Decrease In Accretion Rate Research Articles

Proximity to inlet channel drives spatial variation in sediment carbon across a lagoonal seagrass meadow

Seagrass meadows can be sinks for organic carbon, but estimates of global organic carbon stocks are complicated by substantial spatial variability in organic carbon burial observed within meadows. To improve estimates of organic carbon burial in seagrass meadows, it is necessary to understand the causes of the spatial heterogeneity. This study investigated relationships between spatial patterns in sediment organic carbon storage and accretion rates, hydrodynamics, and proximity to sources of organic carbon in a current-dominated Zostera marina Linnaeus meadow in Menemsha Pond, Massachusetts, USA. Sediment and velocity measurements were conducted at six stations along a 150-m transect across the meadow oriented perpendicular to the pond's unvegetated inlet channel. The meadow's edge near the channel had higher organic carbon than the channel as well as the highest organic carbon within the meadow. With increasing distance from the meadow's edge, all of the following decreased: sediment organic and total carbon, sediment accretion rates, peak tidal velocity, sediment trap mass deposition rate, and the relative contribution of non-seagrass sources to sediment organic carbon. Lower tidal velocities farther from the inlet channel reduced sediment resuspension, consistent with lower sediment trap mass deposition, which should enhance organic carbon content and organic carbon accretion rates. However, the opposite trend of decreasing organic carbon content (>50 % across the transect) and decreasing accretion rates with distance from channel was observed. This suggested that the local hydrodynamic intensity was not controlling organic carbon accretion, which was instead constrained by supply limitation and controlled by the lagoon-scale flow circulation.

A Systematic Analysis of the X-Ray Emission in Optically Selected Tidal Disruption Events: Observational Evidence for the Unification of the Optically and X-Ray-selected Populations

We present a systematic analysis of the X-ray emission of a sample of 17 optically selected, X-ray-detected tidal disruption events (TDEs) discovered between 2014 and 2021. The X-ray light curves show a diverse range of temporal behaviors, with most sources not following the expected power-law decline. The X-ray spectra are mostly extremely soft and consistent with thermal emission from the innermost region of an accretion disk, which cools as the accretion rate decreases. Three sources show formation of a hard X-ray corona at late times. The spectral energy distribution shape, probed by the ratio (L BB/L X) between the UV/optical and X-ray, shows a wide range of L BB/L X ∈ (0.5, 3000) at early times and converges to disklike values of L BB/L X ∈ (0.5, 10) at late times. We estimate the fraction of optically discovered TDEs with L X ≥ 1042 erg s−1 to be at least 40% and show that X-ray loudness is independent of black hole mass. We argue that distinct disk formation timescales are unlikely to be able to explain the diverse range of X-ray evolution. We combine our sample with X-ray-discovered ones to construct an X-ray luminosity function, best fit by a broken power law, with a break at L X ≈ 1044 erg s−1. We show that there is no dichotomy between optically and X-ray-selected TDEs; instead, there is a continuum of early-time L BB/L X, at least as wide as L BB/L X ∈ (0.1, 3000), with optical/X-ray surveys selecting preferentially, but not exclusively, from the higher/lower end of the distribution. Our findings are consistent with unification models for the overall TDE population.

Disk Cooling and Wind Lines as Seen in the Spectral Line Evolution of V960 Mon

We follow up our photometric study of the postoutburst evolution of the FU Ori object V960 Mon with a complementary spectroscopic study at high dispersion that uses time series spectra from the Keck/HIgh Resolution Echelle Spectrograph. Consistent with the photometric results reported in Carvalho et al., we find that the spectral evolution of V960 Mon corresponds to a decrease in the temperature of the inner disk, driven by a combination of a decreasing accretion rate and an increasing inner disk radius. We also find that although the majority of the absorption lines are well matched by our accretion disk model spectrum, there are several strong absorption line families and a few emission lines that are not captured by the model. By subtracting the accretion disk model from the data at each epoch, we isolate the wind and outflow components of the system. The residuals show both broad and highly blueshifted profiles, as well as narrow and only slightly blueshifted profiles, with some lines displaying both types of features.

Modeling the Multiwavelength Evolution of the V960 Mon System

Abstract We study the evolution of the FU Ori object V960 Mon since its outburst, using available multiwavelength photometric time series over 8 yr, complemented by several epochs of moderate-dispersion spectrophotometry. We find that the source fading can be well-described by a decrease in the temperature of the inner disk, which results from a combination of decreasing accretion rate and increasing inner disk radius. We model the system with a disk atmosphere model that produces the observed variations in multiband photometry (this paper) and high-resolution spectral lines (a companion paper).

Constraining the X-ray reflection in low accretion-rate active galactic nuclei using XMM-Newton, NuSTAR, and Swift

Context. An interesting feature of active galactic nuclei (AGN) accreting at low rates is the weakness of the reflection features in their X-ray spectra, which may result from the gradual disappearance of the torus with decreasing accretion rates. It has been suggested that low-luminosity AGN (LLAGN) would exhibit a different reflector configuration than high-luminosity AGN, covering a smaller fraction of the sky or simply having less material. Additionally, we note that the determination of the spectral index (Γ) and the cut-off energy of the primary power-law emission is affected by the inclusion of reflection models, showing their importance in studying accretion mechanisms. This is especially valid in the case of the LLAGN which has previously shown a high dispersion in the relation between Γ and the accretion rate. Aims. Our purpose is to constrain the geometry and column density of the reflector in a sample of LLAGN covering a broad X-ray range of energy by combining data from XMM-Newton+ NuSTAR + Swift. The spectral analysis also allows us to investigate the accretion mechanism in LLAGN. Methods. We used XMM-Newton+ NuSTAR + Swift observations of a hard X-ray flux-limited sample of 17 LLAGN from BASS/DR2 with accretion rates of λEdd = LBol/LEdd < 10−3. We fit all spectra using the reflection model for torus (BORUS) and accretion disk (XILLVER) reflectors. Results. We found a tentative correlation between the torus column density and the accretion rate, with LLAGN showing a lower column density than the high-luminosity objects. We also confirm the relation between Γ and λEdd, with a smaller scatter than previously reported, thanks to the inclusion of high-energy data and the reflection models. Our results are consistent with a break at λEdd ∼ 10−3, which is suggestive of a different accretion mechanism compared with higher accretion AGN.

GRRMHD simulations of MAD accretion discs declining from super-Eddington to sub-Eddington accretion rates

ABSTRACT We present two general relativistic radiation magnetohydrodynamics (GRRMHD) simulations of magnetically arrested discs (MADs) around non-spinning (a* = 0) and spinning (a* = 0.9) supermassive black holes (BHs). In each simulation, the mass accretion rate is decreased with time such that we sample Eddington-scaled rates over the range $3 \gtrsim \dot{M}/\dot{M}_{\rm {Edd}}\gtrsim 0.3$. For the non-spinning BH model, the total and radiative efficiencies increase as the accretion rate decreases, varying over the range $\eta _{\rm {tot}}\sim 9\!-\!16{{\ \rm per\ cent}}$ and $\eta _{\rm {rad}}\sim 6{-}12{{\ \rm per\ cent}}$, respectively. This model shows very little jet activity. In contrast, the spinning BH model has a strong relativistic jet powered by spin energy extracted from the BH. The jet power declines with accretion rate such that $\eta _{\rm {jet}}\sim 18{-}39{{\ \rm per\ cent}}$ while the total and radiative efficiencies are $\eta _{\rm {tot}}\sim 64{-}100{{\ \rm per\ cent}}$ and $\eta _{\rm {rad}}\sim 45{-}79{{\ \rm per\ cent}}$, respectively. We confirm that mildly sub-Eddington discs can extract substantial power from a spinning BH, provided they are in the MAD state. The jet profile out to $100\, GM/c^2$ is roughly parabolic with a power-law index of k ≈ 0.43−0.53 during the sub-Eddington evolution. Both models show significant variability in the outgoing radiation which is likely associated with episodes of magnetic flux eruptions. The a* = 0.9 model shows semiregular variations with a period of $\sim 2000\, GM/c^3$ over the final $\sim 10\, 000\, GM/c^3$ of the simulation, which suggests that magnetic flux eruptions may be an important source of quasi-periodic variability. For the simulated accretion rates, the a* = 0 model is spinning up while the a* = 0.9 model is spinning down. Spinup–spindown equilibrium of the BH will likely be achieved at 0.5 < a*, eq < 0.6, assuming continuous accretion in the MAD state.

Coastal engineering infrastructure impacts Blue Carbon habitats distribution and ecosystem functions

Intertidal estuarine habitats (e.g., saltmarshes and tidal flats) provide important ecosystem services to society, including coastal protection, food provision and Corg sequestration. Yet, estuaries and estuarine habitats have been subjected to intense human pressure, such as land-use change and artificialization of the shoreline to support economic activities and uses. Construction of engineering infrastructures (e.g., piers, bridges) in these areas alters estuary-wide hydromorphological conditions and thus sedimentation patterns at the estuarine scale, which are key drivers of habitats distribution and ecosystem structure, processes and functions. Most of the research on the impact of civil engineering structures on coastal habitats has focused on the biological communities that colonize them or the bottoms where they are placed, whereas their indirect impacts on adjacent habitats has been largely unexplored. Understanding the influence of man-made infrastructures on the distribution of estuarine habitats and functions is critical, particularly considering that shoreline armoring is expected to increase as a way to protect coastal areas from hazards derived from climate change. Shifts in habitat distribution and functions occur in several years or decades and relating them with the occurrence of past historical events is challenging when no monitoring data is available. By examining historical aerial photographs and different biogeochemical properties along a saltmarsh soil record, this study demonstrates that the construction of an infrastructure (i.e. bridge) caused a rapid transformation (~ 30 years) of a bare sandflat into a high marsh community and to significant changes in sediment biogeochemical properties, including the decrease in sediment accretion rate and Corg burial rates since then. This study contributes to increase the knowledge on the impact that the construction in coastal areas of civil engineering infrastructures can cause in intertidal habitats distribution and the ecological functions they provide for climate change adaption and mitigation.

Inside-out planet formation – VII. Astrochemical models of protoplanetary discs and implications for planetary compositions

ABSTRACT Inside-out planet formation (IOPF) proposes that the abundant systems of close-in Super-Earths and Mini-Neptunes form in situ at the pressure maximum associated with the dead zone inner boundary (DZIB). We present a model of physical and chemical evolution of protoplanetary disc midplanes that follows gas advection, radial drift of pebbles, and gas-grain chemistry to predict abundances from ∼300 au down to the DZIB near 0.2 au. We consider typical disc properties relevant for IOPF, i.e. accretion rates $10^{-9}\lt \dot{m}/ (\mathrm{ M}_\odot \:{\rm {yr}}^{-1})\lt 10^{-8}$ and viscosity parameter α = 10−4, and evolve for fiducial duration of 105 yr. For outer, cool disc regions, we find that C and up to $90{{\ \rm per\ cent}}$ of O nuclei start locked in CO and $\rm O_2$ ice, which keeps abundances of $\rm CO_2$ and $\rm H_2O$ one order of magnitude lower. Radial drift of icy pebbles is influential, with gas-phase abundances of volatiles enhanced up to two orders of magnitude at icelines, while the outer disc becomes depleted of dust. Discs with decreasing accretion rates gradually cool, which draws in icelines closer to the star. At ≲ 1 au, advective models yield water-rich gas with C/O ratios ≲ 0.1, which may be inherited by atmospheres of planets forming here via IOPF. For planetary interiors built by pebble accretion, IOPF predicts volatile-poor compositions. However, advectively enhanced volatile mass fractions of $\sim 10{{\ \rm per\ cent}}$ can occur at the water iceline.

Thermal Comptonization in a Changing Corona in the Changing-look Active Galaxy NGC 1566

We present broadband UV/X-ray spectral variability of the changing-look active galactic nucleus (AGN) NGC 1566, based on simultaneous near-ultraviolet and X-ray observations performed by the XMM-Newton, Swift, and NuSTAR satellites at five different epochs during the declining phase of the 2018 outburst. We found that the accretion disk, soft X-ray excess, and X-ray power-law components were extremely variable. Additionally, the X-ray power-law flux was correlated with both the soft excess plus disk and the pure disk fluxes. Our finding shows that at high-flux levels the soft X-ray excess and the disk emission both provided the seed photons for thermal Comptonization in the hot corona, whereas at low-flux levels, where the soft excess was absent, the pure disk emission alone provided the seed photons. The X-ray power-law photon index was only weakly variable (ΔΓhot ≤ 0.06), and it was not well correlated with the X-ray flux over the declining timescale. On the other hand, we found that the electron temperature of the corona increased from ∼22 to ∼200 keV with the decreasing numbers of seed photons from 2018 June to 2019 August. At the same time, the optical depth of the corona decreased from τ hot ∼ 4 to ∼0.7, and the scattering fraction increased from ∼1% to ∼10%. These changes suggest structural changes in the hot corona, such as it was growing in size and becoming hotter with the decreasing accretion rate during the declining phase. The AGN is most likely evolving with a decreasing accretion rate toward a state similar to the low/hard state of black hole X-ray binaries.

Low-resolution Optical Spectroscopy of Recently Discovered Accreting-only Symbiotic Star THA 15–31

Abstract Recently, the discovery and characterization of a new accreting-only symbiotic star THA 15–31 was presented. Motivated by the suggestion that the optical spectrum of the star might show the emission lines with higher ionization potential in comparison with previously studied epochs, we have obtained a low-resolution spectrum of this target. The spectrum does not reveal the presence of suggested He ii emission lines. Moreover, the near-UV excess seems to be even less prominent now in comparison with the previous observations, suggesting a decrease in mass transfer and accretion rate. The search for He ii emission lines should be repeated when the accretion rate is higher.

Enrichment of Jupiter’s Atmosphere by Late Planetesimal Bombardment

Abstract Jupiter’s atmosphere is enriched with heavy elements by a factor of about 3 compared to a protosolar composition. The origin of this enrichment and whether it represents the bulk composition of the planetary envelope remain unknown. Internal structure models of Jupiter suggest that its envelope is separated from the deep interior and that the planet is not fully mixed. This implies that Jupiter’s atmosphere was enriched with heavy elements just before the end of its formation. Such enrichment can be a result of late planetesimal accretion. However, in situ Jupiter formation models suggest a decreasing accretion rate with increasing planetary mass, which cannot explain Jupiter’s atmospheric enrichment. In this study, we model Jupiter’s formation and show that the migration of proto-Jupiter from ∼20 au to its current location can lead to late planetesimal accretion and atmospheric enrichment. Late planetesimal accretion does not occur if proto-Jupiter migrates only a few astronomical units. We suggest that if Jupiter’s outermost layer is fully mixed and is relatively thin (up to ∼20% of its mass), such late accretion can explain its measured atmospheric composition. It is therefore possible that Jupiter underwent significant orbital migration followed by late planetesimal accretion.

Investigations on the optical properties and X‐ray emission in compact radio active galactic nuclei

AbstractCompact radio active galactic nuclei (compact radio AGN) are compact (≤20 kpc), powerful radio sources. Currently, the preferred scenario is that they are at the early stage of AGN evolution. At present, the research of compact radio AGN mainly focuses on the radio band; other bands have not been extensively studied. We present the systemic optical properties and X‐ray emission studies for compact radio AGN, to investigate the accretion properties, AGN evolution, and their X‐ray origin. We find that compact radio AGN has various accretion modes indicated by the accretion rate analysis. In the radio power‐linear size diagram, they generally follow the evolutionary trend toward large‐scale radio galaxies with increasing linear size and decreasing accretion rate. Their hard X‐ray emission may be from jet based on the radio/X‐ray relation and fundamental plane of black hole activity.

Modelling the morphodynamic evolution of Galveston beach, Gulf of Mexico, following Hurricane Ike in 2008

A unique set of field measurements taken along Galveston beach have been compiled to give annual shoreline positions over the period 2010–2016. These have been used, in conjunction with statistical and mathematical modelling, to gain insights into the response of the shoreline after the landfall of Hurricane Ike in 2008, which caused extensive erosion and loss of material from the beach. Over the period 2010–2014, a generally accretive trend is observed along the beach. Within this trend, two different patterns are evident. In the area extending westward of South Jetty the accretion rate is fast until April 2011, after which the accretion rate decreases. The remainder of the beach, including the groyne field in front of the city of Galveston, exhibits the greatest accretive trend after April 2011. It is hypothesized that distinct sandbanks lying offshore of Galveston Island were formed during the passage of Hurricane Ike and control these two different patterns of recovery. To test this hypothesis a novel 1-line model, based on linked analytical solutions, was set up to investigate the beach response to various sediment source distributions. The model was tested against existing survey measurements and performed satisfactorily. An exploration of various sediment supply scenarios with the model supports the hypothesis that offshore sediment stores, one distinct source to the south of South Jetty and a diffuse linear source running the length of the groyne field and seawall, were gradually being fed back to the beach by the prevailing wave conditions.

Constraining X-ray reflection in the low-luminosity AGN NGC 3718 using NuSTAR and XMM–Newton

ABSTRACT One distinctive feature of low-luminosity active galactic nuclei (LLAGNs) is the relatively weak reflection features they may display in the X-ray spectrum, which can result from the disappearance of the torus with decreasing accretion rates. Some material, however, must surround the active nucleus, i.e. the accretion flow itself and, possibly, a flattened-out or thinned torus. In this work, we study whether reflection is indeed absent or undetectable due to its intrinsically weak features together with the low statistics inherent to LLAGNs. Here, we focus on NGC 3718 (L/LEdd ∼ 10−5) combining observations from XMM–Newton and the deepest to date NuSTAR (0.5–79 keV) spectrum of a LLAGNs, to constrain potential reflectors, and analyse how the fitted coronal parameters depend on the reflection model. We test models representing both an accretion disc (Relxill) and a torus-like (MYTorus and Borus) neutral reflector. From a statistical point of view, reflection is not required, but its inclusion allows to place strong constraints on the geometry and physical features of the surroundings: both neutral reflectors (torus) tested should be Compton thin (NH < 1023.2cm−2) and preferentially cover a large fraction of the sky. If the reflected light instead arises from an ionized reflector, a highly ionized case is preferred. These models produce an intrinsic power-law spectral index in the range [1.81–1.87], where the torus models result in steeper slopes. The cut-off energy of the power-law emission also changes with the inclusion of reflection models, resulting in constrained values for the disc reflectors and unconstrained values for torus reflectors.

Line-driven disc wind in near-Eddington active galactic nuclei: decrease of mass accretion rate due to powerful outflow

ABSTRACT Based on recent X-ray observations, ultrafast outflows from supermassive black holes are expected to have enough energy to dramatically affect their host galaxy but their launch and acceleration mechanisms are not well understood. We perform two-dimensional radiation hydrodynamics simulations of UV line-driven disc winds in order to calculate the mass-loss rates and kinetic power in these models. We develop a new iterative technique that reduces the mass accretion rate through the inner disc in response to the wind mass-loss. This makes the inner disc less UV bright, reducing the wind power compared to previous simulations which assumed a constant accretion rate with radius. The line-driven winds in our simulations are still extremely powerful, with around half the supplied mass accretion rate being ejected in the wind for black holes with mass 108–$10^{10}\, \mathrm{ M}_\odot$ accreting at L/LEdd = 0.5–0.9. Our results open up the way for estimating the growth rate of supermassive black hole and evaluating the kinetic energy ejected into the interstellar medium (active galactic nuclei feedback) based on a physical model of line-driven disc winds.

The C/O ratio of He-accreting carbon-oxygen white dwarfs and type Ia supernovae

Type Ia supernovae (SNe Ia) are thermonuclear explosions of carbon-oxygen white dwarfs (CO WDs), and are believed to be excellent cosmological distance indicators due to their high luminosity and remarkable uniformity. However, there exists a diversity among SNe Ia, and a poor understanding of the diversity hampers the improvement of the accuracy of cosmological distance measurements. The variations of the ratios of carbon to oxygen (C/O) of WDs at explosion are suggested to contribute to the diversity. In the canonical model of SNe Ia, a CO WD accretes matter from its companion and increases its mass till the Chandrasekhar mass limit when the WD explodes. In this work, we studied the C/O ratio for accreting CO WDs. Employing the stellar evolution code MESA, we simulated the accretion of He-rich material onto CO WDs with different initial WD masses and different mass accretion rates. We found that the C/O ratio varies for different cases. The C/O ratio of He-accreting CO WDs at explosion increases with a decreasing initial WD mass or a decreasing accretion rate. The various C/O ratios may, therefore, contribute to the diversity of SNe Ia.

Investigation on young radio AGNs based on SDSS spectroscopy

ABSTRACT The gigahertz peaked spectrum (GPS) sources, compact steep spectrum (CSS) radio sources, and high-frequency peaker (HFP) radio sources are thought to be young radio active galactic nuclei (AGNs) at the early stage of AGN evolution. We investigated the optical properties of the largest sample of 126 young radio AGNs based on the spectra in SDSS DR12. We find that the black hole masses MBH range from 107.32 to 109.84$\rm M_{\odot }$ and the Eddington ratios Redd vary from 10−4.93 to 100.37, suggesting that young radio AGNs have various accretion activities and not all are accreting at high accretion rate. Our young radio sources generally follow the evolutionary trend towards large-scale radio galaxies with increasing linear size and decreasing accretion rate in the radio power–linear size diagram. The radio properties of low-luminosity young radio AGNs with low Redd are discussed. The line width of [O iii] λ5007 core (σ[O iii]) is found to be a good surrogate of stellar velocity dispersion σ*. The radio luminosity $L_{\rm 5\, GHz}$ correlates strongly with [O iii] core luminosity L[O iii], suggesting that radio activity and accretion are closely related in young radio sources. We find one object that can be defined as a narrow-line Seyfert 1 galaxy, representing a population of young AGNs with both young jet and early accretion activity. The optical variabilities of 15 quasars with multi-epoch spectroscopy were investigated. Our results show that the optical variability in young AGN quasars presents low variations ($\leqslant \! 60{{\ \rm per\ cent}}$) similar to the normal radio-quiet quasars.

Impact of sand mining on sediment transport and morphological change of Hai Phong coastal area

The paper presents the results of simulating the impact of sand mining on sediment transport and morphological change in Hai Phong coastal area based on Delft3D model. Scenario groups are established: Present scenarios without sand mining and simulated scenarios of the present sand mining (assuming 30% sand compared to plan). The scenario groups are calculated in the dry and rainy seasons for main wind directions (NE, SE, SW) in the case of moderate wind and strong wind. The results show that sand mining reduces sediment flow alongshore (2–81%) and seawards (5–83%). Besides, the increase in depth causes morphological change in this area: Rising the deposition rate (5–10 mm/month) at the sand mining locations; decreasing accretion rate and increasing the erosion rate in the neighboring areas of sand mining location.

Geochronology of an Apollo 16 Clast Provides Evidence for a Basin-Forming Impact 4.3 Billion Years Ago.

We examined lithic breccias from the Apollo sample collection in order to identify ferroan anorthosite samples suitable for geochronology, and better define the age relationships between rocks of the lunar highlands. Clast 3A is a previously unstudied noritic anorthosite from Apollo 16 lithic breccia 60016 with textural evidence of slow subsolidus recrystallization. We estimate a cooling rate of ~10 °C/Myr and calculate a pyroxene solvus temperature of 1,100–1,000 °C. Pyroxene exsolution lamellae (1–3 μm) indicate that the last stage of cooling was rapid at ~0.2 °C/year, typical of rates observed in thick ejecta blankets. We calculate concordant ages from the 147Sm‐143Nd, 146Sm‐142Nd, Rb‐Sr, and Ar‐Ar isotopic systems of 4,302 ± 28, 4,296 + 39/−53, 4,275 ± 38, and 4,311 ± 31 Ma, respectively, with a weighted average of 4,304 ± 12 Ma. The closure temperature of the Sm‐Nd system is ~855 ± 14 °C, whereas the closure temperature of the Ar‐Ar system is 275 ± 25 °C. Cooling from 855 to 275 °C at 10 °C/Myr should result in an age difference between the two isotopic systems of ~60 Myr. The concordant Sm‐Nd, Rb‐Sr, and Ar‐Ar ages imply that they record the time the rock was excavated by a large impact from the midcrust. The ages clearly predate various late accretion scenarios in which an uptick in impacts at 3.8 Ga is preceded by a period of relative quiescence between 4.4 and ~4.1 Ga, and instead are consistent with decreasing accretion rates following the formation of the Moon.

The New Numerical Galaxy Catalogue (ν2GC): properties of active galactic nuclei and their host galaxies

We present the latest results of a semi-analytic model of galaxy formation, "New Numerical Galaxy Catalogue", which is combined with large cosmological N-body simulations. This model can reproduce statistical properties of galaxies at z < 6.0. We focus on the properties of active galactic nuclei (AGNs) and supermassive black holes, especially on the accretion timescale onto black holes. We find that the number density of AGNs at z < 1.5 and at hard X-ray luminosity 10^{ 44 }< erg/s is underestimated compared with recent observational estimates when we assume the exponentially decreasing accretion rate and the accretion timescale which is proportional to the dynamical time of the host halo or the bulge, as is often assumed in semi-analytic models. We show that to solve this discrepancy, the accretion timescale of such less luminous AGNs instead should be a function of the black hole mass and the accreted gas mass. This timescale can be obtained from a phenomenological modelling of the gas angular momentum loss in the circumnuclear torus and/or the accretion disc. Such models predict a longer accretion timescale for less luminous AGNs at z < 1.0 than bright QSOs whose accretion timescale would be 10^{ 7-8 } yr. With this newly introduced accretion timescale, our model can explain the observed luminosity functions of AGNs at z < 6.0.