Lecture 3 Elliptical Profiles PDF

LIGHT PROFILES OF ELLIPTICALS Aim: Know how to quantitatively describe the light distribution in Ellipticals Learning Outcomes. By the end of this Lecture you should be able to: -1- Define the Isophotes and light profiles of Ellipticals -2- Calculate the total luminosities and “sizes” (effective...

LIGHT PROFILES OF ELLIPTICALS Aim: Know how to quantitatively describe the light distribution in Ellipticals Learning Outcomes. By the end of this Lecture you should be able to: -1- Define the Isophotes and light profiles of Ellipticals -2- Calculate the total luminosities and “sizes” (effective radii) of Ellipticals -3- Formulate the different light profiles of different families of Elliptical galaxies So far: Hubble classification is according to observed morphology What is the physical significance of different appearances, ie different light distributions? REMINDER ABOUT LIGHT MEASURING FROM PHYS1005 (Luminosities, Fluxes and Magnitudes)  Flux and luminosity How bright is an object? How intrinsically luminous is an object? – not the same thing Luminosity is the energy per second emitted by the source. Brightness, or flux, is the observed energy per second that we receive per unit area of detector. Flux units: [ ergs/cm2/s ] (cgs system; 1 erg = 10-7 J) or [ W / m2 ] (SI) In stellar spectra, Flux density = flux per Hz [W / m2 / Hz] is often used. Observed flux, F, depends on luminosity L: L = 4 π d2 F F = L / (4 π d2) assuming isotropic emission (equal amounts in all directions)  Flux and luminosity Flux and luminosity are usually measured in wavebands (eg U, B, V..) Bolometric luminosity = luminosity over all wavelengths Bolometric luminosity of the Sun: L⊙ = 3.85 x 1026 W  Optical bands and colours Luminosities/Magnitudes are always defined in terms of a photometric system, where the magnitude is as seen through a particular filter. The most common systems are the Johnson UBV, the Kron Cousins RI filter system and the Sloan ugriz:  Sloan Digital Sky Survey (SDSS) filter transmission The current Standard filters – in the lab Better, more rectangular, shape  SDSS filters, including effect of mirror, other optics and CCD detector transmission So almost all telescopes are most sensitive to g,r,i photons and least sensitive to u and z (Also need to include transmission of the atmosphere, which further reduces u-band sensitivity)  Magnitudes In optical astronomy magnitude is used as a measure of flux. Magnitude scale dates back to Hipparcos (≈ 150 B.C.). Brightest stars had mag 1, the faintest stars had mag 6 Larger magnitudes → fainter objects eye works on a logarithmic scale: mag ~ logm (flux) Norbert Robert Pogson (1850) defined that a star with mag 1 is 100 times brighter than star with mag 6. ie 5 magnitudes = x100 in flux → star of mag 1 is 1001/5 (= 2.512) x brighter than star of mag 2 ie. F1/F2 = 2.512 m2-m1 Then take logs to base m, ie 2.512 So m2 ― m1 = logm (F1/F2) or m1 ― m2 = ― logm (F1/F2) = - log10 (F1/F2) x logm (10) = ―2.5 log10 (F1/F2) (From now on, we use logs to base 10 unless specifically mentioned.)  Magnitudes Apparent magnitude m: the magnitude of an object as seen on Earth Equivalent to flux Absolute magnitude M: the magnitude the object would have at a distance of 10 pc. Equivalent to luminosity m ― M = ―2.5 log (Fobserved/F10pc) F10pc - flux if at 10pc So if d = distance in pc, and as F ~ L d-2 (L is same, so cancels) m ― M = ―2.5 log (100/d2) m ― M = 5 log (d) ― 5 Distance modulus If we know the absolute magnitude of an object, we can work out its distance.  Magnitudes to Absolute Fluxes Apparent magnitudes represent relative fluxes. Have to compare with standard stars where we already know what the absolute flux (W/m2) is for a given magnitude Convert to absolute fluxes with respect to standard stars, usually of zero magnitude, then m - 0 = ― 2.5 log (F /F0) Or m = ― 2.5 log (F /F0) m - observed magnitude F - observed flux - ie what you want F0 – absolute flux of 0th magnitude star  Magnitudes to Absolute Fluxes Usually we are interested in the flux at a particular wavelength, or in a particular waveband. Then we write: mλ = ― 2.5 log (F λ /F λ, 0) Or we often write mλ = ―2.5 log (F λ) ― ZP λ Zeropoint, ZPλ Depends on filter  Optical bands and colours Colour or colour index: difference between magnitude in a shorter waveband and a longer waveband. Instead of mB we often write, as a shortcut, just B. Colours are then written U―B, B―V... One of the main standard stars is Vega (an A star). In the Johnson system Vega has mV = 0.0, and all colours = 0 i.e. B ― V = mB ― mV = 0 Remember: mB ― mV = ―2.5 log (FB/FV) - distance independent  NEW CONCEPTS: Surface brightness, Luminosity/Surface brightness profile, effective radii see section 2.1.1 in “Galaxy Formation and Evolution” see also section 1.3.1 and pages 232-238 in Sparke&Gallagher SMALL ANGLE APPROXIMATION: Two points on the sky separated by a physical separation S corresponding to an angle α, at a distance D from the observer Basic Formula: α=S/D sin α ~ tan α ~ α NB: α in RADIANS!!! S D  Surface brightness profiles How do images of galaxies appear, and what does this tell us about the distribution of stars in them? Surface brightness, I(x), is a measure of flux from unit area on the sky (eg per square arcsec) – an OBSERVED quantity F We can convert into PHYSICAL properties, I(x) = 2 i.e. LUMINOSITY and SIZE α L S 2 Now F = and α2 = 2 4π d 2 d S Lα 2 F So F = Then as I(x) = 2 x 4π S 2 α d L Therefore I(x) = 4π S 2 α i.e. = Luminosity per unit area of the source ( / 4 π) Lengths subtending 1 arcsec2 at the observer - which is independent of distance  Surface brightness (SB) profiles How do images of galaxies appear, and what does this tell us about the distribution of stars in them? Surface brightness is a measure of flux per unit area on the sky (square arcsec) Surface brightness is independent of distance (in local universe) Angular area scales with (distance)-2 Flux scales with (distance)-2 So the distance cancels out. S SB is denoted x µ [mags arcsec-2] or I [L⊙ pc-2] d conversion between units: α µ I = 1 L⊙ pc-2 = M⊙ + 21.57 Lengths subtending 1 arcsec2 at the observer  Isophotes and galaxy sizes surface brightness is a function of radius: surface brightness profile I(R) or µ(R) – Peaks in centre – Falls of towards larger radii How big is a galaxy? Problem: surface brightness gradually drops dimmer far out without a clear cut-off Deeper observations reveal more of the outer extensions (sky brightness, larger errors at fainter intensities) Tidal radius: within rtidal matter is bound to the object by its gravitational force (but difficult/impossible to assess observationally)  Measuring surface brightness profiles Projected surface brightness profile: Azimuthal slicing: φ – Average profile over all azimuthal angles = average over many radial slices – Smooths out spiral arms azimuthal angle For non-circular galaxies → Stretch radial slices to major axis → averaging azimuthally along lines of constant surface brightness, the isophotes – Smooths out features like spiral arms Better measurement of surface brightness profile  Isophotes Isophote plots show changing surface brightness Isophotes: contours of constant surface brightness isophotal radius - is the angular radius where the galaxy light cannot be distinguished against the background (function of detector, exposure time, observing conditions so not a useful quantitative measure) isophotal luminosity Liso is the luminosity integrated to this radius.  Elliptical surface brightness profiles The surface brightness (SB) profiles of ellipticals and bulges of disc galaxies typically follow a characteristic profile called the de Vaucouleurs law: ⎡ ⎛ R ⎞1/ 4 ⎤ I ( R) = I 0 exp ⎢− ⎜ ⎟ ⎥ ⎢⎣ ⎝ a ⎠ ⎥⎦ a is the radius enclosing half the total light SB, in linear units, is solar luminosities per square pc Or, in mag/square arcsec R 1/ 4 µ ( R ) = µ 0 + 1.086( ) a (Sorry, units can be confusing)  Elliptical surface brightness profiles But: de Vaucouleurs law does not fit all ellipticals, some are better fit with the generalized Sersic law, that describes ellipticals as well as bulges and discs. 4 is replaced by the Sersic index n, which is then a free parameter to fit 10 1 ⎡ ⎛R⎞ 1/ n ⎤ I ( R ) = I 0 exp ⎢− ⎜ ⎟ ⎥ ⎢⎣ ⎝ a ⎠ ⎥⎦ R 1/ n µ ( R ) = µ 0 + 1.086( ) n=1 → exponential profile a Sersic index n correlates with galaxy luminosity, e.g. n=10 for giant Es  Galaxy sizes The size of a galaxy is difficult to quantify: surface brightness as a function of radius decreases at large radii difficult to detect the galaxy light against the weak background light from the sky. measurement uncertainty on the intrinsic galaxy intensity increases at large radii (and fainter signal). → galaxy sizes are usually defined in terms of some radius which contains a certain fraction of the light, or corresponds to a particular surface brightness.  Galaxy sizes effective radius Re – radius which contains half of total galaxy light (need to extrapolate observed surface brightness profile to work out the total emission) For large spirals and ellipticals, Re~10 kpc, for the giant elliptical cD galaxies Re can be as large as 100 kpc.  To recap: Surface brightness (SB) is a measure of flux per unit area on the sky (square arcsec) The isophotes are contours of constant surface brightness The profile of an Elliptical is best described by a Sersic profile, dependent on the parameter n which increases with stellar mass. Galaxy sizes are usually defined in terms of some radius which contains a certain fraction of the light. ADDITIONAL MATERIAL (NOT ASSESSED)  Profiles close to the nucleus Close to the centre (nucleus) of ellipticals and early-type spiral bulges, profile deviates from de Vaucouleurs/Sersic law to either a power-law → central 1 arcsec=105 pc cusp or flatten to a so-called core profile Core profiles are associated with 1 arcsec=88 pc the most massive galaxies: may be a signature of major galaxy mergers may be related supermassive black holes in the galaxy nuclei  Profiles close to the nucleus most luminous ellipticals (L > 109 L⊙) show low central surface brightness and large cores → indication of merger? 1 arcsec=105 pc (mergers increase stellar motion, the cores expand) Core radius mark area within which surface brightness is (nearly) constant 1 arcsec=88 pc Careful! Core radius could just mark the change in surface brightness profile that cannot be resolved with our observations Elliptical surface brightness profiles Elliptical galaxies: – Luminous giant ellipticals: L > 1010 L⊙ Low central surface brightness Large cores Large outer envelope – Midsize ellipticals: L > 3 x 109 L⊙ Central cusps – Dwarf and compact ellipticals: : L ≤ 3 x 109 L⊙ Larger cores than midsize ellipticals  Variations in isophotal contours Some galaxies show variations in ellipticity: – Disky shaped isophotes (more elongated along major axis) – Boxy shaped isophotes (more rectangular) – Variation in major axis position angle PA →isophotal twist Position angle PA: measured from north to the major axis disky boxy  Boxy and disky isophotes Very luminous ellipticals tend to be boxy, while the medium luminosity ellipticals are more likely to be disky, which is also associated with oblateness and faster rotation.  How to measure surface brightness profiles Surface brightness profile: the way surface brightness changes with distance to the centre of the galaxy Radial slicing: – Measures along one slice – Problem: extent and shape of profile depends on slice What about non-circular galaxies and non-zero inclination? – For ellipticals: along major axis  Variations in isophotal contours Variation in major axis position angle PA → isophotal twist Position angle PA: measured from north to the major axis  Isophotal twist Isophotal twist indicates triaxial galaxy that is not viewed along any of the principal axes May also indicate the presence of a bar or non-axisymmetric bulges http://ned.ipac.caltech.edu/level5/March02/Kormendy/Kormendy3_3.html  Galaxy sizes de Vaucouleurs radius D25 - surface brightness reaches 25 mag arcsec-2 scale length – surface brightness reaches some fraction of central surface brightness effective radius Re – radius which contains half of total galaxy light Kilgard et al. 2005 ApJS, 159, 214 (need to extrapolate observed surface brightness profile to work out the total emission) For large spirals and ellipticals, Re~10 kpc, for the giant elliptical cD galaxies Re can be as large as 100 kpc.