Timescales of Quasar Accretion Discs: Dependence on Black Hole Mass and Luminosity

Core Concepts

The variability of quasar accretion discs is likely driven by the mass-dependent orbital timescales of the discs, which exhibit a turnover from a negative to a positive correlation with black hole mass at high masses.

Abstract

This research paper investigates the relationship between the timescales of quasar accretion discs and the mass of their central black holes. The authors utilize a thin-disc model with general relativistic corrections to calculate the mean emission radii and orbital timescales of accretion discs across a range of black hole masses, luminosities, and wavelengths.

Key Findings:

• The study reveals that the relationship between orbital timescales and black hole mass is not a simple power law but rather a smoothly broken power law.
• At low black hole masses, the orbital timescale decreases with increasing mass, consistent with previous studies. However, at high black hole masses, the timescale increases with mass, indicating a turnover in the relationship.
• This turnover is attributed to the growing influence of the black hole's event horizon at higher masses, which pushes the inner edge of the accretion disc outwards and affects the overall disc size and orbital periods.
• The authors provide new analytic approximations for calculating the mean emission radii and orbital timescales of accretion discs, accounting for the observed broken power law relationship.

Significance:

• These findings have significant implications for understanding the variability of quasars and the physics of accretion discs.
• The study suggests that the variability of quasar discs is driven by the mass-dependent orbital timescales.
• The new analytic approximations offer improved tools for studying accretion disc properties and interpreting observational data.

Limitations and Future Research:

• The study relies on a simplified thin-disc model, and future research incorporating more complex disc models could refine the findings.
• Further observational studies, particularly of high-mass black holes, are crucial to confirm the predicted turnover in the timescale-mass relationship and validate the proposed model.

Stats

The median luminosity of the accretion disc sample is log Lbol/(erg s−1) ≈47.
The median log MBH/M⊙≈9.35.
The study explores disc parameters in the ranges of log(𝜆rest/Å) = [3; 4], log(MBH/M⊙) = [6; 11], and log(REdd) = [−2; 0].
Three black-hole spins are considered: 𝑎= −1, 𝑎= 0, and 𝑎= +0.78.

Quotes

"The UV-optical variability of quasars appears to depend on black-hole mass 𝑀BH through physical timescales in the accretion disc."
"At low 𝑀BH, we find the textbook behaviour of 𝑡orb ∝𝑀−1/2BH alongside 𝑅mean ≈const, while towards higher masses the growing event horizon imposes 𝑅mean ∝𝑀BH and thus a turnover into 𝑡orb ∝𝑀BH."
"The data show a weak dependence of variability on 𝑀BH consistent with the turnover and a model where disc timescale drives variability amplitudes in the form log 𝐴/𝐴0 = 1/2 × Δ𝑡/𝑡orb, as suggested before."

Key Insights Distilled From

Timescales of Quasar Accretion Discs from Low to High Black Hole Masses and new Variability Structure Functions at the High Masses

by C. Wolf, S. ... at arxiv.org 11-06-2024

https://arxiv.org/pdf/2411.02759.pdf

Deeper Inquiries

How might the presence of a thick accretion disc or a jet alter the observed relationship between black hole mass and disc timescales?

The presence of a thick accretion disc or a jet can significantly alter the observed relationship between black hole mass and disc timescales, derived under the assumption of a simple thin disc model. Here's how:
Thick Accretion Discs:

Different Emission Geometry: Unlike thin discs with a flat, pancake-like structure, thick discs have a more complex, torus-like geometry. This affects the observed emission profile and can lead to different scaling relationships between size, temperature, and black hole mass.
Optical Depth Effects: Thick discs are optically thick, meaning that radiation from the inner regions can be absorbed and re-emitted at larger radii. This can smear out short-timescale variability originating closer to the black hole, making it harder to directly probe the innermost regions and their associated timescales.
Advection Dominated Flows: Thick discs can be associated with advection-dominated accretion flows (ADAFs), where energy is advected into the black hole instead of being radiated away. This can lead to lower luminosities and different temperature profiles compared to standard thin disc models, further complicating the relationship between observed timescales and black hole mass.
Jets:

Non-Thermal Emission: Jets produce non-thermal emission across a wide range of wavelengths, which can dominate over the thermal emission from the accretion disc, especially at radio and X-ray wavelengths. This can mask the intrinsic disc variability and make it difficult to isolate the mass dependence of disc timescales.
Additional Timescales: Jets exhibit their own variability on various timescales, related to processes like jet launching, collimation, and interaction with the surrounding medium. These timescales are not directly related to the accretion disc or black hole mass and can complicate the interpretation of observed variability.
Orientation Effects: The observed properties of jets are highly dependent on their orientation with respect to the observer. Jets viewed close to the line of sight can exhibit relativistic beaming, amplifying their emission and variability, while jets viewed edge-on might be obscured by the dusty torus surrounding the AGN. This orientation dependence can introduce significant scatter in the observed relationship between variability and black hole mass.
In summary, the presence of a thick accretion disc or a jet introduces additional complexities that can obscure the intrinsic relationship between black hole mass and disc timescales expected from simple thin disc models. To disentangle these effects, it's crucial to combine multi-wavelength observations, sophisticated modeling efforts, and careful consideration of orientation effects.

Could other factors, such as magnetic fields or interactions with companion galaxies, contribute to the observed variability in quasars and potentially mask the mass dependence of disc timescales?

Yes, other factors beyond the simple thin disc model, such as magnetic fields and interactions with companion galaxies, can indeed contribute to the observed variability in quasars and potentially mask the mass dependence of disc timescales.
Here's a breakdown of how these factors can influence quasar variability:
Magnetic Fields:

Magnetohydrodynamic Instabilities: Magnetic fields threading through the accretion disc can drive various magnetohydrodynamic (MHD) instabilities, such as the magnetorotational instability (MRI). These instabilities can lead to turbulence and fluctuations in the disc density and temperature, resulting in observable variability.
Magnetic Reconnection Events: Magnetic reconnection, a process where magnetic field lines break and reconnect, can release significant amounts of energy, heating up localized regions of the accretion disc and producing flares or bursts of emission. These events can contribute to both short-term and long-term variability.
Corona Formation and Variability: Magnetic fields are thought to play a crucial role in the formation and dynamics of the X-ray corona, a hot, diffuse region above the accretion disc. Variations in the corona structure and heating mechanisms, potentially driven by magnetic fields, can lead to X-ray variability that propagates down to lower energies, affecting the observed UV-optical variability as well.
Interactions with Companion Galaxies:

Tidal Disruptions and Accretion Rate Fluctuations: Interactions with companion galaxies can tidally disrupt gas clouds and funnel them towards the central black hole, leading to sudden increases in the accretion rate and subsequent brightening of the quasar. These events can introduce significant variability on timescales ranging from months to years.
Fueling of Warps and Eccentricities: Gravitational perturbations from companion galaxies can induce warps or eccentricities in the accretion disc. These distortions can lead to variations in the observed luminosity as different parts of the disc move in and out of our line of sight.
Triggering of Star Formation and Feedback: Galaxy interactions can trigger bursts of star formation in the central regions, which can in turn affect the AGN activity through feedback processes. For example, supernova explosions from newly formed stars can inject energy and momentum into the surrounding medium, potentially influencing the accretion flow and leading to variability.
The challenge lies in disentangling the contributions of these various factors to the observed variability and isolating the underlying mass dependence of disc timescales. This requires careful analysis of multi-wavelength light curves, detailed modeling of the accretion disc and its environment, and statistical studies of large quasar samples with diverse properties.

If the variability of quasar accretion discs can be used as a reliable probe of black hole mass, what implications might this have for our understanding of galaxy evolution and the role of supermassive black holes in shaping the universe?

If the variability of quasar accretion discs can be firmly established as a reliable probe of black hole mass, it would open up exciting new avenues for studying galaxy evolution and the role of supermassive black holes in shaping the universe. Here are some potential implications:
1. Efficient Black Hole Mass Estimation:

Large Samples at High Redshift: Current methods for measuring black hole masses, like reverberation mapping and dynamical modeling, are resource-intensive and limited to relatively nearby objects. Variability-based mass estimates, once calibrated and validated, could be applied to much larger samples of quasars, including those at high redshift, where direct measurements are challenging.
Probing Black Hole Growth Across Cosmic Time: This would allow us to study the evolution of black hole masses across cosmic time, providing crucial insights into the mechanisms driving black hole growth, the connection between black hole accretion and galaxy evolution, and the co-evolution of black holes and their host galaxies.
2. Understanding AGN Feedback:

Connecting Variability to Accretion Physics: By linking variability timescales to physical processes in the accretion disc, we can gain a better understanding of the accretion flow, the efficiency of energy release, and the mechanisms responsible for AGN feedback, such as winds and jets.
Constraining Feedback Models: This knowledge can help us constrain models of AGN feedback, which describe how energy released by the accreting black hole affects the surrounding galaxy, regulating star formation and influencing the evolution of the host galaxy itself.
3. Refining Cosmological Models:

Independent Distance Indicators: If the relationship between variability and black hole mass is well-understood and free from significant biases, quasars could potentially be used as independent distance indicators, similar to Type Ia supernovae.
Probing Dark Energy and Expansion History: This could provide valuable data points for cosmological studies, helping us refine our understanding of dark energy, the expansion history of the universe, and potentially even testing alternative cosmological models.
4. Unveiling the Physics of Accretion Discs:

Testing Accretion Disc Theories: Using variability as a probe can help us test and refine our theoretical models of accretion discs, including the role of magnetic fields, turbulence, and relativistic effects in shaping the observed properties of quasars.
Understanding Disc-Jet Connections: It can also shed light on the connection between the accretion disc and the launching of relativistic jets, providing insights into the mechanisms responsible for these powerful outflows and their impact on the surrounding environment.
Overall, establishing a robust connection between quasar variability and black hole mass would be a major breakthrough in astrophysics, with far-reaching implications for our understanding of galaxy evolution, black hole physics, and cosmology.