source
stringlengths 1
2.05k
⌀ | target
stringlengths 1
11.7k
|
|---|---|
Use qo=0.735. as before. and for definiteness. set In.X=10: numerical solution then gives nezm11. | Use $a = 0.735$, as before, and for definiteness set $\ln \Lambda = 10$; numerical solution then gives $\eta_{\mathrm{cw}} \approx 11$. |
A remarkable feature of (61)) is that not only has zd disappeared. but also the coupling constant. q. | A remarkable feature of \ref{eq:p_exp_1}) ) is that not only has $A_{\mathrm{M}}$ disappeared, but also the coupling constant, $q$. |
The lone-range character of the Coulomb interaction. however. is still apparent in Inv. | The long-range character of the Coulomb interaction, however, is still apparent in $\ln \Lambda$. |
An equation of this sort might reasonably have been expected to vield a value of pew that was either extremely small. so the CW transition takes place almost immeciately after the formation of the bubble. or extremely large. so the transition never takes place at all. | An equation of this sort might reasonably have been expected to yield a value of $\eta_{\mathrm{cw}}$ that was either extremely small, so the CW transition takes place almost immediately after the formation of the bubble, or extremely large, so the transition never takes place at all. |
Instead we get a value of ga Chat is within one or two orders of magnitude of unity. | Instead we get a value of $\eta_{\mathrm{cw}}$ that is within one or two orders of magnitude of unity. |
Up to this point we have been mainlv concerned. with potentials in the tail. | Up to this point we have been mainly concerned with potentials in the tail. |
But we have now to look more closely ab the electric anc magnetic fields in the main. pulse for dipole propagation. | But we have now to look more closely at the electric and magnetic fields in the main pulse for dipole propagation. |
These combine to give a Povnting vector directed outwards. | These combine to give a Poynting vector directed outwards. |
In at space. this vector falls off like 1/4 which tends to zero even when integrated. over the whole sphere. | In flat space, this vector falls off like $1/\chi^4$, which tends to zero even when integrated over the whole sphere. |
When we go to curved space. however. the Povnting vector tends to rensin8/sinhx). intowra | When we go to curved space, however, the Poynting vector tends to $(q V \sin \theta / \sinh \chi )^2$. |
lThe surface area of a sphere is dA?sinh?X. so the of the Poynting vector tends to a constant non-zero value. | The surface area of a sphere is $4 \pi R^2 \sinh^2 \chi$, so the integral of the Poynting vector tends to a constant non-zero value. |
One elfect of curvature is to continuously increase the energy of the plasma. | One effect of curvature is to continuously increase the energy of the plasma. |
lt seems unlikely this extra energy will remain in the [orm of pulses like those of figure 2.. | It seems unlikely this extra energy will remain in the form of pulses like those of figure \ref{fig:HPEPS}. |
We know such pulses propagate unchanged in a flat space. but when they have traveled cosmological distances. so the curvature becomes noticeable. we should expect a eracdual thermalization. | We know such pulses propagate unchanged in a flat space, but when they have traveled cosmological distances, so the curvature becomes noticeable, we should expect a gradual thermalization. |
We will moclelthis thermalization by including a small. constant conductivity. o. in our equations. | We will modelthis thermalization by including a small, constant conductivity, $\sigma$, in our equations. |
Note that e is not directly related to the normal conductivity of the plasma. which (in our cosmological units) would be very high. | Note that $\sigma$ is not directly related to the normal conductivity of the plasma, which (in our cosmological units) would be very high. |
e is just a device to represent the slow thermalization. and will have a value of order unity. | $\sigma$ is just a device to represent the slow thermalization, and will have a value of order unity. |
For technical reasons. which we explain below. we choose o= 1/(23z). | For technical reasons, which we explain below, we choose $\sigma = 1/(2\pi)$ . |
‘There are two reasons why wehave to investigate the ellectof σ: | There are two reasons why wehave to investigate the effectof $\sigma$ : |
where ΕΛ) 1s the integrated thermal energy up to a mass coordinate W,. | where $E_{\rm th}(M_r)$ is the integrated thermal energy up to a mass coordinate $M_r$. |
We set L.(0)=0 and define the nuclear luminosity as Ly,=|e4M,. so that equation (5)) becomes UMRLAY) Equation (7)) expresses that the nuclear luminosity must either go into thermal heating or convective motions. and it is valid at any M,. | We set $L_c(0)=0$ and define the nuclear luminosity as $L_{\rm nuc}=\int\epsilon dM_r$ , so that equation \ref{eq:integrated}) ) becomes = (M_r)-L_c(M_r) Equation \ref{eq:at_mr}) ) expresses that the nuclear luminosity must either go into thermal heating or convective motions, and it is valid at any $M_r$. |
It contains two unknowns. ft, and L.(M,). | It contains two unknowns, $t_h$ and $L_c(M_r)$. |
We set the luminosity at the surface of the convective zone to be zero. L.(M,.)=0. | We set the luminosity at the surface of the convective zone to be zero, $L_c(M_c)=0$. |
This boundary ts required since £j 1s long in the non-convective regions. which prevents significant heat transfer. | This boundary is required since $t_{\rm th}$ is long in the non-convective regions, which prevents significant heat transfer. |
We can then solve for rj. t= (M,). which matches the definition of ft, that Weinberg.et use in the context of type I X-ray bursts on neutron stars. | We can then solve for $t_h$, t_h = (M_c), which matches the definition of $t_h$ that \citet{wei06} use in the context of type I X-ray bursts on neutron stars. |
We substitute fj back into equation (7)) to get the convective luminosity LM) = EM, _= | | We substitute $t_h$ back into equation \ref{eq:at_mr}) ) to get the convective luminosity L_c(M_r) = (M_r)/t_h = ]. |
For steady-state convection. L(M,)=L4,0(M,). | For steady-state convection, $L_c(M_r)=L_{\rm nuc}(M_r)$. |
The ratio ΕΜ)ΕΜ.) is the modification due to the growing nature of the convection and the Z4,:LM,O/L4(M,) term is from long thermal time for the conductive exterior. which forces LM.)=0. | The ratio $E_{\rm th}(M_r)/E_{\rm th}(M_c)$ is the modification due to the growing nature of the convection and the $L_{\rm nuc}(M_c)/L_{\rm nuc}(M_r)$ term is from long thermal time for the conductive exterior, which forces $L_c(M_c)=0$. |
In the upper panel of Figure |) we plot as solid lines the convective luminosity found using equation (9)). | In the upper panel of Figure \ref{fig:luminosity} we plot as solid lines the convective luminosity found using equation \ref{eq:correct}) ). |
These models all have a composition of 0.5 C. 0.48 150. anc 0.02 Ne by mass fraction. with a mass of 1.37M... anc an initial isothermal temperature 7;=10°K. | These models all have a composition of 0.5 $^{12}$ C, 0.48 $^{16}$ O, and 0.02 $^{22}$ Ne by mass fraction, with a mass of $1.37\ M_\odot$ and an initial isothermal temperature $T_i=10^8\ {\rm K}$. |
We solve for p using the Paezynski(1983). fit for the equation of state. and include the Coulomb energy of Chabrier&Potekhi (1998). | We solve for $\rho$ using the \citet{pac83} fit for the equation of state, and include the Coulomb energy of \citet{cp98}. |
. We present central temperatures of 7.=6«10° anc 8«108K. which corresponds to %=I4hrs and 170 s. respectively. | We present central temperatures of $T_c=6\times10^8$ and $8\times10^8\ {\rm K}$, which corresponds to $t_h=14\ {\rm hrs}$ and $170\ {\rm s}$ , respectively. |
The ¢, associated with the latter case is a overestimate since. as mentioned above. at these late times during simmering only inner portion of the core responds to the rising central temperature (in effect decreasing £y, in eq. [8]. | The $t_h$ associated with the latter case is an overestimate since, as mentioned above, at these late times during simmering only inner portion of the core responds to the rising central temperature (in effect decreasing $E_{\rm th}$ in eq. \ref{eq:th}] ]). |
The energy generation rate for C burning is taken from Caughlan&Fowler(1988) with strong screening included from Salpeter&vanHorn(1969). | The energy generation rate for $^{12}$ C burning is taken from \citet{cf88} with strong screening included from \citet{svh69}. |
. Also plotted in Figure I is the convective luminosity for L((M,)=Li((M,). Lee. for steady-state convection (dashed lines). | Also plotted in Figure \ref{fig:luminosity} is the convective luminosity for $L_c(M_r)=L_{\rm nuc}(M_r)$, i.e., for steady-state convection (dashed lines). |
Near the center. ΕΜ} 1$ small and grows less quickly than L4,,M.,). L.(M,) is initially zL4,,M,) (see eq. [9]]). | Near the center, $E_{\rm th}(M_r)$ is small and grows less quickly than $L_{\rm nuc}(M_r)$, so $L_c(M_r)$ is initially $\approx L_{\rm nuc}(M_r)$ (see eq. \ref{eq:correct}] ]). |
At larger/ decreases due to the effects we have highlighted. | At larger $M_r$ , $L_c$ decreases due to the effects we have highlighted. |
If we take a characteristic eddy scale /.. the thermal conduction timescale across an eddy is ~(/./R10°yrs(H/RY10°yrs~104 yrs. where H is the pressure scale height. | If we take a characteristic eddy scale $l_c$, the thermal conduction timescale across an eddy is $\sim(l_c/R)^210^6\ {\rm yrs}\sim(H/R)^210^6\ {\rm yrs}\sim10^4\ {\rm yrs}$ , where $H$ is the pressure scale height. |
Since this timescale is long. the convection is efficient (Hansen&Kawaler1994). | Since this timescale is long, the convection is efficient \citep{hk94}. |
. Using estimates from mixing-length theory. the characteristic convective velocity. Vous. IS related to Fi via 1/3. where Q=-()Inp/olnT)» and e=GM,r is the local gravitational acceleration. and we have set /..z H. | Using estimates from mixing-length theory, the characteristic convective velocity, $V_{\rm conv}$, is related to $F_{\rm conv}$ via V_c =, where $\mathcal{Q}=-(\partial\ln\rho/\partial\ln T)_P$ and $g=GM_r/r^2$ is the local gravitational acceleration, and we have set $l_c\approx H$ . |
In the bottom panel of Figure | we have plotted V... setting the mixing-length to the scale height. /.=H lines). | In the bottom panel of Figure \ref{fig:luminosity} we have plotted $V_c$, setting the mixing-length to the scale height, $l_c=H$ ). |
The shape of these velocity profiles are similar to those Lesaffreetal.(2005) present in the context of studying the convective Urea process. which is active at much earlier times during the simmering. | The shape of these velocity profiles are similar to those \citet{les05} present in the context of studying the convective Urca process, which is active at much earlier times during the simmering. |
The convective velocities are different by as much as ~50% from the naivve estimate of LZ,=Lye lines) near the top of the convective zone. | The convective velocities are different by as much as $\sim50\%$ from the naïvve estimate of $L_c=L_{\rm nuc}$ ) near the top of the convective zone. |
Buoyantly rising eddies ascend until their density matches their surroundings. | Buoyantly rising eddies ascend until their density matches their surroundings. |
The boundary between the convective and isothermal zones is therefore set by a neutral buoyancy condition. | The boundary between the convective and isothermal zones is therefore set by a neutral buoyancy condition. |
In. practice this means that both the pressure and density mustbe continuous. | In practice this means that both the pressure and density mustbe continuous. |
If both the convective and isothermalregions havethe same composition. the boundary is simply set by when the adiabatic temperature of the convective zone reaches the isothermal temperature. 7; | If both the convective and isothermalregions havethe same composition, the boundary is simply set by when the adiabatic temperature of the convective zone reaches the isothermal temperature, $T_i$ |
an exponential distribution with a width fixed to be that observed in the aabsorbers. | an exponential distribution with a width fixed to be that observed in the absorbers. |
We obtain a height which is2005€ that found for the aabsorbers. | We obtain a height which is$\pm$ that found for the absorbers. |
We now attempt to build a model to describe both the extrinsic and intrinsic ssvstems. | We now attempt to build a model to describe both the extrinsic and intrinsic systems. |
We convert our modelled. velocity distribution of outflowing material into a distribution in comoving distance by assuming that each QSO contributes an equal proportion of the high-velocity tail. | We convert our modelled velocity distribution of outflowing material into a distribution in comoving distance by assuming that each QSO contributes an equal proportion of the high-velocity tail. |
For each absorber-QSO pair we transform the model velocity distribution into the distribution in. comoving distance at the redshift of the QSO. | For each absorber-QSO pair we transform the model velocity distribution into the distribution in comoving distance at the redshift of the QSO. |
We convolve the final distribution with a Gaussian to account for the QSO redshift errors and add this to the clustering model with different values of the parameter {ζωα | We convolve the final distribution with a Gaussian to account for the QSO redshift errors and add this to the clustering model with different values of the parameter $R_{\rm
cut}$. |
The result with oy=0.3 is shown in Figure as the solid black line. | The result with $R_{\rm cut}=0.3$ is shown in Figure \ref{fig:los2} as the solid black line. |
The contribution from clustering is shown by the dashed red line. | The contribution from clustering is shown by the dashed red line. |
The model fits well and it implies that a substantial fraction of low-velocity aabsorbers. with e«3000 kkm/s. may also be part of a distribution of outflowing material that is intrinsic to the QSO and/or its host. | The model fits well and it implies that a substantial fraction of low-velocity absorbers, with $v<3000$ km/s, may also be part of a distribution of outflowing material that is intrinsic to the QSO and/or its host. |
This increased value for τμ is now about that of low redshift hhalos. | This increased value for $R_{\rm cut}$ is now about that of low redshift halos. |
Together with the likelihood that 44 varies with redshift. QSO luminosity and halo mass. the fact that only of QSOs show associated absorption does not appear incompatible with our model. | Together with the likelihood that $R_{\rm cut}$ varies with redshift, QSO luminosity and halo mass, the fact that only of QSOs show associated absorption does not appear incompatible with our model. |
In Table 2. we present the fraction of each component (background. galaxy clustering. intrinsic) present in our model in different velocity ranges for both aand aabsorbers. | In Table \ref{table:2} we present the fraction of each component (background, galaxy clustering, intrinsic) present in our model in different velocity ranges for both and absorbers. |
The number of absorbers associated with intervening galaxies in our model is the sum of the background and galaxy clustering numbers. | The number of absorbers associated with intervening galaxies in our model is the sum of the background and galaxy clustering numbers. |
We note that the fractions of intrinsic absorbers presented here may be lower limits: we will return to discuss this in Section ??.. | We note that the fractions of intrinsic absorbers presented here may be lower limits; we will return to discuss this in Section \ref{sec:disc}. |
A key point of interest is whether the line-of-sight distribution of absorbers differs between radio-loud (RL) and radio-quiet (RQ) QSOs. | A key point of interest is whether the line-of-sight distribution of absorbers differs between radio-loud (RL) and radio-quiet (RQ) QSOs. |
The SDSS QSO catalogue has been matched with the FIRST radio survey (Beckeretal.1995).. | The SDSS QSO catalogue has been matched with the FIRST radio survey \citep{1995ApJ...450..559B}. |
In this section we have included only those QSOs in the FIRST survey footprint. | In this section we have included only those QSOs in the FIRST survey footprint. |
RL QSOs have been defined to be those with |.4GHz luminosities greater than 107 W/Hz (Milleretal. 1990). | RL QSOs have been defined to be those with 1.4GHz luminosities greater than $10^{25}$ W/Hz \citep{1990MNRAS.244..207M}. . |
The FIRST radio survey is flux limited to mmJy. which corresponds to ~107" W/Hz at a redshift of 2. close to the mean redshift of the aabsorbers. | The FIRST radio survey is flux limited to mJy, which corresponds to $\sim10^{25}$ W/Hz at a redshift of 2, close to the mean redshift of the absorbers. |
We therefore expect our RL sample to be complete in the ssample. but some RL QSOs in the aabsorber sample will contaminate the RQ sample. | We therefore expect our RL sample to be complete in the sample, but some RL QSOs in the absorber sample will contaminate the RQ sample. |
As the fraction of RL QSOs is low. around of all QSOs. this will not significantly bias the RQ distribution. | As the fraction of RL QSOs is low, around of all QSOs, this will not significantly bias the RQ distribution. |
In the ssample we have 1298 RL and 13179 RQ QSOs. | In the sample we have 1298 RL and 13179 RQ QSOs. |
In the ssumple we tind 543 RL and 5355 RQ QSOs. | In the sample we find 543 RL and 5355 RQ QSOs. |
It is known that a correlation exists between optical and radio luminosity (e.g.Cirasuoloetal.2003:Sikora2007).. | It is known that a correlation exists between optical and radio luminosity \citep[e.g.][]{2003MNRAS.346..447C,2007ApJ...658..815S}. |
We have therefore matched the optical luminosities of our RQ QSO sample to those of our RL QSO sample to avoid any biases. | We have therefore matched the optical luminosities of our RQ QSO sample to those of our RL QSO sample to avoid any biases. |
Optical luminosity is defined from the /-band PSF magnitude. K-corrected to z=2 following Richardsetal.(2006).. | Optical luminosity is defined from the $i$ -band PSF magnitude, K-corrected to $z=2$ following \citet{2006AJ....131.2766R}. |
This matching procedure reduces the RQ samples to 8343 and 3528 for the παπά ssamples respectively. | This matching procedure reduces the RQ samples to 8343 and 3528 for the and samples respectively. |
The velocity distributions are shown in Figure 10.. | The velocity distributions are shown in Figure \ref{fig:db_radio}. |
Comparing the RL and RQ samples. we see clear differences. | Comparing the RL and RQ samples, we see clear differences. |
A narrower and more pronounced spike at 7~0 is seen for the RL QSOs for both παπά aabsorbers. | A narrower and more pronounced spike at $\beta\sim0$ is seen for the RL QSOs for both and absorbers. |
This result for hhas been presented for many fewer QSOs by Vestergaard(2003)... | This result for has been presented for many fewer QSOs by \citet{2003ApJ...599..116V}. |
We also note that the subrelativistic tail of aabsorbers is visible in both the RL and RQ samples. but is clearly more pronounced in the RQ QSOs. | We also note that the subrelativistic tail of absorbers is visible in both the RL and RQ samples, but is clearly more pronounced in the RQ QSOs. |
This high-velocity tail was observed previously in RQ QSOs by Richardsetal.(1999). and Richards(2001).. | This high-velocity tail was observed previously in RQ QSOs by \citet{1999ApJ...513..576R} and \citet{2001ApJS..133...53R}. |
We will discuss these results in more detail in Section ??.. | We will discuss these results in more detail in Section \ref{sec:disc_radio}. |
Associated absorption line systems account for a small fraction of all metal absorbers detected in spectroscopic QSO surveys: however. their study is important for understanding the effect of QSOs on their host galaxies and their local environment. | Associated absorption line systems account for a small fraction of all metal absorbers detected in spectroscopic QSO surveys; however, their study is important for understanding the effect of QSOs on their host galaxies and their local environment. |
In the following subsections we will address the implications of our results for understanding the nature of associated narrow absorbers and for absorption line systems in general. | In the following subsections we will address the implications of our results for understanding the nature of associated narrow absorbers and for absorption line systems in general. |
The primary aim of our paper is to quantify whether some narrow absorption line systems are intrinsic to the QSO and its host galaxy. | The primary aim of our paper is to quantify whether some narrow absorption line systems are intrinsic to the QSO and its host galaxy. |
From our analysis alone. there is clear evidence that a high fraction of aabsorbers are intrinsic to the QSO. | From our analysis alone, there is clear evidence that a high fraction of absorbers are intrinsic to the QSO. |
of ssystems with velocities in the range 0.01<9«0.04 are intrinsic and are well described by an exponential velocity distribution. | of systems with velocities in the range $0.01<\beta<0.04$ are intrinsic and are well described by an exponential velocity distribution. |
A similar. but considerably smaller fraction of high-velocity aabsorbers are attributable to the QSO. | A similar, but considerably smaller fraction of high-velocity absorbers are attributable to the QSO. |
The high-velocity πα is 20-45% the height of that observed in IV. | The high-velocity tail is $\pm$ the height of that observed in . |
. Starburst-driven winds do not reach such highvelocities: it is therefore clear that these absorption line systems are a direct consequence of a QSO induced outflow 2007).. | Starburst-driven winds do not reach such highvelocities; it is therefore clear that these absorption line systems are a direct consequence of a QSO induced outflow \citep[see compilation in Figure 2
of][]{2007ApJ...663L..77T}. . |
Measurement of the galaxy luminosity function (LP) constitutes one of the most fundamental statistical constraints | Measurement of the galaxy luminosity function (LF) constitutes one of the most fundamental statistical constraints |
dynamical parameterso'sare relatedto theintereCMol the Reggetrajectorie | and $\beta_{\{q'q''\}^V}=2.0(\beta_q'+\beta_{q''})$ for anti-symmetric and symmetric valence |
dynamical parameterso'sare relatedto theintereCMol the Reggetrajectories | and $\beta_{\{q'q''\}^V}=2.0(\beta_q'+\beta_{q''})$ for anti-symmetric and symmetric valence |
agreement with this. the optical/X-ray bridge between NGC5I7/NGC5I5 and NOCHLL (Croftetal.2006) also indicates past and/or recent interactions between them. uuplving that the potential probably exteuds to the western side of the cluster as well. | agreement with this, the optical/X-ray bridge between NGC547/NGC545 and NGC541 \citep{croft06} also indicates past and/or recent interactions between them, implying that the potential probably extends to the western side of the cluster as well. |
A surprising result of our analvsis is that around the massive carly-type galaxies of Abell 191 (NGC511. Νέας15. NGC517) an unusually biegh umuber of bright resolved sources are observed (Fig. 7)). | A surprising result of our analysis is that around the massive early-type galaxies of Abell 194 (NGC541, NGC545, NGC547) an unusually high number of bright resolved sources are observed (Fig. \ref{fig:point_sources}) ). |
To study the uunber of sources around these galaxies. two circular reeions were selected with 1 radius: the first is ceutered between NOGCBI and NGC515 (henceforth region A) whereas the second is centered ou NCCSLL (heuceforth reeiou B). | To study the number of sources around these galaxies, two circular regions were selected with $1\arcmin$ radius: the first is centered between NGC547 and NGC545 (henceforth region $A$ ) whereas the second is centered on NGC541 (henceforth region $B$ ). |
The central parts (15" for NGCSLF aud 13” for NCHLL and NGCB515) of galaxies were excluded from the analysis since their brieht X-ray coronae notably reduce the poiut source detection sensitivity. | The central parts $15\arcsec$ for NGC547 and $13\arcsec$ for NC541 and NGC545) of galaxies were excluded from the analysis since their bright X-ray coronae notably reduce the point source detection sensitivity. |
Consideriug only sourceswith at least 10 counts in the 0.5.8 keV energy τοσο, in regions A and B 1L and 9 sources were detected. respectively. | Considering only sourceswith at least 10 counts in the $0.5-8$ keV energy range, in regions $A$ and $B$ $11$ and $9$ sources were detected, respectively. |
The most likely origins of the detected sources are: first. they could be low-mass N-rayv binaries (LAINBs) associated with the salaxies: second. they iav be resolved cosmic X-ray. background (CNB) sources. | The most likely origins of the detected sources are: first, they could be low-mass X-ray binaries (LMXBs) associated with the galaxies; second, they may be resolved cosmic X-ray background (CXB) sources. |
The umber of resolved LAINBs above a certain sensitivity limit can be cetermuned using their average huuinosity fiction (Culfanov200L). | The number of resolved LMXBs above a certain sensitivity limit can be determined using their average luminosity function \citep{gilfanov04}. |
. In the selected regions the source detection scusitivitv is zc7.2«107eresf. | In the selected regions the source detection sensitivity is $\approx7.2 \times10^{38} \ \rm{erg \ s^{-1}}$ . |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.