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UGC 11429 . The very peculiar velocity field of this galaxy, which is in pair, displays a concave curvature towards the South on both sides of the galaxy. Thus, the residual velocity field shows a very high dispersion and a signature typical of a rotation curve having a rotation center abnormally displaced toward the S... |
(van der Kruit & Allen, 1978 . This is obviously not the case from the morphology. UGC 11861 . The morphological position angle of this galaxy is difficult to estimate due to its “Magellanic” structure. |
UGC 11909 . No rotation curve has been computed because of its high inclination (90 ). UGC 11951 . The rotation curve published in Paper II is incorrect due to a typo in the value of the position angle of the major axis. |
UGC 12060 . This galaxy is irregular, barred and has a low surface brightness. These features make the morphological position angle determination difficult. |
UGC 12276 . The previous data reduction (Paper IV) missed a large part of the velocity field. UGC 12276c . The total H [MATH] diameter of the galaxy ( [MATH] 8″) is not much larger than the seeing spot of the observations ( [MATH] 5″). Thus no rotation curve has been computed. |
UGC 12632 . The very high velocity bump on the blue side of the H [MATH] rotation curve is also visible in the HI data (Swaters, 1999 |
Appendix B Tables Appendix C [MATH] profiles Appendix D Individual maps and position-velocity diagrams Appendix E Rotation curves Appendix F Rotation curves tables |
# Source: arxiv 0808.0138 # Title: Subaru and Keck Observations of the Peculiar Type Ia Supernova 2006gz at Late Phases # Sections: all # Downloaded: 2026-03-02T07:58:57.835872+00:00 |
Subaru and Keck Observations of the Peculiar Type Ia Supernova 2006gz at Late Phases Abstract Recently, a few peculiar Type Ia supernovae (SNe) that show exceptionally large peak luminosity have been discovered. Their luminosity requires more than 1 M of 56 Ni ejected during the explosion, suggesting that they might ha... |
Subject headings: white dwarfs – radiative transfer – supernovae: individual (SN 2006gz) 1. INTRODUCTION There is general agreement that Type Ia supernovae (SNe Ia) are thermonuclear explosions of white dwarfs (WDs; e.g., Nomoto, Iwamoto, & Kishimoto 1997; Hillebrandt & Niemeyer 2000). Thanks to the uniformity of their... |
The progenitors of normal SNe Ia (Branch, Fisher, & Nugent 1993; Li et al. 2001) are believed to be WDs having nearly the Chandrasekhar mass (hereafter Ch-SN Ia and Ch-WD). The recent discovery of extremely luminous SNe Ia raises the possibility that not all SNe Ia originate from a single type of progenitor system. How... |
Mpc -1 [MATH] , flat universe). Assuming that this luminosity is powered by the decay chain 56 Ni [MATH] 56 Co [MATH] 56 Fe as in other SNe Ia, they estimated [MATH] (hereafter [MATH] is the mass of |
56 Ni produced and ejected during the explosion). Combining this with other elements whose existence in the ejecta is evident from the spectra, the ejecta and progenitor masses should exceed the Chandrasekhar limit of a nonrotating WD. This was the first observationally based suggestion of an SN Ia from a super-Chandra... |
All of the available data for these SNe Ia are only for the early phases, [MATH] d (hereafter [MATH] is the time since the explosion). At later times, SNe Ia enter the nebular phase, when the Fe-rich innermost ejecta, which are hidden at early phases, can be directly observed (e.g., Axelrod 1988). In this paper, we rep... |
SN 2006gz taken with the 8.2-m Subaru telescope and the 10-m Keck I telescope. In §2 we present the observations and data reduction. Results are shown in §4, along with some comparisons to model calculations (§3). SN 2006gz is intrinsically different from normal SNe Ia. However, our results are not readily interpretabl... |
2. OBSERVATIONS AND DATA REDUCTION Spectroscopy and imaging of SN 2006gz were performed on 2007 September 18 (UT dates are used throughout this paper) with the 8.2-m Subaru telescope equipped with the Faint Object Camera and Spectrograph (FOCAS; Kashikawa et al. 2002). The epoch corresponds to [MATH] d, where [MATH] is... |
[MATH] , respectively. The same field was imaged again on 2007 November 6 by the Subaru/FOCAS ( [MATH] d), although the seeing was not good (FWHM [MATH] ). |
For the Subaru spectroscopy on September 18, we took three spectra with exposure time 1200 s each. We used the [MATH] -wide slit and the R300 grism with the O58 filter (wavelength coverage 5800–10200 Å), the B300 grism with the Y47 filter (4700–9000 Å), and the B300 grism with no filter (3800–7200 Å), in the three sepa... |
Subaru/FOCAS uses an atmospheric dispersion corrector (ADC). Its performance is such that the chromatic elongation due to atmospheric dispersion (Filippenko 1982) is less than [MATH] within the range 3500–11000 Å at altitudes of 30–90 , so the atmospheric dispersion should be negligible regardless of the airmass and th... |
The total exposure time for imaging was 60 s for each of [MATH] [MATH] and [MATH] on September 18, 555 s for [MATH] and 645 s for [MATH] on October 14, and 1000 s for [MATH] on November 6. We obtained images of standard stars (Landolt 1992) near SA98-634 on September 18 and around PG0231+051 on November 6 for photometr... |
In the September Subaru images the SN was not detected. We obtained an upper limit for the SN luminosity as follows. First, the magnitude |
[MATH] which results in 1 photon count per second (ADU) was derived for each band. Then we obtained the sky count [MATH] (corresponding to the sky magnitude [MATH] ) and the dispersion ( [MATH] ) around the SN position. The [MATH] magnitude at the detection limit is calculated as |
[EQUATION] Adopting [MATH] for [MATH] binned images (i.e., the pixel size is nearly equal to the seeing), we estimated the limiting magnitude in each band as [MATH] [MATH] , and [MATH] mag. |
In October, the SN was marginally detected in both the [MATH] and [MATH] Keck images (Fig. 1). Since SN 2006gz was not readily identified in the late-time images, we checked the position of the SN using the stacked [MATH] -band Keck image (with a total exposure time of 555 s). Astrometric transformation between the dis... |
Figure 1 shows a [MATH] section of the LRIS image centered on SN 2006gz. The black circle has a radius of 10 pixels, which is much bigger than the astrometric transformation uncertainty (0.2 pixel), and is used for clarity in the figure. At the center of the circle, a faint stellar source is seen superimposed on some e... |
The photometric reduction was performed using the IRAF package DAOPHOT. The SN was detected by the automatic star detection routine DAOFIND, and then the photometry was performed via PSF fitting. We obtain the [MATH] magnitude of the SN using the [MATH] magnitude of field stars derived from the September Subaru image. ... |
In November the SN was not detected in the Subaru images. Because of the mediocre seeing, we did not obtain a meaningful [MATH] limit: |
[MATH] mag. 3. SN Ia MODELS To quantify the observational results, we have constructed four SN Ia models, based on the W7 model of Nomoto, Thielemann, & Yokoi (1984), which reproduces the basic observational features of normal SNe Ia (Branch et al. 1985). Our model contains the following five parameters (see also Howel... |
[MATH] (mass fraction of electron capture Fe-peak elements, e.g., 54 Fe, 56 Fe, 58 Ni), [MATH] (mass fraction of 56 Ni), and [MATH] (mass fraction of partially burned intermediate-mass elements). The kinetic energy of the ejecta [MATH] ) is given as a function of these parameters, as this is the nuclear energy generati... |
[MATH] (progenitor WD mass), [MATH] (mass of 56 Ni synthesized at the explosion), and [MATH] (kinetic energy of the expanding ejecta). |
For these models, we compute bolometric light curves using a one-dimensional Monte-Carlo radiation transport code (Cappellaro et al. 1997; Maeda et al. 2003) with the phenomenological opacity description for optical photons ( [MATH] ) given by Mazzali et al. (2001a), which crudely takes into account the largest contrib... |
-1 , a value that explains the slightly faster decline of late-time light curves of normal SNe Ia by increasing the fraction of escaping positrons (Cappellaro et al. 1997). |
Synthetic nebular spectra are also computed at [MATH] d (i.e., Subaru/FOCAS observation in September), where [MATH] is obtained for each model by the light-curve calculations. Given the deposited luminosity, which is obtained in the same way as in the light-curve calculations, ionization-recombination equilibrium and r... |
4. RESULTS 4.1. Light Curve: Rapid Fading Figure 2 shows the results of our photometry as combined with the early-phase light curve of Hicken et al. (2007). The early post-maximum decline of SN 2006gz was slower in all bands than that of normal SNe Ia (Hicken et al. 2007), represented here by SN 2003du. However, this i... |
[MATH] upper limit in [MATH] and [MATH] (Subaru) show that eventually the visual luminosity of SN 2006gz declined more rapidly than that of other SNe Ia. Note that SN 2003du has a typical late-time light-curve shape, with a decline rate of 1.5–1.6 mag (100 d) -1 . There have been several SNe Ia whose decline is signifi... |
The September Subaru photometry ( [MATH] d), [MATH] mag, is consistent with the October Keck detection ( [MATH] d) of SN 2006gz at |
[MATH] mag. The most likely magnitude at [MATH] d is [MATH] [MATH] , and [MATH] mag assuming that the decline rate between these two epochs follows the |
56 Ni heating model (see Table 4 for the model prediction). Figure 3 shows the synthetic bolometric light curves of the four models as compared with the observed [MATH] -band light curve. Table 4 summarizes the synthetic multi-band magnitudes as derived from the model spectra. The late-time bolometric correction is [MA... |
Figure 4 shows the synthetic bolometric light curves of the four models as compared with the observationally derived bolometric light curve of SN 2006gz [with [MATH] [MATH] mag, and [MATH] mag]. The models with [MATH] 56 Ni) = 1 M reproduce the peak magnitude fairly well. The behavior before the peak (except SW7) is ve... |
At late epochs, however, the models are more than 1 mag brighter than the observations, with the discrepancy reaching [MATH] mag for SupCh2 and [MATH] mag for SupCh3 in the [MATH] band, where the models predict strong emission lines (see §4.2). Indeed, only model SW7 is marginally consistent with the late-time photomet... |
The failure of the SupCh models stems from the larger binding energy of a WD and the higher density. The peak date ( [MATH] measured from the explosion date and the peak luminosity ( [MATH] ) are roughly estimated by the following relations (e.g., Arnett 1982): |
[EQUATION] Here the subscripts [MATH] and [MATH] mean that these values are expressed in units of M and [MATH] ergs, respectively. The optical depth to [MATH] -rays from the 56 Co decay at late epochs ( [MATH] ) is expressed as follows (e.g., Clocchiatti & Wheeler 1997; Maeda et al. 2003): |
[EQUATION] The luminosity at [MATH] [MATH] ) is then estimated as [EQUATION] where the factor 0.035 accounts for the positron contribution to the heating, with [MATH] being the fraction of positrons trapped within the ejecta ( [MATH] in usual situations). Using these expressions and values listed in Table 3, the expect... |
Other model-independent constraints on [MATH] can be obtained considering the positron channel. Omitting the [MATH] term from eq. (5), we obtain an upper limit on [MATH] |
from the requirement that this positron luminosity should be below the observed luminosity (Fig. 3): [EQUATION] Here we adopted [MATH] mag, a typical value in the model spectrum synthesis calculations. |
4.2. Spectrum: Missing [Fe II] and [Fe III] in the Blue Figure 5 shows the late-time spectrum of SN 2006gz and the comparison with spectra of other SNe Ia. In SN 2006gz, the emissions at |
[MATH] 4700 Å ([Fe II] [MATH] 4814, 4890, 4905; [Fe III] [MATH] 4858, 4701) and at [MATH] 5200 Å ([Fe II] [MATH] 5159, 5262) are extremely weak or undetected. The only confirmed detection is at [MATH] 7200–7300 Å, which is interpreted as the blend of [Fe II] [MATH] 7151, 7171, 7388, 7452 in SNe Ia. This feature may als... |
Indeed, in the SUSPECT database we found only one example of a SN Ia that probably shows a feature at [MATH] 7200–7300 Å as strong as the [Fe II] and [Fe III] in the blue. This is the underluminous SN 1991bg (Filippenko et al. 1992), with [MATH] (Mazzali et al. 1997). Thus, SN 2006gz does not appear to follow the behav... |
Figure 6 shows the synthetic spectra computed for the four models. There is a tendency for more-massive models to show a weaker flux in the [Fe II]–[Fe III] emission at [MATH] 5200 Å relative to the [Fe II] line near 7200 Å. An important quantity to characterize the relative line strengths is the ratio of density to he... |
5. DISCUSSION AND CONCLUSIONS We have presented late-time photometry and spectroscopy of SN 2006gz obtained with the Subaru and Keck I telescopes. These are the first late-time observational data for an SN Ia that was claimed to be overluminous at early phases. Such SNe have been suggested to be the explosions of SupCh... |
The spectrum is characterized by the weakness of the [Fe II] and [Fe III] lines in the blue ( [MATH] Å) relative to emission lines in the red (either [Fe II] or [Ca II] at [MATH] Å). This does not fit into the sequence of the late-time spectral behavior of normal SNe Ia, confirming that SN 2006gz belongs to a different... |
band. The SupCh2 model (with a 2 M WD progenitor synthesizing 1 M of 56 Ni) is in good agreement with the early-phase bolometric light curve (§4.1; but see §5.1), although it predicts a higher late-time luminosity than the Ch-SN Ia models because of the larger |
[MATH] and [MATH] -ray deposition rate. The luminosity of Sup-Ch models exceeds that observed by more than 2 mag in the [MATH] band. Furthermore, one derives [MATH] , under the usual assumptions that the bulk of the deposited radioactive luminosity emerges at visual wavelengths, and that positrons are almost fully trap... |
5.1. Reconsidering the Super Chandrasekhar Model? We should first mention that the peak luminosity of SN 2006gz derived by Hicken et al. (2007) involves large uncertainty, as the host-galaxy extinction is not well constrained. If the host extinction is negligible, the peak luminosity of SN 2006gz is close to that of no... |
From the late-time data, we find that [MATH] is [MATH] and [MATH] mag larger (that is, fainter) than expected from the SW7 [MATH] ) and SupCh2 ( [MATH] models, respectively. This would imply that 0.1–0.2 M of |
56 Ni powers the late-time emission, smaller than the value expected from the light-curve peak ( [MATH] by a factor of [MATH] . Such a large discrepancy cannot be attributed solely to the effect of viewing angle, even if SN 2006gz was a result of an extremely off-axis explosion (see, e.g., Sim et al. 2007 for the effec... |
Alternatively, one may hypothesize that the energy source at early times was not 56 Ni/Co/Fe decay. Strong circumstellar interaction as seen in a peculiar class of SNe Ia (i.e., SNe Ia/IIa 2002ic-like events: Hamuy et al. 2003; Deng et al. 2004; Wang et al. 2004) is not favored, because of the lack of evidence for inte... |
5.2. Positron Escape, Infrared Catastrophe, or Dust Formation? If the early-phase emission is powered by [MATH] of 56 Ni, then one is left with the possibility that some mechanism, which is not at work in normal SNe Ia, must be affecting the late-time emission and the thermal conditions within the ejecta of SN 2006gz. |
One possibility is the escape of positrons produced by the 56 Co decay out of the SN ejecta. The issue has been comprehensively explored by Milne, The, & Leising (2001). They showed that a fraction of the positrons can escape for a radially combed and/or weak magnetic field, leading to the changing light curve at late ... |
[MATH] d, this effect can account for at most [MATH] mag, which is not large enough to completely remedy the present problem. Another possibility is the thermal catastrophe within the |
56 Ni-rich region, which shifts the bulk of the emission from optical to infrared wavelengths (Axelrod 1988). This so-called “infrared catastrophe” (IRC) is expected to take place after the temperature drops below a few 1000 K, depending on the electron density. Observationally, the IRC has not been clearly detected in... |
Finally, it may be possible that the visual light from the 56 Ni-rich region is converted to near-IR/mid-IR wavelengths by dust formed in the C+O-rich region. Before maximum light, SN 2006gz showed the strongest C lines of any SN Ia ever observed, with little evolution in the absorption velocity. This indicates that a ... |
The W7 model has [MATH] cm -3 at the inner edge of the C+O-rich region at 100 d after the explosion. The corresponding density in the SupCh models is a few times higher. Recently, Nozawa et al. (2008) theoretically investigated dust formation in SNe Ib. They found a large amount of carbon grain formation in the C-enhan... |
56 Ni, different oxygen mass fraction, etc.), should be investigated, as well as details of expected observational signatures during the dust formation. In this interpretation, a part of the outer Ca-rich region might be mixed with the C+O-rich region. It may partly explain the relative strength of the feature at [MATH... |
5.3. Future Observations The possible interpretations we listed above are only speculative, but they predict distinct observational signatures, to be tested in future overluminous SNe Ia. First, late-time spectroscopy of other potentially overluminous SNe Ia would be extremely useful to see whether SN 2006gz is special... |
Near-IR light curves could directly show the effects of the IRC and dust distinctly from other scenarios: we expect that a rapid increase in the near-IR brightness should occur simultaneously with a rapid decrease in the visual brightness, while other scenarios do not necessarily predict this behavior. |
A temporal sequence of optical spectra would also be highly useful. In the dust formation scenario, we may see a transient red continuum and emission-line shifts at intermediate phases, as was seen in the peculiar SN Ib 2006jc (Smith, Foley, & Filippenko 2008). |
Finally, the IRC and dust scenarios could be unambiguously distinguished with near-IR through mid-IR spectra. Blackbody radiation from the dust particles should be seen in the dust scenario, while line emission is the dominant cooling process in the IRC scenario. |
We thank the director of Subaru, Masahiko Hayashi, as well as Hiroshi Terada, for kindly allowing us to exchange observing time and targets in the Subaru proposal S07B-057 (PI: K.M.), making the SN 2006gz observations possible. The staffs at the Subaru and Keck Observatories are acknowledged for their excellent assista... |
# Source: arxiv 0808.0145 # Title: MHD mode conversion in a stratified atmosphere # Sections: all # Downloaded: 2026-03-02T07:58:59.156493+00:00 |
\pagerange 296–302 MHD mode conversion in a stratified atmosphere (2007; 10.1017 and in revised form ??) Abstract Mode conversion in the region where the sound and Alfvén speeds are equal is a complex process, which has been studied both analytically and numerically, and has been seen in observations. In order to furth... |
doi: 10.1017/S1743921308014993 keywords: Sun: oscillations, MHD, gravitational waves. Introduction Mode conversion is the process under which an incident wave may be wholly or partially converted into another wave mode, with the remainder of the original wave being transmitted through the plasma. This may occur where t... |
This problem has been investigated extensively in the past, many using analytical techniques. Zhugzhda (1979) Zhugzhda & Dzhalilov (1981) and Zhugzhda & Dzhalilov (1982) investigated the conversion of fast magnetoacoustic waves into slow magnetoacoustic waves as they propagate up through the solar atmosphere from high-... |
We also investigate the mode conversion problem analytically, although we combine this with numerical simulations. We look at a uniform background magnetic field, but, in contrast to the aforementioned work, we investigate downward propagation - so the wave is travelling from low- to high- [MATH] plasma (as shown in Fi... |
In Section the basic equations are set out, and we look at the characteristic wave behaviour in high- and low- [MATH] plasma. Two different situations are then examined: an isothermal atmosphere in Section , and a non-isothermal atmosphere in Section . Finally the conclusions are detailed in Section |
Basic Equations Throughout we use the standard, ideal MHD equations, linearised about the equilibrium [MATH] , and [MATH] ; where [MATH] and [MATH] may be defined as the scale height. So we have the equation of motion |
[EQUATION] the induction equation [EQUATION] the mass continuity equation [EQUATION] and the energy equation [EQUATION] where subscript zero denotes the equilibrium quantities and subscript one the perturbed quantities. In these equations [MATH] is the equilibrium magnetic field, and [MATH] and [MATH] are the equilibri... |
Under the assumption that the [MATH] -dependence is of the form [MATH] , where [MATH] isthe horizontal wavenumber, Equations ( ) – ( ) may be combined to form a pair of wave equations |
[EQUATION] [EQUATION] where [MATH] and [MATH] are the squared sound and Alfvén speeds respectively. These are in agreement with those discovered by Ferraro & Plumpton (1958) |
Examining these equations we can see that if the effects of gravity are negligible and the horizontal wavenumber is small, then the wave operators on the left-hand side are the same when [MATH] . At this point there is a resonance which allows the mode conversion process to occur. Note that when the horizontal wavenumb... |
We solve these equations numerically using the MacCormack finite difference scheme. This is a type of Lax-Wendroff, two-step, predictor-corrector method. We use backward differencing for the predictor steps and forward differencing for the corrector steps, thus ensuring that we have more accurate values on the upper bo... |
As the wave propagates across the [MATH] layer it is important to remember that the slow and fast waves have different properties above and below this region; Table identifies these. We are driving a slow wave in low- [MATH] plasma, the transmitted component of this wave will demonstrate the same characteristics in the... |
Isothermal Atmosphere To begin with we investigate an isothermal atmosphere, so the sound speed will remain constant while the Alfvén speed varies with height. |
3.1 Numerical Simulations The left-hand plot in Figure shows the vertical velocity from the numerical simulation. This displays a strong exponential nature which is due to the gravitational stratification, and this masks what is occurring at the mode-conversion region (dashed line) which lies at [MATH] . We may overcom... |
3.2 Analytical Study The first analytical technique we use to examine mode conversion is the WKB method. This involves expanding the horizontal and vertical velocity components, [MATH] and [MATH] , in inverse powers of [MATH] (the driving frequency). This is valid under the assumption that [MATH] is large, and will giv... |
[EQUATION] where [MATH] and [MATH] are the conversion and transmission coefficients respectively. Note that we have also extracted the exponential dependence seen in the simulations. |
These coefficients are the same as those found previously by Zhugzhda & Dzhalilov (1982) , Zhugzhda & Dzhalilov] , which were possible to determine because the exact analytical solution was known. We use a method developed by Cairns & Lashmore-Davies (1983) to find the coefficients. This method is valid at the mode-con... |
From Cairns & Lashmore-Davies (1983) , we can write the Wave Equations ( ) and ( ) in the general form [EQUATION] [EQUATION] where [MATH] and [MATH] are the main variables, and the conversion and transmission coefficients are given by |
[EQUATION] In order to manipulate Equations ( ) and ( ) into the correct format we take Fourier components in time, we must then impose the conditions that [MATH] is small and [MATH] is large, allowing us to neglect some terms. Finally making the transformation [MATH] and expanding [MATH] about the mode-conversion regi... |
[EQUATION] [EQUATION] By comparing these to Equations ( ) and ( ) we may simply write down the conversion and transmission coefficients |
[EQUATION] As the amount of transmission is easily calculated from the numerical simulations we may compare this directly to what is predicted analytically by Equation ( 12 ). We did this for various values of [MATH] and the results are shown in Figure where the stars indicate the transmission in the numerical simulati... |
Non-Isothermal Atmosphere Exactly the same analysis may be carried out for a non-isothermal atmosphere, where there is no exact analytical solution. We choose a [MATH] curve for the temperature profile, as shown in Figure , as this mimics the steep temperature gradient of the transition region. The form of this profile... |
4.1 Analytical Study Using a WKB analysis on Equations ( ) and ( ) the behaviour away from the mode-conversion region is given by |
[EQUATION] where [MATH] is the plasma beta at [MATH] . This equation tells us that to obtain a constant amplitude in the incident and transmitted waves, as we had in the isothermal case, we must make the transformation [MATH] (shown in the left-hand plot of Figure ). Note that if we set [MATH] we revert back to an isot... |
We may then follow Cairns & Lashmore-Davies (1983) , Cairns & Lashmore-Davies] to find the behaviour around the conversion region, giving exactly the same conversion and transmission coefficients as before. So varying the temperature profile has no effect on the amount of transmission and conversion as a wave propagate... |
As in the isothermal case, the amount of transmission may be calculated directly from the numerical results, so we compare this to the analytical prediction for various values of [MATH] . The agreement between the two is again excellent, as illustrated in the right-hand plot of Figure |
Conclusions Using a combination of analytical techniques and numerical computations we have studied the phenomenon of mode conversion in a simple, one-dimensional model. More specifically, we have studied the downward propagation of linear waves in a gravitationally stratified atmosphere permeated by a uniform, vertica... |
In Section we concentrated on an isothermal atmosphere using a combination of the WKB method, and a method developed by cairns1983 , Cairns & Lashmore-Davies] to examine mode conversion both outside and around the conversion region. This allowed conversion and transmission coefficients to be found. It was then possible... |
This analysis was repeated in Section for a non-isothermal atmosphere. We selected a [MATH] temperature profile to mimic the steep temperature gradient of the transition region. Surprisingly the transmission and conversion coefficients found were identical to those for the isothermal atmosphere. So the temperature prof... |
Although the model set-up is not physically realistic, it has given us a great insight into the mode conversion process, and the techniques which may be utilised in its analysis. We plan to use this knowledge to look at a more realistic model of a two-dimensional coronal null point, extending on work done by McLaughlin... |
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