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Secoi the optical. depth ees of the DACl.lc otaliuit liucWateptiIval Aid∖oanes] Maened:how a (παραπιοumtledaὃς ciet]ποic Ισmνι Waveinn παςLΓαμοςLOH πο ΕΠΗ ΟΕΕ vt iarπα the πω. peyton lopbeans | Second, the optical depth longward of the wavelength is roughly $0.5 x
(\Delta\lambda/100\AA\,)^{-1}$ for the cosmological parameters adopted here (Miralda-Escudé1998), and is dominated by neutral $x=1$ ) IGM outside the Strömmgren sphere. |
mcnΟΙ ol. ο...deebtiniisΠλος ηςPECuraa likὑπlunc ο ΗΝcathofa tie. Ag TD WaelpHhineWa | Therefore, the boundary region of the Strömmgren sphere does not affect the results in a sensitive way. |
le Mao: ansia dp σσWi] nanith ο. ὑδαάβρ] phthantο Μα (phyyppine | We assume that the jump from $x(R_i)$ to unity takes place as a step function at the radius $R_i(t_Q)$. |
Fiewre 1 shows the optical depth around the ine for a quasar at τς | Figure \ref{fig:tau} shows the optical depth around the line for a quasar at $z_s=7$. |
The left panel shows that. Or a xieht quasar lk that of FOO. the optical depth oneward of the wavelength is nearly independeut of the chunping factor. siuplv because the optical depth in tha region is dominated bv the damping wine of the jeutral ICAL (dotted curves in the loft paucl) outside the Strouuneren sphere. whose radius is iuseusitive to C'g as ong as CixLOO (see 82). | The left panel shows that, for a bright quasar like that of F00, the optical depth longward of the wavelength is nearly independent of the clumping factor, simply because the optical depth in that region is dominated by the damping wing of the neutral IGM (dotted curves in the left panel) outside the Strömmgren sphere, whose radius is insensitive to $C_{\rm HII}$ as long as $C_{\rm
HII}\le 100$ (see 2). |
The situation is driuaticallv cüffereut for a faiuter quasar as shown in the rigl piel of Figure 1: because the WT region is much μπαλα, the red damping wing produced by the neutral ΤΝΤ outside the Stromimeren sphere start to reflect the size of the sphere hence the age of the quasar. | The situation is dramatically different for a fainter quasar as shown in the right panel of Figure \ref{fig:tau}; because the HII region is much smaller, the red damping wing produced by the neutral IGM outside the Strömmgren sphere start to reflect the size of the sphere hence the age of the quasar. |
The dependence of the red damping wing ou the chupiug factor is vory weak. because the contribution from the residual neutral hydrogen within the Stromuneren sphere is smell. | The dependence of the red damping wing on the clumping factor is very weak, because the contribution from the residual neutral hydrogen within the Strömmgren sphere is small. |
Ou he other haud. the optical depth shortward of the wavelength within the stretch of the Strónuugreu sphere is always dominated bv the residual neutral hydrogen inside the Strouunercu sphere (dashed. curves). ixd therefore is proportional to οπμ (equation 7)). iu sharp contrast with the situation at the loneward of the wavelength. | On the other hand, the optical depth shortward of the wavelength within the stretch of the Strömmgren sphere is always dominated by the residual neutral hydrogen inside the Strömmgren sphere (dashed curves), and therefore is proportional to $C_{\rm HII}$ (equation \ref{eq:x2}) ), in sharp contrast with the situation at the longward of the wavelength. |
Towever. the optical depth shortwarel of the wavelength it is quite insensitive fo fo (equation 7)). | However, the optical depth shortward of the wavelength it is quite insensitive to $t_Q$ (equation \ref{eq:x2}) ). |
Let us Low translate the theoretical illustration in Figure 1 to observable spectra of quasars around the cnussion Ine shown in Figure 2.. | Let us now translate the theoretical illustration in Figure \ref{fig:tau} to observable spectra of quasars around the emission line shown in Figure \ref{fig:spectra}. |
A logarithmic ordinate is used to better show the flux over many orders of magnitude down to the expected noise level (although 10 spectral line may appear misleadingly fiat). | A logarithmic ordinate is used to better show the flux over many orders of magnitude down to the expected noise level (although the spectral line may appear misleadingly flat). |
We adopt 10 black hole (BIT) mass and bhuuinositv inferred from 10 quasar at 2=5.8 observed by FOO and place it either at κ=lO or τν=T in the top two panels: another quasar with one teuth of this huniünositv is used for 1ο two bottom panels. | We adopt the black hole (BH) mass and luminosity inferred from the quasar at $z=5.8$ observed by F00 and place it either at $z_s=10$ or $z_s=7$ in the top two panels; another quasar with one tenth of this luminosity is used for the two bottom panels. |
Tn all cases. the profile of the enission line is assed to be Caussian with a half-xcidtli of 1.500 kun/s. aud with a central flux that is twice 1ο continu. | In all cases, the profile of the emission line is assumed to be Gaussian with a half-width of $1,500$ km/s, and with a central flux that is twice the continuum. |
The random noise slow at he bottom of each pancl in Figure 2. is estimated asstuming a 107 SCCOxd iuteeration with theNOST (see lttp:/aneusta.stsci.edu for details on the expected backgrounds) with a spectral resolution of R=1L0.000. | The random noise shown at the bottom of each panel in Figure \ref{fig:spectra} is estimated assuming a $10^5~$ second integration with the (see http://augusta.stsci.edu for details on the expected backgrounds) with a spectral resolution of R=10,000. |
Obviously. it is advautaeeous to use high resolution spectroscopy to maximize the miuTOS of pixels that probe the structure of the IIII region on t1e blue side of the emission line (especially for faint aud‘Or very voung quasars). | Obviously, it is advantageous to use high resolution spectroscopy to maximize the number of pixels that probe the structure of the HII region on the blue side of the emission line (especially for faint and/or very young quasars). |
At spectral resolutions this hieh. t1e dominaut absolute relative) noise is either the PoissOl photon noise (for bright sources with Ny,xA0s1) or the detector noise (for fainter sources). rather than t1e zodiacal light or sky. background (see expressions for no]se iu (ποτ Mountain 1998). | At spectral resolutions this high, the dominant absolute ) noise is either the Poisson photon noise (for bright sources with $\dot N_{ph} \gsim 10^{56}~{\rm s}^{-1}$ ) or the detector noise (for fainter sources), rather than the zodiacal light or sky background (see expressions for noise in Gillett Mountain 1998). |
A ground based telesco2ο such Iweck or HET with suffüiieut spectral resolutiOl should therefore work just as well asΝ | A ground based telescope such Keck or HET with sufficient spectral resolution should therefore work just as well as. |
Τ, A ric1 a1uount of information is contained in the profile of the lijc. | A rich amount of information is contained in the profile of the line. |
We see that the red side of the emission line is largely transiuitted even for the fainter quasar adopted at the bottom panels. cousisteut with Figure 1 showiug an optical depth of ~0.1 there (except near the wavelength for the case with f=109 vy. where the radius of the Strónuueren sphere is sufiicicutly siunall that the damping wing of the neutral ICAL coutributes au optical depth significantly above unity.) | We see that the red side of the emission line is largely transmitted even for the fainter quasar adopted at the bottom panels, consistent with Figure 1 showing an optical depth of $\sim 0.1$ there (except near the wavelength for the case with $t_Q=10^6~$ yr, where the radius of the Strömmgren sphere is sufficiently small that the damping wing of the neutral IGM contributes an optical depth significantly above unity.) |
For the brighter quasar shown in the top panels the transiuission ou the red side is luseusitive to cither fo or Cli. whereas for the fainter quasar shown in the bottom panels the transmission on the red side is scusitive to te but not to Cru. | For the brighter quasar shown in the top panels the transmission on the red side is insensitive to either $t_Q$ or $C_{\rm HII}$, whereas for the fainter quasar shown in the bottom panels the transmission on the red side is sensitive to $t_Q$ but not to $C_{\rm HII}$. |
It ls therefore possible to measure the lifetime of a relativelv faint quasar (perhaps the majority of the quasars belong to this category) before reionization is complete. | It is therefore possible to measure the lifetime of a relatively faint quasar (perhaps the majority of the quasars belong to this category) before reionization is complete. |
The primary "uncertain factor is the intrinsic emission profile. | The primary uncertain factor is the intrinsic emission profile. |
The!due side of the emission line is not completelv absorbed. | The blue side of the emission line is not completely absorbed. |
Ou the contrary. we see in the top paucls of Figue2 tha for a quasar observed by FOO with te>10' vr there is a laree range AAz50150À where the flux is at least ten times above the noise (S/N=10). | On the contrary, we see in the top panels of Figure \ref{fig:spectra}
that for a quasar observed by F00 with $t_{Q}>10^7$ yr there is a large range $\Delta\lambda\approx 50-150$ where the flux is at least ten times above the noise (S/N=10). |
Even if the quasar is ten fines famter. one should still be able to detect of order several teus of spectral pixels if fo>109 vy (asstuning R= 101). | Even if the quasar is ten times fainter, one should still be able to detect of order several tens of spectral pixels if $t_{Q}>10^6$ yr (assuming $R=10^4$ ). |
More interestingly. the extent of the fux. transmission T, ou the blue side is a stroug function of Cyyyp but a very weak fuuction of | More interestingly, the extent of the flux transmission $T_\nu$ on the blue side is a strong function of $C_{\rm HII}$ but a very weak function of $t_Q$. |
The idealized case in Figur (2 shows the mean flux fo.processed through a relatively eoutly fuctuating medium. with uo saturated lines sothat Tao~οκυί 3-Ciup}. where jy is a known coustaut of order (1 1.0]. | The idealized case in Figure \ref{fig:spectra}
shows the mean flux processed through a relatively gently fluctuating medium, with no saturated lines [so that $T_\nu\propto \exp(-\beta_\nu
C_{\rm HII})$ , where $\beta|\nu$ is a known constant of order $0.1-1.0$ ]. |
An actual observed fux. distribution O1 the ]due side nav contain nunierous absorption features due to density fluctuations on stall scales. | An actual observed flux distribution on the blue side may contain numerous absorption features due to density fluctuations on small scales. |
Iu the limit when chuupiug is caused by highly overdenuse regious | In the limit when clumping is caused by highly overdense regions |
Pontin. D... Hornig. G.. Priest. E.R. 2005. Geophys. | Pontin, D.I., Hornig, G., Priest, E.R. 2005, Geophys. |
Astrophys. | Astrophys. |
Fluid Dvn. | Fluid Dyn. |
99. 77. | 99, 77. |
Priest. E... Pontin. D.I. 2009. Physics of Plasmas 16 122101.. Priest. E.R.. Titov. V.S. 1996. Phil. | Priest, E.R., Pontin, D.I. 2009, Physics of Plasmas 16 122101.. Priest, E.R., Titov, V.S. 1996, Phil. |
Trans. | Trans. |
Rov. | Roy. |
Soc. | Soc. |
A. 354 (1721) 2951. | A, 354 (1721) 2951. |
Schindler. Ix.. Hesse. M.. Dirn. J. 1988. J. Geophys. | Schindler, K., Hesse, M., Birn, J. 1988, J. Geophys. |
Res. | Res. |
93. 5547. | 93, 5547. |
Titov. V.S.. Hornig. G.. Démmoulin. P. 2002. J. Geoplivs. | Titov, V.S., Hornig, G., Démmoulin, P. 2002, J. Geophys. |
Hes. | Res. |
107(8). | 107(8). |
Wilnot-Smith. A.L.. Hornig. G.. Priest. E.R. 2006. Proc. | Wilmot-Smith, A.L., Hornig, G., Priest, E.R. 2006, Proc. |
Rov. | Roy. |
Soc. | Soc. |
A. 462. 2877. | A, 462, 2877. |
Wilnot-Smith. A.L.. Hornig. (71 Priest. ER. 2009. Geophys. | Wilmot-Smith, A.L., Hornig, G., Priest, E.R. 2009, Geophys. |
Astrophys. | Astrophys. |
Fluid. | Fluid. |
Dvn. | Dyn. |
103 (6) 515. | 103 (6) 515. |
Wilmot-Smith. A.L.. Pontin. D.I.. Hornig. G. 2010. Astron. | Wilmot-Smith, A.L., Pontin, D.I., Hornig, G. 2010, Astron. |
Astrophys. | Astrophys. |
516 Ad. | 516 A5. |
Xiao. C.J. and 1T others 2007. Nature Phys. | Xiao, C.J. and 17 others 2007, Nature Phys. |
3. 609. | 3, 609. |
a simple combination of sectors reproducing the shape of the supposedly cool filaments (see left panel of Fig. 5)). | a simple combination of sectors reproducing the shape of the supposedly cool filaments (see left panel of Fig. \ref{cold.fig}) ). |
We then excluded these regions and extracted the spectra in the same radial bins as above (see Fig. 3)). | We then excluded these regions and extracted the spectra in the same radial bins as above (see Fig. \ref{annuli_temp.fig}) ), |
and generated the temperature profile shown m red in the right panel of Fig. | and generated the temperature profile shown in red in the right panel of Fig. |
4 (see Table 2)). | \ref{temp.fig} (see Table \ref{profile.tab}) ). |
As evident from the comparison of the two profiles. the plateau has largely been removed and the temperature profile Is typical of cool coreclusters (see also Sect. 6)). | As evident from the comparison of the two profiles, the plateau has largely been removed and the temperature profile is typical of cool coreclusters (see also Sect. \ref{discussion.sec}) ). |
This clearly indicates that the masked regions contain cool gas. | This clearly indicates that the masked regions contain cool gas. |
A detailed spectral analysis of the cool filaments is presented in Sect. 5.. | A detailed spectral analysis of the cool filaments is presented in Sect. \ref{spectral_cold.sec}. |
We investigate here the spectral properties of the gas which produces the plateau seen in the global cluster temperature profile. | We investigate here the spectral properties of the gas which produces the plateau seen in the global cluster temperature profile. |
In particular. we focus on the gas located in the range of projected distances from the center of 72-145" (~ 76-152 kpe). which corresponds to the radial range where the plateau in the temperature profile is most evident (Le.. bins no. | In particular, we focus on the gas located in the range of projected distances from the center of $''$ $\sim$ 76-152 kpc), which corresponds to the radial range where the plateau in the temperature profile is most evident (i.e., bins no. |
8-11. see Fig. | 8-11, see Fig. |
4. and Table 2). | \ref{temp.fig}
and Table \ref{profile.tab}) ). |
We divided the annulus from 72-145" into 8 sectors. each having an angular width of 45°. obtaining the regions labeled as WNW (west-northwest). NNW (north-northwest). NNE (north-northeast). ENE (east-northeast). ESE (east-southeast). SSE (south-southeast). SSW (south-southwest). WSW (west-southwest) in the right panel of Fig. 5.. | We divided the annulus from $''$ into 8 sectors, each having an angular width of $45^{\circ}$, obtaining the regions labeled as WNW (west-northwest), NNW (north-northwest), NNE (north-northeast), ENE (east-northeast), ESE (east-southeast), SSE (south-southeast), SSW (south-southwest), WSW (west-southwest) in the right panel of Fig. \ref{cold.fig}. |
We extracted the spectra in these sectors and compared two different spectral models. | We extracted the spectra in these sectors and compared two different spectral models. |
The "IT model" is the absorbed model already used above to derive the global temperature profile. | The “1T model” is the absorbed model already used above to derive the global temperature profile. |
The free parameters are the temperature. &7. the metallicity. Z. and the normalization. (emission. measure. EM). | The free parameters are the temperature, $kT$, the metallicity, $Z$, and the normalization (emission measure, EM). |
The ~2T model" includes a second thermal emission component (apectapec) and has 2 additional free parameters: the temperature. &75. and the normalization. EM». of the second component (the metallicities of the two components are linked). | The “2T model” includes a second thermal emission component ) and has 2 additional free parameters: the temperature, $kT_2$, and the normalization, $_2$, of the second component (the metallicities of the two components are linked). |
The best-fitting parameter values and confidence ranges derived from the fits to the annular spectra in sectors are summarized in. Table 3.. | The best-fitting parameter values and confidence ranges derived from the fits to the annular spectra in sectors are summarized in Table \ref{spectral_study.tab}. |
Although the improvement of adding a second thermal component is formally significant according to the F-test. our results show that the quality of the data is not generally sufficient to demand a model more complex than the IT model. | Although the improvement of adding a second thermal component is formally significant according to the F-test, our results show that the quality of the data is not generally sufficient to demand a model more complex than the 1T model. |
In fact. in most sectors. the IT model already produces a very good fit (reduced chi squared 47 1) and therefore a more complicated model appears unnecessary. | In fact, in most sectors, the 1T model already produces a very good fit (reduced chi squared $\chi^2_{\nu} \sim 1$ ) and therefore a more complicated model appears unnecessary. |
We also note that the second thermal component Is poorly constrained. with temperature errors and up to300%. | We also note that the second thermal component is poorly constrained, with temperature errors and up to. |
. Only in the SSE sector is the reduced chi squared of the IT model unacceptable at significance. and the statistical improvement obtained. by introducing an additional emission component compared to the single-temperature model is the most significant according to the F-test. | Only in the SSE sector is the reduced chi squared of the 1T model unacceptable at significance, and the statistical improvement obtained by introducing an additional emission component compared to the single-temperature model is the most significant according to the F-test. |
The improvement of the 2T model over the IT model in this sector is also evident from the residuals of the fits in Fig. 6.. | The improvement of the 2T model over the 1T model in this sector is also evident from the residuals of the fits in Fig. \ref{spectra.fig}. |
We can therefore conclude that. confirming the hardness ratio map (Fig. 5.. | We can therefore conclude that, confirming the hardness ratio map (Fig. \ref{cold.fig}, , |
right panel). we find spectral evidence for multiphase gas in the SSE sector with a hot component at keV and a cool component at 1.59551! keV. Assuming that 4.92755:the two spectral phases are in pressure equilibrium in the same volume. the ratio of the volumes they occupy is estimated as Vi/V»=(EM,/EM:)-(ΚΑΤΙ/KT» y.so the filling factor of the cool gas is ~0.04. | right panel), we find spectral evidence for multiphase gas in the SSE sector with a hot component at $4.92^{+0.97}_{-0.74}$ keV and a cool component at $1.59^{+0.11}_{-0.23}$ keV. Assuming that the two spectral phases are in pressure equilibrium in the same volume, the ratio of the volumes they occupy is estimated as $V_1/V_2 = ({\rm
EM}_1/{\rm EM}_2) \cdot (kT_1/kT_2)^2 $, so the filling factor of the cool gas is $\sim$ 0.04. |
By contrast. we do not find clear spectral signatures. of cool gas in the sectors NNW. NNE. and ENE. as expected from a visual inspection of the hardness ratio map. | By contrast, we do not find clear spectral signatures of cool gas in the sectors NNW, NNE, and ENE, as expected from a visual inspection of the hardness ratio map. |
However. the lack of spectral evidence for multiphase gas could be due to the limitations. of our data. | However, the lack of spectral evidence for multiphase gas could be due to the limitations of our data. |
Indeed. due to the relatively limited spectral resolution of Chandra. the detection of two different thermal components demands a significant temperature separation. | Indeed, due to the relatively limited spectral resolution of Chandra, the detection of two different thermal components demands a significant temperature separation. |
The temperature difference required to have a marked effect on a single-phase thermal fit at the confidence level is determined as follows. | The temperature difference required to have a marked effect on a single-phase thermal fit at the confidence level is determined as follows. |
Using the response matrices. background. and numerical information of a real spectrum extracted in an arbitrary sector. we simulated spectra with two thermal components separated by AT around the best-fit value of the single temperature fit to the real spectrum. | Using the response matrices, background, and numerical information of a real spectrum extracted in an arbitrary sector, we simulated spectra with two thermal components separated by $\Delta$ T around the best-fit value of the single temperature fit to the real spectrum. |
We then fitted a single temperature model to the mock 2-temperature spectrum. | We then fitted a single temperature model to the mock 2-temperature spectrum. |
We repeated this exercise. Increasing the separation between the two temperature components until X7 exceeds the confidence range. | We repeated this exercise, increasing the separation between the two temperature components until $\chi^2_{\nu}$ exceeds the confidence range. |
For comparison. we performed this procedure by starting from the real spectra in different sectors indicated in Fig. | For comparison, we performed this procedure by starting from the real spectra in different sectors indicated in Fig. |
5 and found consistent results. | \ref{cold.fig} and found consistent results. |
An example of such an analysis is plotted in the left panel of Fig. 7.. | An example of such an analysis is plotted in the left panel of Fig. \ref{EM_distrib.fig}, |
where the dotted and dashed lines are the and 36 limits. | where the dotted and dashed lines are the and $3 \sigma$ limits. |
We found that a ~2.8 keV (3.0 keV) separation is necessary to exclude the presence of single-phase gas at the (30) confidence for our data. | We found that a $\sim$ 2.8 keV (3.0 keV) separation is necessary to exclude the presence of single-phase gas at the $3 \sigma$ ) confidence for our data. |
The fact that the two spectral components detected in sector SSE are separated by ~3.3 keV is consistent with this result. | The fact that the two spectral components detected in sector SSE are separated by $\sim$ 3.3 keV is consistent with this result. |
We note that ΚΤΠ found by the 2T model fit in the SSE sector is the lowest among all of the sectors. falling in the energy range which comprises most of the counts and thus being more easily detectable. | We note that $kT_1$ found by the 2T model fit in the SSE sector is the lowest among all of the sectors, falling in the energy range which comprises most of the counts and thus being more easily detectable. |
Despite this. since a temperature higher than + keV is not observed at any radius in the cluster (Fig. 4)). | Despite this, since a temperature higher than 4 keV is not observed at any radius in the cluster (Fig. \ref{temp.fig}) ), |
the second thermal component found by the 2T model fit appears unrealistically hot so we performed a new spectral fit with the 2T model (apectapec) keeping the temperature of the second thermal component fixed at 4 keV. Such a model has only one additional free parameter than the IT model: the normalization. EM». of the second component (the metallicities of the two components are linked). | the second thermal component found by the 2T model fit appears unrealistically hot so we performed a new spectral fit with the 2T model ) keeping the temperature of the second thermal component fixed at 4 keV. Such a model has only one additional free parameter than the 1T model: the normalization, $_2$, of the second component (the metallicities of the two components are linked). |
The best-fitting parameter values and confidence levels derived from the fits to the annular spectra in sectors are summarized in Table 4.. | The best-fitting parameter values and confidence levels derived from the fits to the annular spectra in sectors are summarized in Table \ref{spectral_study2.tab}. |
The F statistics for the improvement over the IT model. shown in the last column. indicate where the addition of à second thermal component is most significant (sectors SSE. NNW. NNE. and ENE). | The F statistics for the improvement over the 1T model, shown in the last column, indicate where the addition of a second thermal component is most significant (sectors SSE, NNW, NNE, and ENE). |
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