Determining distance. L 4π f. d = d = R θ. Standard candle. Standard ruler

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1 Determining distance Standard candle d = L 4π f 1 2 d L Standard ruler d = R θ θ R

2 Determining distance: Parallax RULER tanπ = R d π R d π R = 1AU = cm Define new distance unit: parsec (parallax-second) 1pc = 1AU tan 1!! 1pc ( ) = 206, 265AU = 3.26ly d = 1 π

3 Determining distance: Parallax

4 Determining distance: Parallax Point spread function (PSF)

5 Determining distance: Parallax Need high angular precision to probe far away stars. d = 1 π Error propagation: σ d = d π 2 σ π 2 = 1 π σ π = σ π π 2 = σ π π d σ d d = σ π π At what distance do we get a given fractional distance error? d = σ d d 1 σ π

6 Determining distance: Parallax e.g., to get 10% distance errors d max = 0.1 σ π Mission Dates σ π d max Earth telescope ~ 0.1 as 1 pc HST Hipparcos ~ 0.01 as 10 pc ~ 1 mas 100 pc Gaia SIM cancelled ~ 20 µas ~ 4 µas 5 kpc 25 kpc

7 Determining distance: Parallax 8 kpc Hipparcos 1 kpc Gaia

8 Determining distance: variable stars

9 Determining distance: variable stars Cepheid variables: Pop I giants, M ~ 5-20 M sun Pulsation due to feedback loop: An increase in T è HeIII (doubly ionized He) è high opacity è radiation can t escape è even higher T and P è atmosphere expands è low T è HeII (singly ionized He) è low opacity è atmosphere contracts è rinse and repeat

10 Determining distance: variable stars RR-Lyrae variables: Pop II dwarfs, M ~ 0.5 M sun

11 Determining distance: variable stars CANDLE Variable stars have a tight period-luminosity relation Measure lightcurves: flux(t) Get period P From P-L relation, get L Use L to get distance Very powerful method. Cepheids can be seen very far away. Used to measure H 0 P-L relation is calibrated on local variables with parallax measurements

12 Determining distance: Tully-Fisher

13 Determining distance: Tully-Fisher Δλ λ = v rot c

14 Determining distance: Tully-Fisher NGC 3198 rotation curve

15 Determining distance: Tully-Fisher HI emission line width HI line is at 1420MHz

16 Determining distance: Tully-Fisher HI absorption line width

17 Determining distance: Tully-Fisher

18 Determining distance: Tully-Fisher CANDLE α L = Cv rot

19 Determining distance: Tully-Fisher 2 v rot = Gm ( < r ) r m(< r) = r 0 ρ( r)4πr 2 dr Flat rotation curve è density profile is a singular isothermal sphere (SIS) ρ( r) = C r 2 m(< r) = r 0 C r 2 4πr 2 dr = 4πCr M = 4πCR 2 v rot = G4πCr r = 4πGC 2 v rot = GM R

20 M = 4 3 π R3 ρ ( < R) Determining distance: Tully-Fisher Dark matter halo definition: = 4 3 π R3 Δρ 0 Δ 200 R = 3M 4πΔρ v rot = GM R = G 4πΔρ M 2 3 M = 3 4πG 3 Δρ v rot L M α 3α L v rot

21 Determining distance: Tully-Fisher Pizagno et al. (2007)

22 Determining distance: Tully-Fisher Pizagno et al. (2007) L = Cv α rot α M i = 2.5log( Cv rot ) + c = 2.5α logv rot + ( c 2.5logC)

23 Determining distance: Faber-Jackson

24 Determining distance: Faber-Jackson

25 Determining distance: Faber-Jackson

26 Determining distance: Faber-Jackson CANDLE L = Cσ v α

27 Determining distance: Fundamental Plane

28 Determining distance: Fundamental Plane

29 Determining distance: Fundamental Plane RULER L = Cσ v α I β R = Sσ v γ I δ

30 Determining distance: Fundamental Plane Bernardi et al. (2007)

31 Determining distance: Surface Brightness Fluctuations

32 Determining distance: Surface Brightness Fluctuations

33 Determining distance: Surface Brightness Fluctuations

34 Determining distance: Surface Brightness Fluctuations d=0.76 Mpc x2 M32 x4 x8

35 Determining distance: Supernovae type Ia SN 1572

36 Determining distance: Supernovae type Ia White dwarfs are made of a C/O core that is supported by electron degeneracy pressure. WD masses cannot exceed 1.4 M sun (Chandrasekhar limit) because then gravity wins. WD that accretes enough mass to surpass this limit, collapses, heats up, and fuses all its C/O in a fast runaway reaction. The energy released unbinds the star. SN Ia

37 Determining distance: Supernovae type Ia ΔM 15 Riess et al. (2006)

38 Determining distance: Supernovae type Ia CANDLE Phillips (1993)

39 The Distance Ladder Method Scatter Reach Systematics Parallax ~d <1 kpc Cepheids 5-10% 30 Mpc Metallicity SBF 5-10% 50 Mpc Stellar LF Tully-Fisher 10-20% >100 Mpc Mass-to-light FP/D n -sigma 10-20% >100 Mpc Kinematics SN Ia 5-10% >1000 Mpc Dust

40 The Distance Ladder SN Ia Tully-Fisher/D n -sigma Cepheids/RR Lyrae parallax

41 Redshift We can measure galaxies radial velocity using the Doppler effect. Doppler effect: when an object is moving away from (or toward) us, the frequency of light that we see from it is shifted. galaxy spectrum è Doppler shift (redshift) è radial velocity

42 Redshift z = λ obs λ emit λ emit Relativistic Doppler Effect 1+ z = 1+ v r c 1 v r c z v r c

43 Hubble Law

44 Hubble Law v r = H 0 d H km s Mpc 1

45 The expansion of the universe is such that galaxies recessional speeds are proportional to their distance. Hubble Law

46 Cosmological Redshift

47 Cosmological Redshift z = λ obs λ emit λ emit Cosmic scale factor: ( ) = R( t) a t ( ) 1 + z = a t 0 a t 1+ z = λ obs λ emit ( ) R t 0 Wavelengths stretch with scale factor: ( ) = 1 a( t)

48 Hubble Law v r = H 0 d H 0 70 km s Mpc 1 H 0 100h km s Mpc 1 h 0.7

49 Hubble Law

50 Hubble Law

51 Hubble Law Riess et al. (2006)