Reanalysis of the Historic AFTAC Bolide Infrasound Database

We have recently digitized and partially reanalyzed the historic bolide infrasonic database. These 10 events were originally detected by the U.S. Air Force Technical Applications Center (AFTAC) from ∼1960 to 1974. In this paper we present the first preliminary reanalysis results for two of the 10 bolide events, namely the Revelstoke bolide of 3/31/1965 as well as the Prince Edward Islands (P.E.I). S. African bolide of 8/03/1963, which were among the largest bolides detected during this time period. These bolides have been investigated initially since they are most likely to have had a significant effect on the computed global influx rate of ReVelle (Global Infrasonic Monitoring of Large Bolides, pp 483–490, 2001) as indicated in Brown et al. (Nature, 420:314–316, 2002). We are in the process of recomputing all relevant infrasonic propagation quantities such as plane wave back azimuth, signal velocities, power spectra, spectrograms, as well as energy estimates using multiple techniques. In a future paper we will present a complete digital reanalysis of the AFTAC bolide infrasonic data and its final resulting global bolide influx implications.     

Monte Carlo Simulation of Solar Active-Region Energy

A Monte Carlo approach to solving a stochastic-jump transition model for active-region energy (Wheatland and Glukhov: Astrophys. J. 494, 858, 1998; Wheatland: Astrophys. J. 679, 1621, 2008) is described. The new method numerically solves the stochastic differential equation describing the model, rather than the equivalent master equation. This has the advantages of allowing more efficient numerical solution, the modeling of time-dependent situations, and investigation of details of event statistics. The Monte Carlo approach is illustrated by application to a Gaussian test case and to the class of flare-like models presented in Wheatland (Astrophys. J. 679, 1621, 2008), which are steady-state models with constant rates of energy supply, and power-law distributed jump transition rates. These models have two free parameters: an index (δ), which defines the dependence of the jump transition rates on active-region energy, and a nondimensional ratio ( ) of total flaring rate to rate of energy supply. For the nondimensional mean energy of the active-region satisfies , resulting in a power-law distribution of flare events over many decades of energy. The Monte Carlo method is used to explore the behavior of the waiting-time distributions for the flare-like models. The models with δ≠0 are found to have waiting times that depart significantly from simple Poisson behavior when . The original model from Wheatland and Glukhov (Astrophys. J. 494, 858, 1998), with δ=0 (i.e., no dependence of transition rates on active-region energy), is identified as being most consistent with observed flare statistics.     

Recent Advances in Bolide Entry Modeling: A Bolide Potpourri

In this paper, we will review recent research on numerous aspects of bolide entry into a planetary atmosphere, including such topics as the entry dynamics, energetics, ablation, deceleration, fragmentation, luminosity, mechanical wave generation processes, a total (panchromatic) power budget including differential and integral efficiencies versus time, etc. Fragmentation, triggered by stagnation pressures exceeding the bolide breaking strength, has been subsequently included in either a collective or non-collective wake behavior limit. We have also utilized the differential panchromatic luminous efficiency of ReVelle and Ceplecha (2002) to compute bolide luminosity. In addition we also introduce the concept of the differential and integral acoustic/infrasonic efficiency and generalized it to the case of mechanical wave efficiency including internal atmospheric gravity waves generated during entry. Unlike the other efficiencies which are assumed to be a constant multiple of the luminous efficiency, the acoustic efficiency is calculated independently using a “first principles” approach. All of these topics have been pursued using either a homogeneous or a porous meteoroid model with great success. As a direct result, porosity seems to be a rather good possibility for explaining anomalous meteoroid behavior in the atmosphere. Invited Paper Presented at Meteoroids 2004; Presented at University of Western Ontario, London, Ontario, Canada, August 16–20, 2004     

A New Look at Mode Conversion in a Stratified Isothermal Atmosphere

Recent numerical investigations of wave propagation near coronal magnetic null points (McLaughlin and Hood: Astron. Astrophys. 459, 641, 2006) have indicated how a fast MHD wave partially converts into a slow MHD wave as the disturbance passes from a low-β plasma to a high-β plasma. This is a complex process and a clear understanding of the conversion mechanism requires the detailed investigation of a simpler model. An investigation of mode conversion in a stratified, isothermal atmosphere with a uniform, vertical magnetic field is carried out, both numerically and analytically. In contrast to previous investigations of upward-propagating waves (Zhugzhda and Dzhalilov: Astron. Astrophys. 112, 16, 1982a; Cally: Astrophys. J. 548, 473, 2001), this paper studies the downward propagation of waves from a low-β to high-β environment. A simple expression for the amplitude of the transmitted wave is compared with the numerical solution.     

Recent Advances in Bolide Entry Modeling:A Bolide Potpourri*

In this paper, we will review recent research on numerous aspects of bolide entry into a planetary atmosphere, including such topics as the entry dynamics, energetics, ablation, deceleration, fragmentation, luminosity, mechanical wave generation processes, a total (panchromatic) power budget including differential and integral efficiencies vs. time, etc. Fragmentation, triggered by stagnation pressures exceeding the bolide breaking strength, has been included with subsequent wake behavior in either a collective or non-collective behavior limit. We have also utilized the differential panchromatic luminous efficiency of ReVelle and Ceplecha (2002c, Proceedings of Asteroids, Comets, Meteors ACM 2002, 29 July–2August, 285–288) to compute bolide luminosity. In addition we also introduce the concept of the differential and integral acoustic/infrasonic efficiency and generalized it to the case of mechanical wave efficiency including internal atmospheric gravity waves generated during entry. Unlike the other efficiencies which are assumed to be a constant multiple of the luminous efficiency, the acoustic efficiency is calculated independently using a 'first principles' approach. All of these topics have been pursued using either a homogeneous or a porous meteoroid model with great success. As a direct result, porosity seems to be a rather good possibility for explaining anomalous meteoroid behavior in the atmosphere.     

Comments on “Effects of Strong Regular Refraction in the Solar Radio Pulse Structure in Spike Events” by Afanasiev and Altyntsev and “Mathematical Modeling of the Formation of Type IIId Solar Decameter Radio Bursts with Echo Components” by Afanasiev

Presented are some comments on the papers by Afanasiev and Altyntsev (Solar Phys. 234, 151, 2006) and by Afanasiev (Solar Phys. 238, 87, 2006) devoted to the study of the influence of solar corona inhomogeneities on the form of radio bursts. It is pointed out that in these papers incorrect use is made of methods used previously in investigations into radio wave propagation through a randomly inhomogeneous ionosphere.     

Electron Densities in Quiescent Prominences Derived from Eclipse Observations

We develop a diagnostic tool for determination of the electron densities in solar prominences using eclipse data. The method is based on analysis of the hydrogen Balmer-line intensities (namely Hα and Hβ) and the white-light emission due to Thomson scattering on the prominence electrons. Our approach represents a generalization of the ratio method already used by Koutchmy, Lebecq, and Stellmacher (Astron. Astrophys. 119, 261, 1983). In this paper we use an extended grid of non-LTE prominence models of Gouttebroze, Heinzel, and Vial (Astron. Astrophys. Suppl. Ser. 99, 513, 1993) and derive various useful relations between prominence radiation properties and electron densities. Simultaneously, an effective geometrical thickness of the prominence can also be obtained. As an example we apply our general technique to original eclipse data of Koutchmy, Lebecq, and Stellmacher (Astron. Astrophys. 119, 261, 1983). Finally, we use our results to determine the color of prominences as it should be seen during total eclipses.     

Genesis—An artificial,low velocity “meteor” fall and recovery: September 8, 2004

Abstract— On September 8, 2004, Genesis, a manmade space capsule, plummeted to Earth after almost three years in space. A ground‐based infrasound array was deployed to Wendover, Nevada, to measure the “hypersonic boom” from the reentry, since the expected initial reentry speed of the body was about 11 km/sec. Due to the complete failure of its dual parachute system, we had a unique opportunity to assess the degree of reliability of our previously developed relations for natural meteors and bolides to analyze this well‐characterized manmade body. At ?20–50 km from the nominal trajectory, we succeeded in recording over two minutes of infrasonic signals from Genesis. Here we report on subsequent analyses of these infrasonic data, including an assessment of the expected entry characteristics on the basis of a bolide/meteor/fireball entry model specifically adapted to modeling reentering manmade objects. From these simulations, we were able to evaluate the line source blast wave relaxation radius, the differential acoustic efficiency, etc., to compute an approximate total power balance during entry. Next, we analyzed the detailed signals arriving from Genesis using a numerical, signal detection and wave processing software package (Matseis/Infra_Tool). We established the initial and subsequent arrivals and evaluated its plane wave back azimuths and elevation arrival angles and the degree of maximum, pair‐wise cross‐correlation, its power spectrum, spectrogram analysis, standard seismic f‐k analysis, etc. From the associated entry parameters, we computed the kinetic energy density conservation properties for the propagating line source blast waves and compared these predictions against observed ground‐based infrasound amplitude and wave period data as a function of range. We discovered that previously computed differential acoustic efficiencies were unreliable at Mach numbers below about 10. This is because we had assumed that a line source explosion was applicable, whereas at very low Mach numbers, typical of recovered meteorites, the detailed source characteristics are closer to those of supersonic objects. When corrections for these unphysical, very high efficiencies were made, agreement between theory and observations improved. We also made an assessment for the energy of the blast wave source from the ground‐based infrasound data using several other techniques that were also adapted from previous bolide studies. Finally, we made a top‐down‐bottom‐up assessment of the line source wave normals propagating via refraction downward into the complex middle atmospheric environment. This assessment proved to be generally consistent with the digital signal processing analysis and with the observed time delay between the known Genesis reentry and the infrasonic observations.     

Fragmentation model of meteoroid motion,mass loss,and radiation in the atmosphere

Abstract— We present the basic differential equations of meteor physics (the single body equations). We solve them numerically including two possible types of fragmentation: into large pieces and into a cluster of small fragments. We have written a Fortran code that computes the motion, ablation and light intensity of a meteoroid at chosen heights, and allows for the ablation and shape density coefficients σ and K, as well as the luminous efficiency τ, to be variable with height/time. We calibrated our fragmentation model (FM) by the best fit to observational values for the motion, ablation, radiation, fragmentation and the terminal masses (recovered meteorites) for the Lost City bolide. The FM can also handle multiple and overlapping meteor flares. We separately define both the apparent and intrinsic values of σ, K, and τ. We present in this paper values of the intrinsic luminous efficiency as function of velocity, mass, and normalized air density. Detailed results from the successful application of the FM to the Lost City, Innisfree, and Benesov bolides are also presented. Results of applying the FM to 15 bolides with very precise observational data are presented in a survey mode (Table 7). Standard deviations of applying our FM to all these events correspond to the precision of the observed values. Typical values of the intrinsic ablation coefficient are low, mostly in the range from 0.004 to 0.008 s² km^?2, and do not depend on the bolide type. The apparent ablation coefficients reflect the process of fragmentation. The bolide types indicate severity of the fragmentation process. The large differences of the “dynamic” and “photometric” mass from numerous earlier studies are completely explained by our FM. The fragmentation processes cannot be modeled simply by large values of the apparent ablation coefficient and of the apparent luminous efficiency. Moreover, our new FM can also well explain the radiation and full dynamics of very fast meteoroids at heights from 200 km to 130 km.     

Oscillatory Response of the 3D Solar Atmosphere to the Leakage of Photospheric Motion

The direct propagation of acoustic waves, driven harmonically at the solar photosphere, into the three-dimensional solar atmosphere is examined numerically in the framework of ideal magnetohydrodynamics. It is of particular interest to study the leakage of 5-minute global solar acoustic oscillations into the upper, gravitationally stratified and magnetised atmosphere, where the modelled solar atmosphere possesses realistic temperature and density stratification. This work aims to complement and bring further into the 3D domain our previous efforts (by Erdélyi et al., 2007, Astron. Astrophys. 467, 1299) on the leakage of photospheric motions and running magnetic-field-aligned waves excited by these global oscillations. The constructed model atmosphere, most suitable perhaps for quiet Sun regions, is a VAL IIIC derivative in which a uniform magnetic field is embedded. The response of the atmosphere to a range of periodic velocity drivers is numerically investigated in the hydrodynamic and magnetohydrodynamic approximations. Among others the following results are discussed in detail: i) High-frequency waves are shown to propagate from the lower atmosphere across the transition region, experiencing relatively low reflection, and transmitting most of their energy into the corona; ii) the thin transition region becomes a wave guide for horizontally propagating surface waves for a wide range of driver periods, and particularly at those periods that support chromospheric standing waves; iii) the magnetic field acts as a waveguide for both high- and low-frequency waves originating from the photosphere and propagating through the transition region into the solar corona. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Polarimetric and Photometric Phase Effects Observed on Transneptunian Object (29981) 1999 TD10

The Kuiper-Belt Object (29981) 1999 TD₁₀, classified as a Scattered-Disk Object, has been observed at three different phase angles with the ESO 8.2-m VLT and FORS 1 instrument in polarimetric mode in November and December 2003. These observations have been used to compute the Stokes parameter q, which represents the linear polarization degree. We have also used the previously published photometric observations to improve the R-band phase function. The main conclusions are as follows: (i) a negative linear polarization degree decreasing with phase angle α up to, at least, α=3°, (ii) for α=3°, (iii) a possible color effect between the R and V band, the polarization degree being more negative in R. The R-band polarimetric observations can be explained by the coherent-backscattering mechanism and fitted by a two-component Rayleigh-scatterer model for a spherical small body. The rotation period of 15.382±0.001 h published by Mueller et al. (2004, Icarus 171, 506–515) and Choi et al. (2003, Icarus 165, 101–111) is confirmed. The R-band phase curve provides H=8.35±0.02 and G=−0.25±0.022 parameters with the IAU H–G formalism.Based on observations obtained at the Cerro Paranal observatory of the European Southern Observatory (ESO) in Chile.     

Neutrino radiation of the AGN black holes

In the framework of ‘microscopic’ theory of black holes (J. Phys. Soc. Jpn. Suppl. B 70, 84, 2001; Astrophys. USSR 4, 659, 1996; 35, 335, 1991, 33, 143, 1990, 31, 345, 1989a; Astrophys. Space Sci. 1, 1992; Dokl. Akad. Nauk USSR 309, 97, 1989b), and references therein, we address the ‘pre-radiation time’ (PRT) of neutrinos from black holes, which implies the lapse of time from black hole’s birth till radiation of an extremely high energy neutrinos. For post-PRT lifetime, the black hole no longer holds as a region of spacetime that cannot communicate with the external universe. We study main features of spherical accretion onto central BH and infer a mass accretion rate onto it, and, further, calculate the resulting PRT versus bolometric luminosity due to accretion onto black hole. We estimate the PRTs of AGN black holes, with the well-determined masses and bolometric luminosities, collected from the literature by Woo Jong-Hak and Urry (Astrophys. J. 579, 530, 2002) on which this paper is partially based. The simulations for the black holes of masses M _BH ≃(1.1⋅10⁶ ÷4.2⋅10⁹) M _⊙ give the values of PRTs varying in the range of about T _BH ≃(4.3⋅10⁵ ÷5.6⋅10¹¹) yr. The derived PRTs for the 60 AGN black holes are longer than the age of the universe (∼13.7 Gyr) favored today. At present, some of remaining 174 BHs may radiate neutrinos. However, these results would be underestimated if the reservoir of gas for accretion in the galaxy center is quite modest, and no obvious way to feed the BHs with substantial accretion.     

Study on Two Methods for Nonlinear Force-Free Extrapolation Based on Semi-Analytical Field

In this paper, two semi-analytical solutions of force-free fields (Low and Lou, Astrophys. J. 352, 343, 1990) have been used to test two nonlinear force-free extrapolation methods. One is the boundary integral equation (BIE) method developed by Yan and Sakurai (Solar Phys. 195, 89, 2000), and the other is the approximate vertical integration (AVI) method developed by Song et al. (Astrophys. J. 649, 1084, 2006). Some improvements have been made to the AVI method to avoid the singular points in the process of calculation. It is found that the correlation coefficients between the first semi-analytical field and extrapolated field using the BIE method, and also that obtained by the improved AVI method, are greater than 90% below a height 10 of the 64×64 lower boundary. For the second semi-analytical field, these correlation coefficients are greater than 80% below the same relative height. Although differences between the semi-analytical solutions and the extrapolated fields exist for both the BIE and AVI methods, these two methods can give reliable results for heights of about 15% of the extent of the lower boundary.     

On Signatures of Twisted Magnetic Flux Tube Emergence

Recent studies of NOAA active region 10953, by Okamoto et al. (Astrophys. J. Lett. 673, 215, 2008; Astrophys. J. 697, 913, 2009), have interpreted photospheric observations of changing widths of the polarities and reversal of the horizontal magnetic field component as signatures of the emergence of a twisted flux tube within the active region and along its internal polarity inversion line (PIL). A filament is observed along the PIL and the active region is assumed to have an arcade structure. To investigate this scenario, MacTaggart and Hood (Astrophys. J. Lett. 716, 219, 2010) constructed a dynamic flux emergence model of a twisted cylinder emerging into an overlying arcade. The photospheric signatures observed by Okamoto et al. (2008, 2009) are present in the model although their underlying physical mechanisms differ. The model also produces two additional signatures that can be verified by the observations. The first is an increase in the unsigned magnetic flux in the photosphere at either side of the PIL. The second is the behaviour of characteristic photospheric flow profiles associated with twisted flux tube emergence. We look for these two signatures in AR 10953 and find negative results for the emergence of a twisted flux tube along the PIL. Instead, we interpret the photospheric behaviour along the PIL to be indicative of photospheric magnetic cancellation driven by flows from the dominant sunspot. Although we argue against flux emergence within this particular region, the work demonstrates the important relationship between theory and observations for the successful discovery and interpretation of signatures of flux emergence.     

Constructing Semi-Empirical Sunspot Models for Helioseismology

One goal of helioseismology is to determine the subsurface structure of sunspots. In order to do so, it is important to understand first the near-surface effects of sunspots on solar waves, which are dominant. Here we construct simplified, cylindrically-symmetric sunspot models that are designed to capture the magnetic and thermodynamics effects coming from about 500 km below the quiet-Sun τ ₅₀₀₀=1 level to the lower chromosphere. We use a combination of existing semi-empirical models of sunspot thermodynamic structure (density, temperature, pressure): the umbral model of Maltby et al. (1986, Astrophys. J. 306, 284) and the penumbral model of Ding and Fang (1989, Astron. Astrophys. 225, 204). The OPAL equation-of-state tables are used to derive the sound-speed profile. We smoothly merge the near-surface properties to the quiet-Sun values about 1 Mm below the surface. The umbral and penumbral radii are free parameters. The magnetic field is added to the thermodynamic structure, without requiring magnetostatic equilibrium. The vertical component of the magnetic field is assumed to have a Gaussian horizontal profile, with a maximum surface field strength fixed by surface observations. The full magnetic-field vector is solenoidal and determined by the on-axis vertical field, which, at the surface, is chosen such that the field inclination is 45° at the umbral – penumbral boundary. We construct a particular sunspot model based on SOHO/MDI observations of the sunspot in active region NOAA 9787. The helioseismic signature of the model sunspot is studied using numerical simulations of the propagation of f, p ₁, and p ₂ wave packets. These simulations are compared against cross-covariances of the observed wave field. We find that the sunspot model gives a helioseismic signature that is similar to the observations.     

Numerical Simulation of a Solar Active Region. I: Bastille Day Flare

We present three-dimensional unsteady modeling and numerical simulations of a coronal active region, carried out within the compressible single-fluid MHD approximation. We focus on AR 9077 on 14 July 2000, and the triggering of the X5.7 GOES X-ray class “Bastille Day” flare. We simulate only the lower corona, although we include a virtual photosphere and chromosphere below. The boundary conditions at the base of this layer are set using temperature maps from line intensities and line-of-sight magnetograms (SOHO/MDI). From the latter, we generate vector magnetograms using the force-free approximation; these vector magnetograms are then used to produce the boundary condition on the velocity field using a minimum energy principle (Longcope, Astrophys. J. 612, 1181, 2004). The reconnection process is modeled through a dynamical hyper-resistivity which is activated when the current exceeds a critical value (Klimas et al., J. Geophys. Res. 109, 2218, 2004). Comparing the time series of X-ray fluxes recorded by GOES with modeled time series of various mean physical variables such as current density, Poynting energy flux, or radiative loss inside the active region, we can demonstrate that the model properly captures the evolution of an active region over a day and, in particular, is able to explain the initiation of the flare at the observed time.     

Comparison of the Characteristics of Magnetic Clouds and Magnetic Cloud-Like Structures for the Events of 1995 – 2003

Using nine years of solar wind plasma and magnetic field data from the Wind mission, we investigated the characteristics of both magnetic clouds (MCs) and magnetic cloud-like structures (MCLs) during 1995 – 2003. A MCL structure is an event that is identified by an automatic scheme (Lepping, Wu, and Berdichevsky, Ann. Geophys. 23, 2687, 2005) with the same criteria as for a MC, but it is not usually identifiable as a flux rope by using the MC (Burlaga et al., J. Geophys. Res. 86, 6673, 1981) fitting model developed by Lepping, Jones, and Burlaga (Geophys. Res. Lett. 95(11), 957, 1990). The average occurrence rate is 9.5 for MCs and 13.6 for MCLs per year for the overall period of interest, and there were 82 MCs and 122 MCLs identified during this period. The characteristics of MCs and MCL structures are as follows: (1) The average duration, Δt, of MCs is 21.1 h, which is 40% longer than that for MCLs (Δt=15 h); (2) the average (minimum B _z found in MC/MCL measured in geocentric solar ecliptic coordinates) is −10.2 nT for MCs and −6 nT for MCLs; (3) the average Dst_min (minimum Dst caused by MCs/MCLs) is −82 nT for MCs and −37 nT for MCLs; (4) the average solar wind velocity is 453 km s⁻¹ for MCs and 413 km s⁻¹ for MCLs; (5) the average thermal speed is 24.6 km s⁻¹ for MCs and 27.7 km s⁻¹ for MCLs; (6) the average magnetic field intensity is 12.7 nT for MCs and 9.8 nT for MCLs; (7) the average solar wind density is 9.4 cm⁻³ for MCs and 6.3 cm⁻³ for MCLs; and (8) a MC is one of the most important interplanetary structures capable of causing severe geomagnetic storms. The longer duration, more intense magnetic field and higher solar wind speed of MCs, compared to those properties of the MCLs, are very likely the major reasons for MCs generally causing more severe geomagnetic storms than MCLs. But the fact that a MC is an important interplanetary structure with respect to geomagnetic storms is not new (e.g., Zhang and Burlaga, J. Geophys. Res. 93, 2511, 1988; Bothmer, ESA SP-535, 419, 2003).     

Coronal Shock Waves,EUV Waves,and Their Relation to CMEs. III. Shock-Associated CME/EUV Wave in an Event with a Two-Component EUV Transient

On 17 January 2010, STEREO-B observed in extreme ultraviolet (EUV) and white light a large-scale dome-shaped expanding coronal transient with perfectly connected off-limb and on-disk signatures. Veronig et al. (Astrophys. J. Lett. 716, L57, 2010) concluded that the dome was formed by a weak shock wave. We have revealed two EUV components, one of which corresponded to this transient. All of its properties found from EUV, white light, and a metric type II burst match expectations for a freely expanding coronal shock wave, including correspondence with the fast-mode speed distribution, while the transient sweeping over the solar surface had a speed typical of EUV waves. The shock wave was presumably excited by an abrupt filament eruption. Both a weak shock approximation and a power-law fit match kinematics of the transient near the Sun. Moreover, the power-law fit matches the expansion of the CME leading edge up to 24 solar radii. The second, quasi-stationary EUV component near the dimming was presumably associated with a stretched CME structure; no indications of opening magnetic fields have been detected far from the eruption region.     

Radio Emission from Masuda Sources

We note that different models, providing comparably good interpretation of the hard X-ray properties of so-called Masuda sources, can make distinctly different predictions for the radio emission produced at the Masuda source by the same population of accelerated electrons. Accordingly, we calculate the radio emission within a few competing models, i.e., those involving magnetic, turbulent, and collisional trapping of the fast electrons in the coronal source. We show that even available incomplete radio observations of the classical Masuda event and a Masuda-like event on 31 December 2007, recently reported by Krucker et al. (Astrophys. J. 714, 1108, 2010) are highly valuable in restricting the physical model of the source. Furthermore, our study proposes that combination of more complete high-resolution X-ray and radio observations can allow unambiguous distinction between the competing Masuda source models.     

An Evaluation of Possible Mechanisms for Anomalous Resistivity in the Solar Corona

A wide variety of transient events in the solar corona seem to require explanations that invoke fast reconnection. Theoretical models explaining fast reconnection often rely on enhanced resistivity. We start with data derived from observed reconnection rates in solar flares and seek to reconcile them with the chaos-induced resistivity model of Numata and Yoshida (Phys. Rev. Lett. 88, 045003, 2002) and with resistivity arising out of the kinetic Alfvén wave (KAW) instability. We find that the resistivities arising from either of these mechanisms, when localized over length scales of the order of an ion skin depth, are capable of explaining the observationally mandated Lundquist numbers.