Total Heating Rate Research Articles

Contribution of anthropogenic aerosols in direct radiative forcing and atmospheric heating rate over Delhi in the Indo-Gangetic Basin

The present work is aimed to understand direct radiation effects due to aerosols over Delhi in the Indo-Gangetic Basin (IGB) region, using detailed chemical analysis of surface measured aerosols during the year 2007. An optically equivalent aerosol model was formulated on the basis of measured aerosol chemical compositions along with the ambient meteorological parameters to derive radiatively important aerosol optical parameters. The derived aerosol parameters were then used to estimate the aerosol direct radiative forcing at the top of the atmosphere, surface, and in the atmosphere. The anthropogenic components measured at Delhi were found to be contributing ∼ 72% to the composite aerosol optical depth (AOD(0.5) ∼ 0.84). The estimated mean surface and atmospheric forcing for composite aerosols over Delhi were found to be about -69, -85, and -78 W m(-2) and about +78, +98, and +79 W m(-2) during the winter, summer, and post-monsoon periods, respectively. The anthropogenic aerosols contribute ∼ 90%, 53%, and 84% to the total aerosol surface forcing and ∼ 93%, 54%, and 88% to the total aerosol atmospheric forcing during the above respective periods. The mean (± SD) surface and atmospheric forcing for composite aerosols was about -79 (± 15) and +87 (± 26) W m(-2) over Delhi with respective anthropogenic contributions of ∼ 71% and 75% during the overall period of observation. Aerosol induced large surface cooling, which was relatively higher during summer as compared to the winter suggesting an increase in dust loading over the station. The total atmospheric heating rate at Delhi averaged during the observation was found to be 2.42 ± 0.72 K day(-1), of which the anthropogenic fraction contributed as much as ∼ 73%.

Direct Coupling of the NEQAIR Radiation and DPLR CFD Codes

The NEQAIR line-by-line radiation code is incorporated into the DPLR flow solver such that NEQAIR is now a callable subroutine of DPLR. The radiant energy source term computed by NEQAIR acts as an energy sink, reducing the convective and radiative heating rates, and brings the shock wave closer to the body. The effects of fluid dynamics/radiation coupling are examined by comparing coupled and uncoupled DPLR-NEQAIR results against FIRE II flight measurements and previous computations. Radiation coupling had the greatest effect at the 1643 s FIRE II trajectory point where the stagnation point total heating rate was reduced by 15.1 %. The coupled 1643 s results were closely correlated to the flight measurements. The change in stagnation point total heating rate was 6% at the 1636 and 1645 s trajectory points, and radiation coupling effects were essentially nonexistent at the 1651 s trajectory point. The coupled DPLR-NEQAIR surface heating rate profiles converged after only two updates of the radiant energy source term.

On the heating of the outer radiation belt to produce high fluxes of relativistic electrons: Measured heating rates at geosynchronous orbit for high‐speed stream‐driven storms

The heating rate of the outer electron radiation belt at geosynchronous orbit is determined for the interval from 36 to 72 h after the onset of high‐speed stream‐driven storms. Multisatellite measurements of the radiation belt temperature are used for 93 high‐speed stream‐driven storms. During the storms, the outer electron radiation belt temperature changes from ∼120 keV to ∼190 keV. The average heating rate of 32 keV d−1 is obtained. The heating rate during the storms is found to be positively correlated with the solar wind velocity and with the Kp index of geomagnetic activity and to be negatively correlated with the solar wind number density. When the solar wind velocity is held fixed, the correlation of the heating rate with Kp vanishes. Expressions for the change in the heating rate as function of the solar wind speed, the solar wind density, and the Kp index are fit to the data. The heating rate is uncorrelated with the amplitude of magnetic field fluctuations in the magnetosphere. Correlations between the heating rate and the level of velocity, density, and magnetic field fluctuations in the magnetosphere and in the solar wind are weaker than the correlations of the heating rate with the solar wind velocity and density. The heating rates correspond to a kinetic energy density change of 3.6 × 10−11 erg cm−3 d−1 at geosynchronous orbit, to a specific entropy change of 4.1 × 106 eV cm2 d−1 at geosynchronous orbit, and to a total heating rate of the geosynchronous orbit region of 5.3 × 106 Watts.

Heating rates for an atom in a far-detuned optical lattice

We calculate single-atom heating rates in a far-detuned optical lattice, in connection with recent experiments. We first derive a master equation, which includes a realistic atomic internal structure and a quantum treatment of the atomic motion in the lattice. The experimental feature that optical lattices are obtained by superimposing laser standing waves of different frequencies is also included, which leads to a micromotional correction to the light shift that we evaluate. We then calculate, and compare to experimental results, two heating rates, the total heating rate (which corresponds to the increase of the total mechanical energy of the atom in the lattice), and the ground-band heating rate (which corresponds to the increase of energy within the ground energy band of the lattice). The total heating rate remarkably is independent of the atomic state and of the sign of the laser detuning. In contrast, the ground-band heating rate in the deep lattice limit is strongly suppressed for blue-detuned lattices with respect to red-detuned lattices.

Observations of the radiation divergence in the surface layer and its implication for its parameterization in numerical weather prediction models

This paper presents the results of 5 months of in situ observations of the diurnal cycle of longwave radiative heating rate in the lower part of the atmospheric boundary layer over grassland, with a particular focus on nighttime conditions. The observed longwave radiative heating is minimal at the evening transition, with a median value of −1.8 K h−1 between 1.3 and 10 m and −0.5 K h−1 between 10 and 20 m, respectively. After the transition, its magnitude gradually decreases during the night. For individual clear calm nights, a minimal radiative heating rate of −3.5 and −2.0 K h−1 was found for the two indicated layers. The total radiative heating rate appears dominantly controlled by the upward longwave flux divergence. Surprisingly, at noon a radiative heating rate of ∼1 K h−1 was found between 1.3 and 10 m for clear calm days. The availability of these radiation divergence measurements enables evaluation of the model performance for the temperature tendency caused by radiation divergence. The mesoscale model MM5 performs poorly for the stable boundary layer, because it overestimates the surface temperature and wind speed, while it underestimates the magnitude of radiative cooling. Some computationally efficient methods based on physical modeling, statistical modeling, and dimensional analysis are proposed by examining the gathered data set. The physical modeling approach appears to perform best.

Assessment of the activation, decay heat, and waste disposal of the US helium-cooled ceramic breeder test blanket module in ITER

The radioactivity inventory and decay heat in the US helium-cooled ceramic breeder (HCCB) test blanket module (TBM) have been assessed at shutdown and for several times thereafter. The sub-module will have its own FW and structural container box that houses the breeder and beryllium pebble bed units, arranged in an edge-on-configuration. Low activation ferritic steel (F82H) is used as the structure and helium is used as a coolant. The breeder beds are made of Li 2TiO 3 pebbles in which lithium has been enriched up to 75% in Li-6. Pulsed operation mode is assumed. During operation in the D-T phase, the total heating rate in the TBM is ∼263 kW. The total amount of tritium generated in the breeder and the beryllium multiplier is ∼9 g and 0.07 g, respectively, after reaching the 0.3 MWa/m 2 fluence limit. At shutdown, the total radioactivity and decay heat levels are ∼0.89 MCi and ∼0.002 MW, respectively. These values drop sharply after 1 min to ∼0.098 MCi and ∼0.0006 MW. The contribution from the F82H structure is the dominant one up to ∼10 years following shutdown. After ∼10 years, the contribution to the total activation and decay heat from the breeder material is the dominant one due to the generated tritium. The WDR of various components are far below unity and thus are well within ITER regulatory guidelines.

Towards a better representation of the solar cycle in general circulation models

Abstract. We introduce the improved Freie Universität Berlin (FUB) high-resolution radiation scheme FUBRad and compare it to the 4-band standard ECHAM5 SW radiation scheme of Fouquart and Bonnel (FB). Both schemes are validated against the detailed radiative transfer model libRadtran. FUBRad produces realistic heating rate variations during the solar cycle. The SW heating rate response with the FB scheme is about 20 times smaller than with FUBRad and cannot produce the observed temperature signal. A reduction of the spectral resolution to 6 bands for solar irradiance and ozone absorption cross sections leads to a degradation (reduction) of the solar SW heating rate signal by about 20%. The simulated temperature response agrees qualitatively well with observations in the summer upper stratosphere and mesosphere where irradiance variations dominate the signal. Comparison of the total short-wave heating rates under solar minimum conditions shows good agreement between FUBRad, FB and libRadtran up to the middle mesosphere (60–70 km) indicating that both parameterizations are well suited for climate integrations that do not take solar variability into account. The FUBRad scheme has been implemented as a sub-submodel of the Modular Earth Submodel System (MESSy).

Radiative and turbulent heating rates in the clear‐air boundary layer

AbstractThe diurnal evolution of a clear‐sky midlatitude summertime boundary layer (BL) was studied using a column model over smooth and homogeneous land, subject to weak, moderate, and strong winds. The high‐resolution BL model (lowest point at 30 cm) was equipped with an adequate turbulence scheme and a narrow‐band long‐wave (LW) radiation scheme, the latter validated using data from the International Comparison of Radiation Codes in Climate Models (ICRCCM).In off‐line ICRCCM experiments, ground emissivity ε < 1 led to extra LW cooling of air near the surface compared to ε = 1. However, much stronger LW cooling at heights of 1–3 m, and warming below 1 m, was obtained by setting the ground colder than air at screen height, a typical condition during clear nights. Conversely, a warm surface anomaly typical of sunny days leads to strong LW warming at 1–3 m, with LW cooling just above the ground. These ground temperature anomalies dominated the LW heating/cooling patterns at heights of up to 3–4 m, perhaps explaining controversies in the observed LW flux divergences close to the ground.Interactive model results indicate that the middle part of a windy clear‐air nocturnal BL (NBL) is dominated by turbulent cooling, while the upper and lower NBL is dominated by LW cooling. Below about 1 m, a fourth layer is formed with LW warming and turbulent cooling, in agreement with the off‐line experiments. When the surface winds fall below about 1–1.5 m s−1 LW cooling dominates in the whole NBL, except very near the surface. In these light wind conditions the Monin–Obukhov theory should be revised to include radiative effects.In clear‐air daytime conditions strong convective BL heating dominates over weak LW cooling except at 1–3 m heights where the cooler air absorbs the thermal emission of the hot ground. The subsequent LW warming of the superadiabatic surface layer appears to be strong enough to induce local turbulent cooling (despite the hot surface) in an ‘hour glass’ pattern independently of wind speed, such that the total diabatic heating rate remains nearly constant with height. Copyright © 2006 Royal Meteorological Society

Thermal properties of poly(ethylene oxide)/lauric acid blends: A SSA–DSC study

A series of poly(ethylene oxide) (PEO)/lauric acid blends with different compositions has been prepared and characterised by differential scanning calorimetry (DSC) in dynamic mode. It has been found that the enthalpy of melting and crystallisation reaches its highest value for PEO/lauric acid blend (1:1, w/w) which makes this system a promising candidate for thermal energy storage applications. Further studies by step-scan alternating (SSA)–DSC revealed that an increase of the temperature step causes that the average total heating rate is also increasing and the heat flow is characterised by higher values. Reversing component of the heat flow during melting reaches lowest values at highest step (step=1°) when the re-crystallisation of PEO is hindered. An increase of step generally leads to an increase of the number of non-equilibrium effects and facilitates the activation of kinetic non-reversing processes, hindering the overall crystallisation of PEO. For lauric acid, due to facile crystallisation and self-association, formation of ordered regular structures takes place faster and is influenced by non-reversing processes in higher proportion.

New pool boiling data for water with copper-foam metal at sub-atmospheric pressures: Experiments and correlation

Over the past decades, pool boiling heat transfer of water has been investigated extensively by many scientists and researchers at system pressures varying from atmospheric to near critical pressure. However, at sub-atmospheric pressures conditions there is a dearth of data, particularly when the vapour pressures are less than 10 kPa. The authors have conducted a detailed study of pool boiling of water in an evaporator where its system pressure was about 1.8 kPa. The heat flux for pool boiling was derived from an uniform radiant heaters up to 5 W/cm 2 (or a total heating rate of 125 W within an area of 25 cm 2), a region that is of interest for the cooling of CPUs.

Self‐consistent Magnetohydrodynamic Modeling of Current Sheet Structure and Heating Using Realistic Descriptions of Transport Processes

A magnetohydrodynamic (MHD) model of an electron-ion, collision-dominated plasma that includes the electrical conductivity and thermoelectric tensors in Ohm's law is used to generate current sheet solutions in parameter ranges that correspond to those of the solar transition region and lower corona. The model contains a prescribed sheared magnetic field with a characteristic length scale L. The characteristic sheet width is 2L, but it is found that the temperature has transition region or coronal values only within a diffusion region (DR) with a width several orders of magnitude smaller than 2L. The heating rate per unit mass and flow speed in the DR are orders of magnitude larger, and the density is orders of magnitude smaller than in the surrounding plasma. The heating rate per unit volume is a maximum in the DR and falls off steadily outside the DR. The Joule heating rate and current density each consist of a conduction component driven by the center-of-mass electric field and a thermoelectric component driven by the temperature gradient. It is found that these components largely cancel, leading to a total heating rate and current density orders of magnitude smaller than either of their components. This suggests that thermoelectric current drive is important in determining current sheet structure. The center-of-mass electric field that provides the energy to maintain the plasma in a steady state is almost entirely the convection electric field. The electron magnetization Me is the product of the electron cyclotron frequency and the electron-ion collision time. Nonzero values of Me cause the conductivity and thermoelectric tensors to be anisotropic. It is found that the large values of Me that occur in the DR increase the heating rates per unit volume and mass by several orders of magnitude and can change the sign of the heating rate per unit mass from negative to positive, corresponding to a change from a cooling process to a heating process. This suggests that electron magnetization, and hence anisotropic transport, is a major factor in current sheet heating.

Plume heat flow in a numerical model of mantle convection with moving plates

Abstract Self-consistent numerical models are presented for a two-dimensional thermal convection with moving plates to estimate the heat flow transported by hot upwelling plumes in both internally and basally heated mantle. The plume heat flow depends on the internal heating rate and convective regimes but does not exceed 30% of basal heat flow when the plates rigidly move as observed on the Earth; the fraction of plume heat flow to basal heat flow becomes higher when the lithosphere behaves as a stagnant lid or as a mechanically not so strong plate. When estimated from the dynamic topography of plume-swells above hot upwelling plumes, the plume heat flow appears to be only a small fraction of the real plume heat flow. As a whole, the apparent plume heat flow estimated from dynamic topography remains only a few percent of the total heat flow on the surface boundary, the value observed for the Earth, even when the basal heating rate exceeds 50% of the total heating rate. Such a high fraction of basal heating rate is necessary for the amplitude of topography above hot upwelling plumes to become comparable to the value observed for the Earth, too. It is necessary to reexamine the earlier inference that the heat released from the core manifests itself as plume heat flow in the Earth.

Meaning of ionospheric Joule heating

The possibility of relating the electric current in the ionosphere to the electric field in the frame of reference either of the neutral atmosphere (as commonly done) or of the plasma raises the question: which should be used in calculating Joule heating? The energy equations for the plasma and for the neutral medium, including collision effects, can be combined with momentum equations to separate energy transfer into work done and heating (this is not the same as separation of energy content into bulk‐flow kinetic energy and thermal energy). Heating/dissipation processes can be unambiguously identified, showing that true electromagnetic (Joule) heating rate is given by J · E in the frame of reference of the plasma. The major part of energy dissipation associated with J and E in the ionosphere is heating by collisions between plasma and neutrals, proportional to the square of the difference in their bulk flow velocities and distributed approximately equally between the two. The conventionally calculated ionospheric Joule heating as J · E in the frame of reference of the neutral atmosphere equals the sum of total heating rate of plasma (only a small part of which is true Joule heating) plus total heating rate of neutrals, plus a term equal to work done on plasma in the neutral‐atmosphere frame of reference; the latter is assumed negligible, with J × B/c balanced entirely by plasma‐neutral collisions and with no net work done on the plasma. This assumption implies that all the magnetic stresses exerted on the plasma at ionospheric heights are taken up by the local neutral medium; hence the dynamics of the neutral atmosphere play an important role in magnetosphere/ionosphere interactions.

Ion transport from collisions and finite guiding centre drift excursions

A study is made of the effects on ion transport of collisions and of finite drift excursions for a variety of guiding centre drift orbit shapes. The drift excursions Δx, where x denotes a normalized flux surface label, are calculated by solving the guiding centre drift equation for individual orbits. Collisions are described by a Fokker–Planck operator valid in all collisionality regimes. The operator describes the interaction between a test particle and a thermal plasma. The test particles represent the thermal ions of the plasma such that the collision operator is made to conserve particle number, momentum and energy. The momentum conservation leads to a new formulation of the ion heat flux from test particle calculations. General Monte Carlo type equations are derived from moments of the collision operator. These equations are solved in a two step computational approach. A plasma equilibrium based on a JET configuration is used in computations which scan a phase space of three dimensionless variables which characterize the guiding centre orbits. The time–space dependent contributions from the drifts across flux surfaces, as well as along field lines, are accumulated to yield the ion heat flux profile qi(x) characterizing a thermal, Ohmically heated plasma. The profile of this ion heat flux is different from those predicted by conventional neoclassical theories as it vanishes on the magnetic axis. The edge value is approximately a third of the experimental value determined from the total Ohmic heating rate. The electron heat flux qe(x), can in principle also be evaluated by the model, but requires a two order of magnitude increase in computing resources.

SOLAR2000 irradiances for climate change research, aeronomy and space system engineering

Improvements to spectral and temporal solar irradiances are often based upon increasingly accurate and precise measurements as well as upon better understood physics. This paper reports on one example in an emerging trend for solar irradiance models that can be characterized as hybrid irradiance modeling. Empirical and physics-based modeling of irradiances are combined and take advantage of strengths within both methods to provide a variety of solar irradiance products to science and engineering users. The SOLAR2000 (S2K) version 1.24 model (v1.24) described in this paper has gone through 17 upgrades since it was originally released in 1999 as v0.10 and now incorporates three theoretical continua, 13 rocket spectra, and time series data from five satellites using 17 instruments. S2K currently produces six integrated irradiance proxies for science and engineering applications in addition to spectrally resolved irradiances in three common wavelength formats. Integrated irradiance proxies include the E10.7 integrated EUV energy flux, Q EUV total thermospheric EUV heating rate, P EUV hemispheric EUV power, T ∞ exospheric temperature, R SN derived sunspot number, and S integrated spectrum. Besides three spectral wavelength and six integrated irradiance formats there are three time frames of historical, nowcast, and forecast irradiance products produced by four model grades. The Research Grade (RG) model is developed for aeronomical and climate change research, the Professional Grade (PG) model is developed for space system engineering applications, the Operational Grade (OP) model is developed for institutional and agency real-time operational space weather applications, and the System Grade (SY) model is developed for commercial operational and production applications. This report describes these model characteristics as well as the current state of operational irradiances which are now in the second release of a first generation forecast methodology. Forecast Generation 1x (FGen 1x) produces a 72-h forecast of E10.7 at high solar activity with 1-sigma uncertainties at the 8% level. All SOLAR2000 irradiance products from each of the versions, grades, and forecast generations are compliant with the ISO CD 21348 solar irradiance draft standard being developed as a standard method to specify all solar irradiances for use by space systems and materials users.

Tidal Effects in Clusters of Galaxies

High-redshift clusters of galaxies show an over-abundance of spirals by a factor of 2-3, and the corresponding under-abundance of S0 galaxies, relative to the nearby clusters. This morphological evolution can be explained by tidal interactions with neighboring galaxies and with the hierarchically growing cluster halo. The efficiency of tidal interactions depends on the size and structure of the cluster, as well as on the epoch of its formation. I simulate the formation and evolution of Virgo-type clusters in three cosmologies: a critical density model Omega_0=1, an open model Omega_0=0.4, and a flat model Omega_0=0.4 with a cosmological constant. The orbits of identified halos are traced with a high temporal resolution (~10^7 yr). Halos with low relative velocities merge only shortly after entering the cluster; after virialization mergers are suppressed. The dynamical evolution of galaxies is determined by the tidal field along their trajectories. The maxima of the tidal force do not always correspond to closest approach to the cluster center. They are produced to a large extent by the local density structures, such as the massive galaxies and the unvirialized remnants of infalling groups of galaxies. Collisions of galaxies are intensified by the substructure, with about 10 encounters within 10 kpc per galaxy in the Hubble time. These very close encounters add an important amount (10-50%) of the total heating rate. The integrated effect of tidal interactions is insufficient to transform a spiral galaxy into an elliptical, but can produce an S0 galaxy. Overall, tidal heating is stronger in the low Omega_0 clusters.

Stability and Evolution of Supermassive Stars (SMS)

Highly condensed gaseous objects with masses larger than 5 × 104 M⊙ are called Supermassive stars. They are thought to be possible precursors of Supermassive Black Holes in the centres of galaxies. In the quasi-stationary contraction phase the hydrostatic equilibrium is determined by radiation pressure and gravitation. The global structure is an n=3 polytrope which is at the stability limit. Small relativistic corrections for example can initiate a free fall collapse due to the "post Newtonian" instability. Since the outcome of the final collapse - Supermassive Black Hole or Hypernova - depends sensitively on the structure and the size of the object, when the instability sets in, it is important to investigate in more detail the contraction phase of the SMS. If the gaseous object is embedded in a dense stellar system, the central star cluster, the interaction and coupling of both components due to dynamical friction change the energy balance and evolution of the SMS dramatically. Dynamical friction between stars and gas, which can be estimated semi-analytically (see Just et al. 1986), has 3 different effects on the 2-component system. 1) The gas is heated by decelerating the stars. This may stall the contraction process for a while until the stars in the "loss cone", these which cross the SMS, lost their kinetic energy (for the total heating rate see Amaro-Seoane & Spurzem 2001). 2) This cooling of the loss cone stars lead to a mass segregation in the stellar component resulting in a much more condensed central stellar core. 3) The inhomogeneities due to the gravitational wakes in the gas changes the effective absorption coefficient of the gas. This affects the condition for hydrostatic equilibrium and may give essential deviations from the n=3 polytrope. We discuss, in which evolutionary stages and parameter range these interaction processes are relevant and how they can influence the stability and evolution of the SMS.

Jicamarca radar observations of the diurnal and semidiurnal tide in the troposphere and lower stratosphere

The mesosphere‐stratosphere‐troposphere (MST) radar at Jicamarca, Peru (12°S, 77°W), made extended (15 day or longer) observations of the horizontal and vertical winds that were used to infer the diurnal and semidiurnal tides. The measurements were made during several months from mid‐1997 through mid‐1998 and using a higher‐power transmitter and finer range resolution during 10 days of August 1998. The three‐component winds are used to estimate amplitudes, phases, and momentum fluxes associated with the tides. Thermal forcing of the diurnal tide is also examined with diurnal water vapor heating rates calculated using data from the NASA Water Vapor Project (NVAP). For the region near Jicamarca the calculations from NVAP showed the temporal variability of the diurnal heating to be dominated by an annual cycle with maximum around the summer solstice. When projected into tidal modes, about 25% of the total water vapor heating rate amplitude near Jicamarca is found to be nonmigrating. The meridional amplitude of the semidiurnal tide was found to be generally greater than the zonal amplitude, although tidal theory predicts that the zonal amplitude should be much greater at the latitude of Jicamarca (assuming the tide was migrating). The phase of the semidiurnal tide lagged (by about 3 hours) the phase expected from surface pressure climatologies. According to tidal theory the migrating semidiurnal tide should transport little meridional momentum flux. However, substantial southward fluxes (〈v′w′〉 ∼ −1 × 10−3 m2 s−2) were observed at Jicamarca, and the meridional component of momentum flux was typically larger in magnitude than the zonal component was. The diurnal tide was somewhat weaker, was less coherent, and transported less momentum. The semidiurnal tide had a very long vertical wavelength throughout the troposphere and into the lower stratosphere, while the diurnal tide was only observed to propagate at heights above the tropopause with a much shorter (∼10 km) vertical wavelength. Below the tropopause the dominant diurnal motions were not traveling waves, but rather convective motions that exhibited little phase progression with altitude. These motions were broadly peaked in frequency around 24 hours and were presumably standing oscillations with no horizontal propagation and probably with small horizontal scale. Despite the lack of coherence of these quasi‐diurnal motions, the associated vertical wind amplitudes were sizable (∼0.02 m s−1), and thus the fluctuations can presumably transport significant horizontal momentum.

Nanoflare heating in the quiet corona: evidence and problems

The content of coronal material in the quiet Sun is not constant, as soft X-ray (SXR) and high-temperature EUV line observations have shown. The observed temporal variations in SXR and EUV flux are interpreted as heating events showing many analogies to flares occurring in active regions. Compared to a large flare in an active region, the thermal energy input of a heating event in the quiet corona is 6 or more orders of magnitude smaller. Heating events in the quiet corona are therefore often called microflares or nanoflares. The total heating rate of nanoflares in the quiet corona has been investigated in several works by many different authors: Do nanoflares provide enough energy to heat the quiet corona? The results of the different studies are controversial. In this review, recent observational studies on nanoflare heating in the quiet corona and their different results are compared and discussed.

The loss-cone problem in dense nuclei

We address the classical problem of star accretion onto a supermassive central gaseous object in a galactic nucleus. The resulting supermassive central gas-star object is assumed to be located at the centre of a dense stellar system for which we use a simplified model consisting of a Plummer model with an embedded density cusp using stellar point masses. From the number of stars belonging to the loss-cone, which plunge onto the central object on elongated orbits from outside, we estimate the accretion rate taking into account a possible anisotropy of the surrounding stellar distribution. The total heating rate in the supermassive star due to the loss-cone stars plunging onto it is estimated. This semi-analytical study, revisiting and expanding classical paper's work, is a starting point of future work on a more detailed study of early evolutionary phases of galactic nuclei. It merits closer examination, because it is one of the key features for the link between cosmology and galaxy formation.