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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
)33.7(log)78.0(log)60.0(log 05.407.4
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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
)19.008.5()log()10.086.0()log( :quiet radio
)07.077.0()10
log()13.012.0() 10
log()10.085.0() 10
log( :quiet radio
)21.017.0()10
log()21.017.0() 10
log()17.039.1() 10
log( :loud radio
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8144140
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BHXr
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sergs
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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.