Rapid planetary rotation can cause the equilibrium shape of a planet to be oblate. While planetary oblateness has mostly been probed by examining the subtle ingress and egress features in photometric transit light curves, we investigate the effect of oblateness on the spectroscopic Rossiter-McLaughlin (RM) signals. We found that a giant planet, with planet-to-star radius ratio of 0.15 and Saturn-like oblateness of 0.098, can cause spectroscopic signatures with amplitudes up to 1.1 ms$^{-1}$ which is detectable by high-precision spectrographs such as ESPRESSO. We also found that the spectroscopic oblateness signals are particularly amplified for transits across rapidly rotating stars and for planets with spin-orbit misalignment thereby making them more prominent than the photometric signals at some transit orientations. We compared the detectability of oblateness in photometry and spectroscopy and found that photometric light curves are more sensitive to detecting oblateness than the spectroscopic RM signals mostly because they can be sampled with higher cadence to better probe the oblateness ingress and egress anomaly. However, joint analyses of the light curve and RM signal of a transiting planet provides more accurate and precise estimate of the planet's oblateness. Therefore, ESPRESSO alongside ongoing and upcoming photometric instruments such as TESS, CHEOPS, PLATO and JWST will be extremely useful in measuring planet oblateness.

中文翻译：

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用光度学和光谱学限制凌日行星的扁率

行星的快速自转会导致行星的平衡形状为扁圆形。虽然行星扁率主要是通过检查光度传输光曲线中微妙的入口和出口特征来探测的，但我们研究了扁率对光谱 Rossiter-McLaughlin (RM) 信号的影响。我们发现，一颗行星与恒星的半径比为 0.15，类土星的扁圆度为 0.098 的巨行星可以产生振幅高达 1.1 ms$^{-1}$ 的光谱特征，这可以被高精度光谱仪检测到比如浓缩咖啡。我们还发现，光谱扁率信号对于快速旋转的恒星和具有自旋轨道未对准的行星的凌日特别放大，从而使它们比某些凌日方向的光度信号更突出。我们比较了光度学和光谱学中扁圆度的可检测性，发现光度光曲线对扁度检测比光谱 RM 信号更敏感，主要是因为它们可以以更高的节奏采样，以更好地探测扁度入口和出口异常。然而，对凌日行星的光变曲线和 RM 信号的联合分析提供了对行星扁率的更准确和精确的估计。因此，ESPRESSO 与正在进行和即将推出的光度测量仪器（如 TESS、CHEOPS、PLATO 和 JWST）在测量行星扁率方面将非常有用。