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Therefore, within the uncertainties quoted in Figure reffig10,, we can conclude that all four mass groups are compatible with the same slope o~—0.6 (formally —0.55+ 0.02). | Therefore, within the uncertainties quoted in \\ref{fig10}, we can conclude that all four mass groups are compatible with the same slope $\alpha \simeq -0.6$ (formally $\alpha=-0.55 \pm 0.02$ ). |
An interesting. feature.Log(age) of is that the spread of the logMacc data values around the best fitting lines is small, typically ~0.25 ddex (rms). | An interesting feature of \\ref{fig10} is that the spread of the $\log \dot M_{\rm acc}$ data values around the best fitting lines is small, typically $\sim 0.25$ dex (rms). |
This proves quite convincingly that the true uncertainty in the relationship between logL4; and logL(Ho) given by refeq4 cannot be as large as the 0.47 ddex value suggested by our elementary fit to the data in the compilation ofDahm (2008), but it has to be intrinsically smaller than the ~0.25 ddex factor that we observe in our own 3346 data. | This proves quite convincingly that the true uncertainty in the relationship between $\log L_{\rm acc}$ and $\log L(H\alpha)$ given by \\ref{eq4} cannot be as large as the $0.47$ dex value suggested by our elementary fit to the data in the compilation ofDahm (2008), but it has to be intrinsically smaller than the $\sim 0.25$ dex factor that we observe in our own 346 data. |
We conservatively assume 0.25 ddex (or a factor of <1.8 in linear units). | We conservatively assume $0.25$ dex (or a factor of $\la 1.8$ in linear units). |
Having established that the data in all four panels of are consistent with the same slope a~—0.6, we can use the intercept Q at MMyr to study how Myce varies with the stellar mass rn. | Having established that the data in all four panels of \\ref{fig10} are consistent with the same slope $\alpha \simeq
-0.6$, we can use the intercept $Q$ at Myr to study how $\dot M_{\rm
acc}$ varies with the stellar mass $m$. |
It appears that the value of Q in the four panels of reffiglO decreases with increasing mass approximately as l, | It appears that the value of $Q$ in the four panels of \\ref{fig10} decreases with increasing mass approximately as $m^{-1}$. |
The formal uncertainty on Q may seem too large to reach this conclusion, but the scatter is due to the grouping of stars of different mass in the same bin. | The formal uncertainty on $Q$ may seem too large to reach this conclusion, but the scatter is due to the grouping of stars of different mass in the same bin. |
It is, therefore, more appropriate to perform a multivariate fit to the three variables (Macc, age and mass). | It is, therefore, more appropriate to perform a multivariate fit to the three variables simultaneously $\dot M_{\rm acc}$, age and mass). |
We opt for a linear multivariate simultaneouslyleast-square fit of the type: where ¢ is in years, m the mass in solar units and c is a constant. | We opt for a linear multivariate least-square fit of the type: where $t$ is in years, $m$ the mass in solar units and $c$ is a constant. |
The formal best fit gives a=--0.61 +0.02, b= and c=—3.27+ 0.24. | The formal best fit gives $a=-0.61 \pm 0.02$ , $b=0.90 \pm
0.10$ and $c=-3.27 \pm 0.24$ . |
However, since the set of parameters a= —0.6, b=1 and c2—3.3 would give almost equally small residuals, we will take them hereafter as a good as well as convenient representation of the dependence of M,acc on stellar mass and age in 3346. | However, since the set of parameters $a=-0.6$ , $b=1$ and $c=-3.3$ would give almost equally small residuals, we will take them hereafter as a good as well as convenient representation of the dependence of $\dot M_{\rm acc}$ on stellar mass and age in 346. |
division is given. by the maximum. of the spectrum. | division is given by the maximum of the spectrum. |
Our calculations show that on small wavelengths. (Iarge waventunber A) spectra are rather similar. | Our calculations show that on small wavelengths (large wavenumber $k$ ) spectra are rather similar. |
"This result is expected as perturbations on these wavelengths are determined. by the internal distribution of clusters within superclusters. and superclusters in our mocels are generated in à similar wav. | This result is expected as perturbations on these wavelengths are determined by the internal distribution of clusters within superclusters, and superclusters in our models are generated in a similar way. |
Calculations bv. Frisch (1995). show that inhomogeneities on very large wavelengths do not inlluence the cüstribution of clusters in models. instead superclusters are modulated. Le. in some regions they are very massive and in others poor. | Calculations by Frisch (1995) show that inhomogeneities on very large wavelengths do not influence the distribution of clusters in models, instead superclusters are modulated, i.e. in some regions they are very massive and in others poor. |
Itegularitv of the structure is given by power on intermediate wavelength. | Regularity of the structure is given by power on intermediate wavelength. |
Analytic caleulations confirm this result. that. moclels with only slightlv. cillerent power spectra in the medium wavelength. region may have very dillerent correlation unctions. | Analytic calculations confirm this result that models with only slightly different power spectra in the medium wavelength region may have very different correlation functions. |
The mixed. model with quasi-regular network of rich superclusters ancl voids has a spectrum which cdilfers rom the speetrum of the random supercluster model only wv about 25 near the maximum. | The mixed model with quasi-regular network of rich superclusters and voids has a spectrum which differs from the spectrum of the random supercluster model only by about 25 near the maximum. |
Dillerences between power spectra of the Voronoi ancl regular τος models. are also small whereas correlation functions are very cilferent. | Differences between power spectra of the Voronoi and regular rod models are also small whereas correlation functions are very different. |
Such small dillerences can result from cdilferent ecometrics of he supercluster population. | Such small differences can result from different geometries of the supercluster population. |
These examples show that the correlation function is much more sensitive to the presence ofa small regularity in the distribution of clusters than it is o the spectrum itself. | These examples show that the correlation function is much more sensitive to the presence of a small regularity in the distribution of clusters than it is to the spectrum itself. |
One feature of the correlation function is not vet explained. | One feature of the correlation function is not yet explained. |
Why does the Voronoi model. show a minimum ancl maximum in the correlation function and the rancom supercluster model. does not? | Why does the Voronoi model show a minimum and maximum in the correlation function and the random supercluster model does not? |
One possible reason could be a dillerence in the distribution of voids. | One possible reason could be a difference in the distribution of voids. |
In the random supercluster model. voids can be very small. which is not the case for the Voronoi model. | In the random supercluster model voids can be very small, which is not the case for the Voronoi model. |
Lo check this possibility we extracted: voids from our model cluster samples. and calculated the integrated distribution of void radii. | To check this possibility we extracted voids from our model cluster samples and calculated the integrated distribution of void radii. |
Here we used. procedures described by Einasto. Einasto Ciramann (1989) ancl Einasto (1991). | Here we used procedures described by Einasto, Einasto Gramann (1989) and Einasto (1991). |
Results for the void. raclii are shown in Figure 6. | Results for the void radii are shown in Figure 6. |
Our calculations show that for most of our models the istribution of void radii is very similar. | Our calculations show that for most of our models the distribution of void radii is very similar. |
A factor which influences the distribution of void. radii is the presence of weak filaments between superclusters. | A factor which influences the distribution of void radii is the presence of weak filaments between superclusters. |
Lf clusters in. high-ensity regions are distributed similarly in dilferent models jen their correlation functions also are similar. as they we. for instance. for models SC.cor.25 and SC.net.20. | If clusters in high-density regions are distributed similarly in different models then their correlation functions also are similar, as they are, for instance, for models SC.cor.25 and SC.net.20. |
Void lameters in these models are. however. completely different. w seen in Figure 6. | Void diameters in these models are, however, completely different, as seen in Figure 6. |
In models with no filaments between gsuperclusters (SC.cor.25) voids are much larger their mean iameter corresponds to the diagonal of the net — whereas in all models where rods between corners are also populated. void. diameters are determined by distances between these rods. Le. by the scale of the net. | In models with no filaments between superclusters (SC.cor.25) voids are much larger – their mean diameter corresponds to the diagonal of the net – whereas in all models where rods between corners are also populated, void diameters are determined by distances between these rods, i.e. by the scale of the net. |
We conclude that voids are determined. by. properties of small filaments and the correlation function. by. the distribution. of clusters in high-density regions (sec also Paper I). | We conclude that voids are determined by properties of small filaments and the correlation function by the distribution of clusters in high-density regions (see also Paper I). |
The errors in the two- and three-point correlations are discussed. by Alo. Jing Borrner (1992). | The errors in the two- and three-point correlations are discussed by Mo, Jing Börrner (1992). |
Errors in the correlation function depend. on high-order correlations. which ave cdillerent for diferent geometrical distributions of clusters. | Errors in the correlation function depend on high-order correlations, which are different for different geometrical distributions of clusters. |
The cüllicultv of the determination of errors lies in the fact that they depend on the distribution of clusters in the ensemble. and there is no unique comparison ensemble of samples available. | The difficulty of the determination of errors lies in the fact that they depend on the distribution of clusters in the ensemble, and there is no unique comparison ensemble of samples available. |
hus parameters describing the errors of the correlation function must be determined for all dillerent ecometrical clistributions of clusters. | Thus parameters describing the errors of the correlation function must be determined for all different geometrical distributions of clusters. |
ln the calculation of the correlation function the number of particles in the Poisson sample is taken as very large. | In the calculation of the correlation function the number of particles in the Poisson sample is taken as very large. |
In this case we can ignore errors of the Poisson sample and calculate the error of the correlation function from the error of the number of pairs (DD(r)}. | In this case we can ignore errors of the Poisson sample and calculate the error of the correlation function from the error of the number of pairs $\langle
DD(r)\rangle $. |
Mo give a formula to calculate the error of (MY(r)) through moments of the two-point ancl three-point correlation function. | Mo give a formula to calculate the error of $\langle
DD(r)\rangle $ through moments of the two-point and three-point correlation function. |
Ehe first. terms have the form: Llere IN. is the total number of clusters in the sample. and b is a constant which depends. on the high-order correlation functions. | The first terms have the form: Here $N$ is the total number of clusters in the sample, and $b$ is a constant which depends on the high-order correlation functions. |
The first term of the Eq. ( | The first term of the Eq. ( |
16) is the Poisson error. due to random errors in sampling of galaxics: the second. termi is the cosmic error or variance. clue to variations in the distribution of clusters in different parts of the Universe. | 16) is the Poisson error, due to random errors in sampling of galaxies; the second term is the cosmic error or variance, due to variations in the distribution of clusters in different parts of the Universe. |
For our models we have calculated errors in. the correlation function from the scatter of cillerent realizations | For our models we have calculated errors in the correlation function from the scatter of different realizations |
The Alagcllanie Dridge is a loosely defined column of gas. comprising mostly neutral hydrogen. found between the Small anc Large. Alagcllanie Clouds (SAIC and LMC respectively). | The Magellanic Bridge is a loosely defined column of gas, comprising mostly neutral hydrogen, found between the Small and Large Magellanic Clouds (SMC and LMC respectively). |
Phe Bridge was cliscovered originally through 21cm observations by Lindman et al. ( | The Bridge was discovered originally through 21cm observations by Hindman et al. ( |
1961). and has been mapped in the line at increased. spatial resolution by Mathewson. Cleary Murray. (1974). ancl at increased. velocity resolution by AleGee Newton (1986). | 1961), and has been mapped in the line at increased spatial resolution by Mathewson, Cleary Murray (1974), and at increased velocity resolution by McGee Newton (1986). |
The most recent oobservations are presented by Putman (1998). and Brünns. ]xerp Staveley-Smith. (2000). | The most recent observations are presented by Putman (1998), and Brünns, Kerp Staveley-Smith (2000). |
The tidal influence of the Magellanic Clouds on each other is widely considered to be the mechanism responsible for the development of the Magellanic Bridge (og. | The tidal influence of the Magellanic Clouds on each other is widely considered to be the mechanism responsible for the development of the Magellanic Bridge (eg. |
Putman 2000: Demers Battinelli 1998: Staveley-Smith ct al. | Putman 2000; Demers Battinelli 1998; Staveley-Smith et al. |
1998). and has been moclelled as such through numerical simulations (eg. | 1998), and has been modelled as such through numerical simulations (eg. |
Gardiner. Sawa Fujimoto 1994: Gardiner Noguchi 1996: and Sawa. Fujimoto Ixumai 1999). | Gardiner, Sawa Fujimoto 1994; Gardiner Noguchi 1996; and Sawa, Fujimoto Kumai 1999). |
The simulations suggest that formation of the Bricdec may have begun during the most recent of a series of close Cloud interactions. around 200 Myr ago. | The simulations suggest that formation of the Bridge may have begun during the most recent of a series of close Cloud/Cloud interactions, around 200 Myr ago. |
Zaritsky οἱ al. ( | Zaritsky et al. ( |
2000) suggest that the SMC may also have been subject to a period of ram pressure. and have measured a shift in the centre of the voung blue population relative to that of the older population. | 2000) suggest that the SMC may also have been subject to a period of ram pressure, and have measured a shift in the centre of the young blue population relative to that of the older population. |
The degree to which this hydrocsynamic ellect has inlluenced the evolution of the Magellanic System has not vet been quantified. | The degree to which this hydrodynamic effect has influenced the evolution of the Magellanic System has not yet been quantified. |
Studies of the morphology of the iin the SMC have been made by a few groups: sshells have been identified and catalogued by Staveley-Smith et al. ( | Studies of the morphology of the in the SMC have been made by a few groups: shells have been identified and catalogued by Staveley-Smith et al. ( |
1997) and. by Stanimirovió ct al. ( | 1997) and by Stanimirović et al. ( |
1999). | 1999). |
The statistical properties of the Interstellar Alecium (ISAT) have been studied. by Stanimirovió et al. ( | The statistical properties of the Interstellar Medium (ISM) have been studied by Stanimirović et al. ( |
1999). Stanimirovié (2000) and Stanimirovié Lazarian (2001). | 1999), Stanimirović (2000) and Stanimirović Lazarian (2001). |
The shell population. its evolution ancl relationship with | The shell population, its evolution and relationship with |
to estimate the radiative cooling rate with a moderate streugth of the maeuetic field in a reliable way. | to estimate the radiative cooling rate with a moderate strength of the magnetic field in a reliable way. |
In the following. we investigate only the case that the radiative ΟΠΟΙΟΥ loss is not significant. | In the following, we investigate only the case that the radiative energy loss is not significant. |
Now that we have the time evolution of the escaping CR particle flux from the source. we cau obtain the observed electron spectrum by solving the propagation of CR clectrous/positrous with the diffusion equation shown in Eq.(3)). | Now that we have the time evolution of the escaping CR particle flux from the source, we can obtain the observed electron spectrum by solving the propagation of CR electrons/positrons with the diffusion equation shown in \ref{diffeq}) ). |
Once we know the Creeu's function of this equation with respect to the time aud position. Gr.ccr) we can obtain the observed clectron spectrin as where f; is the tine when the particle injection has started. which is assumed to be equal to fsedoy in the following discussions. | Once we know the Green's function of this equation with respect to the time and position, $G(t,r,\varepsilon_e;\tau)$, we can obtain the observed electron spectrum as where $t_i$ is the time when the particle injection has started, which is assumed to be equal to $t_{\rm Sedov}$ in the following discussions. |
The mathematical description of G(t.re.:7) was derived by Atovan et al. ( | The mathematical description of $G(t,r,\varepsilon_e;\tau)$ was derived by Atoyan et al. ( |
1995). where £209 is the energy of clectrous/positrons at the time fy which are cooled down to ο at the time f. aud day is the diffusion leugth given by as shown in Eqs(10) and (11) in Atovan et al. ( | 1995), where $\varepsilon_{e,0}$ is the energy of electrons/positrons at the time $t_0$ which are cooled down to $\varepsilon_e$ at the time $t$, and $d_{\rm diff}$ is the diffusion length given by as shown in Eqs.(10) and (11) in Atoyan et al. ( |
1995). | 1995). |
Iu derivius the energv loss rate P(e). we use the formulation shown by Mocderski et al. ( | In deriving the energy loss rate $P(\varepsilon_e)$, we use the formulation shown by Moderski et al. ( |
2005) where op is the Thomson cross section. (4,4:(2.)dz. is the enerev density of iuterstellar photous with the ΟΠΟΙΟΥ between 5. ands.|de. (1ucludiug CMD. starlight and dust cuussion: Porter ct al. | 2005) where $\sigma_T$ is the Thomson cross section, $u_{\rm tot}(\varepsilon_{\gamma})d\varepsilon_{\gamma}$ is the energy density of interstellar photons with the energy between $\varepsilon_{\gamma}$ and $\varepsilon_{\gamma}+d\varepsilon_{\gamma}$ (including CMB, starlight and dust emission; Porter et al. |
2008). and B is the interstellar maguetic eld which we here set as LG. Tere the function fixGe) is the correction factor to include the Nlein-Nishina effect. | 2008), and $B$ is the interstellar magnetic field which we here set as $\mu$ G. Here the function $f_{\rm KN}(x)$ is the correction factor to include the Klein-Nishina effect. |
According to Modoerski et al. ( | According to Moderski et al. ( |
2005). this function can be expressed as where b=7Lee.PEUflint), and the function Γης) is the dilogaritlin According to the recent experiments. cspecially ILE.S.S. (Aharonian et al. | 2005), this function can be expressed as where $\tilde{b}=4\varepsilon_e \varepsilon_{\gamma}/(m_e c^2)^2$, and the function ${\rm Li}_2(z)$ is the dilogarithm According to the recent experiments, especially H.E.S.S. (Aharonian et al. |
2008). the backeround CR clectrou/positron flux ποσα» to have a high enuergv dropping around a few TeV. This dropping is quite naturally explained iu the coutest of the astrophysical origin of CR electrous/positrous because the number of the sources contributing to the TeV energy baud is quite sinall according to the birth rate of SNe/pulsars iu the vienütv of the Earth (I&obavashi et al. | 2008), the background CR electron/positron flux seems to have a high energy dropping around a few TeV. This dropping is quite naturally explained in the context of the astrophysical origin of CR electrons/positrons because the number of the sources contributing to the TeV energy band is quite small according to the birth rate of SNe/pulsars in the vicinity of the Earth (Kobayashi et al. |
2004: IGisvanaka et al. | 2004; Kawanaka et al. |
2010). | 2010). |
Iu fact. since the pulsars which coutribute to the electron flux at the energy 2« should be ποσο thu the cooling time of clectrous/positrous füL/be.) and should be located closer to the Earth than the diffusion leneth dag~VENTESVeooop the ummiber of the pulsus contributing to 2TeV baud should be as sinall as where Ris the local pulsar birth rate per uuit surface area of our Galaxy. | In fact, since the pulsars which contribute to the electron flux at the energy $\varepsilon_e$ should be younger than the cooling time of electrons/positrons $t_{\rm cool}\sim 1/(b\varepsilon_e)$ and should be located closer to the Earth than the diffusion length $d_{\rm diff}\sim 2\sqrt{K(\varepsilon_e)t_{\rm cool}}$, the number of the pulsars contributing to $\gtrsim {\rm TeV}$ band should be as small as where $R$ is the local pulsar birth rate per unit surface area of our Galaxy. |
If we can separate the coutribution of a single voune source from the observed electron spectrum. we can get the information of the CR injection into the ISAL from that source. | If we can separate the contribution of a single young source from the observed electron spectrum, we can get the information of the CR injection into the ISM from that source. |
For this reason. we especially pay attention to the TeV spectral features of CR electrous frou a pulsar in the followines. | For this reason, we especially pay attention to the TeV spectral features of CR electrons from a pulsar in the followings. |
Iu Fies. | In Figs. |
3 aud 1 we show the time evolutions of CR electron spectrum from a nearby pulsar according to the models of the escape euergv το) adopted in the previous section (see also Fig. | 3 and 4 we show the time evolutions of CR electron spectrum from a nearby pulsar according to the models of the escape energy $\varepsilon_{\rm esc}(t)$ adopted in the previous section (see also Fig. |
2). | 2). |
It is clear that there exists a low energy cutoff iu cach spectiuu correspondiug to the value of ο) at that tine. | It is clear that there exists a low energy cutoff in each spectrum corresponding to the value of $\varepsilon_{\rm esc}(t)$ at that time. |
The spectral shapes ecnerally depeud on other parameters such as the high energy break of the iutriusic electron spectrua. the spectral iudex. the duration of clectron/positrou injection from a pulsar. and the total enerev of CR electrous/positrous. | The spectral shapes generally depend on other parameters such as the high energy break of the intrinsic electron spectrum, the spectral index, the duration of electron/positron injection from a pulsar, and the total energy of CR electrons/positrons. |
Towever. the sharp cutoff feature in the low cuerey side of the spectrum is almost independent of these properties. | However, the sharp cutoff feature in the low energy side of the spectrum is almost independent of these properties. |
In Fig. | In Fig. |
3. we cau sce that the low energv cutoff of cach spectrum is slisbtlyv broadened compared with that in Fie. | 3, we can see that the low energy cutoff of each spectrum is slightly broadened compared with that in Fig. |
lt. | 4. |
This is because the model adopted in this figure assumes that τος(1) decreases inore rapidly than in the case of Fig. | This is because the model adopted in this figure assumes that $\varepsilon_{\rm esc}(t)$ decreases more rapidly than in the case of Fig. |
{ and so the CR electrons/positrons in the broader energy rauge can reach the observer while iu the case of Fig. | 4 and so the CR electrons/positrons in the broader energy range can reach the observer while in the case of Fig. |
£1 where BAS) decreases slowly the low energy cutoff becomes very narrow. | 4 where $\varepsilon_{\rm esc}(t)$ decreases slowly the low energy cutoff becomes very narrow. |
Iu either case the dropotf in the low energv side of the spectrum is so steep that oue should assume the intrinsic spectral index as hard asa=0 lif we neelect the enereyv-dependent CR escape effects; | In either case the dropoff in the low energy side of the spectrum is so steep that one should assume the intrinsic spectral index as hard as $\alpha \lesssim 0-1$ if we neglect the energy-dependent CR escape effects. |
As we mentioned in the last section. if the maguetic field The CR electron spectruu with the age aud distauce similar to the Vela pulsar (fae.~L0tvear. rc 290pc). which is thought to be surounded by the supernova remnant (Aschenbach et al. | As we mentioned in the last section, if the magnetic field The CR electron spectrum with the age and distance similar to the Vela pulsar $t_{\rm age}\simeq 10^4{\rm year}$, $r\simeq 290{\rm pc}$ ), which is thought to be surrounded by the supernova remnant (Aschenbach et al. |
1995). is shown in Fie. | 1995), is shown in Fig. |
5. | 5. |
Uere we show the spectrum with the escape model of Ptuskin Zirakashvili (2005) as well as the spectrum without the CR confinement in the. SNR. | Here we show the spectrum with the escape model of Ptuskin Zirakashvili (2005) as well as the spectrum without the CR confinement in the SNR. |
In. addition. the electron fux which have not Όσσα confned iu the SNR (ie. Nese) aud that which have ouce confined and escaped later CV») are shown. | In addition, the electron flux which have not been confined in the SNR (i.e. $\dot{N}_{e,{\rm esc},1}$ ) and that which have once confined and escaped later $\dot{N}_{e,{\rm esc},2}$ ) are shown. |
We cau see that the latter component dominates the flux around the low enerev cutoff. | We can see that the latter component dominates the flux around the low energy cutoff. |
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