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**AGN Eddington Ratio Distributions**

Fred Davies ASTR 278 2/23/12

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Contents Eddington Ratio What does it mean? How do we measure it?

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**Contents Eddington Ratio Two regimes of measurement What does it mean?**

How do we measure it? Two regimes of measurement Local Distant

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**Contents Eddington Ratio Two regimes of measurement**

What does it mean? How do we measure it? Two regimes of measurement Local Distant Implications for AGN growth

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Eddington Limit The Eddington limit is when the radiation pressure force is equal to the gravitational force

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Eddington Limit The Eddington limit is when the radiation pressure force is equal to the gravitational force Assuming electron scattering opacity,

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Eddington Limit The Eddington limit is when the radiation pressure force is equal to the gravitational force Assuming electron scattering opacity,

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Eddington Limit For objects whose luminosity is dominated by accretion (like, for instance, AGN), the luminosity is proportional to the accretion rate:

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Eddington Limit For objects whose luminosity is dominated by accretion (like, for instance, AGN), the luminosity is proportional to the accretion rate: The Eddington limit then describes the maximum accretion rate:

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**Eddington Ratio With this in mind, the Eddington ratio**

is equivalent to In other words, the Eddington ratio is the accretion rate in units of the maximum possible accretion rate.

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Eddington Ratio Measuring the Eddington ratio for a given SMBH requires the measurement of two uncertain quantities: Bolometric luminosity Black hole mass

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**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:

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**Eddington Ratio Distributions: Local**

Heckman et al results: Low-mass black holes have much higher Eddington ratios

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**Eddington Ratio Distributions: Local**

Heckman et al results: Low-mass black holes have growth times comparable to their host bulges Solid: bulges Dashed: BHs

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**Eddington Ratio Distributions: Local**

Kauffman & Heckman 2009 re-analyzed the original Heckman et al sample and separated it into bins of host bulge stellar population age [Dn(4000)]

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**Eddington Ratio Distributions: Local**

Kauffman & Heckman 2009 results: Shape of distribution shifts from lognormal to power-law as you look at older stellar populations Older Younger

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**Eddington Ratio Distributions: Local**

Kauffman & Heckman 2009 results: Lognormal distribution insensitive to black hole mass, but power-law distribution is more complicated Increasing mass

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**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.

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**Eddington Ratio Distributions: Distant**

Differences at higher redshift:

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**Eddington Ratio Distributions: Distant**

Differences at higher redshift: Limited to high luminosity type 1 AGN (QSOs) Host galaxy properties difficult to ascertain

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**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

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**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)

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**Eddington Ratio Distributions: Distant**

Kollmeier et al results for 0.3 < z < 4 AGES survey Hectospec on MMT 407 Type I AGNs Eddington ratio distribution strongly peaked around

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**Eddington Ratio Distributions: Distant**

Kollmeier et al results implied predominantly near-Eddington-limit accretion for luminous AGN

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**Eddington Ratio Distributions: Distant**

Kollmeier et al results implied predominantly near-Eddington-limit accretion for luminous AGN But…

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**Eddington Ratio Distributions: Distant**

Kelly et al showed that those original results were improperly corrected for incompleteness and scatter in the mass estimates

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**Eddington Ratio Distributions: Distant**

Kelly et al result: Wide distribution peaked at Note: The vertical line marks the point where the sample of Eddington ratios is 10% complete. For Eddington ratios below this, completeness drops precipitously.

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**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

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**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

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**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

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**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

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**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: Kelly et al. 2010

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**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:

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**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

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**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

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**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

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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

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