随着本世纪初几个大型激光干涉仪引力波探测器相继投入使用，引力波探测已经进入一个崭新的时代。尽管截止至本论文撰写之时还没有直接探测到宇宙中的引力波信号，这一目标也并非遥不可及。第一代引力波探测器已经实现了二十年前理论预计的灵敏度，对这些仪器所获得数据的分析也得到了很多重要的天体物理结果。人们期望在未来四五年内第二代探测器投入使用之时，我们不但将可以直接探测到引力波，更将打开一扇观测宇宙的新窗口，进入引力波天文学时代。引力波探测离不开对潜在引力波源的认识。引力波源大致可分为独立信号源如快速旋转的不对称中子星和致密双星并合等，和既可以来源于早期宇宙的各种物理过程，也可以由大量不可分辨的天体物理源产生的信号叠加形成的随机背景。本文的研究对象为天体物理的随机引力波背景，其重要性在于它包含恒星形成的历史、源的引力波产能量及其内部物理状态等等信息，也在于它可能覆盖早期宇宙遗留的原初引力波信号，并且可以形成一个限制探测独立信号的“噪声”背景。这种类型的随机背景强烈依赖于源的形成率和单个源辐射引力波的能谱。快速旋转的初生中子星经历r模式不稳定性曾经被认为可以形成一个较强的随机背景信号，并且有可能被第二代地面探测器探测到。但是最近的数值模拟或解析计算研究均表明这一辐射机制的产能率可能远远低于预期，因此我们采用这些新的结果重新计算了该引力波背景的能量密度。我们使用不同的恒星形成率模型来计算中子星形成率，并研究了它对背景能量密度的影响。考虑目前正在运行的第一代地面探测器以及将来的第二代、第三代仪器的设计灵敏度，我们研究了这一背景的可探测性问题。特别地，我们检验了两种联合多个探测器的输出以提高探测能力的方法。这里的可探测性检验不仅仅是信噪比的计算，而是考虑背景能量密度非常依赖的源的物理参数的不确定性，设定信噪比“门槛”来限制可探测的参数空间。

Since the advent of large-scale interferometric gravitational wave (GW) detectorsin the beginning of this century, we have been in a new era of GW detection. Althoughno GWs have been detected directly, the first generation detectors have reached theirdesign sensitivities anticipated more than 20 years ago, and have also enabled impor-tant constraints to be placed on various sources of GW emissions. It is expected thatin the near future we will be able to directly prove the existence of GWs and thusopen a new window to observe our Universe. That will be the time for GW astronomybased on weekly detections with advanced detectors. Searches for GWs depend on ourknowledge of possible GW sources, which can be roughly divided into two categories:individual single sources and stochastic background. The former one is usefully clas-sified to GW transients such as core collapse supernovae and continuous sources suchas inspiralling compact binaries according to the signal duration. A stochastic GWbackground may result from a large variety of cosmological processes developed in thevery early Universe or the superposition of a large number of unresolved sources sincethe beginning of star formation. The object of this study is the astrophysical stochasticGW background. It is important as it contains the information of the star formationhistory and the average emissions and event rate density of sources, and also becauseit could mask the relic GW signals from the very early Universe or form a “noise”background limiting the ability to detect single events. The properties of astrophysicalstochastic backgrounds depend on the source event rate and average emission of indi-vidual sources. Newborn fast-spinning neutron stars with r-mode instabilities used tobe suggested to be a promising source of astrophysical GW background, which couldbe detected by second generation detectors such as Advanced LIGO. However, morerecent studies (both numerical and analytic) predicted much lower efficiency associatedwith this emission mechanism. We recalculate this background signal considering theselatest results of source emission and evaluate its detectability by adopting sensitivitiesof the current network of GWdetectors and future generation instruments. In particular we consider two approaches of combining the measurements of multiple detectors toimprove the detection ability to a stochastic background. Rather than simply calculatethe signal-to-noise ratio (SNR), we have considered the uncertainties of those parame-ters to which the stochastic background is most sensitive and constrained the detectableparameter space by setting a SNR threshold.