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point sources using the routineewavelet. separately for cach observation. | point sources using the routine, separately for each observation. |
At this stage of the algorithi. we did uot attempt to discriminate real sources frou detector artifacts. uor did we attempt to verity that sources detected iu one camera were present in the others. | At this stage of the algorithm, we did not attempt to discriminate real sources from detector artifacts, nor did we attempt to verify that sources detected in one camera were present in the others. |
We extracted event lists from individual sources usine the radius produced byewavelet. which generally was 215” aad enclosed 250% of the PSF. | We extracted event lists from individual sources using the radius produced by, which generally was $\approx$ and enclosed $\approx$ of the PSF. |
The arrival times of the photons were corrected to the solar svsteii birvceuter using the toolbarycen. | The arrival times of the photons were corrected to the solar system barycenter using the tool. |
For sources with at least LOO total events from either observatory Gucliding backgrouud). we computed Fourier periodograis to search for periodic signals. | For sources with at least 100 total events from either observatory (including background), we computed Fourier periodograms to search for periodic signals. |
The range of periods searched for both iustruments was designed to cneoupass those of known maguetars with N-ray pulsations. 512 s (Woods&Thompson2006). | The range of periods searched for both instruments was designed to encompass those of known magnetars with X-ray pulsations, 5–12 s \citep{wt06}. |
. However. we note that after our analysis was completed. Camiloetal.(2007). àunounced the discovery at racio waveleugths of 2 s pulsatious from LE 1517.0-5108. | However, we note that after our analysis was completed, \citet{cam07} announced the discovery at radio wavelengths of 2 s pulsations from 1E 1547.0-5408. |
Periods this short would generally only be ideuti&able in EEPIC-pu data with our search. | Periods this short would generally only be identifiable in EPIC-pn data with our search. |
For the ddata. we used the Ravleigh statistic (Zi:Buccerietal. 1983). | For the data, we used the Rayleigh statistic \citep[$Z_1^2$;][]{buc83}. |
. We searched for signals with frequencies between 1.5 times the Nyquist frequency 5:0. 1.5ναδημ. where fia Is the iterval at which the data were read out) and of the inverse of the total time interval of the observation νου, OL to avoid red noise. | We searched for signals with frequencies between 1.5 times the Nyquist frequency (i.e., $1.5 \times 1/2t_{\rm bin}$, where $t_{\rm bin}$ is the interval at which the data were read out) and of the inverse of the total time interval of the observation (i.e., $0.1/T_{\rm exp}$ ) to avoid red noise. |
We used a frequency step corresponding/Tig) to the inverse of the total time interval (L/T44,). | We used a frequency step corresponding to the inverse of the total time interval $1/T_{\rm exp}$ ). |
For most observations. the data were read out every fig 7231 s. πο the highest frequencies searched correspond. to periods of L1 s. Observations typically lasted between 1.2 ks and 120 ks. so we could identify signals with periods at the upper range of at least 120 s. and im some cases 12.000 3. For the ddata. the Ravleigh Statistic was computationally inefficient to compute for pu observations of bright sources. so we computed discrete fast Fourier transforms. | For most observations, the data were read out every $t_{\rm bin}$ =3.1 s, so the highest frequencies searched correspond to periods of 4.1 s. Observations typically lasted between 1.2 ks and 120 ks, so we could identify signals with periods at the upper range of at least 120 s, and in some cases 12,000 s. For the data, the Rayleigh Statistic was computationally inefficient to compute for pn observations of bright sources, so we computed discrete fast Fourier transforms. |
The data were padded so that the uuuber of points in the ransfornmi was a power of 2. so the frequency resolution was generally finer than Τον, | The data were padded so that the number of points in the transform was a power of 2, so the frequency resolution was generally finer than $1/T_{\rm exp}$. |
The maxinaun frequency considered was the Nyquist frequency. for the data; | The maximum frequency considered was the Nyquist frequency for the data. |
The πι data was taken with a time resolution of at least 73.1 us. providing scusitivity to periods as short as 0.15 x. The MOS data was taken with a time resolution of at cast 2.1 s. and so our search was sensitive to periods as short as L8 xs The lowest frequency. cousidered was LAT. | The pn data was taken with a time resolution of at least 73.4 ms, providing sensitivity to periods as short as 0.15 s. The MOS data was taken with a time resolution of at least 2.4 s, and so our search was sensitive to periods as short as 4.8 s. The lowest frequency considered was $T_{\rm exp}$. |
The coufideuce with which we could exclude that any eiven signal was produced by random noise depenuded upon the nuuber of trial signals examined. Nia. | The confidence with which we could exclude that any given signal was produced by random noise depended upon the number of trial signals examined, $N_{\rm trial}$. |
The vpical oobservation lasted 20 ks. aud contained 3 sources witli 100 counts. and had a time resolution of 3.1 s. so hat there were Niiape20.000 trial frequencics in the eusenmible of periocdograims from cach observation. | The typical observation lasted 20 ks, and contained 3 sources with $>$ 100 counts, and had a time resolution of 3.1 s, so that there were $N_{\rm trial}$$\approx$ 20,000 trial frequencies in the ensemble of periodograms from each observation. |
The vpical oobservation also lasted 20 ks. aud coutained 2:25 sources oer caluera with 2100 counts. | The typical observation also lasted 20 ks, and contained $\approx$ 25 sources per camera with $>$ 100 counts. |
For cach MOS detector. with a time resolution of 2.1 s. the typical sot of periodograms coutaiued IN;,4,2£:200.000 trial periods per observation. | For each MOS detector, with a time resolution of 2.4 s, the typical set of periodograms contained $N_{\rm trial}$$\approx$ 200,000 trial periods per observation. |
For the pu detector. with a time resolution of 73. us. the typical set of periodograms contained τηεδν105 trial periods. | For the pn detector, with a time resolution of 73.4 ms, the typical set of periodograms contained $N_{\rm
trial}$$\approx$$1.8\times10^8$ trial periods. |
In total. we searched 1.5«1011 trial periods. the vast majority of which were from the lieh-time-+vesolution data taken with the EPIC pu. | In total, we searched $1.7\times10^{11}$ trial periods, the vast majority of which were from the high-time-resolution data taken with the EPIC pn. |
The powers produced by randoni noise du a periodoera du which ieasurements have been averaged are distributed as a chi-squared function with 2n degrees of freedom. | The powers produced by random noise in a periodogram in which $n$ measurements have been averaged are distributed as a chi-squared function with $2n$ degrees of freedom. |
Following (Rausomctal.2002).. we refer to the measured Fourier powers with 5-1 as Dae nd normalize them so that the mean power produced by white noise is 1. | Following \citep{rem02}, we refer to the measured Fourier powers with $n$ =1 as $P_{\rm meas}$ , and normalize them so that the mean power produced by white noise is 1. |
The chance probability that noise would produce a signal larger than Po. cal be determined from au exponential distribution: where the approximation is valid for £44,751 (Bausomal.2002). | The chance probability that noise would produce a signal larger than $P_{\rm meas}$ can be determined from an exponential distribution: where the approximation is valid for $P_{\rm meas}$$\gg$ 1 \citep{rem02}. |
. Given the large nuuber of trials for our cutive search. a signal that had a <0.1% chance c resulting from. noise must have a power 44,2532 | Given the large number of trials for our entire search, a signal that had a $<$ chance of resulting from noise must have a power $P_{\rm meas}$$>$ 32.8. |
Such a signal would be detected at a confidence leve equivalent to 30 over the entire search. or ὃσ in a single trial. | Such a signal would be detected at a confidence level equivalent to $\sigma$ over the entire search, or $\sigma$ in a single trial. |
ILowever. a signal could also be cousidered significa if it was cetected with a lower power in iultip observations. ax one night hope would occur given tha hhas three separate cameras that observe the same patch of the sky. | However, a signal could also be considered significant if it was detected with a lower power in multiple observations, as one might hope would occur given that has three separate cameras that observe the same patch of the sky. |
For iustauce. eiven two signals P,,4 aud ομως at the same frequency. the chance probability that their suni exceeds some value is ao chi-squared distribution with 1 degrees of freedom: (secoRansometal.2002.forthegeneralformsumnmnineanarbitraryumberof signals). | For instance, given two signals $P_{\rm meas,1}$ and $P_{\rm meas,2}$ at the same frequency, the chance probability that their sum exceeds some value is a chi-squared distribution with 4 degrees of freedom: \citep[see][for the general form for summing an arbitrary number of signals]{rem02}. |
If we take Poot=Dass for example. a signal has a 0.14 of resulting from noise if if appeared with Pray> 17 in both observations. | If we take $P_{\rm meas,1} = P_{\rm meas,2}$, for example, a signal has a $<$ of resulting from noise if it appeared with $P_{\rm meas,1}$$>$ 17 in both observations. |
Iu principle. one could devise au algoritlin that searched through all of the periodograms roni the same source. and stm the powers at cach requency to search for signals that repeat in the data. | In principle, one could devise an algorithm that searched through all of the periodograms from the same source, and sum the powers at each frequency to search for signals that repeat in the data. |
Iu practice. however. the periocdograms were rot all computed with the same frequency resolution. which imaakes such an effort dificult. | In practice, however, the periodograms were not all computed with the same frequency resolution, which makes such an effort difficult. |
Moreover. when considering observations separated m time. one also has o be coucerued that some candidate signals diifted iu requency. either because of the spin-down of au isolated ous. or Doppler shifts for a pulsar in a binary (sec.e.g..Vaughanetal.199L.forfurther discussion).. | Moreover, when considering observations separated in time, one also has to be concerned that some candidate signals drifted in frequency, either because of the spin-down of an isolated pulsar, or Doppler shifts for a pulsar in a binary \citep[see, e.g.,][for further discussion]{vau94}. |
Therefore, we have adopted a simplified approach iu cxanuning candidate signals. by recording all signals witli powers with less than a chance of resulting from noise in a scarch of asource. For AACTS. the threshold power is ecuerally DP 717. | Therefore, we have adopted a simplified approach in examining candidate signals, by recording all signals with powers with less than a chance of resulting from noise in a search of a. For ACIS, the threshold power is generally $P_{\rm
meas}$$>$ 17. |
For the AIMOS. the threshold power is typically Paya. ld. whereas for the pu the power is Paya, 26. | For the MOS, the threshold power is typically $P_{\rm meas}$$>$ 19, whereas for the pn the power is $P_{\rm
meas}$$>$ 26. |
Any candidate signal was inspected to determine itssignificance. | Any candidate signal was inspected to determine itssignificance. |
With these search criteria. our results up to this poiut were dominated bv signals that are non-periodic nolse or detector artifacts. | With these search criteria, our results up to this point were dominated by signals that are non-periodic noise or detector artifacts. |
In both | In both |
and σοι=fa4/Y. the combined cooling time being {.= mtas/(+¥). where B is the magnetic field. and Y is the Compton y-parameter (?).Y=€,/ep for &<<ep and Y=(eeg)7 for &>>ey. | and $t_{SSC}=t_{syn}/Y$, the combined cooling time being $t_c=(1/t_{syn}+1/t_{SSC})^{-1}$ $t_{syn}/(1+Y)$, where $B$ is the magnetic field, and $Y$ is the Compton y-parameter $, Y \approx \epsilon_e/\epsilon_B$ for $\epsilon_e
<< \epsilon_B$ and $Y \approx (\epsilon_e/\epsilon_B)^{1/2}$ for $\epsilon_e
>> \epsilon_B$. |
We now hypothesize that the lack of emission outside the GBM energy band (1e. E>30 MeV) observed during interval a is due to the optical thickness for pair production. | We now hypothesize that the lack of emission outside the GBM energy band (i.e. $E\gtrsim 30$ MeV) observed during interval a is due to the optical thickness for pair production. |
We assume that the spectrum is a Band spectrum. of a low energy spectral slope of a~—1.03 and peak energy ἕως=2.7 MeV as observed. but with a high-energy spectral slope of B=—2.5?). | We assume that the spectrum is a Band spectrum, of a low energy spectral slope of $\alpha\sim -1.03$ and peak energy $E_{peak}=2.7$ MeV as observed, but with a high-energy spectral slope of $\beta=-2.5$. |
. We note that a Band fit to the data during this interval poorly constrainsf to be less than —1.7. | We note that a Band fit to the data during this interval poorly constrains $\beta$ to be less than $\sim -1.7$. |
The την for pair production is expressed as follows27): where «cy is the Thompson cross-section. R is the compactness of the source. and Nae.(5, is the number of target photons. re. the number of photons with energy above Εμ. where accounts for a photon of energy E in the observer frame being attenuated by pair production by an interaction with softer photons. whose energy (also in the observer frame) is equal to or greater than ΕΕ). | The $\tau_{\gamma\gamma}$ for pair production is expressed as follows: where $\sigma_T$ is the Thompson cross-section, $R$ is the compactness of the source, and $N_{>E_{an}(E)}$ is the number of target photons, i.e. the number of photons with energy above $E_{an}$, where accounts for a photon of energy $E$ in the observer frame being attenuated by pair production by an interaction with softer photons, whose energy (also in the observer frame) is equal to or greater than $E_{an}(E)$. |
For a power-law spectrum of the form one has (where we are supposingBXB«— 1). | For a power-law spectrum of the form one has (where we are supposing $\beta<-1$ ). |
We define E,,, as the energy for which r4€(£,,,=lI. | We define $E_{max}$ as the energy for which $\tau_{\gamma\gamma}(E_{max})=1$. |
Using R=2cE70t,5,/(1+2)6xI0'T7[oru[CL28)] em. and substituting Eqs. (2)) | Using $R=2 c \Gamma^2 \delta t_{obs}/(1+z)=6\times10^{10}\Gamma^2 \left[\delta t_{obs}/((1+z)\rm s)\right]$ cm, and substituting Eqs. \ref{ean}) ) |
and (4)) into Eq. (1)) | and \ref{np}) ) into Eq. \ref{tau}) ) |
we have No afterglow emission was/ detectedC71 BEfor081024B.. so the burst redshift is unknown. | we have No afterglow emission was detected for, so the burst redshift is unknown. |
Hereafter we assume zΞ0.1 as a reference value for short GRBs. i.e. d;=1.3»107 em for the luminosity distance. | Hereafter we assume $z=0.1$ as a reference value for short GRBs, i.e. $d_{L}=1.4\times10^{27}$ cm for the luminosity distance. |
The Band spectrum is given by(2): We note that these equations are obtained from Eq. ( | The Band spectrum is given by: We note that these equations are obtained from Eq. ( |
1) of by using ρω=(2+aEq?).. | 1) of by using $E_{peak}=(2+\alpha)E_0$. |
We note also that the multiplicative factor e* in Eq. ( | We note also that the multiplicative factor $e^{\beta-\alpha}$ in Eq. ( |
1) of is included in the first factor in parenthesis of the above equation. | 1) of is included in the first factor in parenthesis of the above equation. |
We can thus approximate the high energy portion of the Band spectrum as where the normalization constant C=Cp;0.3 Is derived by assuming that the vF, flux at 100 keV is ~1077 erg/cm/s 1).. e. from Eq. (7) | We can thus approximate the high energy portion of the Band spectrum as where the normalization constant $C=C_{Band}\sim0.3$ is derived by assuming that the $\nu F_{\nu}$ flux at 100 keV is $\sim 10^{-7}$ $^{2}$ /s, i.e. from Eq. \ref{Bandlow}) ) |
and then assuming that the spectrum has a Band shape with Έρως2.7 MeV. w=—1.03 (as the observed values). and p=-2.52).. i.e. from Eq. (7)) | and then assuming that the spectrum has a Band shape with $E_{peak}\sim 2.7$ MeV, $\alpha=-1.03$ (as the observed values), and $\beta=-2.5$, i.e. from Eq. \ref{Bandhigh}) ) |
Substituting this into Eq. (5)). | Substituting this into Eq. \ref{gammap}) ), |
we thus obtain The above equation estimates the Lorentz factor required to keep the shell optically thick to pair production above a few tens of MeVs. as observed during interval a. Detailed modeling of the spectrum expected in the IS scenario for a high compactness shell. is beyond the scope of this paper. | we thus obtain The above equation estimates the Lorentz factor required to keep the shell optically thick to pair production above a few tens of MeVs, as observed during interval a. Detailed modeling of the spectrum expected in the IS scenario for a high compactness shell, is beyond the scope of this paper. |
As we have seen. optical thickness to pair production affects the observed spectrum at high energies. but when this happens the consequent scattering of photons from the created pairs. and pair annihilation. also need to be taken into account. | As we have seen, optical thickness to pair production affects the observed spectrum at high energies, but when this happens the consequent scattering of photons from the created pairs, and pair annihilation, also need to be taken into account. |
For instance. when the optical thickness for photon scattering on electrons is high. the spectrum of the observed radiation is modified by the standard assumptions of thin synchrotron and IC emission. and effects related to the so-called electron photosphere need to be considered?). | For instance, when the optical thickness for photon scattering on electrons is high, the spectrum of the observed radiation is modified by the standard assumptions of thin synchrotron and IC emission, and effects related to the so-called electron photosphere need to be considered. |
. Re-heating of the electron population caused by synchrotron self-absorption(&).. IS also a process that needs proper evaluation and can modify the spectrum at low energies. | Re-heating of the electron population caused by synchrotron self-absorption, is also a process that needs proper evaluation and can modify the spectrum at low energies. |
Numerical simulations are the most effective way to take into account all these processes dynamically. | Numerical simulations are the most effective way to take into account all these processes dynamically. |
Within the IS. model. the results of detailed numerical modeling by show that to ensure that the synchrotron emission peaks in the MeV range. as for081024B.. the required values of the IS model parameters likely imply a high compactness. which causes deviations from the simple predictions of the thin case IS model?). | Within the IS model, the results of detailed numerical modeling by show that to ensure that the synchrotron emission peaks in the MeV range, as for, the required values of the IS model parameters likely imply a high compactness, which causes deviations from the simple predictions of the thin case IS model. |
. For high compactness. find that the spectra peak at ~| MeV. display a steep slope at lower energies (with indices of 0.5<24a€ Lin the vF, spectrum). and a sharp cutoff at ~10 MeV. This is consistent with the spectrum observed in slice a of GRB081024B. which we therefore attribute to IS emission | For high compactness, find that the spectra peak at $\sim 1$ MeV, display a steep slope at lower energies (with indices of $0.5\lesssim 2+\alpha\lesssim 1$ in the $\nu F_{\nu}$ spectrum), and a sharp cutoff at $\sim 10$ MeV. This is consistent with the spectrum observed in slice a of GRB081024B, which we therefore attribute to IS emission |
observations extending over multiple solar eycles (Crosby et al. | observations extending over multiple solar cycles (Crosby et al. |
1993: Biesecker 1994; Bai 1993: Aschwanden 20103). | 1993; Biesecker 1994; Bai 1993; Aschwanden 2010a). |
What other predictions can be made from our analytical model? | What other predictions can be made from our analytical model? |
For SOC processes in 3-D space. which ts probably the most common application in the real world. the mean fractal dimension is predicted to be Di=2.0. which can be tested by measurements of fractal dimensions in observations. | For SOC processes in 3-D space, which is probably the most common application in the real world, the mean fractal dimension is predicted to be $D_3\approx 2.0$, which can be tested by measurements of fractal dimensions in observations. |
The 20 largest solar flares observed with TRACE have been analyzed in this respect and an area fractal dimension of D»=1.8940.05 was found at the flare peaks. which translates into a value of D=2.10+0.14 if we use an anisotropic flare arcade model (Aschwanden and Aschwanden 20082). | The 20 largest solar flares observed with TRACE have been analyzed in this respect and an area fractal dimension of $D_2=1.89\pm0.05$ was found at the flare peaks, which translates into a value of $D_3=2.10\pm0.14$ if we use an anisotropic flare arcade model (Aschwanden and Aschwanden 2008a). |
The distribution of flare energies 1s predicted to have à powerlaw slope of cg=1.50. which closely matches the observed statistics of solar flare hard X-ray emission (αςx149— 1.56). | The distribution of flare energies is predicted to have a powerlaw slope of $\alpha_E=1.50$, which closely matches the observed statistics of solar flare hard X-ray emission $\alpha_E \approx 1.49-1.56$ ). |
Since this value is undisputably below the critical limit @=2 of the energy integral. the total released energy is contained in the largest flares and thus rules out any significant nanoflare heating of the solar corona. | Since this value is undisputably below the critical limit $\alpha=2$ of the energy integral, the total released energy is contained in the largest flares and thus rules out any significant nanoflare heating of the solar corona. |
Another prediction. that we did not test here with solar flare data. is the diffusive flare size scaling. | Another prediction, that we did not test here with solar flare data, is the diffusive flare size scaling. |
Straightforward tests could be carried out by gathering statistics of the flare size evolution during individual flares(which are predicted to scale as v(t)eERI £7). as well as from the statistics of a large sample of flares. which is predicted to show a correlation L«T'*. | Straightforward tests could be carried out by gathering statistics of the flare size evolution during individual flares(which are predicted to scale as $x(t) \propto t^{1/2}$ ), as well as from the statistics of a large sample of flares, which is predicted to show a correlation $L \propto T^{1/2}$. |
The application of our fractal-diffusive SOC model to solar flares implies that the subsequent triggering of local magnetic reconnection events during a flare occurs as a diffusive random walk. | The application of our fractal-diffusive SOC model to solar flares implies that the subsequent triggering of local magnetic reconnection events during a flare occurs as a diffusive random walk. |
A similar finding of diffusive random walk was also found in the turbulent flows of magnetic bright points in the lanes between photospheric granular convection cells (Lawrence et al. | A similar finding of diffusive random walk was also found in the turbulent flows of magnetic bright points in the lanes between photospheric granular convection cells (Lawrence et al. |
2001). | 2001). |
The spatio-temporal scaling of the diffusive random walk predicts also the size. duration. and energy of the largest Hare. which is likely to be constrained. by the size. LayxT,12 ofoo. the largest active. region. | The spatio-temporal scaling of the diffusive random walk predicts also the size, duration, and energy of the largest flare, which is likely to be constrained by the size $L_{AR} \propto T_{max}^{1/2}$ of the largest active region. |
The author thanks the Paul Charbonneau for helpful discussions and contributions. | The author thanks the Paul Charbonneau for helpful discussions and contributions. |
This work is partially supported by NASA grant NAGS-13490 and NASA TRACE contract NASS-38099. | This work is partially supported by NASA grant NAG5-13490 and NASA TRACE contract NAS5-38099. |
We acknowledge access to solar mission data and flare catalogs from the at the NASA Goddard Space | We acknowledge access to solar mission data and flare catalogs from the at the NASA Goddard Space Flight Center (GSFC). |
\ref{Aschwanden, M.J., Dennis, B.R., and Benz, A.O. 1998,
\apj 497, 972-993.}
\ref{Aschwanden, M.J. 2004,
{\sl Physics of the Solar Corona - An Introduction}.
Springer/Praxis, New York, ISBN 3-540-22321-5, 842p.}
\ref{Aschwanden, M.J. 2010a,
{\sl The state of self-organized criticality of the Sun
during the last three solar cycles. I. Observations},
\solphys (online first), DOI 10.1007/s11207-011-9755-0.}
\ref{Aschwanden, M.J. 2010b,
{\sl The state of self-organized criticality of the Sun
during the last three solar cycles. II. Theoretical model},
\solphys (in press).}
\ref{Morales, L., and Charbonneau, P. 2008, \apj 682, 654.}
\ref{Morales, L., and Charbonneau, P. 2009, \apj 698, 1893.}
\ref{Norman, J.P., Charbonneau, P., McIntosh, S.W., and Liu, H.L.
2001, \apj 557, 891.}
\ref{Sornette, D. 2004,
{\sl Critical phenomena in natural sciences: chaos, fractals,
self-organization and disorder: concepts and tools},
Springer, Heidelberg, 528 p.}
\ref{Turcotte, D.L. 1999,
{\sl Self-organized criticality},
Rep. Prog. Phys. 62, 1377.}
\ref{Vlahos, L., Georgoulis, M., Kluiving, R., and Paschos, P. 1995,
\aap 299, 897.}
\ref{Willis, J.C. and Yule, G.U. 1922, \nat 109, 177.}
|
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levels. new galaxies and galaxy systems in the outskirts of a supercluster become supercluster members. | levels, new galaxies and galaxy systems in the outskirts of a supercluster become supercluster members. |
This may increase the value of the clumpiness and change the morphological signature of a supercluster at low mass fractions. | This may increase the value of the clumpiness and change the morphological signature of a supercluster at low mass fractions. |
The possible change in morphology depends on the number of galaxies and on the richness of groups removed from or added to the supercluster and is individual for each supercluster. | The possible change in morphology depends on the number of galaxies and on the richness of groups removed from or added to the supercluster and is individual for each supercluster. |
At small distances our sample volume is small. which introduces another selection effect — nearby rich superclusters are split between several superclusters. some parts of these superclusters may be located outside of the sample volume. | At small distances our sample volume is small, which introduces another selection effect – nearby rich superclusters are split between several superclusters, some parts of these superclusters may be located outside of the sample volume. |
This makes the data about nearby superclusters less reliable. | This makes the data about nearby superclusters less reliable. |
The identification of Abell clusters may also be affected by selection effects. | The identification of Abell clusters may also be affected by selection effects. |
It is well known that some Abell clusters consist of several line-of-sight components. | It is well known that some Abell clusters consist of several line-of-sight components. |
A good example of such a cluster is the cluster Abell 1386. recently studied by ?. | A good example of such a cluster is the cluster Abell 1386, recently studied by . |
. Our search discarded. Abell clusters affected by this projection effect. | Our search discarded Abell clusters affected by this projection effect. |
Recently used volume-limited samples of galaxies from the SDSS DR7 to extract superclusters of galaxies and to study the morphology of whole superclusters with the shape parameter (the ratio of the shapefinders Α/Κ). | Recently used volume-limited samples of galaxies from the SDSS DR7 to extract superclusters of galaxies and to study the morphology of whole superclusters with the shape parameter (the ratio of the shapefinders $K_1/K_2$ ). |
To determine superclusters the authors calculated the density field with an Epanechnikov kernel and found systems of galaxies with at least 10 member galaxies. | To determine superclusters the authors calculated the density field with an Epanechnikov kernel and found systems of galaxies with at least 10 member galaxies. |
In2.. we compared the Epanechnikov and B; box spline kernels and found that both kernels are good to describe the overall shape of superclusters. while the B; box spline kernel better resolves the inner structure of superclusters. | In, we compared the Epanechnikov and $B_3$ box spline kernels and found that both kernels are good to describe the overall shape of superclusters, while the $B_3$ box spline kernel better resolves the inner structure of superclusters. |
This is the reason why we used this kernel in the present study. | This is the reason why we used this kernel in the present study. |
The most important difference between our studies is that we used the data about the richer superclusters with at least 300 member galaxies. | The most important difference between our studies is that we used the data about the richer superclusters with at least 300 member galaxies. |
showed that there are both planar and filament-like superclusters (pancakes and filaments) among the superclusters of their sample. while in our sample there are almost no superclusters for which planarity is larger than filamentarity. | showed that there are both planar and filament-like superclusters (pancakes and filaments) among the superclusters of their sample, while in our sample there are almost no superclusters for which planarity is larger than filamentarity. |
However. found that very rich and lummous superclusters tend to be filaments. as we also found in our study. | However, found that very rich and luminous superclusters tend to be filaments, as we also found in our study. |
The overall shapes of superclusters. described by the shape parameters or approximated by triaxial ellipses. have been analysed in222222. | The overall shapes of superclusters, described by the shape parameters or approximated by triaxial ellipses, have been analysed in. |
These studies showed that elongated. prolate structures dominate among superclusters. as we also found in our study. | These studies showed that elongated, prolate structures dominate among superclusters, as we also found in our study. |
In the analysis of the geometry of the structures around the galaxy clusters from simulations showed that these structures tend to lie on planes. | In the analysis of the geometry of the structures around the galaxy clusters from simulations showed that these structures tend to lie on planes. |
Similarly. in our study and in the study by poorer systems are more planar. | Similarly, in our study and in the study by poorer systems are more planar. |
used the shapefinders plane K,-A> (the morphological signature in our study) to study the morphology of superclusters in simulations. | used the shapefinders plane $K_1$ $K_2$ (the morphological signature in our study) to study the morphology of superclusters in simulations. |
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