论文标题
偏心超级二进制黑洞的参数估计偏见：脉冲星时阵列：由被忽略的脉冲星术语造成的偏见
Parameter-Estimation Biases for Eccentric Supermassive Binary Black Holes in Pulsar Timing Arrays: Biases Caused by Ignored Pulsar Terms
论文作者
论文摘要
可以在脉冲星时阵列（PTA）的定时残差中编码来自单个超级二进制黑洞（SMBBHS）的连续纳米赫兹引力波（GWS）。对于每个脉冲星，残差实际上包含一个地球项和脉冲星术语，但通常只有地球项被视为信号，并且脉冲星术语被删除，这会导致SMBBHS的参数估计偏见（PEB），并且当前没有方便的PEB评估。在本文中，我们为具有偏心轨道的SMBBH制定了PEB。在我们的分析中，由于脉冲星距离通常测量很差，因此将脉冲项项的未知阶段视为遵守均匀分布$ u [0,2π）$的随机变量。我们的分析结果符合朱等人的数值工作。 al。 （2016年）的价格为$1.5σ$，这意味着我们的公式有效地估计了PEB的大小。此外，我们发现，对于两个参数 - 地球术语$φ^e $和轨道偏心$ e $，它们的偏见$Δφ^e $和$Δe/e $单调降低，随着$ e $的增加，这部分证实了我们以前的工作中的假设Chen＆Zhang（2018）。此外，我们还计算了由最近观察到的普通光谱过程（CSP）引起的PEB，发现如果连续GW的应变幅度明显强（在我们的情况下，大于$ 3 $乘以$ 3 $倍），则比随机GW背景相比，PEB的PEB来自PULSAR的PEB，而PULSAR的PEB则比CSP的PEB大。我们对PEB的公式可以方便地应用于未来的PTA数据分析中。
The continuous nanohertz gravitational waves (GWs) from individual supermassive binary black holes (SMBBHs) can be encoded in the timing residuals of pulsar timing arrays (PTAs). For each pulsar, the residuals actually contain an Earth term and a pulsar term, but usually only the Earth term is considered as signal and the pulsar term is dropped, which leads to parameter-estimation biases (PEBs) for the SMBBHs, and currently there are no convenient evaluations of the PEBs. In this article, we formulate the PEBs for a SMBBH with an eccentric orbit. In our analyses, the unknown phases of pulsar terms are treated as random variables obeying the uniform distribution $U[0,2π)$, due to the fact that pulsar distances are generally poorly measured. Our analytical results are in accordance with the numerical work by Zhu et. al. (2016) at $1.5σ$ level, implying that our formulae are effective in estimating magnitudes of the PEBs. Additionally, we find that for two parameters -- Earth term phase $φ^E$ and orbital eccentricity $e$, their biases $Δφ^E$ and $Δe/e$ monotonically decrease as $e$ increases, which partly confirms a hypothesis in our previous work Chen & Zhang (2018). Furthermore, we also calculate the PEBs caused by the recently observed common-spectrum process (CSP), finding that if the strain amplitude of the continuous GW is significantly stronger ($3$ times larger, in our cases) than the stochastic GW background, the PEBs from pulsar terms are larger than those from the CSP. Our formulae of the PEBs can be conveniently applied in the future PTA data analyses.
