

The OLIMPO Martin-PuplettDifferential Fourier TransformSpectrometer

OLIMPOPrimaryMirror

DFTS

Cold optics

Simulated OLIMPO measurement of a cluster l.o.s. with th=0.005, Te=10 keV, nonth=0.0001, vpec=500 km/s, Idust=6kJy/sr@150GHzThe data with the error bars are simulated observations from a single pixel of the OLIMPO-FTS, for an integration time of 3 hours. The two lines through the data points represent the input theory (thin) and the best fit for the plotted data realization (thick). The other thin lines represent thermal plus non-thermal SZE, and dust emission.

this shift is due to the peculiar velocity of the cluster

The high-frequency excess is due to a modest amount of dust

dust

thermal + non-thermal

http://planck.roma1.infn.it/olimpo

6

Parameters Determination• In the presence of peculiar velocities, non-thermal populations

(from AGNs in the cluster), and foreground dust, there are simply too many free parameters to be determined with the observation of a few frequency bands, like in ground-based measurements.

• We have carried out detailed simulations of OLIMPO observations in the spectroscopic configuration with an extended 200-300 GHz band.

• The spectroscopic configuration has superior performance in converging to the correct estimate of thermal optical depth and dust parameters, while the photometric configuration, in the absence of priors, tends to converge to biased estimates of the parameters. See de Bernardis et al. A&A 583, A86 (2012).

• No priors

th =(63+27)10-4

T = (9.0+4.1) keV

non-th=(14+9)10-5

TCMB=(24+43)K

Idust150=(5.7+1.6)kJy/sr

Input parameters

th =50x10-4

T = 10 keV

non-th=1x10-4

TCMB=22K

Idust150=6 kJy/sr

OLIMPO

FTS

3h integ.

one

detector

• Prior T=(10+3) keV

th =(49+6)10-4

T = (9.6+0.5)keV

non-th=(11+9)10-5

TCMB=(22+43)K

Idust150=(5.8+0.9)kJy/sr

Observation Program

• In a circumpolar summer long duration flight (>200h) we plan to observe 40 selected clusters and to perform a blind deep integration on a clean sky region

• We have optimized the observation plan distributing the integration time among the different targets according to their brightness and diurnal elevation.

Mission Profile

• We will use a long-duration circumpolar flight launched from Svalbard Islands (June 2014).

• We have tested these flights in collaboration with ASI, and demonstrared the feasibility of launching heavy payloads from the Longyearbyen airport, performing 2-3 weeks flights around the north pole during the Arctic summer.

SORA LAUNCH:July 1st 2009 (1.5 ton)

asm

cm

D 6103

103

1 115

asc

GMr

r

GMc 2

222

• Antenna diameter: 10 m• Range of wavelengths: 0.01 – 20 mm• Bolometric sensitivity (0.3mm, 1h integration): 5x10-9 Jy• Interferometry sensitivity (0.5mm, 300s integration, 16GHz bw) : 10-4 Jy• Interferometer beam: 10-9 arcsec

MillimetronLonger baseline (L2) Shorter wavelength 1

7

3 hours of observations of a rich cluster with a DFTS on Millimetron Absolutely outstanding.

3h integration on the same LOS through a rich cluster

http://chalonge.obspm.fr/Paris14_Kogut.pdf

8

Growth of Cosmic Star‐Formation

SF history:  Hopkins and Beacom, 2006

We would like to chart the onset and early growth of star formation in the epoch prior to z=4 (the first 1.5 Billion years) ?

e.g. was this dominated by massive galaxies or small ones?  How much does dusty SF contribute?

z>4 has large uncertainties and all data on this epoch comes from rest‐frame UV / optical surveys (Lyman break sources)

Require redshift‐resolved far‐IR / submm luminosity functions to complement UV‐based studies.

High‐excitation molecular gas: CO and water

• 5 CO transitions AND 6 water transitions.• 1 confirmed with CARMA, more coming.• CO cooling fit with XDR model.• Water spectrum looks like that of Mrk 231 as measured with Herschel SPIRE, but scaled up and more highly excited.• -> Water is pumped with local far-IR radiation field, but over hundreds of parsecs.• Water abundance ~1.4e-7, explained by XDR chemical model. 44

SUPERSPEC see http://arxiv.org/pdf/1501.02295v1.pdf

7 mm

SuperSpec first 80‐channel test device   

A very compact spectrometer !Erik Shirokoff, chip design

DESHIMA See http://arxiv.org/pdf/1107.3333.pdf

p1

t

UniversoPrimordiale

UniversoStrutturato

510

510

Diapositiva 47

p1 pdb; 24/03/2015

9

Radiazione Cosmica di Fondo a 3K• L’ universo si e’ raffreddato espandendosi. • C’e’ stata un’epoca nel passato in cui l’ universo era talmente

caldo da essere ionizzato. • Questa fase e’ detta di “Primeval Fireball” e dura per i primi

400000 anni dal Big Bang.• In questa fase lo spessore ottico per scattering Thomson era

estremamente alto, ed i fotoni percorrevano un “random walk” da elettrone ad elettrone.

• Quando l’ universo si e’ raffreddato abbastanza da permettere la ricombinazione degli elettroni e protoni in atomi di idrogeno, la sezione d’ urto e’ diminuita drasticamente, e l’ universo e’ diventato trasparente.

LSS• I fotoni che erano in equilibrio con la materia (corpo nero) si propagano fino a noi, raffreddandosi con l’ ulteriore espansione dell’ universo, ma mantenendo la forma di corpo nero. Radiazione cosmica di fondo, CMB.

• I fotoni della CMB subiscono il loro ultimo scattering Thomson quando l’ universo si raffredda a 3000K, ad un redshift zLSS~1100.

• Quindi i fotoni di CMB provengono da una “superficie di ultimo scattering” (last scattering surface) posta a z~1100.

• Questa superficie ha un certo spessore, perche’ l’ universo impiega tempo a diventare trasparente.

zLSS

zLSS

H neutro (trasparente)

H ionizzato (opaco)

LSS (semitrasparente)

LSS• I fotoni che erano in equilibrio con la materia (corpo nero) si propagano fino a noi, raffreddandosi con l’ ulteriore espansione dell’ universo, ma mantenendo la forma di corpo nero. Radiazione cosmica di fondo, CMB.

• I fotoni della CMB subiscono il loro ultimo scattering Thomson quando l’ universo si raffredda a 3000K, ad un redshift zLSS~1100.

• Quindi i fotoni di CMB provengono da una “superficie di ultimo scattering” (last scattering surface) posta a z~1100.

• Questa superficie ha un certo spessore, perche’ l’ universo impiega tempo a diventare trasparente.

zLSS

zLSS

H neutro

H ionizzato

LSS

Random walk

Ultimo scattering

Propagazione libera

LSS• Lo spessore della superficie di ultimo scattering si

puo’ calcolare vedendo quanto e’ profonda la transizione da spessore ottico basso a spessore ottico maggiore di 1.

• In formule

• Dove x(z) e’ la frazione di idrogeno ionizzata.• La soluzione richiede l’ integrazione dell’

equazione di Saha per la frazione ionizzata.• Il risultato e’ un grafico del tipo (vedi corso

astrofisica) :

)()1()(

1)1()())(()(

3

02

)(

0

zxznzn

zzH

cdzzndznz

oe

z

o

Te

z

Te

2000 4000 6000 8000 100000.0

0.2

0.4

0.6

0.8

1.0

X

X

T(K))1()( zTzT o

0 1000

(z)

z0

1

0.5

zLSS

2

1.5

• Lo spessore ottico, che dipende dalla densità e dal numero di elettroni liberi ha un andamento del tipo :

10

0 1000

(z)

z0

1

0.5

zLSS

2

1.5

)()()( z

e ezndz

zdN

Densita’di diffusorial redshift z

Attenuazione

Numero difotoni cheprovengono da un redshift z

• Ma se vogliamo sapere quanti fotoni provengono da un certo redshift, dobbiamo calcolare dN/dz :

0 1000z0

1

0.5

zLSS

2

1.5

)()()( z

e ezndz

zdN

Densita’di diffusorial redshift z

Attenuazione

Numero difotoni cheprovengono da un redshift z

• Ma se vogliamo sapere quanti fotoni provengono da un certo redshift, dobbiamo calcolare dN/dz :

0 1000z0

1

0.5

zLSS

zLSS

2

1.5

)()()( z

e ezndz

zdN

Densita’di diffusorial redshift z

Attenuazione

Numero difotoni cheprovengono da un redshift z

0 1000z0

1

0.5

zLSS

zLSS

2

1.5

)()()( z

e ezndz

zdN

Densita’di diffusorial redshift z

Attenuazione

Numero difotoni cheprovengono da un redshift z

Oggi si conosce (WMAP)zLSS con grande precisione:zLSS=1089+1zLSS=185+2 (FWHM)Bennet et al. 2003

• Le fluttuazioni di densita’ sulla superficie di ultimo scattering producono anisotropia CMB, in piu’ modi.

1) DIRETTAMENTE:• Una sovradensita’ fa perdere energia ai fotoni che provengono da

essa, perche’ devono risalire la buca di potenziale. Per effetto del redshift gravitazionale si ha

• La sovradensita’ causa anche una dilatazione del tempo, per cui noi osserviamo un’ epoca piu’ primordiale (e quindi piu’ calda) laddove ci sono sovradensita’. La dilatazione del tempo e’

• Ma, durante la fase radiativa,

• Quindi in totale

2cT

T

2ct

t

23/2

3

2

3

2/1;

ct

t

a

a

T

TaTta

23

1

cT

T

Effetto Sachs-Wolfe (1967)

• Le fluttuazioni di densita’ sulla superficie di ultimo scattering producono anisotropia CMB in piu’ modi.

2) INDIRETTAMENTE:• Una sovradensita’ attira la materia circostante, e genera quindi un campo di

velocita’ peculiare. I fotoni che subiscono la loro ultima diffusione in zone in movimento con velocita’ peculiare v subiscono un effetto Doppler, quindi

3) ADIABATICAMENTE:• Il mezzo primordiale e’ un plasma di fotoni e materia. • Si dicono perturbazioni adiabatiche quelle in cui le densita’ di radiazione e di

materia fluttuano insieme in modo da mantenere l’ entropia del mezzo costante.• l’ entropia del mezzo e’

• Il numero di particelle di materia e’• Il numero di fotoni e’

• Quindi perturbazioni adiabatiche implica

• La teoria inflazionaria prevede che le fluttuazioni siano di tipo adiabatico.

cT

T v

nnS mm /

mmn 4/33

Tn

4

30

m

m

m

m

m

m

n

n

n

n

S

S

m

m

m

m

T

T

T

T

3

14

4

3

4

3

11

Anisotropia CMB• Quindi in totale

• Sperimentalmente si vede che, a parte l’ anisotropia di dipolo, dovuta al moto della Terra (10-3), l’ anisotropia intrinseca T/T e’ molto piccola (dell’ ordine di 10-4-10-5).

• Quindi l’ universo primordiale era estremamente omogeneo. Le strutture presenti oggi nell’ universo si sono formate grazie all’ azione della gravita’, che ha fatto crescere le piccole perturbazioni di densita’ presenti alla ricombinazione, attirando la materia circostante.

Fluttuazioni adiabatiche

Effetto SW Dffusione da elettroni in moto

ccT

T

m

m v

3

1

3

12