Comenius UPMC Paris Juin 2011 About galaxy NGC

Comenius UPMC Paris Juin 2011 About galaxy NGC 7083, redshift and dark matter Measuring Edwin Hubble’s redshift and Vera Rubin’s dark matter Suzanne FAYE, Lycée Chaptal, Paris, France Michel FAYE, Lycée Louis-le-Grand, Paris, France 1 mfaye 2@wanadoo. fr

Preliminary : Salsa. J colors, pixels and slices Ready now to visit galaxy NGC 7083 !! 2

I - About galaxy NGC 7083 Where? in Indus Constellation (Southern hemisphere) Why Southern hemisphere? Because of very performant telescope ESO – VLT (Chili) Internet: Ask NGC 7083 Right Ascension: 21 hours 35 minutes 45 s Declination: -63 degrees, 54 minutes 15 s Apparent Magnitude: 12 Apparent Diameters: 3. 5’ long; 2, 0’ wide (slide 5) 3

1 - About Indus Constellation southern hemisphere (visible with VLT, Chili) http: //www. starrynightphotos. com/constellations/indus. htm The constellation was one of twelve constellations created by Pieter Dirkszoon Keyser and Frederick de Houtman between 1595 and 1597, and it first appeared in Johann Bayer's Uranometria of 1603. Since Indus was introduced in the 17 th century, and lies in the south, it was not known to classical or early cultures thus they produced no mythology concerning it. NGC 7083 4

2 – Angular dimensions of galaxy NGC 7083 1 - Open Google Earth 2 - Affichage/ Explorer / Ciel (Sky) 3 – Look for : NGC 7083: we obtain Right Ascension and Declinaison 4 – Zoom to have full galaxy 5 – Outils (Tools) / Regle (secondes d’arc) 6 – Make measures (in two perpendicular directions) Answer for the angular sizes of the galaxy: 3, 5’ long; 2, 0’ wide 5

3 – What is the orientation of the galaxy . disc plane; angle i ? We see as an ellipse what is in fact a circle i Towards observation (p/ 2) - i i width i length Answer for angle i : cos(i) = width/length = 2, 0 / 3, 5 => i = 55°; sin(i) = 0, 82 6

4 – What is redshift of a galaxy? Sun Galaxy Absorption lines in the optical spectrum of a distant galaxies (right), as compared to absorption lines in the optical spectrum of the Sun (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decreases). See Doppler-Fizeau effect Dl / l = v /c 7

5 – Part of NGC 7083 spectrum, by VLT - ESO Lines emitted by atoms from the disk of the galaxy Continuum emitted by the core of the galaxy 8

6 - Have a look at Image/ Informations 9

7 – Which lines did VLT astronomers have sent to us? N nitrogen lines H hydrogen S sulfur Core of the galaxy l(pixel) = a*(pixel-reference) + b = CDELT 1 * (pixel+ 1559) + 4937 (Å) Ha Image Information: CRPIX 1 = - 1559. / Reference pixel CRVAL 1 = 4937. / Coordinate at reference pixel CDELT 1 = 0. 986999988556 / Coordinate increment per pixel CTYPE 1 = 'Angstrom ' / Units of coordinate Be careful: 1 Å = 0. 1 nm 10

8 - How can we get the exact number of pixels? « Plot Profile! » or ZOOM and count pixels Raie N II a : X = 140, So λ (nm) = (140 + 1559) x 0, 09870 + 493, 7 → λ = 661, 39 nm 11

9 – Calculate redshift for each line l(pixel) = CDELT 1*(pixel-reference) + b = 0, 09870 * (pixel+ 1559) + 493, 7 (nm) Redshift ∆λ/λ = (l 2 - l 1) / l 1 Vgalaxie= c. ∆λ/λ (km/s) c = 3. 105 km/s l 2 =661. 39 0. 0101 3030 X=156 l 2 =662. 97 0. 0102 3060 658. 35 X=178 l 2 =665. 14 0. 0103 3090 SIIa 671. 60 X=313 l 2 =678. 47 0. 0102 3060 SIIb 673. 10 X=328 l 2 =679, 95 0. 0102 3060 Line Spectrum on Earth λ 1 (nm) Spectrum of NGC 7083 X (pixel) => λ 2 (nm) NIIa 654. 80 X=140 Hα 656. 28 NIIb Let us keep VNGC 7083 = 3. 06*103 km/s Good measurement! 12

10 – What is the distance D of galaxy NGC 7083? Let us use Hubble law : Vgalaxie = H * D , with H ≈ 73 km. s-1. Mpc-1 1 pc = 3, 26 a. l. et 1 a. l. ≈ 9, 47. 1015 m D = VNGC 7083 /H = 3060/73 = 42 Mpc = 4, 2 x 107 pc D = 1. 4 x 108 a. l. D = 1, 3 x 1024 m 13

11 - Measuring the size d. NGC 7083 of the galaxy dgalaxy = α(en radians) * D αNGC 7083 ≈ 3, 5’= 1, 02. 10 -3 rad D = 4, 23 x 107 pc Our Galaxy, Milky Way : d. Milky Way = 25 000 pc NGC 7083: d. NGC 7083 = 4, 2. 104 pc = 1, 7 * d. Milky Way 14

12 - Have sizes of the galaxy with Image/ Informations and apparent diameters acore ≈ 16 pixels = 13’’ Width of the picture ≈ 289 pixels = 237’’ αNGC 7083 ≈ 3, 5’ = 210’’= 256 pixels 15

12 bis- Another way to measure the size dcore of the galaxy : Plot « vertical » profile. Let us evaluate: dcore = 16 pixels; d. NGC 7083 ≈ 256 pixels => dcore / dgalaxy = 16/256 et d. NGC 7083 = 4, 3. 104 pc ; so dcore ≈ 2, 7. 103 pc= 8, 3. 1019 m 16

II – Dancing with a galaxy Redshift of the core + « Relative » Doppler shift by rotating around the core 17

1 – Why is the shift of the spectrum constant for r > R ? Dark matter bounded? Vera Rubin (born 1928) is an astronomer who has done pioneering work on galaxy rotation rates. Her discovery of what is known as "flat rotation curves" is the most direct and robust evidence of dark matter. Turning around the core Dark matter bounded? 2 R 18

2 – What is a flat rotation curve? Let us watch Doppler shift ! * Doppler shift Dl is constant for r > R, which means that the relative speed is then constant * Because of the inclination i of the galaxy plane, Dl / l = Vrelative * sin(i) /c ) Let us imagine V rotation that the arms of the dancer are blocked by ? ? ? Dark Matter!!! 19

3 – How can we measure Dl / l ? You can either use quotient in pixel, or use CDELT 1: 1 pixel ≈ 1 Å or 0, 1 nm; remember sin(i); i = 55 degrees Vrotation = [Dl/l] * c / sin (55) agalaxy = 256 pixels We use line Ha , with rotation shift l (Ha / core) ≈ 6630Å Ha : the brightest line So: Vrotation ≈ (4/6630)* c/0. 82 Vrotation ≈ 2, 21. 105 m/s acore = 16 pixels Around the core of the galaxy: m. V² / r = G m M/ r² so Mcore= V² R / G G=6, 67. 10 -11 SI 2 Dl = 8 pixels ≈ 8 Å or 0, 8 nm R= dcore/2 ≈ (see slide 16) 4, 15. 1019 m Mcore = 3. 1040 kg 20

For the core of the galaxy: m. V² / R = G m Mcore / R² so Mcore= V² R / G G = 6, 67. 10 -11 SI R = dcore/2 ≈ 4, 15. 1019 m Mcore = 3. 1040 kg For the whole galaxy: m. V² / rwhole = G m Mwhole / rwhole ² so Mwhole= V² rwhole / G G = 6, 67. 10 -11 SI rwhole = dgalaxy/2 ≈ 6, 65. 1020 m Mwhole = 4, 8. 1041 kg Mwhole = 16*Mcore > Brighting mass Here is dark matter, a challenge for researchers !! : : : !! Bright galaxies, dark matters, by Vera Rubin 21