Transcript Eddington Ratio Distributions

AGN Eddington Ratio Distributions
Fred Davies
ASTR 278
2/23/12
Contents
• Eddington Ratio
– What does it mean?
– How do we measure it?
Contents
• Eddington Ratio
– What does it mean?
– How do we measure it?
• Two regimes of measurement
– Local
– Distant
Contents
• Eddington Ratio
– What does it mean?
– How do we measure it?
• Two regimes of measurement
– Local
– Distant
• Implications for AGN growth
Eddington Limit
• The Eddington limit is when the radiation
pressure force is equal to the gravitational
force
Frad  Fgrav
Eddington Limit
• The Eddington limit is when the radiation
pressure force is equal to the gravitational
force
Frad  Fgrav
• Assuming electron scattering opacity,
T
GMmp
L

2
2
c 4R
R
Eddington Limit
• The Eddington limit is when the radiation
pressure force is equal to the gravitational
force
Frad  Fgrav
• Assuming electron scattering opacity,
T
GMmp
L

2
2
c 4R
R
LEdd 
4GMmp c
T
M
Eddington Limit
• For objects whose luminosity is dominated by
accretion (like, for instance, AGN), the luminosity is
proportional to the accretion rate:
L  Lacc
2

 Mc
Eddington Limit
• For objects whose luminosity is dominated by
accretion (like, for instance, AGN), the luminosity is
proportional to the accretion rate:
L  Lacc
2

 Mc
• The Eddington limit then describes the maximum
accretion rate:
M Edd 
4GMmp
 c T
Eddington Ratio
• With this in mind, the Eddington ratio
Lbol / LEdd
is equivalent to
M BH / M Edd
In other words, the Eddington ratio is the
accretion rate in units of the maximum
possible accretion rate.
Eddington Ratio
• Measuring the Eddington ratio for a given
SMBH requires the measurement of two
uncertain quantities:
– Bolometric luminosity
– Black hole mass
Eddington Ratio Distributions: Local
• Heckman et al. 2004:
• SDSS sample of 23,000 Type 2 AGNs and
123,000 galaxies
• Black hole mass: host bulge σ + M-σ relation
• Bolometric luminosity: log(Lbol / LOIII )  3.54  0.38
Eddington Ratio Distributions: Local
• Heckman et al. 2004 results:
– Low-mass black holes have much higher
Eddington ratios
High mass  Low mass
Eddington Ratio Distributions: Local
• Heckman et al. 2004 results:
– Low-mass black holes have growth times
comparable to their host bulges
Solid: bulges
Dashed: BHs
Eddington Ratio Distributions: Local
• Kauffman & Heckman 2009 re-analyzed the original
Heckman et al. 2004 sample and separated it into
bins of host bulge stellar population age [Dn(4000)]
Eddington Ratio Distributions: Local
• Kauffman & Heckman 2009 results:
– Shape of distribution shifts from lognormal to
power-law as you look at older stellar populations
Younger
Older
Eddington Ratio Distributions: Local
• Kauffman & Heckman 2009 results:
– Lognormal distribution insensitive to black hole mass, but
power-law distribution is more complicated
Increasing mass
Eddington Ratio Distributions: Local
Dependence of power-law mode
distribution on black hole mass
disappears when plotted against
LOIII/Mbulge; accretion rate is
simply proportional to the stellar
mass in the bulge, modulated by
the age of the stellar population.
Eddington Ratio Distributions: Distant
• Differences at higher redshift:
Eddington Ratio Distributions: Distant
• Differences at higher redshift:
– Limited to high luminosity type 1 AGN (QSOs)
• Host galaxy properties difficult to ascertain
Eddington Ratio Distributions: Distant
• Differences at higher redshift:
– Limited to high luminosity type 1 AGN (QSOs)
• Host galaxy properties difficult to ascertain
– Bolometric correction to continuum luminosity
Eddington Ratio Distributions: Distant
• Differences at higher redshift:
– Limited to high luminosity type 1 AGN (QSOs)
• Host galaxy properties difficult to ascertain
– Bolometric correction to continuum luminosity
– Mass measured using “virial estimators”
calibrated by reverberation mapping of local AGN
• Hβ (z < 0.75), Mg II (0.4 < z < 2.0), C IV (1.6 < z < 5.0)
Eddington Ratio Distributions: Distant
• Kollmeier et al. 2006 results for 0.3 < z < 4
– AGES survey
• Hectospec on MMT
• 407 Type I AGNs
– Eddington ratio distribution
strongly peaked around
Lbol / LEdd ~ 0.25
Eddington Ratio Distributions: Distant
• Kollmeier et al. 2006 results implied predominantly
near-Eddington-limit accretion for luminous AGN
Eddington Ratio Distributions: Distant
• Kollmeier et al. 2006 results implied predominantly
near-Eddington-limit accretion for luminous AGN
But…
Eddington Ratio Distributions: Distant
• Kelly et al. 2010 showed that those original results
were improperly corrected for incompleteness and
scatter in the mass estimates
Eddington Ratio Distributions: Distant
• Kelly et al. 2010 result:
– Wide distribution peaked at Lbol / LEdd ~ 0.05
Note: The vertical line marks the
point where the sample of
Eddington ratios is 10% complete.
For Eddington ratios below this,
completeness drops precipitously.
Implications for AGN Growth
• The apparent AGN downsizing seen in the luminosity
function is truly due to a peak in low-mass black hole
activity
Implications for AGN Growth
• The apparent AGN downsizing seen in the luminosity
function is truly due to a peak in low-mass black hole
activity
• There is a definite correlation between the current
growth rate of black holes and that of their host
galaxy bulges, implying co-evolution
Implications for AGN Growth
• Kauffman & Heckman 2009 results show two
different “accretion modes”
– Lognormal mode similar to high redshift; young
star-forming bulges with gas reserves
– Power-law mode represents accretion of AGB
winds from the evolved stellar populations;
“dead” bulges that have run out of gas
Implications for AGN Growth
• Accretion onto > 108 Msun black holes dominated by
power-law mode accretion
Solid line: lognormal mode
Dashed line: power-law mode
Kauffman & Heckman 2009
Implications for AGN Growth
• Comparing the number density of observed high-mass
SMBHs (QSOs) at z = 1 to the local number density
provides a lower limit to the quasar duty cycle:
 (M BH , z)  QSO (M BH , z) / BH (M BH , z)
Kelly et al. 2010
Implications for AGN Growth
• Assuming that BLQSO “initiation” times are uniformly
spread in time (probably not true), the duty cycle
gives an easy estimate of the amount of time a black
hole spends in the BLQSO phase:
tBL ~  (M BH , z)t ( z) ~ 150Myr (10 M sun )
9
Implications for AGN Growth
• tBL and the typical Eddington ratio of about 0.1
provide a limit on the total accreted mass
during the BLQSO phase ~ 0.1 x MBH
Implications for AGN Growth
• tBL and the typical Eddington ratio of about 0.1
provide a limit on the total accreted mass
during the BLQSO phase ~ 0.1 x MBH
• The amount of time it takes to grow a black
hole from 106 Msun to 109 Msun at an Eddington
ratio of 0.1 corresponds to the age of the
universe at z = 2 >> tBL
Implications for AGN Growth
• tBL and the typical Eddington ratio of about 0.1
provide a limit on the total accreted mass
during the BLQSO phase ~ 0.1 x MBH
• The amount of time it takes to grow a black
hole from 106 Msun to 109 Msun at an Eddington
ratio of 0.1 corresponds to the age of the
universe at z = 2 >> tBL
– Must be a period of obscured near-Eddington
accretion to be consistent with BHMF
Summary
• Locally, the Eddington ratio distribution is a strong
function of black hole mass
• Old, dead galaxy bulges provide a different accretion
environment than young, star-forming bulges,
resulting in a bimodal distribution of Eddington ratio
distributions
• At high redshift, the Eddington ratio distribution is
highly affected by incompleteness and measurement
biases
• Based on constraints on the BLQSO lifetime, it is
likely that most of the SMBH mass is accreted during
an obscured phase