Extragalactica 2024 Past Paper PDF

Exam prep EXTRAGALACTICA A. Selez 2024 1 GALACTICAL OBSERVATIONS 1.1 Orders of magnitude. The Milky Way: · Contains N...

Exam prep EXTRAGALACTICA A. Selez 2024 1 GALACTICAL OBSERVATIONS 1.1 Orders of magnitude. The Milky Way: · Contains Ns ∼ 1011 stars, or M∗ ∼ 5 · 1010 [M⊙ ]1 · The central Black Hole is MBH ∼ 4 · 106 [M⊙ ] · Disk has Rdisk ∼ 10 [kpc]2 · The total mass of gas and dust is Mgas+dust ∼ 10% = 0.1/Mtot · The Dark matter halo is RDM H ∼ 200 [kpc] and MDM H ∼ 1012 [M⊙ ] · The typical speed of stars in a circular orbit is vtyp ∼ 200 [km/s], and a complete orbit at sun’s distance from GC, at Rsun ∼ 8 [kpc], takes tsun−orb ∼ 250 [M yr] The mass percentages are as follows: Mtot ∼ 1.16 · 1012 [M⊙ ] z }| { M∗ ∼ 4.3% MBH ∼ 0.0003% Mgas+dust ∼ 9.9% MDM H ∼ 85.8% Now, there are several close galaxies of interest: · Sagittarius dwarf : Located at d⊙ = 24 [kpc], LSgr = 2 · 107 [L⊙ ] · Large Magellanic Cloud (LMC): Located at d⊙ ∼ 45 − 50 [kpc], LLM C ∼ 109 [L⊙ ] · Andromeda Galaxy (M31): Located at d⊙ ∼ 780 [kpc], LAnd ∼ 4 · 1010 [L⊙ ] Galaxy clusters are gravitationally bound systems that contain > 100 galaxies in a volume of diameter: Dgc ∼ 1 − 5 [kpc] and masses of Mgc ∼ 1015 [M⊙ ] The closest galaxy cluster is the Virgo cluster at d⊙ ∼ 17 [Mpc], and another close example is Coma cluster at d⊙ ∼ 90 [Mpc] Considering a homogeneous and isotropic universe, the relative velocity v between two galaxies at a distance d is: v = H0 d 1A solar mass is defined as M⊙ ∼ 1.989 · 1030 [kg] 2A parsec is 1 [pc] ∼ 3.086 · 1016 [m] 1 With H0 the Hubble constant, which is, according to 2018 Planck observations: H0 = 67.66 ± 0.42 [km/s/Mpc] 1.2 Photometry. Photometry is a technique to measure the intensity of radiation from an astronomical object on a large wavelength scale. There are two ”windows” in the atmosphere: Optical window and Radio window. The rest of the spectrum is obstructed by the atmosphere. Figure 1: Spectral windows of Earth’s atmosphere. The luminosity L of an astronomical object is measured in [erg/s], energy radiated per unit time. We can also consider a range of a spectrum, which gives the luminosity density Lλ [erg/s/Å].3 The bolometric luminosity is the total energy of an integrated object along the whole spectrum: Z ∞ Z ∞ c Lbol = L = Lλ dλ = Lν dν Lλ = Lν 0 0 λ2 The value that is measured is the flux F of an astronomical source, in [erg/s/cm2 ]. For a source at a distance D: L = 4πD2 F → Lλ = 4πD2 Fλ or Lν = 4πD2 Fν The intensity or surface brightness is the density of flux per unit of solid angle or area of the sky [erg/s/cm2 /Hz/arcsec2 ], or in Jansky units, 1 [Jy] = 10−23 [erg/s/cm2 /Hz]. For example, while the center of the galaxy may have the higher surface brightness, the flux may be the same as of the outer parts, if its area is more extensive. Usually, a system of magnitudes is used. In astronomy, apparent magnitude is: m = m0 − 2.5 log(F ) It is generally assumed that Vega has mλ = 0 ∀λ. Knowing the flux density of Vega will allow us to calculate flux density of any object. 3 Can be either by frequency range Lν or wavelength range Lλ 2 The magnitudes AB4 are defined so that m0 = 0 for F0 = 3631 [Jy] 4 NOT ABSOLUTE MAGNITUDES 3 2 GALAXY MORPHOLOGY 2.1 Types of galaxy classification. There are 3 main types of galaxy classification: · Hubble sequence - visual classification · CAS classification - model independent · Photometric decomposition - model dependent 2.2 Hubble classification A visual classification type that relies on: · Galaxy light concentration, relative bulge prominence. · Isophote shape (ε = 10 · (1 − q) = 10 · (1 − b/a)). · Presence of a bar. · Tight or loose arms. Early type −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−→ Late type Figure 2: Physical trends in Hubble sequence. The main benefits of this classification are: · Reflects different formation and evolution processes. · Highlights some physical trends. The main problems with this classification are: 4  · Subjective – depends on the person. · Superficial – doesn’t depend on physical properties. · Inclination – depends on galaxy orientation. · Wavelength – depends on the wavelength. · Incomplete – doesn’t include giant or dwarf galaxies. An alternative system is the Hubble numerical classification. A newer, more refined system is Comprehensive de Vaucouleurs Revised Hubble-Sandage (CVRHS): · (r) - Inner ring · (s) - Inner spiral · (l) - Inner lens · (bl) - barlens · (R) - Outer ring · (R’) - Outer pseudoring · (L) - Outer lens 2.3 CAS classification Classification type that actively uses machine learning to enhance the process. It consists in measuring and analysing the galaxy’s Concentration, Asymmetry, Smoothness. Figure 3: CAS classification definitions. I - initial; R - rotated; B - blurred. Other important parameters are: 5 Gini parameter - measures the relative distribution of flux in galaxy pixels, from G = 0 (uniform) to G = 1 (all flux in one px). n 1 X G= (2i − n − 1)|fi | |f |n(n − 1) i M20 parameter - measures the concentration of light, but not necessarily in the galaxy center.  P  X X i M20 = log10 while ifi < 0.2ftot with Mtot = Mi Mtot Figure 4: CAS including Gini and M20. Figure 5: Gini-M20 classification. 6 2.4 Photometric decomposition It is a parametric technique that uses functional forms to describe the surface brightness distribution of the different structures composing a galaxy. The technique consists in: 1. Measure the intensity I(r) using isophotes, aka regions of constant brightness. 2. Plot in magnitude scale µ(r) = −2.5 log10 (I(r)). 3. Analyze the PSF blur and seeing influence. Model the PSF. 4. Use one or several empirical functions to model the galaxy profile. (a) Photometric decomposition and modeling.. (b) Modeling. Figure 6: Photometric decomposition example(Peng et al.). Some of the functions to fit the profile are: · Exponential function. − Equivalent to a Sersic profile with n = 1. Fitting for disks. r Iexp (r) = I0 · e− h ▷ Where I0 is the central intensity; h is the scale-length. · Sersic profile. − Used to model elliptical galaxies and bulges, high flexibility. h 1/n i Iser (r) = Ie · e −bn ( rre ) − 1 ▷ Where Ie is the effective intensity; re is the effective radius, n is the Sersic index and bn ∼ 2n − 0.327 is the parameter that ensures that re contains half the light. Figure 7: Sersic profile · Ferrers profile. 7  − This represents the projected surface density of a three-dimensional Ferrers ellipsoid and it is generally used to describe the surface brightness of the bar component. Now, the disks can be classified into 3 types: · Type I profiles – follow a single exponential profile along the whole optical extent of the galaxies. · Type II profiles – present a double exponential law with a down-bending beyond the so-called break radius · Type III profiles – exhibit an up-bending in the outer parts of the discs. 8 3 GALAXY KINEMATICS 3.1 Observational tracers of the galaxy kinematics. There are several tracers of galaxy kinematics: · H I line, also known as the 21 cm Hydrogen line − Occurs due to hyperfine splitting of the ground state of the H atom. The transition of the electron spin from parallel to anti-parallel is accompanied by the emission of a photon. Concentrated in diffuse clouds. λ = 21 [cm] → Radio − Benefits – Little affected by extinction. Can be detected up to 30 [kpc] away. − Problems – Poor angular resolution. · CO molecular gas − Rotational transitions. They involve the rotation of the CO molecule, and the rotation of nuclei with respect to others. It is the most abundant molecule in molecular clouds after H2. The latter does not present easily excitable transitions under the conditions prevailing in molecular clouds, therefore, CO is used as a tracer for H2. H2 is found in the form of dense cold clouds, along with many other molecules. λ = 2.6 [mm] → Radio − Benefits – Better angular resolution than H I. − Problems – Less sensitive observations, not detected beyond the stellar disk. · Hα - ionized gas − This emission occurs mainly in the ”HII regions”. They are H+ clouds caused by the photoionization of neutral H by UV photons emitted by young stars. They are inside very hot and very dense molecular clouds. λ = 6565 [Å] → UV / Optical / NIR − Benefits – Good spatial resolution, very bright line. − Problems – Patchy emission, incomplete coverage in separate galactic parts. · Absorption stellar lines − Absorption lines, originated by the absorption of photons emitted by stars by the species present in stellar atmospheres (eg. Mg, Na, Ca). λ = too many to count → UV / Optical / NIR − Benefits – Good spatial resolution, tracer of the stellar movements. − Problems – Higher S/N spectra needed to measure these lines. In order to measure galaxy kinematics, long-slit spectroscopy has been often used. The lines are often approximated as Gaussian curves, sometimes even combining several of them. However, it is not practical, since galaxies are seen as a 2D image. So, an integral field is used instead. 9 Figure 8: Example slit spectroscopy. If combined along the X-axis, we’d get the ”visible” image of the slit region. If combined along Y-axis, we’d get the spectrum. Figure 9: Difference between the two. This method returns a so-called datacube. If combined along the wavelength axis, it becomes a reconstructed 2D image. The velocity curve of the galaxy is derived from Doppler effect that shifts the peak. Since we know where a specific line is located, and we measure the spectrum of a rotating galaxy, we can subtract these shifts and derive the velocities.   v λobs =z → v =z·c= −1 ·c c λref Measurement of this velocity at different points in the galaxy gives us a velocity distribution. The systemic velocity along the line of sight is: vsys = v(0) = vcosm + vpec,gal + vpec,M W + v⊙ + v⊕ + v⊕,rot 3.2 Velocity fields. The radial velocity of a star or a gas cloud located at a radius R and angle θ, with the galaxy at inclination i, is: vobs (x, y) = vsys + v(r) cos(θ) sin(i) 10  · A rotating solid body curve is a straight line, or a uniform gradient in 2D: vv (r) Ω= = const → vobs (x, y) = vsys + Ω(R) x sin(i) R − Where x = R · cos(θ). Which means that said 2D gradient will have vertical contours and will depend only on x. Fits the bulge or the bar. · A flat rotation curve: sin(i) cos(i) v(r) = v0 = const → vobs (x, y) = vsys + p cos2 (i) + tan2 (Φ) − The result is a set of straight lines pointing at the center. Fits the disk and DM halo. · A peaked rotation curve: x vobs (x, y) = vsys + v(R) sin(i) R − The result is a set of straight lines pointing at the center. Fits elliptical galaxies or dense clusters. LOSVD, or Line Of Sight Velocities Distribution, is an important term that describes the velocities of stars (or other objects) along the line of sight in a galaxy. · Usually, a Gaussian modified by Gauss-Hermite polynomials is assumed. · h3 parameter, the third moment: Skewness (measures asymmetry). · h4 parameter, the fourth moment: Kurtosis (measures sharpness of the peak ). · In a rotating disc we expect an anticorrelation between the velocity and h3. · Orbital anisotropy will affect h4 , radial anisotropy leads to h4 > 0, or sharp peak, while tangential anisotropy leads to l4 < 0. Galaxies can also be distinguished based on their specific angular momentum: · Fast rotators - flattened shape, disk-like rotation (S0, flat E, spiral). Rotation supported. · Slow rotators - ”puffy”, more spherical shape (giant E, E0). Random motion supported. 11 4 STAR FORMATION 4.1 SFR and SFH. · Star Formation RATE (SFR or ψ) − Amount of stars forming currently in a galaxy. Units are [M⊙ /yr]. − Tracers: UV continuum, Hα, Lα, emission lines. · Star formation HISTORY (SFH or ψ(t)) − Amount of stars that formed in a galaxy’s entire lifetime. − Constant SFH: ψ(t) = const. Galaxies with steady star formation (some disks). − Exponential decline: ψ(t) = ψ(t0 ) · e−t/τ. Common in older galaxies. − Constant for some time: ψ(t) = ψ(t0 ) · δ(t − t0 ) · Single Stellar Population (SSP or ψ(t0 )) − A single, infinitesimal burst of star formation. There are 2 approaches to studying star formation in other galaxies: · In-situ approach – studying ψ in galaxies at different redshift. Avoids degeneracies of stellar properties and modelling assumptions / issues. · Fossil approach – studying ψ(t) of galaxies nowadays. Higher signal-to-noise, better understanding of the galaxy complexity / morphology, spatial resolution (integral-field spectroscopy), homogeneous dataset, avoiding uncertainties about the progenitors. · Spectral Energy Distribution (SED) − Emission of the galaxy throughout the whole spectro-magnetic spectrum. P − SEDgal = SED∗ − SED of a SSP can be analyzed: ▷ t0 < 0.1 [Gyr] → Mainly giants and supergiants. ▷ 0.1 < t0 < 1 [Gyr] → Less massive stars leave MS. ▷ t0 > 3 [Gyr] → Horizontal branch and white dwarves. Other important concepts are: · Mean luminosity-weighed age and metallicity (MLW): The age and metallicity of an SSP to which the flux-calibrated SED (spectrum) of a galaxy can be approximated. Dominated by young and bright stars. · Mass mean-weighed age and metallicity (MMW): Same as MLW, but normalised in stellar mass. Dominated by old and heavy stars. · Metallicity. Metals - mass fraction of all elements heavier than He. Represented as abundance relative to H. Fe is usually taken as a representative. 12 · Relative abundance ratio: in the galaxies, different metals are a product of different stages of stellar evolution. Relative abundance of different metals provide information about the SFR of the galaxy and can be used as “chemical clocks”. − α-elements: produced by nuclear fusion of He (α particle) and another α-elements: C, O, Mg, Si, S, Ca, Ti... − α-elements are produced in Type II supernovae (death of star with 8–50 [M⊙ ]) in < 0.1 [Gyr] timescales. − Fe is produced in Type Ia supernovae (white dwarf + star) in 1 [Gyr] timescales − α-enhancement: relative abundance ratio of α-elements with respect to Fe. − High [α/F e] – quick star formation process. − Low [α/F e] – SPH is extended in time. 13