Ch.4

1. Ch.4

2. different profiles, sometimes logarithmic sometimes complex and with variable shape Broad Line Region broad lines are important to understand AGN structure for at least two reasons: 1) BLR motions are almost certainly determined by central source, through competion between gravity and radiation pressure 2) BLR reprocesses primary radiation emitted in UV, which cannot be directly observed widths are usually measured in km/s (assuming that broadening is due to Doppler effect) usually measured the FWHM (Full Width at Half Maximum), or the FWZI (Full Width at Zero Intensity, less certain because of confusion with continuum and/or blending) different widths from object to object and from line to line

3. FWHM FWHM, line dispersion, velocity dispersion FWHM is not the same as line standard deviation, or line dispersion, the relation depends on line profile: e.g., for a Gaussian profile: for a rectangular profile: for a triangular profile: moreover, it must be remembered that broadening is due to line of sight velocity dispersion. assuming an isotropic velocity dispersion:

4. Broad Line Region besides main lines, Balmer, Lyman, MgII, CIII], CIV, some line blends are also important, as reported in the table moreover, there is a strong and strongly blended feature between 2000Å and 4000Å, called Small Blue Bump , and due to a blend of FeII lines + Balmer continuum fluxes of emission lines vary in time strongly correlated with continuum fluxes: clear evidence in favor of photoionization by central source. moreover, large part of recombination emission must originate in clouds optically thick to the ionizing flux

5. BLR

6. BLR there is no simple diagnostic for BLR density and temperature, as for HII regions and NLR: this is because electronic densities are higher and forbidden lines are collisionally suppressed however, similarity of relative intensities with those of other ionized gases indicates a gas temperature T ~104 K for such gas, thermal velocity dispersion is but the widths of broad lines are ~ 5000 km/s, would need a gas with T > ~ 109 K another broadening mechanism is necessary, and is attributed to motion of single clouds estimate of electronic density [OIII] 4363Å, 4959Å, 5007Å lines are absent in BLR => collisionally deexcited critical density ~108 cm-3, ne > ~108 cm-3 CIII] 1909Å line is present in BLR, critical density ~1010 cm-3, it could be deduced ne < ~1010 cm-3 however, there is evidence of stratification, CIII] comes from a different region than other lines like CIV, Lyalpha etc. density in the region producing CIV 1549Å is probably ne ~1011 cm-3

7. luminosity of lines emissivity rate of collisional excitation of transition for T=20000 K, q ~2.6 10-9 cm3 s-1 luminosity assuming log[C/H]=-3.48 (cosmic abundance) and C=CIV: filling factor

8. ionization parameter at given chemical composition, emission spectra depend on the Ionization Parameter U number of ionizing photons per unit time (for Hydrogen): ionization rate U = _______________________ (on cloud surface) recombination rate in first approximation, AGN spectra are similar for a large luminosity interval. this suggests that U and ne are ~equal in all the BLRs thus: in approximate agreement with observations from reverberation mapping measurements it is found: use this relation in the previously interrupted equation for computing the luminosity of the CIV line: assuming ne=1011 cm-3 it is found very small filling factor => BLR filamentary or clumpy

9. mass of BLR gas from the expression for line luminosity: we obtain BLR mass can be computed as follows: volume of a cloud number of clouds mass density of a cloud 1011 cm-3 even for most luminous AGNs, the required gas mass is not more than few solar masses

10. covering factor what continuum fraction is absorbed by BLR? lines vary strongly in response to continuum variations => clouds must be optically thick thus, the absorbed continuum fraction is simply the fraction of sky covered by clouds (as seen from the central source location) c/1216Å ( ) flux of ionizing photons: c/912Å Lyman limit line flux: Lyman: (assuming all continuum is absorbed) [ ] attention, in recent literature: in any case the observed W is ~10% than this => covering factor f ~ 0.1

11. photoionization of the BLR photoionization models depend on: a) shape of ionizing continuum (SED) b) chemical abundances c) particle density within the cloud d) column density of the cloud e) ionization parameter • example of ionization equilibrium as a function of U for: • column density 1023 cm-2 • solar abundances • typical SED • ne = 1011 cm-3

12. CIII] CIV photoionization of the BLR - single zone models - emission of each cloud is equal to that of every other clouds - estimate of U has been tried using the ratio CIII]/CIV - constraints for the density from presence of CIII] and absence of [OIII] would suggest ne~109.5 cm-3 - however from such values for U and ne it is inferred a BLR size in disagreement with measurements (too big by a factor ~10) more recent models based on results of reverberation mapping imply a stratified BLR: e.g. CIII] is collisionally suppressed in the region producing CIV reverberation mapping measures BLR size from the time lag between variations of lines and of those of continuum a long monitoring and a frequent sampling are needed in some cases these measurements are done separately for different emission lines in the best studied case of NGC 5548, with detailed calculations, the following fiducial values are found: ne ~ 1011 cm-3, U ~ 0.04 h0-2

13. line profiles assume that each cloud contributes an individual profile with width due to thermal broadening negligible compared to spectral resolution commonly used(hundreds km/s) => can be approximated by delta function line broadening is due to cloud motions, and line profile depends on BLR velocity field. special example: stationary, radiation-driven wind emissivity of each cloud number of clouds/volume cloud cross-section force on cloud:

14. line profiles recombination coefficient of Hydrogen, Menzel-Baker case B (optically thick) cloud cross-section cloud ionized volume number of photons incident on the cloud per second number of recombinations per second = average photon energy mass flux: effective recombination coefficient(takes account of contributions by intermediate transitions) emissivity of a single cloud:

15. line profiles integral is non-zero only when holds the condition: choosing v(rmin)=0, it is found: logarithmic profile however, also other models give the same logarithmic result therefore, profiles alone are not able to discriminate

16. echo mapping or reverberation mapping allows to estimate BLR size and then use it in Virial Theorem to derive mass. e.g. NGC 5548: delay or lag ~4500 km/s ~10 light-days size line width various isodelay surfaces cloud if a continuum variation occurs, there is also a variation of the emission lines excited by such continuum, but variation occurs with delay observing light curves of continuum and emission lines for a given quasar, one can try to determine the delay

17. echo mapping basic assumptions: (1) continuum is produced by a single source which is much smaller than BLR (2) BLR clouds occupy a small fraction of the total BLR volume (small filling factor) and photons propagate freely at velocity of light within such volume (3) there is a simple relation, not necessarily linear, between UV/optical observable continuum and the ionizing continuum driving variability of lines (4) light-travel time through BLR is the most important time scale; in particular: (a) cloud response to continuum variations is rapid compared to (b) is short compared to dynamical time scales on which significant changes in BLR structure can occur cloud response time is estimated (Hydrogen recombination time, ~instantaneous compared to ). dynamical time scale can be approximated by the crossing time of a cloud,

18. light curve CCF echo mapping to estimate the lag, a cross-correlation is used: a weak correlation is found between continuum and line measured at the same epoch, but correlation coefficient increases if we correlate continuum at one epoch with emission line at a delayed epoch CCF=cross-correlation function is a measure of correlation coefficient as a function of lag

19. MBH RBLR-L relation RBLR ~ L0.7 Seyfert galaxies quasars echo mapping Kaspi et al. 2000 BLR size by echo mapping for 17 Seyferts + 17 quasar more recent studies (Peterson et al 2005, Kaspi et al 2007) extend range L ~1039-1047 erg/s and favor RBLR ~ L0.5 in agreement with simple interpretation: RBLR-L relation allows single epoch (SE)determinations of RBLR (and MBH)

20. [ ] rate incid.photons=rate recomb. cloud properties assume L(CIV)=1042 erg/s, rBLR=8 light days ~2x1016 cm covering factor: suppose clouds are placed in a spherical shell total i.e. single cloud independent estimate: comparison L(CIV) and Lcloud(CIV) suppose emitting volume = ionized layer down to Stromgren depth r1=Vc/Ac with fiducial density ne=1011 cm-3 we obtain ask that Nc Lcloud(CIV)=L(CIV)=1042 erg/s and obtain: in good agreement with previous value

21. cloud properties line profiles are smooth and do not show any structure if observed at high resolution, therefore statistical fluctuations in the number of clouds per resolution element must be lower than S/N ratio. numerical simulations indicate Nc > ~ 5x104 some hypotheses on the nature of clouds: - dense condensations in pressure equilibrium with an external thinner and hotter medium able to confine them. some confining medium is needed because clouds are too small to be self-gravitating. indeed, Jeans mass is: - also magnetic confinment has been proposed - stellar athmospheres, but works only with low surface gravity giants. moreover, large number, e.g. Nc~106, and the small fraction of giants on the stellar population (~10-4) would require a total stellar mass ~ within the BLR

22. line-continuum correlations similarity of spectra for large luminosity intervals suggests that emission lines are well correlated with continuum luminosity. in other words, equivalent widths must be nearly the same in any AGN for H beta, it is found a good correlation with non-thermal luminosity (subtracting stars)

23. Baldwin effect for CIV proportionality doesn’t hold, line luminosity increases less than continuum, equivalent width thus decreases for increasing luminosity the effect holds also for but with a weaker power ( ) moreover, correlation for CIV is found also for repeated observations of some individual objects, with examples

24. Baldwin effect possible explanations - U decreases with L - f decreases with L - inclination effects (anisotropic continuum, isotropic lines)

25. summary of BLR properties • width of emission lines (several) thousands km/s • gas temperature 104-5 K (~10 km/s) • Doppler broadening due to bulk motion of the gas in the gravitational field • high velocities imply distances of the order of 1016 cm • only ~10% of continuum emission is absorbed by BLR (covering factor) • BLR volume is almost empty (filling factor 10-7-10-6) • BLR mass is not more than few solar masses • broad lines are very smooth: either many clouds (>105) or coherent structure (wind?) • suppression of forbidden lines indicates ne>109 cm-3 • BLR size varies from few light-days to hundreds of light-days (echo-mapping)

26. Narrow Line Region it is interesting for at least 3 reasons: 1) it is the largest-scale region where ionizing radiation from central source dominates on other sources 2) it is the only AGN component spatially resolved in the optical 3) NLR dynamics can provide information on the way AGNs are fed differently from BLR, electronic densities are low enough that many forbidden transitions are not collisionally suppressed. this allows to use line intensity ratios to measure densities and temperatures of the gas a complication is constituted by dust, because NLR is external to sublimation radius

27. FWHM: overall interval: typical values: extreme values: (NGC 1068) Narrow Line Region NLR characteristic lines. relevant ionization potentials in table are those necessary to reach the observed ionization state for collisionally excited lines, while for recombination lines it is that needed for the next higher ionization state both low ionization lines (e.g. [OI]) and high ionization lines ([OIII] [FeVII] etc) are present: hint that NLR is photoionized by an AGN further info from diagnostic diagram: [OIII]/Hbeta usually > 3 in Seyferts

28. electronic densities determined through intensity ratio between two lines of a single ion (to avoid ambiguities for chemical composition or ionization level) due to two different decays to the same level e.g. [OII]3726,3729, [SII]6716,6731 scheme: 2-level atom with excitation potential emissivity of transition 2 1: rate at which level 2 is populated by collisions: mean time between two collisions of an electron with an ion collision rate per unit volume average rate weighted over electron velocity distribution spontaneous emission collisional excitation spontaneous emission collisional de-excitation solve for n2 and insert in previous Eq. moreover: (g=2J+1= statistical weight, J=quantum number total ang momentum)

29. limit cases 1) low density: radiative de-excitation dominates 2) high density: collisional de-excitation dominates critical density atom with many levels for non-electric dipole transitions (forbidden transitions), critical densities are in the range found in low-density nebulae (HII regions, Planetary Nebulae, NLR)

30. example: [SII] doublet , low-density regime: high-density regime: in the transition region the line ratio changes as a function of electronic density using pairs of lines, it is possible to measure electronic densities. in NLR typically ne~2000 cm-3

31. cloud properties emissivity of gas in the Hbeta line: effective recombination coefficient (takes account of recombinations at all levels n>=4 that finally lead to transition n=4 ->2) total line luminosity size of NLR for nearby AGNs, the NLR is often spacially resolved and it is found thus it must be it is then derived the quantity:

32. [ ] ~0.01 No. incid.phot/s = No. recomb/s ~pc NLR mass remembering that (as for BLR) it is found NLR is much more massive than BLR. line luminosities in the two regions are comparable because emissivity of recombination lines is much higher in BLR (~ne2) size of the clouds: Stromgren depth can be taken as lower limit recalling it is derived:

33. summary of NLR properties width of emission lines ~ hundreds km/s • Doppler broadening due to bulk motion of the gas in the gravitational field • filling factor ~10-2 • mass of NLR millions of solar masses • presence of forbidden lines requires ne ~ 103-4 cm-3 • size of NLR > 100 pc (spacially resolved in many Seyferts)