Lecture Three: ~2% of galaxy mass in stellar light Stellar Populations What defines luminous properties of galaxies face-on edge-on https://www.astro.rug.nl/~etolstoy/pog16/ 18 th April 2016 Sparke & Gallagher, chapter 1, 2 The effect of star formation, spiral arms, gas, dust Stellar Properties: Three main physical properties define a star: Stellar Populations = Stars in Galaxies Effective Temperature Teff L 4 R 2 T 4 e The continuum of a star is a black-body curve, with T ~ Teff max =[2.9/T (K)] mm Surface Gravity log g pressure of stellar photosphere ionisation balance, pressure broadening, molecular abundance etallicity Z or [Fe/H] or chemical composition, elements heavier than He individual elements cause absorption lines where atoms intercept light from the centre of the star a star with [Fe/H] = -2 has 1% as much Fe as the Sun
Temperature (Teff) Surface Gravity (log g) Cool, <3500K A-stars 0.15 ~4 500K log g ~ 4 0.8 1 ~6 000K log g ~ 2 2 ~11 000K log g ~ 0 40 Hot, ~30 000K blue Strength of spectral line depends on Teff of star & also abundance of that element Stars like the Sun are ~72% H; 26% He and 2% "metals" red etallicity (Z or [Fe/H]) etallicity (Z or [Fe/H]) K-giant stars The Sun [Fe/H] = -2.35 [Fe/H] = -1.47 [Fe/H] = -0.92 FeI TiI SiI Zr FeI NiI TiI ZrI VI ZrI FeI Subaru/HDS, R ~ 90k chemical elements in the Sun CaI FeI FeI FeI BaII GIRAFFE, R ~ 20k
Quick Stellar Classification Stellar Types & Ages Standard Spectral Class - based on presence of strong absorption, OBAFGK which was later found to be also a sequence of decreasing Teff. 1-9, are temperature sub-classes (hot-cool) I-V, luminosity class, decreasing log g The Sun is a G2V star >10Gyr 0.15 ~4 500K Classification determined without metallicity... 0.8 1 ~8Gyr ~6 000K 2 ~1.5Gyr ~5yr 40 ~11 000K blue red OBAFGK... Integrated Stellar Populations Spectra are time consuming to obtain in large numbers AGNITUDES & COLOURS Elliptical Galaxy O Connell 1986 PASP, 98, 163
Defining agnitudes The flux received by the detector at the telescope is defined:! f F R T f 0 f F R T d is the flux of the object (in frequency units) is the transmission of filter used We generally don't measure ALL flux from an object, but only that which arrives in a telescope at a given frequency or wavelength range. is the transmission of the telescope, optics, and detector is the transmission of the atmosphere (if any) Consider 2 objects with fluxes f1 and f2 Defining agnitudes The magnitude difference between these objects is: m 1 m 2 = k log 10 f 1 where k =2.5 means that m 1 m 2 =5 when f 2 /f 1 = 100 so or if m 2=m 1+1 then star 1 appears about 2.5 time brighter than star 2 m 1 m 2 = 2.5 log 10 f 1 f 2 f 1 f 2 = 10 0.4(m 1 m 2 ) f 2 Defining agnitudes uch easier to measure relative magnitudes, so most (but not all) magnitude systems are based on magnitudes with respect to a star with a known (or predefined) magnitude: Two Standard Photometric Systems e.g., the Vega system defines a set of A0V stars as having apparent magnitude 0 in all bands
Comparing to Atmospheric Transmission Compare to stellar spectra U B V R Notice that stars of different temperatures have very different spectra, so they have different fluxes through the filters and therefore they have different colors. Photometric calibration is defined to correct for all effects and determine true magnitude of a star in a perfect telescope above the Earth's atmosphere. Stellar spectra Spectrum of an Elliptical galaxy U B V R I Spectra of late-type galaxies U B V R I
absolute magnitude K-correction Correcting for red-shifting of light out of wavelength region True flux: Converting apparent to absolute magnitudes F = L 4 D 2 so we need the distance D to the stars We receive flux f at our telescopes from an object at distance d. If we wanted instead to know what the flux F is of that object if it were at distance D, then 2 f = F The difference in magnitudes m (of f) at d and (of F) at D is then m = 2.5 log We always pick D to be 10 parsecs (10 pc), so if d is measured in parsecs, then D d f F = 5 log d D m = 5 log(d[pc]) 5 If d is measured in 10 6 pc=1 pc, then m = 5 log(d[pc]) + 25 This is most important for high-redshift galaxies. If it is not taken into account conclusions can easily be in error. m is called the distance modulus and is sometimes written µ=m...and is called the absolute magnitude Apparent vs. Absolute mags ESA Hipparcos satellite, launched 1989 bright 12 10 8 6 main sequence red giant branch Nearly ~120 000 stars in Hipparcos catalogue within ~100pc of the Sun Evolutionary Timescales Stars burn hydrogen into helium for most of their lifetimes, until they exhaust the H in their cores, how long does this take? Let s call E the amount of energy released by H burning during its main-sequence lifetime, τms If the star s luminosity on the main sequence is L, then, So if we can determine E, we can determine τms E = L τms The amount of energy released by converting a mass d of H into He is de=0.007c 2 d So if a fraction α of the total mass of the star is burned into He before core H- exhaustion, then E=0.007c 2 α so the main-sequence lifetime is 4H S =0.007 c 2 /L He + 0.7% mass of 4H in energy faint 4 2-0.5 0 0.5 1 1.5 2 B-V blue colour red Perryman et al. 1995, A&A, 304, 69 Typically, α=0.1, so: S = 10/ (L/L ) 1 Gyr From the equations of stellar structure, for the main sequence: L 4 Thus we have the main-sequence lifetime as a function of mass: S = 10A(/ ) 3 Gyr So a star ten times the mass of the sun lives for ~1/1000 of the time: ~10 yr!
Evolutionary Timescales Stellar Evolution odels The main-sequence lifetime is a crucial timescale: it is a clock. By measuring the magnitude and colour of the main sequence turnoff (STO or just TO) we can determine the age of a stellar population and therefore something about its evolution A set of stellar models all with the same composition The brighter and bluer the STO, the younger the population, because brighter, bluer S stars are more massive Examples Globular clusters Isochrones - single age stellar populations A set of stellar models all with the same age and same composition of globular clust Similar sequences 4.5 yr The resulting track in an HR diagram or a CD is called an isochrone ag e All W GCs are old, and their CDs are very similar. They vary primarily due to composition differences metallicity [Fe/H] He content 14 Gyr main-sequence turnoffs variations of other elements Age is an important but secondary consideration The exact location o the HR diagram age metallicity, a quantity related element abundan
Open Clusters Open Clusters low mass, relatively small (~10 pc diameter) clusters of stars in the Galactic disk containing <103 stars. Useful for studying the evolution of the properties of the W s disk Because open clusters live in the disk of our ilky Way, they are subject to strong tides and shearing motions Because they are so small and contain few stars, they also evaporate quickly Therefore they do not live very long unless they are very massive so most of them are quite young The Pleiades cluster is a good example of an open cluster. The fuzziness is starlight reflected from interstellar dust All stars in an open cluster are Which of these clusters is the youngest? at the same distance, formed at the same time have the same composition Which is the oldest? Very useful for testing stellar evolution models! The effect of age in CDs theoretical distribution of group of stars with the When populations get old, the same age isochrones pile up at very similar example: from 4 yr toand 10.6 Gyr luminosities temperatures log(age) The effect of metallicity Isochrones - single age Isochrones: stellar populations (the labels give the log(age)). It is easy to determine ages for young populations Age dating GCs is difficult! This is an opacity effect: more metals mean more absorption, especially in the blue (it s reradiated into the IR), so stars become cooler (redder) and dimmer [Fe/H]=0 [Fe/H]=+0.5 log(age) "Old" isochrones are much closer together than the "younger" isochrones -> Easy to measure the age of a young population but difficult for an old pop 12 Gyr [Fe/H]=-2 but not for old populations! Stellar temperatures and luminosities also depend on composition.
Age-metallicity degeneracy Putting it together Both age and metallicity affect isochrones, and so S turnoff required to separate their effects on stellar populations. 3x lower age 2x higher [Fe/H] Only S turnoff changes! The absolute V magnitude of the STO varies as Uncertainties: V (STO) = 2.7 log(t/gyr) + 0.3[Fe/H] + 1.4 Difficult to measure the location of the main sequence turnoffs Distance uncertainties cause large age uncertainties: 10% distance uncertainty 0.2 mag uncertainty in distance modulus 0.2 mag uncertainty in STO magnitude 20% uncertainty in age The Luminosity Function An Example: Solar Neighbourhood Hipparcos CD: stars within 100 pc of the Sun: bright The luminosity function Φ(v) describes how many stars of each luminosity are present in a given volume (e.g., pc 3 ). We can construct a luminosity function: ( V )d = dn V max where Vmax is the volume over which stars with v could be seen faint blue red
An Example: Solar Neighbourhood An Example: Solar Neighbourhood Hipparcos limit all stars only S Thus we can also determine the mass-to-light ratio of the Solar Neighbourhood: proportion of massive stars to dim low mass stars the V-band luminosity density is 0.053L pc 3 the mass density is (including white dwarfs) 0.039 pc 3 combining, the mass-to-light ratio in solar units is! /L V 0.67 /L This is a lower limit to the total mass per unit luminosity (in a given band) This is the result (in black). ost of the stars are faint. If we weight by the luminosity of the stars: nearly all of the light is in bright stars If we weight by the mass of the stars: most of the stellar mass is in low-mass stars Note this is the present-day luminosity function (PDLF), which is the LF we see after the high-mass stars have evolved away The Initial ass Function (IF) A critical input for stellar population models crucial to understand the formation and evolution of galaxies is the initial mass function, usually shortened to IF. This specifies the distribution of mass in stars immediately after a star formation event: the number of stars dn with masses between and +d is dn = N 0 ()d We normalize ψ() such that N0 is the total number of solar masses formed in the event: Z ()d = The Initial ass Function (IF) To determine ψ(v), we need to determine dn immediately after a starformation event to get the initial luminosity function Φ0 dn = () d If the system has been forming stars at a constant rate (roughly true for the W disk) since time t, then t/ 0() = () S for S () <t 1 otherwise Now we can determine: () = d d t/τms corrects that we only see stars of magnitude that formed in the last fraction t/τms of the population s life 0 [()] specifies the relation between stellar mass and absolute magnitude
Relation between ass and agnitude The Initial ass Function (IF) () can be determined from theory or observation theory doesn t work very well There are a number of different IFs. assume a simple function The simplest IF is that inferred by Salpeter (1955), which is a power-law () / 2.35 ost evidence suggests that the stellar IF is universal, meaning it always have the same form. But this is hard to test. Evolution of Stellar Populations Stars with masses <1.5 live for >2.5 Gyr and put out most energy after the STO e.g., 1 star puts out ES~10.8 L Gyr on the S and EGB~24 L Gyr on RGB, HB and AGB If stars of mass emit a total energy of EGB on the giant branch, then the luminosity of the population will be For these low-mass stars, the S lifetimes are or and so GB d dt L S 10 Gyr 1 3 dn d GB E GB d GB dt 1/3 GB S 10 Gyr energy released on GB per star times the change in the number of stars per unit time Assume the IF to be a power-law with α -2.35 for GB, then dn/d K(/ ) the luminosity is 4 K E GB ( GB ) GB L 30 Gyr Note: GB lifetimes are ~10% of S lifetimes, so the range of masses on the GB is small, approx. that of STO. differentiate and then substitute τms in terms of GB 4 10 Gyr 3 L We can differentiate L to find d ln L dt Evolution of Stellar Populations K E GB ( GB ) 30 Gyr GB d ln E GB d ln GB + (4 ) 4 0.3 1.3+0.3 d ln E GB d ln GB d ln GB dt So as long as α<4, then the luminosity of a coeval population decreases with time, meaning, in the absence of star formation, galaxies (and star clusters) get fainter with time!