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Galaxies and the Universe - Global Systematics

Galaxies and the Universe - Global Systematics - Gala ie...

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Unformatted text preview: 1/15/12 Gala ie and he Uni e e - Global S G G ema ic P I S , , , - .O H ( , , ( ( ) / , ) luminosit f unct ion) . O .T T ; Malmquist bias, .T (1996, PASP 108, 1073) , "A M , (LF). A G , LF; , ( , ) .T F ". T , .I LF ( , : ; ' ) - , .C - - , M S .a .H - . a.ed /keel/gala ie / , M , ema ic .h ml , .N 1/7 1/15/12 Gala ie and he Uni e e - Global S ema ic - - .T - . Statis tics with Hubble t pe T H magnit ude-limit ed O RSA B E+E/S0 173 SB0+SB0/S 48 S0+S0/ 142 SB +SB 42 S +S 123 SB +SB 96 S +S 187 SB 77 S 293 SB +SB 8 S +S 26 SB +IB 9 S +I 13 ... ... S 16 ... ... S 18 ... ... T T S ,S S -S . S 991 ... 285 ( ) - .O H .I , C H V . ' V 0 1 3 5 7 10 L( 1- 5) .T 1977 (Ev olut ion of Gala ies and St ellar Populat ions, . 43). M .A in t he mean - .N HI .S 5800 A SFR UBV 600- 1400 A ) E/S0 , - , V 1977 SFR. L ). W R ema ic .h ml H , / (I . a.ed /keel/gala ie / U-B,B-V. T .F .6 T. .T .a : F . 2. H 3500, 4300, ( E -4 -2 T, E E/S0 S0 S S S S I T A RC2 T, S0- S H T L : (1994 ARA&A 32, 115, , , HI S .T ADS). T H , F , . 2/7 1/15/12 Gala ie and he Uni e e - Global S I E/S0 ema ic - .I ( SDSS, red seq ence), GALEX, , ( S ) SDSS ; ). T - ( K : T (E/S0 / , . 2009 MNRAS 339, 1324). T (B ), .T - " " ; AGN. .a . a.ed /keel/gala ie / ema ic .h ml 3/7 1/15/12 Gala ie and he Uni e e - Global S ema ic An important description of the distribution and occurrence of galaxies is the luminos it function : (L) dL is the number of galaxies in the interval L +/- dL/2 per unit volume. This may be defined for optical luminosity, radio power, far- IR power, ... One always has the hope that this function is fundamental in telling how galaxy masses are distributed; that is, that all kinds of galaxies have about the same visible to invisible mass ratio. The determination of over a wide luminosity range is complicated by Malmquist bias, and the need to reduce all measurements to a common emit t ed-wav elengt h frame - this is a special problem for QSOs and very luminous galaxies, for which we must look to significant redshifts to see any of the brightest examples. The luminosity function may be determined, in principle, very simply; for objects in luminosity bin i, the luminosity function is simply (Li ) = (1/Vm) where Vm is the volume within which each object could have been detected, and the sum runs over all objects in bin i. All the selection effects fall into determining Vm for a given threshold condition, which may be nontrivial. Actually, it always seems to be nontrivial. An important application of Vmis the Schmidt V/Vm test, which can show whether the sample is complete or at least uniform, and can show the presence of some kinds of evolution with cosmic time when applied over a large redshift range. If the objects are uniformly distributed within the survey volume, the sample mean of the statistic V/Vm, where V is the volume of a sphere centered here and with the object at its surface, will be 1/2. [For cosmological applications one must worry about whether this is the right prescription for the volume of the sphere, integrating volume elements to the distance in question.] A value smaller than this implies that there are more objects close to us, which for galaxies normally means that the sample is more incomplete at large distances than we initially assumed. A mean value greater than 1/2 almost always implies cosmological evolution, as for QSOs. The fact that gamma- ray bursts show a value significantly smaller than 1/2 even for the most complete flux samples is one of their major puzzles. From the magnitude- limited RSA catalog, the redshift distribution of catalog entries is shown here (less a single object at 9875 km/s). From the wide range of cz we see that the volumes sampled at various luminosities differ by factors of order 106. Thus careful allowances for sample properties is crucial to measuring the LF. This is clear when comparing the distribution of apparent and absolute magnitude shown in the figures below (again from the RSA, skipping three naked- eye members of the Local Group): .a . a.ed /keel/gala ie / ema ic .h ml 4/7 1/15/12 Gala ie and he Uni e e - Global S ema ic To derive the proper relative numbers, one must correct for the different volumes within which each object would appear in the catalog. This apparent distribution declines fainter than absolute blue magnitude - 21.5, while the space density continues to increase greatly to fainter absolute magnitudes. An important analytic approximation to the overall galaxy luminosity function is the Schechter (1976, ApJ 203, 297) form Φ (L) dL = * (L/L* ) α e-(L/L* ) (dL/L* ) where * (L/L* ) is the normalizing factor, set by the number of galaxies per Mpc3, L* is a characteristic luminosity, and α is an asymptotic slope to be fit; a value around - 5/4 usually agrees with the data. The plot (from Schechter's paper, reproduced by permission of the AAS) shows the fit to the mean of galaxy counts in 13 clusters. L* appears to be constant among various clusters, and maybe even for non- cluster galaxies, at a given cosmic epoch, so that one may read references to "an L* galaxy". This is sometimes taken as a characteristic scale for galaxy formation. The brightest cD galaxies may require some additional process; they may violate the LF shape in that there should be virtually no galaxies so luminous in the observable Universe if the Schechter function held absolutely. Different kinds of galaxies have different LF shapes and normlizations; this explains why Hubble thought of the LF as approximately Gaussian, from studies of (giant) spirals, while Zwicky counted everything, dissented vigorously and as usual correctly, and found a divergence at faint magnitudes. Zwicky distinguished dwarf, pygmy, and gnome galaxies (see his idiosyncratic book Morphological Ast ronom ). The LF must converge somewhere to avoid Olbers' paradox. The LF is simple only for dwarfs; the various types are distributed in Virgo as follows, from Fig. 1 of Binggeli, Sandage, and Tammann 1988 (Ann. Rev. 26, 509 - an excellent reference for the whole topic, figure reproduced from the ADS). .a . a.ed /keel/gala ie / ema ic .h ml 5/7 1/15/12 Gala ie and he Uni e e - Global S ema ic The differences may be clues to how different galaxy types form - in some biassing schemes, for example, ellipticals need stronger peaks than disks. On the other hand, if merging is important, this may tell us about the history of mergers rather than galaxy formation. It does seem to be quite consistent in shape among clusters of galaxies, so that it tells something basic and general about how galaxies have developed. Similar clues are hidden in some of the basic correlations among global galaxy properties involving dynamics - the Tully- Fisher and Faber- Jackson relations. The Tully- Fisher relation, often employed as a distance indicator for spirals, is a tight relation between galaxy absolute magnitude and velocity scale of the disk (for example, at the 20% - of - peak level in an integrated H I profile, with appropriate inclination corrections). There are broad theoretical reasons why such a relation might hold, but no deep understanding at this point. The Faber- Jackson relation was also found empirically, from the fact that elliptical- galaxy luminosity and central velocity dispersion are related approximately as L ~ 4 . A generalization, the f undament al plane, was found by noting that scatter about the F- J relation is correlated with metallicity (usually through a simple index of Mg absorption), although it turned out that this may not be the most basic parametrization. Not only is the fundamental plane a useful distance and environment probe, but it sets strong constraints on dynamical evolution; any transformations of galaxies must leave them very close to this plane. Since (in log space) the fundamental plane is, as far as we can tell, a plane, there are transformations of variables which correspond to .a . a.ed /keel/gala ie / ema ic .h ml 6/7 1/15/12 Gala ie and he Uni e e - Global S ema ic orthogonal variables imbedded in it; Burstein and coworkers have explored the interpretation of these so- called κ parameters. Basics of the "fundamental plane" may be found in the review by Kormendy and Djorgovski (1989, ARA&A 27, 235). Their Figure 2 (reproduced from the ADS) compares the observed Faber- Jackson relation (upper left) to more exact projections of the galaxy distribution in the volume of radius, surface brightness, and velocity dispersion. In the observable parameters, R ~ σ 1.4 +/- 0.15 I-0.9 +/- 0.1 where R is an effective or core (but not isophotal) radius, σ is the velocity dispersion (one- dimensional, in the line of sight), and I is an averaged intensity (commonly the mean within the effective radius). Some of the earlier relations, such as L ~ σ 4 and Dn ~ σ 4/3 for diameter to reach a particular mean surface brightness, are projections of this plane along different observable axes. One mapping of particular theoretical interest (in which galaxies are widely spread) is the &sigma - plane, corresponding roughly to the density - cooling rate prescription needed to describe a galaxy's initial collapse. The virial theorem suggests a relation of about the FP form, with departures of the scaling exponents from 2 and 1 coming about if there is systematic variation in the (M/L) ratio with luminosity or other global parameters. The narrowness of the fundamental plane tells us that evolution by merging, if it is significant for ellipticals, must carry galaxies along but not across the plane. There are simulations suggesting that the FP parameters are indeed preserved during (some kinds of) merging. Recent work indicates the the fundamental plane shifts at least in luminosity with redshift, as expected for a broad class of galaxy- evolution schemes. « Galaxy components | Gas in galaxies » Course Home | Bill Keel's Home Page | Image Usage and Copyright Info | UA Astronomy k [email protected] . a.ed Ls cags 820 at hne: /09 .a . a.ed /keel/gala ie / ema ic .h ml 20-09 0020 7/7 ...
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