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Thus an accurate measurement of filament motion is verv useful in predicting (he occurrence of a CME. as well as to constrain or construct the CME triggering mechanisms (Gopalswaany et al.
Thus an accurate measurement of filament motion is very useful in predicting the occurrence of a CME, as well as to constrain or construct the CME triggering mechanisms (Gopalswamy et al.
2006).
2006).
Nevertheless. only several filaments have been reconstructed so lar about their 3D shape and evolution using the STEREO data.
Nevertheless, only several filaments have been reconstructed so far about their 3D shape and evolution using the STEREO data.
The 3D physical picture of filament eruption is far from being completely understood.
The 3D physical picture of filament eruption is far from being completely understood.
IC is disadvantageous to reconstruct a 3D configuration of solar features by only using STEREO data because of the large separation angle between the two satellites.
It is disadvantageous to reconstruct a 3D configuration of solar features by only using STEREO data because of the large separation angle between the two satellites.
With the launch of the Solar Dynamics Observatory (SDO: Sehwer et al.
With the launch of the Solar Dynamics Observatory (SDO; Schwer et al.
2002). this would be much improved by using data of 5DO and STEREO.
2002), this would be much improved by using data of SDO and STEREO.
In this work. we make the 3D reconstruction of a polar crown Lilament using observations fom the three different viewpoints. and use a visualization method to display the reconstructed filament.
In this work, we make the 3D reconstruction of a polar crown filament using observations from the three different viewpoints, and use a visualization method to display the reconstructed filament.
Section 2
Section 2
(Havashi1951).
\citep{Hayashi1981}.
JT110lrOds. 2001: 2001)). Havashi(1981) (Sasselov&Lecar
$T\sim 110-170$ \citeyear{Fraser2001}; \citeyear{Podolak2004}) \citet{Hayashi1981} \citep{Sasselov2000, Lecar2006, Garaud2007}.
T—110170 Z7—2500 2.3,nu. Carretal.(2001) Thi&Bik(2005). Πο R«0.1 Salvketal.(2008) Tz60 I0 (Z=200 teirperatures appropriate to both the occurrence and detection of ILO are present over a wide range of radii because stellar radiation heats the disk atmosphere.
$T\sim 110-170$ $T\sim 2500$ $\mu$ \citet{Carr2004} \citet{Thi2005} $_2$ $T>1200$ $R<0.4$ \citet{Carr2008} \citet{Salyk2008} $T\gtrsim 60$ $_2$ $T\gtrsim 200$ temperatures appropriate to both the occurrence and detection of $_2$ O are present over a wide range of radii because stellar radiation heats the disk atmosphere.
Aloreover. as we slow in this letter. several lines of IT20 can be detected byΠοσο at very low abunudances close to the mid-plane where the bulk of the water is frozen.
Moreover, as we show in this letter, several lines of $_2$ O can be detected by at very low abundances close to the mid-plane where the bulk of the water is frozen.
The detection of these lines will complement the previous measureients of the near-infrared and infrared water lines.
The detection of these lines will complement the previous measurements of the near-infrared and mid-infrared water lines.
The calculation is done as follows: (1) We use an X-rav hradiated disk code to calculate the tempcrature structure and molecular abundauces for a generic T Tami disk. (
The calculation is done as follows: (1) We use an X-ray irradiated disk code to calculate the temperature structure and molecular abundances for a generic T Tauri disk. (
2) The results ave iuput iuto a nulti-zone radiative transfer code that includes the caleulatioun of the excitation of the ΠΟ lines. (
2) The results are input into a multi-zone radiative transfer code that includes the calculation of the excitation of the $_2$ O lines. (
3) A ray-tracing code is used to obtain line fixes aud line shapes.
3) A ray-tracing code is used to obtain line fluxes and line shapes.
These three steps are discussed in more detail below.
These three steps are discussed in more detail below.
The thermalchemical structure of the disk ds calculated with the code described by Glassgold(2001) with imunor corrections aud updates (Moijeriuketal. 2008).
The thermal-chemical structure of the disk is calculated with the code described by \citet{Glassgold2004} with minor corrections and updates \citep{Meijerink2008}.
. The disk is ilhuninated by stell X-ravs with a thermal spectra with temperature Py=1 keV and luminosity Ly=2<107 ere |
The disk is illuminated by stellar X-rays with a thermal spectrum with temperature $T_X=1$ keV and luminosity $L_X=2\times10^{30}$ erg $^{-1}$.
Du regions where the X-raysare stronely attenuated. the disk is ionized by the decay products o 02? A] at a rate ως. 1,
In regions where the X-raysare strongly attenuated, the disk is ionized by the decay products of $^{26}$ Al at a rate $\zeta_{26}=4\times10^{-19}$ $^{-1}$.
The density strcture is giveu by the generic T Tauri disk model (P:vola d'Alessio. private conmnmnuication) with accretion rate Af=10SALT wr! and stellar paramcters AZ.=0.5 AL... Πο=ο... aud 7.=1000 Ik. The disk is fred. aud the density varies continuously from &=0.028 to 2500. AU.
The density structure is given by the generic T Tauri disk model (Paola d'Alessio, private communication) with accretion rate $\dot{M} = 10^{-8}\,{\rm M}_{\sun}$ $^{-1}$ and stellar parameters $M_*=0.5$ $_\odot$, $R_*=2{\rm R}_\odot$, and $T_*=4000$ K. The disk is flared, and the density varies continuously from $R = 0.028$ to $>$ 500 AU.
The model density does not include modifications suchasholes. gaps. andrimssugeested.forexample.bv the spectral energy distributions measured with Spitzer (6.8. Dullemond et al. 2007))
The model density does not include modifications suchasholes, gaps, andrimssuggested,forexample,by the spectral energy distributions measured with (e.g., Dullemond et al. \citeyear{Dullemond2007}) )
.The adopted model has a power law erainsizedistributionwith iudex p=3.5 aud Wun and maxim grain sizes of η=0.005 aud Grae=LOOO pan. respectively. resulting iu a ecometric
.The adopted model has a power law grainsizedistributionwith index $p=-3.5$ and minimum and maximum grain sizes of $a_{min}=0.005$ and $a_{max}=1000$ $\mu$ m, respectively, resulting in a geometric
In order to measure the amplitude of the final spike, the difficulty lies in the determination of the beginning of the Spike: there is no particular feature marking this point.
In order to measure the amplitude of the final spike, the difficulty lies in the determination of the beginning of the spike: there is no particular feature marking this point.
Instead, we used the minimum flux of the dip, whose value is close to the flux near the end of the dip.
Instead, we used the minimum flux of the dip, whose value is close to the flux near the end of the dip.
Thus, the amplitude was taken to be the difference between the top of the spike and the minimum flux of the dip.
Thus, the amplitude was taken to be the difference between the top of the spike and the minimum flux of the dip.
Using the parameters given by the fits, we looked for links between the X-ray and radio behaviors of1915--105.
Using the parameters given by the fits, we looked for links between the X-ray and radio behaviors of.
. We confirm the association between X- dips and radio flares: among the 54 X-ray dips listed on table 1, 52 are directly followed by a radio flare, only the 2 shortest dips being not followed by a detectable activity.
We confirm the association between X-ray dips and radio flares: among the 54 X-ray dips listed on table 1, 52 are directly followed by a radio flare, only the 2 shortest dips being not followed by a detectable activity.
We thus confirm that X-ray dips during a, 6, A and rv classes are always followed by radio flares.
We thus confirm that X-ray dips during $\alpha$ , $\beta$, $\lambda$ and $\nu$ classes are always followed by radio flares.
Fig.
Fig.
5 shows the distribution of the delay between the X-ray spike and the peak of the radio flare, for 34 X-ray dips.
\ref{histos_spike} shows the distribution of the delay between the X-ray spike and the peak of the radio flare, for 34 X-ray dips.
For 18 other dips, a flare is also detected but the date of the spike is not known because of the lack of X-ray coverage.
For 18 other dips, a flare is also detected but the date of the spike is not known because of the lack of X-ray coverage.
The average delay between the X-ray spike and the peak of the radio flare is 1040 + 185 s (at lo), a value consistent with the one calculated by Rodriguezetal.
The average delay between the X-ray spike and the peak of the radio flare is 1040 $\pm$ 185 s (at $\sigma$ ), a value consistent with the one calculated by \citet{Rodriguez:2008a}.
As for the derived start time of the ejection, according(2008a).. to the van der Laan model, the ejection of matter is coincident with the time of the X-ray spike within less than 5 minutes.
As for the derived start time of the ejection, according to the van der Laan model, the ejection of matter is coincident with the time of the X-ray spike within less than 5 minutes.
Since this connexion between X-ray dips and radio flares seems ubiquitous, it is interesting to look for cycles followed by detectable flares.
Since this connexion between X-ray dips and radio flares seems ubiquitous, it is interesting to look for cycles followed by detectable flares.
Firstly, very short cycles, such as the two A cycles observed on MJD 52171.799, are not followed by a detectable radio activity (upper limit of ~2 mJy).
Firstly, very short cycles, such as the two $\lambda$ cycles observed on MJD 52171.799, are not followed by a detectable radio activity (upper limit of $\sim$ 2 mJy).
Given that A cycles longer that 100 s, such as the one displayed on Fig. 1,,
Given that $\lambda$ cycles longer that 100 s, such as the one displayed on Fig. \ref{exemples1},
right, are followed by a weak radio flare, an explanation may simply be that such flares trigger too small ejections to be detected by the Ryle Telescope.
right, are followed by a weak radio flare, an explanation may simply be that such flares trigger too small ejections to be detected by the Ryle Telescope.
Then, the 0, « and classes are not followed by distinct radio flares, either.
Then, the $\theta$, $\kappa$ and $\rho$ classes are not followed by distinct radio flares, either.
T'hesep classes were not included in the analysis so far.
These classes were not included in the analysis so far.
& and p classes display very short cycles, between 10 and 50 s. These cycles recur very quickly, with less than 100s between two consecutive X-ray spikes.
$\kappa$ and $\rho$ classes display very short cycles, between 10 and 50 s. These cycles recur very quickly, with less than 100s between two consecutive X-ray spikes.
Our fits show that the radio flares of ppeak around 1000 s after the end of the cycle, and last typically 1200 s, thus they could not be seen individually during these classes.
Our fits show that the radio flares of peak around 1000 s after the end of the cycle, and last typically 1200 s, thus they could not be seen individually during these classes.
Note that a weak radio flux is detectable, at ~3-4 mJy (as already seen by Klein-Woltetal. which could be compatible with the sum of very(2002))), small radio ejections occurring after each cycle.
Note that a weak radio flux is detectable, at $\sim$ 3–4 mJy (as already seen by \citet{KleinWolt:2002}) ), which could be compatible with the sum of very small radio ejections occurring after each cycle.
0 classes display longer cycles, with X-ray dips lasting typically between 300 and 600 s. These cycles also recur quickly, with less than 1000s between two consecutive X-ray spikes.
$\theta$ classes display longer cycles, with X-ray dips lasting typically between 300 and 600 s. These cycles also recur quickly, with less than 1000s between two consecutive X-ray spikes.
In this case too, individual flares will not be distinguishable, but should produce a varying radio flux.
In this case too, individual flares will not be distinguishable, but should produce a varying radio flux.
Radio observations during this class show a strong radio flux, at ~10-80 mJy etal.2002).
Radio observations during this class show a strong radio flux, at $\sim$ 10–80 mJy \citep{KleinWolt:2002}.
. This flux is highly variable, but(Klein-Wolt displays no specific pattern.
This flux is highly variable, but displays no specific pattern.
This value of —10-80 mJy is significantly lower than the maximum fluxes observed after 5 and v cycles of comparable duration.
This value of $\sim$ 10–80 mJy is significantly lower than the maximum fluxes observed after $\beta$ and $\nu$ cycles of comparable duration.
Thus, this radio activity could be explained by radio flares, but of lower amplitude.
Thus, this radio activity could be explained by radio flares, but of lower amplitude.
Note that 0 cycles are also characterized by less pronounced X- dips: the Hardness Ratio is lower and the minimum flux higher than during other cyclic classes.
Note that $\theta$ cycles are also characterized by less pronounced X-ray dips: the Hardness Ratio is lower and the minimum flux higher than during other cyclic classes.
This may explain their different behavior regarding radio activity.
This may explain their different behavior regarding radio activity.
To put it in a nutshell, observations of 0, « and p classes are not entirely conclusive.
To put it in a nutshell, observations of $\theta$, $\kappa$ and $\rho$ classes are not entirely conclusive.
On the one hand, they can be understood within the framework of radio ejections: the distinct emissions of matter are simply too quick to be separated in the radio lightcurve.
On the one hand, they can be understood within the framework of radio ejections: the distinct emissions of matter are simply too quick to be separated in the radio lightcurve.
On the other hand, the observed radio flux is lower than expected if we followed the trend given by 8, A and classes.
On the other hand, the observed radio flux is lower than expected if we followed the trend given by $\beta$, $\lambda$ and $\nu$ classes.
This probably means that several features determinev the characteristics of the radio activity: the length of the X-ray dips may not be the only parameter required to explain all the radio flares.
This probably means that several features determine the characteristics of the radio activity: the length of the X-ray dips may not be the only parameter required to explain all the radio flares.
Now, let us look for correlations between the various parameters at hand.
Now, let us look for correlations between the various parameters at hand.
The amplitude of the final X-ray spike is not related to the width or amplitude of the following radio flare: the maximum X-ray flux seems tobe random.
The amplitude of the final X-ray spike is not related to the width or amplitude of the following radio flare: the maximum X-ray flux seems tobe random.
No link was found between the minimum flux during a dip and the characteristics of the following flare either.
No link was found between the minimum flux during a dip and the characteristics of the following flare either.
A slight link, although not statistically significant, was found between the minimum X-ray flux and the
A slight link, although not statistically significant, was found between the minimum X-ray flux and the
no counterpart detected at 3.6 cm, while the spectral index between 1.3 cm and 6.9 mm suggests optically thick free-free emission.
no counterpart detected at 3.6 cm, while the spectral index between 1.3 cm and 6.9 mm suggests optically thick free-free emission.
However, imaging the source with a tapered uv distribution shows the presence of extended emission with a total 1.3 cm flux of 3.0 mJy, the extended component accounting for of the flux.
However, imaging the source with a tapered uv distribution shows the presence of extended emission with a total 1.3 cm flux of 3.0 mJy, the extended component accounting for of the flux.
A 3.6 cm image made with a similar tapered uv-coverage shows a 3.5c point source with a total flux of 3.5 mJy, indicating that the emission is optically thin between 3.6 cm and 1.3 cm.
A 3.6 cm image made with a similar tapered uv-coverage shows a $\sigma$ point source with a total flux of 3.5 mJy, indicating that the emission is optically thin between 3.6 cm and 1.3 cm.
There is no detection of the source in the CORNISH survey or the catalog of ? which may be due to a combination of sensitivity and spatial filtering by the interferometer.
There is no detection of the source in the CORNISH survey or the catalog of \citet{beck91} which may be due to a combination of sensitivity and spatial filtering by the interferometer.
Since the emission measure is less than 2.7x108 pc cm$, this source is classified as a UC region.
Since the emission measure is less than $2.7 \times 10^8$ pc $^{-6}$, this source is classified as a UC region.
The uv-tapered images also led to the identification of a nearby UCΗπ region (12000 coordinates: 19 03” 465.0, 5° 40’ 42") with 3.6 cm, 1.3 cm and 6.9 mm fluxes of 4.3, 3.3 and 3.4 mJy respectively. —
The uv-tapered images also led to the identification of a nearby UC region (J2000 coordinates: $^h$ $^m$ $^s$ .0, $^\circ$ $'$ $''$ ) with 3.6 cm, 1.3 cm and 6.9 mm fluxes of 4.3, 3.3 and 3.4 mJy respectively. –
The 1.3 cm flux density in this source is mJy, while the 6.9 mm flux density is 6.0+1.2 mJy, which gives a spectral index of 4.1*05, which is inconsistent with free-free emission.
The 1.3 cm flux density in this source is $0.4 \pm 0.2$ mJy, while the 6.9 mm flux density is $6.0 \pm 1.2$ mJy, which gives a spectral index of $4.1^{+1.4}_{-0.9}$, which is inconsistent with free-free emission.
This suggests that dust emission contributes to the 6.9 mm flux density.
This suggests that dust emission contributes to the 6.9 mm flux density.
One can obtain an estimate of the contribution of dust emission by fitting the 1.2 mm, 870 pm and 24 um flux densities with a grey-body of the form B,(T4)(1—εν) where T; is the dust temperature and τν is the optical depth and is given by ro(v/vo, where f is the dust emissivity and is assumed to be 2.
One can obtain an estimate of the contribution of dust emission by fitting the 1.2 mm, 870 $\mu$ m and 24 $\mu$ m flux densities with a grey-body of the form $B_\nu(T_d)~(1-e^{-\tau_\nu})$ where $T_d$ is the dust temperature and $\tau_\nu$ is the optical depth and is given by $\tau_0(\nu/\nu_0)^\beta$, where $\beta$ is the dust emissivity and is assumed to be 2.
It should be noted that previous work (e.g. ?)) typically requires more than one temperature component to fit the SED at wavelengths shorter than ~50 um. However, since we have only three data points, itis not possible to carry out a multi-temperature fit in our case.
It should be noted that previous work (e.g. \citealt{mini05}) ) typically requires more than one temperature component to fit the SED at wavelengths shorter than $\sim 50~\mu$ m. However, since we have only three data points, it is not possible to carry out a multi-temperature fit in our case.
The consequence of using a single temperature model would be to overestimate the dust temperature and consequently the contribution of dust emission to the 6.9 mm emission.
The consequence of using a single temperature model would be to overestimate the dust temperature and consequently the contribution of dust emission to the 6.9 mm emission.
We obtain a dust temperature of 47 K from this fit, and estimate the contribution to the 6.9 mm flux density to be 3.4 mJy.
We obtain a dust temperature of 47 K from this fit, and estimate the contribution to the 6.9 mm flux density to be 3.4 mJy.
Taking this into account, the free-free spectral index is 2.8+1.6, which is marginally consistent with optically thick free-free emission. —
Taking this into account, the free-free spectral index is $2.8 \pm 1.6$, which is marginally consistent with optically thick free-free emission. –
The 1.3 cm map of this source (Fig. 2))
The 1.3 cm map of this source (Fig. \ref{g40.62k}) )
shows two sources, one of which is coincident with the maser location.
shows two sources, one of which is coincident with the maser location.
The continuum associated with the maser source is not detected at 3.6 cm, and has 1.3 cm and 6.9 mm flux densities of 0.9+0.3 mJy and 3.9+1.7 mJy respectively.
The continuum associated with the maser source is not detected at 3.6 cm, and has 1.3 cm and 6.9 mm flux densities of $0.9 \pm 0.3$ mJy and $3.9 \pm 1.7$ mJy respectively.
The other stronger source, at 12000 coordinates (19 06" 01°.48, 6? 46' 35".5), has 3.6 cm, 1.3 cm and 6.9 mm flux densities of 3.0+0.6 mJy, 2.0+0.2 mJy and 3.8+1.3 mJy respectively.
The other stronger source, at J2000 coordinates $^h$ $^m$ $^s$ .48, $^\circ$ $'$ $''$ .5), has 3.6 cm, 1.3 cm and 6.9 mm flux densities of $3.0 \pm 0.6$ mJy, $2.0 \pm 0.2$ mJy and $3.8 \pm 1.3$ mJy respectively.
The two sources are unresolved in the MAMBO and LABOCA maps.
The two sources are unresolved in the MAMBO and LABOCA maps.
A grey-body fit to the 1.2 mm, 870 um and 21 um data (the latter being from MSX since the MIPS data is completely saturated) gives the contribution of dust to the 6.9 mm emission as 1.7 mJy.
A grey-body fit to the 1.2 mm, 870 $\mu$ m and 21 $\mu$ m data (the latter being from MSX since the MIPS data is completely saturated) gives the contribution of dust to the 6.9 mm emission as 1.7 mJy.
Taking into account the error bars, the maser source is consistent with a HCHu region, while the nearbysource appears to be a UC region.
Taking into account the error bars, the maser source is consistent with a HC region, while the nearbysource appears to be a UC region.
The latter is not detected in CORNISH (3c limit of 0.9 mJy), which suggests that the emission measure is between 8.5x107 and 2.7x108 pe cm~, similar to that of 38.66+0.08.
The latter is not detected in CORNISH $\sigma$ limit of 0.9 mJy), which suggests that the emission measure is between $8.5 \times 10^7$ and $2.7 \times 10^8$ pc $^{-6}$, similar to that of 38.66+0.08.
The GLIMPSE source in Table is coincident with the maser source. -
The GLIMPSE source in Table \ref{table3} is coincident with the maser source. –
There are two possible MIPSGAL counterparts for this source as indicated in Table 1..
There are two possible MIPSGAL counterparts for this source as indicated in Table \ref{table1}.
The infrared flux densities of the two sources are given in Table 3 by the suffixes ‘A’ and 'B' respectively (‘A’ referring to the position in Table 1,, and ‘B’ referring to the source in the footnote).
The infrared flux densities of the two sources are given in Table \ref{table3} by the suffixes `A' and `B' respectively (`A' referring to the position in Table \ref{table1}, and `B' referring to the source in the footnote).
Based on the properties of the GLIMPSE source, the source ‘A’ is more likely to be the infrared counterpart for the maser. —
Based on the properties of the GLIMPSE source, the source `A' is more likely to be the infrared counterpart for the maser. –
There are two possible GLIMPSE point sources (labeled ‘A’ and ‘B’ in Table 3)) that could be mid- counterparts to the maser.
There are two possible GLIMPSE point sources (labeled `A' and `B' in Table \ref{table3}) ) that could be mid-infrared counterparts to the maser.
The separation of the ‘A’ and ‘B’ sources from the maser are 0.7" and 1.4” respectively, while the separation between the two sources and the 24 um MIPS source are 2.0" and 2.1" respectively. —
The separation of the `A' and `B' sources from the maser are $''$ and $1.4''$ respectively, while the separation between the two sources and the 24 $\mu$ m MIPS source are $''$ and $''$ respectively. –
This is the strongest source at centimeter wavelengths in our sample, with a 3.6 cm flux density of 59.5 mJy.
This is the strongest source at centimeter wavelengths in our sample, with a 3.6 cm flux density of 59.5 mJy.
The 6 cm flux density measured by the CORNISH survey is 105.4 mJy, which is much higher than what is expected from extrapolating the 3.6 cm flux density using optically thin free-free emission.
The 6 cm flux density measured by the CORNISH survey is 105.4 mJy, which is much higher than what is expected from extrapolating the 3.6 cm flux density using optically thin free-free emission.
However, this is most probably due to the complex and extended structure in the source which canbe seen in the 3.6 cm and 1.3 cm maps.
However, this is most probably due to the complex and extended structure in the source which canbe seen in the 3.6 cm and 1.3 cm maps.
Since the emission is optically thin to at least 6 cm, the emission measure is lower than 8.5x107 pc cm$, and is a UC region.
Since the emission is optically thin to at least 6 cm, the emission measure is lower than $8.5 \times 10^7$ pc $^{-6}$, and is a UC region.
The relatively evolved nature of the source is also evident in this being the only source detected in the 2MASS survey at J—band. —
The relatively evolved nature of the source is also evident in this being the only source detected in the 2MASS survey at $J$ –band. –
This source is detected at 1.3 cm at the 8c level though the signal to noise ratio in the integrated flux density is less.
This source is detected at 1.3 cm at the $\sigma$ level though the signal to noise ratio in the integrated flux density is less.
The 3.6 cm image shows a 3σ source with a peak intensity of 0.4 mJy/beam located 0.6" away from the 1.3 cm source.
The 3.6 cm image shows a $\sigma$ source with a peak intensity of 0.4 mJy/beam located $''$ away from the 1.3 cm source.
However, it is not clear whether this source is real, and it is not possible to obtain a good estimate of the integrated intensity of the source.
However, it is not clear whether this source is real, and it is not possible to obtain a good estimate of the integrated intensity of the source.
Consequently, this is reported as a at 3.6 cm in Table 2..
Consequently, this is reported as a non-detection at 3.6 cm in Table \ref{table2}. .
Assuming that the 3.6 cm source is real and is unresolved, the source would be classified as a hypercompact region.
Assuming that the 3.6 cm source is real and is unresolved, the source would be classified as a hypercompact region.
the two homotopically inequivalent maps of (2.3)), corresponding to the two ways a D4-brane wraps a 2-sphere, and A; the homologous maps for a D4-antibrane.
the two homotopically inequivalent maps of \ref{eq:homo}) ), corresponding to the two ways a $4$ -brane wraps a 2-sphere, and $\tilde{\lambda}_i$ the homologous maps for a $4$ -antibrane.
The point is that there exists a homotopic deformation which makes A;=λο and λι, leaving us with just 2 (plus the trivial) homotopically inequivalent maps and, consequently, 2 charges.
The point is that there exists a homotopic deformation which makes $\lambda_1=\tilde{\lambda}_2$ and $\lambda_2=\tilde{\lambda}_1$ , leaving us with just 2 (plus the trivial) homotopically inequivalent maps and, consequently, 2 charges.
Roughly speaking, this means that the"one-way" wrap of the D4-brane is actually identified with the “other-way” wrap of the D4-antibrane.
Roughly speaking, this means that the“one-way” wrap of the D4-brane is actually identified with the “other-way” wrap of the $4$ -antibrane.