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Phen we expect the lepton enrichment to have an cllect on the afterglow emission until later than fairs | Then we expect the lepton enrichment to have an effect on the afterglow emission until later than $t_{pair}$. |
A shell of cireumburst medium that enters the GRB front at radius r;, leaves the front at raclius ru;~rin|ND34). where à is the shell velocity reached when it exits the GRB ront. the corresponding Lorentz factor σα=56rA) xung elven bv equations (31)). (33)) or (360). | A shell of circumburst medium that enters the GRB front at radius $r_{in}$ leaves the front at radius $r_{out} \sim r_{in} + \Delta/(1-\beta_\pm)$, where $\beta_\pm$ is the shell velocity reached when it exits the GRB front, the corresponding Lorentz factor $\gamma_\pm \equiv \gamma (x=\Delta)$ being given by equations \ref{ngcol}) ), \ref{gsph}) ) or \ref{gd}) ). |
The GIU ejectacollide with the pairwind ο”. (assumingthat 54 <1) i£ the GRB ejecta are outside the pont. ry 247A. | The GRB ejectacollide with the pair-wind at $r_c \sim [1+(\gamma_\pm/\Gamma)^2]
r_{out}$ (assumingthat $\gamma_\pm \ll \Gamma$ ) if the GRB ejecta are outside the front, $r_c > 2\, \Gamma^2 \Delta$ . |
Hf the GRB ejecta interact with the xur-wind while the laver is still within the GI front. its xur-loading and. Lorentz factor are lower. | If the GRB ejecta interact with the pair-wind while the layer is still within the GRB front, its pair-loading and Lorentz factor are lower. |
along magnetic field lines and impact the lower stellar atinosphiere. | along magnetic field lines and impact the lower stellar atmosphere. |
This catastrophic release of magnetic energv causes emission from the radio to the X-ray. (Llawlevetal.1995.2003:Ostenetal.2005:Fulrmeister2007:Berger 2003). | This catastrophic release of magnetic energy causes emission from the radio to the X-ray \citep{Hawley1995, Hawley2003, Osten2005, Fuhrmeister2007, Berger2008}. |
. On M cdwarls. (he most clistinet observational characteristic is the tremendous increase in the blue and near-ultraviolet continuum enission. up to several magnitudes in a few minutes or less (Hawley&Pettersen1991:Eason1992:Kowalskietal. 2010). | On M dwarfs, the most distinct observational characteristic is the tremendous increase in the blue and near-ultraviolet continuum emission, up to several magnitudes in a few minutes or less \citep{Hawley1991,Eason1992, Kowalski2010}. |
. The initial burst. or impulsive phase. is also cliaracterized in the oplical spectrum by increases in chromospheric line emission. parücululv in the hydrogen Balmer lines (Ilawley&Pettersen1991:MartinArcilasehnutt 2004). | The initial burst, or impulsive phase, is also characterized in the optical spectrum by increases in chromospheric line emission, particularly in the hydrogen Balmer lines \citep{Hawley1991, Mart'in2001, Fuhrmeister2004}. |
. The impulsive phase is followed by a gradual decay phase which can last from tens of minutes to hours for the largest flares (Moffett.1974:Zhilvaevetal.2007). | The impulsive phase is followed by a gradual decay phase which can last from tens of minutes to hours for the largest flares \citep{Moffett1974, Zhilyaev2007}. |
. The rate at which flares occur is of significant. current interest. | The rate at which flares occur is of significant current interest. |
Recently. numerous planets have been discovered. around. Al cdbwarfs. including some of only a few Earth masses (Udryetal.2007;Charbonneau2009:ForveilleAlavorοἱ 2010). | Recently, numerous planets have been discovered around M dwarfs, including some of only a few Earth masses \citep{Udry2007,Charbonneau2009, Forveille2009, Mayor2009, Correia2010}. |
. The atmospheres of these planets may be greatly alfected by the amount of hieh-energv radiation incident upon them. | The atmospheres of these planets may be greatly affected by the amount of high-energy radiation incident upon them. |
Cool. red. M dwarls produce little hish-energy raciation during quiescence. so the flaring rate is an important [actor in determining planet habitability (Heathοἱal.1999:Segura2005:Tarteret2007:WalkowiezSeguraοἱal. 2010). | Cool, red M dwarfs produce little high-energy radiation during quiescence, so the flaring rate is an important factor in determining planet habitability \citep{Heath1999, Segura2005, Tarter2007, Walkowicz2008, Segura2010}. |
. Additionally. characterizing the AI dwar! fLuwing rate is important for new instruments such as Pan-STARRS (Ixaiser2004).. the Palomar Transit Factory. (Ranetal.2009). and ihe Large Svnoptic Survey Telescope (LSSTScienceCollaborations: 2009).. whieh will carry ont large. all-sky surveys in the time-clomain. | Additionally, characterizing the M dwarf flaring rate is important for new instruments such as Pan-STARRS \citep{Kaiser2004}, the Palomar Transit Factory \citep{Rau2009} and the Large Synoptic Survey Telescope \citep{LSST2009}, which will carry out large, all-sky surveys in the time-domain. |
Elfectively selecting rare. exolic transients [rom the large sample of M dwar! flares (hat will be observed in these survevs requires reliable knowledge of expected flare characteristics ancl rates. | Effectively selecting rare, exotic transients from the large sample of M dwarf flares that will be observed in these surveys requires reliable knowledge of expected flare characteristics and rates. |
Traditionally. the frequency of flares on M. cwarls has been determined (through photometric monitoring of individual stars. | Traditionally, the frequency of flares on M dwarfs has been determined through time-resolved photometric monitoring of individual stars. |
Lacyetal.(1976). ancl Gershbere&Shakhovskaia(1983) have amassecl several hundred hours of optical observations on dozens of the most magnetically active and well-known flare stars and have derived power law relationships between (he total energv in the band and the frequency. of a flare. with less energetic flares occurring more frequently. | \citet{Lacy1976} and \citet{Gershberg1983} have amassed several hundred hours of optical observations on dozens of the most magnetically active and well-known flare stars and have derived power law relationships between the total energy in the band and the frequency of a flare, with less energetic flares occurring more frequently. |
Studies on individual stars have confined the power law form of the frequency distribution. albeit with a range of exponents (Walkeral.1984:Robinsonet1995:Leto1997: 1999). | Studies on individual stars have confirmed the power law form of the frequency distribution, albeit with a range of exponents \citep{Walker1981, Pettersen1984, Robinson1995, Leto1997, Robinson1999}. |
. At ullvaviolet wavelengths. Audardοἱal.(2000) and Sanz-Foreada&Micela(2002). found that the EUVE flare frequency distributions for active stars also had a power law form. | At ultraviolet wavelengths, \citet{Audard2000} and \citet{Sanz-Forcada2002} found that the EUVE flare frequency distributions for active stars also had a power law form. |
In addition. Auderedetal.(2000) demonstrated that large flares occur prelerentially on the X-ray brightest stars. | In addition, \citet{Audard2000} demonstrated that large flares occur preferentially on the X-ray brightest stars. |
observed in (he various dusty rines using the optical depth ratio: where του and 7,5» are (he measured slant optical depths in the summed spectral channels covering the ranges 2.87-2.98 jun and 3.13-3.25 pam. These optical depths are computed [rom the appropriately normalized (transmission profiles using (he procedures described in Seetion 2. above. so for each occultation cul through the rings we can derive p as a function of radius. | observed in the various dusty rings using the optical depth ratio: where $\tau_{2.9}$ and $\tau_{3.2}$ are the measured slant optical depths in the summed spectral channels covering the ranges 2.87-2.98 $\mu$ m and 3.13-3.25 $\mu$ m. These optical depths are computed from the appropriately normalized transmission profiles using the procedures described in Section \ref{obssec} above, so for each occultation cut through the rings we can derive $\rho$ as a function of radius. |
While p itself is useful for studyinge variations in the opacity dips strengthe within a single oceultation cut. for comparing data Irom different cuts through cifferent rines il is also worthwhile to have a radiallv-averaged. optical depth ratio for each occultation eut through each ring feature. | While $\rho$ itself is useful for studying variations in the opacity dip's strength within a single occultation cut, for comparing data from different cuts through different rings it is also worthwhile to have a radially-averaged optical depth ratio for each occultation cut through each ring feature. |
Simple racial averages are not appropriate in (his situation because the value of p becomes ill-defined when the optical depth is low. | Simple radial averages are not appropriate in this situation because the value of $\rho$ becomes ill-defined when the optical depth is low. |
Thus we instead compute aweighted average of p. where the weight is simply the optical depth at 3.2 jum: where Ds5 and D;» ave the ring leatures equivalent cepts at (hie (wo wavelengths (see Equation 2)). | Thus we instead compute a average of $\rho$, where the weight is simply the optical depth at 3.2 $\mu$ m: where $\mathcal{D}_{2.9}$ and $\mathcal{D}_{3.2}$ are the ring feature's equivalent depths at the two wavelengths (see Equation \ref{eqdepth}) ). |
Thus (p) is the ratio of the equivalent depths at 2.9;an and 3.2/an. which is the most sensible average statistic [or a narrow ring. | Thus $\langle\rho\rangle$ is the ratio of the equivalent depths at $\mu$ m and $\mu$ m, which is the most sensible average statistic for a narrow ring. |
The specific radial ranges used in the calculation of (p) differ for each ring feature. | The specific radial ranges used in the calculation of $\langle\rho\rangle$ differ for each ring feature. |
They are 139.000-141.000 km [or the F ring. 133.450-133.510. 133.540-133.650 and 137.000-133.730 for the inner. central and outer Encke gap ringlets. and km for the Charming Rineglet. | They are 139,000-141,000 km for the F ring, 133,450-133,510, 133,540-133,650 and 137,000-133,730 for the inner, central and outer Encke gap ringlets, and 119,880-119,980 km for the Charming Ringlet. |
The radial range lor the F ring is deliberately broad in order to include all of its multiple strands ancl encompass its substantial orbital eccentricity (Boshefa£2002:Murray.2008). | The radial range for the F ring is deliberately broad in order to include all of its multiple strands and encompass its substantial orbital eccentricity \citep{Bosh02, Murray08}. |
. When doimg each integration we deliberately exclude all data where 7,» is less than 5 times σ.. the standard deviation of 74» in the empty regions adjacent {ο the ring feature. | When doing each integration we deliberately exclude all data where $\tau_{3.2}$ is less than 5 times $\sigma_{\tau}$, the standard deviation of $\tau_{3.2}$ in the empty regions adjacent to the ring feature. |
We also exclude anv data where the transmission falls below 0.1 (i.e. 7> 2.3). in order to avoid regions where the optical depth may be saturated. | We also exclude any data where the transmission falls below 0.1 (i.e. $\tau>2.3$ ), in order to avoid regions where the optical depth may be saturated. |
The resulting values of (p) are recorded in Tables |- 3.. but we will use both the localized. single-sample values of p and the radially-averaged (quantities (p) in the discussions below. | The resulting values of $\langle\rho\rangle$ are recorded in Tables \ref{obstab}- – \ref{charmtab}, but we will use both the localized, single-sample values of $\rho$ and the radially-averaged quantities $\langle\rho\rangle$ in the discussions below. |
Figure 7 shows histograms of the derived (p) values for the various ring features. | Figure \ref{rhodist} shows histograms of the derived $\langle\rho\rangle$ values for the various ring features. |
The shading in the histograms represent data with different. sienal-lo-noise ratios. parametrized as the ratio of the peak optical depth at 3.2 ji (Faas) to the standard deviation of (he optical deptli values (0,) in nearby empty regions. | The shading in the histograms represent data with different signal-to-noise ratios, parametrized as the ratio of the peak optical depth at 3.2 $\mu$ m $\tau_{max}$ ) to the standard deviation of the optical depth values $\sigma_\tau$ ) in nearby empty regions. |
Note that in both the Encke Gap and Charming Rinelet distributions. (he data with τσ between | Note that in both the Encke Gap and Charming Ringlet distributions, the data with $\tau_{max}/\sigma_\tau$ between |
Tr(Days)| | longer term flares are added, the structure function continues rising, with a change of slope around 40 days but no discrete peak. |
FSRQ P.|BLLac P 0-5 0.33 0.15 5-20 0.130.38 20-50 0.15 0. | The peaky, choppy nature of the FSRQ and BL Lac structure functions indicates that the variability characteristics differ significantly across the sample. |
53 50-150 0. 19 0.58 150-250 |0.59 0.52 250-350 |0.16 0. I9 350-150. |0.59 0.56 120-650. |0. | This can be due to individual objects behaving uniquely, therefore making up an ensemble with a range of typical behaviors. |
27 0.39 650-850 | 0.52 0. 15 Table | Or, the mean variability can be disproportionately affected by a few measurements with high variability amplitude. |
1: IN-Sproba | Simulations using lightcurve features such as fast shifts in amplitude for only some objects do indeed create noisy, peaked structure functions; however the simulation results vary greatly across instantiations. |
bilities 273 data | Because each blazar is observed typically only four times, it is not possible to measure specific lightcurve features directly from the data. |
come fro | Furthermore, the complicated structure functions do not allow us to identify blazar lightcurve features such as the flares' exact durations or recurrence rates. |
mthe same underl | Instead, the modelling shows us that the blazar lightcurves show average variability that is indeed larger than that of type I quasars on both short and long timescales, and that the blazars' fluctuations over the timescales measured cover a wide range of amplitudes. |
ying distri | We can further investigate the influence of the window function through the structure function of 3C 273. |
bution. | We use the same method as in section \ref{v_sampling_section} to generate evenly-sampled and QUEST-sampled datasets for 3C 273. |
Calculated separately forFSRQ andBL Lac | The structure functions calculated from these datasets are shown in figure \ref{3c273sf_sampled}, using the FSRQ sampling cadence in panel (a) and the BL Lac cadence in panel (b). |
samplin | The hollow circles indicate the evenly-sampled data; the asterisks indicate the QUEST-sampled data. |
g | Error bars are determined using subsets of the total sample, as in the main analysis. |
caceuces. | The structure functions are consistent with each other, showing that windowing does not significantly alter the structure function results for the blazar. |
pl 4" eo | | -04r- . | Incidentally, 3C 273 is an example of an individual blazar that does not adhere to the description of its class's ensemble variability. |
E -o4b +i 4 * 4 ETIN ! J -14r * 4 14 | This object typically does show strong short timescale variability, but over the timescales studied its average variability amplitude does not increase dramatically with $\tau$. |
x E | l l 1 l L | MOJAVE \cite{mojave}) ) has monitored hundreds of blazars' radio brightnesses and polarizations using the VLBA. |
a] Γι 1 ∣ Log( | Their sample includes 5 of our BL Lacs and 31 of our FSRQs. |
TimeLag (Days)3 Log | The maximum apparent FSRQ jet speeds $\beta_{app}$ measured by are shown in figure \ref{betahist} in units of the speed of light. |
l TimeLag(Days)) Fig.Y.— St | Table \ref{vfor3bs_table} liststhe median $V$ values for FSRQs with different ranges of $\beta_{app}$ . |
ructureFuuction | The range of $V$ increases with $\beta_{app}$ , with FSRQs withhigher $\beta_{app}$ showing more high amplitude variability. |
'The calculated spectra show remarkably good overall fit to observations up to energies ~5-10? GeV, where the transition to extragalactic cosmic rays with the characteristic GZK suppression above 3x1010 GeV likely occurs. | The calculated spectra show remarkably good overall fit to observations up to energies $\sim 5\cdot {10}^{9}$ GeV, where the transition to extragalactic cosmic rays with the characteristic GZK suppression above $3\times10^{10}$ GeV likely occurs. |
To a good approximation the bending of the observed spectrum at around the knee energy 3-109 GeV is reproduced although no special efforts were made to force the theory to fit the data. | To a good approximation the bending of the observed spectrum at around the knee energy $3\cdot {10}^{6}$ GeV is reproduced although no special efforts were made to force the theory to fit the data. |
The bending is due to the combined effect of the summation over different types of SNRs and over different types of accelerated nuclei. | The bending is due to the combined effect of the summation over different types of SNRs and over different types of accelerated nuclei. |
'The complicated chemical composition of high energy cosmic rays is illustrated in Figure 3 where the calculated mean logarithmic atomic number of cosmic rays <In(A)> is presented. | The complicated chemical composition of high energy cosmic rays is illustrated in Figure 3 where the calculated mean logarithmic atomic number of cosmic rays $<\ln ( A) >$ is presented. |
The increase of <In(A)> at energies from 10° GeV to 107 GeV is due to thedependence of the knee position on charge pkneeοςZ for each kind of ion accelerated in Types Ia, IIP, Ib/c SNRs. | The increase of $<\ln ( A) >$ at energies from ${10}^{5}$ GeV to ${10}^{7}$ GeV is due to thedependence of the knee position on charge $p_{\mathrm{knee}}\propto Z$ for each kind of ion accelerated in Types Ia, IIP, Ib/c SNRs. |
Type IIb SNRs with normal composition dominate at rigidities p/Z>5.106 GV. | Type IIb SNRs with normal composition dominate at rigidities $p/Z>5\cdot {10}^{6}$ GV. |
They have a knee at about Pknee/Z.7:5-10" GV and provide progressively heavier composition to the very high energies. | They have a knee at about $p_{\mathrm{knee}}/Z\approx 5\cdot {10}^{7}$ GV and provide progressively heavier composition to the very high energies. |
It should be pointed out that the increase of «In(A)> at E>3x105 GeV predicted in our calculations is not supported by the available observations. | It should be pointed out that the increase of $<ln (A)>$ at $E>3\times10^{8}$ GeV predicted in our calculations is not supported by the available observations. |
If confirmed, these observations may signify the dominant contribution of extragalactic cosmic rays with light composition at these energies. | If confirmed, these observations may signify the dominant contribution of extragalactic cosmic rays with light composition at these energies. |
'The obtained cosmic ray spectrum shown by the solid line in Figure 2b is very attractive for the explanation of cosmic ray data. | The obtained cosmic ray spectrum shown by the solid line in Figure 2b is very attractive for the explanation of cosmic ray data. |
However, the use of the escape length (7) at ultra high energies is not justified. | However, the use of the escape length (7) at ultra high energies is not justified. |
Experimentally, the value of X. is determined from the abundance of secondary nuclei in cosmic rays with good statistics only up to about 100 GeV/n (Strongetal.2007).. | Experimentally, the value of $X_{e} $ is determined from the abundance of secondary nuclei in cosmic rays with good statistics only up to about $100$ GeV/n \citep{Strong07}. |
If cosmic ray transport in the Galaxy is described as diffusion, the diffusion coefficient can be expressed through the escape length as D=vH/2X. (here μα0.003 g/cm? is the surface mass density of Galactic gas disk, H54 kpc is the height of the Galactic cosmic-ray halo), which gives D=1.3:1075(pc/ZGeV)99 cm?/s. | If cosmic ray transport in the Galaxy is described as diffusion, the diffusion coefficient can be expressed through the escape length as $D\approx v \mu H/2X_{e}$ (here $\mu
\approx 0.003$ ${\mathrm{cm}}^{2}$ is the surface mass density of Galactic gas disk, $H\approx 4$ kpc is the height of the Galactic cosmic-ray halo), which gives $D\approx 1.3\cdot
{10}^{28} (p c/Z \mathrm{GeV})^{0.54}$ ${\mathrm{cm}}^{2} $ /s. |
The diffusion approximation can be used when the diffusion mean free path 3D/v is less than the size of the system H, which results in the condition pc/Z«2-10" GeV. At somewhat higher energies the particles accelerated in the galactic disk fly straight away from the Galaxy with a flat (source) energy spectrum and close to hundred percent anisotropy. | The diffusion approximation can be used when the diffusion mean free path $3D/v$ is less than the size of the system $H$, which results in the condition $pc/Z<2\cdot {10}^{7}$ GeV. At somewhat higher energies the particles accelerated in the galactic disk fly straight away from the Galaxy with a flat (source) energy spectrum and close to hundred percent anisotropy. |
Certainly this picture does not represent the reality that may be due to the strong intermittency of very high energy cosmic rays produced by random short bursts of not very numerous sources. | Certainly this picture does not represent the reality that may be due to the strong intermittency of very high energy cosmic rays produced by random short bursts of not very numerous sources. |
The dash line in Figure 2b shows the results of calculations made under the assumption that cosmic ray particles with energies pc>2-10"Z GeV freely escape from the Galaxy without being detected by observer at the Earth. | The dash line in Figure 2b shows the results of calculations made under the assumption that cosmic ray particles with energies $pc>2\cdot {10}^{7}Z$ GeV freely escape from the Galaxy without being detected by observer at the Earth. |
'The predicted spectrum may fit observations only below about 5-10" GeV in this case. | The predicted spectrum may fit observations only below about $5\cdot {10}^7$ GeV in this case. |
'The validity of diffusion approximation extends to higher energies in the diffusion model with distributed reacceleration on the interstellar turbulence where X,ος(p/Z)-/? at high rigidities, see Seo&Ptuskin (1994). | The validity of diffusion approximation extends to higher energies in the diffusion model with distributed reacceleration on the interstellar turbulence where $X_{e}\propto (p/Z)^{-1/3}$ at high rigidities, see \citet{Seo94}. |
However, this scaling does not reproduce the observed cosmic ray spectrum for the calculated source spectrum, see also discussion in Section 3. | However, this scaling does not reproduce the observed cosmic ray spectrum for the calculated source spectrum, see also discussion in Section 3. |
It is worth noting that the uncertainty in our knowledge of parameters of the interstellar turbulence does not allow to decide between two basic models of cosmic ray propagation: the plain diffusion model and the diffusion model with distributed reacceleration, see Ptuskinetal. (2006b). | It is worth noting that the uncertainty in our knowledge of parameters of the interstellar turbulence does not allow to decide between two basic models of cosmic ray propagation: the plain diffusion model and the diffusion model with distributed reacceleration, see \citet{Ptusk}. . |
. 'The physical pattern of cosmic ray propagation is different in the models with a Galactic wind. | The physical pattern of cosmic ray propagation is different in the models with a Galactic wind. |
The wind model with selfconsistently calculated | The wind model with selfconsistently calculated |
dominated by the chosen efficiency of convective overshoot, associated with the core mass at the first thermal pulse is relatively small. | dominated by the chosen efficiency of convective overshoot, associated with the core mass at the first thermal pulse is relatively small. |
Thus, iis a strong lower bound on the total energy output of TP-AGB stars stemming almost entirely from observational constraints. | Thus, is a strong lower bound on the total energy output of TP-AGB stars stemming almost entirely from observational constraints. |
We compute aas a function of initial mass for each cluster (Table 2)). | We compute as a function of initial mass for each cluster (Table \ref{tab:fuel}) ). |
Core growth in TP-AGB stars demonstrates that the TP-AGB phase contributes a significant portion of a intermediate mass star’s overall light generation. | Core growth in TP-AGB stars demonstrates that the TP-AGB phase contributes a significant portion of a intermediate mass star's overall light generation. |
Our results emphasize the strong link between the observables of the IFMR and the lower limit on the integrated light during the lifetime of TP-AGB stars. | Our results emphasize the strong link between the observables of the IFMR and the lower limit on the integrated light during the lifetime of TP-AGB stars. |
We now quantify the level of agreement between aand the predicted total light output by current evolutionary models of TP-AGB star. | We now quantify the level of agreement between and the predicted total light output by current evolutionary models of TP-AGB star. |
We define NumEmi[ ΩΩ preny (Odtisthe predictedtotalenergyintheT P—AGB phaseandisobtainedt AGBstellartracks | We define $=\lmin / \lmod$ where $\lmod$ is the predicted total energy in the TP-AGB phase and is obtained by integrating TP-AGB stellar tracks. |
Wechoosethelatest PADOVA groupT P—AGBtracks. producedbyBertelliet al.(2008.2009).. as | We choose the latest PADOVA group TP-AGB tracks, produced by \citet{Bertelli08, Bertelli09}, as they make predictions for a wide range of metallicities and incorporate up to date physics. |
aanditserroronaclusterbyclusterbasis. | In Table \ref{tab:fuel}, we list and its error on a cluster by cluster basis. |
T heweightedmeano f ΠΟΙΝΗ pleisO.56+0.04. | The weighted mean of in our sample is $0.56\pm0.04$ . |
The individual ffor cach cluster is within 2¢ of this mean while all but the cluster with the smallest progenitor mass, NGC 6819, and Praesepe are within 1o of this mean. | The individual for each cluster is within $2\sigma$ of this mean while all but the cluster with the smallest progenitor mass, NGC 6819, and Praesepe are within $1\sigma$ of this mean. |
Unless Bertelli substantially under-represent the energy output of the TP-AGB phase, the IFMR provides an estimate of the total light emitted in the TP-AGB phase accurate to within a factor of ~2. | Unless \citet{Bertelli08,Bertelli09} substantially under-represent the energy output of the TP-AGB phase, the IFMR provides an estimate of the total light emitted in the TP-AGB phase accurate to within a factor of $\sim2$. |
If we make the reasonable assumption (Section ??)) that the available fuel in the star during the TP-AGB phase comes primarily from nuclear burning. the quantity |—fri is the fraction of total predicted energy accounted for by nucleosynthetic products that were expelled into the ISM rather than added to the core. | If we make the reasonable assumption (Section \ref{sec:fuel}) ) that the available fuel in the star during the TP-AGB phase comes primarily from nuclear burning, the quantity $1- \fecore$ is the fraction of total predicted energy accounted for by nucleosynthetic products that were expelled into the ISM rather than added to the core. |
Assuming Bertellietal.(2008,2009) correctly predict the total energy output in TP-AGB stars, the product (1—fr.sw)*]Luarui(dt is the amount of light unaccounted for by core mass growth. | Assuming \citet{Bertelli08, Bertelli09} correctly predict the total energy output in TP-AGB stars, the product $(1- \fecore)* \lmod$ is the amount of light unaccounted for by core mass growth. |
Setting (1—fesu)*fLyrou(0dt=[|(dt in equation |,, we obtain the available fuel, in solar masses go). that comes from the stellar yield of the star. | Setting $(1- \fecore)* \lmod = \int L_{M_i}(t)dt$ in equation \ref{eq:fuel}, we obtain the available fuel, in solar masses ), that comes from the stellar yield of the star. |
In equation 2.. we make a distinction between the yield of He and that of CO. | In equation \ref{eq:fueltp}, we make a distinction between the yield of He and that of CO. |
In practice, the binding energy of He is 1/10 that of CO; thus, me make the approximation that He is the sole component of the stellar yield. | In practice, the binding energy of He is $1/10$ that of CO; thus, me make the approximation that He is the sole component of the stellar yield. |
The calculated ffrom each cluster is shown in Table 2.. | The calculated from each cluster is shown in Table \ref{tab:fuel}. |
We find our sample's weighted mean 20.082-0.01 M... | We find our sample's weighted mean $=0.08\pm0.01\ \msol$ . |
Every individual measurement of the stellar yield is within two σ of this mean. | Every individual measurement of the stellar yield is within two $\sigma$ of this mean. |
These results indicate that every star born at ~1.5M.<M,«6M.deposits ~0.1M. of He into the ISM during the TP-AGBphase. | These results indicate that every star born at $\sim1.5\msol < \mi < 6\msol$deposits $\sim 0.1\ \msol$ of He into the ISM during the TP-AGBphase. |
We discuss potential ramifications and tests of this prognosis in the | We discuss potential ramifications and tests of this prognosis in the |
the oldest” electrons. in the downstream region. or by AN(S) xs "fors.«5cy. or by a Latter shape for Hn«ocu. where ως ds the minimum energy of electrons accelerated at the As the first step we fit the SED in the racio-NUR-optical regimes with a svnchrotron model. and we derive the relevant. parameters of the svnchrotron spectrum (injection spectrum a. break [frequency £y. cut-olf. frequency κ) and the slope of the energy. distribution of the electron population as injected at the shock (p =2a| 1). | the “oldest” electrons in the downstream region, or by $N$ $\gamma$ ) $\propto \gamma^{-p}$ for $\gamma_{*} < \gamma < \gamma_{b}$, or by a flatter shape for $\gamma_{\rm low} < \gamma < \gamma_{*}$, where $\gamma_{\rm low}$ is the minimum energy of electrons accelerated at the As the first step we fit the SED in the radio-NIR-optical regimes with a synchrotron model, and we derive the relevant parameters of the synchrotron spectrum (injection spectrum $\alpha$, break frequency $\nu_{\rm b}$, cut-off frequency $\nu_{\rm c}$ ) and the slope of the energy distribution of the electron population as injected at the shock (p $= 2 \alpha +1$ ). |
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