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The Fundamental Plane Relationship of Astrophysical

Black Holes

The Fundamental Plane Relationship of Astrophysical

Black Holes

Ran WangSupervisor: Xuebing Wu

Peking University

Ran WangSupervisor: Xuebing Wu

Peking University

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TopicsTopicsTopicsTopics

• Introduction – the black hole fundamental plane (FP)

• The sample– Selection– Properties

• Results – the FP relation and correlation tests

• Discussion• Summary

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IntroductionIntroductionIntroductionIntroduction

• Dominant energy producing mechanism in black hole systems – accretion.

• For observation, strong X-ray emission and sometimes accompanied by a relativistic jet.

• Such kind of systems exist at different scales from black hole X-ray binaries (XRBs) to active galactic nuclei (AGNs).

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Analogy between Stellar-mass BH and Supermassive BH systems:

Analogy between Stellar-mass BH and Supermassive BH systems:

Common physics: BH, accretion disk, jet, ...

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Introduction – the black hole Introduction – the black hole FPFP

Introduction – the black hole Introduction – the black hole FPFP

• The non-linear relationship between X-ray emission, core radio emission, and black hole mass, also called black hole fundamental plane (FP), was discovered and studied (eg. Merloni et al. 2003; Heinz & Sunyaev et al. 2003; Falcke et al. 2004).

• Merloni et al. (2003) studied a sample of XRBs and AGNs and fitted a FP relation among 5GHz radio luminosity (LR), X-ray 2-10keV luminosity (Lx), and black hole mass (MBH).

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Introduction – the black hole Introduction – the black hole FPFP

Introduction – the black hole Introduction – the black hole FPFP

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Merloni et al. (2003)

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IntroductionIntroductionIntroductionIntroduction

• The reliability of the FP in Merloni et al. (2003) was challenged.– Non-uniform sample– Distance – distance effect: (Bregman

2005; Merloni et al. 2006)

– Have LX/LEDD in a large range – 10-6 to 1

– Various methods in the black hole mass estimation.

• We test the black hole FP relationship with a uniform broad-line AGN sample in this work

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The sampleThe sampleThe sampleThe sample

• A RASS-SDSS-FIRST cross identified sample based on the X-ray-emitting SDSS AGN catalog in Anderson et al. (2003)– 964 broad permitted line AGNs (FWHM > 1000km s-1)

that have 0.1-2.4 X-ray data from RASS.– 132 sources are detected by the FIRST survey at

1.4GHz and a 3σ sensitivity of 0.45mJy (White et al. 1997).

– We use Hβ λ4861Å and Mg II λ2798Å lines to determine the BH mass, thus excluded sources with low SNR optical spectra.

– We also excluded 4 sources that have only C IV lines (z>2) in the SDSS spectra to reduce the scatter in BH mass estimation.

– Finally, 115 sources are selected and divided into radio loud (76) and radio quiet (39) subsamples .

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Black hole mass estimates

• Virial law (Kaspi et al. 2000)

• R-LHβrelation (Wu et al. 2004)

• McLure -Jarvis (2002) relation

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The sampleThe sampleThe sampleThe sample

• The advantage of this sample– X-ray: 0.1-2.4keV from

ROSAT All-Sky Survey (RASS).

– Optical spectra from the SDSS survey.

– Radio: 1.4GHz from the FIRST survey.

– X-ray to Eddington luminosity ratios distribute from 10-3.5 to 1.

– Redshift: 0<z<2– Minimize the scatters

introduced by observations and calculations.

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Results – Correlation testsResults – Correlation testsResults – Correlation testsResults – Correlation tests

• We test the intrinsic correlation between MBH, and LX/Lr.– The partial Kendall τtest indicates

the BH mass is correlated to the X-ray and radio luminosities (Pnull < 0.05).

– But this correlation disappears in the radio quiet sub-sample when scaling the luminosities with Eddington luminosity (Pnull~0.6).

• Distance effect in Lr-LX correlation.– The partial Kendall τtest suggests

the LX-Lr correlation still exists when excluding the effect introduced by distance.

– We can also see the correlation in a flux plot.

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ResultsResultsResultsResults

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Discussion – the black hole FPDiscussion – the black hole FPDiscussion – the black hole FPDiscussion – the black hole FP

• Theoretically, the FP relationship reflect the common physics of a disc-jet system around the central black hole.

• The slopes of the FP should be different with different X-ray emission mechanism (Yuan & Cui 2005):– Dominated by accretion

flow– Dominated by jet

• Jet emission may dominate the X-ray when the accretion rate drop to certain critical value and give a slope > 1 (Heinz 2004).

Yuan & Cui 2005

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Heinz (2004, MNRAS)

Scaling relations for scale-invariant cooled jets (both Lr & Lx are from jets):

For canonical synchrotron spectrum of p=2,αr=0.5,αx=1

Consistent with our results for radio-loud AGNs!

lg

lg F

( ) PN

- r

-x

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DiscussionDiscussionDiscussionDiscussion

• Beaming effect is most likely to be responsible for the steeper slope in radio loud sources.– Doppler beaming can increase the jet intrinsic power by a factor of

δ2+α.– The differences between observed radio luminosity and that derived

from the radio quiet FP relation increase with radio loudness.– Thus the observed radio-loud FP is unreliable unless the beaming

effect can be removed.– The difficulty is that the beaming factor is hard to measure directly.

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DiscussionDiscussionDiscussionDiscussion

• Radio-quiet FP:– We compared our radio-quiet FP relationship with

different physical models.• Accretion disc models listed in Merloni et al. (2003)• The multicolor thermal emission from the inner part of a

standard thin disk.• Radiation cooling jet.

– Our result can be marginally matched when:

• The X-ray luminosity has a nonlinear dependence on accretion rate with a power-law index ~2 – the radiatively inefficient accretion flow.

– However, our sample have higher X-ray to Eddington luminosity ratios than that expected from the radiatively inefficient accretion flow models.

– The soft X-ray emission in AGNs is complex and may be contributed by different mechanisms.

2 1~B M m

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SummarySummarySummarySummary

• We studied the black hole FP relationship with a uniform sample of broad line AGN.

• Our found the FP relationship have a weak dependence on the black hole mass.

• The FP relationships are different for radio loud and radio quiet AGNs.

• The FP relationship for radio loud AGNs is likely to be affected by the Doppler beaming.

• The radio-quiet FP relationship is possibly consistent with the theoretical prediction from the accretion-flow-dominated X-ray model.

• More theoretical and observational studies are needed.

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The endThe end

ThanksThanksThe endThe end

ThanksThanks

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ResultsResultsResultsResults

• On the log Lr-log LX plot, We do not see the clear trend that tracks of different mass bins are parallel to each other.

• We can not see this trend on the logLr /LEdd -log LX/LEdd plot either.

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• However, when we plotted the sources in different radio loudness bins, we see the parallel tracks.

• The X-ray and radio luminosities are correlated in each radio loudness bin

ResultsResultsResultsResults

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DiscussionDiscussionDiscussionDiscussion

• The black hole FP relationships – We obtained different FP relationships from that in

Merloni et al. (2003)– We use 0.1-2.4keV X-ray emission instead of 2-

10keV.– We use 1.4GHz rest frame radio luminosity instead

of 5GHz.– These differences will only change the constant

term if the emission can be described as power laws with a typical spectral index in each band for all sources.

– Otherwise, the slope items may be affected.