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arXiv 1507.00780astro-ph.SR
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精密径向速度统计不确定性的天体物理学来源及其近似

Astrophysical Sources of Statistical Uncertainty in Precision Radial Velocities and Their Approximations

Thomas G. Beatty, B. Scott Gaudi

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22 pages, 23 figures. Submitted to PASP
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摘要：

我们调查天体物理学的贡献，恒星光谱的精确径向速度测量的统计不确定性。我们解析地确定了由高斯、洛伦兹、福格特和旋转轮廓加宽的孤立谱线的质心的不确定性，发现对于所有情况和假设弱线，不确定性是线质心是$σ_V\approx C\,Θ^{3/2}/(W I_0^{1/2})$，其中$Θ$是线的半峰全宽，$W$是等效宽度，$I_0$是连续信噪比，其中$C$是取决于特定线轮廓的阶数单位的常数。我们用这个结果来激励近似解析表达式的总径向速度的不确定性与给定的光子噪声，分辨率，波长，有效温度，表面重力，金属丰度，宏观湍流，和恒星旋转的恒星光谱。我们使用这些关系来确定主要贡献的统计不确定性，在精确的径向速度测量的有效温度和质量的函数的主序星。对于大于$\sim1.1\,M_\odot$的恒星，我们发现恒星自转在中等和高分辨率光谱（$R\gtrsim30,000$）的速度不确定性中占主导地位。对于质量较小的恒星，各种来源的贡献取决于光谱分辨率和波长，由于辐射热光度降低而产生的光子噪声通常对固定曝光时间和距离的低质量恒星变得越来越重要。在大多数情况下，大于60，000的分辨率在统计精度方面几乎没有什么好处。我们确定了各种光谱类型的恒星的最佳波长范围，发现最佳区域取决于恒星的有效温度，但对于中M矮星和更早的最有效的波长区域是从6000到9000。

英文摘要：

We investigate astrophysical contributions to the statistical uncertainty of precision radial velocity measurements of stellar spectra. We analytically determine the uncertainty in centroiding isolated spectral lines broadened by Gaussian, Lorentzian, Voigt, and rotational profiles, finding that for all cases and assuming weak lines, the uncertainty is the line centroid is $σ_V\approx C\,Θ^{3/2}/(W I_0^{1/2})$, where $Θ$ is the full-width at half-maximum of the line, $W$ is the equivalent width, and $I_0$ is the continuum signal-to-noise ratio, with $C$ a constant of order unity that depends on the specific line profile. We use this result to motivate approximate analytic expressions to the total radial velocity uncertainty for a stellar spectrum with a given photon noise, resolution, wavelength, effective temperature, surface gravity, metallicity, macroturbulence, and stellar rotation. We use these relations to determine the dominant contributions to the statistical uncertainties in precision radial velocity measurements as a function of effective temperature and mass for main-sequence stars. For stars more than $\sim1.1\,M_\odot$ we find that stellar rotation dominates the velocity uncertainties for moderate and high resolution spectra ($R\gtrsim30,000$). For less massive stars, a variety of sources contribute depending on the spectral resolution and wavelength, with photon noise due to decreasing bolometric luminosity generally becoming increasingly important for low-mass stars at fixed exposure time and distance. In most cases, resolutions greater than 60,000 provide little benefit in terms of statistical precision. We determine the optimal wavelength range for stars of various spectral types, finding that the optimal region depends on the stellar effective temperature, but for mid M-dwarfs and earlier the most efficient wavelength region is from 6000A to 9000A.

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