A GAMMA-RAY BURST DATABASE OF BATSE SPECTRAL LAG AND INTERNAL LUMINOSITY FUNCTION VALUES

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1 The Astrophysical Journal Supplement Series, 169:62Y74, 2007 March # The American Astronomical Society. All rights reserved. Printed in U.S.A. A A GAMMA-RAY BURST DATABASE OF BATSE SPECTRAL LAG AND INTERNAL LUMINOSITY FUNCTION VALUES Jon Hakkila, Timothy W. Giblin, Kevin C. Young, 1 Stephen P. Fuller, 2 Christopher D. Peters, Chris Nolan, 3 and Sarah M. Sonnett 4 Department of Physics and Astronomy, College of Charleston, Charleston, SC 29424; hakkilaj@cofc.edu and David J. Haglin and Richard J. Roiger Department of Computer and Information Sciences, Minnesota State University, Mankato, MN Received 2006 September 20; accepted 2006 November 28 ABSTRACT We present a database of spectral lags and internal luminosity function ( ILF) measurements for gamma-ray bursts (GRBs) in the BATSE catalog. Measurements were made using 64 ms count rate data and are defined for various combinations of the four broadband BATSE energy channels. We discuss the processes used for measuring lags and ILF characteristics. We discuss the statistical and systematic uncertainties in measuring these attributes, as well as the role of temporal resolution in measuring lags and/or ILFs these are particularly noticeable for GRBs belonging to the Short class. Correlative and clustering properties of the lag and ILF are examined, including the ability of these attributes to predict GRB time history morphologies. We conclude that the ILF and lag have great potential for studying GRB physics when used with other burst attributes. Subject headinggs: gamma rays: bursts methods: data analysis Online material: machine-readable tables 1. INTRODUCTION The relation between observed properties and physical models of gamma-ray bursts (GRBs) has provided new insights into GRB physics. Interesting behaviors are those where burst attributes are clustered (indicative of new classes) or correlated (indicative of related behaviors). Both clustering and correlative behaviors have historically been difficult to identify in bursts because GRBs exhibit such a wide range of individual behaviors, and because the characteristics of an individual burst often evolve significantly. An example of clustering is the delineation between the Short and Long GRB classes. Short GRBs typically have short durations, are faint, and have hard spectra (Kouveliotou et al. 1993; Mukherjee et al. 1998; Nakar & Piran 2002a; Hakkila et al. 2003a; Balázs et al. 2004). They are also characterized by short spectral lags (Norris & Bonnell 2006; Donaghy et al. 2006) and narrow pulses (i.e., FWHM of roughly 65 ms; Norris et al. (1994), although eight Short GRBs in the BATSE catalog and six in the current Swift catalog have been found to have episodes of extended emission (Norris & Bonnell 2006). Application of data mining tools to GRB classification has shown that Short BATSE GRBs generally have T 90 < 1:954 or 1:954 T 90 < 4:672 and HR 3;21 > 3:01 (Hakkila et al. 2003a), where T 90 is the duration in which 90% of the burst emission occurs, and HR 3;21, a measure of the spectral hardness, is the ratio of the fluence in the 100Y 300 kev range to the 20Y100 kev range (Mukherjee et al. 1998). 1 Current address: Department of Physics, University of California at Berkeley, Berkeley, CA Current address: Department of Physics and Astronomy, Clemson University, Clemson, SC Discovery Informatics Program, College of Charleston, Charleston, SC Current address: Institute for Astronomy, University of Hawaii at Manoa, Honolulu, HI Note that the quoted high degree of accuracy is a byproduct of the data mining classification approach used and of the measured values of specific training instances, rather than an indicator of the accuracy to which the subset of Short GRBs can be delineated from Long ones. The contrast between the properties of the high-energy prompt emission of the Short class and the Long class has led to theoretical models involving compact merger scenarios (Goodman 1986; Eichler et al. 1989; Paczynski 1990; Narayan et al. 1992; Mészáros & Rees 1992; Katz & Canel 1996), with the instances of extended emission caused by a wind impinging on a stellar companion (MacFadyen et al. 2005). Examples of correlative behaviors in Long GRBs include spectral lag and peak luminosity (Norris et al. 2000), spectral lag with jet opening angle ( Norris et al. 2000), and burst variability with peak luminosity (Norris et al. 2000; Reichart et al. 2001). Characterizing the wide range of GRB properties for correlative studies is often limited by counting statistics. There are not often meaningful ways to subdivide burst counts into spectral and temporal properties with sufficient signal-to-noise ratio that a meaningful new statistic can be adequately developed and/or explored. It has been known for some time that the morphology of GRB time histories (i.e., light curves) is not stochastic, but that the pulse structure provides insights into GRB physics. For example, there is strong evidence that the majority of GRB pulses result from internal shocks in relativistic outflows; these arguments have been made based on short pulse durations, pulse width evolution, spectral evolution, and short interpulse durations (Daigne & Mochkovitch 1998; Ramirez-Ruiz & Fenimore 2000; Nakar & Piran 2002a, 2002b). However, other explanations such as electromagnetic outflow are also possible; see Lyutikov & Blandford (2003). In addition, a number of bursts exhibit a soft component indicative of external shocks that could be interpreted as onset of afterglow (Connaughton 2002; Giblin et al. 2002). Supportive evidence for a structured arrangement of GRB pulses and pulse widths has recently been verified (Hakkila &

2 BATSE ILF AND LAG DATABASE 63 Giblin 2006) using two GRB attributes: spectral lags and components of the internal luminosity function ( ILF). Spectral lags are the average time by which hard prompt emission leads soft prompt emission; lags are generally obtained from the peak of the cross-correlation function (CCF) between two energy channels ( Band 1997). The ILF is the distribution of luminosity within a GRB (Horack & Hakkila 1997), and is obtained from the flux distribution. Lags and the ILFs have been used to sort GRB morphologies into a continuum of time profiles having similar appearances ( Hakkila & Giblin 2006). This delineation is valuable because lag is related to the intrinsic characteristic of peak luminosity, and the ILF is related to the intrinsic characteristic of the number of pulses. The similarity of time history morphologies thus appears to be primarily intrinsic as opposed to extrinsic. Thus, characteristics related to the relativistic outflow are generally more pronounced than cosmological effects. Because of their usefulness in clustering and correlative studies, a public database of spectral lags and ILF measurements is of great potential use to the astronomical community. We include such a database here, obtained from the Burst And Transient Source Experiment ( BATSE) that was flown on NASA s Compton Gamma-Ray Observatory. BATSE was composed of eight largearea detectors having four broadband energy channels (channel 1 between20and50kev,channel2between50and100kev, channel 3 between 100 and 300 kev, and channel 4 between 300 kevand roughly 2 MeV). These measurements can be used in conjunction with other published BATSE GRB characteristics. The database is also described here, along with some cautionary notes about its use, and some correlative and clustering properties of these attributes with other known GRB characteristics. The lag and ILF data are part of a larger database that is available online along with a suite of data mining tools (the GRB ToolSHED; Haglin et al. 2000, 2005; Hakkila et al. 2003b; Giblin et al. 2004) CATALOG DESCRIPTION We have measured lags and ILF values using the BATSE 64 ms discrimination data. 6 This data type is advantageous because of its four-channel energy bins and high temporal resolution. It has the disadvantage of being a heterogeneous data type made by combining BATSE DISCLA, PREB, and DISCSC data. PREB (preburst) data is 64 ms time resolution data spanning the s before a trigger, while DISCSC is 64 ms time resolution data covering roughly four minutes following the trigger early in the Compton Gamma-Ray Observatory mission (prior to trigger 2099) or 10Y11 minutes following the trigger late in the mission (after trigger 2099). The combination of PREB and DISCSC data generally span a burst s duration, except when a significant precursor is present or when burst emission continues more than 11 minutes past the trigger. Inclusion of the lower time resolution DISCLA data allows the 64 ms burst data to be extended beyond that which can be obtained using DISCSC data alone (Horack & Hakkila 1997). Time intervals undersampled by DISCSC and PREB data have thus been filled in using the continuous 1024 ms time resolution DISCLA data type through a count rate normalization process at NASA s Goddard Space Flight Center. Other GRB characteristics, such as GRB number, flux and fluence data, durations, and spectral hardnesses are not included TABLE 1 Number of Bursts in the BATSE Lag Catalog Lag Energy Channels All Lags Lags of Zero Positive Lags All Combinations Note. Errors are fit to the empirical relation lag nm ¼ 10 A (lag nm ) B (lag is in units of seconds), where N is the number of bursts used to establish the fit for channels n and m. here. These characteristics are part of the BATSE Current Catalog and will eventually be published in the BATSE 5B Catalog Spectral Lag Data The spectral lag is the time delay between hard and soft prompt GRB emission. BATSE s four broadband energy channels can be used to produce six different lag combinations (lag 21,lag 31, lag 32,lag 41,lag 42,andlag 43 ). The CCF is measured for each channel combination using the procedures defined by Band (1997) using the aforementioned 64 ms data. A fit is made to each CCF distribution function so that the peak and corresponding lag can be determined statistically. The CCF is assumed to have a shape fitted by a GRB pulse model (Norris et al. 1996) near its peak; the time interval over which this function is valid is small when the burst is dominated by narrow pulses, and large when it is dominated by broad ones. The time-asymmetric pulse function has more degrees of freedom than a cubic (Norris et al. 2000) and produces an accurate fit even when the CCF is dominated by broad pulses. The fitted CCF range can strongly affect the lag measurement (Wu & Fenimore 2000; Norris et al. 2000), because multiple peaks in the CCF (typically caused by timescales on which pulse structure repeats) introduce a source of contamination. The number of bursts found in the resulting data set is summarized in Table 1. Only the lags that could be measured are included for each BATSE trigger listed in the table. Thus, no measurements at all could be made for some bursts with very low signal-to-noise. GRBs with no 64 ms data are of course excluded. Few lag measurements exist in the 300 kev to 1 MeV range since channel 4 signal is weak in some bursts and nonexistent for many others (NHE bursts; see Pendleton et al. 1997). The lag with the greatest number of represented bursts is lag 32 because channels 2 and 3 have the strongest signals (GRBs usually peak around 300 kev; e.g., Kaneko et al. 2006). Uncertainties are estimated by averaging the lag values obtained from several measurements spanning a range of temporal shifts (typically, 5Y8 trial measurements made over a broad range of CCF values in the vicinity of the CCF peak). The error distribution for each set of lag measurements lagnm (for channels n and m, with both lag nm and lagnm measured in units of seconds) can be fitted by an empirical function lagnm 1s ¼ 10 A lag B nm : ð1þ 1s 5 These tools are found at and 6 Available from 7 The values may be found at catalog/current.

3 64 HAKKILA ET AL. Vol. 169 TABLE 2 Error Coefficients for Lags Lag Energy Channels nm A B N The resulting coefficients are given in Table 2. A small, negative value of the A coefficient indicates a smaller lag uncertainty than does a larger value of A. A small value of the B coefficient indicates that lag uncertainties depend weakly on lag, while larger B values indicate stronger lag dependencies. Since lags from all BATSE energy channel combinations are fitted with positive B values, long lags typically have larger uncertainties than short lags. However, larger uncertainties and a greater dependence on the lag are found when the energy difference between channels is large, such as for lag measurements involving channel four. Some GRBs have CCFs for which only one trial measurement could be made. An error has been assigned to these bursts using the aforementioned empirical relations, and bursts for which uncertainties have been assigned are tagged in the data file. Lag uncertainties for GRBs with a single trial measurement and (lag nm )/(1 s) (0:032) 1/B 10 A/B have been set equal to s. The entire lag database is contained in Table 3. Each record represents the best value obtained for a GRB lag, which is typically determined by the greatest number of measurements obtained by a single operator. Column (1) contains the BATSE trigger number, columns (2) and (3) are the starting and ending times (in seconds) of the interval assumed to contain the burst signal, column (4) is the lag (seconds), column (5) is the lag uncertainty (seconds), column (6) contains the number of trial measurements used to obtain the lag and uncertainty, column (7) indicates the energy channels across which the measurement was made, column (8) is an indicator of the operator who made the measurement (used to search for systematic measurement errors) and column (9) is a note concerning the uncertainty (note of 0 indicates that the uncertainty is taken from the measurements, note of 1 represents that the uncertainty has been obtained using equation (2.1) and Table 3, and note of 2 indicates that a lag near zero was assigned a minimum uncertainty of 32 ms). We demonstrate the best fits for two sample bursts having very different lags; BATSE triggers 829 (Fig. 2) and 3035 (Fig. 3). The time histories of these GRBs are shown in Figure 2a and Figure 3a, respectively, while the corresponding CCFs are shown in Figure 2b and Figure 3b. Trigger 829 is a multipeaked FRED (fast rise exponential decay) burst with a long lag of lag 31 ¼ 2:368 0:001. Trigger 3035 is a complex, spiky burst (Fig. 3a) with a short lag of lag 31 ¼ 2:368 0: Internal Luminosity Function Data The internal luminosity function ( ILF), or (L), is the observed luminosity distribution from a GRB or other transient event measured in counts per second (Horack & Hakkila 1997). The quantity (L)L represents the fraction of time that a GRB s luminosity is found between L and L þ L. As such, the ILF summarizes information about the distribution of luminosity within a burst without explicitly describing the order in which the emission occurred. The detector s signal-to-noise ratio places a lower limit on the effectiveness with which faint luminosities can be sampled, while binning of the detector s integration window limits the temporal resolution of the ILF. The ILF can be calculated from BATSE data for any consecutive combination of the four broadband energy channels, so 10 combinations can be produced easily (Ch1, Ch2, Ch3, Ch4, Ch1+2, Ch2+3, Ch3+4, Ch1+2+3, Ch2+3+4, and Ch ). To obtain accurate ILF measurements, the effects of background must be understood and removed (without doing this, the faint distribution would be dominated by background). The signal-tonoise ratio used in measuring the ILF can be increased by combining energy channels, although some of the ILF s potential value can be lost in this manner because burst temporal characteristics are often energy-dependent Measuring the ILF A description of the method used to calculate our ILF values has been given by Hakkila & Giblin (2006). We expand on this description with the following procedure: 1. A representative background level is obtained (typically just following the burst) so that average Poisson fluctuations can be estimated. Different choices of the background interval typically do not alter the measured ILF properties significantly unless background is chosen from a portion of the time history containing (a) burst emission, (b) emission from some other transient source, (c) poor temporal resolution (rebinned data from TABLE 3 Energy-dependent Lags of BATSE GRBs Trigger Start Time End Time Lag Error Measurements Channels Observer Note Ch21 a Ch31 a Ch32 a Ch41 a Ch42 a Ch43 a Ch21 b Ch31 b Ch32 b 0 Notes. Col. (1) contains the BATSE trigger number, cols. (2) and (3) are the starting and ending times (in seconds) of the interval assumed to contain the burst signal, col. (4) is the lag (seconds), col. (5) is the lag uncertainty (seconds), col. (6) contains the number of trial measurements used to obtain the lag and uncertainty, col. (7) indicates the energy channels across which the measurement was made, col. (8) is an indicator of the operator who made the measurement (used to search for systematic measurement errors), and col. (9) is a note concerning the uncertainty (note of 0 indicates that the uncertainty is taken from the measurements, note of 1 represents that the uncertainty has been obtained using eq. (1) and Table 3, and note of 2 indicates that a lag near zero was assigned a minimum uncertainty of 32 ms). Table 3 is published in its entirety in the electronic edition of the Astrophysical Journal Supplement. A portion is shown here for guidance regarding its form and content.

4 No. 1, 2007 BATSE ILF AND LAG DATABASE 65 DISCLA data), or (d) residual background left from a rapidly changing background. Equivalent time intervals are used in the ILF calculation for all energy channels and energy channel combinations. 2. A linear fit is obtained to model time-dependent background variations in each energy channel, which are then removed. 3. Occasionally, some burst time intervals have poor time resolution (e.g., a small number of GRBs have pulses in the 1024 ms pretrigger DISCLA data, and some GRBs continue to burst once the DISCSC data collection period has expired). Monte Carlo models of Poisson variations are used to artificially create identical temporal resolution in these time intervals (a noisification process), thus providing an estimate of the time history with 64 ms resolution. 4. The ILF distribution function is constructed by binning count rates relative to a defined minimum (e.g., 1, 2, or 3 above the background). Expected Poisson background rates are subtracted from each ILF bin so that only estimated source counts remain. Typically, there are many more ILF bins containing faint flux than there are containing bright flux. Thus, the methodology described here allows us to extend the range of the ILF to flux values less than the 3 cutoff used by Horack & Hakkila (1997) allowing the ILF to be measured for many faint GRBs. 5. The number of bins used in calculating the ILF is initially estimated using an algorithm that allots more bins to long bursts (having many 64 ms bins) and to bright bursts (having a large dynamic flux range). Long, bright bursts are initially allotted the largest number of bins, which is similar to the 40 bins used by Horack & Hakkila (1997). Once the binned data has been collected, an iterative process removes bins with too few counts to be statistically meaningful, then redistributes the ILF values into the remaining bins. The process stops when the remaining bins each contain at least five measurements (a minimum number assumed for Gaussian statistics). Sometimes this condition is not reached, and the number of bins becomes very small. This latter condition occurs when a burst is very faint, very short, or both very faint and very short. 6. The ILF is normalized by the requirement that (L)L ¼ 1. In addition, the peak luminosity L peak corresponding to the peak flux F peak is normalized to a value of unity in the ILF calculation. If the GRB redshift can be measured, then the internal luminosities can be recalibrated to an absolute scale rather than to a relative one. However, information that can be used to characterize the shape of the distribution is still available even without this calibration. 7. Errors ( i (L)) are obtained for the luminosity in each of the i bins using propagation of error and standard Poisson statistics: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i (L) ¼ N 2 back;i N 2 i ; ð2þ where N i is number of counts in bin i and N back;i indicates the estimated number of counts in the bin resulting from Poisson variations in the background. The approach listed here expands on the methodology used by Horack & Hakkila (1997), who calculated the ILF specifically using energy channels 2+3 and a minimum threshold of 3 above background. Their analysis avoided using fluxes that were too close to the background because of perceived uncertainty in deconvolving background from ILF signal. The updated technique described here statistically filters out the background and allows us to trace the ILF structure closer to it. In addition, the original choice of energy channels 2+3 provided a strong signalto-noise ratio and limited the ILF to two energy channels that have relatively similar temporal characteristics. The generic coding procedure that we implemented allows the ILF calculations to be extended to a large number of energy channel combinations and limiting thresholds at no additional compromise Fitting the ILF We have parameterized the ILF in a way that allows us to summarize its properties as simple attributes. The process is generic to the wide variety of energy channel and threshold combinations described above. Horack & Hakkila (1997) fitted the ILF with a quasi-power-law function of the form (L) ¼ CL ; with normalization constant C and power-law index. The values of are generally negative, since most of the emission is weighted toward low luminosities. We initially calibrated our ILF calculations using this fitting function, and compared our results to Horack & Hakkila (1997) in order to verify other aspects of the procedure. A systematic bias was noticed: GRBs with large values of (e.g., 0) were relatively insensitive to the choice of the low-luminosity cutoff L min (corresponding to a minimum flux, F min,at1,2,or3 above background), whereas GRBs with small -values ( T0) changed noticeably between 1 and higher cutoff luminosities (Stallworth et al. 2003). As a result, the fitting function was modified to have the form (L) ¼ CL 10 ½log (L)Š 2 : We refer to the additional fitting parameter as the curvature index, and note that introducing it solves the aforementioned problem by recognizing that GRB ILFs with small -values also tend to change slope at fainter luminosities. Introduction of this parameter also recognized that some GRBs have inherently different ILF values than other GRBs. Nine parameters are obtained from fitting the ILF with the nonlinear least-squared routine MPFIT. Three of these (the ILF power-law index, the curvature index, and the fitting constant C ) describe the functional form of the ILF. The internal luminosity range R ¼ F peak /F min ¼ L peak /L min indicates the range of fluxes between F min and F peak that could be fitted; it is a quantity that has a meaning similar to the 64 ms peak flux. The formal fitting errors in the coefficients are given by C,, and. The overall goodness-of-fit is given by 2, while indicates the number of degrees of freedom used in the fit. The model parameters and are found to adequately describe GRB luminosity structure. The power-law index indicates the amount of lower-luminosity emission relative to the peak luminosity. A large -value ( 0) indicates that the distribution function shows only a slight luminosity decline between the peak and the threshold. In other words, the burst has a large amount of lower-luminosity emission relative to the peak emission. Singlepulsed FREDs (fast rise exponential decay bursts) are examples of bursts that typically have large -values. Conversely, a small ( T0) indicates that the distribution function drops off rapidly between the peak luminosity and the threshold; this occurs for a burst that is depleted in low-luminosity emission. The curvature index indicates how the low-intensity emission deviates from its expected variations near the peak (characterized by ). A near-zero -value indicates a GRB for which the emission near threshold is as expected from the emission near the peak. A small -value (T0) describes a GRB for which the faint end of the distribution function is deficient from what would be expected ð3þ ð4þ

5 66 HAKKILA ET AL. Vol. 169 TABLE 4 Distribution of the 2124 Bursts in the BATSE ILF Catalog with ILF Measurements Energy Channels Cutoff ( Above Background) Quality 0 Quality 1 Quality Total... All Combinations from the bright end of the distribution function. In general, and are orthogonal parameters that are also highly correlated, so that only one parameter (usually ) other than the normalization C is sufficient for summarizing the ILF characteristics. We have made ILF fits for all bursts in the current BATSE catalog that have 64 ms data. 8 For each or these GRBs, all 10 of the prescribed energy channel combinations were attempted, using all three predefined threshold levels (1, 2, and 3 ). A quality factor, q, has been introduced to indicate measurements that have large uncertainties due to short duration and/or low signal-tonoise ratios. A quality factor of q ¼ 0 indicates that too few 64 ms bins were available to perform a reliable fit. In other words, the 5 or fewer degrees of freedom available for the model fit produced essentially meaningless data, and ILF fit parameters obtained when q ¼ 0 should be ignored. A quality factor of q ¼ 1 indicates that 6Y10 degrees of freedom were available for the model fit. The model fit in this case is suspect because the formal 2 generally underestimates the actual uncertainty in the fit. A quality factor of q ¼ 2 indicates that the model fit used more than 10 degrees of freedom. The 2 is an additional indicator of the quality of the fit in these cases; a large value of 2 indicates that the GRB s ILF has more structure than can be easily represented by the simple model The ILF Database The results of the ILF measurements are summarized in Table 4. A total of ILF measurements were obtained with 8 See quality factors of q ¼ 2 and another 7414 measurements were obtained with quality factors of q ¼ 1. The largest number of high-quality measurements were obtained when the signal was traced as close to the background as possible ( ¼ 1) and/or when the signal-to-noise ratio was large (e.g., for energy channel combinations 1 þ 2 þ 3, 2 þ 3 þ 4, and 1 þ 2 þ 3 þ 4), whereas the smallest number of high-quality measurements were obtained when only a small range of signal was available ( ¼ 3) and/or when the signal-to-noise ratio was small (e.g., energy channel 4). Some energy channel combinations produced reliable ILF fits when sampled to the 1 threshold but not to the 2 or 3 thresholds. The overall database is presented in Table 5 and Table 6. ILF measurements were successfully processed for 2124 GRBs. Table 5 contains information concerning the background and foreground time intervals used in the ILF calculations for all GRBs. Column (1) contains the BATSE Trigger ID, while columns (2) and (3) contain the background start and end times (BGS and BGE) and columns (3) and (4) contain the burst (foreground) start and end times (FGS and FGE). Table 6 contains the 30 records of measured ILF values for all GRBs. In these records, column (1) is the BATSE Trigger ID, and column (2) identifies the number of sigma above background at which the cutoff threshold is set (1, 2, or 3 ). Column (3) lists the energy channel combination from which the flux counts data are being taken for the ILF measurement as a three-letter code ( 1, 2, 3, 4, 1+2, 2+3, 3+4, 123, 234, or all ). Column (4) is the ILF normalization constant C, with its formal error of C listed in column (5). Column (6) is the ILF power-law index, with its formal error of listed in column (7).

6 No. 1, 2007 BATSE ILF AND LAG DATABASE 67 TABLE 5 Burst Time Intervals Used to Calculate the BATSE Internal Luminosity Function Measurements Trigger BGS BGE FGS FGE Notes. Col. (1) contains the BATSE trigger ID, cols. (2) and (3) contain the background start and end times (BGS and BGE), and cols. (4) and (5) contain the burst (foreground) start and end times (FGS and FGE). Table 5 is published in its entirety in the electronic edition of the Astrophysical Journal Supplement. A portion is shown here for guidance regarding its form and content. Column (8) is the ILF curvature index, with its formal error of listed in column (9). Column (10) indicates the formal 2,with the number of degrees of freedom listed in column (11). Column (12) indicates the internal luminosity range R. Column(13) identifies the quality factor q of the measurement. We have examined our analysis technique to determine whether or not additional errors occur as a result of the human operator s participation in the measurement process. An external error has been estimated by running ILF fitting models on a specific burst subset by several human operators. Our calibration sample consists of five bursts independently analyzed by six human operators ( BATSE triggers 249, 973, 1039, 1533, and 1700). The difference between the independently calculated external errors (E ext ) and internal errors (E int ) in the power-law and curvature indices is an offset error (E oaset ¼ E ext E int ) that is not identified in the formal measurement of these parameters. This additional source of error is attributed to the choice of background and burst intervals selected by the human operator, as well as any Monte Carlo noisification of some 1024 ms background intervals. The results of our analysis indicate that ILF power-law index and curvature errors are roughly twice as large as the formally quoted internal errors for GRBs with reasonable signal-to-noise that have large ILF power-law indices. A larger scatter is obtained for faint GRBs, and GRBs with very small power-law indices are more susceptible to the choice of the time interval containing the burst signal Characterizing the ILF Fit Parameters The fit parameters and are found to be highly-correlated. Figure 1 demonstrates this correlation for 901 high-quality (q ¼ 2) GRBs having their ILFs measured in channels 2 þ 3 with the TABLE 6 Internal Luminosity Function Measurements of BATSE GRBs Trigger n sig Channel C C 2 / R q All All All Notes. The 30 records for each GRB have the following formats: col. (1) is the BATSE Trigger ID, col. (2) is the cutoff threshold above background (1, 2, or 3 ), and col. (3) lists the three-letter energy channel combination nm. Cols. (4) and (5) are the ILF normalization constant C and its uncertainty C, cols. (6) and (7) are the ILF power-law index and its uncertainty, and cols. (8) and (9) are the ILF curvature index and its uncertainty. Col. (10) is the formal 2, with the number of degrees of freedom in col. (11). Col. (12) is the internal luminosity range R and col. (13) identifies the measurement s quality factor q. Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal Supplement. A portion is shown here for guidance regarding its form and content.

7 68 HAKKILA ET AL. Vol. 169 TABLE 7 Correlation between Curvature Coefficient and Power-Law Index, Fitted by ¼ A þ B Energy Channels Number of GRBs Intercept A Slope B :4062 0:0111 1:1838 0: :2721 0:0083 1:1216 0: :2881 0:0116 1:0943 0: :2464 0:1569 1:7585 0: :3802 0:0076 1:1604 0: :2496 0:0110 1:1010 0: :2523 0:0126 1:0855 0: :0728 0:0089 1:1029 0: :2622 0:0009 1:1038 0: :3297 0:0103 1:1268 0:0004 Fig. 1. ILF curvature indices vs. ILF power-law indices for bursts measured in channels 2+3 with thresholds set at 2 above background and having quality factors of 2. There is a strong correlation between the two attributes. Short bursts are denoted as diamonds, while Long bursts are indicated by asterisks. flux threshold set 1 above background. A Spearman rank order correlation test finds this the probability that this correlation is random to be only p ¼ 4:5 ; A simple linear relation between the two parameters is ¼ A þ B; where A ¼ 1:2496 0:0110 and B ¼ 1:1010 0:0005 are the best-fit coefficients. This correlation indicates that GRBs with large power-law indices ( 0) are best fitted with a simple power-law and no curvature index. The ILFs of these bursts are described by a simple functional form over their observed luminosity range from peak luminosity to threshold luminosity. However, GRBs with small power-law indices ( T0) have ILFs with pronounced curvatures, such that the slope of the distribution near the peak luminosity indicates a depletion of highluminosity emission relative to moderate-luminosity emission, while the slope of the distribution near the threshold luminosity indicates a depletion of low-luminosity emission relative to moderate-luminosity emission. Thus, GRBs with small powerlaw indices produce a large amount of their emission from a relatively narrow range of luminosities. Similarly strong correlations are found for ILF fits obtained using other energy channel combinations; the coefficients obtained from these correlations are shown in Table 7. Most of the energy channel combinations produce similar coefficients, with only channel 4 being noticeably different. This means that, although both and are needed to characterize the ILF, only one is needed as an indicator of the ILF since it implies the value of the other. We demonstrate the best fits for two sample bursts having very different ILF values; BATSE triggers 829 (Fig. 2) and 3035 (Fig. 3). Both bursts are measured using channels 2+3 with a cutoff threshold 1 above background. Both are high-quality measurements with more than 30 degrees of freedom, good fits (1 2 < 2), and large internal luminosity ranges (R > 50). Trigger 829 is a multipeaked FRED burst (Fig. 2a) that produces large ILF indices ( ¼ 0:35 0:33, ¼ 0:21 0:25; Fig. 2c) indicating that there is a moderate amount of high-luminosity emission relative to low-luminosity emission. Trigger 3035 is a complex, spiky burst (Fig. 3a) that has small ILF indices ( ¼ 4:20 0:17, ¼ 1:92 0:11; Fig. 3c) indicating a large amount of moderate-luminosity emission relative to high- and low-luminosity emission. ð5þ Notes. These results have been obtained for GRBs having high-quality ILF measurements (q ¼ 2) with a 64 ms flux cutoff at 1 above threshold. The GRBs are further chosen so that their GRB class (e.g., Long or Short) can be identified via T 90 and HR 3; DISCUSSION 3.1. Clustering Properties of the GRB Lag and ILF Databases Characteristics of Long GRBs It has been shown (Hakkila & Giblin 2006) that the spectral lag and the ILF power-law index are morphology indicators for GRB time histories; the types of morphologies that have been identified in this fashion are shown in Figure 4. Long lags typically delineate GRBs with fewer, broader pulses than those with short lags. GRBs with large ILF -values typically have only one or two pulses. This is contrasted with short-lag, small -valued GRBs characterized by many narrow pulses, and long-lag, small -valued GRBs characterized by a few broad pulses. The ordering of GRB time history morphologies by lag and ILF demonstrates that these attributes primarily measure intrinsic characteristics (as discussed by Hakkila & Giblin 2006). Cosmological time dilation is apparently less important than the intrinsic lag caused by jet structure and kinematics. Lag is an intrinsic attribute that anticorrelates with burst peak luminosity ( long-lag bursts are less luminous than short-lag bursts in the comoving frame; Norris et al. 2000); this relationship indicates that short-lag bursts are luminous and are typically found at large redshift. If cosmological time dilation were of primary importance, then it would tend to cause the most distant, most luminous GRBs to have the broadest pulses and the longest lags. It would also make intermediate- and long-lag bursts into stretchedout versions of short-lag bursts with similar ILF values. Instead, long-lag bursts typically have fewer pulses than short-lag bursts, indicating that the two burst types are inherently different. In addition, the rather small overlap in lag between GRBs of different morphological types indicates that most bursts with a specific morphological type (e.g., narrow-pulsed bursts with complex time profiles) have lags that delineate them from bursts of a different morphology (e.g., intermediate-pulse width bursts with complex time profiles). If cosmological time dilation were as important as the burst s intrinsic characteristics, then the overlap in lag between the two morphological types should smear out this delineation. Similarly, the relationship between the number of pulses and the ILF suggests that this attribute is also primarily intrinsic, and that viewing angle is probably less important than jet structure in defining the observed number of pulses. It has also been shown that some GRB time history morphologies are related to specific types of energy production and outflow. Long GRBs with simple time histories (single- or

8 No. 1, 2007 BATSE ILF AND LAG DATABASE 69 Fig. 2a Fig. 3a Fig. 2b Fig. 3b Fig. 2c Fig. Fig. 2aFig. 2. Time 2bFig. history 2c (a) forchannels1(lightest) to4(darkest), CCF for channels 1 and 3 (b), and ILF (channel 2+3, 2 measurement; c) forbatse Trigger 829. Fig. 3c Fig. 3aFig. 3. 3bFig. Time history 3c (a) for channels 1 (lightest) to4(darkest), CCF for channels 1 and 3 (b) and ILF (channel 2+3, 2 measurement; c) for BATSE Trigger double-pulsed bursts) are more likely than complex bursts to be associated with type Ibc supernovae ( Bosnjak et al. 2006) and/or with low-luminosity afterglows ( Liang & Zhang 2006; Nardini et al. 2006). Furthermore, long-lag bursts typically have lower Lorentz factors and broader jet opening angles than short-lag bursts ( Norris 2002). Short-lag, long, complex bursts are expected to have canonical afterglows and are unlikely to be associated with supernovae ( Hakkila & Giblin 2006). This expected morphology is relevant to the classification of Swift GRB , a nearby burst having all of these characteristics ( Della Valle et al. 2006; Gehrels et al. 2006; Cobb et al. 2006), and for which a new classification scheme has been suggested because no supernova accompanied the burst. The observed characteristics of this burst are in agreement with its time history morphology ( Hakkila & Giblin 2006), indicating that a new classification scheme is not needed, and suggesting that a supernova was not observed because

9 70 HAKKILA ET AL. Vol. 169 Fig. 4. ILF power law index vs. 31 lag for 901 BATSE GRBs. Regions are identified in which GRBs are found to have similar time history morphologies. the large Lorentz factor and narrow jet opening angle expected for this type of GRB is not conducive to supernova formation, rather than because a supernova fell below the detection limits. We have attempted to use pattern recognition algorithms to verify whether or not the regions containing GRBs having similar time history morphologies ( Hakkila & Giblin 2006) actually represent disparate classes of Long burst. In other words, we wanted to determine if GRBs cluster in ILF versus lag 31 space. Two unsupervised clusterers, the tree structure algorithm ESX ( Roiger et al. 1999) and a Kohonen neural network (Kohonen 1982), were applied to the, logt 90, and lag 31 data. An unsupervised algorithm is a data mining program that attempts to find clumps or clusters within a data set that might be indicative of class structure. Both clusterers ignored the lag attribute in the data set, and both delineated the data on the basis of ILF power-law index and log T 90. However, their results were neither consistent with one another nor could they reproduce groups corresponding to the time history regions identified in Figure 8 below. A back propagation neural network ( Knight 1990) was then applied in an attempt to reproduce the morphological types shown in Figure 8. This technique trains itself on data that are assumed to be representative of certain classes, then develops rules for identifying unknowns in this class. However, the back propagation neural network was unable to build an accurate model reproducing the specified regions. This might indicate that the regions do not represent clusters within the data. It more likely indicates that duration, lag, and the ILF are inadequate in describing characteristics of time histories that the human eye sees as morphologically similar (e.g., see the figures in Hakkila & Giblin 2006) Characteristics of Short GRBs The ILFs and lags of the Short class of GRBs (Kouveliotou et al. 1993; Mukherjee et al. 1998; Hakkila et al. 2003a; Balázs et al. 2004) deserve special attention (note: we assume that the intermediate class of GRBs is really only a subset of Long GRBs and occurs as a result of selection effects; Hakkila et al. 2003a). On the 64 ms timescale, Short GRBs typically exhibit only a few narrow pulses. Thus, their ILF properties are similar to those of short FREDs and other simple, narrow-pulsed GRBs: they exhibit large ILF power-law indices ( 0). Unlike FREDs, very few of them have nonzero lags (Norris & Bonnell 2006; Hakkila & Giblin 2006). Thus, in the versus lag 31 parameter space, Short GRBs occupy a region also containing some short-lag FREDs and a few quiescent GRBs (discussed in x 3.3); this is demonstrated in Figure 8. Few Short bursts are visible in the plot because most have measured lags consistent with a mean of hlag 31 i 0 (within the measurement error); most have lags too small to be visible on the log (lag 31 ) plot, and the ones present appear to represent the statistical tail of the distribution. Overall, it appears that the ILF and lag are able to discern the class of Short GRBs. The placement of Short GRBs in this diagram is likely due in part to an instrumental bias resulting from the limited resolution of the 64 ms data. Temporal variations shorter than 64 ms are commonly found in Short GRBs (Norris 1994; Norris et al. 1996), and these variations are averaged out within individual 64 ms bins (Lee & Petrosian 1996). This has the effect of diluting the ILF variations and internal luminosity range, and increasing the ILF to larger values. Thus, the ILF power-law indices of Short GRBs are generally larger than they would be if higher time resolution data were available. Short GRBs have lags that are too short to be measured with the 64 ms time resolution available, and thus almost always are measured to be zero seconds. When TTE data are used to measure the ILF values, some Short GRBs are found to have small, positive lags (Norris & Bonnell 2006). Thus, the ILF and lag properties of Short GRBs as obtained from 64 ms data are unreliable and offer limited usefulness Correlative Properties of the GRB Lag and ILF Databases Horack & Hakkila (1997) demonstrated that the ILF correlates and/or anticorrelates with a variety of basic GRB properties,

10 No. 1, 2007 BATSE ILF AND LAG DATABASE 71 Fig. 5. Internal luminosity range R vs. ILF power-law index for Short (diamonds) and Long (asterisks) bursts measured in channels 2 þ 3 with thresholds set at 1 above background and having quality factors of q ¼ 2. including T 90, hardness ratios, and fluence (time integrated flux) from a sample of 50 bright GRBs. Figure 5 is a plot of the internal luminosity range R versus the ILF power-law index for a large burst sample. This figure demonstrates that faint GRBs are morphologically different than bright GRBs, because faint GRBs tend to have smaller -values than bright GRBs. GRBs with small -values are associated either with complex bursts having many short pulses or with Long Smooth bursts ( Hakkila & Giblin 2006). Figure 6 is a plot of the log (T 90 ) duration versus ILF powerlaw index for 891 GRBs. We note that the durations of the Short GRBs all have similar values of near 1:5. A Spearman rank order correlation test identifies the probability that the anticorrelation between and log (T 90 ) is random to be only p ¼ 4:7 ; A linear fit to the relationship using singular value decomposition results in ¼ 0:566 2:061log (T 90 ). However, a linear fit does not completely capture the large spread in -values observed, especially for T 90 > 10 s. The reasons for this are discussed in x 3.3. Figure 7 is a plot of ILF power-law index versus number of pulses N pulses for 278 GRBs. An anticorrelation is observed, and verified with a Spearman rank order correlation test finding a probability that this correlation is random to be only p ¼ 8:1 ; A linear fit to the relationship of the form results in the best-fit relationship log N pulses ¼ 1:027 1:253. Thus, a small ILF power-law index is an indicator for a large number of pulses. The plot again has a very large spread in, which is addressed in x 3.3. The anticorrelations demonstrated in Figures 6 and 7 imply that there should be a correlation between the number of pulses in a GRB and its duration. Figure 8 is a plot of log (T 90 ) duration vs. N pulses for 278 GRBs. A Spearman rank order correlation test finds the probability that this correlation is random to be only p ¼ 2:3 ; ; this is similar to a result obtained independently by Quilligan et al. (2002). A linear fit to the relationship of the form results in the best-fit relationship log (T 90 ) ¼1:120 þ 0:460 log N pulses, again with a large spread in associated -values. The explanation for the correlation is that longer GRBs have more pulses, and more interpulse durations, than shorter GRBs. This also demonstrates that the ILF is sensitive to pulse structure. Table 8 indicates correlations between (based on channel 2 þ 3) and other key GRB attributes of peak flux, duration, fluence, and hardness. The strong correlation of with peak flux Fig. 6. ILF power-law index vs. log T 90 (s) for bursts measured in channels 2 þ 3 with thresholds set at 1 above background and having quality factors of q ¼ 2. Short bursts are identified by diamonds. There is a strong anticorrelation of with T 90, such that a large -value generally indicates a shorter burst, while a small -value indicates a longer burst. The solid line represents the best fit to the data (described in the text). is similar to the correlation between and R, and indicates that faint bursts have different morphological structures than bright bursts (see also Fig. 5). The strong correlation between and spectral hardness is another indicator that burst morphology changes as a function of peak flux, since faint Long GRBs are typically softer than bright Long GRBs (Mallozzi et al. 1995). The moderately strong correlation between and fluence is a mixture of the strong correlation between and peak flux and the strong anticorrelation between and T 90, since fluence contains some overlap with both of these properties Pulse Morphologies of Long GRBs The correlations between, T 90, and N pulses shown in Figures 6, 7, and 8 all exhibit large data spreads, suggesting that some additional parameter is present that prevents the bursts from following a tight-knit relationship. Figure 4 demonstrates that, for long-lag bursts, pulse shape is clearly a contributor to this spread, because small -values can be produced by a burst composed of long-lag, cuspless pulses or by a burst made up of a large number Fig. 7. ILF power-law index vs. Number of pulses N pulses for Long bursts measured in channels 2 þ 3 with thresholds set at 1 above background and having quality factors of 2. There is a strong anticorrelation of with N pulses,such that a small -value generally indicates a large number of pulses, while a large -value indicates a small number of pulses.