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(c) The single power-law may be rejected in favor of a specific alternative model using [MATH] , here we study the double and Fermi power-law distributions (see [MATH] 4.3 ). |
The best estimates for the characteristic cut-off energy and shape parameters determined via steps ( ), ( ) and ( ), are [MATH] or [MATH] and [MATH] or [MATH] respectively. The presence of flux suppression at the highest energies |
can be evaluated using step ( ). By applying these methods to the toy Monte-Carlo set of CRPropa events we illustrate in [MATH] how the procedure may be implemented on an actual CR detector, i.e. a detector with systematic and statistical event energies. Suppression in the tail is clear in Figure and Figure 10 ; the ta... |
[MATH] [MATH] ). The methods are sufficient and robust. Indeed, many of them have been applied by the Auger collaboration which reports suppression with [MATH] confidence |
These tools serve as a basis for further investigation of the CR spectrum such as evidence for more detailed spectral information. They can be applied to any data set, astrophysical or otherwise, to provide information both about data already collected and help to optimize future observations for detecting tail suppres... |
Appendix A Binned vs. Un-Binned The statistical superiority of an un-binned maximum likelihood estimate of the pure power-law spectral index to the logarithmically binned least- [MATH] method often used has been established in |
and expanded upon more recently in In this section we compare the binned to the un-binned fitting method for the two suppressed models, i.e. the double and Fermi power-laws (see [MATH] 2.3 ). |
To calculate the binned estimators we minimize a [MATH] function that relates the logarithmically binned (width [MATH] ) histogram of the data to that expected by a model. The function is |
[EQUATION] where [MATH] is the number of bins, [MATH] is the number of events in the [MATH] bin [MATH] and [MATH] is determined by Gaussian errors when [MATH] and Poissonian errors when [MATH] We minimize with respect to the parameters [MATH] |
(with [MATH] fixed) using the number of events in a bin expected by the model M, [EQUATION] To study the asymptotic bias and error produced by the two estimation techniques we draw [MATH] sets of [MATH] events from a pure power-law and separately from a double distribution. For each Monte-Carlo set we estimate the best... |
using both the likelihood Eq( ) and the [MATH] Eq( 14 ) methods. The un-binned estimator of the pure power-law spectral index (see [MATH] 3.1 has been shown |
to have an error estimate within [MATH] of the Cramer-Rao lower bound for a sample with as few as [MATH] events. In Figure and Figure we plot the results of the simulations. We can conclude that the un-binned fitting method is most important when fitting a power-law in the tail of a distribution; the binned estimator p... |
[MATH] The (binned) methods used to report parameters like the “ankle” and the “knee” in and are sufficient but limited by the bin width. |
Appendix B Statistical Error: Monte-Carlo Example To illustrate the effect the statistical energy smearing has on a pure power-law we generate [MATH] MC events from a power-law distribution with [MATH] and [MATH] A histogram of these events is represented by the black filled circles plotted in Figure By minimizing Eq( ... |
[MATH] (with [MATH] , see [MATH] 4.1 ). A power-law with these parameters is plotted as the dashed line in Figure To each MC event [MATH] we then add a random number [MATH] drawn from a normal distribution with mean zero and variance [MATH] The new events are histogram-ed with blue open circles in Figure We fit these e... |
[EQUATION] (compare with Eq( )) as the p.d.f. and we find that [MATH] . The smearing does not effect the estimated spectral index, though it does increase the error of the estimate. The dashed curve in Figure shows Eq( 15 ) evaluated at the best fit values. Notice that the histogram of the smeared energies deviates fro... |
Appendix C Results of CRPropa Toy Set By applying the statistical tools presented in this paper (summarized by steps ( )-( in [MATH] ) to the toy set of [MATH] CRPropa events (see [MATH] 2.2 we illustrate how the tools might be implemented on an actual CR detector. By construction, this toy set has parameter estima... |
and HiRes In preparation for this paper we generated 14 CRPropa simulations of [MATH] events with different injection spectral indexes, |
[MATH] , and with different values of maximum generation energy, [MATH] The (after propagation) estimated characteristic break point energy, i.e. [MATH] or [MATH] , is found to be independent of the spectral index at the site of generation, [MATH] The estimated spectral index [MATH] is found to be linearly related to t... |
In Figs. and 10 we plot the toy data set and the best fit models in two (non-binned) ways not commonly seen in the CR literature. The first is a rank-frequency plot. For each event (black filled circle) we plot [MATH] along the horizontal axis and the log of the number of events with energy greater than [MATH] along th... |
[MATH] where [MATH] is the model cumulative distribution function. From the rank-frequency plot we derive an instructive visualization tool in Figure 10 we plot the difference between the number of events above a given energy for the toy set |
[MATH] and that expected by the best fit models [MATH] The best fit pure power-law parameters for the toy set described in [MATH] 2.2 are |
[MATH] and [MATH] where the first error is statistical and the second systematic. The tail power significance [MATH] is [MATH] The best fit double power-law parameters for the toy set are |
[MATH] [MATH] [MATH] and [MATH] The correlation coefficients are [MATH] [MATH] and [MATH] , see Figure 11 The likelihood ratio significance is [MATH] The best fit Fermi power-law parameters for the toy set are |
[MATH] [MATH] [MATH] and [MATH] The correlation coefficients are [MATH] [MATH] and [MATH] , see Figure 12 The likelihood ratio significance is [MATH] |
# Source: arxiv 0808.2722 # Title: Modelling the evolution and nucleosynthesis of carbon-enhanced metal-poor stars # Sections: all # Downloaded: 2026-03-02T07:58:22.425676+00:00 |
Modelling the evolution and nucleosynthesis of carbon-enhanced metal-poor stars (2008; ?? and in revised form ??) Abstract We present the results of binary population simulations of carbon-enhanced metal-poor (CEMP) stars. We show that nitrogen and fluorine are useful tracers of the origin of CEMP stars, and conclude t... |
keywords: Stars: AGB and post-AGB, stars: evolution, stars: binaries, stars: abundances, stars: mass function Introduction One of the most striking results of recent large surveys for very metal-poor stars in the Galactic halo is the large proportion of highly carbon-enriched objects among them. These carbon-enhanced m... |
[MATH] , make up at least 10 per cent and probably as much as 20–25 per cent of very metal-poor stars with [MATH] Frebel et al. (2006) , Frebel et al. 2006] 2006_Lucatello , Lucatello et al. 2006] ). |
The majority (about 80 per cent, according to Aoki et al. (2007) , Aoki et al. 2007] ) of CEMP stars are also enriched in Ba and other heavy elements produced by slow neutron captures (the [MATH] -process) in asymptotic giant branch (AGB) stars. For these so-called CEMP-s stars a likely scenario is pollution by mass tr... |
Within the mass transfer scenario, the large proportion of CEMP-s stars requires the existence of a sufficient number of binary systems with primary components that have undergone AGB nucleosynthesis. In recent studies ( Lucatello et al. (2005b) Komiya et al. (2007) , Lucatello et al. 2005b; Komiya et al. 2007] ) it ha... |
In this contribution we explore the effect of some of these uncertainties on the number fraction of CEMP stars by means of a binary population synthesis study. Apart from carbon, we concentrate on nitrogen and fluorine enrichments as possible tracers of the origin of CEMP stars, the latter motivated by the recent disco... |
Nitrogen and fluorine in CEMP stars Apart from carbon, substantial enhancements of nitrogen with respect to iron are common among CEMP stars, typically with [MATH] . Detailed AGB nucleosynthesis models of low initial mass ( [MATH] ) produce carbon (by the 3 [MATH] reaction during thermal pulses and subsequent convectiv... |
[MATH] ) than at solar metallicity (around [MATH] ). One may thus expect a population of so-called nitrogen-enhanced metal-poor (NEMP) stars, with [MATH] . Although a few examples of such stars are known, mostly at |
[MATH] , they appear to be very rare ( Johnson et al. (2007) , Johnson et al. 2007] ). As we show in Sect. 3 the number of NEMP stars sets an additional constraint on possible changes to to IMF at low metallicity. |
Recently, Schuler et al. (2007) derived a super-solar fluorine abundance of [MATH] in the halo CEMP star HE 1305+0132. This is the most iron-deficient star, [MATH] , for which the fluorine abundance has been measured. Enhancements of carbon and nitrogen are also measured ( [MATH] [MATH] ), and Ba and Sr lines are seen ... |
Fluorine can be made in AGB stars as a by-product of the [MATH] reaction under neutron-rich conditions during thermal pulses ( Lugaro et al. (2004) , Lugaro et al. 2004] ). Fluorine enhancements of up to 30 times solar have been measured among Galactic AGB stars ( Jorissen et al. (1992) , Jorissen et al. 1992] ), demon... |
In Fig. we show the enhancements of F and C+N relative to hydrogen as observed in HE 1305+0132 and compare these to the abundance ratios in the material lost by AGB stars at |
[MATH] according to the Karakas & Lattanzio (2007) models. The figure shows that AGB stars with masses between 1.7 and [MATH] produce fluorine and carbon in the right amounts to account for the observed abundances, after accretion of the material by a low-mass companion and subsequent dilution in its envelope by a fact... |
Binary population nucleosynthesis of CEMP stars We have simulated populations of metal-poor halo stars in binary systems using the rapid synthetic binary nucleosynthesis code of |
Izzard et al. (2004) and Izzard et al. (2006) . The code uses fits to detailed single-star evolution and nucleosynthesis models, in particular the AGB models of Karakas & Lattanzio (2007) , and follows the surface abundances as a star evolves through dredge-up episodes. A prescription for hot bottom burning in massive ... |
Bondi & Hoyle (1944) prescription, and by Roche-lobe overflow (RLOF). In binaries with AGB primaries, RLOF is usually unstable and leads to the ejection of a common envelope without any further accretion onto the companion. In our default model we assume efficient thermohaline mixing, in accordance with the findings of... |
In all models we use solar-scaled initial abundances according to Anders & Grevesse (1989) with [MATH] , corresponding to [MATH] , which is the lowest metallicity for which we have detailed AGB models. We select stars with ages between 10 and 13.7 Gyr (roughly corresponding to the age of the halo) and [MATH] (thus incl... |
[MATH] and [MATH] , following the definition of Johnson et al. (2007) . Note that these definitions partly overlap. We can compare our model results with the statistics of the SAGA database of metal-poor stars ( Suda et al. (2008) , Suda et al. 2008] ). We selected 375 stars from the database in a metallicity range |
[MATH] and [MATH] . Of these, 296 have a C abundance measurement and 69 classify as CEMP stars, yielding a CEMP fraction of 18–23 %. Only one star classifies as a NEMP star, giving a very small nominal NEMP fraction of [MATH] 0.3 %. If we consider an extended metallicity range [MATH] in order to improve the number stat... |
In our default model (1A) we assume that the initial primary masses [MATH] are distributed according to the solar neighbourhood IMF as derived by Kroupa et al. (1993) , the initial periods come from a flat distribution in [MATH] and the initial mass ratios from a flat distribution in [MATH] . In Table we present the re... |
[MATH] ) to CEMP stars. Although all our CEMP stars are also enriched in Ba, in this model the majority have [MATH] In the next rows of Table we vary some of the uncertain physical ingredients in our models, while keeping the input distributions the same. In model 2A we switch off thermohaline mixing, which has the eff... |
In Table we present CEMP and NEMP fractions of the default physical model while varying the initial distributions of binary parameters. In model 1B we assume mass ratios and periods drawn from the distributions derived by Duquennoy & Mayor (1991) for the local population of G dwarfs (i.e. a log-normal period distributi... |
[MATH] ). This leads to an increase by a factor of 1.5–2 in the number of CEMP and NEMP stars as the peak in the period distribution coincides with the period range in which mass transfer is effective. |
Models 1C, 1D and 1E explore the effect of varying the initial mass function, by assuming the default [MATH] and [MATH] distributions in combination with a log-normal form of the IMF. The Miller & Scalo (1979) |
IMF also represents the solar neighbourhood but gives somewhat higher CEMP and NEMP fractions than the Kroupa et al. (1993) IMF. Model 1D assumes the IMF suggested by Lucatello et al. (2005b) as required to reproduce the large CEMP fraction (it has a median mass of |
[MATH] , compared to [MATH] for the Miller & Scalo IMF). It results in a larger CEMP fraction but still falls short of the observed value. The discrepancy between our and Lucatello’s results arises mainly because in our (default) models the initial primary mass and period range contributing to CEMP stars are smaller th... |
Conclusions The detection of a large fluorine overabundance in the CEMP star HE 1305+0132 is well explained within the AGB binary mass transfer scenario ( Lugaro et al. (2008) , Lugaro et al. 2008] ). On the other hand, models of rapidly rotating massive stars do not produce fluorine Meynet et al. (2006) , Meynet et al... |
Our binary population synthesis models show that the paucity of NEMP stars among metal-poor halo stars is incompatible with a strongly modified IMF at low metallicity, heavily weighted towards intermediate-mass stars, as has been suggested by |
Komiya et al. (2007) in order to explain the high proportion of CEMP stars. Another possible explanation for the ubiquity of CEMP-s stars is that low-metallicity AGB stars undergo much more efficient dredge-up than shown by the detailed evolution models available to date. |
Acknowledgements. We would like to thank Takuma Suda for making the SAGA database of metal-poor stars available to us in electronic form ahead of publication. |
# Source: arxiv 0808.2733 # Title: Long term radio variability of AGN # Sections: all # Downloaded: 2026-03-02T07:58:23.604634+00:00 |
Long term radio variability of AGN Abstract: A large number of AGN have been monitored for nearly 30 years at 22, 37 and 87 GHz in Metsähovi Radio Observatory. These data were combined with lower frequency 4.8, 8.0 and 14.5 GHz data from the University of Michigan Radio Astronomy Observatory, higher frequency data at 9... |
Introduction Active galactic nuclei (AGN) are variable across the whole electromagnetic spectrum. The radio regime is of special interest because we can directly observe the synchrotron radiation from the jet. The total flux density variations and flares seen in the flux curves are usually explained with shock-in-jet m... |
We have used a sample of 90 AGN to study their long-term variability timescales and flare characteristics . Our extensive database enables us to study the correspondence between the shock model and the observations, and also the statistical differences between the different AGN types (27 high polarisation quasars (HPQs... |
Variability timescales We used four statistical methods to study variability timescales in a sample of 80 AGN at 7 frequency bands between 4.8–230 GHz. We used the Structure Function (SF), the Discrete Correlation Function (DCF), the Lomb-Scargle periodogram, and wavelets. In the wavelet analysis we used only frequenci... |
, the SF gives a timescale related to short variations such as the rise and the decay times of flares. The DCF and the Lomb-Scargle periodogram give the time between flares, and therefore indicates how often shocks are formed in the jet. We found that especially the Lomb-Scargle periodogram easily produces spurious spi... |
As an example, in Fig. the SF, the DCF and the Lomb-Scargle periodogram results at 22 GHz are shown for the quasar 4C 29.45. The DCF in Fig. b gives a timescale of 3.49 years which is very close to the timescale 3.29 years obtained with the Lomb-Scargle periodogram (Fig. c). Indeed, when examining the flux curve in Fig... |
None of the sources in our sample showed strict periodicity in our analyses. Flares are seen in these sources on average every 4 years at 22 and 37 GHz and the rise and the decay times of flares are between 1 to 2 years. This is also seen in Fig. d, where a SF timescale of 1.2 years is found for the source 4C 29.45. Th... |
, which show that shocks are formed more easily in slower jet flows which are often associated with BLOs. This will be studied further in a forthcoming paper |
, where we will calculate the Lorentz factors for a large sample of sources from different classes. Even though none of the sources in our sample are strictly periodic, many of them show episodes of quasiperiodic behaviour. Therefore we were interested to see whether we could “predict” upcoming active states in these s... |
) has shown that strong gamma-ray activity is connected to a growing flare in the radio regime, and therefore sources that are active in the radio are good candidates to be detected by GLAST. |
Thus, based purely on our statistical wavelet analysis combined with analyses of and visual inspection of our flux curves at 37 GHz until the end of 2007, we came up with a list of six potential sources. These sources show quasiperiodic behaviour in the wavelet analysis and in at least one Fourier-based method with suc... |
Flare characteristics We have studied the flare characteristics of 55 sources with 159 well-monitored flares at 8 frequency bands between 4.8–230 GHz. We calculated several parameters for each flare, e.g. the amplitude, the duration, and the time delays between the frequency bands. We were not able to calculate all the... |
An example of an “average” blazar is in Fig. , where the flux curve of the BLO source 0235+164 at 37 GHz is shown. In the flux curve of this source we can identify the median or average values of all the parameters from the different analyses. The flare peaking at 1987 has a peak flux density of 4.4 Jy, and also the me... |
We compared the duration of the flares with the relative peak flux densities, and found that there is only a slight positive correlation of 0.15 between the values. We can see almost as high peak flux densities in flares lasting for 2 years as for flares lasting for 13 years. The correlation disappears altogether when ... |
). This indicates that the energy release in a flare does not increase with the duration of the flares. Our sample includes sources from various AGN classes and are mostly blazars. The BL Lacertae objects and their timescales are studied in more detail in |
. In addition to the flare parameters, we studied the correspondence between the observations and the shock model by Marscher & Gear |
and its generalisation by Valtaoja et al. We found that the observed peak fluxes and the time delays between the flares adhere quite well to the predictions of the shock model, even though there is large scatter in the data. We note that our definition of a flare is based on visual inspection and therefore many of the ... |
Conclusions We studied the long-term radio variability of a sample of 90 sources using statistical timescale analysis methods and visual inspection of the flare parameters. Our main results are the following: |
Fourier-based methods the DCF and the periodogram give very similar results as wavelets, but wavelets should be used when quasi-periodities are studied because they give information on the locality of the timescale. With wavelets it is possible to see if a timescale is long-lasting or just a short transient phenomenon ... |
Variability behaviour is complex and no clear periodicities could be found at radio frequencies. Episodes of quasi-periodic behaviour are common, and therefore false periodicities may be found if the temporal coverage is inadequate. |
Flares are seen, on average, every 4 years in all the source types at 37 GHz but when intrinsic redshift-corrected timescales are studied, the quasars have shorter timescales of 2 years compared to the 3-4 years of BLOs. This could indicate that shocks are produced less frequently in BLOs than in quasars. |
Median duration of a flare is 2.5 years at 22 and 37 GHz, but the range in durations is between 0.3 and 13.2 years. When comparing the duration with intrinsic redshift- and Doppler-corrected peak luminosities, we found that the energy release in a flare does not increase with the duration of the flare. |
Flares adhere quite well to the predictions of the shock model but the scatter in the data, due to poor sampling and complicated structure of the flares, is still large. |
By combining the median duration of flares, 2.5 years, with the average time between the flares, 4 years, we see that multifrequency campaigns should last for 5-7 years in order to catch the source in both its highest and lowest activity states. Long-term monitoring is essential in understanding the true behaviour of t... |
# Source: arxiv 0808.2742 # Title: J1420--0545: The radio galaxy larger than 3C236 # Sections: all # Downloaded: 2026-03-02T07:58:24.738787+00:00 |
J1420–0545: The radio galaxy larger than 3C236 Abstract We report the discovery of the largest giant radio galaxy, J1420-0545: a FR type II radio source with an angular size of 17.4’ identified with an optical galaxy at [MATH] =0.3067. Thus, the projected linear size of the radio structure is 4.69 Mpc (if we assume tha... |
galaxies: active – galaxies: distances and redshifts – galaxies: individual (J1420 [MATH] 0545) Introduction The existence of bright hot spots at the edges of most of FR type II radio sources indicates that the jets ejected from a ”central engine” in the AGN encounter resistance to their propagation. These supersonical... |
Wellman et al. 1997 ) there are arguments that the cocoons in many observed radio sources are still overpressured with respect to the IGM. Only the very tenuous material in the bridges of the oldest and largest sources is expected to have attained such an equilibrium state, in which the radiating particles and the magn... |
The above approach was applied by us (Machalski et al., 2007b to a sample of giant radio galaxy (GRG) candidates located in the southern sky hemisphere with the aim of studying properties of the cosmological evolution of the IGM. The radio galaxy discussed in this paper is a member of that sample. The source J1420 [MAT... |
as a 17.4’ large FR type II radio structure consisting of two extended lobes with a total flux density of only 87 mJy and a central compact core. The core is unresolved with the 5″ [MATH] 5″ beam in the FIRST survey and has a flux density of 2.7 mJy. The structure is highly collinear and symmetric; the ratio of separat... |
as well as 50 cm observations with the Giant Metrewave Radio Telescope (GMRT). These observations, the final 1.4 GHz map of the investigated radio galaxy obtained from a combination of the NVSS and Effelsberg data, and the 619 MHz GMRT map are presented in § 2. The radio core position coincides perfectly with that of a... |
[MATH] of galaxies identified with very faint GRGs can be 1 [MATH] lower than the mean value, we have estimated a value of [MATH] for J1420 [MATH] 0545 (cf. Machalski et al. 2007b ). The independent photometry and optical spectroscopy of the host galaxy that confirm the above estimate are given in § 3, while some physi... |
New radio observations 2.1 Effelsberg observations The observations were carried out with the 100 m telescope on 2006 April 26–27, using the 21 cm single-horn receiver installed at the primary focus of the antenna. The 60′ [MATH] 60′ sky area centred at R.A.(J2000.0)=14 20 24 and decl.(J2000.0)= [MATH] 05°45′29″ was sc... |
package. The resulting 1.4 GHz map of the source J1420 [MATH] 0545, superposed on the optical DSS image, is shown in Figure . We still do not detect a bridge at this frequency. |
2.2 GMRT observations The observations of J1420 [MATH] 0545 centered at the radio core position were carried out on 2007 November 11, in the 50 cm band. The observations were made in the standard manner, with observations of the target source interspersed with observations of the phase calibrator J1351 [MATH] 148. The ... |
is shown in Figure . This map also shows no bridge with a surface brightness exceeding the above rms noise level; however, it indicates that the radio core has a very flat spectrum, as its 619 MHz flux density is likely below 1.3 mJy. |
Optical observations To check the DSS apparent magnitudes and to derive an absolute magnitude of the host galaxy, an independent photometry was made at Mount Suhora Observatory with the 60 cm telescope. After the initial standard reductions, aperture photometry was performed on the galaxy and calibration stars using th... |
[MATH] =19.65 [MATH] 0.08 mag, and [MATH] =21.0 [MATH] 0.2 mag. Thus, our photometry is fully compatible with the DSS magnitudes. The combined data give an optical spectral index of [MATH] 3.45 and an absolute red magnitude [MATH] of [MATH] 22.1 [MATH] 0.1, if we use the cosmological parameters given in the Abstract. |
The optical spectra of the host galaxy were obtained at La Palma on 2007 August 16. The observations conducted in the Service Programme mode were made with the ISIS double beam spectrograph (the red and blue arms) on the 4.2 m William Herschel Telescope (WHT). |
The galaxy was observed in good weather and seeing conditions through a 2″ wide slit. Four spectra (two per arm) were taken with the grating R316R, set up for a central wavelength of 6447Å and a dispersion of 0.92Å pixel -1 at the red arm, and the grating R300B, set up for a central wavelength of 4503Å and a dispersion... |
The obtained spectra were reduced using the standard IRAF longslit package. All the spectra were corrected for bias, flat fields, and cosmic rays, as well as being wavelength- and flux density-calibrated. The wavelength calibration was performed by using exposures to CuAr/CuNe arc lamps, wherea the flux calibration was... |
absorption lines is dominated by evolved stars. The spectrum of the S0-type galaxy UGC 04345, as a typical spectrum of an early morphological type galaxy, is shown in Figure 3 [MATH] |
for comparison’s sake. A Gaussian profile was fitted to the lines and bands recognized in the spectrum, and the wavelengths corresponding to the profile centers are used to calculate the redshift. The emission line and absorption bands detected, as well as the resulting redshifts of these features, are listed in Table ... |
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