Acta Polytechnica https://doi.org/10.14311/AP.2025.65.0092 Acta Polytechnica 65(1):92–100, 2025 © 2025 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague CORRELATION BETWEEN X-RAY AND GAMMA DATA OF SWIFT MEASUREMENTS Istvan I. Racza,∗, Lajos G. Balazsb,c, Istvan Horvatha, Sandor Pintera,c a University of Public Service, Department of Natural Sciences, 2 Ludovika tér, H-1083 Budapest, Hungary b HUN-REN Research Centre for Astronomy and Earth Sciences, Konkoly Thege Miklós Astronomical Institute, Konkoly-Thege Miklós út 15-17, H-1121 Budapest, Hungary c Eötvös Loránd University, Faculty of Science, Institute of Physics and Astronomy, Department of Astronomy, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary ∗ corresponding author: racz.istvan@uni-nke.hu Abstract. Several studies over the last two decades have used canonical correlation analysis (CCA) to study the relationships between main γ-ray (e.g. fluence, peak flux, and duration) and main X-ray (flux, decay and spectral index, and hydrogen column density) data from gamma-ray bursts (GRBs). In this paper, we revisit this approach using a much larger dataset to identify potential new insights into these relationships. We used CCA to investigate the interrelationship of the aforementioned gamma-ray and X-ray parameters. Using the derived canonical variables, we calculated their correlations (canonical loadings) with the original data. Consistently with previous research, the analysis revealed that gamma-ray fluence and X-ray flux have the strongest correlation, while the X-ray decay index and spectral index have a lower contribution. Interestingly, our analysis of a much larger dataset reveals that the HI column density makes a significant contribution to the overall correlation. This finding, in the context of the collapsar model for long GRBs, could be interpreted as an indication that the progenitor star ejected an HI envelope during the GRB. Keywords: Gamma-ray burst, spectroscopic, statistical, catalogs. 1. Introduction Since the Big Bang, the gamma-ray bursts (GRBs) have been the most intense and brightest events in the Universe [1, 2]. GRBs, are usually short, powerful bursts of radiation that can last anywhere from a few milliseconds to several minutes. They were first iden- tified in the late 1960s [3]. These bursts are important probes of the early Universe because they come from far-off galaxies, frequently billions of light years away. The main characteristic of gamma-ray bursts is their enormous energy output; some bursts can release more energy in a matter of seconds than the Sun will in a bil- lion years. According to how long they last, GRBs are typically divided into two categories: short GRBs, which last less than two seconds, and long GRBs, which can last anywhere from two to several minutes. Short GRBs are thought to result from neutron star mergers [4], while long GRBs are thought to be the result of massive stars collapsing into black holes (the collapsar model) [5, 6]. Evidence for the first case can be found in the connection with gravitational waves, which have already been observed several times [7–11]. Apart from the two primary models, it was observed in the 1990s and early 2000s that there are other va- rieties of GRBs [12, 13], which have medium lengths of a few seconds and spectral hardnesses that differ from the two mentioned above [14–16]. Although the physical composition of this intermediate group is still unknown, it appears that the intermediate GRBs and X-ray flash events are related [17–20]. Apart from the initial gamma-ray emission, Gamma-Ray Bursts (GRBs) often emit an afterglow that radiates at differ- ent wavelengths, such as X-rays, ultraviolet, optical, and radio waves. This afterglow can yield impor- tant insights into the surroundings and mechanisms of these explosive events [21, 22]. 2. Materials and methods 2.1. Data The Neil Gehrels Swift Observatory (formerly Swift telescope) is a multi-wavelength observatory that fo- cuses on studying gamma-ray burst (GRB) science. It uses three instruments to observe GRBs and after- glows in gamma-ray, X-ray, ultraviolet, and optical wavebands. The main objectives are to determine the origin, classify bursts, and study their evolution and interaction with the environment. Swift discovers around 100 bursts per year and provides accurate posi- tion estimates, multi-wavelength lightcurves, gamma- ray spectrum, and X-ray spectra. Launched in 2004 as part of NASA’s MIDEX program, Swift is the most comprehensive study of GRB afterglows to date. The Burst Alert Telescope (BAT) is designed to pro- vide key GRB triggers and a draft location with an er- ror of about 4-arcmin. The imaging energy range is 15– 150 keV with a non-coded response of up to 500 keV. 92 https://doi.org/10.14311/AP.2025.65.0092 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 65 no. 1/2025 Correlation between X-ray and gamma data of Swift measurements Swift’s X-Ray Telescope (XRT) is designed to mea- sure the GRB and afterglow fluxes, spectra, and lightcurves over a broad dynamic range, encompassing flux ranges greater than seven orders of magnitude. Within 10 seconds of target acquisition for a typical GRB, the XRT can pinpoint GRBs to within 5-arcsec. It can also study the X-ray counterparts of GRBs starting 20–70 seconds after the burst discovery and continuing for days to weeks [23, 24]. The telescope’s energy resolution is around 260 eV and its energy range is 0.2–10 keV, while it is often used for the 0.3–10.0 keV region. We can see an example γ and X-ray lightcurve plot on Figure 1. Swift BAT was triggered by more than 1 600 GRBs up to the end of 2023 from which 1 357 were detected by the XRT instrument simultaneously. For our study, we used several observed and calculated data from both the BAT and XRT instruments: T90 duration, fluence, 1 sec peak flux from the gamma detectors and 11 hours flux, 24 hours flux, decay index, spec- tral index, and X HI column density from the X-ray instrument. The BAT instrument gives critical data on the GRBs including the T90 duration, which indicates the period when 90 % of the burst’s total background- subtracted counts are identified. We also used the fluence, representing the total energy received in ergs per square centimetre and the 1-second peak pho- ton flux, indicating the highest photon count rate in a single second during the burst. In combination with the BAT data, the XRT database provides information about GRBs’ after- glow phase. Key data points include 11- and 24-hour flux data, which follow the GRB’s X-ray brightness after the first burst. We also used the initial temporal index and the spectral index, given by the XRT to characterise the afterglow decay rate and X-ray energy distribution, respectively. Furthermore, the intrinsic HI column density calculation provides an estimate of how much interstellar hydrogen the X-rays have gone through in the vicinity of the burst, revealing information about the environment around the GRB. 2.2. Mathematical summary Canonical correlation assumes we have two sets of variables: X and Y . The first set, X, con- tains xi = {x1, x2, . . . , xm} and Y , the second one, yi = {y1, y2, . . . , yr} variables. We make n observa- tions for each variable. Using the linear combination of the X variables we develop: U = m∑ i=1 ai · xi, (1) and using that of Y : V = r∑ i=1 bi · yi, (2) 10 0.01 0.1 1 10 100 1000 10 10 10 10 10 10 10 10 10 O b se rv e d f lu x d e n s ity ( J y) Time since BAT trigger (s) BAT−XRT data for GRB 080129 −9 −8 −7 −6 −5 −4 −3 −3 3 5 Figure 1. Swift observation of gamma and X-ray emission (lightcurve) from the GRB 080129. Black/red markers show gamma/X-ray flux [25]. variables and ask: how can be the a and b set of co- efficients selected that the corr(U, V ), the correlation between U and V variables, obtained above, has the maximum value. For more details, see [26–28]. To maximise the correlation between U and V , the coefficients a = {a1, a2, . . . , ak} and b = {b1, b2, . . . , bl} must meet the following criteria:[ −λRxx Rxy Rxy −λRyy ] [ a b ] = 0, (3) where Rxx is the correlation matrix between the x variables, Ryy is the correlation matrix between the y variables, and Rxy is the x-y cross-correlation matrix. If the determinant is zero, then this equation has a non-trivial solution (a and b are not zero): det [ −λRxx Rxy Rxy −λRyy ] = 0. (4) This determinant equation gives a polynomial equa- tion for λ2, with min(k, l) solutions. The square root of each solution, λ, is known as the canonical corre- lation coefficient. Once λ is known, the associated a and b coefficients can be calculated, defining a pair of canonical variables U and V , also known as canonical factors. We may readily comprehend the canonical factors by calculating the canonical factor structure matrix. We take the largest correlation and the corresponding (U, V ) pair and calculate their correlation with the input variables. The matrix produced in this manner contains information on the contribution of the input variables to the calculated canonical ones. We can con- tinue similarly with the other canonical factors. Based on the canonical factor structure, we can calculate the 93 I. I. Racz, L. G. Balazs, I. Horvath, S. Pinter Acta Polytechnica proportion of input variable variances explained by the computed canonical variables. The proportion of variance of variables defining U explained by V , also known as redundancy of the X set of variables with regard to V , and vice versa. The generated canonical correlations should be checked for substantial departures from randomness. For this, we use Wilk’s lambda parameter counting approach [29]. This procedure leads to a χ2 distribu- tion test, which can be used to quickly determine the significance of the obtained result. The null hypothe- sis we employ is that the canonical variables X and Y are unconnected, or uncorrelated. The approach effectively applies a significance test to the collection of variables X and Y . 3. Results As written above, we examined 1 357 GRBs that had BAT and XRT observations. From this dataset, how- ever, we could only use those where all the parameters we are examining have been measured. Moreover, we examined the values of the 8 variables and about 200 data points seemed incorrect (with 3σ confidence level). These values were too large or small (likely outlier). For this, we used the box-plot outlier search procedure. Finally, we have 930 points of observation left. It should be noted that the logarithm of most parameters (duration, fluence, peak flux, N(HI), X-ray flux) should be used in the procedure, as this is the only way to ensure that the correlation is derived from the bulk of the data, as it brings the data distribution closer to normal. After the data of the variables were cleaned, the remaining variables were separated into two sets and we have determined the number of dimensions (canon- ical variables) that are significant in explaining the association between the 2 sets of variables (γ and X-ray data). Then, we were able compute the correlation matrix within and between the two datasets and visualised the variables in X and Y variables to see how they relate to each other. These cross-correlation plots are shown in Figure 2. The figure shows the correlations between the different parameters, as well as the signif- icance of these correlations with asterisks. The X-ray fluxes show the strongest correlation between each other, which is completely obvious. However, a weak but highly significant correlation can also be seen between the X-ray 11 h flux and the gamma T90 pa- rameters. A similar correlation with duration can be seen with the intrinsic hydrogen column density. Another observable fact is that there is a moderately strong correlation between gamma fluence and X- ray flux. This pairwise plots clearly showed that for both X and Y matrices, there is some visible corre- lation between variables. In this situation, canonical correlation analysis is ideal for exploring the overall relationship between the two sets. In the next step, we calculated the canonical corre- lation coefficients for the two groups as above. The variable U was calculated from the BAT data, while the variable V was derived from the X-ray data. Next, we examined the relationship between these canonical variables and compared them with previous results. In our analysis, we evaluated the relationships be- tween canonical variables to examine how gamma-ray bursts’ (GRBs) gamma-ray and X-ray properties inter- act. The canonical correlation analysis revealed strong associations, with Wilks’ Lambda values providing in- sight into the significance of these associations. From our Wilks’ Lambda analysis, for the full dataset, the test for the first three canonical correla- tions gave a Lambda of 0.527 (F = 44.22, p < 10−10) from the first to third canonical correlation, indicat- ing a strong association between the GRB gamma and X-ray variables across multiple dimensions. The second-to-third canonical test yielded a Lambda of 0.960 (F = 4.75, p < 0.001), showing that even as we move to higher canonical dimensions, a notable relationship persists between the variable sets, albeit with a slightly reduced significance. Finally, the third canonical test gave a Lambda of 0.992 (F = 2.57, p = 0.053), suggesting a weak, yet non-trivial link between the variable sets in these later dimensions. 4. Discussion The investigation of the canonical variables produced from the canonical correlation analysis sheds light on the link between gamma-ray bursts’ optical and X-ray features. Tables 1 and 2 highlight the important find- ings from the BAT and XRT datasets. The correlation coefficients between each pair of canonical variables U and V help us to understand the relationships be- tween the two sets of variables. It is vital, to again, notice that the canonical variables U are the gamma, whereas the V coefficients are derived from the X-ray data. Our results support the conclusion that while the first canonical dimension (U1) is strongly associated with the main GRB properties, such as T90, fluence, and peak flux, suggesting a primary linkage between these gamma-ray properties and the X-ray afterglow’s evolution, subsequent canonical variables (U2, U3) re- veal increasingly subtle relationships, capturing more nuanced aspects of the GRB dynamics and potentially different phases of the bursts. This graded strength of association through successive canonical dimensions reflects the complexity of the GRB processes, and the Lambda values underscore the decreasing influence of higher canonical variables on the explaining variance in the data. According to the Table 2, the first canonical vari- able (U1) has a substantial negative correlation with T90 (r = −0.611), fluence (r = −0.946), and peak flux (r = −0.763). This suggests that the param- eters determined from the BAT data are strongly connected to the first canonical axis, implying a link 94 vol. 65 no. 1/2025 Correlation between X-ray and gamma data of Swift measurements Corr: 0.532*** Corr: −0.113. Corr: 0.611*** Corr: 0.184** Corr: 0.526*** Corr: 0.482*** Corr: 0.171* Corr: 0.522*** Corr: 0.458*** Corr: 0.966*** Corr: −0.192** Corr: −0.068 Corr: 0.080 Corr: −0.086 Corr: −0.076 Corr: −0.064 Corr: −0.150* Corr: −0.188** Corr: −0.203** Corr: −0.134* Corr: 0.010 Corr: 0.154* Corr: 0.155* Corr: 0.036 Corr: 0.071 Corr: 0.057 Corr: −0.060 Corr: 0.073 T90 Fluence Peak Flux X Flux 11h X Flux 24h Decay Index Spectral Index N(HI) T 90 F luence P eak F lux X F lux 11h X F lux 24h D ecay Index S pectral Index N (H I) 1 2 −7.0−6.5−6.0−5.5−5.0−4.5−0.50.00.51.0 −14 −13−12 −11 −14 −13 −12 −4 −2 0 1.501.752.002.25 −2 −1 0 1 0 10 20 30 −7.0 −6.5 −6.0 −5.5 −5.0 −4.5 −0.5 0.0 0.5 1.0 −14 −13 −12 −11 −14 −13 −12 −4 −2 0 1.50 1.75 2.00 2.25 −2 −1 0 1 BAT & XRT data Figure 2. Cross-correlation matrix of the GRBs’ parameters (“outliers” excluded). The number of asterisks indicates the significance of the correlation. T90 Fluence PeakFlux U1 −0.520 −0.911 −0.785 U2 0.853 0.094 −0.605 U3 0.065 0.430 −0.148 11hFlux 24hFlux Decay ind. Sp. index N(HI) V 1 −0.927 −0.825 0.091 0.273 −0.206 V 2 −0.012 −0.020 −0.856 0.257 −0.424 V 3 −0.109 −0.066 −0.409 −0.706 0.228 Table 1. The connection between the U (from BAT data) and V (from XRT data) canonical correlation coefficients and the GRB parameters using only the data before the July of 2008 for the comparison. Bold-face indicates the 3σ significance level. T90 Fluence PeakFlux U1 −0.611 −0.946 −0.763 U2 0.788 0.120 −0.642 U3 −0.092 0.324 −0.088 11hFlux 24hFlux Decay ind. Sp. index N(HI) V 1 −0.942 −0.898 0.131 0.216 −0.216 V 2 −0.083 −0.028 −0.916 −0.023 −0.439 V 3 −0.316 −0.522 −0.085 −0.708 0.121 Table 2. The connection between the U (from BAT data) and V (from XRT data) canonical correlation coefficients and the GRB parameters, based on the entire dataset up to the end of 2023. Boldface indicates the 3σ significance level. 95 I. I. Racz, L. G. Balazs, I. Horvath, S. Pinter Acta Polytechnica between the length and intensity of gamma-ray bursts and the early stages of the X-ray afterglow. The sec- ond canonical variable (U2) has a substantial connec- tion with T90 (r = 0.788), but less so with fluence (r = 0.120), and in the opposite direction with peak flux (r = 0.642), showing a more complicated dy- namic between different elements of the gamma-ray bursts. For the V variables, the first canonical variable (V 1) has a large negative correlation with the 11-hour flux (r = −0.942) and the 24-hour flux (r = −0.898), whereas the spectral index and HI column density have lesser, but still significant relationships. This implies that the early X-ray fluxes and their spectrum features acquired from the XRT data are strongly connected to the optical properties of the gamma-ray bursts, supporting the close relationship between the BAT and XRT data. Further investigation of these findings can aid in understanding the links between the distinct phases of gamma-ray bursts and the processes of the central engine. The Table 2 also shows other examples of weak, but extremely significant correlations, which are high- lighted in bold. These substantial correlations, despite their modest levels, indicate that even minor interac- tions between variables can be statistically significant. For example, the spectral index and HI column den- sity have modest, but substantial correlations with the first canonical variable V 1, showing that these param- eters, while not highly associated, play an important role in the overall relationship between the BAT and XRT datasets. These findings emphasise the necessity of taking into account even slight correlations when evaluating the intricate interplay between the distinct phases of gamma-ray bursts. Furthermore, the second and third canonical vari- ates (U2, U3, and V 2, V 3) reveal more intricate inter- actions, shedding information on how many compo- nents of the GRB development interact. The substan- tial association of U2 with T90 and peak flux, but not with fluence, and V 2 with the decay index imply that these variables represent the developing dynamics of the GRB as it transitions from the prompt emission to the afterglow phase. These findings are critical for creating a complete model of the GRB behaviour and deepening our knowledge of the fundamental mecha- nisms that drive such catastrophic occurrences. The term “complete model” here refers to a model that incorporates the many stages of the GRB event as well as the physical characteristics involved, includ- ing the connection between the prompt emission and the afterglow that follows. Such a model aims to ex- plain the physical processes that take place during the explosion, including the dynamics and interactions between the different components of the observation (e.g. T90 duration, peak flux, and decay index). This model can be particularly useful for groups of GRBs with significant variations in spectral energy distribu- tion between the early and late phases, i.e. not limited to a specific type, but rather covering the entire GRB phenomena. Overall, the canonical correlation analysis provides a strong framework for investigating the complex corre- lations between the GRB observational features. The substantial connections found between the canonical variables highlight the interrelated nature of GRBs’ prompt and afterglow phases, providing crucial infor- mation for future theoretical and observational studies. Future research might improve on these findings by including more factors and broadening the dataset, re- fining our understanding of the fundamental processes that underlie GRB events. 4.1. Comparison with previous results Previous comparable investigations such as the one presented at the GAMMA-RAY BURST: Sixth Huntsville Symposium in 2008 have shed light on the relationships between gamma-ray bursts and their observational features. The 2008 research produced many important findings: (a) In comparison to the X-ray decay index and spectral index, the gamma-ray fluence and early X-ray flux were shown to be the most significant contributions to the canonical correlation. (b) The HI column density contributed significantly to the canonical correlation. This discovery was interpreted in terms of the collapsar hypothesis for long GRBs, implying that the progenitor’s ejection of an HI envelope was critical in creating the GRB. Our recent investigation confirms these previous findings, emphasising the importance of the gamma- ray fluence and early X-ray flux in the canonical cor- relation analysis. The gamma-ray fluence and early X-ray flux continue to make significant contributions to the canonical correlations, as seen by the boldface coefficients in Table 2. These findings are consistent with prior conclusions, emphasising the significance of these characteristics in understanding the link between GRBs’ prompt and afterglow phases. Our investigation found that the HI column den- sity made a significant contribution to the canonical correlation, as seen in the last row of Table 2. This conclusion is consistent with the 2008 study and lends credence to the collapsar concept of long GRBs. The strong association between the HI column density and canonical factors shows that the GRB progenitor’s ejection of an HI envelope plays an important role in the observed X-ray afterglow features. This consistent finding across investigations emphasises the reliability of the HI column density as a critical parameter in a GRB study. Furthermore, our approach has offered a better un- derstanding of the canonical relationships with other factors. For example, while the spectral index and X-ray decay index make smaller contributions, they nonetheless play a role in the overall correlation struc- ture. This detailed knowledge helps to enhance our 96 vol. 65 no. 1/2025 Correlation between X-ray and gamma data of Swift measurements 0.52 0.91 0.78 0.59 0.52 0 0 0 0.33 0.58 0.51 0.93 0.82 0 −0.27 0.21 −0.85 0 0.6 0 0 0.22 0 0 −0.21 0 0 0 0 0.86 −0.26 0.42 0 −0.43 0 0 0 0 0 0 0 0 0 0 0 0.41 0.71 −0.23 −0.85 −0.68 −0.5 −0.32 −0.14 0.04 0.22 0.39 0.57 0.75 0.93 U 1 V 1 U 2 V 2 U 3 V 3 T90 Fluence Peak flux X flux 11h X flux 24 X decay index X spectral index N(HI) (a). 2008 research. 0.61 0.95 0.76 0.54 0.48 0 −0.12 0.12 0.35 0.54 0.44 0.94 0.9 −0.13 −0.22 0.22 −0.79 −0.12 0.64 0 0 0.15 0 0 −0.13 0 0.11 0 0 0.92 0 0.44 0.09 −0.32 0.09 0 0 0 0 0 0 0 0 0.32 0.52 0 0.71 −0.12 −0.79 −0.61 −0.44 −0.27 −0.09 0.08 0.25 0.43 0.6 0.77 0.95 U 1 V 1 U 2 V 2 U 3 V 3 T90 Fluence Peak flux X flux 11h X flux 24 X decay index X spectral index N(HI) (b). Current investigation up to 2023. Figure 3. The correlations between the canonical variables U and V and the GRB parameters in the 2008 research and the current investigation up to 2023. The graphs provide the correlations and significance levels for each parameter, allowing for a visual comparison of the results. The colour blue denotes a positive association, whereas red shows a negative correlation. The brightness of the colour and the flatness of the circle indicate the strength of the association. The image displays only relationships with a significance level of 3σ. models of GRB behaviour and promotes additional research into the interactions of many observable fea- tures. Figure 3 depicts the correlations between the canon- ical variables U and V and the GRB parameters for both the 2008 study and our current investigation up to 2023. The plots in the image indicate the cor- relations and significance levels of each parameter, allowing for a visual comparison of the results. The consistent patterns found in the two datasets support the canonical correlation analysis and the significance of the identified factors in the GRB study. Overall, the comparison of earlier data reveals a re- markable consistency in the major discoveries regard- ing GRB characteristics. Here, of course, we note that the strength of the correlation between the variables N(HI) and V 2 has lost significance. Alternatively, the now computed V 3 has changed sign, which in the case of the coefficient shows the opposite direction. Moreover, this V 3 shows even stronger correlations now than in 2008. To summarise, Gamma-ray flu- ence, early X-ray flux, and HI column density have all been shown to provide significant contributions to canonical correlations, emphasising their relevance in GRB research. These findings not only support previous studies, but also pave the way for further investigations into the intricate systems behind GRBs. 4.2. Changing X-ray spectra parameters In this work, we investigated the X-ray photons of the GRB. The correlation between the parameters obtained from the X-ray spectra and the canonical variables is well established. In the next work, we will try to refine the spectrum obtained from X-ray photons. Our previous results show that in many cases, the internal hydrogen column density can change signifi- cantly during the spectrum fitting procedure [30, 31]. A very good example of it can be seen in Figure 4. We plan to carry out the following steps to use higher quality input data for the spectral fitting: (a) unified settings and models on all GRB’s spectra, (b) only (reliable) spectroscopic redshifts, (c) use more/newer redshift data, (d) higher resolution Galactic foreground HI density maps calculated from Planck maps, (e) initial values are important for a correct iteration. To date, the Swift has observed nearly 300 GRBs for which reliable X-ray spectra have been obtained by the Swift XRT instrument, and they have spectroscop- ically measured redshifts. These redshifts are often not very accurate at first, so significant differences may be found compared to the initial data after a few days. Additionally, subsequently released data do not always get incorporated into the automatic processing procedures. For all redshift measurements described in (b) and (c), we need to check the value in the published databases and then verify their validity in the GCN notes. In addition, we are also planning to use a reli- able value not found in the databases, but published in the literature. The precomputation mentioned in (d) will have to be done as follows. As it was already shown from ISO measurements, the FIR based estima- 97 I. I. Racz, L. G. Balazs, I. Horvath, S. Pinter Acta Polytechnica 10−4 10−3 0.01 c o u n ts s k e V Swift−XRT PC spectrum of GRB 080129 10.5 2 5 0.5 1 1.5 2 ra ti o Energy (keV) (a). Time-averaged X-ray spectra (UK Swift Science Data Centre (UKSSDC), Evans et al., 2009 [32]). (b). Our previous result from Racz et al., 2017 [30], the GRB080129’s refitted XRT spectrum with the new values (foreground N(H) and redshift). The significant difference between the two fits is also easily visible to the eye. Figure 4. X-ray spectrum fitting of the 080129 GRB Swift XRT. We previously are shown that the intrinsic hydrogen column density can vary significantly during the initial parameters of the spectral fitting process. tion of Galactic ISM column densities must include measurements at wavelengths beyond 100 µm (see e.g. [33, 34]). Accordingly, we used the 5 arcmin reso- lution Planck visible V-band renormalised (Av_RQ) extinction map1 as a starting point estimating the Galactic foreground column density, that is based on the multiband Planck sky survey corrected using visual extinctions of quasars from the Sloan Digital Sky Survey [35]. From this whole-sky extinction field image, we extracted the dust extinction for each GRB. We note that an alternative estimate could be based on NIR extinction of stars [36]. Assuming that the dust is properly mixed in the interstellar material [37], we can calculate the Galactic hydrogen column density using [38]: N(H) = 2.21(±0.09) × 1021 · Av, (5) where Av is the visual extinction read from Planck images. We note here that there is a variation of extinction to gas density in the Galactic ISM (see e.g. [39, 40]). The resulting hydrogen column density values can be used directly in the re-fitting of the spectra. For some well-detected GRB cases with a high hy- drogen column density, we performed refitting of the spectra. By re-fitting the X-ray spectra of the GRBs, it is clear how divergent the intrinsic hydrogen col- umn density is (Figure 5). In dozens of cases, we got discrepancies of orders of magnitude. On average, we got a value 4.5 × 1021 cm−2 higher than the value in the official catalog, which corresponds to an increase of approximately 50 %. With the new data, we will have to carry out the entire investigation again in order to check the ro- bustness of the obtained correlations and to find the 1COM_CompMap_Dust-DL07-AvMaps_2048_R2.00.fits N N + Q) li) N N + Q) N � N + Q) li) • • • � N + Q) � 1e+21 • ... • • • ..... • • • • • • • • • • 5e+21 • • • • • • • • I • • • • • • • • • • • • • 2e+22 5e+22 2e+23 Intrinsic NH new [cm-2] In tr in si c NH f ro m c at al og [ cm -2 ] Figure 5. The variation of the hydrogen column density for selected high N(H) GRBs in cm−2. The vertical axis shows the N(H) value from the catalogue, while the horizontal axis shows our calculated column densities. previously hidden connections. But this work is be- yond the scope of this article. 5. Conclusion We used canonical correlation analysis to investigate the relationship between gamma (fluence, 1 sec peak flux, and duration) and X-ray data (11 hours flux, 24 hours flux, decay index, spectral index, and HI col- umn density). Using the canonical variables obtained from the study, we calculated their correlations (canon- ical loadings) with the originals. The canonical load- ings indicated that the gamma-ray fluence and early X-ray flux contribute the most to the correlation, as opposed to the X-ray decay index and spectral index. 98 vol. 65 no. 1/2025 Correlation between X-ray and gamma data of Swift measurements An interesting finding appears to be that the HI col- umn density contributes significantly to the connec- tion. Accepting the collapsar model of long GRBs, this phenomenon may suggest that the stellar wind of the massive progenitor star prior to the burst had created a substantial HI envelope that was already present at the moment of the GRB. We compared the results to previous studies and found comparable results; the previous associations remained significant in the same way. Because, as previously demonstrated, the precision of fitting to the X-ray spectra has a significant im- pact on the calculation of the inherent column density. Thus, in this article and in a few circumstances, we have investigated this phenomena and proposed a so- lution. However, this study is still continuing and requires further investigation. Acknowledgements The authors would like to thank the Hungarian TKP2021- NVA-16 programme for their support. 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Ph.D. thesis, University of Helsinki, Finland, 2005. 100 https://doi.org/10.1007/s11214-005-5097-2 https://doi.org/10.1117/12.409162 https://www.swift.ac.uk/burst_analyser/00301981 https://doi.org/10.1016/0167-9473(85)90003-9 https://doi.org/10.1093/mnras/stz2314 https://doi.org/10.1111/j.1365-2966.2009.14913.x https://doi.org/10.1111/j.1365-2966.2009.14913.x https://doi.org/10.1051/0004-6361:20035611 https://doi.org/10.1051/0004-6361/201424945 https://doi.org/10.1051/0004-6361/201321235 https://doi.org/10.1093/pasj/psy123 https://doi.org/10.1111/j.1365-2966.2009.15598.x https://doi.org/10.1111/j.1365-2966.2009.15598.x Acta Polytechnica 65(1):92–100, 2025 1 Introduction 2 Materials and methods 2.1 Data 2.2 Mathematical summary 3 Results 4 Discussion 4.1 Comparison with previous results 4.2 Changing X-ray spectra parameters 5 Conclusion Acknowledgements References