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If these galaxies lose a significant fraction of the ISM on an average and heavier galaxies lose very little mass then we can comfortably satisfy the constraints from enrichment of the IGM. | If these galaxies lose a significant fraction of the ISM on an average and heavier galaxies lose very little mass then we can comfortably satisfy the constraints from enrichment of the IGM. |
We now turn our attention to the ratio of escape fractions or photons and metals. | We now turn our attention to the ratio of escape fractions for photons and metals. |
Figure (39) shows the ratio fiz/ or the first IMF listed in Table (11). | Figure \ref{ratiofigs}) ) shows the ratio $f_\mathrm{esc,Z}/f_{\mathrm{esc},\gamma}$ for the first IMF listed in Table \ref{sfmodels}) ). |
It is interesting to note that he ratio fzg/fose. ds of order unity. differing from unity by at most a factor of a few. | It is interesting to note that the ratio $f_\mathrm{esc,Z}/f_{\mathrm{esc},\gamma}$ is of order unity, differing from unity by at most a factor of a few. |
Thus the fraction of ionizing photons hat escape galaxies is broadly of the same order as the fracti of metals that must leak into the IGM in order to explain t observed enrichment of the IGM. | Thus the fraction of ionizing photons that escape galaxies is broadly of the same order as the fraction of metals that must leak into the IGM in order to explain the observed enrichment of the IGM. |
We have not plotted this rati or other IMFs in Table {1 1) as the expected change can be seen rom Figure 2. | We have not plotted this ratio for other IMFs in Table \ref{sfmodels}) ) as the expected change can be seen from Figure 2. |
Indeed. the change in the ratio is less than a facor wo us we consider IMFs lised in rows 2.4 of the Table n. | Indeed, the change in the ratio is less than a factor two as we consider IMFs listed in rows $2-4$ of the Table \ref{sfmodels}) ). |
The last row in the Table (19) is more appropriate for late time sar ormation and we need not discuss that here. | The last row in the Table \ref{sfmodels}) ) is more appropriate for late time star formation and we need not discuss that here. |
Most studies of reionization have tended to focus on escape of ionizing photons. | Most studies of reionization have tended to focus on the escape of ionizing photons. |
In order to satisfy observations of or the luminosity function of high redshift galaxies. these ofl invoke a top heavy IMF for the first generation of stars (Cen20( | In order to satisfy observations of $\tau$ or the luminosity function of high redshift galaxies, these often invoke a top heavy IMF for the first generation of stars \citep{2003ApJ...591L...5C, 2003ApJ...595....1H,
2003ApJ...588L..69W, 2004PASP..116..103B}. . |
IS+1 While it is clear that the core component of X-ray emission surrounding PSR iis extended. an important consideration is how much of the X-ray emission detected could be from an unresolved source potentially corresponding to the pulsar itself. | $15\pm1$ While it is clear that the core component of X-ray emission surrounding PSR is extended, an important consideration is how much of the X-ray emission detected could be from an unresolved source potentially corresponding to the pulsar itself. |
We here consider the upper limits we can place on the temporal. morphological and spectral contributions of a central point source. | We here consider the upper limits we can place on the temporal, morphological and spectral contributions of a central point source. |
In principle. PSR mmavy be directly detectable in these data through its pulsations. | In principle, PSR may be directly detectable in these data through its pulsations. |
Because any emission from the pulsar is embedded in the surrounding extended component. pulsations will inevitably be contaminated by this extended emission. and the signal-to-noise ratio of the pulses will thus depend on the extraction radius and energy range in which data are considered. | Because any emission from the pulsar is embedded in the surrounding extended component, pulsations will inevitably be contaminated by this extended emission, and the signal-to-noise ratio of the pulses will thus depend on the extraction radius and energy range in which data are considered. |
We therefore searched for pulsations by considering events in five possible circular extraction regions. of radii 275. 5". 10% 15" and 20β. each centered on the pulsar position. | We therefore searched for pulsations by considering events in five possible circular extraction regions, of radii $2\farcs5$ , $5''$ , $10''$, $15''$ and $20''$, each centered on the pulsar position. |
For each extraction radius. we considered photons in the energy ranges 0.5-2. 2-5. 5-10 and 0.5-10 keV. We then determined the phase of each photon by folding the data at the ephemeris listed in Table 2.. which was kindly supplied to us by M. Kramer from pulsar timing observations at the Jodrell Bank Observatory. | For each extraction radius, we considered photons in the energy ranges 0.5β2, 2β5, 5β10 and 0.5β10 keV. We then determined the phase of each photon by folding the data at the ephemeris listed in Table \ref{tab_psr}, which was kindly supplied to us by M. Kramer from pulsar timing observations at the Jodrell Bank Observatory. |
Because our two observations were only separated by two days. we combined data from both runs when searching for pulsations. | Because our two observations were only separated by two days, we combined data from both runs when searching for pulsations. |
With the phases corresponding to the known pulsar period in hand. we applied to the data the Zz test (Buccherietal. 1983)). a binning-independent method of looking for the wth harmonic of a pulsating signal in sparsely-sampled data. | With the phases corresponding to the known pulsar period in hand, we applied to the data the $Z_n^2$ test \cite{bbb+83}) ), a binning-independent method of looking for the $n$ th harmonic of a pulsating signal in sparsely-sampled data. |
Inthe absence of pulsations. the quantity Zz will be distributed like V with 27 degrees of freedom. | Inthe absence of pulsations, the quantity $Z_n^2$ will be distributed like $\chi^2$ with $2n$ degrees of freedom. |
For each of the extraction radii and energy ranges listed above. we have calculated Zz for our observations for harmonies in the range |<7x5. | For each of the extraction radii and energy ranges listed above, we have calculated $Z_n^2$ for our observations for harmonics in the range $1 \le n \le 5$. |
Amongst these data. the most significant statistic is Z=9.5. which occurs for an extraction radius of 15" and an energy range 0.5β keV. The probability of such a signal emerging by chance is4.956... which is consistent with chance occurrence given the number of different extraction radii and energy ranges searched. | Amongst these data, the most significant statistic is $Z_2^2=9.5$, which occurs for an extraction radius of $15''$ and an energy range 0.5--10 keV. The probability of such a signal emerging by chance is, which is consistent with chance occurrence given the number of different extraction radii and energy ranges searched. |
We therefore conclude that there is no significant pulsed signal in the data. | We therefore conclude that there is no significant pulsed signal in the data. |
We can estimate an upper limit on the amplitude of any pulsations as follows. | We can estimate an upper limit on the amplitude of any pulsations as follows. |
For a sinusoidal signal of pulsed fraction f embedded in an event list containing N photons. we expect Z=O0.5fΒ°N (Leahy.Elsner.&Weisskopf 1983)). | For a sinusoidal signal of pulsed fraction $f$ embedded in an event list containing $N$ photons, we expect $Z_1^2 = 0.5f^2N$ \cite{lew83}) ). |
Since we do not know the optimal extraction radius in which pulses are most likely to dommate over surrounding extended emission. we conservatively consider a 20β extraction radius. | Since we do not know the optimal extraction radius in which pulses are most likely to dominate over surrounding extended emission, we conservatively consider a $20''$ extraction radius. |
This corresponds to ~75% of the energy of a central pointsource". but also most likely suffers from significant contamination from surrounding emission. | This corresponds to $\sim75\%$ of the energy of a central point, but also most likely suffers from significant contamination from surrounding emission. |
The resulting values of Z can be used to determine upper limits on f for the entire core region. | The resulting values of $Z_1^2$ can be used to determine upper limits on $f$ for the entire core region. |
For 0.5- 2-5. 5-10 and 0.5-10 keV. we determine upper limits on fΒ£ for a sinusoidal pulsed signal from PSR oof11%.4%.. and respectively. | For 0.5--2, 2β5, 5β10 and 0.5β10 keV, we determine upper limits on $f$ for a sinusoidal pulsed signal from PSR of, and respectively. |
The upper limits on the pulsed fraction for an unresolved pulse are a factor of two lower in each case. | The upper limits on the pulsed fraction for an unresolved pulse are a factor of two lower in each case. |
The intensity profiles in Figure 3. show that while cuts through the pulsar along a north-south axis are consistent with a point source. those m an east-west direction demonstrate the presence of extended emission immediately surrounding the pulsar. | The intensity profiles in Figure \ref{fig_core_slice} show that while cuts through the pulsar along a north-south axis are consistent with a point source, those in an east-west direction demonstrate the presence of extended emission immediately surrounding the pulsar. |
However. unlike other cases in which an unresolved source is clearly superposed on a smooth nebula citemss+02)). there is no obvious decomposition of the profile seen in the upper panel of Figure 3. into two such separate components. | However, unlike other cases in which an unresolved source is clearly superposed on a smooth nebula \\cite{mss+02}) ), there is no obvious decomposition of the profile seen in the upper panel of Figure \ref{fig_core_slice} into two such separate components. |
The profile shown could be interpreted as a centrally peaked nebula. with no central point source. but it could equally be regarded as an unresolved source embedded in lower level nebular emission. | The profile shown could be interpreted as a centrally peaked nebula, with no central point source, but it could equally be regarded as an unresolved source embedded in lower level nebular emission. |
Thus we must adopt a conservative upper limit on Γ point source. in which we assume that all the flux in the central bin corresponds to unresolved emission. | Thus we must adopt a conservative upper limit on a point source, in which we assume that all the flux in the central bin corresponds to unresolved emission. |
Integrating under the appropriately normalized PSF. we find that in the energy range 0.5-10 keV. ~1010 counts in the combined MOSI+MOS2 data set could be from an unresolved source at the pulsar position. ( | Integrating under the appropriately normalized PSF, we find that in the energy range 0.5β10 keV, $\sim1010$ counts in the combined $+$ MOS2 data set could be from an unresolved source at the pulsar position. ( |
Note that only ~75% of these counts would fall within the 18" extraction radius shown in Figure 2.. owing to the large wings of the PPSF.) | Note that only $\sim75\%$ of these counts would fall within the $18''$ extraction radius shown in Figure \ref{fig_mos_zoom}, owing to the large wings of the PSF.) |
The corresponding upper limit on the EPIC MOS rate from the pulsar is 0.0123 cts s. | The corresponding upper limit on the EPIC MOS count-rate from the pulsar is 0.0123 cts $^{-1}$. |
The spectrum of the core region is well fit by Γ power law. | The spectrum of the core region is well fit by a power law. |
If the emission from the pulsar has Γ blackbody spectrum. then it should be spectrally distinct from the rest of the core. | If the emission from the pulsar has a blackbody spectrum, then it should be spectrally distinct from the rest of the core. |
Thus. we can constrain the temperature of a central source by determining. what contribution Γ thermal source could make to the core's spectrum (Slane.Helfand.&Murray 2002)). | Thus, we can constrain the temperature of a central source by determining what contribution a thermal source could make to the core's spectrum \cite{shm02}) ). |
Specifically. we adopt a hard upper limit on the foreground column density of Nj<2Β«107? emβ’. above all values of Ny listed in Table 3.. | Specifically, we adopt a hard upper limit on the foreground column density of $N_H < 2 \times 10^{22}$ $^{-2}$, above all values of $N_H$ listed in Table \ref{tab_spec}. |
We assume that the neutron star's radius as viewed by a distant observer is R4,=12 km. and that the distance to the source is 4+ kpe. | We assume that the neutron star's radius as viewed by a distant observer is $R_\infty =
12$ km, and that the distance to the source is 4 kpc. |
We can then fit a two component spectral model to the core's spectrum (as measured by the combination of MOSI. MOS? and pn). in which we allow the photon index and flux of the power-law component to be free parameters. and find the maximum temperature of the blackbody component which still yields an acceptable fit to the spectrum. | We can then fit a two component spectral model to the core's spectrum (as measured by the combination of MOS1, MOS2 and pn), in which we allow the photon index and flux of the power-law component to be free parameters, and find the maximum temperature of the blackbody component which still yields an acceptable fit to the spectrum. |
This results in an upper limit on the surface temperature of the blackbody (as viewed at infinity) 147 eV. and an unabsorbed bolometric luminosity 10 erg s. | This results in an upper limit on the surface temperature of the blackbody (as viewed at infinity) $T_\infty < 147$ eV, and an unabsorbed bolometric luminosity $L^{bol}_{\infty} < 8.7\times10^{33}$ erg $^{-1}$. |
We note that a blackbody model will overestimate a neutron star's temperature when compared to more realistic atmosphere models (Pavlov&Zavlin 2000)). strengthening the upper limits made from blackbody fits here. | We note that a blackbody model will overestimate a neutron star's temperature when compared to more realistic atmosphere models \cite{pz00}) ), strengthening the upper limits made from blackbody fits here. |
oobservations of this source suggested the presence of three components of emission: an unresolved source centered on the pulsar. embedded ina compactregion of radius 20". and further surrounded by a diffuse nebula of extent ~5! (Finley. 1996)). | observations of this source suggested the presence of three components of emission: an unresolved source centered on the pulsar, embedded ina compactregion of radius $20''$ , and further surrounded by a diffuse nebula of extent $\sim5'$ \cite{fsp96}) ). |
From the ddata. there was the suggestion that this latter diffuse component had a cometary morphology. with a fan-like tail extending out behind the pulsar at a position angle ~210Β° (north through east). | From the data, there was the suggestion that this latter diffuse component had a cometary morphology, with a fan-like tail extending out behind the pulsar at a position angle $\sim210^\circ$ (north through east). |
In the data | In the data |
view. | view. |
We then fit a Gaussian profile to the Ha line and determined the best-fit [NII] and [ΞΞ Ξ fluxes for the same profile, requiring the Ha signal-to-noise to be >10 (Figure 1)). | We then fit a Gaussian profile to the $\alpha$ line and determined the best-fit [NII] and [OIII] fluxes for the same profile, requiring the $\alpha$ signal-to-noise to be $> 10$ (Figure \ref{fig:cl}) ). |
We found no significant offset in the velocity when fitting these lines independently. | We found no significant offset in the velocity when fitting these lines independently. |
For each pixel we infer the [Or11/A45007/H ratio (assumingCase B recombination) and measure the ratio adopting an average selective extinction [Nu]/Haof E(B-V) β0.28 (Hainlineetal.2009). | For each pixel we infer the $\lambda5007$ $\beta$ ratio (assumingCase B recombination) and measure the $\alpha$ ratio adopting an average selective extinction of E(B-V) $= 0.28$ \citep{Hainline09}. |
. The resulting data show no evidence of shock ionization or AGN in the standard BPT diagnostic diagram (Baldwinetal.1981). | The resulting data show no evidence of shock ionization or AGN in the standard BPT diagnostic diagram \citep{Baldwin81}. |
. We can examine possible variations in the N/O abundance using the photoionization models presented in pita (2002). | We can examine possible variations in the N/O abundance using the photoionization models presented in \cite{Kewley02}. |
. The [Orn]/[Ou] flux from Hainlineetal. (2009),, corrected for reddening via the Ha/Hy ratio, suggests an ionization parameter log(U)ββ2.9 for the integrated spectrum. | The ] flux from \cite{Hainline09}, corrected for reddening via the $\alpha$ $\gamma$ ratio, suggests an ionization parameter $\log(U) = -2.9$ for the integrated spectrum. |
We compute the metallicity of each pixel from both the [Nu]/Ha and [Nu]/[Ou] ratios using this ionization parameter and find excellent agreement, with an average offset 0.02 and lo scatter of 0.08 in 124-logO/H. | We compute the metallicity of each pixel from both the $\alpha$ and ] ratios using this ionization parameter and find excellent agreement, with an average offset 0.02 and $\sigma$ scatter of $0.08$ in $12 + \log{O/H}$. |
'The source-plane reconstruction is done independently for the A3 and regions, yielding two independent measurements of the A4/A5metallicity distribution. | The source-plane reconstruction is done independently for the A3 and A4/A5 regions, yielding two independent measurements of the metallicity distribution. |
The results are shown in Figures 3 and 4.. | The results are shown in Figures \ref{fig:source} and \ref{fig:n2}. |
[Nu]/Ha peaks in the center of the galaxy roughly coincident with the global minimum of [Or]/Ho, with [Nu]/Ha decreasing and /Ξ Ξ± increasing at larger radii. | $\alpha$ peaks in the center of the galaxy roughly coincident with the global minimum of $\alpha$ , with $\alpha$ decreasing and $\alpha$ increasing at larger radii. |
This is the expected signature of a metallicity gradient as seen in local disk galaxies (e.g. Magrinietal. 2007)). | This is the expected signature of a metallicity gradient as seen in local disk galaxies (e.g. \citealt{Magrini07}) ). |
Using Pettini&Pagel (2004)"s calibration to convert the measured [Nu]/Ha to an inferred metallicity 12+ logO/H, we extract pixels within a slit oriented along the direction of highest magnification to maximize spatial sampling and resolution. | Using \cite{Pettini04}' 's calibration to convert the measured $\alpha$ to an inferred metallicity $12 + \log{O/H}$ , we extract pixels within a slit oriented along the direction of highest magnification to maximize spatial sampling and resolution. |
We bin pixels within the extraction slitbased | We bin pixels within the extraction slitbased |
excluded frou the analysis. | excluded from the analysis. |
The resulting total live time of the central CCD (the CCD on which SAN Jis08.L3658 is located) is listed in Table L.. | The resulting total live time of the central CCD (the CCD on which SAX J1808.4β3658 is located) is listed in Table \ref{tab:log}. |
The MOS1L in the 0.510 keV enerev baud is shown in Figure d. (top) where we clearly see that SAN J1s08.13658 was detected. | The MOS1 in the 0.5β10 keV energy band is shown in Figure \ref{fig:image} (top) where we clearly see that SAX J1808.4β3658 was detected. |
This source is the brightest source ou the ceutral CCD. strongly indicating that caving theDeppoSA.X 2000 outburst observations most of the cdetecteoc Hux originated from SAN Jlsds.l365 aud not roni an unrelated feld source as was sugeeste w the BeppoSA data AWVijnaudsctal.2002).. | This source is the brightest source on the central CCD, strongly indicating that during the 2000 outburst observations most of the detected flux originated from SAX J1808.4β365 and not from an unrelated field source as was suggested by the data \citep{wijnandsetal2002_bepposax}. |
Campanaetal.(2002) reached similar conchisious using a quiesceut observation of the source ac hey suggestedoo that the systematic offset of heBeppoSANX position with regards to that of SAN Jls0S.L3658 might have been caused by he presenec of two faint sources close to SAN JLso0s8.b3658 (Fig.αΌΞ½, top paucl: see also Fie. | \citet{campanaetal2002} reached similar conclusions using a quiescent observation of the source and they suggested that the systematic offset of the position with regards to that of SAX J1808.4β3658 might have been caused by the presence of two faint sources close to SAX J1808.4β3658 \citep[Fig.~\ref{fig:image}, top panel; see also Fig. |
1 in2002). | 1 in. |
Moreover. due to the source βadutuess during the observations. ouly hee MediMedii EnergySnerey ConcentratorConceutrator Spectrometer 'oduced useful dat: ββ§β―β§βββββ§βββΎβββββββββββΎββ§uandsetal.2002)) audatc lis imstruimnent was only seusitive iu the energy range 1.310 keV. Therefore. images of the data in he 0.51.3 keV aud the 1.3.10 keV ΞΏΟΞΏΞΉΞΏΞ½ bands were made (ΞΟΞΏΟ, L.. | Moreover, due to the source faintness during the observations, only the Medium Energy Concentrator Spectrometer produced useful data \citep{wijnandsetal2002_bepposax}
and this instrument was only sensitive in the energy range 1.3β10 keV. Therefore, images of the data in the 0.5β1.3 keV and the 1.3β10 keV energy bands were made (Figs. \ref{fig:image}, |
muddle aud bottom panel) and SAN JIsO0S.[3658 is detected in both energy ranges. | middle and bottom panel) and SAX J1808.4β3658 is detected in both energy ranges. |
Iu contrast. the two extra sources are only detected iu the 1.510 keV band. demoustrating the fractional flaxuu coutribution ofββ theββββββΈββ₯β
β₯β
ββ₯βββ΄ββ΄βͺβββΆβ©β©βββ―βΊβ§βββͺβββΈββ₯β
β₯β
ββ₯βββ΄ββ΄βͺββ― two 50" other sources to the combined" flux increases. with7 photon energy. | In contrast, the two extra sources are only detected in the 1.3β10 keV band, demonstrating that the fractional flux contribution of the two other sources to the combined flux increases with photon energy. |
More, liesose differences MYoypqpeos]diu sonet:"UN PAvectra add further evidenceThe to the suggestiou iat those two extra sources nieht. have caused the svsteniatic offset in the obscrvatious. | These differences in source spectra add further evidence to the suggestion that those two extra sources might have caused the systematic offset in the observations. |
It should be noted that theBeppoSAN fluxes quoted Wy,WijnandsCatetal.(2002) IH).1 Stellaβ²ββββetal.(2000)9 or SAN JLs0a8.l3658 are likelyud close to its true Hux. | It should be noted that the fluxes quoted by \citet{wijnandsetal2002_bepposax} and \citet{stellaetal2000} for SAX J1808.4β3658 are likely close to its true flux. |
A sinall contamination of the fluxes by the wovo dclose-byN sourcesurces is likely.Likely. bbut thOSC ΟΞΏΟΞΏβmu are considerablv less buuinous than SAX 1505.. . ββ βΆβ©β©β
β±ββΊβββ―βΌβ§βββββ₯β
βΈβββͺβ₯β
βΈββββΈββΈβ³βͺβββββ―βββ§βββͺββ΄ββ΄ββͺββββΈβ β΄ββ΄β―ββ§ | A small contamination of the fluxes by the two close-by sources is likely, but those sources are considerably less luminous than SAX J1808.4--3658 and therefore the contamination should be small. |
ββ The ΟΞ±Ξ½ source spectra were extracted usinm a circle with a radius of 207 on the position of SANβ²β½β½ββ J1508.13658. | The X-ray source spectra were extracted using a circle with a radius of $''$ on the position of SAX J1808.4β3658. |
ββ
β For the MOSIApe camera. the backeround. spectrum was extracted usingββ a circleβ with a radius of 200% on the siue position. but excluding the detected poiut sources in this region. | For the MOS1 camera, the background spectrum was extracted using a circle with a radius of $''$ on the same position, but excluding the detected point sources in this region. |
Because of the use of the Small Window mode. ouly a limited field) could be use to extract the background spectrum for the MOS2 camera (i.c.. an annulus was used on the source position with that | Because of the use of the Small Window mode, only a limited field could be use to extract the background spectrum for the MOS2 camera (i.e., an annulus was used on the source position with an inner radius of $''$ and an outer radius of $''$. |
The RME aud ARF files were ereated with he SAS tools aud. | The RMF and ARF files were created with the SAS tools and. |
arfyen. The spectra obtaincd. were then grouped unus7 the FTOOLs iuto bius with a uiui of 20 counts per in to validate the use of the u statistics. | The spectra obtained were then grouped using the FTOOL into bins with a minimum of 20 counts per bin to validate the use of the $\chi^2$ statistics. |
The MOST and ΓOS2 spectra are shown in Figure 2 iid were fitted GisineoeXSPECversion1.10:UTAvrad.1996) smnultaueouslv. using nathe same model (sce Tab, | The MOS1 and MOS2 spectra are shown in Figure \ref{fig:spectrum} and were fitted \citep[using XSPEC version 11.1.0;][]{arnaud1996} simultaneously using the same model (see Tab. |
2 or the fit paraneters). | \ref{tab:spectrum} for the fit parameters). |
The coliuun density was allowed to float and the value obtained: was always consisteut: with:the value (1.22Β«1023 "n ββββββββ
βΈββΊβ§β₯β
βͺβ―βββΈββΈβ¨ββ½β―βΈβββ§β΄ββ΄βΏββ
βΈββΊ. | The column density was allowed to float and the value obtained was always consistent withthe value $1.22\times10^{21}$ $^{-2}$ ) inferred from the $A_{\rm v}$ measured |
depth unity. <7Ξ½ΟI. (Fig. 5)) | depth unity, $<\tau>_{x,y,t} = 1$, (Fig. \ref{T-z}) ) |
1s. however. rather different from its spectrum at local instantaneous unit optical depth (Fie. 2)). | is, however, rather different from its spectrum at local instantaneous unit optical depth (Fig. \ref{T-tau}) ), |
with different asvnuuetries especially noticeable for the fundamental mode. | with different asymmetries especially noticeable for the fundamental mode. |
The temperature al <7>=1 has the same asymmetry as (he velociv. | The temperature at $<\tau>=1$ has the same asymmetry as the velocity. |
What changes the asvinmetry of (he temperature spectrum between measuring it al local 7=1 and average <7>=1? | What changes the asymmetry of the temperature spectrum between measuring it at local $\tau = 1$ and average $<\tau> = 1$? |
We analvze the first non-radial Dincdamental. mode that has the most prominent asvimet(ryv and agrees closely with the corresponding, solar (=740 mode. | We analyze the first non-radial fundamental mode that has the most prominent asymmetry and agrees closely with the corresponding solar $\ell=740$ mode. |
Figure 6 shows the velocity and temperature prolile of this mode at average continuum optical depth one. | Figure \ref{V-Tavgtau} shows the velocity and temperature profile of this mode at average continuum optical depth one. |
It is clear that the velocity and temperature have (he same profiles. | It is clear that the velocity and temperature have the same profiles. |
Figure 7 shows the velocity. and temperature profiles measured al local optical depth one. which is where one would see them. | Figure \ref{V-Ttau} shows the velocity and temperature profiles measured at local optical depth one, which is where one would see them. |
The velocity spectrum is hardly changed. but the amplitude of the temperature [Iunctuations is reduced by more than an order of magnitude. | The velocity spectrum is hardly changed, but the amplitude of the temperature fluctuations is reduced by more than an order of magnitude. |
The high temperature sensitivity of the Jf opacity obscures hieh temperature eas and alters the height at which the gas is observed. | The high temperature sensitivity of the $H^{-}$ opacity obscures high temperature gas and alters the height at which the gas is observed. |
This reduces the magnitude of the observed temperature fluctuations. but (his reduction is not as great on (he high Irequency side as on the low Irequency side. | This reduces the magnitude of the observed temperature fluctuations, but this reduction is not as great on the high frequency side as on the low frequency side. |
Hence. (he mode asymmetry is changed. | Hence, the mode asymmetry is changed. |
Whvis the reduction of (he temperature f[Iuctuations different at high and low Irequencies? | Why is the reduction of the temperature fluctuations different at high and low frequencies? |
At the fixed geometrical height <7>=1. the temperature [hictuations were larger on the low lrequeney side of (he mode. | At the fixed geometrical height $<\tau>=1$, the temperature fluctuations were larger on the low frequency side of the mode. |
This produces a larger opacity variation on the low frequency side of the mode (Fig. 3)). | This produces a larger opacity variation on the low frequency side of the mode (Fig. \ref{K-Tavgtau}) ), |
which in turn leads to a larger variation in the height where local T(r.g.Ll)=1 (Fig. 9)). | which in turn leads to a larger variation in the height where local $\tau(x,y,t)=1$ (Fig. \ref{Z-Ttau}) ). |
The radiation temperature we see 15 equal to (he gas temperature al optical depth unity. according to the Eddineton-Barbier relations. | The radiation temperature we see is equal to the gas temperature at optical depth unity, according to the Eddington-Barbier relations. |
The phases of temperature and height of unit optical depth are such that where the temperature al fixed geometrical depth is largest we observe (he temperature al greatest height. (smallest z) (Fig 6)). | The phases of temperature and height of unit optical depth are such that where the temperature at fixed geometrical depth is largest we observe the temperature at greatest height (smallest z) (Fig \ref{Z-T_phase}) ). |
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