J. Astron. Space Sci. 23(3), 167–176 (2006)
THE PEAK ENERGY–DURATION CORRELATION AND
POSSIBLE IMPLICATIONS ON GAMMA RAY BURST PROGENITOR
Department of Astronomy and Atmospheric Sciences, Kyungpook National University
1370 Sankyuk-dong, Buk-gu, Daegu 702-701, Korea
(Received June 26, 2006; Accepted July 19, 2006)
We investigate the correlation between the peak energy and the burst duration usingavailable long GRB data with known redshift, whose circumburst medium type hasbeen suggested via afterglow light curve modeling. We find that the peak energy andthe burst duration of the observed GRBs are correlated both in the observer frameand in the GRB rest frame. For our total sample we obtain, for instance, the Spear-man rank-order correlation values
in the observer frame and in the GRB rest frame,
respectively. We note that taking the effects of the expanding universe into accountreduces the value a bit. We further attempt to separate our GRB sample into the “ISM”GRBs and the “WIND” GRBs according to environment models inferred from the af-terglow light curves and apply statistical tests, as one may expect that clues on theprogenitor of GRBs can be deduced directly from prompt emission properties otherthan from the ambient environment surrounding GRBs. We find that two subsamplesof GRBs show different correlation coefficients. That is, the Spearman rank-order cor-relation are
for the “ISM” GRBs and “WIND” GRBs, respectively,
after taking the effects of the expanding universe into account. It is not yet, however,statistically very much significant that the GRBS in two types of circumburst mediashow statistically characteristic behaviors, from which one may conclude that all thelong bursts are not originated from a single progenitor population. A larger size ofdata is required to increase the statistical significance.
: gamma rays: bursts – methods: data analysis
Gamma-ray bursts(GRBs) are brief and intense phenomena, whose peak energy in their spectra
400 keV (e.g., Barraud et al. 2003). Since they were first detected in the
late 1960s (Klebesadel, Strong, & Olson 1973), we have learned a great deal of the observed GRBswith their counterparts in lower energy bands, so called afterglows (e.g., Costa et al. 1997, Frailet al. 1997, Metzger et al. 1997, van Paradijs et al. 1997). Follow-up observations of afterglow oflong GRBs have played crucial roles in establishing facts that (1) GRBs are cosmological (Mao &Paczy ski 1992, Meegan et al. 1992, Piran 1992), (2) opening angle corrected energy is clustered
ergs which is comparable to ordinary supernova energy (Panaitescu & Kumar 2001b,
Piran et al. 2001, Frail et al. 2001, Bloom, Frail, & Kulkarni 2003), (3) GRBs, at least long bursts,are closely related to the death of massive young stars (Woosley 1993, Paczy ski 1998, MacFadyen
& Woosley 1999), and (4) the afterglow emission is due to the electron synchrotron radiation froma decelerating relativistic blast wave, which suggests an indirect hint of the emission mechanism ofGRBs (Paczy ski & Rhoads 1993, Sari & Piran 1995, Waxman 1997a,b, Wijers, Rees, &
It is widely accepted that the fireball internal/external shock model succeeds in explaining both
the prompt emission and afterglow, in which highly relativistic shocks with Lorentz factor
collide each other and are subsequently decelerated by the circumburst medium (
1994, Kobayashi, Piran, & Sari 1997, Daigne & Mochkovitch 1998, 2000).
The shock may be spherical or initially confined to a narrow cone. An engine of GRBs is, however,apparently to power conical ejecta to produce the observed GRBs and their afterglows. For, inmany cases the rate of decay in afterglow flux has been observed to steepen, which is naturallyaccounted for by a collimated conical jet (Rhoads 1999, Sari, Piran, & Halpern 1999). After all,an afterglow light curve depends fairly strongly on physical properties of a whole GRB system,especially the mass-loss rate of the progenitor and the ambient density distribution (Chevalier &Li 1999, Panaitescu & Kumar 2001a,b, 2002). Hence, afterglow observations are well suited todetermining not only the geometry of the explosion but also the distribution of circumburst matter.
Some insights about the GRB progenitor can be obtained from properties of the circumburst
medium surrounding GRBs, which can be inferred from features of the afterglow emission. GRBambient environments are grouped into two types in general: “ISM” and “WIND”. One may considera constant circumburst matter density, the “ISM” case. If the ejecta is expelled during the merging oftwo compact objects, it is expected that the medium surrounding the GRB source is homogeneous.
We also note that a quasi-homogeneous environment around a massive star can be created by thepre-shock wave (e.g., Chevalier, Li, & Fransson 2004). Another possibility is that the circumburstmedium is dominated by a wind outflow from a progenitor star, the “WIND” case. If a collapsingmassive star is the origin of the relativistic fireball, the circumburst medium is the wind ejectedby the star prior to its collapse, in which case a constant mass-loss rate and wind speed results inan ¾ profile. The question of a wind versus a constant-density surrounding medium is a crucial
issue for the progenitor of GRBs (e.g., Mirabal et al. 2003). Density profiles derived from afterglowmodelling are particularly intriguing, in the sense that most of events are consistent with a constantdensity environment and only in a few cases a wind profile is preferred. This immediately has raisedthe question of why such evidence is not seen in all GRBs with afterglows. The absence of clearwind signature in some afterglow light curves can be explained by different classes of progenitors ofthe long bursts (e.g., Chevalier & Li 1999, 2000).
The analysis of the prompt emission from GRBs may provide us with valuable hints to the
central source accelerating the outflow from which the radiation emanates (Fenimore, Madras, &Nayakshin 1996, Kobayashi, Piran, & Sari 1997, Beloborodov, Stern, & Svensson 1998, Fenimore1999, Chang & Yi 2000, Amati et al. 2002, Ghirlanda, Ghisellini, & Lazzati 2004, Liang & Dai2004, Liang, Dai, & Wu 2004). The significant advances in our understanding of the nature ofGRBs have been made through statistical studies of GRB light curves. For instance, statisticalstudies of the direction and of the observed flux of GRBs have restricted models of the spatialdistribution of GRBs to a cosmological distribution (e.g., Chang & Yi 2001). Recently, the emissionproperties of GRBs are studied in terms of the peak energy of the
Ghisellini, & Celotti 2004, Yamazaki, Ioka, & Nakamura 2004). Correlations between
the time-integrated isotropic emitted energy
CORRELATION AND IMPLICATIONS ON GRB PROGENITOR
refs.: (1) Ghirlanda, Ghisellini, & Lazzati 2004, (2) Bloom et al. 1999,
(3) HETE Fregate Archival Data, http://space.mit.edu/HETE/Bursts/GRB021004,
(4) Chevalier & Li 2000, (5) Panaitescu & Kumar 2002, (6) Frail, Waxman, & Kulkarni 2000,
(7) Chevalier & Li 1999, (8) Chevalier, Li, & Fransson 2004, (9) Panaitescu & Kumar 2001a,
(10) Frail et al. 2003, (11) Yost et al. 2003, (12) Halpern et al. 2000, (13) Panaitescu 2005,
(14) Price et al. 2002, (15) Greiner et al. 2003, (16) Piro et al. 2005, (17) Price et al. 2003,
(18) Berger et al. 2003, (19) Smith et al. 2005, (20) Starling et al. 2005, (21) Li & Chevalier 2003,
(22) Kumar & Panaitescu 2003, (23) Taylor et al. 2005, (24) Granot et al. 2005
also derived (Amati et al. 2002, Ghirlanda, Ghisellini & Lazzati 2004, Lamb, Donaghy & Graziani2004, Yonetoku et al. 2004, Ghirlanda, Ghisellini, & Firmani 2005, Ghirlanda et al. 2005). Thesecorrelations may shed light on the central radiation engine for the prompt GRB emission.
In this paper we investigate the correlation between the peak energy
is an important quantity of GRBs in the fireball
in the source frame depends on the fireball bulk Lorentz factor
also interested in the question of whether GRBs show similar behaviors in the prompt emissionwhen they are divided, as mentioned earlier, by two types of the circumburst medium derived fromafterglow light curves. We attempt to look for in the prompt emission of GRBs fingerprints left by theprogenitor of GRBs. By doing so, one may wish to deduce whether their central engine really worksin a different way as density profiles derived from afterglow modelling imply a different kind of theGRB progenitor. To study spectral features of the prompt emission of GRBs is a complementary,yet direct approach to constrain the nature of the progenitor. Particularly, using data of the GRBswhose redshift
is known we are also able to infer how the correlation changes by the cosmological
expansion of the universe, that is, cosmological time dilation and redshift in energy. This paperis organized as follows. In 2 we describe GRB data we use in this analysis and present results
obtained from a study of the correlation between the peak energy and the duration. In 3 discussions
2. CORRELATION BETWEEN PEAK ENERGY AND DURATION
In order to investigate a relation between the peak energy and the duration we have compiled
data of the observed GRBs from published literatures and public databases as indicated in Table 1.
Figure 1. The relation between the peak energy
the two GRB subsamples grouped by the environment type. Open circles and crosses represent “ISM” and“WIND” GRBs, respectively. Vertical arrows indicate that quoted peak energy values are lower limits.
We choose the GRBs whose afterglow light curves are modeled in terms of the density profile oftheir ambient medium so that one can determine what kind of environment the source resides in.
Some of GRBs are equally well (or poorly) described by the two types of media at the same time.
We exclude these cases in our analysis. Of those chosen bursts, we further select the GRBs whoseredshift , peak energy
into two subsamples so that we separate GRBs into the “ISM” GRBs and the “WIND” GRBs. Theselected bursts are observed by BATSE½, BeppoSAX¾, Ulysses¿, HETE-2 . We list the GRBs usedin our analysis in Table 1 with the environment type.
CORRELATION AND IMPLICATIONS ON GRB PROGENITOR
Table 2. Obtained correlation coefficients and the chance probability. The linear correlation coefficient, theSpearman rank-order correlation, the Kendall’s , and corresponding chance probabilities for the total sampleand two subsamples of the “ISM” and the “WIND” GRBs are shown.
Note. Calculations are repeated before and after correction of effects of the cosmological expansion by afactor of
In Figure 1, we show the relation between the peak energy
log-log plot for the two subsamples of GRBs divided by the environment type. Open circles andcrosses represent the “ISM” GRBs and the “WIND” GRBs, respectively. Vertical arrows indicatethat quoted peak energy values are to be considered as lower limits. We calculate a linear correlationcoefficient with all the data in the total sample and with those in two subsamples. We also calculate
has an equal or larger value than its observed in the null
hypothesis. According to the obtained probability the whole data set shows a significant correlation,that is,
. To examine additional statistical tests of data sets, we
employ the Spearman rank-order correlation test. It returns a correlation value
pairs of uncorrelated variables would yield a value of
or more discrepant than the one obtained from the data set. We find again with the total sample thatthe peak energy of GRBs appears to correlate quite significantly with the duration, that is, Ö ³ ¼
. General trends of test results are similar to those of the Spearman
rank-order correlation test. We find that linear correlations in two subsamples become different, thatis,
and the “WIND” GRBs, respectively. The “ISM” GRBs and the “WIND” GRBs statistically differin the Spearman
value. That is, the “WIND” GRBs seem more correlated than the “ISM” GRBs,
for the “WIND” GRBs, respectively. One
may wish to check with a larger sample in the future whether it is ascribed to the small size of thesample or it is intrinsic. The obtained statistical parameters are summarized in Table 2. Note thatwhen we calculate slopes and correlations, we take the lower limit of the peak energy
two GRBs as the value at the duration.
Cosmological objects should be redshifted in energy, as well as extended in time due to the
cosmological expansion of the universe. For a cosmological source at redshift
is related to the redshift-corrected peak energy
time dilation by an amount proportional to
the cosmological expansion, we rescale the peak energy
ing corrected effects of the cosmological expansion, we show the relation between the peak energy
in Figure 2 for the two subsamples of GRBs. In order to com-
pare the correlation coefficients with those obtained before taking cosmological expanding effects
into account, we repeat same calculations after rescaling the GRB parameter to a factor of
The correlation coefficients resulted from the whole data tend to become less steep as redshift iscorrected. For instance, the Spearman
. We also find that the “ISM” GRBs and the “WIND” GRBs
for the “WIND” GRBs, respectively. A summary of parameters that we have investigated and theircorresponding
There are some limits in this analysis. First of all, the number of data may be too small to draw
a conclusive statement. Particularly, the data set contains two lower limit values. We have repeatedsame calculations without those data points, yet have obtained similar conclusions in general. Forinstance, linear correlation coefficients and chance probabilities are
, without and with redshift-correction, respectively.
The Spearman correlation and corresponding chance probabilities are
respectively. Hence, the correlation between the peak energy
apparently exist both in the observer frame and in the source frame. Distinction between the “ISM”GRBs and the “WIND” GRBs becomes less obvious. For the “ISM” GRBs and the “WIND” GRBs,
redshift correction. When the redshift is taken into account, the data does not show correlations anymore. A summary of resulting values are shown in Table 3. Secondly, one must avoid a systematicmismatch in assigning the GRB environment since the conclusion that can be drawn in an attemptsuch as in this paper is critically based on the grouping of GRBs. Sometimes it may be hard tounanimously distinguish between two circumburst environments by current afterglow light curvemodelling since there is a degeneracy of the parameters in the current afterglow model. Hence morecautious study on the GRB environments are desired for the definite classification.
3. DISCUSSIONS AND CONCLUSION
The spectroscopic finding of SN 2003dh in the afterglow light curve from GRB 030329 (Stanek
et al. 2003, Hjorth et al. 2003) supports the previous identification of the nearby SN 1998bw withGRB 980425 (Galama et al. 1998, Iwamoto et al. 1998), providing a link between a GRB and thesupernova explosion of a massive star. The implication of the supernova light is that the GRBprogenitor is a massive star. An essential consequence of a massive star progenitor is that the envi-ronment for the progenitor is determined by the mass-loss wind from the star, of which signature isinterestingly not found clearly in all afterglow light curves. This is at odds with the simple expecta-tion of massive star progenitors. Several complications in modelling and interpreting the afterglowlight curve still await to be fully understood (e.g., Chevalier, Li, & Fransson 2004). At present,however, it is fair to say that only a fraction of long GRB afterglows appears to be associated withthe death of massive stars. That is, the observed GRBs have been born in two distinct types of natalenvironments.
A summary of our findings is as follows. Firstly, we find correlations between the peak energy
both in the observer frame and in the source frame with high prob-
ability (cf. Band et al. 1993). This correlation is expected from an analogous correlation that holdsbetween the hardness-ratio and the duration for long and bright GRBs (Dezalay et al. 1996, Horack& Hakkila 1997). It is also found in Table 2 that removing effects of the cosmological expansion in-deed reduces correlation values both in the total sample. The implication of our correlation analysisis that conclusions of the correlation between the hardness-ratio and the duration should be derived
CORRELATION AND IMPLICATIONS ON GRB PROGENITOR
Figure 2. Similar plot as Fig. 1, but the peak energy
to remove effects of the cosmological expansion.
with due care, taking effects of the cosmological expansion into account. Secondly, we obtain a pos-sible signature that all the long GRBs are not originated from a single population, as inferred fromthe properties of the ambient environment surrounding GRBs. That is, the “ISM” GRBs and the“WIND” GRBs might be intrinsically different, one groups has a correlation coefficient above theaverage value and the other below the average. The two most generally accepted classes of GRBsare those arising from the bimodal distribution of their durations (Kouveliotou et al. 1993), whichseparates long and short GRBs, the spectrum of short events being, on average, harder than that forlonger events. A widely assumed scenario is that short bursts are likely to be produced by the mergerof compact objects, while the core collapse of massive stars is likely to give rise to long bursts (e.g.,
2002 and Piran 2005). However, it is still unclear whether long GRBs consist of more
than one population. For instance, various attempts to separate different classes of GRBs have beenmade (Tavani 1998, Balastegui, Ruiz-Lapuente, & Canal 2001). It should noted, however, that ourresults are somewhat inconclusive due to a low significance resulting from a small size of data sets.
Table 3. Similar table as Table 2, resulting from the data without two lower limit values in
Our finding does not rule out the fact that long GRBs may be originated from different progenitorpopulations.
This work was supported by the Korea Research Foundation Grant
(KRF-2004-003-C00093). This research has made use of data obtained through the High Energy
Astrophysics Science Archive Research Center Online Service, provided by the NASA/Goddard
Space Flight Center.
Amati, L., Frontera, F., Tavani, M., in´t Zand, J. J. M., Antonelli, A., Costa, E., Feroci, M., Guidorzi,
C., Heise, J., Masetti, N., Montanari, E., Nicastro, L., Palazzi, E., Pian, E., Piro, L., & Soffitta,P. 2002, A&A, 390, 81
Balastegui, A., Ruiz-Lapuente, P., & Canal, R. 2001, MNRAS, 328, 283Band, D., Matteson, J., Ford, L., Schaefer, B., Palmer, D., Teegarden, B., Cline, T., Briggs, M., Pa-
ciesas, W., Pendleton, G., Fishman, G., Kouveliotou, C., Meegan, C., Wilson, R., & Lestrade,P. 1993, ApJ, 413, 281
Barraud, C., et al. 2003, A&A, 400, 1021Beloborodov, A., Stern, B., & Svensson, R. 1998, ApJ, 508, L25Berger, E., Soderberg, A. M., Frail, D. A., & Kulkarni, S. R. 2003, ApJ, 587, L5Bloom, J. S., Frail, D. A., & Kulkarni, S. R. 2003, ApJ, 594, 674Bloom, J. S., Kulkarni, S. R., Djorgovski, S. G., Eichelberger, A. C., Cote, P., Blakeslee, J. P.,
Odewahn, S. C., Harrison, F. A., Frail, D. A., Filippenko, A. V., Leonard, D. C., Riess, A. G.,Spinrad, H., Stern, D., Bunker, A., Dey, A., Grossan, B., Perlmutter, S., Knop, R. A., Hook,I. M., & Feroci, M. 1999, Nature, 401, 453
Chang, H.-Y. & Yi, I. 2000, ApJ, 542, L17Chang, H.-Y. & Yi, I. 2001, ApJ, 554, 12Chevalier, R. & Li, Z.-Y. 1999, ApJ, 520, L29Chevalier, R. & Li, Z.-Y. 2000, ApJ, 536, 195Chevalier, R., Li, Z.-Y., & Fransson, C. 2004, ApJ, 606, 369Costa, E., et al. 1997, Nature, 387, 783Daigne, F. & Mochkovitch, R. T. 1998, MNRAS, 296, 275Daigne, F. & Mochkovitch, R. T. 2000, A&A, 358, 1157Dezalay, J. P., Lestrade, J. P., Barat, C., Talon, R., Sunyaev, R., Terekhov, O., & Kuznetsov, A. 1996,
CORRELATION AND IMPLICATIONS ON GRB PROGENITOR
Fenimore, E. 1999, ApJ, 518, 375Fenimore, E., Madras, C. D., & Nayakshin, S. 1996, ApJ, 473, 998Frail, D. A., Waxman, E., & Kulkarni, S. R. 2000, ApJ, 537, 191Frail, D. A., Kulkarni, S. R., Nicastro, S. R., Feroci, M., & Taylor, G. B. 1997, Nature, 389, 261Frail, D. A., Kulkarni, S. R., Sari, R., Djorgovski, S. G., Bloom, J. S., Galama, T. J., Reichart, D. E.,
Berger, E., Harrison, F. A., Price, P. A., Yost, S. A., Diercks, A., Goodrich, R. W., & Chaffee,F. 2001, ApJ, 562, L55
Frail, D. A., Yost, S. A., Berger, E., Harrison, F. A., Sari, R., Kulkarni, S. R., Taylor, G. B., Bloom,
J. S., Fox, D. W., Moriarty-Schieven, G. H., & Price, P. A. 2003, ApJ, 590, 992
Galama, T. J., et al. 1998, Nature, 395, 670Ghirlanda, G., Ghisellini, G., & Celotti, A. 2004, A&A, 422, L55Ghirlanda, G., Ghisellini, G., & Firmani, C. 2005, MNRAS, 261, L10Ghirlanda, G., Ghisellini, G., Firmani, C., Celotti, A., & Bosnjak, Z. 2005, MNRAS, 360, 45Ghirlanda, G., Ghisellini, G., & Lazzati, D. 2004, ApJ, 616, 331Granot, J., Ramirez-Ruiz, E., & Loeb, A. 2005, ApJ, 618, 413Greiner, J., et al. 2003, ApJ, 599, 1223Halpern, J. P., Uglesich, R., Mirabal, N., Kassin, S., Thorstensen, J., Keel, W. C., Diercks, A.,
Bloom, J. S., Harrison, F., Mattox, J., & Eracleous, M. 2000, ApJ, 543, 697
Hjorth, J., et al. 2003, Nature, 423, 847Horack, J. M. & Hakkila, J. 1997, ApJ, 479, 371Iwamoto, K., et al. 1998, Nature, 395, 672Klebesadel, R. W., Strong, I. B., & Olson, R. A. 1973, ApJ, 182, L85Kobayashi, S., Piran, T., & Sari, R. 1997, ApJ, 490, 92Kouveliotou, C., Meegan, C. A., Fishman, G. J., Bhat, N. P., Briggs, M. S., Koshut, T. M., Paciesas,
W. S., & Pendleton, G. N. 1993, ApJ, 413, L101
Kumar, P. & Panaitescu, A. 2003, MNRAS, 346, 905Lamb, D. Q., Donaghy, T. Q., & Graziani, C. 2004, New Ast. Rev., 48, 459Li, Z.-Y. & Chevalier, R. 2003, ApJ, 589, L69Liang, E. W. & Dai, Z. G. 2004, ApJ, 608, L9Liang, E. W., Dai, Z. G., & Wu, X. F. 2004, ApJ, 606, L29MacFadyen, A. I., & Woosley, S. E. 1999, ApJ, 524, 262Mao, S. &
Meegan, C. A., Fishman, G. J., Wilson, R. B., Horack, J. M., Brock, M. N., Paciesas, W. S., Pendle-
ton, G. N., & Kouveliotou, C. 1992, Nature, 355, 143
, P. & Rees, M. J. 1993, ApJ, 405, 278
Metzger, M. R., Djorgovski, S. G., Kulkarni, S. R., Steidel, C. C., Adelberger, K. L., Frail, D. A.,
Costa, E., & Frontera, F. 1997, Nature, 387, 879
Mirabal, N., Halpern, J. P., Chornock, Ryan, Filippenko, Alexei V., Terndrup, D. M., Armstrong, E.,
Kemp, J., Thorstensen, J. R., Tavarez, M., & Espaillat, C. 2003, ApJ, 595, 935
Panaitescu, A. 2005, MNRAS, 363, 1409Panaitescu, A. & Kumar, P. 2001a, ApJ, 554, 667Panaitescu, A. & Kumar, P. 2001b, ApJ, 560, L49Panaitescu, A. & Kumar, P. 2002, ApJ, 571, 779Piran, T. 1992, ApJ, 389, L45
Piran, T. 2005, Rev. Mod. Phys., 76, 1143Piran, T., Kumar, P., Panitescu, A., & Piro, L. 2001, ApJ, 560, L167Piro, L., De Pasquale, M., Soffitta, P., Lazzati, D., Amati, L., Costa, E., Feroci, M., Frontera, F.,
Guidorzi, C., in´t Zand, J. M. J., Montanari, E., & Nicastro, L. 2005, ApJ, 623, 314
Price, P. A., et al. 2002, ApJ, 572, L51Price, P. A., et al. 2003, ApJ, 589, 838Rees, M. J., &
Rhoads, J. E. 1999, ApJ, 525, 737Sari, R. & Piran, T. 1995, ApJ, 455, L143Sari, R., Piran, T., & Halpern, J. P. 1999, ApJ, 519, L17Smith, I. A., Tilanus, R. P. J., Tanvir, N., Barnard, V. E., Moriarty-Schieven, G. H., Frail, D. A.,
Wijers, R. A. M. J., Vreeswijk, P., Rol, E., & Kouveliotou, C. 2005, A&A, 439, 987
Stanek, K. Z., et al. 2003, ApJ, 591, L17Starling, R. L. C., Wijers, R. A. M. J., Hughes, M. A., Tanvir, N. R., Vreeswijk, P. M., Rol, E., &
Taylor, G. B., Momjian, E., Pihlstr¨om, Y., Ghosh, T., & Salter, C. 2005, ApJ, 622, 986Tavani, M. 1998, ApJ, 497, L21van Paradijs, J., et al. 1997, Nature, 386, 686Waxman, E. 1997a, ApJ, 485, L5Waxman, E. 1997b, ApJ, 489, L33Wijers, R. A. M. J., Rees, M. J., &
Woosley, S. E. 1993, ApJ, 405, 273Yamazaki, R., Ioka, K., & Nakamura, T. 2004, ApJ, 607, L103Yonetoku, D., Murakami, T., Nakamura, T., Yamazaki, R., Inoue, A. K., & Ioka, K. 2004, ApJ, 609,
Yost, S. A., Harrison, F. A., Sari, R., & Frail, D. A. 2003, ApJ, 597, 459
intradermal test with vitamin K1 might be done, although caution Background: KRAK Study is a Polish multi-centre patch test study is warranted not to sensitize the patient. utilizing the new Polish Baseline Series (introduced in June 2010),which basically consists of European Baseline Series supplemented Conflicts of interest: The authors have declared no conflicts. with two frequent and re
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