We obtain a type of Ayón-Beato-García (ABG) related black hole solutions with five parameters: the mass $m$, the charge $q$, and three dimensionless parameters $\alpha$, $\beta$ and $\gamma$ associated with nonlinear electrodynamics. We find that this type of black hole is regular under the conditions: $\alpha \gamma \ge 6$, $\beta \gamma \ge 8$, and $\gamma >0$. Here we focus on the saturated case: $\alpha =6/\gamma$ and $\beta =8/\gamma$, such that only three parameters $m$, $q$ and $\gamma$ remain, which leads to a new family of ABG black holes. For such a family of black holes, we investigate the influence of the charge $q$ and the parameter $\gamma$ on the horizon radius and the Hawking temperature. In addition, we calculate the quasinormal mode frequencies of massless scalar field perturbations by using the sixth-order WKB approximation method and the unstable circular null geodesic method in the eikonal limit. On the one hand, our results show that the increase of the charge $q$ makes the scalar waves decay faster at first and then slowly except for the case of $\gamma =2$. On the other hand, they show that the increase of the parameter $\gamma$ makes the scalar waves decay at first sharply and then slowly. In particular, $\gamma =1$ can be regarded as the critical value for the transition from an unstable configuration to a stable one. Finally, we compute the shadow radius for the new family of ABG black holes and use the shadow data of the $M87^{*}$ black hole detected by the Event Horizon Telescope to provide an upper limit on the charge $q$ of the new black holes. We find that the increase of the charge $q$ makes the shadow radius decrease monotonically, while the increase of the parameter $\gamma$ makes the shadow radius increase at first rapidly and then almost remain unchanged, especially the parameter $\gamma$ has a significant impact on the shadow radius when it is less than one. Moreover, using the shadow data of the $M87^{*}$ black hole, we find that the upper limit of the charge $q$ increases rapidly at first and then slowly but does not exceed the mass of the $M87^{*}$ black hole at last when the parameter $\gamma$ is increasing and going to infinity, and that the data restrict the frequency range of the fundamental mode with $l=1$ to $1.4\times {10}^{-6}\mathrm{Hz}\sim 1.9\times {10}^{-6}\mathrm{Hz}$.

中文翻译：

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一个新的 Ayón-Beato-García 黑洞家族的准正规模式和阴影

我们获得了一种具有五个参数的 Ayón-Beato-García (ABG) 相关黑洞解：质量 $米$， 费用 $q$, 和三个无量纲参数 $\alpha$, $\beta$ 和 $\gamma$与非线性电动力学有关。我们发现这种类型的黑洞在以下条件下是有规律的：$\alpha \gamma \ge 6$, $\beta \gamma \ge 8$， 和 $\gamma >0$. 这里我们关注饱和情况：$\alpha =6/\gamma$ 和 $\beta =8/\gamma$, 这样只有三个参数 $米$, $q$ 和 $\gamma$仍然存在，这导致了一个新的 ABG 黑洞家族。对于这样一个黑洞家族，我们调查电荷的影响$q$ 和参数 $\gamma$地平线半径和霍金温度。此外，我们利用六阶WKB近似方法和eikonal极限中的不稳定圆零测地线方法计算了无质量标量场扰动的准正规模频率。一方面，我们的结果表明，电荷的增加$q$ 使标量波先衰减快，然后慢慢衰减，除了 $\gamma =2$. 另一方面，他们表明参数的增加$\gamma$使标量波先急剧衰减，然后缓慢衰减。特别是，$\gamma =1$可以看作是从不稳定构型过渡到稳定构型的临界值。最后，我们计算新的 ABG 黑洞家族的阴影半径，并使用$米87^{*}$ 事件视界望远镜探测到的黑洞以提供电荷的上限 $q$的新黑洞。我们发现电荷的增加$q$ 使阴影半径单调减小，而参数的增加 $\gamma$ 使阴影半径先快速增加，然后几乎保持不变，尤其是参数 $\gamma$小于 1 时对阴影半径有显着影响。此外，使用阴影数据$米87^{*}$ 黑洞，我们发现电荷的上限 $q$ 开始迅速增加然后缓慢但不超过质量 $米87^{*}$ 黑洞最后当参数 $\gamma$ 增加并趋于无穷大，并且数据限制了基模的频率范围 $升=1$ 至 $1.4\times {10}^{-6}\mathrm{赫兹}～1.9\times {10}^{-6}\mathrm{赫兹}$.