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Owing to the lower thermal pressure and mixing of the ISM and RSG gas, both the bow shock and the tail are narrower in the slow models; e.g., the model B width is approximately half that of model Bag. | Owing to the lower thermal pressure and mixing of the ISM and RSG gas, both the bow shock and the tail are narrower in the slow models; e.g., the model B width is approximately half that of model $_{\rm ad}$. |
The forward shock of the fast model shows similar characteristics to model Bag; the combination of a large stellar velocity through the ISM, and an initially hot and lower density ISM, means that the fast-moving gas does not have enough time to cool beyond its initial condition. | The forward shock of the fast model shows similar characteristics to model $B_{\rm ad}$; the combination of a large stellar velocity through the ISM, and an initially hot and lower density ISM, means that the fast-moving gas does not have enough time to cool beyond its initial condition. |
The fast model achieves the same shocked ISM temperature, Tjsm, as the adiabatic case in which the star was moving approximately half as fast (see Fig. | The fast model achieves the same shocked ISM temperature, $T_{\rm ISM}$, as the adiabatic case in which the star was moving approximately half as fast (see Fig. |
8 [middle panel]). | \ref{fig: nprof} [middle panel]). |
Furthermore, this hot gas also flows along the bow shock and eventually settles in the core of the tail along the x axis, as it did in the adiabatic model. | Furthermore, this hot gas also flows along the bow shock and eventually settles in the core of the tail along the $x$ axis, as it did in the adiabatic model. |
However, the shocked RSG wind temperature is approximately 0000 K, much lower than the adiabatic counterpart and similar to the value for the slow models. | However, the shocked RSG wind temperature is approximately 000 K, much lower than the adiabatic counterpart and similar to the value for the slow models. |
The evolution of the forward and reverse shock positions for models B and Dy, i.e.the position of maximum temperature along the symmetry axis, is shown in Fig. 9.. | The evolution of the forward and reverse shock positions for models B and $_{\rm L}$, i.e.the position of maximum temperature along the symmetry axis, is shown in Fig. \ref{fig: shockpos}. |
Not only are the oscillations in the shock position less violent than the adiabatic case, an equilibrium shock position is attained more rapidly for the models with radiative cooling, after only 0000 years. | Not only are the oscillations in the shock position less violent than the adiabatic case, an equilibrium shock position is attained more rapidly for the models with radiative cooling, after only 000 years. |
The strong cooling in both the forward and reverse shocks in the slow models results in the excitation of R-T type instabilities (see below), which causes the gas to mix, hence the small difference between the positions of the RSG and ISM components. | The strong cooling in both the forward and reverse shocks in the slow models results in the excitation of R-T type instabilities (see below), which causes the gas to mix, hence the small difference between the positions of the RSG and ISM components. |
In contrast, there is little mixing between the two layers in the fast model's bow shock, the forward shock has significant width, thus the hottest gas extends much further into the impinging ISM flow. | In contrast, there is little mixing between the two layers in the fast model's bow shock, the forward shock has significant width, thus the hottest gas extends much further into the impinging ISM flow. |
The typical cooling time scale in the bow shock for x<0 is ~100000 years, and is of the order of both the characteristic dynamical time scale for the shocked ISM, Rso/v., which | The typical cooling time scale in the bow shock for $x < 0$ is $\sim$ 000 years, and is of the order of both the characteristic dynamical time scale for the shocked ISM, $R_{\rm SO} / v_*$ , which |
(2)) and (3)) can be ignored. | \ref{en_cons}) ) and \ref{x}) ) can be ignored. |
The angular function will therefore be given by the integral The main contribution to this iuteeral is provided by the clectrous with w approaching €. which is the result of Doppler aberration. | The angular function will therefore be given by the integral The main contribution to this integral is provided by the electrons with $\bg{\omega}$ approaching $\bg{\Omega}^\prime$, which is the result of Doppler aberration. |
Therefore. we may put in Eq. (6)) | Therefore, we may put in Eq. \ref{ang_3term}) ) |
Ow=µε aud 11Qwelqun | $\bg{\Omega}\bg{\omega}\approx \mu_s$ and $1-\beta\bg{\Omega}\bg{\omega}\approx 1-\mu_s$. |
The following integral over ji!=Ow ther arises: The integration leads to a very simple result: The angular function (8)) is presented iu the left panel of Fie. l.. | The following integral over $\mu^\prime=\bg{\Omega}^\prime\bg{\omega}$ then arises: The integration leads to a very simple result: The angular function \ref{ang_limit}) ) is presented in the left panel of Fig. \ref{figure}. |
It has a simple. apple-like shape (iu polar coordinates). which is the result of the combined action of two effects. namely the effect of selection of electrous according to the incidence angle by photons aud the Doppler aberration effect. as discussed iu the h-roductiou. | It has a simple, apple-like shape (in polar coordinates), which is the result of the combined action of two effects, namely the effect of selection of electrons according to the incidence angle by photons and the Doppler aberration effect, as discussed in the Introduction. |
Using formula (5)). we cau find the mean photon free path that corresponds to the aneular function eiven bv Eq. (8): A2(Noor) | Using formula \ref{lambda}) ), we can find the mean photon free path that corresponds to the angular function given by Eq. \ref{ang_limit}) ): $\lambda=(N_e\sigma_T)^{-1}$, |
bas it should be in the Thomson lait. | as it should be in the Thomson limit. |
Tt is not difficult to include ναιπάπα corrections in the expression (8)). | It is not difficult to include Klein-Nishina corrections in the expression \ref{ang_limit}) ). |
We shall do that to the first order of. accuracy. | We shall do that to the first order of accuracy. |
We- assume as before. that +favfiner2«. 1. | We assume as before that $\gamma h\nu/m_ec^2\ll 1$ . |
Iu this limit. hrfrienD(]1}, and. therefore. we can expand the ratio 17/7 given by Eq. (2)) | In this limit, $h\nu/\gamma
m_ec^2\ll (1-\beta)$, and, therefore, we can expand the ratio $\nu^\prime/\nu$ given by Eq. \ref{en_cons}) ) |
as follows: The expression in square brackets in the equation above nuplies that corrections need to be made to the three terms in Eq. (6)). | as follows: The expression in square brackets in the equation above implies that corrections need to be made to the three terms in Eq. \ref{ang_3term}) ), |
namely three additional terius proportional to Jic? appear. | namely three additional terms proportional to $h\nu/m_ec^2$ appear. |
Note that the fomth term in the expression N (Eq. |3]]) | Note that the fourth term in the expression $X$ (Eq. \ref{x}] ]) |
leads to a correction to the angular function of the order of (σος7. which will be neglected here. | leads to a correction to the angular function of the order of $(\gamma h\nu/
m_ec^2)^2$, which will be neglected here. |
The final result (the calculation is very similar to the oue that had led to Eq. [8]]) | The final result (the calculation is very similar to the one that had led to Eq. \ref{ang_limit}] ]) |
is If the electron energy is uot too high. sav 5<10. correctionis of the form 5" to the aueular function become important. | is If the electron energy is not too high, say $\gamma\lesssim 10$, corrections of the form $\gamma^{-n}$ to the angular function become important. |
These can be found as follows. | These can be found as follows. |
Ou introducing spherical coordinates with the polar axis potting aloug £. we obtain Tuteegration of the first and second bracketed terms iu Eq. (6)) | On introducing spherical coordinates with the polar axis pointing along $\bg{\Omega^\prime}$, we obtain Integration of the first and second bracketed terms in Eq. \ref{ang_3term}) ) |
then reduces to whereas the third term cau be expaucded as follows: hupleaueutius the straightforward iuteerations in Eqs. (12)) | then reduces to whereas the third term can be expanded as follows: Implementing the straightforward integrations in Eqs. \ref{int_a}) ) |
and (13)) and keeping only the leading terms (of order ~7), we derive We can finally combine Eqs. (10}) | and \ref{int_b}) ) and keeping only the leading terms (of order $\gamma^{-2}$ ), we derive We can finally combine Eqs. \ref{ang_limit1}) ) |
aud (11)) to obtain We tiplementeda series of Monte-C'arlo simulations to determine the parameter range of applicability of formula (15)): +22. shexO.027.2, | and \ref{ang_limit2}) ) to obtain We implementeda series of Monte-Carlo simulations to determine the parameter range of applicability of formula \ref{ang_limit_corr}) ): $\gamma\gtrsim 2$, $\gamma h\nu\lesssim 0.02 m_ec^2$. |
Tn the case of olectrouns obevine a relativistic Maswellian distribution. which is described bv the function dN.x(5?Lyteeoxpsme{kTds. Eq. (153) | In the case of electrons obeying a relativistic Maxwellian distribution, which is described by the function $dN_e\propto\gamma(\gamma^2-1)^{1/2}\exp{(-\gamma m_ec^2/kT_e)}\,d\gamma$, Eq. \ref{ang_limit_corr}) ) |
should be convolved with this function. | should be convolved with this function. |
The result is where T, is the temperature of the electrons aud DIan.:)=[ote“de ds the incomplete Cama ↕≯∏∐↸⊳↑↕ | The result is where $T_e$ is the temperature of the electrons and $\Gamma(\alpha,z)=\int_z^\infty x^{\alpha-1} e^{-x}dx$ is the incomplete Gamma function. |
∪∐∙⊟≻↥⋅∐⋯↕⋜↧∐⊓⊔↕↴∖↴⋜↧∶↴∙⊾∪∪≼↧⋜∏∏∐⋅∪⊼↕⋯⋜↧↑↕∪∐↕↕⋟∕≍⋮⊺↿≧ 2in,05, hieT,<lon,(32, | Formula \ref{ang_maxwel1}) ) is a good approximation if $kT_e\gtrsim 2 m_ec^2$ , $h\nu kT_e\lesssim 0.01
(m_ec^2)^2$. |
Tt is interesting to compare the first of these conditions with the correspoucding constraint on the applicability. of the approximation (15)) (see text following that equation). | It is interesting to compare the first of these conditions with the corresponding constraint on the applicability of the approximation \ref{ang_limit_corr}) ) (see text following that equation). |
Evideutlv. the relatively poor convergence of the series (16)) is due to the contribution of the low-cuerey tail of the Maxwellian distribution. Le. clectrous with 5x(4)=34D.fn, e. | Evidently, the relatively poor convergence of the series \ref{ang_maxwel1}) ) is due to the contribution of the low-energy tail of the Maxwellian distribution, i.e. electrons with $\gamma\lesssim\langle\gamma\rangle= 3kT_e/m_ec^2$ . |
Various examples of the aneular function corresponding to the scattering on hieh-teniperature electrous.as resulted from Aloute-Carlo siuulations or calculated from Eq. (16)). | Various examples of the angular function corresponding to the scattering on high-temperature electrons,as resulted from Monte-Carlo simulations or calculated from Eq. \ref{ang_maxwel1}) ), |
are preseuted in Fie. 1.. | are presented in Fig. \ref{figure}. . |
scale for which the background is unknown (the rise time). and {ο provide a representative background flux. | scale for which the background is unknown (the rise time), and to provide a representative background flux. |
Figure 3 illustrates the procedure and the results. | Figure 3 illustrates the procedure and the results. |
The upper panel shows the first event [rom AR. 11029. which occurred around 20:00 UT on 24 Oct. The one-minute [ας values are shown versus time (solid curve). with the three vertical dotted lines indicating /,. /,.p. and /. Che end time) for the event. as given bv the SWPC event lists. | The upper panel shows the first event from AR 11029, which occurred around 20:00 UT on 24 Oct. The one-minute flux values are shown versus time (solid curve), with the three vertical dotted lines indicating $t_{\rm s}$ , $t_{\rm p}$ , and $t_{\rm e}$ (the end time) for the event, as given by the SWPC event lists. |
The averaging interval is the interval to the left of the first vertical line. and the resulting background estimate is shown bv the dotted horizontal line. | The averaging interval is the interval to the left of the first vertical line, and the resulting background estimate is shown by the dotted horizontal line. |
This event is assigned a peak flux 1.6xLOWm? in the SWPC event lists (DI.6). | This event is assigned a peak flux $1.6\times 10^{-7}\,{\rm W}\,{\rm m}^{-2}$ in the SWPC event lists (B1.6). |
The background estimate is 3.11x10Wm7. so the resulting backeround-subtracted peak flux is 1.29x10‘Wain7? (DI.3). | The background estimate is $3.11\times 10^{-8}\,{\rm W}\,{\rm m}^{-2}$, so the resulting background-subtracted peak flux is $1.29\times 10^{-7}\,{\rm W}\,{\rm m}^{-2}$ (B1.3). |
The lower panel of Figure 3 shows the effect of background subtraction for all events. displaved as a cumulative nunmber distribution. (he number of events with a larger (or equal) peak Πας, versus peak [Iux. | The lower panel of Figure 3 shows the effect of background subtraction for all events, displayed as a cumulative number distribution, the number of events with a larger (or equal) peak flux, versus peak flux. |
The plot is shown in a log-log representation. | The plot is shown in a log-log representation. |
The peak-IIux values belore background subtiraction are indicated by the crosses. and the baekground-subtracted. values are shown bv the diamonds. | The peak-flux values before background subtraction are indicated by the crosses, and the background-subtracted values are shown by the diamonds. |
The procedure introduces substantial changes in the peak-fhix values. in particular for smaller events. | The procedure introduces substantial changes in the peak-flux values, in particular for smaller events. |
The cumulative number distribution shown in the lower panel of Figure 3 is expected to Follow a power law. according to equation (1)). | The cumulative number distribution shown in the lower panel of Figure 3 is expected to follow a power law, according to equation \ref{eq:fsize_dist}) ). |
Specifically. Che model cumulative number distribution corresponding; to the frequeney-size distribution equation (1)) is where Vy=A4Tis the number of events above size 54 in lime T7. | Specifically, the model cumulative number distribution corresponding to the frequency-size distribution equation \ref{eq:fsize_dist}) ) is where $N_1=\lambda_1 T$is the number of events above size $S_1$ in time $T$. |
Inspection of Figure 3 suggests an absence of large events by comparion wilh the power-law form. [or the background-subtracted distribution (he distribution falls away rapidly al laree 5. | Inspection of Figure 3 suggests an absence of large events by comparion with the power-law form, for the background-subtracted distribution – the distribution falls away rapidly at large $S$. |
To «quantilv (his behavior. we consider comparison of the observed. (background-subtracted) distribution with (wo models: a simple power-law. and a power law wilh an upper exponentia rollover. | To quantify this behavior, we consider comparison of the observed (background-subtracted) distribution with two models: a simple power-law, and a power law with an upper exponential rollover. |
The probabilitydistributions for peak flux for the two models are and respectively. with 8>54. | The probabilitydistributions for peak flux for the two models are and respectively, with $S\geq S_1$. |
In equation (7)) 7 is the upper rollover and is anormalizationconstant. which depends on 544. 7. and 5, (see Appendix D). | In equation \ref{eq:PS_plr}) ) $\sigma $ is the upper rollover and $B$ is anormalizationconstant, which depends on $\gamma_{\rm plr}$ , $\sigma$ , and $S_1$ (see Appendix B). |
The [requency-peak flux | The frequency-peak flux |
Dlass oss rate of the star) blows into a medium of uniform density po. | mass loss rate of the star) blows into a medium of uniform density $\rho_{0}$. |
“Phis generates a bu»ble wit ra structure dividel into tiree distinct regions: an Outer srock. separating the uncisturbecd ambient. ISM. from ai she‘AL of swept up ancl gajoCkcL ISM: a bubble of hot sjocked stellar wind material YOULLed at its outer edge by a contact ciscontinulty between it an he shell of shocked. 18M. and at its inner edge by ¢I reverse shock between it and tve thirel innermost region of 10 [πουν expanding stellar wind. | This generates a bubble with a structure divided into three distinct regions: an outer shock, separating the undisturbed ambient ISM from a shell of swept up and shocked ISM; a bubble of hot shocked stellar wind material, bounded at its outer edge by a contact discontinuity between it an the shell of shocked ISM, and at its inner edge by a reverse shock between it and the third innermost region of the freely expanding stellar wind. |
Afer several thousane ECALs he shell of swept up ISM cools ancl collapses down t«H orm clenser. cold. (P~ 107IX) shell. which is the source of 16 the optical emission associated wit1 the nebula. | After several thousand years the shell of swept up ISM cools and collapses down to form denser, cold $T\sim 10^{4} \K$ ) shell, which is the source of the the optical emission associated with the nebula. |
In the standard Weaver (1977). model therma conduction leads to evaporation of matter olf the dense shell of swept-up ISM into the hot bubble interior. cooling it ancl significantly. increasing its density. | In the standard Weaver (1977) model thermal conduction leads to evaporation of matter off the dense shell of swept-up ISM into the hot bubble interior, cooling it and significantly increasing its density. |
In common with many of the hverodyvnamical simulations of bubbles we do not include conduction. | In common with many of the hydrodynamical simulations of bubbles we do not include conduction. |
Magnetic fields may suppress conduction. even at. very low B-licld strengths that otherwise are dynamically unimportant (Soker 1994: Band Liang 1988). | Magnetic fields may suppress conduction, even at very low B-field strengths that otherwise are dynamically unimportant (Soker 1994; Band Liang 1988). |
Given the limited. observational knowledge on the state of magnetic fields ancl conduction within bubbles we choose to ignore both! | Given the limited observational knowledge on the state of magnetic fields and conduction within bubbles we choose to ignore both! |
We shall consider two simulations. both with Ly=«107mergs . | We shall consider two simulations, both with $L_{\rm W} = 6.3 \times 10^{37} \ergps$ . |
LopTo obtain ⋠⋠⋅dillerent temperatures in. the hot bubble we vary the wind mass loss rate between | To obtain different temperatures in the hot bubble we vary the wind mass loss rate between |
the star comprising most of its mass is assunied to behave like a polvtrope with iudex s=3/2. so that inside the star pressure P is related to the deusitv p via Pxpe. | the star comprising most of its mass is assumed to behave like a polytrope with index $n=3/2$, so that inside the star pressure $P$ is related to the density $\rho$ via $P\propto\rho^{5/3}$. |
This approximation works very well iu. hielilv ionized. dense. and fully couvective interiors of voung stars. | This approximation works very well in highly ionized, dense, and fully convective interiors of young stars. |
The total enerey of such a star (a stun of its thermal and eravitationa )] is Eye—OMT)GAD/R (Iippeuhaln Weigert 1991). | The total energy of such a star (a sum of its thermal and gravitational ) is $E_{tot}=-(3/7)GM^2/R$ (Kippenhahn Weigert 1994). |
Evolution of protostellar properties luminosity £. radius Rasa function of time jor. equivalently. stellar mass M(£)] is them governed by the following equation: |LuL. The Ll.s. | Evolution of protostellar properties – luminosity $L$, radius $R$ – as a function of time [or, equivalently, stellar mass $M(t)$ ] is then governed by the following equation: )= +L_D-L. The l.h.s. |
of this equation represcuts the chauge iu the total stellar energw. the first and second terius iu the r.l.s. | of this equation represents the change in the total stellar energy, the first and second terms in the r.h.s. |
are the eravitational potential energy and the thermal energy brought in with the accreted material. while Lp(Al.R) is a deuterimm huninosity of a protostar. | are the gravitational potential energy and the thermal energy brought in with the accreted material, while $L_D(M, R)$ is a deuterium luminosity of a protostar. |
Stellar luuineosity £ is the luuinosity carried towards the photosphere by the convective motions m the stellar interior. | Stellar luminosity $L$ is the luminosity carried towards the photosphere by the convective motions in the stellar interior. |
It is different from the inteerated cuussivity of the stellar surface since the star also intercepts aud reraciates a fraction of energy released in the accretion clisk. | It is different from the integrated emissivity of the stellar surface since the star also intercepts and reradiates a fraction of energy released in the accretion disk. |
Rate at which thermal energy gets accreted by the star Is where 5 is 21Hthe ratio of specific heats of accreted gas (which can be different from >=5/3 characteristic for the stellar interior). kp is the Boltzmann constaut. µ ας. T ave the mean molecular weight aud the temperature of the accreted gas. | Rate at which thermal energy gets accreted by the star is where $\gamma$ is the ratio of specific heats of accreted gas (which can be different from $\gamma=5/3$ characteristic for the stellar interior), $k_B$ is the Boltzmann constant, $\mu$ and $T$ are the mean molecular weight and the temperature of the accreted gas. |
Dimensionless pariuneter à can be written as where T5; is the stellar virial temperature. | Dimensionless parameter $\alpha$ can be written as where $T_{vir}$ is the stellar virial temperature. |
Cas accreting from the disk experiences strong dissipation iu the boundary laver near the stellar surface. | Gas accreting from the disk experiences strong dissipation in the boundary layer near the stellar surface. |
In this laver eas temperature can become an appreciable fraction of Ty | In this layer gas temperature can become an appreciable fraction of $T_{vir}$. |
However. the cooling time in the boundary laver anc the outermost lavers of the star is very short so that the accreted gas cools οποιο] aud. should ultimately join stellar interior with temperature Lo which is much lower than T,;, [unless A is extremely high. in excess of 10| AL. ft. κος Popham | However, the cooling time in the boundary layer and the outermost layers of the star is very short so that the accreted gas cools efficiently and should ultimately join stellar interior with temperature $T$ which is much lower than $T_{vir}$ [unless $\dot M$ is extremely high, in excess of $10^{-4}$ $_\odot$ $^{-1}$, see Popham (1997)]. |
Thus. under the conditions considered in this work (1997)].oue expect à<1 but the actual value of this parameter is rather poorly constrained (t depends on the gas therimodynauiies. radiative trausport. aud the viscosity prescription in the boundary laver which ive poorly coustrained). | Thus, under the conditions considered in this work one expect $\alpha\ll 1$ but the actual value of this parameter is rather poorly constrained (it depends on the gas thermodynamics, radiative transport, and the viscosity prescription in the boundary layer which are poorly constrained). |
As here we are primarily interested in the effects of disk irradiation we set a=0 for simplicitv?. | As here we are primarily interested in the effects of disk irradiation we set $\alpha=0$ for . |
. Tn this case equation (1)) can be rewritten as This is an evolution equation for R aud cau be easily inteerated munerically once the dependencies of £5 aud L ou stellar parameters ave known. | In this case equation \ref{eq:energy_eq}) ) can be rewritten as This is an evolution equation for $R$ and can be easily integrated numerically once the dependencies of $L_D$ and $L$ on stellar parameters are known. |
For Lp we adopt the expression obtained in Staller (1998) bv integrating the rate of energy release due to D burning within the η—3/2 polvtrope:n where Lpy=1.92<10"E. and fp is the fractional D abundance relative to the initial D umuber abundance [D/IT| taken to be 2«105, | For $L_D$ we adopt the expression obtained in Stahler (1998) by integrating the rate of energy release due to D burning within the $n=3/2$ polytrope:, where $L_{D,0}=1.92\times 10^{17}~L_\odot$ and $f_D$ is the fractional D abundance relative to the initial D number abundance [D/H] taken to be $2\times 10^{-5}$. |
Parameter fp is uot constant in fiue — dtf evolves since D burus in the stellar iuterior while the new D is being brought in with the accreting material (with the initial abundance [D/ITI|). | Parameter $f_D$ is not constant in time – it evolves since D burns in the stellar interior while the new D is being brought in with the accreting material (with the initial abundance [D/H]). |
As a result. one fiuds (Staller 1988: Hartiuaun 1997) where Jp=9.2«10% eres e+ is the cnerey released by D fusion per gru of stellar material Gassing |D/II[—2.10 "Jj. | As a result, one finds (Stahler 1988; Hartmann 1997) where $\beta_D=9.2\times 10^{13}$ ergs $^{-1}$ is the energy released by D fusion per gram of stellar material (assuming $=2\times 10^{-5}$ ). |
The most important aspect of this work which distinguishes it from) DHartmiaun (1997) is the calculation of £. | The most important aspect of this work which distinguishes it from Hartmann (1997) is the calculation of $L$. |
In the approximation adopted by Tartimaun (1997) £ is a function of Rand AL ouly. | In the approximation adopted by Hartmann (1997) $L$ is a function of $R$ and $M$ only. |
Iu our case situation is differcut: nraciation of the stellar surface eives rise to au outer convectivelv stable laver below the stellar photosphere (Rafikov 2007). similar to the radiative laver that form im the atimosphercs of the close-in giant planets nraciated by their pareut stars (Caullot1996: Burrows 2000). | In our case situation is different: irradiation of the stellar surface gives rise to an outer convectively stable layer below the stellar photosphere (Rafikov 2007), similar to the radiative layer that form in the atmospheres of the close-in giant planets irradiated by their parent stars (Guillot1996; Burrows 2000). |
This external radiative zone suppresses the local radiative flux conuüues frou stellar iuterior and this changes the inteerated stellar buuinositv. which becomes a function of imradiation intensity. | This external radiative zone suppresses the local radiative flux coming from stellar interior and this changes the integrated stellar luminosity, which becomes a function of irradiation intensity. |
As a result. in irracliated case L depends uot only on AR and AL but also ou AL (which determines the streneth of the radiation flux). | As a result, in irradiated case $L$ depends not only on $R$ and $M$ but also on $\dot M$ (which determines the strength of the irradiation flux). |
Rafikov (2007) has demonstrated that for a given opacity behavior at the stellar surface(parametrized m lis case to be a power-law function of gas pressure 7? and temperature T. 8x ΠΤΙ} the degree of Iuninosity | Rafikov (2007) has demonstrated that for a given opacity behavior at the stellar surface(parametrized in his case to be a power-law function of gas pressure $P$ and temperature $T$ , $\kappa\propto P^{\alpha}T^\beta$ ) the degree of luminosity |
Dv virtue of its unusual characteristics. HD 17156b is one of the most valuable extrasolar planets for understauxding planet lormation and orbital dynamics. | By virtue of its unusual characteristics, HD 17156b is one of the most valuable extrasolar planets for understanding planet formation and orbital dynamics. |
Discovered via the Doppler technique by the N21Ix consortium (Fischer et al. | Discovered via the Doppler technique by the N2K consortium (Fischer et al. |
2007). the planet was found to transit its host star by the collaboration (Barbieri et al. | 2007), the planet was found to transit its host star by the collaboration (Barbieri et al. |
2007). | 2007). |
Additional (ransil observations aud refined svstemi parameters are given by Gillon et al. ( | Additional transit observations and refined system parameters are given by Gillon et al. ( |
2008). Narita οἱ al. ( | 2008), Narita et al. ( |
2008). and Irvin et al. ( | 2008), and Irwin et al. ( |
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