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Two mass-cut boundaries ( cut and mix ) and the fraction of materials ejected from the mixing region ( ) are essential parameters to determine [MATH] and [MATH] |
(e.g., Iwamoto et al., 2005 ; Nomoto et al., 2006 . The kinetic energies of explosion of faint supernovae (SN1997D and SN1999br) are estimated to be [MATH] (0.4-0.6) [MATH] 10 51 erg, which is [MATH] 1/3 to 1/2 times smaller than the typical kinetic energy of supernova explosion. However, an explosion with slightly les... |
Regarding cut , the initial mass-cut within the incomplete Si-burning layer suppresses the ejection of 53 Mn as discussed in fallback supernova models (Meyer & Clayton, 2000 ; Meyer, 2005 . Although a proper choice of cut in the narrow incomplete Si-burning layer may explain the amounts of SLRs in the solar system incl... |
The position of the outer boundary of the mixing region, mix , was varied from within the incomplete Si-burning layer to the bottom of H-burning shell, and the ejection fraction, , was given values between 10 -4 -10 -2 . Note that mix and were required to be within the C/O-burning region or the He-burning region and [M... |
Modeling the solar system SLRs with a supernova with mixing-fallback We determined and [MATH] to minimize deviations of modeled abundances of 26 Al, 41 Ca, 53 Mn, and 60 Fe (see Eq.(1)) from their estimated initial abundances in the early solar system; 26 Al/ 27 Al = (5.0 [MATH] 0.5) [MATH] 10 -5 41 Ca/ 40 Ca = (1.4 [M... |
(e.g., Kita et al., 2005 . Because the initial abundances of 53 Mn and 60 Fe have not been well determined yet, we chose plausible abundances for them and gave larger uncertainties than for 26 Al and 41 Ca based on ranges of reported initial abundances. Note that the choice of plausible initial abundances for 53 Mn and... |
Short-lived radionuclides from supernovae with mixing-fallback Calculated initial abundances of 26 Al, 41 Ca, 53 Mn, and 60 Fe normalized to meteoritic initial abundances for non-fallback supernovae are shown in Figure 2a-d as a function of the mass of the exploding star. The dilution factor, , is estimated to be in th... |
The abundances of SLRs estimated for faint supernova of different masses with mixing-fallback are shown in Figure 3 as a function of mix and . It is clearly seen that injection of 53 Mn and 60 Fe is suppressed and the abundances of SLRs agree with their solar system abundances as long as the outer boundary of mixing re... |
The obtained and [MATH] increase from 7 [MATH] 10 -5 to 2 [MATH] 10 -3 and from 0.8 to 1.1 Myr, respectively, with increasing mix in the C/O-burning layer. Both parameters affect the abundances of 26 Al and 41 Ca, while those of 53 Mn and 60 Fe are affected mainly by when [MATH] [MATH] 1 Myr. Thus, increases with mix b... |
In addition of the calculations shown in Fig.3, we calculated the abundances of SLRs with the ejection fraction =10 -4 , which has been proposed for hyper-metal-poor stars (Iwamoto et al., 2005 , but the abundance of 53 Mn was about ten times lower than the estimate for the initial solar system, as in the simple fallba... |
The best estimates for the faint supernovae with mixing-fallback are shown in Figure 4, where the calculated abundances of SLRs reproduce their solar system abundances within a factor of 2. It should be emphasized here that a narrow range of mixing-fallback parameters ( mix and ) is not required to match the solar syst... |
A faint supernova with mixing-fallback as a source of solar system SLRs Previous supernova models, which attempted to explain the initial abundances of solar system SLRs, had the problems of over-injection of 53 Mn and 60 Fe compared to 26 Al and 41 Ca. Such problems can be solved in the faint supernova model with mixi... |
Manganese-53 is synthesized mainly in the incomplete Si-burning layer, while 26 Al, 41 Ca, and 60 Fe are produced more abundantly in outer regions (Fig. 1). Although a small fraction of the 53 Mn is ejected, most falls back only to the collapsing core when the outer region of the mixing layer is located in the C/O-burn... |
Aluminum-26 is the only nuclide, among SLRs considered in this study, that forms abundantly in the He and H layers and the explosive O-burning layer of a massive star with the solar metallicity. If the oute r boundary of the mixing region is located in the C/O layer, more than 80 % of 26 Al should have its origin in th... |
We conclude that 26 Al, 41 Ca, 53 Mn, and 60 Fe in the early solar system could have been brought from a single massive star that experienced a less-energetic supernova explosion. The estimated dilution factor, , may provide a geometric constraint on the supernova and the solar system materials as discussed by Sahijpal... |
It is difficult to evaluate which case is more plausible for the solar system forming environment at present. However, in either case, the supernova explosion should have occurred nearby the solar system materials, which supports the idea of the birth of the solar system in a star-cluster containing massive stars. The ... |
We thank an anonymous reviewer for helpful comments. This work is partly supported by Grant-in-Aid for Scientific Research (18654037), Fujiwara Natural History Foundation (S.T.) and by NASA grants NAG5-11543, NNG05GG48G, and NNX08AG58B (G. R. H.). |
# Source: arxiv 0808.1834 # Title: Diffusion of cosmic-rays and the Gamma-ray Large Area Telescope: Phenomenology at the 1-100 GeV regime # Sections: all # Downloaded: 2026-03-02T07:58:36.977666+00:00 |
Diffusion of cosmic-rays and the Gamma-ray Large Area Telescope: Phenomenology at the 1–100 GeV regime Abstract This paper analyzes astrophysical scenarios that may be detected at the upper end of the energy range of the Gamma Ray Large Area Space Telescope (GLAST), as a result of cosmic-ray (CR) diffusion in the inter... |
[MATH] -rays: theory, [MATH] -rays: observations Introduction 1506. This is the number of cosmic photons with energies above 10 GeV that were detected during the 9 years lifetime of the Energetic Gamma Ray Experiment Telescope (EGRET, Thompson et al. 2005). Out of this number of photons, 187 photons were found within 1... |
The role of diffusion The [MATH] -decay [MATH] -ray flux from a source of proton-density [MATH] is given by [EQUATION] where [MATH] is the minimum pion energy given by [MATH] and |
[EQUATION] with [MATH] being the differential cross-section for the production of [MATH] of energy [MATH] by a proton of energy [MATH] in a [MATH] collision. For an study of different parameterizations of this cross section see, e.g., (e.g., Domingo-Santamaria & Torres 2005, Kelner et al. 2006). The limits of integrati... |
[MATH] where [MATH] is the differential number density of protons at an instant [MATH] and distance [MATH] from the source. Just for comparison, the spectrum of cosmic-rays in the Earth vicinity is (e.g., Dermer 1986) |
[MATH] The particle’s differential number density [MATH] satisfies the radial-temporal-energy dependent diffusion equation [EQUATION] |
where [MATH] is the energy loss rate of the particles, [MATH] is the source function, and [MATH] is the diffusion coefficient, for which we assume a dependence on the particle’s energy. The energy loss rate are due to ionization and nuclear interactions, which timescale is [MATH] , with the latter dominating over the f... |
Aharonian & Atoyan (1996) presented a solution for the diffusion equation with an arbitrary diffusion coefficient, and impulsive injection spectrum [MATH] , such that [MATH] . For the particular case in which [MATH] and [MATH] it reads |
[EQUATION] where [EQUATION] stands for the radius of the sphere up to which the particles of energy [MATH] have time to propagate after their injection. In case of continuous injection of accelerated particles, [MATH] the previous solution needs to be convolved with the function [MATH] in the time interval [MATH] If th... |
[MATH] and for times [MATH] less than the energy loss time, [MATH] (Atoyan et al. 1995). We will assume typical values, [MATH] and [MATH] |
In the case of energy-dependent propagation of CRs, a large variety of [MATH] -ray spectra is expected (e.g., Aharonian & Atoyan 1996, Gabici & Aharonian 2007, Torres et al. 2008). Diffusion of CRs have also been explored as an explanation for the high energy observations of the Galactic Center (e.g., Hinton & Aharonia... |
We use a source (cloud) parameterized in units of [MATH] and [MATH] 1 kpc. [MATH] , defined in the case of an impulsive accelerator, is the age for which the timescale for the corresponding nuclear loss becomes comparable to the age of the accelerator itself. [MATH] is the value of the diffusion coefficient for which t... |
Setting, as an example, reasonable parameters for the energy injected by the accelerator into cosmic-rays (e.g., [MATH] erg for an impulsive source and |
[MATH] erg/s for a continuous one) and for the interstellar medium density (e.g., [MATH] = 1 cm -3 ), we have found several scenarios for the appearance of hadronic maxima produced by diffusion. Examples are shown in Fig. , for the two types of accelerators. We have found that two kinds of peaks at this energy regime a... |
Fig. shows, as contour plots, the energy at which the maximum of the SED is found for the cases of impulsive acceleration of cosmic rays, at different distances, ages of the accelerator, and diffusion coefficient. The energy-dependent propagation effects underlying our expectations for the diffusion of CRs in the studi... |
We now focus on the case of one unresolved but composite GLAST source. We thus consider two separate accelerator-cloud complexes that are close to the line of sight such that GLAST observe them as a single source, within its PSF. This kind of scenarios would yield the observational signature of an inverted spectrum. Fi... |
Solution validity and timescales Essentially, if we use the equations given above to compute [MATH] -ray fluxes, we are assuming that there is no significant cosmic-ray gradient in the target (i.e., the gamma-ray emissivity is constant throughout the cloud). This assumption may be valid when the size of the cloud is le... |
Here we did not parameterize on the mass of the cloud, but rather on the value of [MATH] [MATH] , i.e., the mass of the cloud in units of 10 divided by the distance squared in kpc, which we now call [MATH] for brevity. In order for the solutions to apply, then, two conditions need to be satisfied, [MATH] and the size o... |
[MATH] The nuclear loss rate is [MATH] The second condition (i.e, [MATH] ) would be immediately satisfied if, say, [MATH] , with [MATH] . Then, an astrophysical scenario (not unique!) which fulfills also the first condition ( [MATH] ) too is found when |
[MATH] To be viable, of course [MATH] kpc, what can be used to define a minimum value of [MATH] , given an specific model with fixed [MATH] [MATH] , and [MATH] . A final check can be done by comparing that the density obtained by replacing the previous inequalities, |
[MATH] is in the range found in molecular clouds (which for the ages considered, is always fulfilled). Table 2 shows the configurations used in the different figures of our work, together with the minimum value of [MATH] such that [MATH] [MATH] , and [MATH] are all maintained and the solutions used applicable. |
It is also interesting to discuss the different timescales within the cloud (see Gabici et al. 2007). In the former work, it was shown that dynamical and advection cloud timescales do not play a relevant role in this problem. To estimate the degree of cloud penetration by cosmic ray it suffices to compare the loss and ... |
[EQUATION] where the diffusion coefficient inside the cloud has been parameterized as [EQUATION] In here, [MATH] would account for a possible suppression of the diffusion coefficient inside the cloud as compared with that of the environment. For the proton-proton timescale to be larger than the time it takes for cosmic... |
[EQUATION] With the parameters summarized in Table 2, it can be shown that plenty of clouds exist such that the diffusion timescale is shorter than the energy loss one at all energies, and especially at the ones we focus at the higher end of GLAST, and so we can neglect this effect. Our values of [MATH] and typical gal... |
[MATH] Concluding remarks Compton peaks (of which the first example could have been found already, Aharonian et al. 2006) are not the only way to generate a maximum in a SED in the range of 1–100 GeV. A large variety of parameters representing physical conditions in the vicinity of a CR accelerator could produce a rath... |
As noted recently , a double peak could also be seen -coming from the same place in the sky- if we consider two populations of CRs interacting with the same cloud, for instance, the usual [MATH] Galactic bath of cosmic rays (producing a photon-spectrum peaking in the GeV regime) and the escaped CRs from the nearby sour... |
We acknowledge support by grants MEC-AYA 2006-00530, CSIC-PIE 200750I029, and FPI BES-2007-15131, and A. Sierpowska-Bartosik, S. Funk, and J. Hinton for discussions. A. Y. R. M. acknowledges Stanford University for hospitality during a visit. |
# Source: arxiv 0808.1849 # Title: A general method of estimating stellar astrophysical parameters from photometry # Sections: all # Downloaded: 2026-03-02T07:58:38.298177+00:00 |
A general method of estimating stellar astrophysical parameters from photometry (Received 20 December 2007 / Accepted 21 July 2008 ) |
Abstract Context. Applying photometric catalogs to the study of the population of the Galaxy is obscured by the impossibility to map directly photometric colors into astrophysical parameters. Most of all-sky catalogs like ASCC or 2MASS are based upon broad-band photometric systems, and the use of broad photometric band... |
Aims. This paper presents an algorithm for determining stellar astrophysical parameters (effective temperature, gravity and metallicity) from broad-band photometry even in the presence of interstellar reddening. This method suits the combination of narrow bands as well. |
Methods. We applied the method of interval-cluster analysis to finding stellar astrophysical parameters based on the newest Kurucz models calibrated with the use of a compiled catalog of stellar parameters. |
Results. Our new method of determining astrophysical parameters allows all possible solutions to be located in the effective temperature-gravity-metallicity space for the star and selection of the most probable solution. |
Key Words.: methods: data analysis – techniques: photometric – stars: fundamental parameters Introduction Estimating the astrophysical parameters of stars is one of the core problems in astrophysics and the key solving a number of astrophysical questions. Indeed, the knowledge of effective temperature, luminosity class... |
The number of stars with detailed spectral information is very limited compared to the wealth of data in photometry. The problem of determining astrophysical parameters with photometry is usually solved with the help of the narrow-band photometric systems (for instance, the Strömgren photometric system) that provide qu... |
The history of stellar parameter determination from broad-band photometry was started by Johnson in the middle of the 50s of the last century (see, for example, Johnson Johnson53 ( 1953 where the author defined extinction-free colors for the UBV photometric system). Later, some broad-band photometric systems showed the... |
A major problem of using extinction-free colors is how to determine extinction-free colors themselves from the observed ones. Indeed, as we show below, to calculate the extinction-free indices and to use them for the estimation of astrophysical parameters we have to accept some initial guesses about the estimated astro... |
In this study we minimize the amount of information to be assumed a priori for the estimation of astrophysical parameters of the star. We will not make guesses about the astrophysical parameters of the star (temperature, gravity or metallicity) based on the position of the star, e.g. relative to the galactic plane. |
We do not discuss the dependence of the estimated parameter on the synthetic model grid adopted in this study and do not compare different synthetic model grids. The estimated parameters will always depend on the consistency of the synthetic models used in the study. However, in the case of Johnson B,V,J,H, and [MATH] ... |
The synthetic grid of magnitudes and colors To start with the determination of the astrophysical parameters from photometry we have to provide a synthetic grid fine enough to give us synthetic magnitudes and colors for each point of the grid. |
In this section we describe the definition of terms used in the paper, the computation of the synthetic grid of colors and magnitudes, the influence of extinction and the definition of the extinction-free colors. We create a grid of synthetic colors, use an assumed extinction law (Cardelli et al. extinc ( 1989 ) to fin... |
2.1 Definition of synthetic magnitudes The definition of synthetic magnitudes depends on the type of detector used in the observation that we are going to approximate. If the detected flux corrected for the atmospheric extinction is [MATH] and the stellar flux at the surface of the star is [MATH] |
(this is the flux delivered by synthetic atmosphere models), they are related to each other as [EQUATION] where [MATH] is the interstellar extinction at the wavelength [MATH] |
[MATH] the stellar radius, and [MATH] the distance to the star, [MATH] and [MATH] are in the same units. In the case of photon-counting devices the magnitude of the star [MATH] in the filter [MATH] is |
[EQUATION] We discuss the zero-points of photometric systems [MATH] in Sect. 2.2 Theoretical models used in the study We used the latest Kurucz models of theoretical spectra (Castelli & Kurucz Kurucz2006 ( 2003 ), because these models can provide wider coverage in parameter space compared to other libraries. The grid u... |
To calculate absolute magnitudes from Kurucz models, we had to adopt stellar radii for each point in the [MATH] grid. We took radii from the theoretical track systems of Palla & Stahler ( Palla_Stahler ( 1993 ), D’Antona & Mazzitelli ( D'Antona ( 1994 ) for pre-main sequence stars, and Geneva tracks (Schaller et al. Ma... |
We used the following sets of filters in the study: Johnson B and V filters from the UBVBUSER code (Buser Buser ( 1978 ) and 2MASS J, H, and |
[MATH] filters (Cutri et al. 2MASS ( 2006 ). 2.3 Extinction in the case of a broad-band photometric system To compute a set of extinction-free indices, we have to compute first reddened magnitudes and colors for a wide range of interstellar extinction. This gives us synthetic color excesses for each model in the grid. ... |
The extinction law used in the study (Cardelli et al. extinc ( 1989 ) was constructed with the use of O- and early B-stars. This extinction law is a polynomial approximation of the extinction for the wavelength [MATH] |
[MATH] In fact, this value of [MATH] is a parameter related to OB stars. This also means that extinction constructed with the use of an extinction law [MATH] will give different values of the extinction for different spectral classes in the same photometric band and with the same distance and ISM between star and obser... |
[MATH] with the use of [MATH] from Cardelli et al. ( extinc ( 1989 ): [EQUATION] The output [MATH] differs from the input [MATH] and this difference depends on the spectral class, gravity, and metallicity of the star. This difference is a physical phenomenon. Indeed, an O5 star and an M5 star being placed at the same d... |
2.4 Extinction-free color indices Extinction-free color indices (or Q-values) are the final target for our computations of synthetic colors. With the use of these indices, we are able to reduce the number of models in our grid, because we can use a unique grid of synthetic models for any star independent of the individ... |
The construction of extinction-free color indices has some problems that we consider below. The Q-values are by definition [EQUATION] |
However, [MATH] is not constant, but depends on the spectral class, gravity and metallicity of star (see, for example, Grebel & Roberts Grebel95 ( 1995 ). The excess ratio depends as well on the extinction itself. By definition, [MATH] , so to remove extinction from the excess ratio, we have to replace [MATH] with [MAT... |
Calibration of theoretical models As we see from Eq. ( ), we have to bring our theoretical models into accordance with the zeropoint of the photometric system ( [MATH] ). |
To provide this calibration, we compiled a catalog of stars with temperature, gravity, and metallicity known from spectroscopy. The catalog is a combination from the catalogs of Borkova & Marsakov ( borkova ( 2005 ) and Cayrel de Strobel et al. ( cayrel ( 1997 ) with the addition of the catalogs of Soubiran el al. ( so... |
[MATH] [MATH] and 2MASS [MATH] [MATH] [MATH] magnitudes. A subsample of 1287 stars was selected with [MATH] mag, [MATH] mag, [MATH] mag, [MATH] mag, |
[MATH] mag, parallaxes with [MATH] better than 10% and distances within 100 pc. We assume that the stars from this subsample are extinction-free and use the subsample to calibrate our theoretical models. |
To calibrate the theoretical sequences, we selected all stars from the subsample with [MATH] [MATH] and photometric errors in all bands better than 0.05 mag and absolute magnitudes in the B band [MATH] mag. |
On the basis of this calibration subsample of 58 selected stars, we calibrated the synthetic models [EQUATION] Although, the parameters from literature cover only a small fraction of the full parameter space, we applied the corrections to the full sythetic grid. Comparison of our calibrated colors with the colors for V... |
[MATH] mag. The 2MASS [MATH] photometric system differs slightly from the Johnson [MATH] (see Carpenter carpenter ( 2001 and Koen et al. Koen ( 2007 ). |
The interval-cluster method of the astrophysical parameters estimation Parameters like effective temperature, gravity, metallicity, extinction, and distance on the basis of broad-band photometry must be determined directly from photometry without any a priori assumption about physical properties of stars that can restr... |
[MATH] the logarithm of gravity, [M/H] the metallicity, [MATH] the extinction in the Johnson V band [MATH] is used as the parameter for extinction hereafter), and r the distance to the star. From observations (or from a synthetic grid in the case of simulations), we have a magnitude space { [MATH] }={ [MATH] that can b... |
Let us suppose that there are two different subsets in the parameter space [MATH] } and { [MATH] }. These two classes can be populated by stars within any given temperature range, gravity range, and metallicity range. Let us as well have two subsets in the color space [MATH] } and { [MATH] } containing the synthetic co... |
Figure illustrates the problem: stars within two different metallicities and gravities ([M/H]=-0.5, [MATH] and [M/H]=0.0, [MATH] ) occupy the same space in the 2-color diagram even in the absence of extinction. It is obvious that for this range of colors there are at least two different solutions in parameter space for... |
In this case, there are at least two possible solutions for the parameters of a star: [MATH] } (dwarf) and { [MATH] } (supergiant). The idea of the method we propose here is the location of all probable solutions { [MATH] } and an estimation of the probability that the star can belong to the solution { [MATH] }. |
To reduce the number of parameters in the parameter space, we transform the colors of the star into the extinction-free color indices described above. The method is illustrated in the following 5 bands: Johnson B and V magnitudes (B,V filters are from UBVBUSER code, Buser Buser ( 1978 and 2MASS J, H, and [MATH] magnitu... |
Our method consists of three steps: 1. interval analysis: select all theoretical models in our grid which satisfy the extinction-free color indices of the star; |
2. cluster analysis: group all possible solutions in parameter space and find a set of solutions; 3. selection of the best solution: consider all possible solutions to select the only one as the most probable solution for the star in process. |
The final solution for the star is a set of parameters (mean values and variances): [MATH] [MATH] [MATH] [MATH] [MATH] [MATH] [MATH] [MATH] }, |
[MATH] , where n is the number of possible solutions for the star. One of these solutions will be selected as “the most probable” due to criteria we describe below. |
4.1 The first part of the method: interval analysis In this step we locate possible solutions in parameter space ( [MATH] [MATH] , [M/H]). The table of the theoretical models is constructed with steps [MATH] dex, [MATH] dex, and [MATH] dex and has 249922 entries in the parameter space. For each entry there is one combi... |
[MATH] ). The “observed” values for the star are magnitudes ( [MATH] [MATH] [MATH] [MATH] [MATH] ) and colors [MATH] [MATH] [MATH] [MATH] ). |
4.1.1 Selection of grid points The selection of grid points satisfying the set of “observed” colors is carried out in the space of extinction-free color indices. The value [MATH] does not depend on extinction. If we know stellar parameters ( [MATH] ), we can find a stellar excess ratio [MATH] . Then we can construct an... |
to select grid points satisfying to the input index Q: [EQUATION] The difference between synthetic [MATH] and the “observed” index |
[MATH] in this ideal case will be zero. However, we know nothing about parameters of the star except our assumption that the stellar parameters are inside our synthetic grid. |
Let us try each of the grid points for the input colors of the star. We take the difference [EQUATION] in each grid point. We do the same for [MATH] and [MATH] All points that satisfy the following equations |
[EQUATION] are selected as possible solutions. The definition of [MATH] comes from the definition of Q: [EQUATION] The problem are the quantities of [MATH] and [MATH] which are unknown a priori. In this step we take the maximum value of [MATH] in our theoretical grid (averaged over all points in the grid |
[MATH] , maximum value [MATH] ) for all points, and double the value of [MATH] as a rough estimation of [MATH] Finally, [EQUATION] |
The same is done for the estimation of [MATH] and [MATH] After the initial selection of grid points in accordance with Eq. ( 4.1.1 we return from the extinction-free space to the color space and remove all “artifact” entries (those with negative extinction and colors out of the bounding box for the input star). |
We assume that the ratio [MATH] is constant for a given temperature, gravity, and metallicity and that is only depends on these parameters and not on [MATH] itself. |
For each of the selected grid points, we can find reddening for each color and extinction for each band, [EQUATION] where [MATH] is the observed color for the star and [MATH] is the synthetic color at the selected grid point, [MATH] . Also, |
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