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In order to increase the sample we then reran the pairing algorithan with the remaining early-(wpe galaxies alter relaxing the matching constraints to: maximum clilference between absolute magnitudes of 3nmumae: maximum difference between T (vpes of 3: maximum difference between. galaxy inclinations of 35°: maximum difference in plate scale of80%. | In order to increase the early-type sample we then reran the pairing algorithm with the remaining early-type galaxies after relaxing the matching constraints to: maximum difference between absolute magnitudes of mag; maximum difference between $T$ types of 3; maximum difference between galaxy inclinations of $\arcdeg$; maximum difference in plate scale of. |
. This resulted in 8 additional early-type pairs for a total of 34 matched pairs of early-type galaxies. | This resulted in 8 additional early-type pairs for a total of 34 matched pairs of early-type galaxies. |
This sample. combined with our 31 lale-(wpe pairs. we shall refer to as the "extended sample.” | This sample, combined with our 31 late-type pairs, we shall refer to as the “extended sample.” |
[istograms of the IIubble types. distances. inclinations and absolute 2 magnitudes for (he matched aud extended sample are presented in Figures 1. ancl 2. respectively. | Histograms of the Hubble types, distances, inclinations and absolute $B$ magnitudes for the matched and extended sample are presented in Figures \ref{fig-hmatchsample} and \ref{fig-hextsample} respectively. |
These figures show there are similar distributions for each property in the active and inactive galaxies. | These figures show there are similar distributions for each property in the active and inactive galaxies. |
Although this is expected for the matehed sample. it also remains (rue for the extended sample. aud demonstrates that the additional 8 early-twpe galaxy. pairs in the extended sample are reasonably welb-suited for comparison of the properties of active and inactive earlv-(vpe galaxies. | Although this is expected for the matched sample, it also remains true for the extended sample, and demonstrates that the additional 8 early-type galaxy pairs in the extended sample are reasonably well-suited for comparison of the properties of active and inactive early-type galaxies. |
Relevant information for the sample galaxies is presented in Table 1. [or the active galaxies and Table 2. for the inactive galaxies. | Relevant information for the sample galaxies is presented in Table \ref{tab-active} for the active galaxies and Table \ref{tab-control} for the inactive galaxies. |
Coliunns 5-9 of each of these tables list the galaxy. Z7 twpe. distance. absolute magnitude. inclination. and activity ivpe trom 11οetal.(1997a). | Columns 5-9 of each of these tables list the galaxy $T$ type, distance, absolute magnitude, inclination, and activity type from \citet{ho97a}. |
. These data comprise WWEPC? images obtained both with the planetary and wide field cameras. | These data comprise WFPC2 images obtained both with the planetary and wide field cameras. |
Relevant data on the images. notably the camera. filler. ancl exposure times. are listed in columns 2-4 of Tables 1 and 2.. | Relevant data on the images, notably the camera, filter, and exposure times, are listed in columns 2-4 of Tables \ref{tab-active} and \ref{tab-control}. |
All of the images were initially reduced by the archives on-the-fly reprocessing pipeline. | All of the images were initially reduced by the archive's on-the-fly reprocessing pipeline. |
The only additional processing was removal with the appropriate IRAF tasks. | The only additional processing was cosmic-ray removal with the appropriate IRAF tasks. |
Specilieallv. when (wo or more images were available we used the CRREJ task in the STSDAS package. otherwise we used ihe COSMICRAY task in the NOAO package. | Specifically, when two or more images were available we used the CRREJ task in the STSDAS package, otherwise we used the COSMICRAY task in the NOAO package. |
To identily circumnuclear dust structure in (hese images we used the structure map technique proposed by Pogee&Martini(2002). | To identify circumnuclear dust structure in these images we used the structure map technique proposed by \citet{pogge02}. |
. Structure maps enhance structure as [ime as (he scale of the point spread function in an image and are well suited to the identification | Structure maps enhance structure as fine as the scale of the point spread function in an image and are well suited to the identification |
Asp04 mixture. | Asp04 mixture. |
The differences are taken at the same density and temperature and reflect the differences in the actual opacity caleulations. | The differences are taken at the same density and temperature and reflect the differences in the actual opacity calculations. |
The differences are generally less (han in the radiative interior. | The differences are generally less than in the radiative interior. |
Near the base of the CZ the difference is of order ofI. | Near the base of the CZ the difference is of order of. |
.. since the (vo independent opacity caleulatious agree remarkably well with each other. 1 15 unlikely that (he discrepaney caused by reduced abundances can be due to uncertainties in opacilies. | Since the two independent opacity calculations agree remarkably well with each other, it is unlikely that the discrepancy caused by reduced abundances can be due to uncertainties in opacities. |
To separate oul the contribution of each element we construct a series of solar envelope models with the GS98 mixture. with (he abundance of one element at a time reduced bv the amount shown in the third column of Table 1. | To separate out the contribution of each element we construct a series of solar envelope models with the GS98 mixture, with the abundance of one element at a time reduced by the amount shown in the third column of Table 1. |
Two of these models (Lor reduction in O and Fe abundances) are also shown in Fig. | Two of these models (for reduction in O and Fe abundances) are also shown in Fig. |
1. | 1. |
The results using OPAL opacity tables are summarized in Table 1. which lists the required opacity modification to restore the density profile to that inferred by inversions. | The results using OPAL opacity tables are summarized in Table 1, which lists the required opacity modification to restore the density profile to that inferred by inversions. |
It also lists the logarithmic derivative of the required opacily modification with respect to abundance of each element. | It also lists the logarithmic derivative of the required opacity modification with respect to abundance of each element. |
It is clear that the derivative is significant for abundant elements like O. Ne. Fe. | It is clear that the derivative is significant for abundant elements like O, Ne, Fe. |
Thus the required opacity modification can be controlled by adjusting the abundance of some of these elements. | Thus the required opacity modification can be controlled by adjusting the abundance of some of these elements. |
And we see from Fig. | And we see from Fig. |
l. that the model with the increased Ne abunclance is actually consistent with seismic results. | 1, that the model with the increased Ne abundance is actually consistent with seismic results. |
If. we believe that the abundance determination of O. Fe have improved significantly in recent times. then there may not be much uncertainty in their estimated abundance and we do not have much freedom to vary those abundances. | If we believe that the abundance determination of O, Fe have improved significantly in recent times, then there may not be much uncertainty in their estimated abundance and we do not have much freedom to vary those abundances. |
The photospheric abundance of Ne however. max involve higher uncertainties since it can not be determined spectroscopically due to lack of suitable photospheric lines and has to be determined fom coronal lines. | The photospheric abundance of Ne however, may involve higher uncertainties since it can not be determined spectroscopically due to lack of suitable photospheric lines and has to be determined from coronal lines. |
This could also involve uncertainties due to possible fractionation in these lavers. as the coronal Ne abundance may not reflect that in the photosphere. | This could also involve uncertainties due to possible fractionation in these layers, as the coronal Ne abundance may not reflect that in the photosphere. |
Thus we speculate that the ellect of reduction in abundance of other elements like C. N. and O max be compensated by an increase in (he Ne abundance. | Thus we speculate that the effect of reduction in abundance of other elements like C, N, and O may be compensated by an increase in the Ne abundance. |
The required Ne abundance can be estimated by constructing models with different values of Ne abundance to estimate (he required abundance to match the clensity profile. | The required Ne abundance can be estimated by constructing models with different values of Ne abundance to estimate the required abundance to match the density profile. |
IC turns oul that we need an increase in Ne abundance by 0.63+0.06 dex when OP opacities are used. and by 0.67+0.06 dex when OPAL opacities are used. | It turns out that we need an increase in Ne abundance by $0.63\pm0.06$ dex when OP opacities are used, and by $0.67\pm0.06$ dex when OPAL opacities are used. |
This corresponds (ο an increase in abundance by a [factor of just over d. | This corresponds to an increase in abundance by a factor of just over 4. |
It can be seen from Fie. | It can be seen from Fig. |
1 (hat the envelope models constructed using these abundances have (he correct density profile. | 1 that the envelope models constructed using these abundances have the correct density profile. |
We can also estimate the required increase in Ne abundance from (he partial derivative eiven in Table 1. but that eives a somewhat larger estimate. presumably because the derivative itself would increase when Ne abundance increases by a [actor of 4. | We can also estimate the required increase in Ne abundance from the partial derivative given in Table 1, but that gives a somewhat larger estimate, presumably because the derivative itself would increase when Ne abundance increases by a factor of 4. |
peeimary seismic inversions for sound speed and density are independent of opacities. bul we need to use Opacilies in order to infer (he temperature and hydrogen abundance profiles in the solar interior (Gough Ixosoviehev 1988: Shibahashi Takata 1996; Antia Chitre 1993). | Primary seismic inversions for sound speed and density are independent of opacities, but we need to use opacities in order to infer the temperature and hydrogen abundance profiles in the solar interior (Gough Kosovichev 1988; Shibahashi Takata 1996; Antia Chitre 1998). |
We therefore check Che differences in the inlerred temperature aud X. profile of the Sun arising from the use of the two different opacity tables. | We therefore check the differences in the inferred temperature and $X$ profile of the Sun arising from the use of the two different opacity tables. |
Figure 3 shows the difference | Figure 3 shows the difference |
ealaxv bevond 5-6 disk seale lengths. and an accurate determination of the HII gas velocity dispersion. would provide a tighter constraint for the shape and the clensitv profile of the dark matter halo. | galaxy beyond 5-6 disk scale lengths, and an accurate determination of the HI gas velocity dispersion, would provide a tighter constraint for the shape and the density profile of the dark matter halo. |
In fact. having such data for other galaxies would allow the above method to be applied to a svstematic study of the dark matter halo properties in different galaxies. | In fact, having such data for other galaxies would allow the above method to be applied to a systematic study of the dark matter halo properties in different galaxies. |
We thank (he anonvmous referee for helpful comments which ereatly improved the presentation of results in the paper. | We thank the anonymous referee for helpful comments which greatly improved the presentation of results in the paper. |
We thank Shashikant Gupta for his help with optimizing ihe numerical code. | We thank Shashikant Gupta for his help with optimizing the numerical code. |
the uncertainties are rather larec. | the uncertainties are rather large. |
FWIIM size is approximately constant. | FWHM size is approximately constant. |
Ouly one distinct footpoiut is measurable iu this eveut although imaging over a larger energy baud suggests the existence of a second. very faint footpoiut. | Only one distinct footpoint is measurable in this event although imaging over a larger energy band suggests the existence of a second, very faint footpoint. |
One circular CGassian source was the best model for this case. | One circular Gaussian source was the best model for this case. |
Within the mnecrtaintics. radial position asx well as EWIIM are constant. | Within the uncertainties, radial position as well as FWHM are constant. |
While some of the described events display a clear decrease of radial distance with energv (simular to previous results) constant positions are also observed. | While some of the described events display a clear decrease of radial distance with energy (similar to previous results) constant positions are also observed. |
Iu the classical thick-target model. one would expect a decrease of the height of a source with increasing encre. | In the classical thick-target model, one would expect a decrease of the height of a source with increasing energy. |
There are a umber of effects that can influence the measured positions and sizes. | There are a number of effects that can influence the measured positions and sizes. |
The nost obvious is projection effects. | The most obvious is projection effects. |
Iu observations woe ieasure the position of the source in radial directiou from the center of the Sun. | In observations we measure the position of the source in radial direction from the center of the Sun. |
For sources at or close to the hub. these positions are directly related to the height of the source above the photosphere. | For sources at or close to the limb, these positions are directly related to the height of the source above the photosphere. |
Closer to the center of the Sum. sources at clifferent heights iu the chromosphere will be secu in projection on top of cach-other. | Closer to the center of the Sun, sources at different heights in the chromosphere will be seen in projection on top of each-other. |
This would result in an observed coustant radial position as a function of euergv. | This would result in an observed constant radial position as a function of energy. |
To avoid this we focused on uear lub eveuts. | To avoid this we focused on near limb events. |
However. even for near lib events. an effect duc to the heliocentric angle is expected. | However, even for near limb events, an effect due to the heliocentric angle is expected. |
Table 1 lists the cosine of the heliocentric aneles of the flaring region. | Table 1 lists the cosine of the heliocentric angles of the flaring region. |
The 2005 August 22 event is the furthest away from the limb at a helioceutric augle of 0=62°. correspondius to f=cos(0)=0.17. | The 2005 August 22 event is the furthest away from the limb at a heliocentric angle of $\theta=62\degr$, corresponding to $\mu=\cos(\theta)=0.47$. |
This introduces a factor L/L48 o the effective heights P;=Mlpittedv1p which could affect the density fits. | This introduces a factor $1/\sqrt{1-\mu^2}$ to the effective heights $h_{true}=h_{fitted}/\sqrt{1-\mu^2}$ which could affect the density fits. |
While no density fit was yossible for the 2005 August 22 event (νὰp- SS) because the positious as a fiction of energy were constant within uncertaiuty. in all the other eveuts Vl72>0.96 and the resulting effect is smaller than he uncertainties of the fits. | While no density fit was possible for the 2005 August 22 event $\sqrt{1-\mu^2}=0.88$ ) because the positions as a function of energy were constant within uncertainty, in all the other events $\sqrt{1-\mu^2}\ge 0.96$ and the resulting effect is smaller than the uncertainties of the fits. |
Therefore. the influence of he heliocentric anele ou the measured source heights and derived. deusities is negligible. | Therefore, the influence of the heliocentric angle on the measured source heights and derived densities is negligible. |
The contribution of xojection to the measured sizes can be estimated using a siunple ecometrical model. | The contribution of projection to the measured sizes can be estimated using a simple geometrical model. |
For a source with fitted rorizoutal extent (major axis) e the fitted vertical extent (uuinor axis) b is conirposed of: where ενω Is the true vertical extent. | For a source with fitted horizontal extent (major axis) $a$ the fitted vertical extent (minor axis) $b$ is composed of: where $b_{true}$ is the true vertical extent. |
For eveutsz exactly at the limb jj=0. thus 5=Oy)... | For events exactly at the limb $\mu=0$, thus $b=b_{true}$. |
Assuming a circular shape of the footpoiut at a eiven height the extent perpendicular to the radial direction. which is unaffected by projection effects. cam be used to estimate the true vertical size. | Assuming a circular shape of the footpoint at a given height the extent perpendicular to the radial direction, which is unaffected by projection effects, can be used to estimate the true vertical size. |
Figure 6 illustrates the effect. | Figure \ref{plotsix} illustrates the effect. |
Iu all of the observed eveuts. the measured source size ds larger by at least a factor of three compared o the expected size in a thick-tarect model (Fie. 6)). | In all of the observed events, the measured source size is larger by at least a factor of three compared to the expected size in a thick-target model (Fig. \ref{plotsix}) ). |
Even when projection effects are included. the sizes are still more than a factor of 2 larger than expected roni the thick target model. | Even when projection effects are included, the sizes are still more than a factor of 2 larger than expected from the thick target model. |
Currently there is only one explanation ic. ultithreaded loop density structure hat has been investigated m more detail aud that was used to explain the observed size in the event analyzed w?.. | Currently there is only one explanation i.e. multi-threaded loop density structure that has been investigated in more detail and that was used to explain the observed size in the event analyzed by \citet{Koet10}. |
Another possibility related to the density structure is a double-exponeutial density structure with a second. arecr scale-height at higher altitudes as proposed by ?.. | Another possibility related to the density structure is a double-exponential density structure with a second, larger scale-height at higher altitudes as proposed by \citet{Sa10}. |
This night affect the height of the sources as a function of enerey aud possibly the sizes. | This might affect the height of the sources as a function of energy and possibly the sizes. |
However. it is unlikely that he effect will be large enough to explain the observed sizes. | However, it is unlikely that the effect will be large enough to explain the observed sizes. |
Moreover. in terius of the positions m the eveuts xeseuted here a deusitv structure with a single scale-weight is sufficient to explain the observed function of radial distance versus enerev. | Moreover, in terms of the positions in the events presented here a density structure with a single scale-height is sufficient to explain the observed function of radial distance versus energy. |
However there are other effects such as magnetic mirroring. pitch augle scattering or N-rav albedo that are expected to affect the size of the ποιος, | However there are other effects such as magnetic mirroring, pitch angle scattering or X-ray albedo that are expected to affect the size of the source. |
Iu the standard thick-target model. magnetic rirroriug is neglected. | In the standard thick-target model, magnetic mirroring is neglected. |
However. in a couvergiug maenetic field it is expected that some particles are müirrored back roni the footpoiuts. if they were injected at a pitch anele relative to the magnetic field lines. | However, in a converging magnetic field it is expected that some particles are mirrored back from the footpoints, if they were injected at a pitch angle relative to the magnetic field lines. |
The mirroring xomt depends on the iuitial pitch angle of the electrous mt is independent ou the electron euerev. | The mirroring point depends on the initial pitch angle of the electrons but is independent on the electron energy. |
The bulk of he cussion is expected to onreginate from the densest wart of the chromosphere to which the clectrous are able to penetrate. | The bulk of the emission is expected to originate from the densest part of the chromosphere to which the electrons are able to penetrate. |
A single imurroriug point would lead ο a constant position as a function of cuerey such as observed iu the 2005 August 23 event. | A single mirroring point would lead to a constant position as a function of energy such as observed in the 2005 August 23 event. |
A behavior as in the stronger source of the 2003 April 26 eveut could also be euvisaged. | A behavior as in the stronger source of the 2003 April 26 event could also be envisaged. |
Ifthe stopping depth for low cuereectic clectrous is substantially higher than the mirroring point. those electrons will eucounuter a thück-target. while lieher energetic electrons will be mirrored. | If the stopping depth for low energetic electrons is substantially higher than the mirroring point, those electrons will encounter a thick-target, while higher energetic electrons will be mirrored. |
Therefore. a decrease of radial position with energy will be observed at low energies. a constant position at higher energies. | Therefore, a decrease of radial position with energy will be observed at low energies, a constant position at higher energies. |
The size of INR sources will depend ou the pitch angle spread of the clectrous. | The size of HXR sources will depend on the pitch angle spread of the electrons. |
Field aligned clectrous will penetrate deeper while electrons with a large pitch angle will be mirrored higher. | Field aligned electrons will penetrate deeper while electrons with a large pitch angle will be mirrored higher. |
This would make the source larger. | This would make the source larger. |
Ou the other haud. iu the extreme case of injection at a 90° angle to the magnetic field the clectrous will stay at the height of the injection point. eradually losiug energy. | On the other hand, in the extreme case of injection at a $\degr$ angle to the magnetic field the electrons will stay at the height of the injection point, gradually losing energy. |
This would result iu a constant position aud a source size determuned by the size of the acceleration region. | This would result in a constant position and a source size determined by the size of the acceleration region. |
Another effec that night not be negligible is collisional pitch angle x‘atterine. | Another effect that might not be negligible is collisional pitch angle scattering. |
It ds likely to increase the size of the x»rce (7). but this imerease is not expected to be arge enough to explain the observations. | It is likely to increase the size of the source \citep{Co00}, but this increase is not expected to be large enough to explain the observations. |
Additional scatcring due to various plasma waves cau be anticipated (c.g.7T). | Additional scattering due to various plasma waves can be anticipated \citep[e.g.][]{Bi10,Ha09, St02}. |
While this can be substantial. it is difficult to qnautity the level of turbulence in a faring atimosplicre. | While this can be substantial, it is difficult to quantify the level of turbulence in a flaring atmosphere. |
Photon backscattering (albedo) from the photosphliere can change the observed position aud size as shown by | Photon backscattering (albedo) from the photosphere can change the observed position and size as shown by |
One aclditional variable nucleus.4-254.0. matched (he position of a lower significance source indicated in the 1.33Ms Chandra survey (Brandt 2002). | One additional variable nucleus, matched the position of a lower significance X-ray source indicated in the 1.38Ms Chandra survey (Brandt 2002). |
This X-ray source. however. was not listed among the 2Ms detections. | This X-ray source, however, was not listed among the 2Ms detections. |
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