$β$ Pic b和$β$ Pic c的精确动力学质量和轨道拟合
Precise Dynamical Masses and Orbital Fits for $β$ Pic b and $β$ Pic c
摘要：
我们提出了一个全面的轨道分析的系外行星$β$ Picnic b和c，解决了以前报道的张力之间的动力学和演化质量的限制$β$ Picnic b。我们使用MCMC轨道代码orvara来拟合15年的径向速度和相对天体测量（包括最近的重力测量），来自依巴谷和盖亚的绝对天体测量，以及$β$ Pic A和b之间的单个相对径向速度测量。我们测量了$β$ Pic b的$9.3^{+2.6}_{-2.5}\, M_{\rm Jup}$和$β$ Pic c的$8.3\pm 1.0\,M_{\rm Jup}$的模型无关质量。这些质量对于输入数据选择的适度变化是鲁棒的。我们发现$β$ Pic b的$0.119 \pm 0.008$的偏心率受到很好的约束，而$β$ Pic c的偏心率为$0.21^{+0.16}_{-0.09}$，两个轨道平面在$\sim$ 0.5 $^\circ$内对齐。这两颗行星的质量都在热启动演化模型预测的$\sim$ 1 $σ$范围内，不包括冷启动。我们验证了我们的方法$N$体合成数据集成使用REBOUND。我们表明，orvara可以占三体效应的$β$ PIC系统下降到一个水平$\sim$ 5倍小于重力的不确定性。系统的质量和轨道参数从orvara的近似治疗的多行星轨道是一个因素的$\sim$ 5小于我们在这里得到的不确定性。未来的重力观测将改善对$β$ Pic c质量和（特别是）偏心率的限制，但改善对$β$ Pic b质量的限制可能需要数年的额外RV监测和未来盖亚数据发布的更高精度。
英文摘要：
We present a comprehensive orbital analysis to the exoplanets $β$ Pictoris b and c that resolves previously reported tensions between the dynamical and evolutionary mass constraints on $β$ Pic b. We use the MCMC orbit code orvara to fit fifteen years of radial velocities and relative astrometry (including recent GRAVITY measurements), absolute astrometry from Hipparcos and Gaia, and a single relative radial velocity measurement between $β$ Pic A and b. We measure model-independent masses of $9.3^{+2.6}_{-2.5}\, M_{\rm Jup}$ for $β$ Pic b and $8.3\pm 1.0\,M_{\rm Jup}$ for $β$ Pic c. These masses are robust to modest changes to the input data selection. We find a well-constrained eccentricity of $0.119 \pm 0.008$ for $β$ Pic b, and an eccentricity of $0.21^{+0.16}_{-0.09}$ for $β$ Pic c, with the two orbital planes aligned to within $\sim$0.5$^\circ$. Both planets' masses are within $\sim$1$σ$ of the predictions of hot-start evolutionary models and exclude cold starts. We validate our approach on $N$-body synthetic data integrated using REBOUND. We show that orvara can account for three-body effects in the $β$ Pic system down to a level $\sim$5 times smaller than the GRAVITY uncertainties. Systematics in the masses and orbital parameters from orvara's approximate treatment of multiplanet orbits are a factor of $\sim$5 smaller than the uncertainties we derive here. Future GRAVITY observations will improve the constraints on $β$ Pic c's mass and (especially) eccentricity, but improved constraints on the mass of $β$ Pic b will likely require years of additional RV monitoring and improved precision from future Gaia data releases.
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