A multiwavelength study of a double impulsive flare

Extensive data from the Solar Maximum Mission (SMM) and ground-based observatories are presented for two flares; the first occurred at 12:48 UT on 31 August, 1980 and the second just 3 min later. They were both compact events located in the same part of the active region. The first flare appeared as a typical X-ray flare: the Caxix X-ray lines were broadened ( 190±40 km s^-1) and blue shifted ( 60±20 km s^-1) during the impulsive phase, and there was a delay of about 30 s between the hard and soft X-ray maxima. The relative brightness of the two flares was different depending on the spectral region being used to observe them, the first being the brighter at microwave and hard X-ray wavelengths but fainter in soft X-rays. The second flare showed no significant mass motions, and the impulsive and gradual phases were almost simultaneous. The physical characteristics of the two flares are derived and compared. The main difference between them was in the pre-flare state of the coronal plasma at the flare site: before the first flare it was relatively cool (3 × 10⁶ K) and tenuous (4 × 10⁹ cm^-3), but owing to the residual effects of the first flare the coronal plasma was hotter (5 × 10⁶ K) and more dense (3 × 10¹¹ cm^-3) at the onset of the second flare. We are led to believe from these data that the plasma filling the flaring loops absorbed most of the energy released during the impulsive phase of the second flare, so that only a fraction of the energy could reach the chromosphere to produce mass motions and turbulence.A simple study of the brightest flares observed by the SMM shows that at least 43% of them are multiple. Thus, the situation studied here may be quite common, and the difference in initial plasma conditions could explain at least some of the large variations in observed flare parameters. We draw a number of conclusions from this study. First, the evolution of the second flare is substantially affected by the presence of the first flare. Secondly, the primary energy release in the second event is in the corona. Thirdly, the flares occur in a decaying magnetic region, probably as a result of the interaction of existing sheared loops; there is no evidence of emerging magnetic flux. Also, magnetic structures of greatly varying size participate in the flare processes. Lastly, there is some indication that the loops are not symmetrical or stable throughout the flares, i.e. the magnetic field does not act as a uniform passive bottle for the plasma, as is often assumed in flare models.NOAA/Space Environment Laboratory, currently at NASA/MSFC, Ala., U.S.A.Now at Sacramento Peak Observatory, Tucson, Ariz., U.S.A.     

Solar and stellar flares

Short-lived increases in the brightness of many red dwarfs have been observed for the last 30 yr, and a variety of more or less exotic models have been proposed to account for such flares. Information about flares in the Sun has progressed greatly in recent years as a result of spacecraft experiments, and properties of coronal flare plasma are becoming increasingly better known. In this paper, after briefly reviewing optical, radio and X-ray observations of stellar flares, we show how a simplified model which describes conductive plus radiative cooling of the coronal flare plasma in solar flares has been modified to apply to optical and X-ray stellar flare phenomena. This model reproduces many characteristic features of stellar flares, including the mean UBV colors of flare light, the direction of flare decay in the two-color diagram, precursors, Stillstands, secondary maxima, lack of sensitivity of flare color to flare amplitude, low flux of flare X-rays, distinction between so-called spike flares and slow flares, Balmer jumps of as much as 6–8, and emission line redshifts up to 3000 km s^–1. In all probability, therefore, stellar flares involve physical processes which are no more exotic (and no less!) than those in solar flares. Advantages of observing stellar flares include the possibilities of (i) applying optical diagnostics to coronal flare plasma, whereas this is almost impossible in the Sun, and (ii) testing solar flare models in environments which are not generally accessible in the solar atmosphere.     

Size Distrtibutions of the >10 MeV Solar Proton Events

As has been recognized recently, data on size (frequency) distributions for different sets of solar flare parameters are very helpful in modeling flare and acceleration processes. Relying upon a new arising paradigm of particle acceleration at different sources at/near the Sun (flares, shock waves, etc.), in this paper, we analyze long-term data (1955–1996) from several Catalogues of Solar Proton Events (SPEs). Above 1 p.f.u. (proton cm^–2 s^–1 sr^–1) of the >10 MeV protons, we have separated in all 320 events associated with identified sources (flares). Then, within this database of flare-related events, a second group (a subgroup) has been formed of the 159 events, additionally having a certain or probable sudden storm commencement (SSC) association (SSC-related events). The basic result is that the power-law slope of size distribution for the 320 flare-related events at integral energy intensities is about 1.37 ± 0.05 over the entire range of the proton intensities, from 1.0 to 10⁵ p.f.u. This slope is in general agreement with earlier analyses of integral energy distributions, but steeper than that for differential energy distributions. A second result is that the SSC-associated events have a double power-law distribution with two different exponents, near 1.00 ± 0.04 and 1.53 ± 0.03 below and above 10³ p.f.u., respectively. The longitude distributions of the proper sources for these two groups display different behaviour suggesting different origins of the two particle populations. A certain difference was also found to exist in the slopes of integral size distributions at >10 MeV and >500 MeV. This may point to a dependence of slope on the proton energy under consideration.     

Rates of Flaring in Individual Active Regions

Rates of flaring in individual active regions on the Sun during the period 1981–1999 are examined using United States Air Force/Mount Wilson (USAF/MWL) active-region observations together with the Geostationary Operational Environmental Satellite (GOES) soft X-ray flare catalog. Of the flares in the catalog above C1 class, 61.5% are identified with an active region. Evidence is presented for obscuration, i.e. that the increase in soft X-ray flux during a large flare decreases the likelihood of detection of soft X-ray events immediately following the large flare. This effect means that many events are missing from the GOES catalog. It is estimated that in the absence of obscuration the number of flares above C1 class would be higher by (75±23)%. A second observational selection effect – an increased tendency for larger flares to be identified with an active region – is also identified. The distributions of numbers of flares produced by individual active regions and of mean flaring rate among active regions are shown to be approximately exponential, although there are excess numbers of active regions with low flare numbers and low flaring rates. A Bayesian procedure is used to analyze the time history of the flaring rate in the individual active regions. A substantial number of active regions appear to exhibit variation in flaring rate during their transit of the solar disk. Examples are shown of regions with and without rate variation, illustrating the different distributions of times between events (waiting-time distributions) that are observed. A piecewise constant Poisson process is found to provide a good model for the observed waiting-time distributions. Finally, applications of analysis of the rate of flaring to understanding the flare mechanism and to flare prediction are discussed.     

Flare event statistics on UV Ceti-type stars

A statistical study of 228 flares on the three UV Ceti-type stars, i.e., YZ CMi, AD Leo, and EV Lac, is presented. Observations were gathered by Ichimura and Shimizu over a total monitoring time of 907 hours distributed over 18 years (1971 to 1988). Period analysis of flare activity was performed, and no periodicity was detected on the three stars for either the flare number rate or the energy rate in time-scales ranging from a year up to 14 years. Average colour of flares at peak was (U-B)=–0.98±0.17 and (B-V)=0.05±0.13. Cumulative number distributions of flare event time-integrated energies were solved by a least-squares method on a log-log plot for a power-law function to get both the constant of and the gradient , which were found to be similar among the three stars. The gradient showed that rare large flare events radiate most of the energy released by all the flare events in the monitoring time. The flare number rate and energy rate are similar if the power-law distributions are extended up to a specific maximum energy. In reality, the Kolmogorov-Smirnov test showed that the observed cumulative number distributions of flare event energy were not necessarily a power-law function. The monte-Carlo simulation, however, indicates that the monitoring time and/or the patrol observation time interval may not be long enough to get the average flare number rate and energy rate, especially at the upper energy limits which are statistically unreliable.     

Distinctions between the characteristics of before and after DH CMEs associated flares

A detailed analysis of characteristics of coronal mass ejections and flares associated with deca-hectometer wavelength type-II radio bursts (DH-CMEs and DH-flares) observed in the period 1997–2008 is presented. A sample of 62 limb events is divided into two populations known as after-flare CMEs (AF-CMEs) and before-flare CMEs (BF-CMEs) based on the relative timing of the flare and CME onsets. On average, AF-CMEs (1589 km s⁻¹) have more speed than the BF-CMEs (1226 km s⁻¹) and the difference between mean values are highly significant (P∼2%). The average CME nose height at the time of type-II start is at larger distance for AF-CMEs than the BF-CMEs (4.89 and 3.84 R _o, respectively). We found a good anti-correlation for accelerating (R _a=−0.89) and decelerating (R _d=−0.78) AF-CMEs. In the case of decelerating BF-CMEs, the correlation seems to be similar to that for decelerating AF-CMEs (R _d=−0.83). The number of decelerating AF-CMEs is 51% only; where as, the number of decelerating BF-CMEs is 83%. The flares associated with BF-CMEs have shorter rise and decay times than flares related to AF-CMEs. We found statistically significant differences between the two sets of associated DH-type-II bursts characteristics: starting frequency (P∼4%), drift rate (P∼1%), and ending frequency (P∼6%). The delay time analysis of DH-type-II start and flare onset times shows that the time lags are longer in AF-CME events than in BF-CME events (P≪1%). From the above results, the AF-CMEs which are associated with DH-type-II bursts are found to be more energetic, associated with long duration flares and DH-type-IIs of lower ending frequencies.     

Solar flares in the EUV observed from OSO-5

Solar flares in three broad EUV spectral bands have been observed from OSO-5 with a grating spectrophotometer. Results are given for three large flares of March 12, March 21 and April 21, 1969. In general the time dependence of flare intensity in each band is characterized by a slowly varying component with impulsive bursts superimposed. Bands 2 (465–630 Å) and 3 (760–1030 Å) are quite similar in their time variations, but band 1 (280–370 Å) shows less impulsive structure, and declines more slowly. Absolute EUV intensities for the flares are estimated, and a comparison made with the 2800 mc s^–1 radio emission. A flare model is proposed to account for the EUV time variations during a large flare.     

The EVE Doppler Sensitivity and Flare Observations

The Extreme-ultraviolet Variability Experiment (EVE; see Woods et al., 2009) obtains continuous EUV spectra of the Sun viewed as a star. Its primary objective is the characterization of solar spectral irradiance, but its sensitivity and stability make it extremely interesting for observations of variability on time scales down to the limit imposed by its basic 10 s sample interval. In this paper we characterize the Doppler sensitivity of the EVE data. We find that the 30.4 nm line of He ii has a random Doppler error below 0.001 nm (1 pm, better than 10 km s⁻¹ as a redshift), with ample stability to detect the orbital motion of its satellite, the Solar Dynamics Observatory (SDO). Solar flares also displace the spectrum, both because of Doppler shifts and because of EVE’s optical layout, which (as with a slitless spectrograph) confuses position and wavelength. As a flare develops, the centroid of the line displays variations that reflect Doppler shifts and therefore flare dynamics. For the impulsive phase of the flare SOL2010-06-12, we find the line centroid to have a redshift of 16.8 ± 5.9 km s⁻¹ relative to that of the flare gradual phase (statistical errors only). We find also that high-temperature lines, such as Fe xxiv 19.2 nm, have well-determined Doppler components for major flares, with decreasing apparent blueshifts as expected from chromospheric evaporation flows.     

Simulation of photosphere and chromosphere of two powerful solar flares (October 28, 2003 and September 1, 1990)

The spectra of two powerful flares with approximately the same intensities in the optical region but with different spectral features and power in other regions are studied. One of them is the unique flare which occurred on October 28, 2003, importance X17.2/4B, ranking third in magnitude among the recorded flares. Another occurred on September 1, 1990, 3B importance. The flares vary in the Balmer decrement. The flare of October 28, 2003, has a ratio of I(H_β)/I(H_α) = 1.47. This is the largest value for solar flares ever observed. The flares also differ in magnitude of the D Na I lines emission: the emission of the flare of October 28, 2003, is substantially larger than that of the other flare. The chromosphere models of the flares are computed using the observed profiles of Balmer lines and D Na I lines. The satisfactory agreement of the calculated and observed profiles is obtained for the two-component models in which a hot component occupies 6% of the area. The hot component of the chromosphere model is characterized with the dense condensation available in the upper layers. For the flare of October 28, 2003, this condensation is located deeper and its substance concentration is greater than that for another flare. The H_α line intensity for the model hot component alone is approximately 30 and the continuous spectrum intensity is approximately 3% of the undisturbed level. The photosphere model is computed using the observed profiles of photosphere lines for the flare of October 28, 2003. It is found that very broad profiles of individual sigma-components of the Fe I λ 525.0 nm line may be only explained by the presence of magnetic fields having different directions. A great difference is detected between values of the magnetic field strength obtained in the splitting of sigma-components and those provided by simulation.     

High abnormal rotation rates of sunspots and flare productivity

Solar activity, such as flares and CMEs, affect the interplanetary medium, and Earth’s atmosphere. Therefore, to understand the Space Weather, we need to understand the mechanisms of solar activity. Towards this end, we use 1135 events of solar H_α flares and the positional data of sunspots from the archive of Solar Geophysical Data (SGD) for the period January–April, 2000 and compute the abnormal rotation rates that lead to high flare productivity. We report that the occurrence of 5 or more flares in a day in association with a given sunspot group can be defined as high flare productivity and the sunspots that have an abnormal rotation rates of ～4–10 deg day^?1 trigger high flare productivity. Further, in order to compare the flare productivity expressed as the strength of the flux emitted, especially the soft X-ray (SXR) flares in the frequency range of 1–8 Å, we compute the flare index of SXR flares and find that 8 out of 28 active regions used in this study satisfy the requirement for being flare productive. This enables us to conclude that the high rotation rates of sunspots are an important mechanism to understand the flare productivity, especially numerical flare productivity that includes flares of all class.     

The statistical analyses of flares detected in B band photometry of UV Ceti type stars

In this study, we present the unpublished flare data collected from 222 flares detected in the B band observations of five stars and the results derived by statistical analysis and modeling of these data. Six basic properties have been found with a statistical analysis method applied to all models and analyses for the flares detected in the B band observation of UV Ceti type stars. We have also compared the U and B bands with the analysis results. This comparison allowed us to evaluate the methods used in the analyses. The analyses provided the following results. (1) The flares were separated into two types, fast and slow flares. (2) The mean values of the equivalent durations of the slow and the fast flares differ by a factor of 16.2 ± 3.7. (3) Regardless of the total flare duration, the maximum flare energy can reach a different Plateau level for each star. (4) The Plateau values of EV Lac and EQ Peg are higher than the others. (5) The minimum values of the total flare duration increase toward the later spectral types. This value is called the Half-Life value in models. (6) Both the maximum flare rise times and the total flare duration obtained from the observed flares decrease toward the later spectral types.     

A dwarf nova in Taurus

In searchs for flare stars in the vicinity of the Pleiades cluster, three flares were detected in 1970,1972, and 1977 in a star with the coordinates α ₁₉₅₀ = 3 ^h 48 ^m ·9, δ _l950 = 25‡15’.8. The star’s brightness at a minimum is >21 ^m ·5. The star was tentatively assigned to the U Gem type. To confirm this assumption, we examined photographic plates for the period of 1947–1987. As a result, we found 12 more flares. The average recurrence time based on the 1963–1977 observations is about 330 days, and the maximum flare amplitude is >6 ^m .Narrow superflares and steady-state flares lasting over 40 days have been observed in the star. The results show that this is a dwarf nova of the UGSU subtype. Translated from Astrofizika, Vol. 42, No. 1, pp. 47–52, January–March, 1999.     

A solar super‐flare as cause for the 14C variation in AD 774/5?

We present further considerations regarding the strong ¹⁴C variation in AD 774/5. For its cause, either a solar super‐flare or a short gamma‐ray burst were suggested. We show that all kinds of stellar or neutron star flares would be too weak for the observed energy input at Earth in AD 774/5. Even though Maehara et al. (2012) present two super‐flares with ∼10³⁵ erg of presumably solar‐type stars, we would like to caution: These two stars are poorly studied and may well be close binaries, and/or having a M‐type dwarf companion, and/or may be much younger and/or much more magnetic than the Sun – in any such case, they might not be true solar analog stars. From the frequency of large stellar flares averaged over all stellar activity phases (maybe obtained only during grand activity maxima), one can derive (a limit of) the probability for a large solar flare at a random time of normal activity: We find the probability for one flare within 3000 years to be possibly as low as 0.3 to 0.008 considering the full 1σ error range. Given the energy estimate in Miyake et al. (2012) for the AD 774/5 event, it would need to be ∼2000 stronger than the Carrington event as solar super‐flare. If the AD 774/5 event as solar flare would be beamed (to an angle of only ∼24°), 100 times lower energy would be needed. A new AD 774/5 energy estimate by Usoskin et al. (2013) with a different carbon cycle model, yielding 4 ot 6 time lower ¹⁴C production, predicts 4–6 times less energy. If both reductions are applied, the AD 774/5 event would need to be only ∼4 times stronger than the Carrington event in 1859 (if both had similar spectra). However, neither ¹⁴C nor ¹⁰Be peaks were found around AD 1859. Hence, the AD 774/5 event (as solar flare) either was not beamed that strongly, and/or it would have been much more than 4‐6 times stronger than Carrington, and/or the lower energy estimate (Usoskin et al. 2013) is not correct, and/or such solar flares cannot form (enough) ¹⁴C and ¹⁰Be. The 1956 solar energetic particle event was followed by a small decrease in directly observed cosmic rays. We conclude that large solar super‐flares remain very unlikely as the cause for the ¹⁴C increase in AD 774/5. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characteristics of DH type II bursts, CMEs and flares with respect to the acceleration of CMEs

A detailed investigation on DH-type-II radio bursts recorded in Deca-Hectometer (hereinafter DH-type-II) wavelength range and their associated CMEs observed during the year 1997–2008 is presented. The sample of 212 DH-type-II associated with CMEs are classified into three populations: (i) Group I (43 events): DH-type-II associated CMEs are accelerating in the LASCO field view (a>15 m s⁻²); (ii) Group II (99 events): approximately constant velocity CMEs (−15<a<15 m s⁻²) and (iii) Group III (70 events): represents decelerating CMEs (a<−15 m s⁻²). Our study consists of three steps: (i) statistical properties of DH-type-II bursts of Group I, II and III events; (ii) analysis of time lags between onsets of flares and CMEs associated with DH-type-II bursts and (iii) statistical properties of flares and CMEs of Group I, II and III events. We found statistically significant differences between the properties of DH-type-II bursts of Group I, II and III events. The significance (P _a ) is found using the one-way ANOVA-test to examine the differences between means of groups. For example, there is significant difference in the duration (P _a =5%), ending frequency (P _a =4%) and bandwidth (P _a =4%). The accelerating and decelerating CMEs have more kinetic energy than the constant speed CMEs. There is a significant difference between the nose height of CMEs at the end time of DH-type-IIs (P _a ≪1%). From the time delay analysis, we found: (i) there is no significant difference in the delay (flare start—DH-type-II start and flare peak—DH-type-II start); (ii) small differences in the time delay between the CME onset and DH-type-II start, delay between the flare start and CME onset times. However, there are high significant differences in: flare duration (P _a =1%), flare rise time (P _a =0.5%), flare decay time (P _a =5%) and CMEs speed (P _a ≪1%) of Group I, II and III events. The general LASCO CMEs have lower width and speeds when compared to the DH CMEs. It seems there is a strong relation between the kinetic energy of CMEs and DH-type-II properties.     

The Hard X-Ray Burst Spectrometer on the Solar Maximum Mission

The primary scientific objectives of the Hard X-Ray Burst Spectrometer (HXRBS) to be flown on the Solar Maximum Mission are as follows: (1) To determine the nature of the mechanisms which accelerate electrons to 20–100 keV in the first stage of a solar flare and to > 1 MeV in the second stage of many flares; and (2) to characterize the spatial and temporal relation between electron acceleration, storage and energy loss throughout a solar flare.Measurements of the spectrum of solar X-rays will be made in the energy range from 20 to 260 keV using an actively-shielded CsI(Na) scintillator with a thickness of 0.635 cm and a sensitive area of 71 cm². Continuous measurements with a time resolution of 0.128 s will be made of the 15-channel energy-loss spectrum of events in this scintillator in anticoincidence with events in the CsI(Na) shield. Counting-rate data with a time resolution as short as 1 ms will also be available from a limited period each orbit using a 32K-word circulating memory triggered by a high event rate.In the first year after launch, it is expected that approximately 1000 flares will be observed above the instrument sensitivity threshold, which corresponds to a 20–200 keV X-ray flux of 2 × 10^–1 photons (cm² s)^–1 lasting for at least one second.     

Impulsive and hot thermal solar flares

Some X-class flares (hot thermal flares, HTF) observed with the Hinotori satellite show unique behavior: slow time variability, a compact hard X-ray source containing dense (n > 10¹¹ cm^–3) and hot (T > 3 × 10⁷ K) plasma, and unusually weak microwave emission in spite of the intense magnetic field (B > 330 G) required theoretically to sustain the hot plasma. These observations show that HTF's have essentially thermal characteristics throughout the flare evolution, while in impulsive flares, there is a transition in the energy release mode from particle acceleration (impulsive phase) to plasma heating (gradual phase). This behavior can be explained in a unified manner by employing parallel DC electric field acting over large distances.     

Solar Flares and Coronal Mass Ejections: A Statistically Determined Flare Flux – CME Mass Correlation

In an effort to examine the relationship between flare flux and corresponding CME mass, we temporally and spatially correlate all X-ray flares and CMEs in the LASCO and GOES archives from 1996 to 2006. We cross-reference 6733 CMEs having well-measured masses against 12 050 X-ray flares having position information as determined from their optical counterparts. For a given flare, we search in time for CMEs which occur 10 – 80 minutes afterward, and we further require the flare and CME to occur within ± 45° in position angle on the solar disk. There are 826 CME/flare pairs which fit these criteria. Comparing the flare fluxes with CME masses of these paired events, we find CME mass increases with flare flux, following an approximately log-linear, broken relationship: in the limit of lower flare fluxes, log (CME mass)∝0.68×log (flare flux), and in the limit of higher flare fluxes, log (CME mass)∝0.33×log (flare flux). We show that this broken power-law, and in particular the flatter slope at higher flare fluxes, may be due to an observational bias against CMEs associated with the most energetic flares: halo CMEs. Correcting for this bias yields a single power-law relationship of the form log (CME mass)∝0.70×log (flare flux). This function describes the relationship between CME mass and flare flux over at least 3 dex in flare flux, from ≈ 10⁻⁷ – 10⁻⁴ W m⁻².     

Estimation of an upper limit for the solar neutron emission during large flares

Solar neutron emission during large flares is investigated by using neutron monitor data from the mountain stations Chacaltaya (Bolivia), Mina Aguilar (Argentine), Pic-du-Midi (France) and Jungfraujoch (Switzerland). Registrations from such days on which large flares appeared around the local noon time of the monitor station are superimposed with the time of the optical flare as reference point.No positive evidence for a solar neutron emission was found with this method, However, by using an extrapolation of the neutron transport functions given by Alsmiller and Boughner a rough estimation of mean upper limits for the solar neutron flux is possible. The flux limits are compared with Lingenfelter's model calculations.From the Chacaltaya measurements it follows: N ₀2.8 × 10^{–3 N} cm^–2 s^–1 per proton flare, E > 50 MeV, if P0 = 125 MV N ₀1.4 × 10^{–2 N} cm^–2 s^–1 per proton flare, E > 50 MeV, if P ₀ = 60 MV and from Pic-du-Midi measurements: N ₀6.7 × 10^{–3 N} cm^–2 s^–1 per proton flare, E > 50 MeV, if P ₀ = 125 MV N ₀4 × 10^{–2 N} cm^–2 s^–1 per proton flare, E > 50 MeV, if P ₀ = 60 MV P ₀ = characteristic rigidity of the producing proton spectrum on the Sun.The flux limits estimated for some special proton flares are consistent with Lingenfelter's predictions for the acceleration phase but are too small for the slowing down phase. Therefore it is believed that Lingenfelter's assumption of isotropic proton emission from the flare region is not fulfilled.     

Flares of red dwarf stars and the galactic X-ray background

The mean density of the UV Cet-type flare stars in the solar neighbourhood is estimated. If differences of activity levels on different flare stars are taken into account, their summary flare activity is equivalent to 0.03 YZ CMi's flare activity per cubic parsec or to 4×10²⁶ erg s^–1 pc^–3 in U-passband. From the X-ray flare observation on YZ CMi of 19.10.74 we estimate the luminosity of stellar flares in soft and intermediate X-ray. The ratio of X-ray to optical radiation for stellar flares is close to the respective ratio for strong solar chromospheric flares. It is shown the set of red-dwarf flare stars has all essential features of an ensemble of discrete X-ray sources to represent the galactic diffuse X-ray background.     

Investigation of X-Ray Flares with Long Rising Phases

We have used Yohkoh and GOES X-ray observations to investigate flares with a long rising phase. We have found that a characteristic feature of such flares is a long time interval, Δ t ≥ 20 min, between the temperature maximum and the maximum of the emission measure. We have carried out detailed analysis for 10 limb flares of this type. Time variation of the heating function, E_H(t), has been determined for their loop-top X-ray kernels. The time variation of E_H(t), together with the temperature–density diagnostic diagrams, have been used to explain the large value of the time interval, Δ t. The main point is that for these flares the heating function E_H(t) decreases so slowly after the temperature maximum, that for the long time, Δ t, the energy flux reaching flare foot points is sufficient to maintain significant chromospheric evaporation. Investigation of the flare evolution in the temperature–density diagnostic diagrams allowed us to work out a new method of determination of the density for flare kernels. This method can be applied to all the kernels for which their altitudes can be estimated. The advantage of this method is that for the density determination it is not necessary to assume what is the extension of the emitting plasma along the line of sight.