Coronal Heating Rate Research Articles

Modeling the Energy-dependent Broadband Variability in the Black Hole Transient GX 339–4 Using AstroSat and NICER

We present a spectro-timing analysis of the black hole X-ray transient GX 339–4 using simultaneous observations from AstroSat and the Neutron Star Interior Composition Explorer (NICER) during the 2021 outburst period. The combined spectrum obtained from NICER, Large Area X-ray Proportional Counter and SXT data is effectively described by a model comprising a thermal disk component, hard Comptonization component, and reflection component with an edge. Our analysis of the AstroSat and NICER spectra indicates the source to be in a low/hard state, with a photon index of ∼1.64. The power density spectra obtained from both AstroSat and NICER observations exhibit two prominent broad features at 0.22 Hz and 2.94 Hz. We generated energy-dependent time lag and fractional root mean square (frms) at both frequencies in a broad energy range of 0.5–30 keV and found the presence of hard lags along with a decrease in variability at higher energy levels. Additionally, we discovered that the correlated variations in accretion rate, inner disk radius, coronal heating rate, and the scattering fraction, along with a delay between them, can explain the observed frms and lag spectra for both features.

Exploring the Broadband Spectral and Timing Characteristics of GRS 1915+105 with AstroSat and NICER Observations

In this study, we undertake a spectral-timing analysis of the black hole X-ray binary source GRS 1915+105 using simultaneous observations carried out by AstroSat (Large Area X-ray Proportional Counter, LAXPC and Soft X-ray Telescope, SXT) and Neutron Star Interior Composition Explorer (NICER) in 2017. The source showed two flux levels (high and low), whose energy spectra can be described by the thermal comptonization of disk photons. The spectral parameters obtained by the joint fitting of SXT/LAXPC and NICER/LAXPC were consistent. The power density spectra from LAXPC and NICER revealed a broad, prominent feature at ∼2 Hz. The energy dependence of the fractional rms and time lag of this feature cannot be explained by only variations of coronal spectral parameters. Instead, a model where the coronal heating rate varies first and induces a change in the disk temperature and inner radius can explain the variation. Our results underline the importance of simultaneous observations by AstroSat and NICER and highlight the need for more sophisticated models to explain the spectral-temporal behavior of black hole systems.

Periodic Coronal Rain Driven by Self-consistent Heating Process in a Radiative Magnetohydrodynamic Simulation

The periodic coronal rain and in-phase radiative intensity pulsations have been observed in multiple wavelengths in recent years. However, due to the lack of three-dimensional coronal magnetic fields and thermodynamic data in observations, it remains challenging to quantify the coronal heating rate that drives the mass cycles. In this work, based on the MURaM code, we conduct a three-dimensional radiative magnetohydrodynamic simulation spanning from the convective zone to the corona, where the solar atmosphere is heated self-consistently through dissipation resulting from magnetoconvection. For the first time, we model the periodic coronal rain in an active region. With a high spatial resolution, the simulation well resembles the observational features across different extreme-ultraviolet wavelengths. These include the realistic interweaving coronal loops, periodic coronal rain, and periodic intensity pulsations, with two periods of 3.0 hr and 3.7 hr identified within one loop system. Moreover, the simulation allows for a detailed three-dimensional depiction of coronal rain on small scales, revealing adjacent shower-like rain clumps ∼500 km in width and showcasing their multithermal internal structures. We further reveal that these periodic variations essentially reflect the cyclic energy evolution of the coronal loop under thermal nonequilibrium state. Importantly, as the driver of the mass circulation, the self-consistent coronal heating rate is considerably complex in time and space, with hour-level variations in 1 order of magnitude, minute-level bursts, and varying asymmetry reaching ten times between footpoints. This provides an instructive template for the ad hoc heating function and further enhances our understanding of the coronal heating process.

X-Ray Spectral and Temporal Properties of LMXB 4U 1608-52—Observed with AstroSat and NICER

We report results from a detailed study of the neutron star X-ray binary, 4U 1608-52, using observations with AstroSat (Large Area X-ray Proportional Counter/Soft X-ray Telescope) and the Neutron Star Interior Composition Explorer during its 2016 and 2020 outbursts. The 0.7–20.0 keV spectra could be well described with the disk blackbody and thermal Comptonization model. The best-fitting inner disk temperature is ∼1 keV and radius ∼ 22.17−2.38+2.57 –27.19 −1.85+2.03 km and no significant evolution was observed in the disk radius after performing flux and time-resolved spectroscopy. We used a multi-Lorentzian approach to fit the power density spectra and obtained broadband noise variability. We estimated the energy-dependent fractional rms and time lag of the broadband noise, and these variations are quantitatively modeled as being due to the coherent variation of the disk emission and the coronal heating rate. Thus, the rapid temporal modeling is consistent with the longer-term spectral evolution where the inner disk radius does not vary, and instead, the variations can be attributed to accretion rate variations that change the inner disk temperature and the coronal heating rate.

Coronal Heating Rate in the Slow Solar Wind

This Letter reports the first observational estimate of the heating rate in the slowly expanding solar corona. The analysis exploits the simultaneous remote and local observations of the same coronal plasma volume, with the Solar Orbiter/Metis and the Parker Solar Probe instruments, respectively, and relies on the basic solar wind magnetohydrodynamic equations. As expected, energy losses are a minor fraction of the solar wind energy flux, since most of the energy dissipation that feeds the heating and acceleration of the coronal flow occurs much closer to the Sun than the heights probed in the present study, which range from 6.3 to 13.3 R ⊙. The energy deposited to the supersonic wind is then used to explain the observed slight residual wind acceleration and to maintain the plasma in a nonadiabatic state. As derived in the Wentzel–Kramers–Brillouin limit, the present energy transfer rate estimates provide a lower limit, which can be very useful in refining the turbulence-based modeling of coronal heating and subsequent solar wind acceleration.

On the energy dependence of the QPO phenomenon in the black hole system MAXI J1535-571

ABSTRACT Previous analysis of AstroSat observations of the black hole system MAXI J1535-571 have revealed the presence of a strong Quasi-Periodic Oscillation (QPO) whose frequency is correlated with the high energy spectral index. Here, we fit the spectra as emitted from a truncated disc with an inner hot corona, study the QPO frequency dependence on other spectral parameters and model the energy-dependent r.m.s and time-lag of the QPO to identify the physical spectral parameters whose variation are responsible for the QPO. The QPO frequency is found to also correlate with the scattering fraction (i.e. the fraction of the soft photons Comptonized) and its dependence on the accretion rate and inner disc radii is consistent with it being the dynamical frequency. The time-lag between the hard and soft photons is negative for QPO frequency >2.2 Hz and is positive for lesser values, making this the second black hole system to show this behaviour after GRS 1915+105. Modelling the energy-dependent time-lag and r.m.s requires correlated variation of the accretion rate, inner disc radii, and the coronal heating rate, with the latter having a time-lag compared to the other two for QPO frequencies less than <2.2 Hz and which changes sign (i.e. the coronal heating variation precedes the accretion rate one) for higher values. The implications of the results are discussed.

X-ray activity from different types of stars

X-ray emission is an important indicator of stellar activity. In this paper, we study stellar X-ray activity using the XMM-Newton and LAMOST data for different types of stars. We provide a sample including 1259 X-ray-emitting stars, of which 1090 have accurate stellar parameter estimations. Our sample size is much larger than those used in previous works. We find a bimodal distribution of the X-ray to optical flux ratio (log(fX/fV)) for G and K stars. We interpret that this bimodality is due to two subpopulations with different coronal heating rates. Furthermore, using the full widths at half maxima calculated from Hα and Hβ lines, we show that these stars in the inactive peaks have smaller rotational velocities. This is consistent with the magnetic dynamo theory that presumes stars with low rotational velocities have low levels of stellar activity. We also examine the correlation between log(fX/fV) and luminosity of the excess emission in the Hα line, and find a tight relation between the coronal and chromospheric activity indicators.

A Combined Chandra and LAMOST Study of Stellar Activity

Abstract We probed stellar X-ray activity over a wide range of stellar parameters, using Chandra and Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) data. We measured the X-ray-to-bolometric luminosity ratio ( ) for 484 main-sequence stars and found a bimodal distribution for G and K types. We interpret this bimodality as evidence of two subpopulations with different coronal temperatures, which are caused by different coronal heating rates. Using the metallicity and velocity information, we find that both of the subpopulations are mostly located in the thin disk. We find no trend of R X with stellar age for stars older than ∼4 Gyr; there is a trough in the R X versus age distribution, with the lowest range of R X appearing at ages around 2 Gyr. We then examined the correlation between R X and R Hα (proxy of chromospheric activity): we find that the two quantities are well correlated, as found in many earlier studies. Finally, we selected a sample of 12 stars with X-ray flares and studied the light-curve morphology of the flares. The variety of flare profiles and timescales observed in our sample suggests the contribution of different processes of energy release.

DEPENDENCE OF OCCURRENCE RATES OF SOLAR FLARES AND CORONAL MASS EJECTIONS ON THE SOLAR CYCLE PHASE AND THE IMPORTANCE OF LARGE-SCALE CONNECTIVITY

ABSTRACT We investigate the dependence of the occurrence rates of major solar flares (M- and X-class) and front-side halo coronal mass ejections (FHCMEs), observed from 1996 to 2013, on the solar cycle (SC) phase for six active McIntosh sunspot group classes: Fkc, Ekc, Dkc, Fki, Eki, and Dki. We classify SC phases as follows: (1) ascending phase of SC 23 (1996–1999), (2) maximum phase of SC 23 (2000–2002), (3) descending phase of SC 23 (2003–2008), and (4) ascending phase of SC 24 (2009–2013). We find that the occurrence rates of major flares and FHCMEs during the descending phase are noticeably higher than those during the other phases for most sunspot group classes. For the most active sunspot group class, Fkc, the occurrence rate of FHCMEs during the descending phase of SC 23 is three times as high as that during the ascending phase of SC 23. The potential of each McIntosh sunspot group class to produce major flares or FHCMEs is found to depend on the SC phase. The occurrence rates (R) of major flares and FHCMEs are strongly anti-correlated with the annual average latitude of the sunspot groups (L): for major flares and for FHCMEs. This finding indicates the possible role of large-scale coronal connectivity, e.g., trans-equatorial loops, in powerful energy releases. Interestingly, this relationship is very similar to that between the volumetric coronal heating rate and X-ray loop lengths, indicating common energy release mechanisms.

GLOBAL ENERGETICS OF SOLAR FLARES. I. MAGNETIC ENERGIES

We present the first part of a project on the global energetics of solar flares and coronal mass ejections (CMEs) that includes about 400 M- and X-class flares observed with AIA and HMI onboard SDO. We calculate the potential energy, free energy, and the flare-dissipated magnetic energy. We calculate these magnetic parameters using two different NLFFF codes: The COR-NLFFF code uses the line-of-sight magnetic field component $B_z$ from HMI to define the potential field, and the 2D coordinates of automatically detected coronal loops in 6 coronal wavelengths from AIA to measure the helical twist of coronal loops caused by vertical currents, while the PHOT-NLFFF code extrapolates the photospheric 3D vector fields. We find agreement between the two codes in the measurement of free energies and dissipated energies within a factor of $ \approx 3$. The size distributions of magnetic parameters exhibit powerlaw slopes that are approximately consistent with the fractal-diffusive self-organized criticality model. The magnetic parameters exhibit scaling laws for the nonpotential energy, $E_{np} \propto E_p^{1.02}$, for the free energy, $E_{free} \propto E_p^{1.7}$ and $E_{free} \propto B_{\varphi}^{1.0} L^{1.5}$, for the dissipated energy, $E_{diss} \propto E_p^{1.6}$ and $E_{diss} \propto E_{free}^{0.9}$, and the energy dissipation volume, $V \propto E_{diss}^{1.2}$. The potential energies vary in the range of $E_p = 1 \times 10^{31} - 4 \times 10^{33}$ erg, while the free energy has a ratio of $E_{free}/E_p \approx 1%-25%$. The Poynting flux amounts to $F_{flare} \approx 5 \times 10^{8} - 10^{10}$ erg cm$^{-2}$ s$^{-1}$ during flares, which averages to $F_{AR} \approx 6 \times 10^6$ erg cm$^{-2}$ s$^{-1}$ during the entire observation period and is comparable with the coronal heating rate requirement in active regions.

MHD modeling of coronal loops: the transition region throat

The expansion of coronal loops in the transition region may considerably influence the diagnostics of the plasma emission measure. The cross sectional area of the loops is expected to depend on the temperature and pressure, and might be sensitive to the heating rate. The approach here is to study the area response to slow changes in the coronal heating rate, and check the current interpretation in terms of steady heating models. We study the area response with a time-dependent 2D MHD loop model, including the description of the expanding magnetic field, coronal heating and losses by thermal conduction and radiation from optically thin plasma. We run a simulation for a loop 50 Mm long and quasi-statically heated to about 4 MK. We find that the area can change substantially with the quasi-steady heating rate, e.g. by ~40% at 0.5 MK as the loop temperature varies between 1 and 4 MK, and, therefore, affects the interpretation of DEM(T) curves.

HIGH-LUNDQUIST NUMBER SCALING IN THREE-DIMENSIONAL SIMULATIONS OF PARKER'S MODEL OF CORONAL HEATING

Parker's model is one of the most discussed mechanisms for coronal heating and has generated much debate. We have recently obtained new scaling results in a two-dimensional (2D) version of this problem suggesting that the heating rate becomes independent of resistivity in a statistical steady state [Ng and Bhattacharjee, Astrophys. J., 675, 899 (2008)]. Our numerical work has now been extended to 3D by means of large-scale numerical simulations. Random photospheric footpoint motion is applied for a time much longer than the correlation time of the motion to obtain converged average coronal heating rates. Simulations are done for different values of the Lundquist number to determine scaling. In the high-Lundquist number limit, the coronal heating rate obtained so far is consistent with a trend that is independent of the Lundquist number, as predicted by previous analysis as well as 2D simulations. In the same limit the average magnetic energy built up by the random footpoint motion tends to have a much weaker dependence on the Lundquist number than that in the 2D simulations, due to the formation of strong current layers and subsequent disruption when the equilibrium becomes unstable. We will present scaling analysis showing that when the dissipation time is comparable or larger than the correlation time of the random footpoint motion, the heating rate tends to become independent of Lundquist number, and that the magnetic energy production is also reduced significantly.

HEATING OF THE SOLAR CHROMOSPHERE AND CORONA BY ALFVÉN WAVE TURBULENCE

A three-dimensional MHD model for the propagation and dissipation of Alfven waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100 km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfven waves using the reduced MHD approximation. The increase of Alfven speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheric and chromospheric parts of the flux tube. Part of the wave energy is transmitted through the TR and produces turbulence in the corona. We find that the hot coronal loops typically found in active regions can be explained in terms of Alfven wave turbulence, provided the small-scale footpoint motions have velocities of 1-2 km/s and time scales of 60-200 s. The heating rate per unit volume in the chromosphere is 2 to 3 orders of magnitude larger than that in the corona. We construct a series of models with different values of the model parameters, and find that the coronal heating rate increases with coronal field strength and decreases with loop length. We conclude that coronal loops and the underlying chromosphere may both be heated by Alfvenic turbulence.

Self-Consistent Models of the Solar Wind

The origins of the hot solar corona and the supersonically expanding solar wind are still the subject of much debate. This paper summarizes some of the essential ingredients of realistic and self-consistent models of solar wind acceleration. It also outlines the major issues in the recent debate over what physical processes dominate the mass, momentum, and energy balance in the accelerating wind. A key obstacle in the way of producing realistic simulations of the Sun-heliosphere system is the lack of a physically motivated way of specifying the coronal heating rate. Recent models that assume the energy comes from Alfvén waves that are partially reflected, and then dissipated by magnetohydrodynamic turbulence, have been found to reproduce many of the observed features of the solar wind. This paper discusses results from these models, including detailed comparisons with measured plasma properties as a function of solar wind speed. Some suggestions are also given for future work that could answer the many remaining questions about coronal heating and solar wind acceleration.

On the relationship between coronal heating, magnetic flux, and the density of the solar wind

The stark differences between the current solar minimum and the previous one offer a unique opportunity to develop new constraints on mechanisms for heating and acceleration of the solar wind. We have used a combination of numerical simulations and analysis of remote solar and in situ observations to infer that the coronal heating rate, H, scales with the average magnetic field strength within a coronal hole, Bch. This was accomplished in three steps. First, we analyzed Ulysses measurements made during its first and third orbit southern and northern polar passes (i.e., during near‐solar minimum conditions) to deduce a linear relationship between proton number density (np) and radial magnetic field strength (Br) in the high‐speed quiescent solar wind, consistent with the results of McComas et al. (2008) and Ebert et al. (2009). Second, we used Wilcox Solar Observatory measurements of the photospheric magnetic field to show that the magnetic field strength within coronal holes (Bch) is approximately correlated with the strength of the interplanetary field at the location of Ulysses. Third, we used hydrodynamic simulations to show that np in the solar wind scales linearly with H. Taken together, these results imply the chain: H ∝ np ∝ Br ∝ Bch. We also explored ideas that the correlation between np and Br could have resulted from interplanetary processes, or from the superradial expansion of the coronal magnetic field close to the Sun, but find that neither possibility can produce the observed relationship. The derived heating relationship is consistent with (1) empirical heating laws derived for closed‐field line regions and (2) theoretical models aimed at understanding both the heating and acceleration of the solar wind.

AN EFFICIENT APPROXIMATION OF THE CORONAL HEATING RATE FOR USE IN GLOBAL SUN-HELIOSPHERE SIMULATIONS

The origins of the hot solar corona and the supersonically expanding solar wind are still the subject of debate. A key obstacle in the way of producing realistic simulations of the Sun-heliosphere system is the lack of a physically motivated way of specifying the coronal heating rate. Recent one-dimensional models have been found to reproduce many observed features of the solar wind by assuming the energy comes from Alfven waves that are partially reflected, then dissipated by magnetohydrodynamic turbulence. However, the nonlocal physics of wave reflection has made it difficult to apply these processes to more sophisticated (three-dimensional) models. This paper presents a set of robust approximations to the solutions of the linear Alfven wave reflection equations. A key ingredient to the turbulent heating rate is the ratio of inward to outward wave power, and the approximations developed here allow this to be written explicitly in terms of local plasma properties at any given location. The coronal heating also depends on the frequency spectrum of Alfven waves in the open-field corona, which has not yet been measured directly. A model-based assumption is used here for the spectrum, but the results of future measurements can be incorporated easily. The resulting expression for the coronal heating rate is self-contained, computationally efficient, and applicable directly to global models of the corona and heliosphere. This paper tests and validates the approximations by comparing the results to exact solutions of the wave transport equations in several cases relevant to the fast and slow solar wind.

Time-dependent hydrodynamical simulations of slow solar wind, coronal inflows, and polar plumes

Aims. We explore the effects of varying the areal expansion rate and coronal heating function on the solar wind flow. Methods. We use a one-dimensional, time-dependent hydrodynamical code. The computational domain extends from near the photosphere, where nonreflecting boundary conditions are applied, to 30 , and includes a transition region where heat conduction and radiative losses dominate.Results. We confirm that the observed inverse relationship between asymptotic wind speed and expansion factor is obtained if the coronal heating rate is a function of the local magnetic field strength. We show that inflows can be generated by suddenly increasing the rate of flux-tube expansion and suggest that this process may be involved in the closing-down of flux at coronal hole boundaries. We also simulate the formation and decay of a polar plume, by including an additional, time-dependent heating source near the base of the flux tube.

Forward Modeling of Active Region Coronal Emissions. II. Implications for Coronal Heating

In Paper I, we introduced and tested a method for predicting solar active region coronal emissions using magnetic field measurements and a chosen heating relationship. Here, we apply this forward-modeling technique to 10 active regions observed with the Mees Solar Observatory Imaging Vector Magnetograph and the Yohkoh Soft X-ray Telescope. We produce synthetic images of each region using four parameterized heating relationships depending on magnetic field strength and geometry. We find a volumetric coronal heating rate (dEH/dV, not to be confused with dEH/dA quoted by some authors) proportional to magnetic field and inversely proportional to field-line loop length (BL−1) best matches observed coronal emission morphologies. This parameterization is most similar to the steady-state scaling of two proposed heating mechanisms: van Ballegooijen's "current layers" theory, taken in the AC limit, and Parker's "critical angle" mechanism, in the case where the angle of misalignment is a twist angle. Although this parameterization best matches the observations, it does not match well enough to make a definitive statement as to the nature of coronal heating. Instead, we conclude that (1) the technique requires better magnetic field measurement and extrapolation techniques than currently available, and (2) forward-modeling methods that incorporate properties of transiently heated loops are necessary to make a more conclusive statement about coronal heating mechanisms.

Coronal magnetohydrodynamic waves and oscillations: observations and quests

Coronal seismology, a new field of solar physics that emerged over the last 5 years, provides unique information on basic physical properties of the solar corona. The inhomogeneous coronal plasma supports a variety of magnetohydrodynamics (MHD) wave modes, which manifest themselves as standing waves (MHD oscillations) and propagating waves. Here, we briefly review the physical properties of observed MHD oscillations and waves, including fast kink modes, fast sausage modes, slow (acoustic) modes, torsional modes, their diagnostics of the coronal magnetic field, and their physical damping mechanisms. We discuss the excitation mechanisms of coronal MHD oscillations and waves: the origin of the exciter, exciter propagation, and excitation in magnetic reconnection outflow regions. Finally, we consider the role of coronal MHD oscillations and waves for coronal heating, the detectability of various MHD wave types, and we estimate the energies carried in the observed MHD waves and oscillations: Alfvénic MHD waves could potentially provide sufficient energy to sustain coronal heating, while acoustic MHD waves fall far short of the required coronal heating rates.

Calculating the Thermal Structure of Solar Active Regions in Three Dimensions

We describe a technique to obtain the temperature and density distribution in an active region for a specified plasma heating model. The technique can be applied in general to determine the magnetic field and thermal structure self-consistently. For simplicity, we illustrate the application of this technique in the limit of small plasma β, in which the plasma dynamics decouples from that of the magnetic field, a good approximation in active regions, in which the magnetic field is strong. We select a particular active region, observed in 1996 August, to demonstrate the methodology. We apply the technique to a force-free magnetic field with a plasma heating model in which the volumetric coronal heating rate is directly proportional to the strength of the local magnetic field, and we compute the expected extreme-ultraviolet and soft X-ray emissions from the resulting thermal structure. We compare our solutions with one-dimensional loop models and analytic loop scaling laws. In the future, we plan to compare these emission images with those obtained by the SOHO EUV Imaging Telescope (EIT) and the Yohkoh Soft X-Ray Telescope (SXT) and to explore the relationship between coronal emission and various coronal heating models.