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# GRB 240715A: Revealing Novel Intrinsic Mechanism by Different Individual Pulse

Wen-Jun Tan, Chen-Wei Wang, Shao-Lin Xiong, Shi-Jie Zheng, Jiang He, Xiao-Yun Zhao, Yue Huang, Shu-Xu Yi, Bing Li, He Gao, et al.

► To cite this version:

Wen-Jun Tan, Chen-Wei Wang, Shao-Lin Xiong, Shi-Jie Zheng, Jiang He, et al. GRB 240715A: Revealing Novel Intrinsic Mechanism by Different Individual Pulse. The Astrophysical Journal Letters, 2025, 995 (1), pp.L16. 10.3847/2041-8213/ae2020. hal-05396499

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GRB 240715A: Revealing a Novel Intrinsic Mechanism by Different Individual Pulses

Wen-Jun Tan¹,² ID, Chen-Wei Wang¹,² ID, Shao-Lin Xiong¹ ID, Shi-Jie Zheng¹, Jiang He¹,² ID, Xiao-Yun Zhao¹, Yue Huang¹, Shu-Xu Yi¹ ID, Bing Li¹ ID, He Gao³,⁴ ID, Bo-bing Wu¹ ID, Bing Zhang⁵,⁶,⁷ ID, Frédéric Daigne⁸, Maria-Grazia Bernardini⁹,²² ID, Bin-Bin Zhang¹⁰,¹¹,¹² ID, Stéphane Basa¹³ ID, Bertrand Cordier¹⁴, Jin-Song Deng¹⁵,¹⁶ ID, Yong-Wei Dong¹, Damien Dornic¹⁷, Olivier GODET¹⁸, Xu-Hui Han¹⁶ ID, Mao-Hai Huang¹⁹, Cyril Lachaud²⁰, Hua-Li Li¹⁶ ID, Pierre Maggi²¹ ID, Frédéric Piron²² ID, Yu-Lei Qiu¹⁶, Stéphane Schanne¹⁴, Li-Ming Song¹ ID, Damien Turpin¹⁴, Susanna Vergani²³ ID, Jing Wang¹⁶, Ping Wang¹ ID, Jian-Yan Wei¹⁶,², Chao Wu¹⁶, Li-Ping Xin¹⁶ ID, Yang Xu¹⁶ ID, Li Zhang¹, and Shuang-Nan Zhang¹,² ID

¹ State Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, People's Republic of China;
xiongsl@ihep.ac.cn

² University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, People's Republic of China

³ Institute for Frontier in Astronomy and Astrophysics, Beijing Normal University, Beijing 102206, China, Department of Astronomy, Beijing Normal University,
Beijing 100875, People's Republic of China

⁴ Department of Astronomy, Beijing Normal University, Beijing 100875, People's Republic of China

⁵ The Hong Kong Institute for Astronomy and Astrophysics, University of Hong Kong, Fokfulam Road, Hong Kong, People's Republic of China

⁶ Department of Physics, the University of Hong Kong, Pokfulam Road, Hong Kong, People's Republic of China

⁷ Nevada Center for Astrophysics, University of Nevada, Las Vegas, NV 89154, USA

⁸ Sorbonne Université, CNRS, UMR 7095, Institut d'Astrophysique de Paris, 98 bis bd Arago, F-75014 Paris, France

⁹ INAF—Osservatorio Astronomico di Brera, Via Emilio Bianchi 46, 23807 Merate, Italy

¹⁰ School of Astronomy and Space Science, Nanjing University, Nanjing 210093, People's Republic of China

¹¹ State Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, People's Republic of China

¹² Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, People's Republic of China

¹³ Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France

¹⁴ CEA Paris-Saclay, Irfu/Département d'Astrophysique, 91191 Gif sur Yvette, France

¹⁵ School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 101408, People's Republic of China

¹⁶ National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, People's Republic of China

¹⁷ CPPM, Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France

¹⁸ Institut de Recherche en Astrophysique & Planétologie, Université de Toulouse/CNRS/CNES, 9 avenue du colonel Roche, 31028 Toulouse, France

¹⁹ Chinese Academy of Sciences, Beijing 100049, People's Republic of China

²⁰ APC, Univ. Paris Diderot, CNRS/IN2P3, CEA/Irfu, Obs de Paris, Sorbonne Paris Cité, France

²¹ Observatoire Astronomique de Strasbourg, Université de Strasbourg, CNRS, 11 rue de l'Université, F-67000 Strasbourg, France

²² LUPM, CC 72, CNRS/IN2P3, Université de Montpellier, place E. Bataillon 34095 Montpellier CEDEX 05, France

²³ LUX, Observatoire de Paris, PSL University, CNRS, Sorbonne University, 92190 Meudon, France

Received 2025 October 10; revised 2025 November 14; accepted 2025 November 16; published 2025 December 5

Abstract

The Space-based multiband astronomical Variable Objects Monitor (SVOM) detected its first short gamma-ray burst (GRB), GRB 240715A, in flight, which was jointly observed by Fermi. Based on observational data of SVOM/GRM and Fermi/GBM, we perform a comprehensive temporal and spectral analysis of individual pulses in the prompt emission of this burst, and novel characteristics are revealed. First, opposite evolutions of spectral lag are found in the first and third pulse of this burst. Second, the large negative lag of the first pulse is an outlier in the short GRB sample, especially when the pulse duration is considered. Spectral analysis shows that the negative lag of the first pulse is caused by the evolution of the spectrum index and is irrelevant to $E_{\text{peak}}$, which is inconsistent with the previous study. The intrinsic mechanism is probably attributed to electron cooling in the decaying magnetic field, which leads to the continuous hardening of the spectrum index and results in negative lag. Furthermore, spectral analysis also shows that the third pulse is more likely to be described by a quasi-thermal spectrum, indicating the existence of photospheric emission. It is difficult to explain how the synchrotron radiation appears before photospheric emission in a single GRB, and some assumptions are discussed.

Unified Astronomy Thesaurus concepts: Gamma-ray bursts (629)

1. Introduction

The Space-based multiband astronomical Variable Objects Monitor (SVOM) is a Sino-French mission committed to gamma-ray burst (GRB) studies and the discovery and multiwavelength follow-up of cosmic transients (J. Wei et al. 2016; M. G. Bernardini et al. 2021). The mission, which was launched on 2024 June 22, includes a satellite with a

multiwavelength science payload and a dedicated ground segment made of robotic telescopes in China and Mexico. The satellite carries two wide-field monitors for GRB prompt emission detection, called ECLAIRs (a 4–150 keV coded mask imager; O. Godet et al. 2014) and Gamma-Ray Monitor (GRM; 15–5000 keV; Y. Dong et al. 2010). ECLAIRs is in charge of providing precise localization (<13′ at a 90% confidence level) and X-ray energy cover, while GRM is responsible for obtaining the broad energy spectrum measurement. Besides these two monitors, two narrow-field telescopes for GRB follow-up are also equipped: the Microchannel X-ray Telescope (energy between 0.2 and 10 keV; D. Götz et al. 2023) and the Visible Telescope (from 450 to 650 nm for the

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blue channel and from 650 to 1000 nm for the red channel; J. Wei et al. 2016).

GRBs are the most violent explosions in the Universe. Traditionally, GRBs can be divided into long GRBs and short GRBs by a simple but effective criterion: $T_{90}$ (E. P. Mazets et al. 1981; C. Kouveliotou et al. 1993). As research deepens, more physical classifications have been proposed, corresponding to two different origin models for GRBs, namely, type I (usually short) and type II (usually long) GRBs (B. Zhang 2006). Generally speaking, type I bursts are produced by the merger of compact binaries with shorter durations and harder spectra (S. I. Blinnikov et al. 1984; B. Paczynski 1986; P. Meszaros & M. J. Rees 1992), while type II bursts are related to the core collapse of supermassive stars, which are usually longer and softer (S. E. Woosley 1993; B. Paczyński 1998; S. E. Woosley & J. S. Bloom 2006).

GRB 240715A is the first short GRB that triggered the GRM in flight (J. He et al. 2025) with real-time burst message processing. The prompt emission of this burst reveals novel characteristics. First, it exhibits an opposite evolution of the spectral lag in two pulses, which means there is a relatively large negative spectral lag excluding statistical fluctuations in the first pulse. Furthermore, this GRB also shows a possible photospheric emission in the latter pulse. Both phenomena require a new mechanism explanation that cannot be covered by current models.

The spectral lag of GRBs, attributed to the fact that higher-energy gamma-ray photons arrive earlier than lower-energy gamma-ray photons, is quite a common characteristic in the prompt emission of GRBs (L. X. Cheng et al. 1995; J. P. Norris et al. 1996). Some studies showed that long GRBs usually have larger positive spectral lags, whereas short GRBs tend to exhibit negligible, sometimes negative, lags (J. P. Norris et al. 2000; T. Yi et al. 2006).

Some papers argued that negative spectral lags may be unreal, because if there are two nearly overlapping pulses with the second one being harder than the first one, then fake negative lags will appear when calculating the lag of the whole light curve (Z. Y. Peng et al. 2011; P. Y. Minaev et al. 2014). Therefore, lag calculation for pulses in GRBs has also been studied. R.-J. Lu et al. (2018) mainly studied pulses of long GRBs and gave the correlation of observed quantities, such as lag-energy, lag-pulse width, and lag index-pulse width. T. Yi et al. (2006) systematically studied the pulse lag of short GRBs and found that ~17% of short GRBs have a negative spectral lag excluding the statistical fluctuation effect, which is significantly different from that of long GRBs.

Several models are proposed to interpret the spectral lag. These models fall broadly into two categories. One invokes the kinematic process, the so-called “high-latitude” effect (the curvature effect), which expresses that photons at higher latitudes would arrive at the observer later with softened observed energy due to a smaller Doppler factor, resulting in a lag. R.-F. Shen et al. (2005) and R. J. Lu et al. (2006) studied this effect in detail and found that the curvature effect marginally interpreted the observed lags. Other models mainly considered the dynamic process, which expresses that the spectral evolution during the prompt phase of the GRB can explain the observed lag (B. Wu & E. Fenimore 2000; D. Kocevski & E. Liang 2003; F. Ryde 2005; Z. Y. Peng et al. 2011; R.-J. Lu et al. 2018). Because of the continuous cooling effect of radiated electrons, the peak energy ($E_{peak}$) of the

energy spectra moves from high to low energies in gamma rays, resulting in the peak of the light curve also moving from the higher energy band to the lower one, further resulting in the observed spectral lag. Based on a simple but general emission model, Z. L. Uhm & B. Zhang (2016) interpreted some observed spectral lag features by considering the intrinsic curved spectral shape, the decay of the magnetic field strength, and the rapid bulk acceleration of the emission zone. The above models aimed to explain the positive lag. However, a small fraction of the observed negative lags is still in debate; the relatively popular model is inverse Comptonization (A. Roychoudhury et al. 2014; M. K. Vyas et al. 2024).

There are two leading scenarios that explain the radiation mechanism that powers the prompt emission of GRBs. The first is the synchrotron radiation model, which is relevant for the internal shock model (A. Shemi & T. Piran 1990; M. J. Rees & P. Meszaros 1992, 1994; P. Meszaros & M. J. Rees 1993; N. M. Lloyd & V. Petrosian 2000; M. G. Baring & M. L. Braby 2004), magnetic dissipation driven by Poynting flux (V. V. Usov 1992; C. Thompson 1994; P. Mészáros & M. J. Rees 1997; M. Lyutikov & R. Blandford 2003; N. Vlahakis & A. Königl 2003), or internal-collision-induced magnetic reconnection and turbulence at a large radius (B. Zhang & H. Yan 2011; W. Deng et al. 2015). The second scenario is known as the photospheric emission model, produced from relativistic outflows as a natural consequence of the fireball model (J. Goodman 1986; B. Paczynski 1986). In this model, the optical depth at the base of the outflow is significantly greater than unity (T. Piran 1999), and a bright quasi-thermal spectral component is expected.

In the context of the photospheric emission model, the standard blackbody spectrum (Planck spectrum) is broadened for two main reasons. First, other dissipative processes such as synchrotron radiation or Comptonization of thermal photons occur beneath the photosphere, modifying the shape of the blackbody spectrum (A. Pe'er et al. 2005, 2006; M. J. Rees & P. Mészáros 2005). Second, the geometric broadening of the structured jet can also modify the shape of the blackbody spectrum (M. A. Abramowicz et al. 1991; A. Pe'er 2008). In this latter scenario, the luminosity, Lorentz factor, and photosphere radius are found to be a function of the angle (C. Lundman et al. 2013; Y.-Z. Meng et al. 2018, 2019; X. I. Wang et al. 2021). Consequently, the observed spectrum is a superposition of comoving blackbodies with different temperatures, originating from various angles relative to the line of sight (F. Ryde et al. 2010; S.-J. Hou et al. 2018). This structural broadening results in a predominance of low-energy photons and produces a softer spectrum, typically described as a multicolor blackbody (mBB). Furthermore, a hybrid jet model was proposed to interpret cases with superposition of a dominant synchrotron component and a subdominant thermal component (M. Axelsson et al. 2012; S. Guiriec et al. 2013; H. Gao & B. Zhang 2015; Y.-Z. Meng et al. 2022; C.-W. Wang et al. 2025a). In addition, the transition from fireball to Poynting-flux-dominated outflow has also been observed (B. B. Zhang et al. 2018a).

This Letter is organized as follows. Observations and data reduction are described in Section 2. Detailed temporal and spectrum analysis is presented in Section 3. A brief discussion and explanation of the observed phenomena of this GRB is presented in Section 4. A summary is given in Section 5.
Throughout the Letter, a standard cosmology with parameters $H_0 = 67.4 \text{ km s}^{-1} \text{ Mpc}^{-1}$, $\Omega_M = 0.315$, and $\Omega_\Lambda = 0.685$ is adopted (Planck Collaboration et al. 2020). All parameter errors in this work are for the 68% confidence level if not otherwise stated.

## 2. Observations and Data Reduction

As a scintillator-based instrument, GRM consists of three gamma-ray detectors (GRDs) operating in the 15 keV–5 MeV energy range. The three identical detectors are inclined by 30° with respect to the axis of the ECLAIRs telescope and spaced from each other in the perpendicular plane of 120° (Y. Dong et al. 2010; M. G. Bernardini et al. 2021).

GRB 240715A triggered SVOM/GRM at 05:44:03.400 UT on 2024 July 15 in flight with all three GRDs (SVOM/GRM Team et al. 2024) when SVOM was in the commissioning phase. It is the first short GRB that triggered the GRM in flight (J. He et al. 2025). At that time, ECLAIRs was not in operation. The duration ($T_{90}$) in the 15–5000 keV light curve is about 0.17 s. We extract the 15–5000 keV light curve with a time bin of 5 ms from event-by-event data combined from all three GRDs of GRM. The light curve mainly shows three pulses, especially in the time–energy diagram (Figure 1(a)). Moreover, we extract the light curve in seven energy bands, 15–30, 30–70, 70–100, 100–300, 300–500, 500–2000, and 2000–5000 keV, and multiwavelength light curves are shown in Figure 1(b). For GRM spectrum analysis, we extract the energy spectrum of all three detectors of GRM using GECAMTools-v20240514.<fnref n="24" /> The energy range used for spectral fitting is 20–5000 keV for GRM detectors. Hereafter, we take the ground trigger time (2024-07-15T05:44:03.000) as $T_0$.

GRB 240715A also triggered the Fermi Gamma-ray Burst Monitor (GBM; C. de Barra et al. 2024). The GBM is one of the two instruments on board the Fermi Gamma-ray Space Telescope (E. Bissaldi et al. 2009; C. Meegan et al. 2009), which consists of 14 detectors with different orientations: 12 sodium iodide (NaI) scintillation detectors (labeled from n0 to nb) and two bismuth germanate (BGO) scintillation detectors (b0 and b1). For GBM spectrum analysis, we extract the energy spectrum of the NaI detectors with an incident angle smaller than 40° (that is, n9 and na) and the BGO detector b1 using GBM data tools<fnref n="25" /> (C.-W. Wang et al. 2025b). The energy range used for spectral fitting is 8–900 keV for the NaI detectors and 0.3–35 MeV for the BGO detectors.

Swift/XRT conducted a target of opportunity for GRB 240715A about 33 minutes after $T_0$, but only a likely afterglow has been detected, and some upper limits are given (C. Salvaggio et al. 2024). Some optical follow-up observations were also conducted. However, no new optical source was detected consistent within the XRT position, and a few upper limits are given (V. Lipunov et al. 2024; S. Tinyanont et al. 2024). The absence of an optical counterpart and of the identification of the possible host galaxy prevented the redshift determination.

## 3. Data Analysis

The first pulse and the third pulse of this GRB exhibit different behaviors in the temporal and spectral domains,

including negative spectral lag in the first pulse and possible photospheric emission in the third pulse.

### 3.1. Pulse Fitting

In order to study the pulse properties, it is very important to separate different pulses. From the light curve in Figure 1(a), GRB 240715A has two bright, well-shaped pulses, which lie at the left and right ends of the light curve. This Letter focuses mainly on these two pulses. As the shape of these two pulses is relatively narrow and symmetrical, we choose two Gaussian functions to fit these two pulses. Meanwhile, it can also be seen from the light curve that there is a small pulse-like structure between these two pulses. Therefore, we used another Gaussian function to fit this small pulse in the middle. We used a triple Gaussian to fit the three pulses of the light curve:

$$L = N_1 G(t, t_{p1}, s_1) + N_2 G(t, t_{p2}, s_2) + N_3 G(t, t_{p3}, s_3) + B, \quad (1)$$

where $G(t, t_p, s) = \exp(-(t - t_p)^2/s)$. $N_1, N_2, N_3, t_{p1}, t_{p2}$, and $t_{p3}$ are the normalizations, peak times of three pulses. $s = 2\sigma^2$, where $\sigma$ is the standard deviation of the Gaussian function. B is the constant background. The reason why the constant background is chosen is that we first fitted the whole light curve using a first-order polynomial and found that the normalization of the first-order term was very small (from $10^{-3}$ to $10^{-2}$). Moreover, the time range used for pulse fitting is very short ($T_0-0.1$ to $T_0+0.5$ s), so there were no significant changes in the background.

We extract the light curves in four energy bands, i.e., 15–50, 50–200, 200–500, and 500–2000 keV, with a time bin of 10 ms from event-by-event data combined from all three GRDs of GRM and then fit the light curve in each energy band with a triple-Gaussian function (Figure 1(c)). The fitting parameters are listed in Table 1. Then we calculate the time delay of the peak in the lowest energy band relative to that in each high energy band for each Gaussian model (Figure 1(d)) and the pulse width of each energy band (Figure 1(e)), which is defined as the full width at half-maximum (FWHM) of the Gaussian function. As the energy increases, the first pulse peaks at later times, whereas the third pulse peaks at lower times, and the peak of the middle pulse basically does not move. Additionally, as the energy increases, the widths of the first pulse and the third pulse are slightly reduced, but the width of the middle pulse is basically unchanged. Combined with pulse-peak shifting and pulse width reducing, the whole picture looks like the first pulse and the third pulse slowly approach each other as the energy increases and finally enhance the brightness of the second pulse in the high energy band.

### 3.2. Spectral Lag

Based on the pulse fitting, we can determine at which time period a certain pulse is dominant and then determine the start and end times of each pulse for calculating the spectral lag (mainly the end time of the first pulse and start time of the third pulse). We calculate the spectral lag of the first pulse ($T_0+0.1$ to $T_0+0.28$ s), the second pulse ($T_0+0.28$ to $T_0+0.33$ s), the third pulse ($T_0+0.33$ to $T_0+0.5$ s), and the whole light curve ($T_0+0.1$ to $T_0+0.5$ s). To investigate in detail the pulse

<footnote n="24">²⁴ https://github.com/zhangpeng-sci/GECAMTools-Public</footnote>

<footnote n="25">²⁵ https://fermi.gsfc.nasa.gov/ssc/data/analysis/gbm/gbm_data_tools/gdt-docs/</footnote>
b

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 1.** Light curves and pulse fitting. (a) Light curves of SVOM/GRM and Fermi/GBM with 5 ms bin width and the time-energy diagram of SVOM/GRM within the energy range from 10 to 1000 keV. (b) Multiwavelength light curves of SVOM/GRM with 10 ms bin width. (c) The triple-pulse fitting of the light curves in each energy band with the triple-Gaussian function. (d) The time delay of the peak of each pulse. (e) The width of each pulse in each energy band.</figcaption></figure>

behavior of each energy band, we estimate the spectral lag with respect to 15–30 keV for six energy bands based on the signal significance, 30–70, 70–100, 100–300, 300–500, and

500–2000 keV, of all three GRDs of GRM. Considering the signal significance, the light curve above 2000 keV is not chosen.
<table><caption>**Table 1**
Fitting Parameters of Three Pulses with a Triple-Gaussian Function</caption><thead><tr><th>Pulse No.</th><th>Parameters</th><th>15–50<br>(keV)</th><th>50–200<br>(keV)</th><th>200–500<br>(keV)</th><th>500–2000<br>(keV)</th></tr></thead><tbody><tr><td rowspan="3">P<sub>1</sub></td><td>N<sub>1</sub> (100 counts s<sup>-1</sup>)</td><td>59.9<sup>+5.4</sup><sub>-5.8</sub></td><td>106<sup>+8.4</sup><sub>-15</sub></td><td>57.8<sup>+6.5</sup><sub>-2.1</sub></td><td>19.1<sup>+5.1</sup><sub>-5.2</sub></td></tr><tr><td>t<sub>p1</sub> (ms)</td><td>250<sup>+2.4</sup><sub>-2.5</sub></td><td>255<sup>+3.2</sup><sub>-3.1</sub></td><td>265<sup>+1.5</sup><sub>-2.2</sub></td><td>268<sup>+5.0</sup><sub>-4.0</sub></td></tr><tr><td>s<sub>1</sub> (ms<sup>2</sup>)</td><td>756.0<sup>+140</sup><sub>-149</sub></td><td>694.0<sup>+139</sup><sub>-125</sub></td><td>344.0<sup>+110</sup><sub>-318</sub></td><td>414.0<sup>+229</sup><sub>-188</sub></td></tr><tr><td rowspan="3">P<sub>2</sub></td><td>N<sub>2</sub> (100 counts s<sup>-1</sup>)</td><td>22.6<sup>+3.2</sup><sub>-1.9</sub></td><td>77.0<sup>+7.0</sup><sub>-7.0</sub></td><td>38.9<sup>+4.8</sup><sub>-5.2</sub></td><td>19.7<sup>+3.6</sup><sub>-4.2</sub></td></tr><tr><td>t<sub>p2</sub> (ms)</td><td>310<sup>+6.9</sup><sub>-9.5</sub></td><td>305<sup>+4.3</sup><sub>-5.8</sub></td><td>303<sup>+1.9</sup><sub>-8.7</sub></td><td>305<sup>+8.9</sup><sub>-8.9</sub></td></tr><tr><td>s<sub>2</sub> (ms<sup>2</sup>)</td><td>804.0<sup>+143</sup><sub>-269</sub></td><td>913.0<sup>+615</sup><sub>-317</sub></td><td>811.0<sup>+135</sup><sub>-371</sub></td><td>1410<sup>+508</sup><sub>-524</sub></td></tr><tr><td rowspan="3">P<sub>3</sub></td><td>N<sub>3</sub> (100 counts s<sup>-1</sup>)</td><td>38.4<sup>+4.2</sup><sub>-4.3</sub></td><td>183<sup>+4.7</sup><sub>-1.9</sub></td><td>82.3<sup>+5.9</sup><sub>-7.0</sub></td><td>15.8<sup>+2.9</sup><sub>-4.2</sub></td></tr><tr><td>t<sub>p3</sub> (ms)</td><td>376<sup>+4.0</sup><sub>-4.1</sub></td><td>361<sup>+1.1</sup><sub>-1.1</sub></td><td>355<sup>+2.0</sup><sub>-1.9</sub></td><td>348<sup>+4.2</sup><sub>-5.2</sub></td></tr><tr><td>s<sub>3</sub> (ms<sup>2</sup>)</td><td>931.0<sup>+51.4</sup><sub>-105</sub></td><td>482<sup>+62</sup><sub>-65</sub></td><td>367<sup>+67</sup><sub>-64</sub></td><td>428.0<sup>+233</sup><sub>-161</sub></td></tr><tr><td rowspan="2">Bkg</td><td>B (100 counts s<sup>-1</sup>)</td><td>25.6<sup>+1.1</sup><sub>-1.1</sub></td><td>14.6<sup>+0.89</sup><sub>-0.86</sub></td><td>2.66<sup>+0.36</sup><sub>-0.36</sub></td><td>1.83<sup>+0.29</sup><sub>-0.25</sub></td></tr><tr><td>Stat/d.o.f.</td><td>1.33</td><td>1.71</td><td>1.46</td><td>3.61</td></tr></tbody></table>

The modified cross-correlation function (CCF), more suitable for transient signals like GRBs, proposed by D. L. Band (1997) is adopted to compute the spectral lag,

$$ \text{CCF}(k\Delta t; c_1, c_2) = \frac{\sum_{i=\max(1,1-k)}^{\min(N,N-k)} c_{1i}c_{2i(k+i)}}{\sqrt{\sum_{i} c_{1i}^2 \sum_{i} c_{2i}^2}}, \quad (2) $$

where $\Delta t$ is the time bin of the light curve, $k\Delta t$ ($k = ..., -1, 0, 1, ...$) is a multiple of the time bin and represents the time delay, and $c_1$ and $c_2$ are the count rates of two light curves in each energy band. We use this formula to calculate the CCF for a series of time delays $k\Delta t$ and determine the spectral lag as the time delay that corresponds to the maximum of the CCF versus time delay (see, e.g., M. G. Bernardini et al. 2015). We take two small time intervals before and after the burst to perform background subtraction, as the background did not change much during the burst. We adopt 1 ms as the temporal binning to calculate the CCF, as the burst is bright enough. To estimate the uncertainty on the spectral lag, we generate 1000 Monte Carlo simulated light curves based on the observed initial light curve with Poisson probability distribution and calculate the lag of each simulated light curve (T. N. Ukwatta et al. 2010). Then we take the $1\sigma$ uncertainty of the distribution as the uncertainty on the spectral lag.

The result shows that the first pulse has a relatively large negative lag, the middle pulse exhibits almost no spectral lag, and the third pulse has a normal positive lag (Figure 2(a)). This means that in the first pulse, low-energy photons arrive earlier than high-energy photons; in the second pulse, low-energy photons and high-energy photons arrive simultaneously; and the third pulse has the opposite behavior with respect to the first pulse. Moreover, the negative lag of the first pulse increases with energy, as well as the positive lag of the third pulse, forming the phenomenon that the lags of both pulses evolve with energy symmetrically (Figure 2(a)). Finally, the opposite evolution of the spectral lag in the first pulse and the third pulse together results in an inverted “V” shape of the overall spectral lag shape of the whole light curve (Figure 2(b)).

From the above analysis, the spectral lag of GRB 240715A has two characteristics: one is that two pulses with opposite spectral lag evolution occur in the same GRB, and the other is that the negative lag of the first pulse is relatively large,

especially considering the duration (which is expressed as the width of the pulse in our work) of the pulse. In order to further study the rarity and uniqueness of this behavior, as well as to avoid the fact that the brightness of different pulses varying at different energy bands would cause the overall lag to be misestimated (P. Y. Minaev et al. 2014), we search the bright short bursts, which consist of well-shaped pulses in the Fermi GBM Burst Catalog,<fnref n="26" /> just like some work that focuses on long bursts (R.-J. Lu et al. 2018). These short bursts are composed of either single pulses, double pulses, or triple pulses. We fit each pulse of these GRBs with a Gaussian function and calculate the width of these pulses in the 50–300 keV band, as well as the spectral lag of these pulses between energy bands of 50–100 and 150–300 keV. The width and lag results are listed in Table A1. As shown in Figure 2(c) and Table A1, most bright short bursts with well-shaped pulses do not have evident spectral lags within the errors, but a small fraction of the pulses of short bursts indeed exhibit a negative lag excluding statistical fluctuations, just as stated in T. Yi et al. (2006). None of the short bursts considered exhibit the same spectral lag behavior as seen in GRB 240715A, except for GRB 240715A. Another exception is bn230418883; however, the lag is so small that it can be regarded as no opposite evolution when errors are taken into account ($-2_{-1}^{+3}$ and $+3_{-5}^{+6}$ ms for each pulse). It is clearly shown that it is very rare for the spectral lag of two pulses in the same GRB to evolve in opposite ways.

In addition, as shown in Figure 2(e), the negative lag of the first pulse in GRB 240715A ($-12_{-6}^{+5}$ ms) is relatively large among the short GRB samples, about twice as long as the normal negative lag in other GRBs. Such a relatively large negative lag is even more peculiar when the duration of the pulse is considered. The pulse lag is not large in the sample of the whole GRB light curve, as shown in Figure 2(d). However, when both the lag and duration of the pulse are considered, it is clear that the ratio of the lag (absolute value) to the duration of the pulse of GRB 240715A is among the highest in our sample, as well as the sample in T. Yi et al. (2006), especially the negative lag of the first pulse. Even though there are several pulses with negative lags in other GRBs, it is truly unique to have such a large negative lag in such a short

<footnote n="26">²⁶ https://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 2.** (a) Spectral lag of each pulse of GRB 240715A. (b) Spectral lag of the whole light curve of GRB 240715A. (c) Spectral lags of each pulse for short GRBs from the GBM sample. The bars in different colors represent the lag of different pulses. The left panel shows the negative lags of pulses in GRBs, and the right panel shows the positive lags of pulses in GRBs. (d) The burst duration versus burst lag (in absolute value). The GRB sample is from N. Gehrels et al. (2006), M. G. Bernardini et al. (2015), A. Goldstein et al. (2017), and S. Xiao et al. (2022). (e) The histogram of the lags of the pulses in short GRBs, and the lag of the first pulse of GRB 240715A is labeled. (f) The pulse duration versus the ratio of the pulse lag and pulse duration (in absolute value). The type II GRB sample is from R.-J. Lu et al. (2018).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 3.** Spectrum fitting results. (a) Top panel: the light curve of GRM and the seven slices for the fine time-resolved spectrum were marked with different colors. The following three panels are, respectively, the photon index, $E_{\text{peak}}$, and flux of each slice fitted with GRM plus GBM data. (b) The $E_{\text{p,z}}$ and $E_{\text{iso}}$ correlation diagram. The best fit for type II (gray points) and type I (blue points) GRBs and MGFs (yellow points) are plotted (solid lines) with the $1\sigma$ boundary (dashed line) marked. The red dashed line represents the evolution of the $E_{\text{p,z}}$ and $E_{\text{iso}}$ of GRB 240715A as the redshift changes from 0.001 to 3. The GRB sample is from L. Lan et al. (2023), and the MGF sample is from H.-M. Zhang et al. (2020) and S. Mereghetti et al. (2024). (c) $E_{\text{peak}}$ distribution of short GRBs observed by Fermi/GBM and GRB 240715A. The red bar represents $E_{\text{peak}}$ and the error of GRB 240715A. The $E_{\text{peak}}$ data reference is R.-J. Lu et al. (2017).</figcaption></figure>

duration. As shown in Figure 2(f), the ratio of the lag (absolute value) to the duration of the first pulse in GRB 240715A is close to 0.5, which means that half of the apparent duration of the first pulse is dominated by the delay of the high-energy emission relative to the low-energy emission. Furthermore, it can be seen from Figure 2(f) that in the pulse of short bursts, the shorter the duration, the larger the ratio tends to be.

### 3.3. Spectral Analysis

We use the Pyxspec software (C. Gordon & K. Arnaud 2021) to conduct the spectral analysis. The time-integrated spectrum of the GRB 240715A prompt emission is computed from $T_0+0.18$ to $T_0+0.43$ s and is well fitted by a cutoff power-law (CPL) model with a power-law photon index $\alpha = -0.86 \pm 0.04$ and $E_{\text{peak}} = 2000_{-231}^{+273}$ keV. The $E_{\text{peak}}$ value found for GRB 240715A is on the higher end of the $E_{\text{peak}}$ distribution built from Fermi/GBM short GRBs but still not an outlier (Figure 3(c)). Moreover, since there is no redshift

measurement for GRB 240715A, we plot the rest-frame peak energy $E_{\text{p,z}} - E_{\text{iso}}$ curve at different redshifts ranging from 0.001 to 3 in the Amati relation (L. Amati et al. 2002) diagram (Figure 3(b)). It is worth noting that apart from the traditional type I and Type II GRBs, a third track was recently found for magnetar giant flares (MGFs; J. Yang et al. 2020; H.-M. Zhang et al. 2020; O. J. Roberts et al. 2021; D. Svinkin et al. 2021; S. Mereghetti et al. 2024). We find that GRB 240715A is consistent with type I bursts with redshift in the range of 0.1–3.

For the time-resolved spectrum, we first divide the light curve into three coarse time slices based on the pulse profile, which are denoted as S-I. In order to investigate the evolution of the energy spectrum in detail, we further divide the light curve into seven fine time slices (denoted as S-II). The boundaries of each slice of S-I and S-II are listed in Table 2.

For each slice, we perform a detailed spectral fit with the CPL model; the ratio of Profile-Gaussian likelihood to the degree of freedom (PGSTAT/d.o.f.; G. H. Jacoby &
<table><caption>**Table 2**
The Spectral Results of GRB 240715A</caption><thead><tr><th>t<sub>1</sub><br>(s)</th><th>t<sub>2</sub><br>(s)</th><th>α</th><th>E<sub>peak</sub><br>(keV)</th><th>PGSTAT/d.o.f.</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-weight: bold;">S-I</td></tr><tr><td>0.19</td><td>0.28</td><td>-1.03<sup>+0.04</sup><sub>-0.04</sub></td><td>2949.30<sup>+480.88</sup><sub>-645.05</sub></td><td>240.44/195</td></tr><tr><td>0.28</td><td>0.33</td><td>-0.65<sup>+0.05</sup><sub>-0.05</sub></td><td>2936.46<sup>+304.89</sup><sub>-341.89</sub></td><td>238.66/195</td></tr><tr><td>0.33</td><td>0.39</td><td>-0.60<sup>+0.06</sup><sub>-0.06</sub></td><td>975.37<sup>+87.38</sup><sub>-106.55</sub></td><td>216.45/195</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">S-II</td></tr><tr><td>0.19</td><td>0.23</td><td>-1.49<sup>+0.10</sup><sub>-0.09</sub></td><td>888.87<sup>+237.03</sup><sub>-162.75</sub></td><td>202.32/195</td></tr><tr><td>0.23</td><td>0.26</td><td>-1.12<sup>+0.04</sup><sub>-0.05</sub></td><td>3231.48<sup>+360.93</sup><sub>-557.97</sub></td><td>222.76/195</td></tr><tr><td>0.26</td><td>0.29</td><td>-0.64<sup>+0.07</sup><sub>-0.07</sub></td><td>2608.33<sup>+462.37</sup><sub>-371.52</sub></td><td>227.21/195</td></tr><tr><td>0.29</td><td>0.32</td><td>-0.62<sup>+0.07</sup><sub>-0.08</sub></td><td>2419.90<sup>+404.6</sup><sub>-259.69</sub></td><td>224.59/195</td></tr><tr><td>0.32</td><td>0.34</td><td>-0.55<sup>+0.07</sup><sub>-0.08</sub></td><td>2743.66<sup>+417.35</sup><sub>-318.59</sub></td><td>203.94/195</td></tr><tr><td>0.34</td><td>0.37</td><td>-0.43<sup>+0.09</sup><sub>-0.11</sub></td><td>836.78<sup>+108.52</sup><sub>-90.37</sub></td><td>208.62/195</td></tr><tr><td>0.37</td><td>0.41</td><td>-0.27<sup>+0.28</sup><sub>-0.22</sub></td><td>107.98<sup>+12.9</sup><sub>-11.72</sub></td><td>139.77/195</td></tr></tbody></table>

J. Barnes 1996) is taken into account to test the goodness of fit. The CPL model is expressed as

$$N(E) = A \left(\frac{E}{E_0}\right)^\alpha \exp\left(-\frac{E}{E_c}\right), \qquad (3)$$

where A is the normalization constant (photons · cm⁻² · s⁻¹ · keV⁻¹), α is the power-law photon index, E₀ is the pivot energy fixed at 1 keV, and E_c is the characteristic cutoff energy in keV. The peak energy E_p is related to E_c through E_p = (2 + α)E_c.

The best-fit parameters obtained by the CPL models are listed in Table 2, and the corresponding spectral evolution of the fine time slices is plotted in Figure 3. The evolution of the energy spectrum parameters is relatively strong, and two interesting phenomena are displayed. First, the photon index exhibits a very regular evolution from soft to hard over time and systematically exceeds the synchrotron “death line” (R. D. Preece et al. 1998) defined by α = -2/3 in the time slice of the third pulse, reaching the highest value of ~-0.27. Second, previous studies of time-resolved spectra of simple pulses in GRBs indicate that peak energy displays two prevailing trends: (1) hard-to-soft tracking, which means that the peak energy monotonically decays independently of the flux evolution, and (2) intensity tracking, meaning the peak energy generally follows the trajectory of the flux (L. A. Ford et al. 1995; R. J. Lu et al. 2010; R.-J. Lu et al. 2012). However, in this GRB, Epeak remains basically unchanged after reaching its maximum value in the first pulse and exhibits a “hard-to-soft” spectral evolution pattern in the third pulse.

### 3.4. Possible Photospheric Emission of the Third Pulse

Since the photon index exceeds the “death line” in the third pulse, we study the spectra of the third pulse (0.33–0.39 s) in detail. In addition to the CPL model, we also fit the data with the BAND model, the BAND-Cut model, the combination of CPL and blackbody (expressed as bbodyrad) model, and a quasi-thermal spectral model, namely, the mBB model (S.-J. Hou et al. 2018).

The BAND model is expressed as (D. Band et al. 1993)

$$N(E) = \begin{cases} A \left(\frac{E}{100 \text{ keV}}\right)^\alpha \exp\left(-\frac{E}{E_c}\right), & E < (\alpha - \beta)E_c, \\ A \left[\frac{(\alpha - \beta)E_c}{100 \text{ keV}}\right]^{\alpha - \beta} \exp(\beta - \alpha) \left(\frac{E}{100 \text{ keV}}\right)^\beta, & E \ge (\alpha - \beta)E_c, \end{cases} \qquad (4)$$

where A is the normalization constant (photons · cm⁻² · s⁻¹ · keV⁻¹), α and β are the low-energy and high-energy power-law spectral indices, E_c is the characteristic energy in keV, and the peak energy E_p is related to E_c through E_p = (2 + α)E_c.

The BAND-Cut model is expressed as

$$N(E) = \begin{cases} AE^{\alpha_1} \exp\left(-\frac{E}{E_1}\right), & E < E_b, \\ AE_b^{\alpha_1 - \alpha_2} \exp(\alpha_2 - \alpha_1) E^{\alpha_2} \exp\left(-\frac{E}{E_2}\right), & E \ge E_b, \end{cases} \qquad (5)$$

where A is the normalization constant (photons · cm⁻² · s⁻¹ · keV⁻¹) and α₁ and α₂ represent the spectral indices of the low-energy power-law segment and the medium-energy power-law segment smoothly connected at the break energy E_b = (E₁E₂)/(E₂ - E₁)(α₁ - α₂). The peak energy of the νFν spectrum is defined as E_p = (2 + α₂)E₂, which is located at the high-energy exponential cutoff.

The bbodyrad(BB) model is expressed as

$$N(E) = \frac{1.0344 \times 10^{-3} \times AE^2}{\exp\left(\frac{E}{kT}\right) - 1}, \qquad (6)$$

where A = R<sub>km</sub><sup>2</sup>/D<sub>10</sub><sup>2</sup> is the normalization constant, R<sub>km</sub> is the source radius in kilometers, D<sub>10</sub> is the distance to the source in units of 10 kpc, and kT is the temperature in keV.

The mBB model is expressed as

$$N(E) = \frac{8.0525(m + 1)K}{\left[ \left( \frac{T_{\text{max}}}{T_{\text{min}}} \right)^{m+1} - 1 \right]} \left( \frac{kT_{\text{min}}}{\text{keV}} \right)^{-2} I(E), \qquad (7)$$

where

$$I(E) = \left(\frac{E}{kT_{\text{min}}}\right)^{m-1} \int \frac{E}{kT_{\text{min}}} \frac{x^{2-m}}{e^x - 1} dx, \qquad (8)$$

where x = E/kT, m is the power-law index of the dependence of the luminosity distribution on the temperature, and the temperature ranges from the minimum T<sub>min</sub> to the maximum T<sub>max</sub>.

We comprehensively use the Bayesian information criterion (BIC; G. Schwarz 1978) and the Akaike information criterion (AIC; H. Akaike 1998, 1974) to perform a model comparison. BIC = -2 ln L + k ln N, while AIC = -2 ln L + 2k, where L represents the maximum-likelihood value, k denotes the number of free parameters in the model, and N signifies the number of data points. For each model, BIC and AIC values are calculated. Among the BIC and AIC values calculated for each model, the smallest is determined as BIC<sub>min</sub> and AIC<sub>min</sub>. Models having ΔBIC = BIC-BIC<sub>min</sub> or ΔAIC = AIC-AIC<sub>min</sub> larger than 4 have considerably less support (K. P. Burnham & D. R. Anderson 2004). The best-fit parameters for each model
<table><caption>**Table 3**
Fitting Results of Each Model for the Third Pulse</caption><thead><tr><th>Model</th><th>Parameter</th><th>Parameter</th><th>Parameter</th><th>Parameter</th><th>PGSTAT/d.o.f.</th><th>BIC (ΔBIC)</th><th>AIC (ΔAIC)</th></tr></thead><tbody><tr><td rowspan="2">CPL</td><td>α</td><td>E<sub>peak</sub> (keV)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>-0.60<sup>+0.06</sup><sub>-0.06</sub></td><td>975.37<sup>+87.38</sup><sub>-106.55</sub></td><td></td><td></td><td>216.45/195</td><td>237.62 (3.43)</td><td>224.45 (6.72)</td></tr><tr><td rowspan="2">BAND</td><td>α</td><td>E<sub>peak</sub> (keV)</td><td>β</td><td></td><td></td><td></td><td></td></tr><tr><td>-0.59<sup>+0.07</sup><sub>-0.06</sub></td><td>999.15<sup>+115.18</sup><sub>-105.43</sub></td><td>-5.96<sup>+2.48</sup><sub>-2.74</sub></td><td></td><td>215.72/194</td><td>242.18 (7.99)</td><td>225.72 (7.99)</td></tr><tr><td rowspan="2">BAND-Cut</td><td>α</td><td>E<sub>1</sub> (keV)</td><td>β</td><td>E<sub>2</sub> (keV)</td><td></td><td></td><td></td></tr><tr><td>0.60<sup>+0.19</sup><sub>-0.22</sub></td><td>53.09<sup>+13.65</sup><sub>-11.82</sub></td><td>-0.83<sup>+0.09</sup><sub>-0.07</sub></td><td>1079.93<sup>+205.58</sup><sub>-201.12</sub></td><td>206.55/193</td><td>238.31 (4.12)</td><td>218.55 (0.82)</td></tr><tr><td rowspan="2">CPL+BB</td><td>α</td><td>E<sub>peak</sub> (keV)</td><td>kT (keV)</td><td></td><td></td><td></td><td></td></tr><tr><td>-0.47<sup>+0.11</sup><sub>-0.11</sub></td><td>1060.64<sup>+158.23</sup><sub>-112.07</sub></td><td>23.14<sup>+5.83</sup><sub>-7.43</sub></td><td></td><td>208.76/193</td><td>240.52 (6.33)</td><td>220.76 (3.03)</td></tr><tr><td rowspan="2">mBB</td><td>m</td><td>kT<sub>min</sub> (keV)</td><td>kT<sub>max</sub> (keV)</td><td></td><td></td><td></td><td></td></tr><tr><td>0.03<sup>+0.09</sup><sub>-0.10</sub></td><td>12.67<sup>+2.36</sup><sub>-2.41</sub></td><td>546.31<sup>+95.30</sup><sub>-68.14</sub></td><td></td><td>207.73/194</td><td>234.19 (-)</td><td>217.73 (-)</td></tr><tr><td rowspan="2">Synchrotron</td><td>B(G)</td><td>p</td><td>γ<sub>cool</sub> (10<sup>6</sup>keV)</td><td></td><td></td><td></td><td></td></tr><tr><td>1445.05<sup>+165.02</sup><sub>-173.81</sub></td><td>5.17<sup>+0.66</sup><sub>-1.28</sub></td><td>5.44<sup>+0.18</sup><sub>-0.09</sub></td><td></td><td>341.77/194</td><td>362.93 (128.74)</td><td>351.77 (134.04)</td></tr></tbody></table>

are listed in Table 3, and Figure 4 shows the fitting results and goodness of fit of each model. Combined with the energy spectrum fitting results, we found that the following facts can explain that the energy spectrum of the third pulse could be photospheric emission rather than synchrotron radiation.

1. The high-energy photon index of the BAND model is ~-6, indicating that the high-energy segment of the spectrum is actually a cutoff rather than a power-law extension.

2. The BAND model and the CPL model have the same low-energy photon indices, which both exceed the “death line,” and the same $E_{\text{peak}}$. The residual of the low-energy segment in the BAND model has a structure (Figure 4(a)) below 50 keV, which indicates a break is needed at the low-energy segment. Moreover, the ΔAIC of the CPL model is larger than 6, and both the ΔAIC and ΔBIC of the BAND model are larger than 6 compared to the mBB model, indicating these two models are not the best.

3. With BAND-Cut model, the structure of the residuals at low energy disappears because the low-energy break is introduced (Figure 4(b)). Between the low-energy photon index and the high-energy cutoff, the BAND-Cut model has a middle-energy photon index of ~-0.8. The mBB model can also fit well. The mBB model and the BAND-Cut model have the same low-energy break and high-energy cutoff (Figure 4(c)), and the ΔAIC and ΔBIC between these two models are relatively small. However, the low-energy photon index of the BAND-Cut model is ~+0.6, corresponding to the $F\nu$ spectrum index ~+1.6, which is consistent with the index of a blackbody spectrum with Rayleigh-Jeans approximation in the low-energy segment. Moreover, BAND-Cut is a semiempirical phenomenological model, so it is more appropriate to describe data with the mBB model, which has physical meaning. In addition, the CPL+BB model also fits the data well, but it gives a relatively large

ΔBIC and ΔAIC, so the mBB model should be chosen instead of the CPL+BB model.

4. Since the third pulse is a well-shaped single pulse, indicating that its emission originates from a single dissipation process, it can be directly fitted with the physical model of synchrotron radiation to determine whether it is synchrotron radiation or not. We use a parametric synchrotron model, which has been developed and packaged as a Python package by J. M. Burgess et al. (2020), to do the fit. The cool synchrotron photon spectrum of this model is in the form

$$N(E) = (E; K, B, p, \gamma_{\text{cool}}, \gamma_{\text{inj}}, \gamma_{\text{max}}), \quad (9)$$

where K is the arbitrary normalization constant of flux, B is the magnetic field strength (unit: Gauss), p is the electron injection index, $\gamma_{\text{cool}}$ is the energy of electron cooling during the synchrotron cooling time, $\gamma_{\text{inj}}$ is the electron injection energy, and $\gamma_{\text{max}}$ is the maximum electron energy. The units of the latter three parameters are keV. We choose to fix $\gamma_{\text{inj}} = 10^5$ and $\gamma_{\text{max}} = 10^8$, as the former has a strong degeneracy with B and the latter does not affect the spectrum shape and is usually fixed in the code. The detailed description can be referred to J. M. Burgess et al. (2020) and J.-M. Chen et al. (2021). The fitting results of the synchrotron model are poor (Figure 4(d)). (1) Due to the limitation of the “death line,” the $F\nu$ spectrum index close to 2 at the low-energy segment cannot be described by synchrotron model. Although the index of 2 can be given by synchronous self-absorption, it generally appears in the optical and near-IR band rather than the X-ray energy band. (2) The electron index p is too large to be a realistic value. The $(p - 1)/2$ in the $F\nu$ spectrum is essentially the predicted spectral index of the synchrotron radiation spectrum in the energy segment between the “death line” at the low-energy segment and the cutoff at the high-
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 4.** Spectral fitting results and “death line” of the photosphere of the third pulse. (a)–(d) The observed photon count spectrum and $F\nu$ energy spectrum of the BAND model, BAND-Cut model, mBB model, and synchrotron model, respectively. (e) The corner plot of the posterior probability distributions of the parameters of the mBB model. (f) The so-called “photosphere death line” constraints. The red line is for a strict blackbody, and the blue line is for a relativistic mBB outflow. The red dashed line represents the rest-frame peak energy $E_{\text{p,z}}$ and the observed isotropic $\gamma$-ray luminosity $L_{\text{iso}}$ of the third pulse as the redshift varies.</figcaption></figure>

energy segment, where a large *p* indicates that the model directly fits the high-energy cutoff and cannot describe the middle-energy photon index ~-0.8. In the

$F\nu$ spectrum of the BAND-Cut model, the low-energy spectrum index is ~+1.6, and the middle-energy spectrum index is ~+0.2. In fact, neither the fast cooling
model nor the slow cooling model can give the prediction that the $F_ν$ spectrum will continue to rise after the low-energy “death line” segment, which proves that the synchrotron radiation physical model cannot describe the observed data, not to mention it gives the largest $\Delta$BIC and $\Delta$AIC.

In summary, we believe that the best model of the third pulse is the mBB model, which indicates that the third pulse could be interpreted as matter-dominated photospheric emission. Further, we investigated whether the fitting results exceeded the so-called “photosphere death line” constraints. As discussed in B. Zhang et al. (2012), the photospheric emission model has an upper limit for the peak energy of a GRB defined by

$$E_p \le \zeta kT_0 \approx 1.2 \text{MeV} \zeta L_{52}^{1/4} R_{0.7}^{-1/2}, \quad (10)$$

where $L_{52}$ is the luminosity in units of $10^{52}$ erg s$^{-1}$, $R_0$ is the initial fireball radius in units of $10^7$ cm, and the factor $\zeta$ is taken as 3.92 for a strict blackbody and 2.82 for a relativistic mBB outflow. Figure 4(f) shows the $E_{p,z} - L_{iso}$ curve for the third pulse of different redshifts, where $R_0$ is taken as a typical value of $10^7$ cm for photospheric emission. In the redshift range from 0.03 to 0.4, $E_{p,z}$ does not exceed the “photosphere death line,” which further indicates that photospheric emission cannot be ruled out.

# 4. Discussion

## 4.1. The Reason for the Negative Lag in the First Pulse

In previous studies, there were few observations of negative lags. The observed negative lags were very small—most of them were consistent with zero within the error—and some authors even thought that there should be no significant negative lag (R. J. Lu et al. 2006; P. Y. Minaev et al. 2014). Therefore, the intrinsic mechanism of negative lags has barely been considered. In GRB 240715A, due to the presence of a well-shaped pulse with significant negative lag, the intrinsic mechanism of the soft-to-hard evolution of the energy spectrum needs to be formally investigated.

As interpreted in R.-J. Lu et al. (2018), the temporal evolution of $E_{peak}$ can phenomenologically explain the result of spectral lag, which is actually the shift of the peak intensity of the light curve and the peak time of the peak energy. However, such an interpretation cannot explain the negative lag of the first pulse of GRB 240715A because the energy bands where negative lag occurs are much lower than the $E_{peak}$ of this pulse (Figure 2(a)), which means that the evolution of $E_{peak}$ has no significant influence on the negative lag of the first pulse. This is inconsistent with previous work in which $E_{peak}$ evolution leads to the lag (B. Wu & E. Fenimore 2000; D. Kocevski & E. Liang 2003; F. Ryde 2005; Z. Y. Peng et al. 2011; R.-J. Lu et al. 2018) and provides a new alternative perspective on the emergence of lag: the evolution of the low-energy spectral index $\alpha$ can also lead to the generation of lag (M. Hafizi & R. Mochkovitch 2007; G. Ghirlanda et al. 2009; R. Mochkovitch et al. 2016). Specifically, for GRB 240715A, as the low-energy spectral index $\alpha$ hardens with time (Figure 3(a)), more high-energy photons arrive later, causing the observed negative lag of the first pulse. To illustrate this assumption, we perform a simple but validated simulation and find out that in addition to $E_{peak}$, the evolution of $\alpha$ alone can

also lead to negative lag (Figure B1; see Appendix B for details).

One of the possible intrinsic mechanisms of $\alpha$ evolving from soft to hard is the cooling of electrons in the decaying magnetic field (Z. L. Uhm & B. Zhang 2014). In an expanding jet such as GRBs, it is natural for magnetic field strength to decrease globally as the radius increases. In such a decaying magnetic field, the early injected electrons experience a stronger cooling effect due to the stronger magnetic field and have a wider distribution, whereas the later injected electrons have a narrower distribution due to a weaker cooling effect in the weaker magnetic field, resulting in a hardening of the energy spectrum index, thus plausibly explaining the observed negative lag.

## 4.2. Possible Photospheric Emission in the Third Pulse

In previous analyses, it can be seen that in GRB 240715A, synchrotron radiation appears before photospheric radiation, which is very difficult to understand. It is very rare to observe the transition between the thermal component and the nonthermal component in a single GRB. A representative event is GRB 160625B, which is the opposite case of GRB 240715A (B. B. Zhang et al. 2018a). In GRB 160625B, the transition from photosphere to synchrotron radiation between well-separated emission episodes within a single GRB was observed. Generally speaking, a matter-dominated fireball produces the photospheric emission before the Poynting-flux-dominated outflow is launched. Because the wind escaping the photosphere travels more slowly than light, the emission from the colliding shells would lag behind the photosphere radiation.

A similar situation to GRB 240715A occurs in GRB 170817A. The tail emission after the main pulse of GRB 170817A can be fitted by a blackbody model (A. Goldstein et al. 2017; B. B. Zhang et al. 2018b). It is explained as a nearly isotropic component from photospheric emission from a cocoon. However, unlike the third pulse of GRB 240715A, the tail of GRB 170817A is very weak and not a well-shaped pulse. Most importantly, the radiation of the cocoon is isotropic, observed at a large viewing angle, whereas such a high $E_{peak}$ of the third pulse in GRB 240715A indicates that it is obviously generated by a relativistic jet observed at a small viewing angle and therefore is unlikely to be produced by the cocoon.

From the above discussion, it can be seen that it is very difficult to explain the quasi-thermal radiation in the third pulse of GRB 240715A. A plausible assumption is that different pulses correspond to different episodes of central engine activity. It is possible that the engine is initially magnetized but later becomes matter-dominated. After the magnetized central engine generates synchrotron radiation, it immediately becomes matter-dominated and produces a relativistic structured nondissipative outflow with a large opening angle. For this wide outflow observed at a viewing angle much smaller than the opening angle, an mBB spectrum can be observed (C. Lundman et al. 2013). Under such an assumption, the time interval between the activities of the central engine should be very short, and the photospheric emission is produced immediately after the synchrotron radiation; thus, the time interval between the observed two pulses can be very short, and even the photons of the two radiation components overlap with each other. Meanwhile, because the magnetic field is dissipated to a relatively weak
level during the generation of synchrotron radiation in the first pulse, it is difficult to produce synchrotron radiation even if electrons are accelerated in the later jet. As a result, only clean photospheric emission is observed.

## 5. Summary

GRB 240715A is the first short GRB detected by SVOM/GRM in flight. It has three pulses in the prompt emission, with different pulses having their own interesting properties. In this study, we comprehensively analyzed the characteristics of these pulses and found enlightening phenomena that reveal intrinsic mechanisms that are different from those in previous studies.

Observationally, the first and third pulses of GRB 240715A exhibit opposite evolution of spectral lag, which means the first pulse shows negative lag while the third pulse shows positive lag. The negative lag of the first pulse is relatively large, being an outlier in short GRB samples, and the lag itself accounts for about half of the pulse duration.

Through spectral analysis, we found that the negative lag of the first pulse is caused by the evolution of the spectral index and is irrelevant to $E_{\text{peak}}$. One possible intrinsic mechanism is the electron cooling in the decaying magnetic field, which leads to the continuous hardening of the spectrum index and results in negative lag (Z. L. Uhm & B. Zhang 2014). However, to fully understand the intrinsic mechanism, more detailed calculations or the proposal of new models are still required.

The spectral analysis also shows that the third pulse is more likely to be described by a quasi-thermal spectrum, which indicates the existence of photospheric emission. It is difficult to explain why photospheric emission appears after synchrotron radiation in a single GRB. Among many assumptions, a possible one is that after the magnetized central engine generates synchrotron radiation, it immediately becomes matter-dominated and produces a relativistic structured outflow with a large opening angle. For this wide jet observed at a

viewing angle much smaller than the opening angle, an mBB spectrum can be observed. This is just a simple assumption, and a more persuasive model requires more profound theoretical research. Future joint observation from ECLAIRs and GRM for more samples would better depict the low-energy spectral shape of GRBs systematically, which is also one clear asset of SVOM compared to current GRB missions (M. G. Bernardini et al. 2017).

Based on its outstanding performance and rapid multi-wavelength follow-up capabilities, SVOM will provide more comprehensive and precise measurements for such GRBs with novel and unique characteristics. The SVOM mission will fully explore the scientific potential of transient astrophysical phenomena and play a crucial role in time-domain and multimessenger astronomy.

## Acknowledgments

The Space-based multiband Variable Objects Monitor (SVOM) is a joint Chinese-French mission led by the Chinese National Space Administration (CNSA), the French Space Agency (CNES), and the Chinese Academy of Sciences (CAS). We gratefully acknowledge the unwavering support of NSSC, IAMCAS, XIOPM, NAOC, IHEP, CNES, CEA, and CNRS.

This study is supported by the National Key R&D Program of China (2024YFA1611703). This work is supported by the National Natural Science Foundation of China (12273042, 12494572), the SVOM project (a mission under the Strategic Priority Program on Space Science of the Chinese Academy of Sciences), the Strategic Priority Research Program of the Chinese Academy of Sciences (grant Nos. XDA30050000, XDB0550300) and the National Key R&D Program of China (2021YFA0718500). We appreciate the public data and software of Fermi/GBM. We appreciate the software GECAMTools-v20240514 provided by Peng Zhang.
## Appendix A
### Pulse Lag Sample

The pulse width and pulse lag of each short GRB in the GBM sample is listed in Table A1.

<table><caption>Table A1
The Lag and Width of Pulses of Short GRBs</caption><thead><tr><th>GRB</th><th>Pulse Width (ms)</th><th>Lag (ms)</th><th>GRB</th><th>Pulse Width (ms)</th><th>Lag (ms)</th></tr></thead><tbody><tr><td>bn130504314</td><td>97.44 ± 40.20</td><td>3.00<sup>+8.00</sup><sub>-12.00</sub></td><td>bn150922234</td><td>37.24 ± 16.57</td><td>2.00<sup>+5.00</sup><sub>-6.00</sub></td></tr><tr><td>bn130504314</td><td>166.15 ± 61.32</td><td>3.00<sup>+5.00</sup><sub>-11.00</sub></td><td>bn150922234</td><td>47.10 ± 40.60</td><td>1.00<sup>+1.00</sup><sub>-5.00</sub></td></tr><tr><td>bn130912358</td><td>52.66 ± 28.71</td><td>-6.50<sup>+8.00</sup><sub>-11.50</sub></td><td>bn150922234</td><td>44.06 ± 15.72</td><td>0.00<sup>+5.00</sup><sub>-3.00</sub></td></tr><tr><td>bn130912358</td><td>74.47 ± 43.85</td><td>-1.50<sup>+21.00</sup><sub>-10.50</sub></td><td>bn160726065</td><td>37.24 ± 16.57</td><td>-6.00<sup>+5.00</sup><sub>-5.00</sub></td></tr><tr><td>bn141011282</td><td>13.93 ± 9.08</td><td>-1.00<sup>+0.00</sup><sub>-3.00</sub></td><td>bn160726065</td><td>139.32 ± 74.12</td><td>-4.00<sup>+8.00</sup><sub>-3.00</sub></td></tr><tr><td>bn141011282</td><td>33.30 ± 14.82</td><td>-4.00<sup>+4.00</sup><sub>-7.00</sub></td><td>bn170206453</td><td>235.50 ± 165.75</td><td>1.00<sup>+2.50</sup><sub>-3.50</sub></td></tr><tr><td>bn180402406</td><td>91.21 ± 49.72</td><td>4.00<sup>+8.00</sup><sub>-10.00</sub></td><td>bn170206453</td><td>372.36 ± 234.40</td><td>0.50<sup>+5.50</sup><sub>-2.50</sub></td></tr><tr><td>bn180402406</td><td>37.24 ± 16.57</td><td>1.00<sup>+9.00</sup><sub>-7.00</sub></td><td>bn170206453</td><td>139.32 ± 74.12</td><td>6.50<sup>+7.00</sup><sub>-4.00</sub></td></tr><tr><td>bn180703949</td><td>235.50 ± 74.12</td><td>15.00<sup>+19.00</sup><sub>-21.00</sub></td><td>bn191227723</td><td>33.30 ± 9.08</td><td>0.00<sup>+3.00</sup><sub>-1.50</sub></td></tr><tr><td>bn180703949</td><td>407.90 ± 90.78</td><td>13.00<sup>+13.00</sup><sub>-18.00</sub></td><td>bn191227723</td><td>37.24 ± 7.41</td><td>0.00<sup>+1.00</sup><sub>-4.00</sub></td></tr><tr><td>bn180728882</td><td>33.30 ± 16.57</td><td>9.00<sup>+13.00</sup><sub>-9.00</sub></td><td>bn191227723</td><td>44.06 ± 28.71</td><td>-3.00<sup>+3.00</sup><sub>-2.00</sub></td></tr><tr><td>bn180728882</td><td>166.52 ± 74.12</td><td>2.00<sup>+39.00</sup><sub>-15.00</sub></td><td>bn230418883</td><td>52.66 ± 40.60</td><td>-2.00<sup>+1.00</sup><sub>-3.00</sub></td></tr><tr><td>bn200219317</td><td>210.64 ± 104.83</td><td>0.00<sup>+18.00</sup><sub>-16.00</sub></td><td>bn230418883</td><td>52.66 ± 28.71</td><td>3.00<sup>+5.00</sup><sub>-6.00</sub></td></tr><tr><td>bn200219317</td><td>166.52 ± 74.12</td><td>5.00<sup>+7.00</sup><sub>-19.00</sub></td><td>bn230418883</td><td>74.47 ± 37.06</td><td>0.00<sup>+5.00</sup><sub>-4.00</sub></td></tr><tr><td>bn200605762</td><td>105.32 ± 40.60</td><td>0.00<sup>+10.00</sup><sub>-17.00</sub></td><td>bn240821775</td><td>105.32 ± 52.41</td><td>2.00<sup>+8.00</sup><sub>-2.00</sub></td></tr><tr><td>bn200605762</td><td>91.21 ± 33.15</td><td>7.00<sup>+16.00</sup><sub>-10.00</sub></td><td>bn240821775</td><td>117.75 ± 43.85</td><td>10.00<sup>+15.00</sup><sub>-8.00</sub></td></tr><tr><td>bn211124104</td><td>47.10 ± 23.44</td><td>-1.50<sup>+6.50</sup><sub>-3.00</sub></td><td>bn240821775</td><td>128.99 ± 52.41</td><td>9.00<sup>+13.00</sup><sub>-13.00</sub></td></tr><tr><td>bn211124104</td><td>117.75 ± 74.12</td><td>-3.00<sup>+4.00</sup><sub>-15.00</sub></td><td>bn121127914</td><td>123.41 ± 51.96</td><td>-7.00<sup>+24.00</sup><sub>-19.00</sub></td></tr><tr><td>bn221022612</td><td>33.30 ± 12.84</td><td>1.50<sup>+5.00</sup><sub>-5.00</sub></td><td>bn130628860</td><td>33.30 ± 14.82</td><td>-3.00<sup>+4.00</sup><sub>-4.00</sub></td></tr><tr><td>bn221022612</td><td>16.65 ± 12.84</td><td>0.50<sup>+4.50</sup><sub>-5.50</sub></td><td>bn130628860</td><td>44.06 ± 28.71</td><td>-1.00<sup>+8.00</sup><sub>-12.00</sub></td></tr><tr><td>bn230906538</td><td>28.84 ± 14.82</td><td>-2.50<sup>+3.00</sup><sub>-5.00</sub></td><td>bn140209313</td><td>372.36 ± 74.12</td><td>16.00<sup>+15.00</sup><sub>-15.00</sub></td></tr><tr><td>bn230906538</td><td>74.47 ± 28.71</td><td>-5.00<sup>+3.00</sup><sub>-5.00</sub></td><td>bn160822672</td><td>20.77 ± 5.70</td><td>-1.00<sup>+1.00</sup><sub>-2.00</sub></td></tr><tr><td>bn231205101</td><td>72.54 ± 33.15</td><td>6.00<sup>+4.00</sup><sub>-13.00</sub></td><td>bn170708046</td><td>45.26 ± 21.43</td><td>4.00<sup>+6.00</sup><sub>-5.00</sub></td></tr><tr><td>bn231205101</td><td>113.77 ± 49.72</td><td>2.00<sup>+7.00</sup><sub>-11.00</sub></td><td>bn171108656</td><td>20.84 ± 7.46</td><td>2.00<sup>+1.00</sup><sub>-3.00</sub></td></tr><tr><td>bn240810880</td><td>74.47 ± 33.15</td><td>0.50<sup>+5.50</sup><sub>-20.00</sub></td><td>bn190427190</td><td>24.60 ± 12.93</td><td>-2.00<sup>+2.00</sup><sub>-4.00</sub></td></tr><tr><td>bn240810880</td><td>235.50 ± 90.78</td><td>13.00<sup>+19.50</sup><sub>-24.50</sub></td><td>bn201227635</td><td>47.85 ± 17.36</td><td>1.00<sup>+3.00</sup><sub>-4.00</sub></td></tr><tr><td>bn130416770</td><td>13.93 ± 7.41</td><td>0.00<sup>+4.00</sup><sub>-4.00</sub></td><td>bn230116374</td><td>56.24 ± 19.00</td><td>-1.00<sup>+4.00</sup><sub>-8.00</sub></td></tr><tr><td>bn130416770</td><td>15.80 ± 7.41</td><td>1.00<sup>+5.00</sup><sub>-2.00</sub></td><td>bn230525449</td><td>17.43 ± 7.38</td><td>1.00<sup>+1.00</sup><sub>-1.00</sub></td></tr><tr><td>bn130416770</td><td>23.55 ± 14.82</td><td>3.00<sup>+3.00</sup><sub>-6.00</sub></td><td>bn240615744</td><td>39.82 ± 14.46</td><td>3.00<sup>+4.00</sup><sub>-4.00</sub></td></tr><tr><td></td><td></td><td></td><td>bn240625314</td><td>61.43 ± 22.14</td><td>17.00<sup>+2.00</sup><sub>-7.00</sub></td></tr></tbody></table>
## Appendix B
Simulation of the Lag Generation

We take the form of the photon flux density $N(t, E)$ observed at a given time $t$ and photon energy $E$ as

$$N(E, t) = I(t) * \phi(E, t), \qquad (B1)$$

where $I(t)$ and $\phi(E, t)$ are the intensity and normalized photon spectrum, respectively. We first take $I(t)$ as the same Gaussian profile as the first pulse in GRB 240715A:

$$I(t) = A * \exp\left[-\frac{(t - \mu)^2}{\sigma}\right]. \qquad (B2)$$

Then we take $I(t)$ as the FRED profile (J. P. Norris et al. 2005) for generalization,

$$I(t) = \frac{A^* \lambda}{\exp\left(\frac{\tau_r}{t} + \frac{t}{\tau_d}\right)}, \qquad (B3)$$

where $\lambda = \exp(2\mu)$, $\mu = \sqrt{\tau_r/\tau_d}$, and $\tau_r$ and $\tau_d$ are the rising and decaying timescales, respectively. For the Gaussian case, we take $\phi(E, t)$ as the CPL model in order to be consistent with the observation. For the FRED case, we take $\phi(E, t)$ as the BAND function (D. Band et al. 1993) with its high-energy photon index $\beta$ fixed to -2. $E_{\text{peak}}$ is fixed to 3000 keV for both spectrum models. For the low-energy photon index, $\alpha$, we take it as a linear evolution over time from soft to hard, just consistent with the spectral result in Section 3.3, i.e.,

$$\alpha(t) = \alpha_0 + k_{\alpha}(t - t_0), \qquad k_{\alpha} > 0. \qquad (B4)$$

In order to avoid the influence of $E_{\text{peak}}$ and only investigate the influence of the evolution of $\alpha$ of the spectrum, five energy bands the same as those used to calculate lag from 30 to 2000 keV are chosen to calculate the light curves. The simulated light curves are displayed in Figure B1 for the Gaussian and FRED cases. In the Gaussian case, the simulation results are quite consistent with the observations within the error (Figure B1, Panel B).

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /><figcaption>**Figure B1.** Simulation of the lag generation. (a) Simulated Gaussian light curves in different energy bands along with $\alpha$ evolve from soft to hard. The parameters of $A = 60$, $\mu = 0.25$, $\sigma = 0.001$, $\alpha_0 = -1.5$, $k_\alpha = 7.3$, and $t_0 = 0.19$ s are adopted to be consistent with the observations. (b) The lag versus energy of the simulated Gaussian light curves. (c) Simulated FRED light curves in different energy bands along with $\alpha$ evolve from soft to hard. The parameters of $A = 60$, $\tau_r = 0.2$, $\tau_d = 0.5$, $\alpha_0 = -1.5$, $k_\alpha = 0.2$, and $t_0 = 0$ are adopted. (d) The lag versus energy of the simulated Gaussian light curves.</figcaption></figure>
ORCID iDs

Wen-Jun Tan https://orcid.org/0009-0006-5506-5970

Chen-Wei Wang https://orcid.org/0009-0008-8053-2985

Shao-Lin Xiong https://orcid.org/0000-0002-4771-7653

Jiang He https://orcid.org/0000-0003-4856-5783

Shu-Xu Yi https://orcid.org/0000-0001-7599-0174

Bing Li https://orcid.org/0000-0002-0238-834X

He Gao https://orcid.org/0000-0002-3100-6558

Bo-bing Wu https://orcid.org/0000-0001-6650-3776

Bing Zhang https://orcid.org/0000-0002-9725-2524

Maria-Grazia Bernardini https://orcid.org/0000-0001-6106-3046

Bin-Bin Zhang https://orcid.org/0000-0003-4111-5958

Stéphane Basa https://orcid.org/0000-0002-4291-333X

Xu-Hui Han https://orcid.org/0000-0002-6107-0147

Hua-Li Li https://orcid.org/0000-0002-7457-4192

Pierre Maggi https://orcid.org/0000-0001-5612-5185

Frédéric Piron https://orcid.org/0000-0001-6885-7156

Li-Ming Song https://orcid.org/0000-0003-0274-3396

Susanna Vergani https://orcid.org/0000-0001-9398-4907

Ping Wang https://orcid.org/0000-0003-0466-2223

Li-Ping Xin https://orcid.org/0000-0002-9422-3437

Yang Xu https://orcid.org/0000-0002-8694-4672

Shuang-Nan Zhang https://orcid.org/0000-0001-5586-1017

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