The NANOGrav Search for Signals from New Physics: MCMC chains

MCMC chains for the GWB analyses performed in the paper "The NANOGrav 15 yr Data Set: Search for Signals from New Physics". 

The data is provided in pickle format. Each file contains a NumPy array with the MCMC chain (with burn-in already removed), and a dictionary with the model parameters' names as keys and their priors as values. You can load them as

with open ('path/to/file.pkl', 'rb') as pick:
temp = pickle.load(pick)

params = temp[0]
chain = temp[1]

The naming convention for the files is the following:

igw: inflationary Gravitational Waves (GWs)

sigw: scalar-induced GWs

sigw_box: assumes a box-like feature in the primordial power spectrum.

sigw_delta: assumes a delta-like feature in the primordial power spectrum.

sigw_gauss: assumes a Gaussian peak feature in the primordial power spectrum.

pt: cosmological phase transitions

pt_bubble: assumes that the dominant contribution to the GW productions comes from bubble collisions.

pt_sound: assumes that the dominant contribution to the GW productions comes from sound waves.

stable: stable cosmic strings

stable-c: stable strings emitting GWs only in the form of GW bursts from cusps on closed loops.

stable-k: stable strings emitting GWs only in the form of GW bursts from kinks on closed loops.

stable-m: stable strings emitting monochromatic GW at the fundamental frequency.

stable-n: stable strings described by numerical simulations including GWs from cusps and kinks.

meta: metastable cosmic strings

meta-l: metastable strings with GW emission from loops only.

meta-ls metastable strings with GW emission from loops and segments.

super: cosmic superstrings.

dw: domain walls

dw-sm: domain walls decaying into Standard Model particles.

dw-dr: domain walls decaying into dark radiation.

For each model, we provide four files. One for the run where the new-physics signal is assumed to be the only GWB source. One for the run where the new-physics signal is superimposed to the signal from Supermassive Black Hole Binaries (SMBHB), for these files "_bhb" will be appended to the model name. Then, for both these scenarios, in the "compare" folder we provide the files for the hypermodel runs that were used to derive the Bayes' factors.

In addition to chains for the stochastic models, we also provide data for the two deterministic models considered in the paper (ULDM and DM substructures). For the ULDM model, the naming convention of the files is the following (all the ULDM signals are superimposed to the SMBHB signal, see the discussion in the paper for more details)

uldm_e: ULDM Earth signal.

uldm_p: ULDM pulsar signal

uldm_p_cor: correlated limit

uldm_p_unc: uncorrelated limit

uldm_c: ULDM combined Earth + pulsar signal direct coupling 

uldm_c_cor: correlated limit

uldm_c_unc: uncorrelated limit

uldm_vecB: vector ULDM coupled to the baryon number

uldm_vecB_cor: correlated limit

uldm_vecB_unc: uncorrelated limit 

uldm_vecBL: vector ULDM coupled to B-L

uldm_vecBL_cor: correlated limit

uldm_vecBL_unc: uncorrelated limit

uldm_c_grav: ULDM combined Earth + pulsar signal for gravitational-only coupling

uldm_c_grav_cor: correlated limit

uldm_c_cor_grav_low: low mass region  

uldm_c_cor_grav_mon: monopole region

uldm_c_cor_grav_low: high mass region

uldm_c_unc: uncorrelated limit

uldm_c_unc_grav_low: low mass region  

uldm_c_unc_grav_mon: monopole region

uldm_c_unc_grav_low: high mass region

For the substructure (static) model, we provide the chain for the marginalized distribution (as for the ULDM signal, the substructure signal is always superimposed to the SMBHB signal)

本数据集包含论文《The NANOGrav 15 yr Data Set: Search for Signals from New Physics》中开展的引力波背景（Gravitational Wave Background, GWB）分析所用的马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）链。

数据以pickle格式存储。每个文件包含两部分：其一为已移除燃烧期（burn-in）的MCMC链的NumPy数组，其二为以模型参数名称为键、对应先验分布为值的字典。可通过如下代码加载：
python
with open ('path/to/file.pkl', 'rb') as pick:
temp = pickle.load(pick)

params = temp[0]
chain = temp[1]

文件命名规范如下：

1. igw：暴胀引力波（inflationary Gravitational Waves, GWs）
2. sigw：标量诱导引力波（scalar-induced GWs）
- sigw_box：假设原初功率谱存在类盒状特征
- sigw_delta：假设原初功率谱存在类δ峰特征
- sigw_gauss：假设原初功率谱存在类高斯峰特征
3. pt：宇宙学相变（cosmological phase transitions）
- pt_bubble：假设引力波产生的主导贡献来自泡泡碰撞
- pt_sound：假设引力波产生的主导贡献来自声波
4. stable：稳定宇宙弦
- stable-c：仅通过闭合环上尖点（cusps）产生引力波暴的稳定宇宙弦
- stable-k：仅通过闭合环上扭结（kinks）产生引力波暴的稳定宇宙弦
- stable-m：以基频辐射单色引力波的稳定宇宙弦
- stable-n：通过数值模拟描述的、包含尖点与扭结引力波辐射的稳定宇宙弦
5. meta：亚稳态宇宙弦（metastable cosmic strings）
- meta-l：仅通过环辐射引力波的亚稳态宇宙弦
- meta-ls：通过环与弦段辐射引力波的亚稳态宇宙弦
6. super：宇宙超弦（cosmic superstrings）
7. dw：畴壁（domain walls）
- dw-sm：衰变至标准模型粒子的畴壁
- dw-dr：衰变至暗辐射的畴壁

针对每个模型，我们提供四个文件：其一为假设新物理信号为唯一GWB源的运行结果；其二为将新物理信号与超大质量双黑洞并合（Supermassive Black Hole Binaries, SMBHB）信号叠加的运行结果，此类文件的模型名称后会追加`_bhb`后缀。针对上述两种场景，我们还在`compare`文件夹中提供了用于推导贝叶斯因子的超模型运行结果文件。

除随机过程模型的MCMC链数据外，我们还提供了论文中考虑的两种确定性模型（超轻暗物质ULDM与暗物质亚结构）的数据。针对ULDM模型，文件命名规范如下（所有ULDM信号均叠加于SMBHB信号之上，详细讨论参见论文）：

- uldm_e：ULDM地球信号
- uldm_p：ULDM脉冲星信号
- uldm_p_cor：关联极限
- uldm_p_unc：非关联极限
- uldm_c：ULDM地球+脉冲星联合信号（直接耦合）
- uldm_c_cor：关联极限
- uldm_c_unc：非关联极限
- uldm_vecB：耦合至重子数的矢量型ULDM
- uldm_vecB_cor：关联极限
- uldm_vecB_unc：非关联极限
- uldm_vecBL：耦合至B-L荷的矢量型ULDM
- uldm_vecBL_cor：关联极限
- uldm_vecBL_unc：非关联极限
- uldm_c_grav：ULDM地球+脉冲星联合信号（仅引力耦合）
- uldm_c_cor：关联极限
- uldm_c_cor_grav_low：低质量区
- uldm_c_cor_grav_mon：单极子区
- uldm_c_cor_grav_low：高质量区
- uldm_c_unc：非关联极限
- uldm_c_unc_grav_low：低质量区
- uldm_c_unc_grav_mon：单极子区
- uldm_c_unc_grav_low：高质量区

针对亚结构（静态）模型，我们提供了边际化分布的MCMC链数据（与ULDM信号一致，亚结构信号始终叠加于SMBHB信号之上）