Ch.4
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
different profiles, sometimes logarithmic
sometimes complex and with variable shape
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:
FWHM
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:
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
BLR
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
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
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
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
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)
flux of ionizing photons:
c/1216Å (
)
c/912Å
Lyman limit
line flux:
(assuming all continuum is absorbed)
[ attention, in recent literature:
Lyman:
]
in any case the observed W is ~10% than this => covering factor f
~ 0.1
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
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
CIII]
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
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
functionand line profile depends on BLR velocity
line broadening is due to cloud motions,
field.
special example: stationary, radiation-driven wind
emissivity of each cloud
number of clouds/volume
cloud
cross-section
force on cloud:
line profiles
recombination coefficient of Hydrogen,
Menzel-Baker case B (optically thick)
cloud
crosssection
number of photons incident
on the cloud per second
=
number of
recombinations per
second
cloud ionized
volume
average photon energy
mass flux:
emissivity of a single
cloud:
effective recombination
coefficient(takes account of
contributions by intermediate
transitions)
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
echo mapping or reverberation mapping
allows to estimate BLR
size
delay
or lag
and then use it in Virial
Theorem to derive mass. e.g.
NGC 5548:
~10 light-days
various isodelay
surfaces
cloud
size
~4500 km/s
line width
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
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
particular:
through BLR is the most important time scale; in
(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
time, ~instantaneous compared to
(Hydrogen recombination
).
dynamical time scale can be approximated by the crossing time of a cloud,
echo mapping
light curve
CCF
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
quasar
s
Seyfert galaxies
echo mapping
Kaspi et al. 2000
BLR size by echo mapping for
17 Seyferts + 17 quasar
MBH
RBLR-L relation
RBLR ~ L0.7
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)
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
single cloud
i.e.
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
rate incid.photons=rate
recomb.
[
]
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
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)
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
Baldwin effect
possible explanations
- U decreases with L
- f decreases with L
- inclination effects
(anisotropic continuum,
isotropic lines)
summary of BLR properties
• width of emission lines (several) thousands km/s
• gas temperature 10 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 10 cm
• only ~10% of continuum emission is absorbed by BLR (covering factor)
• BLR volume is almost empty (filling factor 10 -10 )
• BLR mass is not more than few solar masses
• broad lines are very smooth: either many clouds (>10 ) or coherent structure
4-5
16
-7
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5
(wind?)
• suppression of forbidden lines indicates n >10 cm
• BLR size varies from few light-days to hundreds of light-days (echo-mapping)
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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
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
FWHM:
overall interval:
typical values:
extreme values:
(NGC 1068)
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:
spontaneous
emission
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
collisional
excitation
spontaneous collisional
emission
de-excitation
solve for n2 and
insert in previous Eq.
moreover:
(g=2J+1= statistical weight,
J=quantum number total ang
momentum)
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)
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
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:
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
~0.01
~pc
recalling
it is derived:
[
No. incid.phot/s = No.
recomb/s
]
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 n ~ 10 cm
• size of NLR > 100 pc (spacially resolved in many Seyferts)
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