A “zoo” of galaxies Are all the other galaxies in the Are all the other galaxies in the UniverseA “zoo” similar of galaxies to the Milky Way? Universe Hubblesimilar Ultra Deep to Field the Milky Way? elliptical galaxy

spiral galaxy

Hubble Ultra Deep Field

Hubble Ultra Deep Field Are all the other galaxies in the Universe similar to the Milky Way?

M 87 - (in Virgo cluster)

- spheroid - no disc - red-yellow color—> old stars Hubble Ultra Deep Field The shape of elliptical galaxies

M 87 Ellipticity = 1 - b/a

ellipticity ✏ =1 b/a E0,E1,E2,...En E0 E1 E2 a b … E7

n = 10✏ Hubble Ultra Deep Field Classification of Ellipticals ellipticity ✏ =1 b/a E0,E1,E2,...En

n = 10✏ Are all the other galaxies in the Universe similar to the Milky Way?

• Lenticular Lenticular Galaxy galaxy: has a disk like a spiral galaxy but much less dusty gas (intermediate - intermediate between spirals and ellipticals between - dusty stellar disc - less dusty spheroid spiral and elliptical) Hubble Ultra Deep Field Are all the other galaxies in the Universe similar to the Milky Way?

Spirals

Hubble Ultra Deep Field Grand design spirals

Grand Design Spirals M51 Are all the other galaxies in the Universe similar to the Milky Way?

Barred Spiral

• Barred spiral galaxy: has a bar of stars across Hubblethe Ultra bulge Deep Field Classification of Spirals

disk/bulge

pitch angle

disc/bar The Hubble’s sequence Hubble Sequence (not evolutionary!) This is NOT an evolutionary sequence Irregulars Cluster of galaxies

HST MCS J0416.1–2403 GravitationalGa Dynamics

1. Virial theorem 2. Time scales for relaxation

see notes

3.4 Scaling Relations

107 gas, which can be determined from the strength of the 3.4.3 The Fundamental Plane 21-cm line, to the stellar mass a much tighter correlation The Tully–Fisher and Faber–Jackson relations specify is obtained, see Fig. 3.21(b). It reads aconnectionbetweentheluminosityandakinematic 4 9 2 vmax property of galaxies. As we discussed previously, vari- Mdisk 2 10 h− M , (3.19) = × ⊙ 100 km/s ous relations exist between the parameters of elliptical ! " galaxies. Thus one might wonder whether a relation ex- and is valid over five orders of magnitude in disk mass ists between observables of elliptical galaxies for which M M M .Ifnofurtherbaryonsexistinspirals disk gas the dispersion is smaller than that of the Faber–Jackson (such= as, e.g.,∗ + MACHOs), this close relation means that relation. Such a relation was indeed found and is known the ratio of baryons and dark matter in spirals is constant as the fundamental plane. over a very wide mass range. Scaling Relations for GalaxiesTo explain this relation, we will consider the vari- ous relations between the parameters of ellipticals. In 3.4.2 The Faber–Jackson Relation Sect. 3.2.2 we saw that the effective radius of normal el- Arelationforellipticalgalaxies,analogoustotheTully– lipticals is related to the luminosity (see Fig. 3.7). This Fisher relation, was found by Sandra Faber and Roger implies a relation between the surface brightness and Jackson. They discovered that the velocity dispersion in the effective radius,

the center of ellipticals, σ0,scaleswithluminosity(see 0.83 Re I − , (3.21) Spirals Fig. 3.22), Ellipticals: ∝ ⟨ ⟩e SMBHs Tully-Fischer L σ 4 , Faber-Jackson where I is the average surface brightness withinM the relation 0 3.4 eScaling Relations ∝ effective⟨ ⟩ radius, so that or 107 gas, which can be determined from the strength of the 3.4.3 The Fundamental Plane 21-cm line, to the stellar mass a much tighter correlation 5.64 The Tully–Fisher and Faber–Jackson relations2 specify 4 log(σ0) 0is. obtained,1MB see Fig.const 3.21(b).4 It. reads (3.20) L 2πR I . 8.32 (3.22) L v = − L+ aconnectionbetweentheluminosityandakinematice eM 10 M rot(max) 4 = ⟨ ⟩ BH 9 2 0 vmax property of galaxies. As we discussed previously, vari- 1 Mdisk 2 10 h− M , (3.19) / “Deriving” the Faber–Jackson= /× scaling⊙ 100 km/s relation isous pos- relations exist between the parameters of elliptical ⇡ 200 km s ! " galaxies. Thus one might wonder whether a relation ex- and is valid over five orders of magnitude in disk mass From this, a relation between the luminosity and I e sible under the same assumptions as the Tully–Fisherists between observables of elliptical galaxies for which ⇣ ⌘ Mdisk M Mgas.Ifnofurtherbaryonsexistinspirals ⟨ ⟩ ∗ the dispersion is smallerresults, than that of the Faber–Jackson (such= as, e.g.,+ MACHOs), this close relation means that relation. However, the dispersion of ellipticalsrelation. about Such a relation was indeed found and is known the ratio of baryons and dark matter in spirals is constant as the fundamental plane. this relation is largerover a very than wide mass that range. of spirals about the 2 0.66 To explain this relation,L we willRe considerI e the vari-I e− ous relations between the parameters∝ ⟨ of ellipticals.⟩ ∝ ⟨ In ⟩ Tully–Fisher relation.3.4.2 The Faber–Jackson Relation Sect. 3.2.2 we saw that the effective radius of normal el- Arelationforellipticalgalaxies,analogoustotheTully– lipticals is relatedor to the luminosity (see Fig. 3.7). This Tully–Fisher Relation E NCYCLOPEDIA OF A STRONOMY AND A STROPHYSICS Fisher relation, was found by Sandra Faber and Roger implies a relation between the surface brightness and Jackson. They discovered that the velocity dispersion in the effective radius, McConnell & Ma 2012 M Pierce, P Murdin - Encyclopedia of Astronomy and Astrophysics Schneider 2006 1.5 the center of ellipticals, σ0,scaleswithluminosity(see 0.83 Re I − , I e L− (3.21). (3.23) Fig. 3.22), ∝ ⟨ ⟩e ⟨ ⟩ ∝ 4 L σ0 , where I e is the average surface brightness within the ∝ effective⟨ ⟩ radius, so that or Hence, more luminous ellipticals have smaller surface 2 log(σ0) 0.1MB const . (3.20) L 2πR I . (3.22) = − + = e ⟨ ⟩brightnesses,e as is also shown in Fig. 3.7. By means “Deriving” the Faber–Jackson scaling relation is pos- From this, a relation between the luminosity and I sible under the same assumptions as the Tully–Fisher of the Faber–Jacksone relation, L is related to σ0,the results, ⟨ ⟩ relation. However, the dispersion of ellipticals about central velocity dispersion, and therefore, σ , I ,and this relation is larger than that of spirals about the 2 0.66 0 e L Re I e I e− ⟨ ⟩ Tully–Fisher relation. ∝ ⟨ ⟩ ∝ ⟨R⟩ are related to each other. The distribution of elliptical or e

1.5 galaxies in the three-dimensional parameter space (Re, I L− . (3.23) ⟨ ⟩e ∝ I e, σ0) is located close to a plane defined by Hence, more luminous⟨ ⟩ ellipticals have smaller surface brightnesses, as is also shown in Fig. 3.7. By means of the Faber–Jackson relation, L is related to σ0,the central velocity dispersion, and therefore,1.4σ0, I e,and0.85 Tully–Fisher Relation E NCYCLOPEDIA OF A STRONOMY AND A STROPHYSICS Re σ0 ⟨I⟩ e− . (3.24) Re are related to each other. The distribution of⟨ elliptical⟩ galaxies in the three-dimensional∝ parameter space (Re, I , σ ) is located close to a plane defined by ⟨ ⟩e 0

1.4 Writing0.85 this relation in logarithmic form, we obtain Re σ I − . (3.24) ∝ 0 ⟨ ⟩e Fig. 3.22. The Faber–Jacksonmagnitude relation~ log (Luminosity) expresses a relation be- tween the velocity dispersion and the luminosity of ellipticalWriting this relation in logarithmic form, we obtain Fig. 3.22. The Faber–Jackson relation expresses a relation be- log Re 0.34 µ e 1.4logσ0 const , (3.25) tween the velocity dispersion and the luminosity of elliptical galaxies. It can be derived from the virial theorem log Re 0.34 µ e 1.4logσ0 const= , (3.25)⟨ ⟩ + + galaxies. It can be derived from the virial theorem = ⟨ ⟩ + + magnitude ~ log (Luminosity)

~ log( projection corrected rotational velocity ) Fig. 1.— The M relation for our full sample of 72 galaxies listed in Table A1 and at http://blackhole.berkeley.edu.Brightest Figure 1. B, R, I and H band calibrations of the Tully–Fisher relation. Solid circles are galaxies with distances measured using cluster galaxies (BCGs)• that are also the central galaxies of their clusters are plotted in green, other elliptical and S0 galaxies are plotted in red, and late-type spiral galaxies are plotted in blue. NGC 1316 is the most luminous galaxy in the Fornax cluster, but it lies at the Cepheids, solid triangles are galaxiesFigure 1. B with, R, I and distancesH band calibrations estimated of the Tully–Fisher via relation. surface Solid circles brightness are galaxies with fluctuation distances measured measurements using within dE companions Fig. 1.— The M relation for our full sample of 72 galaxies listed in Table A1 and at http://blackhole.berkeley.edu.Brightest • cluster outskirts; the green symbol here labels the central galaxy NGC 1399. M87 lies near the center of the Virgo cluster, whereas NGC Cepheids, solid triangles are galaxies with distances estimated via surface brightness fluctuation measurements within dE companions cluster galaxies (BCGs) that4472 are (M49) also lies the1Mpctothesouth.Theblack-holemassesaremeasuredusingthedynamicsofmasers(triangles),stars(stars)orgas central galaxies of their clusters are plotted in green, other elliptical and S0 galaxies are plotted ⇠ and open circles are systems thoughtand open circlesto be are groupsystems thought members to be group members with withat least at least one one galaxy galaxy with a Cepheid with distance, a Cepheid and therefore thoughtdistance, to and therefore thought to (circles). Error bars indicate 68% confidence intervals. For most of the maser galaxies, the error bars in M are smaller than the plotted in red, and late-type spiral galaxies are plotted in blue. NGC 1316 is the most luminous galaxy in the Fornax• cluster, but it1 lies at the be at a similar distance. The dashed line is a least-squares fit to the solid points in each panel. symbol. The black dotted line shows the best-fitting power law for the entire sample: log10(M /M )=8.32 + 5.64 log10(/200 km s ). be at a similar distance. The dashed line is a least-squares fit to the solid points in each panel. cluster outskirts; the green symbol here labels the central galaxy NGC 1399. M87 lies near the center• of the Virgo cluster, whereas1 NGC When early-type and late-type galaxies are fit separately, the resulting power laws are log10(M /M )=8.39 + 5.20 log10(/200 km s ) 4472 (M49) lies 1Mpctothesouth.Theblack-holemassesaremeasuredusingthedynamicsofmasers(triangles),stars(stars)orgas1 • for the early-type (red dashed line), and log10(M /M )=8.07 + 5.06 log10(/200 km s )forthelate-type(bluedot-dashedline).The ⇠ • b,i i (circles). Error bars indicateplotted 68% values confidence of are derived intervals. using kinematic For most data of over the the maser radii rinf galaxies, 250 km s using either reflect the assumed distances in Table A1. towards a ‘Great Attractor’ located at a distance of about is negligible compared with the remaining systematic the non-uniform distribution of matter within 10 Mpc definition). Rusli (2012) presented seven new stellar dy- Most of the dynamical models behind our compiled val- 60 Mpc in the direction of the Hydra–Centaurus cluster and internal extinction corrections,uncertainty in the respectively. absolute calibration of the The Cepheids compare the two definitionsnamical of measurements for 12 of galaxiesM along with whose central velocitylight ratioues of (MM/Lbulge have) derived assumed from that mass kinematics follows light. and This dynam- ofcomplex. the These Local peculiar Group, velocities are (2) usually retarded assumed expansion velocities of • themselves ( 0.13 mag, or 7% in distance). The rms kinematics within rinf aredispersions. notably We have di↵erent used the from long-slit kine- kinematics fromical modelingassumption of can stars be appropriate or gas in (see the inner Table regions A1 of for refer- zero points give the absolute magnitude∼ for galaxies to result from the gravitational accelerations produced by dispersions of the relations are given in parentheses. 1 Rusli (2012) and references therein to derive according galaxies, where dark matter does not contribute signifi- i 1 severalthe irregularities hundred in the large-scale km distribution s− near of mass. the Virgo cluster of galaxies matics at larger radii. Asto Equation shown 1; in our Table values 1, appear excluding in Tables A1 andences). 1. cantly Where to the necessary, total enclosedM/L mass. Still,is converted several measure- to V -band with log W 2.5, or VmaxGiven these calibrations,160 km the absolute s− . magnitude In all of any R With this assumption, various research groups have used 1 r< rinf can reduce by upFor to the 10-15%.M Mbulge Tenrelation, of the we 12 have up- compiledusing the galaxyments are colors. based on The kinematic values data of outM tobulge largeare radii. scaled to = spiral galaxy= can be predicted from its rotational velocity and (3) a large-scale streaming of about 400 km s− • these ‘flow maps’ to constrain the mean mass density bulge stellar masses for 351 early-type galaxies. Among Furthermore, some galaxies exhibit contradictions be- bandpasses, the random uncertaintyand its distance estimated in the from zero its measured point apparent dated galaxies are massive ( > 250 km s using either reflect the assumed distances in Table A1. ! magnitude. towardsof the universe a ( ‘Great) as well as Attractor’ to examine the degree located to at a distance of about them, 13 bulge masses are taken from H¨aring & Rix tween the dynamical estimates of M/L and estimates of is negligible compared with the remaining systematic which the distribution of galaxies follows the distribution definition). Rusli (2012)(2004), presented who used seven spherical new Jeans stellar models dy- to fit stellarMostM/L of thefrom dynamical stellar population models synthesis behind models our (e.g., compiled Cap- val- Application of the Tully–Fisher relation to field 60of mass. Mpc These in investigations the direction appear to favor of low the values Hydra–Centaurus cluster namical measurements ofkinematics.M along For with 22 more central galaxies, velocity we multiply theuesV - of Mpellaribulge ethave al. 2006; assumed Conroy & van that Dokkum mass 2012). follows For this light. This uncertainty in the absolute calibration of the Cepheids of ! ( 0.2) and also imply that mass is generally traced by band• luminosity in Table A1 with the bulge mass-to- reason, we adopt a conservative approach and assign a galaxies complex.∼ These peculiar velocities are usually assumed dispersions. We have used the long-slit kinematics from assumption can be appropriate in the inner regions of themselves ( 0.13 mag, orThe 7% Tully–Fisher in distance). relations have beenThe used to estimate rms the the distribution of galaxies. Rusli (2012) and references therein to derive according galaxies, where dark matter does not contribute signifi- ∼ distances to several hundred spiral galaxies within an 1 toDistant result clusters from and the the Hubble gravitational constant accelerations produced by 3 dispersions of the relationsexpansion are velocity given of about in 8000 parentheses. km s− . An example of to Equation 1; our values appear in Tables A1 and 1. cantly to the total enclosed mass. Still, several measure- the resulting ‘Hubble flow’ is shown in figure 2. Since theThe errors irregularities in the distances of individual in the galaxies large-scale measured distribution of mass. For the M Mbulge relation, we have compiled the ments are based on kinematic data out to large radii. Given these calibrations, thethe absolute velocities are a magnitude combination of both of the any expansion using the Tully–Fisher relations are about 15% when using bulge stellar• masses for 35 early-type galaxies. Among Furthermore, some galaxies exhibit contradictions be- and any local peculiar velocities induced by gravity, the Withhigh-quality this observational assumption, data. As a result, various the absolute research groups have used spiral galaxy can be predicted from its rotational velocity them, 13 bulge masses are taken from H¨aring & Rix tween the dynamical estimates of M/L and estimates of deviations in velocity can be correlated with position on theseerrors can‘flow become large maps’ for distant to galaxies. constrain Since there the mean mass density and its distance estimatedthe from sky to produceits measured maps of the deviations apparent from the mean are still significant peculiar velocities out to velocities of (2004), who used spherical Jeans models to fit stellar M/L from stellar population synthesis models (e.g., Cap- of the universe (!) as well as to examine the degree to kinematics. For 22 more galaxies, we multiply the V - pellari et al. 2006; Conroy & van Dokkum 2012). For this magnitude. Copyright © Nature Publishing Group 2001 Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998 band luminosity in Table A1 with the bulge mass-to- reason, we adopt a conservative approach and assign a and Institute of Physics Publishing 2001 which the distribution of galaxies follows the distribution Dirac House, Temple Back, Bristol, BS1 6BE, UK 3 Application of the Tully–Fisher relation to field of mass. These investigations appear to favor low values of ! ( 0.2) and also imply that mass is generally traced by galaxies ∼ 3 The Tully–Fisher relations have been used to estimate the the distribution of galaxies. distances to several hundred spiral galaxies within an 1 expansion velocity of about 8000 km s− . An example of Distant clusters and the Hubble constant the resulting ‘Hubble flow’ is shown in figure 2. Since The errors in the distances of individual galaxies measured the velocities are a combination of both the expansion using the Tully–Fisher relations are about 15% when using and any local peculiar velocities induced by gravity, the high-quality observational data. As a result, the absolute deviations in velocity can be correlated with position on errors can become large for distant galaxies. Since there the sky to produce maps of the deviations from the mean are still significant peculiar velocities out to velocities of

Copyright © Nature Publishing Group 2001 Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998 and Institute of Physics Publishing 2001 Dirac House, Temple Back, Bristol, BS1 6BE, UK 3