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K-Correction Surface Brightness Tully-Fisher Relation Spiral Rotation

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K-Correction Surface Brightness Tully-Fisher Relation Spiral Rotation Key concepts:! ! !K-correction! !! !Surface brightness! ! !Tully-Fisher relation! ! !Spiral rotation curves! !! ! How to compare galaxies properly! K-corrections! Normally we observe through filters = over some specific dλ. For a typical galaxy spectrum at z=0:! where T is the filter transfer function.! •" Due to redshift effects, the light emitted between λ1 and λ2 becomes light observed between λ1(1+z) and λ2(1+z). Thus both wavelength and bandpass change!! •" Looking at galaxies at higher z through same filter, we therefore receive emission from shorter wavelengths at a slower rate. ! •" Knowing the spectral shape, we can correct for this via the K- correction.! (origin of the term K-correction has been attributed to both Hubble and Wirtz)! Nearby Galaxy! A! Distant Galaxy! C! B! We measure B, but want to measure C to compare to A. ! E! Sa! Sc! Poggianti 1997! K correction in J, H and K band for three types of galaxies. ! Typically given as ! Type !a !b! E/S0 !3.13 !0.24! Sabc !2.63 !-0.107! Sd/Irr !0.62 !0.14 ! !!(V-band values)! •" K-corrections in the optical band large for elliptical galaxies, since they emit little flux in the UV.! •" Smaller corrections for spirals and irregulars.! •" K-corrections depend on observed filter:! –" smaller as you observe further in the red! –" negative in the near-IR! Surface brightness! To quantify the stellar content, look at the total luminosity (in some filter) of a galaxy. How? They don't have sharp edges.! ! Define surface brightness as µ = flux/angular area (mag/arcsec2).! 2 centrally, in B filter, µB ~ 21 mag/arcsec ! 2 further out, µB ~ 25 mag/arcsec ! Surface brightness is independent of distance.! Why? Consider a square galaxy.! move 2 times farther! Covers 16 pixels! Covers 4 pixels! Total flux is 4 times less, but number of pixels (angular area) less by the same factor.! Isophotes! Contours of constant surface brightness are isophotes. ! ! Measures of galaxy 'size'! 1." Holmberg radius! rH = semi-major axis of the! 2 µB~26.5 mag/arcsec isophote! 2." r25 = same idea but for ! 2 !µB~25 mag/arcsec .! Luminosity or absolute magnitude ! refers to light within rH or r25.! Chandra X-ray (greyscale) compared to K band! Light distribution! Elliptical! ! Ellipticals have de Vaucouleur profiles, r1/4 (solid line in figure).! ! Disks have exponential profiles, e-r/r0.! ! Spirals have the combination of the above due to the bulge and disk components.! ! Spiral! ! Isophotes measure the distribution of luminous matter in galaxies. To estimate distribution of dark matter we need rotation curves.! Rotation curves and mass measurements of spirals! ! Rotation causes Doppler shift of spectral lines Most common: HI 21cm, CO, Hα = ISM emission lines. Stellar absorption lines are much, much fainter.! Example Bosma 1978 Mass determination! Recall for a given mass distribution! ! m = mass of e.g. star! Mr= galactic mass within r! V(r )= rotation speed! ! So if V (r ) constant, then Mr ~ r (haven't reached 'edge').! Correlations! ! Rotation curves can be correlated with luminosity. This is the Tully- Fisher relation. The higher the luminosity, the higher the maximum rotational velocity.! ! ! ! Exact form depends of type: Sa, Sb, Sc! Spirals display double-peak profiles (lots of matter rotates at same velocity for flat rotation curve). ! ! ! ! Tully-Fischer: ! Hence, basically a plot between luminosity and mass of a galaxy - not surprisingly correlated. With the luminosity determined, you can calculate the distance.! Tully-Fisher relations of two clusters at different distances.! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Also note, the more massive a galaxy is, the faster it rotates.! Where does Tully-Fisher derive from?! Start with gravitational force = centripetal force! ! ! ! ! Assume roughly constant mass-to-light ratio for spirals! ! ! ! Roughly constant surface brightness for spirals! ! Recall! ! ! ! ! ! ! ! But, M/L is not same for all spirals:! ! Sa! ! Sb! ! Sc! So the Tully-Fisher relations are slightly different:! ! ! Sa! ! ! Sb! ! ! Sc! ! Rubin et al 1985! Integrated colors of galaxies! ! red! blue! Thus, more massive, blue stars in late-type galaxies.! Integrated spectra of E, S, and Irr (Kennicutt et al)! E! Sa! Sc! Sm/Im! OII! OIII ! Hα! Hβ! SII! blue! red! Dropouts! Schneider! Miley et al.! Color gradients! Individual galaxies have color gradients, i.e. color depends on location. Bulges are redder than disks:! !! •" Star formation! •" less ongoing star formation! •" agrees with more gas available in disk than in spheroidal components! •" Metallicity ! •" more electrons per atom ! !-> more electrons to cause opacity effects ! !-> less radiation escape star ! !-> pushes layers outwards somewhat ! !-> decreasing surface temp ! !-> redder! ! Supermassive black holes (M-sigma relation)! SgrA*! Correlation between black hole mass and velocity of bulge components. Indicates formation of galaxy is linked to formation of supermassive black hole.! Population synthesis Computer modeling of galaxy colors or spectra. Inputs: •" Age •" Star formation rate versus time •" IMF •" Metallicity •" Library of spectra of model atmospheres of stars •" Models of stellar evolution Findings: Biggest reason for galaxy color/spectrum variation with Hubble type is star formation rate versus time Schematic star formation histories: 6! E, bulges! 4! SFR! 2 ! Sc! Sb! Sa! 2! 4! 6! 8! 10! Time (Gyrs)! Tracers of current star formation 1." Luminosity of Hα emission (what kinds of stars responsible?). Must assume IMF to get total star formation rate (SFR). ! -42 ! ! !SFR(M/yr)=8x10 LHα (erg/s)! 2." Far infrared emission (FIR) from dust heated by starlight. Wavelength 10-1000µm (near IR is mostly starlight). Requires satellite observations.! 3." Far UV light (~2000Å). UV dominated by short-lived stars with <108 yr lifetimes.! -43 ! ! !SFR(M/yr)=1.5x10 LUV (erg/s)! !where LUV is in the range 1500-2800Å. Sensitive to extinction and form of IMF. Requires satellite observations (except for high-redshift galaxies).! ! 4. Radio continuum emission! Arp 220 - A starburst Galaxy! VLBA Image of the core of Arp 220 at 1.4 GHz - Lonsdale et al. in prep! SFR vs Hubble type! ! -1 E ~ 0 !M yr ! -1! S0 # 0.004 !M yr -1 Sa ~ 0.3 !M yr ! -1 Sb ~ 3 !M yr ! -1 Sc ~ 5 !M yr ! -1 Sd-Im ~ 1 !M yr (smaller galaxies)! ! There are large variations, huge range, often in bursts.! ! Note: spread within a Hubble type > difference between types.! ! Specific frequency of globular clusters! ! NGC = number of globular clusters in a galaxy! ! SN = NGC L15/LV! ! where !SN is the specific frequency of globular clusters, ! ! LV is V-band luminosity! !L15 is luminosity of standard galaxy with MV=-15! ! Sa: SN ~ 1.2! Sc: SN ~ 0.5! E: SN ~ 5 and above! ! Giant ellipticals have largest SN , and are found in centers of clusters (as we will see). Provides some information about galaxy formation/ evolution.! Next time: ! ! !Spiral structure! !! ! Read chapter 25.3!.
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