Ch.6

1. Ch.6

2. basic cosmological formulae metric of Robertson-Walker Friedmann equations at present time: critical density density parameter

3. basic cosmological formulae second Friedmann equation second equation is depending on first one, because and are also related through energy conservation equation: for non-relativistic matter constituting the present Universe: and also: at present epoch: deceleration parameter: density, deceleration, and curvature parameters are inter-related: models depend on 1 parameter

4. cosmological constant dark energy or vacuum energy Concordance Model ~ open concordance EdS closed

5. Friedmann models, Einstein-deSitter

6. Friedmann models, { {

7. Mattig formula relation between radial coordinate and redshift of a given source depends on cosmological model needed to compute luminosity distance travel of photons from source position to observer:

8. Mattig formula

9. Mattig formula Mattig 1958 for q0<1/2 with other substitutions the same expression is found

10. luminosity distance valid for q0 > 0 q0=1/2 (Einstein - de Sitter): for q0=0 we can expand the square root for small values of q0z (this is also an approximation for small z and generic q0 values) q0=0: there is also an alternative formula by Terrell (1977), exact, valid for every

11. [ ] luminosity distance, start again from Friedmann equations, with -term

12. [ ] luminosity distance, in this case, the integral must be computed numerically

13. luminosity distance, luminosity distance is needed to compute the luminosity of the source for example, in the optical band: these equations hold for bolometric fluxes, luminosities and magnitudes. for monochromatic magnitudes, or for magnitudes in a given photometric band, formula must be improved with K-correction where A(z) is defined as dimensionless luminosity distance, in units of c/Ho:

14. luminosity distance in units of c/H0 A(z) z

15. look-back time time elapsed from emission to observation we need a z-t relation, we write in differential form: for q0=0 or q0=1/2 it integrates trivially

16. look-back time http://burro.astr.cwru.edu/JavaLab/web/main.html

17. quasar surveys quasars: probes of the history of the Universe (i) properties of the quasar population as a function of redshift (ii) cosmic time of the first appearence of quasars -> constraints on galaxy formation large quasar samples are needed, not affected by selection effects (unbiased) measured quantity: number of quasars per square degree, function of F and z luminosity function (LF) number of quasars per unity luminosity interval and per unity comoving volume total spatial density these counts are difficult because quasars are few and faint: ~40 quasars/deg2 at B=21 cf 1600 stars/deg2 at galactic poles important is the adoption of selection criteria for the construction of samples of candidate quasars (which are to be later spectroscopically confirmed)

18. main selection criteria radio position only concerns radio-loud quasars radio position + UV excess id. colors UV excess, later multi-band non-stellar color low resolution slitlessspectroscopy many objects together, identified through em. lines X-ray emission property shared by ~all AGNs variability id., requires repeated measures, function of z and L absence of proper motion IR luminosity

19. counts count all the sources down to a given limit flux S euclidean case: flat and static Universe population of sources with same luminosity L number of sources per square degree uniform density: logN -3/2 logS

20. counts in the optical band magnitudes are often used density increases by 100.6~4 for each magnitude: 80% of the sources lie within 1 mag from limit flux if sources do not have all the same L, but assuming that luminosity distribution is the same at each distance r, then we can separate dependency on L and r, and we have (still assuming n=no): dependency on limit flux is still -3/2 this is expected for a uniform population otherwise, if slope is steeper or this is an indication that density increases with r

21. quasar counts in various bands -1.6 -1.7 0.85 radio Ryle 1968 optical Koo 1986 X-ray Boyle 1993

22. Eddington effect because of errors and slope, measured count is higher than true number effect of measurement errors near the limit flux differential counts A(m) and cumulative counts N(m) Gaussian random errors around true value m’ convolution to solve for A(m) we make a Taylor expansion

23. Eddington effect [ m’ -> m ] consider counts with slope k k=0.6 for uniform euclidean case if measurement errors are small but if

24. K-correction we know the relation between bolometric fluxes and luminosities radiation observed at is emitted at for monochromatic fluxes and luminosities, we must take into account how frequency transforms thus relation between flux and luminosity becomes factor (1+z) accounts for change of frequency interval this holds in general (a) for power-law spectra, we can compute the emitted spectrum at and obtain a specific expression (b) z>0 z=0 figure shows two effects: (a) displacement along the spectrum (b) variation of frequency interval

25. K-correction usually the opposite is done: starting from measured flux, luminosity is determined in terms of magnitudes, factor is inserted as follows: the expression for absolute magnitude becomes: this for the power-law case, otherwise it is used the more general form with the choice of an appropriate SED shape K-correction must be applied not only to AGNs, but also to galaxies, and every other source at non negligible redshift

26. K-correction K-corrections in UBV bands computed for a realistic spectrum, the average quasar spectrum here shown (arbitrarily translated in ordinate) K-correction in B compared with model power-law K-correction

27. problems and difficulties euclidean counts: we have assumed has same shape everywhere. but it is not so: quasar LF at z~0 is very different from what it was at z~2. this is a critical problem for quasars, which span a wide L interval, so that at a given flux they contribute to the counts for a large interval of distances completeness: in principle, all sources with flux greater than the limit S must be detected. probability of losing sources increases toward the limit flux, mimicking the effect of a distribution decreasing with distance. completeness tests are not that rigorous, usually only a comparison with previous surveys is done. it is important to perform surveys with different selection criteria in the same sky area to compensate merits and defects of the different techniques (e.g. Selected Area 57, color/proper motion/variability) variability: as luminosities vary, sources near the limit flux can happen to be above or below the detection threshold in different epochs. this alters the counts similarly to Eddington effect, with the possible addition of a dipendency of variability on L and z

28. problems and difficulties prominence of emission lines: equivalent widths vary significantly among different quasars. those surveys that rely critically on line prominence detect more easily strong-lined objects, and can lose weak-lined ones. it is possible to estimate and correct incompleteness if sensibility of the survey to EW can be quantified, and EW distribution is approximately known absorption lines: spectra of high redshift quasars show absorption lines due to intervening matter along the line of sight, in particular at wavelengths below ( -forest), where continuum is almost totally suppressed. this can change the probability of detecting a high-z quasar, compared to a non-absorbed quasar internal absorption: dust either in the emission line regions, or in the disk of the host galaxy. in rest-frame UV, extinction can be as high as ~0.8 mag, so reducing detection probability for a quasar with z> ~2. or in a torus, as that invoked for unified schemes, and this can completely remove obscured quasars from traditional surveys. it’s the so-called quasar-2, for which favorable bands are hard X-rays and IR

29. color selection initially it was simply the UV-excess: most famous survey of this kind is Palomar Bright Quasar Survey by Schmidt and Green 1983, which provided the PG (Palomar Green) quasar sample, 114 quasars at magnitude ~16 over ~10000 square degrees then this technique improved with the use of more photometric bands to search, in a two- (or many-) color diagram, objects with at least one color index different from stars e.g. Warren et al 1991 here, small circles are low-redshift quasars, and big circles are high-redshift quasars

30. color selection Koo Kron and Cudworth use U, J, F, N bands, and complement selection with variability and proper motion criteria

31. color selection Sloan Digital Sky Survey http://www.sdss.org/ locations of stars (black) and of extended sources (orange) in two-color diagrams within ugriz system

32. color selection it is possible to simulate quasar colors assuming an SED and parametrically modeling emission lines. the tracks so found show color change as a function of z, and possible intersection with the location of stars. remedy is to add more photometric bands Giallongo and Trevese 1990

33. multi-band color selection COMBO-17 survey http://www.mpia-hd.mpg.de/COMBO/combo_index.html 5 broad bands (~UBVRI) +12 narrow bands =17 bands in total limit magnitude depends on the band, e.g. 25.7 in B some selected fields, e.g. CDFS telescope: ESO 2.2m use of sequences of “template” model SEDs for various classes of astronomical objects comparison of measured photometry with “template” computed photometry classification determination of a “photometric” redshift selection of AGN-candidates comparison and calibration with spectroscopic redshifts for reference sources spettroscopical confirmation

34. Lyα CIV CIII] MgII effect of the emission lines emission lines can increase quasar luminosity so that it can become detectable (where it would be undetectable for continuum only) and/or, they can increase UV-excess because of K-correction, favoring selection of a quasar if a strong emission line is present in the U band B=19.8 19.2 18.25 UV-excess vanishes beyond z~2, due to absorption by Lyα forest wavy shape of the lines of limit magnitude indicates the effect of emission lines (Cavaliere Giallongo Vagnetti 1989)

35. effect of the emission lines spectra of 8000 quasars from SDSS showing position and intensity of main emission lines as a function of redshift U B R I V

36. slitlessspectroscopy it consists in making the spectrum of a wide sky area with a dispersing element in front of the telescope, an objective-prism, or a ”grism” (prism with one side ruled as a grating) useful for z> ~2 because Lyα and CIV are shifted in the optical however, it depends not much on z, because of the wider observed band compared to photometry integration times are longer, compared to photometric measures, but the advantage is that many spectra are simultaneously observed problems: - higher limit flux - uncertain determination of the limit flux, affected by emission lines - some redshift intervals with few lines - strong-line objects favored (and low-luminosity objects because of Baldwin effect)

37. other selection criteria: variability magnitude variation must be higher than photometric error efficient technique also for extended objects (galaxies with low luminosity variable nuclei) objects with high proper motion are excluded non variable objects Trevese et al 1994 Bershady Trevese Kron 1998

38. variability • variability increases with redshift, so it is more probable to select high redshift objects • probability increases also with sampling interval and with the number of observation epochs Green et al 2006, simulation for the Large Synoptic Survey Telescope, a telescope with 8.4m diameter to be used for imaging surveys in the time domain (www.lsst.org) in project to be operating in 2020: “Good probability of detection is achieved after only 2 epochs, and after 12 epochs in a year, almost all the AGNs to i<24 will be detected as variable”

39. COMBO-17: quasars galaxies stars synergic AGN selection by variability in SN surveys STRESS: Southern inTermediate Redshift ESO Supernova Search monitoring of Chandra deep field South (CDFS), 8 epochs in 3 years: variable objects discarded as SNe can recovered and become useful as AGN candidates (Trevese et al 2008) spettroscopical follow-up (Boutsia et al 2009) quasar NELG galaxy location of stars select AGNs, specially with extended image, which would not be found on the basis of color location of galaxies

40. main quasar surveys and counts Hartwick & Shade 1990

41. logN-logS test for a non-Euclidean Universe ( ) K-correction number of sources in the volume between r and r+dr relation between geometric distance and luminosity distance relation between comoving radial coordinate r and redshift volume element

42. logN-logS hypothesis: constant comoving density surface density of sources Euclidean (cumulative) counts ( ~ S-5/2 ) Euclidean differential counts differential counts normalized to Euclidean

43. logN-logS example: z for q0=1/2 and α=0.7 counts are expected flatter than Euclidean. the same holds also for reasonable values of qo and α to fit the steep observed counts, it is needed a number of sources increasing with distance, and thus with redshift

44. V Vmax V/Vmax test or luminosity-volume test Euclidean case source if sources are uniformly distributed, half are expected to be found within a volume Vmax/2, and half beyond this Vmax/2 for each source, determine the maximum volume within which it could be detected, for given L V is the volume limited by the spherical surface where the source lies n(r)=n0: uniformly distributed sources volumes V are uniformly distributed between 0 and Vmax

45. V/Vmax statistic uncertainty

46. V/Vmax cosmological case compute absolute magnitude solve for zmax for which a source with absolute magnitude M would be observed at mlim element of comoving volume volume integral: compute for z’=z and for z’=zmax for each quasar (i=1,2 ... N) <V/Vmax>: if distribution is uniform, it must 1/2 Vmin if there is also a lower limit to z because of the selection criterion (e.g. for slitless spectroscopy), then the available volume is used (Avni and Bahcall 1980) test is efficient also in presence of multiple selection criteria: e.g. Vmax (R,O)

47. V/Vmax results high z: trend inverts

48. mlim log z mlim mlim M luminosity function large samples are needed to count significant numbers of sources in bins of M and z. more than one sample is needed, otherwise a ficticious M-z correlation would be found (most objects lie near the limit magnitude) interstellar absorpton if the sample is volume-limited (all the quasars within the volume Vmax) luminosity function (LF) is found by the count in each absolute magnitude interval if the sample is flux-limited each quasar must be weighted with the inverse of the available volume count also in z because LF depends strongly on z result is a LF with double-power-law shape with a break for a particular value of L

49. Seyfert 1 luminosity function extrapolation of quasars at z=0 >102 some possible evolutionary forms, up to z~2: power-law luminosity evolution (LE), e.g. Boyle et al 1991: exponential evolution (also LE), e.g. Cavaliere et al 1985: look-back time

50. luminosity function DE LE • there are the two classical models of density evolution and luminosity evolution: • DE: density decreases with t L~ const • LE: density ~ const L decreases with t (i.e. with decreasing z) • quasars more numerous and/or more luminous in the past • up to z~2.5 data ~ agree with LE • instead, beyond z~3 LF decreases, probably because quasars are forming continuity equation (Cavaliere et al 1971, 1983): considers quasar population as a fluid in the unidimensional space of luminosities change of individual QSOs (LE) source function: birth and death of quasars (DE)