Flare Loops Research Articles

Magnetohydrodynamic Turbulence Formation in Solar Flares: 3D Simulation and Synthetic Observations

Turbulent plasma motion is common in the universe and invoked in solar flares to drive effective acceleration leading to high-energy electrons. Unresolved mass motions are frequently detected in flares from extreme ultraviolet (EUV) observations, which are often regarded as turbulence. However, how this plasma turbulence forms during the flare is still largely a mystery. Here we successfully reproduce observed turbulence in our 3D magnetohydrodynamic simulation where the magnetic reconnection process is included. The turbulence forms as a result of an intricate nonlinear interaction between the reconnection outflows and the magnetic arcades below the reconnection site, in which the shear-flow-driven Kelvin–Helmholtz instability (KHI) plays a key role in generating turbulent vortices. The turbulence is produced above high-density flare loops and then propagates to chromospheric footpoints along the magnetic field as Alfvénic perturbations. High turbulent velocities above 200 km s−1 can be found around the termination shock, while the low atmosphere reaches turbulent velocities of 10 km s−1 at a layer where the number density is about 1011 cm−3. The turbulent region with maximum nonthermal velocity coincides with the region where the observed high-energy electrons are concentrated, demonstrating the potential role of turbulence in acceleration. Synthetic views in EUV and fitted Hinode-EUV Imaging Spectrometer spectra show excellent agreement with observational results. An energy analysis demonstrates that more than 10% of the reconnection-downflow kinetic energy can be converted to turbulent energy via KHI.

Solar flare hard X-rays from the anchor points of an eruptive filament

Context.We present an analysis of a GOES M1.8 flare with excellent observational coverage in UV, extreme-UV (EUV), and X-ray, including observations from the Interface Region Imaging Spectrograph (IRIS), from the Solar Dynamics Observatory (SDO) with the Atmospheric Imaging Assembly (AIA), from the Hinode/EUV Imaging Spectrometer (EIS), from the Hinode/X-ray Telescope (XRT), and from Solar Orbiter with the Spectrometer/Telescope for Imaging X-rays (STIX). Hard X-ray emission is often observed at the footpoints of flare loops and is occasionally observed in the corona. In this flare, four nonthermal hard X-ray sources are seen.Aims.Our aim is to understand why we can observe four individual nonthermal sources in this flare and how we can characterize the physical properties of these four sources.Methods.We used the multiwavelength approach to analyze the flare and characterize the four sources. To do this, we combined imaging at different wavelengths and spectroscopic fitting in the EUV and X-ray range.Results.The flare is eruptive with an associated coronal mass ejection, and it shows the classical flare picture of a heated flare loop seen in EUV and X-rays, and two nonthermal hard X-ray footpoints at the loop ends. In addition to the main flare sources, we observed two outer sources in the UV, EUV, and nonthermal X-ray range located away from the main flare loop to the east and west. The two outer sources are clearly correlated in time, and they are only seen during the first two minutes of the impulsive phase, which lasts a total of about four minutes.Conclusions.Based on the analysis, we determine that the outer sources are the anchor points of an erupting filament. The hard X-ray emission is interpreted as flare-accelerated electrons that are injected upward into the filament and then precipitate along the filament toward the chromosphere, producing Bremsstrahlung. While sources like this have been speculated to exist, this is the first report of their detection.

The Transition Region of Solar Flare Loops

The transition region between the Sun’s corona and chromosphere is important to the mass and energy transfer from the lower atmosphere to the corona; consequently, this region has been studied intensely with ultraviolet and extreme ultraviolet (EUV) observations. A major result of these studies is that the amount of plasma at low temperatures, <105 K, is far too large to be compatible with the standard theory of thermal conductivity. However, it is not clear whether the disagreement lies with a problem in the observations or a problem in the theory. We address this issue by analyzing high–spatial and temporal resolution EUV observations from an X1.6-class flare, taken with the Interface Region Imaging Spectrograph and the Solar Dynamic Observatory/Atmospheric Imaging Assembly (AIA). These data allow us to isolate the emission of flare loops from that of surrounding structures. We compare the emission measures (EMs) derived from the C ii 1334.525 Å and Si iv 1402.770 Å transition region spectral lines, the Fe xxi 1354.066 Å flare line, and the AIA 171 Å coronal images. We find that the EM ratios are incompatible with a standard conduction-dominated transition region model. Furthermore, the large increases in the EM magnitudes due to flare heating make it highly unlikely that the disagreement between data and theory is due to observational uncertainties in the source of the emission. We conclude that the standard Spitzer–Härm thermal conductivity must be invalid for, at least, flare loops. We discuss the possibility that turbulent suppression of thermal conduction can account for our results.

Delayed Development of Cool Plasmas in X-Ray Flares from the Young Sun-like Star κ 1 Ceti

The Neutron star Interior Composition Explorer (NICER) X-ray observatory observed two powerful X-ray flares equivalent to superflares from the nearby young solar-like star κ 1 Ceti in 2019. NICER follows each flare from the onset through the early decay, collecting over 30 counts s−1 near the peak, enabling a detailed spectral variation study of the flare rise. The flare in September varies quickly in ∼800 s, while the flare in December has a few times longer timescale. In both flares, the hard-band (2–4 keV) light curves show typical stellar X-ray flare variations with a rapid rise and slow decay, while the soft X-ray light curves, especially of the September flare, have prolonged flat peaks. The time-resolved spectra require two temperature plasma components at kT ∼0.3–1 and ∼2–4 keV. Both components vary similarly, but the cool component lags by ∼200 s with a four to six times smaller emission measure (EM) compared to the hot component. A comparison with hydrodynamic flare loop simulations indicates that the cool component originates from X-ray plasma near the magnetic loop footpoints that mainly cools via thermal conduction. The time lag represents the travel time of the evaporated gas through the entire flare loop. The cool component has a several times smaller EM than its simulated counterpart, suggesting a suppression of conductive cooling, possibly by the expansion of the loop cross-sectional area or turbulent fluctuations. The cool component’s time lag and EM ratio provide important constraints on the flare loop geometry.

Identifying the energy release site in a solar microflare with a jet

Context. One of the main science questions of the Solar Orbiter and Parker Solar Probe missions deals with understanding how electrons in the lower solar corona are accelerated and how they subsequently access interplanetary space. Aims. We aim to investigate the electron acceleration and energy release sites as well as the manner in which accelerated electrons access the interplanetary space in the case of the SOL2021-02-18T18:05 event, a GOES A8 class microflare associated with a coronal jet. Methods. This study takes advantage of three different vantage points, Solar Orbiter, STEREO-A, and Earth, with observations drawn from eight different instruments, ranging from radio to X-ray. Multi-wavelength timing analysis combined with UV/EUV imagery and X-ray spectroscopy by Solar Orbiter/STIX (Spectrometer/Telescope for Imaging X-rays) is used to investigate the origin of the observed emission during different flare phases. Results. The event under investigation satisfies the classical picture of the onset time of the acceleration of electrons coinciding with the jet and the radio type III bursts. This microflare features prominent hard X-ray (HXR) nonthermal emission down to at least 10 keV and a spectrum that is much harder than usual for a microflare with γ = 2.9 ± 0.3. From Earth’s vantage point, the microflare is seen near the limb, revealing the coronal energy release site above the flare loop in EUV, which, from STIX spectroscopic analysis, turns out to be hot (i.e., at roughly the same temperature of the flare). Moreover, this region is moving toward higher altitudes over time (∼30 km s−1). During the flare, the same region spatially coincides with the origin of the coronal jet. Three-dimensional (3D) stereoscopic reconstructions of the propagating jet highlight that the ejected plasma moves along a curved trajectory. Conclusions. Within the framework of the interchange reconnection model, we conclude that the energy release site observed above-the-loop corresponds to the electron acceleration site, corroborating that interchange reconnection is a viable candidate for particle acceleration in the low corona on field lines open to interplanetary space.

A Statistical Analysis of Magnetic Field Changes in the Photosphere during Solar Flares Using High-cadence Vector Magnetograms and Their Association with Flare Ribbons

We analyze high-cadence vector magnetograms (135 s) and flare-ribbon observations of 37 flares from the Solar Dynamics Observatory to understand the spatial and temporal properties of changes in the photospheric vector magnetic field and their relationship to footpoints of reconnected fields. Confirming previous studies, we find that the largest permanent changes in the horizontal field component lie near the polarity inversion line, whereas changes in the vertical field are less pronounced and are distributed throughout the active region. We find that pixels swept up by ribbons do not always exhibit permanent changes in the field. However, when they do, ribbon emission typically occurs several minutes before the start time of field changes. The changes in the properties of the field show no relation to the size of active regions, but are strongly related to the flare-ribbon properties such as ribbon magnetic flux and ribbon area. For the first time, we find that the duration of permanent changes in the field is strongly coupled with the duration of the flare, lasting on average 29% of the duration of the GOES flare. Our results suggest that changes in photospheric magnetic fields are caused by a combination of two scenarios: contraction of flare loops driven by magnetic reconnection and coronal implosion.

A Model for Gradual-phase Heating Driven by MHD Turbulence in Solar Flares

Coronal flare emission is commonly observed to decay on timescales longer than those predicted by impulsively driven, one-dimensional flare loop models. This discrepancy is most apparent during the gradual phase, where emission from these models decays over minutes, in contrast to the hour or more often observed. Magnetic reconnection is invoked as the energy source of a flare, but should deposit energy into a given loop within a matter of seconds. Models which supplement this impulsive energization with a long, persistent ad hoc heating have successfully reproduced long-duration emission, but without providing a clear physical justification. Here we propose a model for extended flare heating by the slow dissipation of turbulent Alfvén waves initiated during the retraction of newly reconnected flux tubes through a current sheet. Using one-dimensional simulations, we track the production and evolution of MHD wave turbulence trapped by reflection from high-density gradients in the transition region. Turbulent energy dissipates through nonlinear interaction between counter-propagating waves, modeled here using a phenomenological one-point closure model. Atmospheric Imaging Assembly EUV light curves synthesized from the simulation were able to reproduce emission decay on the order of tens of minutes. We find this simple model offers a possible mechanism for generating the extended heating demanded by observed coronal flare emissions self-consistently from reconnection-powered flare energy release.

Excitation of Multiperiodic Kink Motions in Solar Flare Loops: Possible Application to Quasiperiodic Pulsations

Magnetohydrodynamic (MHD) waves are often invoked to interpret quasiperiodic pulsations (QPPs) in solar flares. We study the response of a straight flare loop to a kink-like velocity perturbation using three-dimensional MHD simulations and forward model the microwave emissions using the fast gyrosynchrotron code. Kink motions with two periodicities are simultaneously generated, with the long-period component (P L = 57 s) being attributed to the radial fundamental kink mode and the short-period component (P S = 5.8 s) to the first leaky kink mode. Forward modeling results show that the two-periodic oscillations are detectable in the microwave intensities for some lines of sight. Increasing the beam size to (1″)2 does not wipe out the microwave oscillations. We propose that the first leaky kink mode is a promising candidate mechanism to account for short-period QPPs. Radio telescopes with high spatial resolutions can help distinguish between this new mechanism and such customary interpretations as sausage modes.

Parametric Evolution of Power-law Energy Spectra of Energetic Electrons in the Coronal Loops

Fast electron beams (FEBs) are one of the main products of various active events and are ubiquitous in solar, space and cosmic plasmas. They reveal themselves in hard X-ray and radio emissions. The observed characteristics of X-ray and radio emissions sensitively depend on the energy distribution of FEBs, which usually have a power-law energy spectrum. As FEBs travel in the solar atmosphere, their energy distribution can considerably vary due to the interaction with ambient plasmas. Tang et al. investigated the evolution of the energy spectrum of the FEBs traveling along a flare loop and discussed the possible effects on associated hard X-ray (HXR) and radio emissions. Considering the ubiquitous coronal loops in active regions, in the present paper, we investigate the parametric evolution of the energy spectra of FEBs when propagating along coronal loops. Here, we take the sunpot atmospheric model as an approximate coronal loop atmosphere model. The results show that the energy loss has an important impact on the cutoff behavior and energy spectra of FEBs when precipitating in a coronal loop with density ratio n b /n e = 0.01. The initially single power-law spectrum with a steepness cutoff can evolve into a more complex double power-law spectrum or two “knees” power-law spectrum with a flattened steepness cutoff behavior or saturation cutoff behavior. Our calculations also demonstrate that the energy spectrum evolution is not obvious if n b /n 0 = 0.001 as Tang et al. asserted. The present results are helpful for a more comprehensive understanding of the dynamic spectra of HXR and radio emissions from FEBs.

Interrogating solar flare loop models with IRIS observations 2: Plasma properties, energy transport, and future directions

During solar flares a tremendous amount of magnetic energy is released and transported through the Sun’s atmosphere and out into the heliosphere. Despite over a century of study, many unresolved questions surrounding solar flares are still present. Among those are how does the solar plasma respond to flare energy deposition, and what are the important physical processes that transport that energy from the release site in the corona through the transition region and chromosphere? Attacking these questions requires the concert of advanced numerical simulations and high spatial-, temporal-, and spectral-resolution observations. While flares are 3D phenomenon, simulating the NLTE flaring chromosphere in 3D and performing parameter studies of 3D models is largely outwith our current computational capabilities. We instead rely on state-of-the-art 1D field-aligned simulations to study the physical processes that govern flares. Over the last decade, data from the Interface Region Imaging Spectrograph (IRIS) have provided the crucial observations with which we can critically interrogate the predictions of those flare loop models. Here in Paper 2 of a two-part review of IRIS and flare loop models, I discuss how forward modelling flares can help us understand the observations from IRIS, and how IRIS can reveal where our models do well and where we are likely missing important processes, focussing in particular on the plasma properties, energy transport mechanisms, and future directions of flare modelling.

Observations and modeling of spectral line asymmetries in stellar flares

Context. Stellar flares are energetic events occurring in stellar atmospheres. They have been observed on various stars using photometric light curves and spectra. On some cool stars, flares tend to release substantially more energy than solar flares. Spectroscopic observations have revealed that some spectral lines exhibit asymmetry in their profile in addition to an enhancement and broadening. Asymmetries with enhanced blue wings are often associated with coronal mass ejections, while the origin of red asymmetries is currently not well understood. A few mechanisms have been suggested, but no modeling has been performed so far. Aims. We observed the dMe star AD Leo using the 2-meter Perek telescope at Ondřejov observatory, with simultaneous photometric light curves. In analogy with solar flares, we modeled the Hα line emergent from an extensive arcade of cool flare loops and explain the observed asymmetries using the concept of coronal rain. Methods. We solved the non-LTE (departures from local thermal equilibrium) radiative transfer in Hα within cool flare loops taking the velocity distribution of individual rain clouds into account. For a flare occurring at the center of the stellar disk, we then integrated radiation emergent from the whole arcade to obtain the flux from the loop area. Results. We observed two flares in the Hα line that exhibit a red wing asymmetry corresponding to velocities up to 50 km s−1 during the gradual phase of the flare. Synthetic profiles generated from the model of coronal rain have enhanced red wings that are quite compatible with observations.

Flares detected in ALMA single-dish images of the Sun

Context. The millimeter and submillimeter radiation of solar flares is poorly understood. Without spatial resolution, millimeter emission cannot be easily compared to flare emission in other wavelengths. Though the Atacama Large Millimeter-submillimeter Array (ALMA) offers sufficient resolution for the first time, ALMA cannot be used on demand to observe when a flare occurs, and when used as an interferometer, its field of view is smaller than an active region. Aims. We used readily available large-scale single-dish ALMA observations of solar millimeter flares and compared them to well-known features observed in other wavelengths. The properties of these other flare emissions, correlating in space and time, could then be used to interpret the millimeter brightenings and vice versa. The aim is to obtain reliable associations limited by the time and space resolution of single-dish observations. Methods. Ordinary interferometric ALMA observations require single-dish images of the full Sun for calibration. We collected such observations at 3 mm and 1 mm and searched for millimeter brightenings during times listed in a flare catalog. Results. All of the flares left a signature in millimeter waves. We found five events with nine or more images that could be used for comparison in time and space. The millimeter brightenings are associated with a variety of flare features in cool (Hα, 304 Å), intermediate (171 Å), and hot (94 Å) lines. In several cases, the millimeter brightening peaked at the footpoint of a hot flare loop. In other cases the peak of the millimeter brightening coincided with the top or footpoint of an active Hα filament. We also found correlations with post-flare loops and the tops of a hot loop. In some images, the millimeter radiation peaked at locations where no feature in the selected lines was found. Conclusions. The wide field of view provided by the single-dish ALMA observations allowed for a complete overview of the flare activity in millimeter waves for the first time. The associated phenomena often changed in type and location during the flare. The variety of phenomena detected in these millimeter observations may explain the sometimes bewildering behavior of millimeter flare emissions previously observed without spatial resolution.

Interrogating solar flare loop models with IRIS observations 1: Overview of the models, and mass flows

Solar flares are transient yet dramatic events in the atmosphere of the Sun, during which a vast amount of magnetic energy is liberated. This energy is subsequently transported through the solar atmosphere or into the heliosphere, and together with coronal mass ejections flares comprise a fundamental component of space weather. Thus, understanding the physical processes at play in flares is vital. That understanding often requires the use of forward modelling in order to predict the hydrodynamic and radiative response of the solar atmosphere. Those predictions must then be critiqued by observations to show us where our models are missing ingredients. While flares are of course 3D phenomenon, simulating the flaring atmosphere including an accurate chromosphere with the required spatial scales in 3D is largely beyond current computational capabilities, and certainly performing parameter studies of energy transport mechanisms is not yet tractable in 3D. Therefore, field-aligned 1D loop models that can resolve the relevant scales have a crucial role to play in advancing our knowledge of flares. In recent years, driven in part by the spectacular observations from the Interface Region Imaging Spectrograph (IRIS), flare loop models have revealed many interesting features of flares. For this review I highlight some important results that illustrate the utility of attacking the problem of solar flares with a combination of high quality observations, and state-of-the-art flare loop models, demonstrating: 1) how models help to interpret flare observations from IRIS, 2) how those observations show us where we are missing physics from our models, and 3) how the ever increasing quality of solar observations drives model improvements. Here in Paper one of this two part review I provide an overview of modern flare loop models, and of electron-beam driven mass flows during solar flares.

Microwave imaging of quasi-periodic pulsations at flare current sheet

Quasi-periodic pulsations (QPPs) are frequently detected in solar and stellar flares, but the underlying physical mechanisms are still to be ascertained. Here, we show microwave QPPs during a solar flare originating from quasi-periodic magnetic reconnection at the flare current sheet. They appear as two vertically detached but closely related sources with the brighter ones located at flare loops and the weaker ones along the stretched current sheet. Although the brightness temperatures of the two microwave sources differ greatly, they vary in phase with periods of about 10–20 s and 30–60 s. The gyrosynchrotron-dominated microwave spectra also present a quasi-periodic soft-hard-soft evolution. These results suggest that relevant high-energy electrons are accelerated by quasi-periodic reconnection, likely arising from the modulation of magnetic islands within the current sheet as validated by a 2.5-dimensional magnetohydrodynamic simulation.

Numerical Modeling of Energetic Electron Acceleration, Transport, and Emission in Solar Flares: Connecting Loop-top and Footpoint Hard X-Ray Sources

The acceleration and transport of energetic electrons during solar flares is one of the outstanding topics in solar physics. Recent X-ray and radio imaging and spectroscopy observations have provided diagnostics of the distribution of nonthermal electrons and suggested that, in certain flare events, electrons are primarily accelerated in the loop top and likely experience trapping and/or scattering effects. By combining the focused particle transport equation with magnetohydrodynamic (MHD) simulations of solar flares, we present a macroscopic particle model that naturally incorporates electron acceleration and transport. Our simulation results indicate that physical processes such as turbulent pitch-angle scattering can have important impacts on both electron acceleration in the loop top and transport in the flare loop, and their influences are highly energy-dependent. A spatial-dependent turbulent scattering with enhancement in the loop top can enable both efficient electron acceleration to high energies and transport of abundant electrons to the footpoints. We further generate spatially resolved synthetic hard X-ray (HXR) emission images and spectra, revealing both the loop-top and footpoint HXR sources. Similar to the observations, we show that the footpoint HXR sources are brighter and harder than the loop-top HXR source. We suggest that the macroscopic particle model provides new insights into understanding the connection between the observed loop-top and footpoint nonthermal emission sources by combining the particle model with dynamically evolving MHD simulations of solar flares.

Additional Stochastic Acceleration of Nonthermal Electrons during Their Interaction with Whistler Turbulence in Flare Loops

Additional Stochastic Acceleration of Nonthermal Electrons during Their Interaction with Whistler Turbulence in Flare Loops

Complex Type II Solar Radio Event on 4 July 2022

Abstract On 4 July 2022, a complex low-frequency solar radio burst was observed in Metsähovi Radio Observatory of Aalto University. The radio burst was observed at a frequency range between 20 and 80 MHz. In GOES (Geostationary Operational Environmental Satellite) class, the event was classified as C5.1. However, coronal mass ejection (CME) was not associated to this event. The observed radio burst was a long-lasting (~10 minutes) event, and it could be mainly classified as type II solar radio event. Also type III solar events were observed before long-lasting type II event. The event includes common frequency drifting emission structures, both fundamental and harmonic structures, but also rarely observed continuum-like or stationary structure. It is assumed that the continuum-like radio emission structure is originated from the stationary flare (coronal) loop, which was visible over the whole event. The drifting emission structure means accelerated electrons, which are produced by the shock related phenomena. The paper provides the observations from this event on radio wavelength, and also soft-X-ray regime and optical wavelength (AIA 171). In addition, a possible, simplified scenario is presented for forming the drifting and continuum solar radio emissions in type II solar burst.

Rapid variations of Si IV spectra in a flare observed by interface region imaging spectrograph at a sub-second cadence

We report on observations of highly-varying Si IV 1402.77 Å line profiles observed with the Interface Region Imaging Spectrograph (IRIS) during the M-class flare from 18 January 2022 at an unprecedented 0.8 s cadence. Moment analysis of this line observed in flare ribbon kernels showed that the intensity, Doppler velocity, and non-thermal broadening exhibited variations with periods below 10 s. These variations were found to be correlated with properties of the Gaussian fit to a well-resolved secondary component of the line redshifted by up to 70 km s−1, while the primary component was consistently observed near the rest wavelength of the line. A particularly high correlation was found between the non-thermal broadening of the line resulting from the moment analysis and the redshift of the secondary component. This means that the oscillatory enhancements in the line broadening were due to plasma flows (away from the observer) with varying properties. A simple de-projection of the Doppler velocities of the secondary component based on a three-dimensional reconstruction of flare loops rooted in the kernel suggests that the observed flows were caused by downflows and compatible with strong condensation flows recently predicted by numerical simulations. Furthermore, peaks of the intensity and the trends of Doppler velocity of the Gaussian fit to the secondary component (averaged in the ribbon) were found to correspond to one of the quasi-periodic pulsations (QPPs) detected during the event in the soft X-ray flux (as measured by the Geostationary Operational Environmental Satellite, GOES) and the microwave radio flux (as measured by the Expanded Owens Valley Solar Array, EOVSA). This result supports a scenario in which the QPPs were driven by repeated magnetic reconnection.

Flare quasi-periodic pulsation associated with recurrent jets

Quasi-periodic pulsations (QPPs), which carry time features and plasma characteristics of flare emissions, are frequently observed in light curves of solar/stellar flares. In this study, we investigated non-stationary QPPs associated with recurrent jets during an M1.2 flare on 2022 July 14. A quasi-period of ∼45±10 s, determined by the wavelet transform technique, is simultaneously identified at wavelengths of soft/hard X-ray and microwave emissions, which are recorded by the Gravitational Wave High-Energy Electromagnetic Counterpart All-sky Monitor, Fermi and the Nobeyama Radio Polarimeters, respectively. A group of recurrent jets with an intermittent cadence of about 45 ± 10 s are found in the Atmospheric Imaging Assembly (AIA) image series at 304 Å, but they are 180 s earlier than the flare QPP. All observational facts suggest that the flare QPPs could be excited by recurrent jets, and they should be associated with non-thermal electrons that are periodically accelerated by a repeated energy release process, such as repetitive magnetic reconnection. Moreover, the same quasi-period is discovered at double footpoints connected by a hot flare loop in AIA 94 Å, and the phase speed is measured to be ∼1,420 km s−1. Based on the differential emission measure, the average temperatures, number densities, and magnetic field strengths at the loop top and footpoint are estimated to be ∼7.7/6.7 MK, ∼7.5/3.6 × 1010 cm−3, and ∼143/99 G, respectively. Our measurements indicate that the 45-s QPP is probably modulated by the kink-mode wave of the flare loop.

Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes

Sausage modes are a leading mechanism for interpreting short-period quasi-periodic pulsations (QPPs) of solar flares. Forward modeling their radio emission is crucial for identifying sausage modes observationally and for understanding their connections with QPPs. Using the numerical outputs from three-dimensional magnetohydrodynamic simulations, we forward model the gyrosynchrotron emission of flare loops modulated by sausage modes and examine the influence of fine structures of loops. The temporal evolution of the emission intensity is analyzed for an oblique line of sight crossing the loop center. We find that the low- and high-frequency intensities oscillate in phase in the periods of sausage modes for models with or without fine structures. For low-frequency emissions where the optically thick regime arises, the modulation magnitude of the intensity is dramatically reduced by the fine structures at some viewing angles. On the contrary, for high-frequency emissions where the optically thin regime holds, the effects of fine structures or the viewing angle are marginal. Our results show that the periodic intensity variations of sausage modes are not wiped out by fine structures, and that sausage modes remain a promising candidate mechanism for QPPs, even when the flare loops are fine-structured.