分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： The cosmological luminosity-distance can be measured from gravitational wave (GW) standard sirens, free of astronomical distance ladders and the associated systematics. However, it may still contain systematics arising from various astrophysical, cosmological and experimental sources. With the large amount of dark standard sirens of upcoming third generation GW experiments, such potential systematic bias can be diagnosed and corrected by statistical tools of the large scale structure of the universe. We estimate that, by cross-correlating the dark siren luminosity-distance space distribution and galaxy redshift space distribution, multiplicative error $m$ in the luminosity distance measurement can be constrained with $1\sigma$ uncertainty $\sigma_m\sim 0.1$. This is already able to distinguish some binary black hole origin scenarios unambiguously. Significantly better constraints and therefore more applications may be achieved by more advanced GW experiments.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Measuring weak lensing cosmic magnification signal is very challenging due to the overwhelming intrinsic clustering in the observed galaxy distribution. In this paper, we modify the Internal Linear Combination (ILC) method to reconstruct the lensing signal with an extra constraint to suppress the intrinsic clustering. To quantify the performance, we construct a realistic galaxy catalogue for the LSST-like photometric survey, covering $20\,000\deg^2$ with mean source redshift at $z_s\sim 1$. We find that the reconstruction performance depends on the width of the photo-z bin we choose. Due to the correlation between the lensing signal and the source galaxy distribution, the derived signal has smaller systematic bias but larger statistical uncertainty for a narrower photo-z bin. We conclude that the lensing signal reconstruction with the Modified ILC method is unbiased with a statistical uncertainty $<5\%$ for bin width $\Delta z^P = 0.2$.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We carry out a thermal energy census of hot baryons at $z < 1$, by cross-correlating the \emph{Planck} MILCA y-map with 0.8 million clusters/groups selected from the Yang et.al (2021) catalog. The thermal Sunyaev-Zel'dovich (tSZ) effect around these clusters/groups are reliably obtained, which enables us to make our model constraints based on one-halo (1h) and two-halo (2h) contributions, respectively. (1) The total measurement S/N of the one-halo term is 63. We constrain the $Y$-$M$ relation over the halo mass range of $10^{13}$-$10^{15} M_\odot/h$, and find $Y\propto M^{\alpha}$ with $\alpha= 1.8$ at $z=0.14$ ($\alpha=2.1$ at $z=0.75$). The total thermal energy of gas bound to clusters/groups increases from $0.1\ \rm meV/cm^3$ at $z=0.14$ to $0.22\ \rm meV/cm^3$ at $z=0.75$. (2) The two-halo term is used to constrain the bias-weighted electron pressure $\langle b_yP_e \rangle$. We find that $\langle b_yP_e \rangle$ (in unit of $\rm meV/cm^3$) increases from $0.24\pm 0.02$ at $z=0.14$ to $0.45\pm 0.02$ at $z=0.75$. These results lead to several implications. (i) The hot gas fraction $f_{\rm gas}$ in clusters/groups monotonically increase with halo mass, where $f_{\rm gas}$ of a $10^{14} M_\odot/h$ halo is $\sim 50\%$ ($25\%$) of the cosmic mean at $z=0.14\ (0.75)$. (ii) By comparing the 1h- and 2h-terms, we obtain tentative constraint on the thermal energy of unbound gas. (iii) The above results lead to significant suppression of matter and weak lensing power spectrum at small scales. These implications are important for astrophysics and cosmology, and we will further investigate them with improved data and gas modeling.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We carry out a thermal energy census of hot baryons at $z < 1$, by cross-correlating the \emph{Planck} MILCA y-map with 0.8 million clusters/groups selected from the Yang et.al (2021) catalog. The thermal Sunyaev-Zel'dovich (tSZ) effect around these clusters/groups are reliably obtained, which enables us to make our model constraints based on one-halo (1h) and two-halo (2h) contributions, respectively. (1) The total measurement S/N of the one-halo term is 63. We constrain the $Y$-$M$ relation over the halo mass range of $10^{13}$-$10^{15} M_\odot/h$, and find $Y\propto M^{\alpha}$ with $\alpha= 1.8$ at $z=0.14$ ($\alpha=2.1$ at $z=0.75$). The total thermal energy of gas bound to clusters/groups increases from $0.1\ \rm meV/cm^3$ at $z=0.14$ to $0.22\ \rm meV/cm^3$ at $z=0.75$. (2) The two-halo term is used to constrain the bias-weighted electron pressure $\langle b_yP_e \rangle$. We find that $\langle b_yP_e \rangle$ (in unit of $\rm meV/cm^3$) increases from $0.24\pm 0.02$ at $z=0.14$ to $0.45\pm 0.02$ at $z=0.75$. These results lead to several implications. (i) The hot gas fraction $f_{\rm gas}$ in clusters/groups monotonically increase with halo mass, where $f_{\rm gas}$ of a $10^{14} M_\odot/h$ halo is $\sim 50\%$ ($25\%$) of the cosmic mean at $z=0.14\ (0.75)$. (ii) By comparing the 1h- and 2h-terms, we obtain tentative constraint on the thermal energy of unbound gas. (iii) The above results lead to significant suppression of matter and weak lensing power spectrum at small scales. These implications are important for astrophysics and cosmology, and we will further investigate them with improved data and gas modeling.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Contamination of interloper galaxies due to misidentified emission lines can be a big issue in the spectroscopic galaxy clustering surveys, especially in future high-precision observations. We propose a statistical method based on the cross-correlations of the observational data itself between two redshift bins to efficiently reduce this effect, and it also can derive the interloper fraction f_i in a redshift bin with a high level of accuracy. The ratio of cross and auto angular correlation functions or power spectra between redshift bins are suggested to estimate f_i, and the key equations are derived for theoretical discussion. In order to explore and prove the feasibility and effectiveness of this method, we also run simulations, generate mock data, and perform cosmological constraints considering systematics based on the observation of the China Space Station Telescope (CSST). We find that this method can effectively reduce the interloper effect, and accurately constrain the cosmological parameters for f_i<1%~10%, which is suitable for most future surveys. This method also can be applied to other kinds of galaxy clustering surveys like line intensity mapping.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We numerically investigate non-Gaussianities in the late-time cosmological density field in Fourier space. We explore various statistics, including the two-point and three-point probability distribution function (PDF) of phase and modulus, and two \& three-point correlation function of of phase and modulus. We detect significant non-Gaussianity for certain configurations. We compare the simulation results with the theoretical expansion series of \citet{2007ApJS..170....1M}. We find that the $\mathcal{O}(V^{-1/2})$ order term alone is sufficiently accurate to describe all the measured non-Gaussianities in not only the PDFs, but also the correlations. We also numerically find that the phase-modulus cross-correlation contributes $\sim 50\%$ to the bispectrum, further verifying the accuracy of the $\mathcal{O}(V^{-1/2})$ order prediction. This work demonstrates that non-Gaussianity of the cosmic density field is simpler in Fourier space, and may facilitate the data analysis in the era of precision cosmology.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： The integrated Sachs-Wolfe (ISW) effect probes the decay rate ($DR$) of large scale gravitational potential and therefore provides unique constraint on dark energy (DE). However its constraining power is degraded by the ISW measurement, which relies on cross-correlating with the large scale structure (LSS) and suffers from uncertainties in galaxy bias and matter clustering. In combination with lensing-LSS cross-correlation, $DR$ can be isolated in a way free of uncertainties in galaxy bias and matter clustering. We applied this proposal to the combination of the DR8 galaxy catalogue of DESI imaging surveys and Planck cosmic microwave background (CMB) maps. We achieved the first $DR$ measurement, with a total significance of $3.2\sigma$. We verified the measurements at three redshift bins ($[0.2,0.4)$, $[0.4, 0.6)$, $[0.6,0.8]$), with two LSS tracers (the "low-density points" and the conventional galaxy positions). Despite its relatively low S/N, the addition of $DR$ significantly improves dark energy constraints, over SDSS baryon acoustic oscillation (BAO) data alone or Pantheon supernovae (SN) compilation alone. For flat $w$CDM cosmology, the improvement in the precision of $\Omega_m$ is a factor of 1.8 over BAO and 1.5 over SN. For the DE equation of state $w$, the improvement factor is 1.3 over BAO and 1.4 over SN. These improvements demonstrate $DR$ as a useful cosmological probe, and therefore we advocate its usage in future cosmological analysis.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We report a $5\sigma$ detection of the pairwise kinematic Sunyaev-Zel'dovich (kSZ) effect, combining galaxy clusters in DESI imaging surveys and the Planck temperature maps. The detection is facilitated by both improvements in the data and in the analysis method. For the data, we adopt the recently released galaxy group catalog (Y20: \cite{yang2020extended}) with $\sim 10^6$ robustly-identified groups, and construct various galaxy cluster samples for the kSZ measurement. The Y20 catalogue also provides estimation of halo mass, which further improves the kSZ measurement by $\sim 10\%$. For the analysis method, we derive an optimal estimator of pairwise kSZ through the maximum likelihood analysis. It also handles potential systematic errors self-consistently. The baseline cluster sample, containing the $1.2\times 10^5$ richest galaxy clusters of typical mass ~$ 10^{14} M_{\odot}/h$ at typical redshift $0.2$-$0.5$, rules out the null hypothesis at $5\sigma$. When fitting with a pairwise kSZ template from simulations, the signal is detected at $4.7\sigma$ and the average optical depth is constrained as $\bar{\tau}_e=(1.66\pm 0.35)\times 10^{-4}$. We perform various internal checks, with different cluster selection criteria, different sky coverage and redshift range, different CMB maps, different filter sizes, different treatments of potential systematics and the covariance matrix. The kSZ effect is consistently detected with $2.5\leq $S/N$\leq 5.6$ and acceptable $\chi^2_{\rm min}$, across a variety of cluster samples. The S/N is limited by both the Planck resolution and the photo-z accuracy, and therefore can be significant improved with DESI spectroscopic redshift information and with other CMB experiments.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We measure the cross-correlation between galaxy groups constructed from DESI
Legacy Imaging Survey DR8 and \emph{Planck} CMB lensing, over overlapping sky
area of 16876 $\rm deg^2$. The detections are significant and consistent with
the expected signal of the large-scale structure of the universe, over group
samples of various redshift, mass, richness $N_{\rm g}$ and over various scale
cuts. The overall S/N is 40 for a conservative sample with $N_{\rm g}\geq 5$,
and increases to $50$ for the sample with $N_{\rm g}\geq 2$. Adopting the
\emph{Planck} 2018 cosmology, we constrain the density bias of groups with
$N_{\rm g}\geq 5$ as $b_{\rm g}=1.31\pm 0.10$, $2.22\pm 0.10$, $3.52\pm 0.20$
at $0.1
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We discover a linear relation between two sets of galaxy-lensing cross-correlations. This linear relation holds, as long as light follows the geodesic and the metric is Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW). Violation of the cosmological principle (and equivalently the FLRW metric) will break this linear relation. Therefore it provides a powerful test of the cosmological principle, based on direct observables and relied on no specific cosmological models. We demonstrate that stage IV galaxy surveys and CMB-S4 experiments will be able to test this linear relation stringently and therefore test the cosmological principle robustly.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Low Density Points (LDPs, \citet{2019ApJ...874....7D}), obtained by removing
high-density regions of observed galaxies, can trace the Large-Scale Structures
(LSSs) of the universe. In particular, it offers an intriguing opportunity to
detect weak gravitational lensing from low-density regions. In this work, we
investigate tomographic cross-correlation between Planck CMB lensing maps and
LDP-traced LSSs, where LDPs are constructed from the DR8 data release of the
DESI legacy imaging survey, with about $10^6$-$10^7$ galaxies. We find that,
due to the large sky coverage (20,000 deg$^2$) and large redshift depth ($z\leq
1.2$), a significant detection ($10\sigma$--$30\sigma$) of the CMB lensing-LDP
cross-correlation in all six redshift bins can be achieved, with a total
significance of $\sim 53\sigma$ over $ \ell\le1024$. Moreover, the measurements
are in good agreement with a theoretical template constructed from our
numerical simulation in the WMAP 9-year $\Lambda$CDM cosmology. A scaling
factor for the lensing amplitude $A_{\rm lens}$ is constrained to $A_{\rm
lens}=1\pm0.12$ for $z<0.2$, $A_{\rm lens}=1.07\pm0.07$ for $0.2
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： In certain cases of astronomical data analysis, the meaningful physical quantity to extract is the ratio $R$ between two data sets. Examples include the lensing ratio, the interloper rate in spectroscopic redshift samples, the decay rate of gravitational potential and $E_G$ to test gravity. However, simply taking the ratio of the two data sets is biased, since it renders (even statistical) errors in the denominator into systematic errors in $R$. Furthermore, it is not optimal in minimizing statistical errors of $R$. Based on the Bayesian analysis and the usual assumption of Gaussian error in the data, we derive an analytical expression of the posterior PDF $P(R)$. This result enables fast and unbiased $R$ measurement, with minimal statistical errors. Furthermore, it relies on no underlying model other than the proportionality relation between the two data sets. Even more generally, it applies to the cases where the proportionality relation holds for the underlying physics/statistics instead of the two data sets directly. It also applies to the case of multiple ratios ($R\rightarrow {\bf R}=(R_1,R_2,\cdots)$). We take the lensing ratio as an example to demonstrate our method. We take lenses as DESI imaging survey galaxies, and sources as DECaLS cosmic shear and \emph{Planck} CMB lensing. We restrict the analysis to the ratio between CMB lensing and cosmic shear. The resulting $P(R$), for multiple lens-shear pairs, are all nearly Gaussian. The S/N of measured $R$ ranges from $5.3$ to $8.4$. We perform several tests to verify the robustness of the above result.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： In certain cases of astronomical data analysis, the meaningful physical quantity to extract is the ratio $R$ between two data sets. Examples include the lensing ratio, the interloper rate in spectroscopic redshift samples, the decay rate of gravitational potential and $E_G$ to test gravity. However, simply taking the ratio of the two data sets is biased, since it renders (even statistical) errors in the denominator into systematic errors in $R$. Furthermore, it is not optimal in minimizing statistical errors of $R$. Based on the Bayesian analysis and the usual assumption of Gaussian error in the data, we derive an analytical expression of the posterior PDF $P(R)$. This result enables fast and unbiased $R$ measurement, with minimal statistical errors. Furthermore, it relies on no underlying model other than the proportionality relation between the two data sets. Even more generally, it applies to the cases where the proportionality relation holds for the underlying physics/statistics instead of the two data sets directly. It also applies to the case of multiple ratios ($R\rightarrow {\bf R}=(R_1,R_2,\cdots)$). We take the lensing ratio as an example to demonstrate our method. We take lenses as DESI imaging survey galaxies, and sources as DECaLS cosmic shear and \emph{Planck} CMB lensing. We restrict the analysis to the ratio between CMB lensing and cosmic shear. The resulting $P(R$), for multiple lens-shear pairs, are all nearly Gaussian. The S/N of measured $R$ ranges from $5.3$ to $8.4$. We perform several tests to verify the robustness of the above result.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
Ming Li
Jun Pan
Pengjie Zhang
Jie Wang
Longlong Feng
Liang Gao
Xi Kang
Guoliang Li
Weipeng Lin
Haihui Wang
摘要： The Fourier transformation is an effective and efficient operation of Gaussianization at the one-point level. Using a set of N-body simulation data, we verified that the one-point distribution functions of the dark matter momentum divergence and density fields closely follow complex Gaussian distributions. The one-point distribution function of the quotient of two complex Gaussian variables is introduced and studied. Statistical theories are then applied to model one-point statistics about the growth of individual Fourier mode of the dark matter density field, which can be obtained by the ratio of two Fourier transformed cosmic fields. Our simulation results proved that the models based on the Gaussian approximation are impressively accurate, and our analysis revealed many interesting aspects about the growth of dark matter's density fluctuation in Fourier space.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Calibrating the redshift distributions of photometric galaxy samples is essential in weak lensing studies. The self-calibration method combines angular auto- and cross-correlations between galaxies in multiple photometric redshift (photo-$z$) bins to reconstruct the scattering rates matrix between redshift bins. In this paper, we test a recently proposed self-calibration algorithm using the DECaLS Data Release 9 and investigate to what extent the scattering rates are determined. We first mitigate the spurious angular correlations due to imaging systematics by a machine learning based method. We then improve the algorithm for $\chi^2$ minimization and error estimation. Finally, we solve for the scattering matrices, carry out a series of consistency tests and find reasonable agreements: (1) finer photo-$z$ bins return a high-resolution scattering matrix, and it is broadly consistent with the low-resolution matrix from wider bins; (2) the scattering matrix from the Northern Galactic Cap is almost identical to that from Southern Galactic Cap; (3) the scattering matrices are in reasonable agreement with those constructed from the power spectrum and the weighted spectroscopic subsample. We also evaluate the impact of cosmic magnification. Although it changes little the diagonal elements of the scattering matrix, it affects the off-diagonals significantly. The scattering matrix also shows some dependence on scale cut of input correlations, which may be related to a known numerical degeneracy between certain scattering pairs. This work demonstrates the feasibility of the self-calibration method in real data and provides a practical alternative to calibrate the redshift distributions of photometric samples.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Calibrating the redshift distributions of photometric galaxy samples is essential in weak lensing studies. The self-calibration method combines angular auto- and cross-correlations between galaxies in multiple photometric redshift (photo-$z$) bins to reconstruct the scattering rates matrix between redshift bins. In this paper, we test a recently proposed self-calibration algorithm using the DECaLS Data Release 9 and investigate to what extent the scattering rates are determined. We first mitigate the spurious angular correlations due to imaging systematics by a machine learning based method. We then improve the algorithm for $\chi^2$ minimization and error estimation. Finally, we solve for the scattering matrices, carry out a series of consistency tests and find reasonable agreements: (1) finer photo-$z$ bins return a high-resolution scattering matrix, and it is broadly consistent with the low-resolution matrix from wider bins; (2) the scattering matrix from the Northern Galactic Cap is almost identical to that from Southern Galactic Cap; (3) the scattering matrices are in reasonable agreement with those constructed from the power spectrum and the weighted spectroscopic subsample. We also evaluate the impact of cosmic magnification. Although it changes little the diagonal elements of the scattering matrix, it affects the off-diagonals significantly. The scattering matrix also shows some dependence on scale cut of input correlations, which may be related to a known numerical degeneracy between certain scattering pairs. This work demonstrates the feasibility of the self-calibration method in real data and provides a practical alternative to calibrate the redshift distributions of photometric samples.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
Ying Zu
Huanyuan Shan
Jun Zhang
Sukhdeep Singh
Zhiwei Shao
Xiaokai Chen
Ji Yao
Jesse B. Golden-Marx
Weiguang Cui
Eric Jullo
Jean-Paul Kneib
Pengjie Zhang
Xiaohu Yang
摘要： Concentration is one of the key dark matter halo properties that could drive
the scatter in the stellar-to-halo mass relation of massive clusters. We derive
robust photometric stellar masses for a sample of brightest central galaxies
(BCGs) in SDSS redMaPPer clusters at $0.17
分类： 天文学 >> 天文学 提交时间： 2023-02-19
Ji Yao
Huanyuan Shan
Pengjie Zhang
Xiangkun Liu
Catherine Heymans
Benjamin Joachimi
Marika Asgari
Maciej Bilicki
Hendrik Hildebrandt
Konrad Kuijken
Tilman Tröster
Jan Luca van den Busch
Angus Wright
Ziang Yan
摘要： Galaxy shear - cosmic microwave background (CMB) lensing convergence cross-correlations contain additional information on cosmology to auto-correlations. While being immune to certain systematic effects, they are affected by the galaxy intrinsic alignments (IA). This may be responsible for the reported low lensing amplitude of the galaxy shear $\times$ CMB convergence cross-correlations, compared to the standard Planck $\Lambda$CDM (cosmological constant and cold dark matter) cosmology prediction. In this work, we investigate how IA affects the Kilo-Degree Survey (KiDS) galaxy lensing shear - Planck CMB lensing convergence cross-correlation and compare it to previous treatments with or without IA taken into consideration. More specifically, we compare marginalization over IA parameters and the IA self-calibration (SC) method (with additional observables defined only from the source galaxies) and prove that SC can efficiently break the degeneracy between the CMB lensing amplitude $A_{\rm lens}$ and the IA amplitude $A_{\rm IA}$. We further investigate how different systematics affect the resulting $A_{\rm IA}$ and $A_{\rm lens}$, and validate our results with the MICE2 simulation. We find that by including the SC method to constrain IA, the information loss due to the degeneracy between CMB lensing and IA is strongly reduced. The best-fit values are $A_{\rm lens}=0.84^{+0.22}_{-0.22}$ and $A_{\rm IA}=0.60^{+1.03}_{-1.03}$, while different angular scale cuts can affect $A_{\rm lens}$ by $\sim10\%$. We show that appropriate treatment of the boost factor, cosmic magnification, and photometric redshift modeling is important for obtaining the correct IA and cosmological results.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
Ji Yao
Huanyuan Shan
Pengjie Zhang
Xiangkun Liu
Catherine Heymans
Benjamin Joachimi
Marika Asgari
Maciej Bilicki
Hendrik Hildebrandt
Konrad Kuijken
Tilman Tröster
Jan Luca van den Busch
Angus Wright
Ziang Yan
摘要： Galaxy shear - cosmic microwave background (CMB) lensing convergence cross-correlations contain additional information on cosmology to auto-correlations. While being immune to certain systematic effects, they are affected by the galaxy intrinsic alignments (IA). This may be responsible for the reported low lensing amplitude of the galaxy shear $\times$ CMB convergence cross-correlations, compared to the standard Planck $\Lambda$CDM (cosmological constant and cold dark matter) cosmology prediction. In this work, we investigate how IA affects the Kilo-Degree Survey (KiDS) galaxy lensing shear - Planck CMB lensing convergence cross-correlation and compare it to previous treatments with or without IA taken into consideration. More specifically, we compare marginalization over IA parameters and the IA self-calibration (SC) method (with additional observables defined only from the source galaxies) and prove that SC can efficiently break the degeneracy between the CMB lensing amplitude $A_{\rm lens}$ and the IA amplitude $A_{\rm IA}$. We further investigate how different systematics affect the resulting $A_{\rm IA}$ and $A_{\rm lens}$, and validate our results with the MICE2 simulation. We find that by including the SC method to constrain IA, the information loss due to the degeneracy between CMB lensing and IA is strongly reduced. The best-fit values are $A_{\rm lens}=0.84^{+0.22}_{-0.22}$ and $A_{\rm IA}=0.60^{+1.03}_{-1.03}$, while different angular scale cuts can affect $A_{\rm lens}$ by $\sim10\%$. We show that appropriate treatment of the boost factor, cosmic magnification, and photometric redshift modeling is important for obtaining the correct IA and cosmological results.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
Shamik Ghosh
Yang Liu
Le Zhang
Siyu Li
Junzhou Zhang
Jiaxin Wang
Jiazheng Dou
Jiming Chen
Jacques Delabrouille
Mathieu Remazeilles
Chang Feng
Bin Hu
Zhi-Qi Huang
Hao Liu
Larissa Santos
Pengjie Zhang
Zhaoxuan Zhang
Wen Zhao
Hong Li
Xinmin Zhang
摘要： AliCPT is the first Chinese cosmic microwave background (CMB) experiment which will make the most precise measurements of the CMB polarization in the northern hemisphere. The key science goal for AliCPT is the detection of primordial gravitational waves (PGWs). It is well known that an epoch of cosmic inflation, in the very early universe, can produce PGWs, which leave an imprint on the CMB in form of odd parity $B$-mode polarization. In this work, we study the performance of the component separation and parameter estimation pipelines in context of constraining the value of the tensor-to-scalar ratio. Based on the simulated data for one observation season, we compare five different pipelines with different working principles. Three pipelines perform component separation at map or spectra level before estimating $r$ from the cleaned spectra, while the other two pipelines performs a global fit for both foreground parameters and $r$. We also test different methods to account for the effects of time stream filtering systematics. This work shows that our pipelines provide consistent and robust constraints on the tensor-to-scalar ratio and a consistent sensitivity $\sigma(r) \sim 0.02$. This showcases the potential of precise $B$-mode polarization measurement with AliCPT-1. AliCPT will provide a powerful opportunity to detect PGWs, which is complementary with various ground-based CMB experiments in the southern hemisphere.
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