arXiv subjects

Furen Deng

Publications and source records attributed to Furen Deng.

At least 37 records · Page 2Linked to original sources

arXiv2025

AKRA 2.0: Accurate Kappa Reconstruction Algorithm for masked shear catalog

Cosmic shear surveys serve as a powerful tool for mapping the underlying matter density field, including non-visible dark matter. A key challenge in cosmic shear surveys is the accurate reconstruction of lensing convergence ($κ$) maps from shear catalogs impacted by survey boundaries and masks, which seminal Kaiser-Squires (KS) method are not designed to handle. To overcome these limitations, we previously proposed the Accurate Kappa Reconstruction Algorithm (AKRA), a prior-free maximum likelihood map-making method. Initially designed for flat sky scenarios with periodic boundary conditions, AKRA has proven successful in recovering high-precision $κ$ maps from masked shear catalogs. In this work, we upgrade AKRA to AKRA 2.0 by integrating the tools designed for spherical geometry. This upgrade employs spin-weighted spherical harmonic transforms to reconstruct the convergence field over the full sky. To optimize computational efficiency, we implement a scale-splitting strategy that segregates the analysis into two parts: large-scale analysis on the sphere (referred to as AKRA-sphere) and small-scale analysis on the flat sky (referred to as AKRA-flat); the results from both analyses are then combined to produce final reconstructed $κ$ map. We tested AKRA 2.0 using simulated shear catalogs with various masks, demonstrating that the reconstructed $κ$ map by AKRA 2.0 maintains high accuracy. For the reconstructed $κ$ map in unmasked regions, the reconstructed convergence power spectrum $C_κ^{\rm{rec}}$ and the correlation coefficient with the true $κ$ map $r_\ell$ achieve accuracies of $(1-C_\ell^{\rm{rec}}/C_\ell^{\rm{true}}) \lesssim 1\%$ and $(1-r_\ell) \lesssim 1\%$, respectively. Our algorithm is capable of straightforwardly handling further issues such as inhomogeneous shape measurement noise, which we will address in subsequent analysis.

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arXiv2025

Jet reorientation revealed by intermittent jet activity in radio galaxy 0954+556

Intermittent jet activity of AGNs is a common phenomenon, whereas significant jet reorientation during episodic jet activity in relatively young radio galaxies are rarely reported. The quasar 0954+556 at redshift of 0.903 is an intriguing source exhibiting an unusual radio jet structure with significantly different jet directions at kpc and pc scales. At kpc scales, images from the VLA exhibit a bright core, a linear jet extending 24 kpc to the northwest, and a discrete jet component 16 kpc to the northeast. At pc scales, images from the VLBA show a two-component structure with a projected separation of 360 pc in the north-south direction. The peculiar structure of 0954+556 might result from jet reorientation. Here, our aim was to investigate the possible mechanism via multiscale and multifrequency deep radio images. We performed VLA and VLBA observations of 0954+556. Together with some existing data in the NRAO data archive, we made multiple VLA images at 1.4-22 GHz and VLBA images at 1.7-43 GHz for various image analyses of the jet structure. We identified the location of the radio core at pc scales, detected the faint counter-jets at both pc and kpc scales for the first time, and revealed a diffuse emission region connecting pc and kpc scale forward jets. Our spectral index distribution and spectral aging analysis indicate that 0954+556 might undergo at least two episodes of jet activity during the current AGN phase. Moreover, pc scale polarization maps display a well-resolved spine-sheath polarization structure. It seems that the jet direction of 0954+556 changed significantly during intermittent jet activity. This may explain the different jet orientations and spectral ages observed from kpc to pc scales. The research provides a strong case that AGN jet direction might change rapidly on timescales of one million years.

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arXiv2025

Synthesis imaging with a lunar orbit array: I. global sky map and its systematics

Ground-based radio astronomical observation at frequencies below 30 MHz is hampered by the Ionosphere and radio frequency interference (RFI). The Discovering Sky at the Longest wavelength (DSL) mission, also known as the Hongmeng mission, employs a linear array of satellites on a circular orbit around the Moon to make interferometric observations in this band. Though vastly different from the usual ground-based arrays, the interferometric visibility data collected by such an array is linearly related to the sky map, and the reconstruction is in principle an inversion problem of linear mapping. In this paper, we investigate a number of issues in the algorithm of global map reconstruction, focusing on the impact of sub-pixel noise induced by the finite pixelization of the sky, and errors due to regularization. We find that in the reconstruction process, if one builds up the beam matrix, which relates the sky pixels to the visibilities, by naively evaluating its elements at each of the pixel centers, then the sub-pixel noise can give rise to a significant aliasing effect. However, this effect can be effectively mitigated by a simple pixel-averaging method. Based on evaluation of the image quality using the correlation coefficient between the input and reconstructed map, and the signal-to-noise ratio, we discuss the selection strategy of the regularization parameter, and show that the sky can be well reconstructed with a reasonable choice of the regularization parameter.

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arXiv2025

Reconstructing the Anisotropic Ultra-long Wavelength Spectra using a Single Antenna on Lunar-orbit

The ultra-long wavelength sky ($ν\lesssim 30$ MHz) is still largely unexplored, as the electromagnetic wave is heavily absorbed and distorted by the ionosphere on Earth. The far-side of the Moon, either in lunar-orbit or on lunar-surface, is the ideal site for observations in this band, and the upcoming Moon-based interferometers will obtain multi-frequency high-resolution sky maps. Making use of the lunar occultation of the sky and the anisotropy of antenna primary beam response, we propose a novel method to reconstruct the ultra-long wavelength spectral shape in multiple directions in the sky using only one antenna on lunar orbit. We apply the method to one antenna on one of the nine daughter satellites of the proposed Discovering the Sky at Longest wavelength (DSL) project. Using simulated observation data between 1 - 30 MHz from one dipole antenna, we find that the spectra for different regions on the sky can be reconstructed very well and the free-free absorption feature in each region can be derived from the reconstructed spectra. This work demonstrates the feasibility to reconstruct the anisotropic ultra-long wavelength spectra with very limited instrumentation on a lunar-orbit, with mature technologies already in place. It extends the application of such kind of satellite in revealing the distribution of free electrons in the Galactic interstellar medium from the distribution of absorption features in the ultra-long wavelength sky.

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arXiv2025

Beamforming in Interferometer Arrays with Cross-couplings

For an interferometric array, an image of the sky can be synthesized from interferometric visibilities, which are the cross-correlations of the received electric voltages of pairs of array elements. However, to search for transient targets such as the fast radio burst (FRB), it is more convenient to use the beam-forming technique, where the real-time voltage outputs of the array elements are used to generate data streams (beams) which are sensitive to a specific direction. This is usually achieved by a weighted sum of the array element voltages, with the complex weight adjusted so that all outputs have the same phase for that direction. Alternatively, beams can also be formed from the weighted sum of the short time averaged correlation (visibility) data. We shall call these two approaches the electric voltage beam forming (EBF) and cross-correlation beam forming (XBF), respectively. All beams formed with the EBF can also be formed by the XBF method, but the latter can also generate beams which can not be generated by the former. We discuss the properties of these two kinds of beams, and the amount of computation required in each case. For an array with large number of elements, the XBF would require much more computation resource, although this is partly compensated by the fact that it allows integration over time. We study the impact of cross-coupling between array elements on the beamforming, first using a toy model, then for the case of the Tianlai Cylinder Pathfinder Array. In both cases, we find that the impact of the cross-coupling on the beam profile is relatively small. The understanding gained in this study is helpful in designing and understanding the beam-forming FRB digital backend for compact arrays such as the Tianlai array.

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arXiv2025

CRAFTS for HI cosmology: I. data processing pipeline and validation tests

We present the calibration procedures and validation of source measurement with the data of the Commensal Radio Astronomy FAST Survey (CRAFTS) for \HI intensity mapping by the Five-hundred-meter Aperture Spherical Radio Telescope (FAST). Using 70-hour drift-scan observation with the L-band (1.05-1.45GHz) 19-beam receiver, we obtain the data covering $270\,\rm deg^2$ sky area. We employ both the pulsar backend and the spectrum backend to calibrate the spectral time-ordered-data (TOD) before projecting them onto HEALPix maps. We produce calibrated TOD with frequency resolution of 30kHz and time resolution of 1s and the map data-cube with frequency resolution of 30kHz and spatial resolution of $2.95\,\rm arcmin^2$. We examine the pointing errors, noise overflow, RFI contamination and their effect on the data quality. The resulting noise level is $\sim$ 5.7mJy for the calibrated TOD and 1.6mJy for the map, consistent with the theoretical predictions within 5\% at RFI-free channels. We also validate the data by Principal Components Analysis (PCA) and find the residual map looks thermal noise dominated after removing 30 modes. We identify 447 isolated bright continuum sources in our data matching the NRAO-VLA Sky Survey (NVSS) catalog, with relative flux error of 8.3\% for TOD and 6.6\% for the map-level. We also measure the \HI emission of 90 galaxies with redshift $z<0.07$ and compare with \HI-MaNGA spectra, yielding an overall relative \HI integral flux error of 16.7\%. These results provide an important first step in assessing the feasibility of conducting cosmological \HI detection with CRAFTS.

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arXiv2025

GalaxyGenius: Mock galaxy image generator for various telescopes from hydrodynamical simulations

We introduce GalaxyGenius, a Python package designed to produce synthetic galaxy images tailored to different telescopes based on hydrodynamical simulations. Its implementation will support and advance research on galaxies in the era of large-scale sky surveys. The package comprises three main modules: data preprocessing, ideal data cube generation, and mock observation. Specifically, the preprocessing module extracts necessary properties of star and gas particles for a selected subhalo from hydrodynamical simulations and creates the execution file for the following radiative transfer procedure. Subsequently, building on the above information, the ideal data cube generation module executes a widely used radiative transfer project, specifically the SKIRT, to perform the SED assignment for each particle and the radiative transfer procedure to produce an IFU-like ideal data cube. Lastly, the mock observation module takes the ideal data cube and applies the throughputs of aiming telescopes, while also incorporating the relevant instrumental effects, point spread functions (PSFs), and background noise to generate the required mock observational images of galaxies. To showcase the outcomes of GalaxyGenius, we created a series of mock images of galaxies based on the IllustrisTNG and EAGLE simulations for both space and ground-based surveys, spanning ultraviolet (UV) to infrared (IR) wavelength coverage, including CSST, Euclid, HST, JWST, Roman, and HSC. GalaxyGenius offers a flexible framework to generate mock galaxy images with customizable recipes. These generated images can serve as valuable references for verifying and validating new approaches in astronomical research. They can also serve as training sets for relevant studies using deep learning in cases where real observational data are insufficient.

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arXiv2025

Forecast measurement of the 21 cm global spectrum from Lunar orbit with the Vari-Zeroth-Order Polynomial (VZOP) method

The cosmic 21 cm signal serves as a crucial probe for studying the evolutionary history of the Universe. However, detecting the 21 cm signal poses significant challenges due to its extremely faint nature. To mitigate the interference from the Earth's radio frequency interference (RFI), the ground and the ionospheric effects, the Discovering the Sky at the Longest Wavelength (DSL) project will deploy a constellation of satellites in Lunar orbit, with its high-frequency daughter satellite tasked with detecting the global 21 cm signal from cosmic dawn and reionization era (CD/EoR). We intend to employ the Vari-Zeroth-Order Polynomial (VZOP) for foreground fitting and subtracting. We have studied the effect of thermal noise, thermal radiation from the Moon, the Lunar reflection, anisotropic frequency-dependent beam, inaccurate antenna beam pattern, and RFI contamination. We discovered that the RFI contamination can significantly affect the fitting process and thus prevent us from detecting the signal. Therefore, experimenting on the far side of the moon is crucial. We also discovered that using VZOP together with DSL, after 1080 orbits around the Moon, which takes about 103 days, we can successfully detect the CD/EoR 21 cm signal.

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arXiv2025

Exploring cosmological constraints of the weak gravitational lensing and galaxy clustering joint analysis in the CSST photometric survey

We explore the joint weak lensing and galaxy clustering analysis from the photometric survey operated by the China Space Station Telescope (CSST), and study the strength of the cosmological constraints. We employ a high-resolution JiuTian-1G simulation to construct a partial-sky light cone to $z=3$ covering 100 deg$^2$, and obtain the CSST galaxy mock samples based on an improved semi-analytical model. We perform a multi-lens-plane algorithm to generate corresponding synthetic weak lensing maps and catalogs. Then we generate the mock data based on these catalogs considering the instrumental and observational effects of the CSST, and use the Markov Chain Monte Carlo (MCMC) method to perform the constraints. The covariance matrix includes non-Gaussian contributions and super-sample covariance terms, and the systematics from intrinsic alignments, galaxy bias, photometric redshift uncertainties, shear calibration, and non-linear effects are considered in the analysis. We find that the constraint result is comparable to that from Stage III surveys, and it can be significantly improved further in the full CSST survey with 17500 deg$^2$. This indicates the CSST photometric survey is powerful for exploring the Universe.

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arXiv2025

FAST Drift Scan Survey for HI Intensity Mapping. II. Stacking-based Beam Construction of the 19-feed Array at $1.4$ GHz

Neutral hydrogen (HI) intensity mapping (IM) presents great promise for future cosmological large-scale structure surveys. However, a major challenge for HIIM cosmological studies is to accurately subtract the foreground contamination. An accurate beam model is crucial for improving the quality of foreground subtraction. In this work, we develop a stacking-based beam reconstruction method utilizing the radio continuum point sources within the drift-scan field. Based on the Five-hundred-meter Aperture Spherical radio Telescope (FAST), we employ two sets of drift-scan survey data and merge the measurements to construct the beam patterns of the 19 FAST L-band feeds. To model the beams, we utilize the Zernike polynomial (ZP), which effectively captures asymmetric features of the main beam and the different side lobes. Due to the symmetric location of the beams, the main features of the beams are closely related to the distance from the center of the feed array, e.g., as the distance increases, side lobes become more pronounced. This modeling pipeline leverages the stable drift-scan data to extract beam patterns while accounting for and excluding the reflector's changing effects. It provides a more accurate measurement beam and a more precise model beam for FAST HIIM cosmology surveys.

astro-ph.IM↗

arXiv2025

FAST drift scan survey for HI intensity mapping: simulation on hunting HI filament with pairwise stacking

Filaments stand as pivotal structures within the cosmic web. However, direct detection of the cold gas content of the filaments remains challenging due to its inherent low brightness temperature. With the TNG hydrodynamical simulations, we demonstrate the effectiveness of isolating faint filament HI signal from the FAST HI intensity mapping (IM) survey through pairwise stacking of galaxies, which yields an average HI filament signal amplitude of $\sim 0.29\ {μ{\rm K}}$ at $z\simeq 0.1$. However, our simulations reveal a non-negligible contribution from HI-rich galaxies within or near the filaments. Particularly, the faint galaxies dominantly contribute to the extra filament HI signal. Our simulation also shows that the measurement uncertainty is produced by both thermal noise and background variation caused by brightness leakage from surrounding random galaxies. Given a fixed total observation time, a wide-field HI IM survey, which includes a large number of galaxy pairs, can simultaneously reduce thermal noise to below the filament signal level and minimize background variation to a negligible level. Through the end-to-end simulation, this work demonstrates the critical role of the galaxy pairwise stacking method in future filament HI detection, outlining a road map for filament HI detection in the next-generation HI IM surveys.

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arXiv2025

Loop I/NPS morphology predictions in the ultralong-wavelength band

Loop I/North Polar Spur (NPS) is the giant arc structure above the Galactic plane observed at radio wavelengths ($\lesssim 10$ GHz). There has been long-standing debate about its origin. While many people believe that it black consists of nearby supernova remnants (SNRs), some others consider it as a giant bubble close to the Galactic Center (GC), associated with the Fermi Bubble and the eROSITA X-ray bubble. At ultra-long wavelengths (wavelength $\gtrsim 10$ m or frequency $\lesssim 30$ MHz), particularly below $\sim 10$ MHz, the free-free absorption of the radio signal by diffuse electrons in the interstellar medium (ISM) becomes significant, resulting in different sky morphologies from those at higher frequencies. In this paper, we develop emissivity models for the two Loop I/NPS origin scenarios, and predict the Loop I/NPS morphology at ultra-long wavelengths in both scenarios, taking into account the free-free absorption effect.We find that in the SNRs model, the full Loop I/NPS will still be a bright arc even at $\sim 1$ MHz. In the GC model, the arc is fully visible only above $\sim 3$ MHz. While below this frequency, it is visible only at Galactic latitudes $b\gtrsim 30\degree$; the $b\lesssim 30 \degree$ part becomes invisible due to the absorption by the ISM electrons between the GC and the Sun. The upcoming space missions aiming at ultra-long wavelengths, such as the DSL and the FARSIDE, can potentially distinguish these two scenarios and provide decisive information about the origin of the Loop I/NPS.

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arXiv2025

A Multi-Mechanism Hybrid Model of Peaked-Spectrum Radio Sources

The peaked-spectrum (PS) sources exhibit turnover characteristics in their broad radio spectra. However, the mechanism underlying this phenomenon remains elusive. The two most common hypotheses are synchrotron self-absorption (SSA) and free-free absorption (FFA). By incorporating multiple absorption scenarios, we propose a multi-mechanism hybrid (MMH) model, which aligns well with current observational data and provides a good physical explanation. Using the GLEAM survey data, we identified a sample of 4,315 sources with peak frequencies approximately between 72--3000 MHz, most of which are MHz-peaked-spectrum sources (MPS). Our analysis shows that instead of SSA, the FFA is the dominant mechanism in producing the spectral turnover for most of the sources in this sample. The index of the optically thick spectrum alpha_thick has a lower boundary due to the FFA, and the steeper alpha_thick indicates a complex multi-absorption mechanism. In particular, the external FFA produces substantial alpha_thick, which exhibits a weak correlation with the peak frequency. Future ultra-long wavelength observations would also provide data on the spectrum of these sources at even lower frequencies. Determining the absorption mechanism that shaped the spectrum of these sources would be a crucial part of understanding their nature.

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arXiv2025

Future Cosmology: New Physics and Opportunity from the China Space Station Telescope (CSST)

The China Space Station Telescope (CSST) is the next-generation Stage~IV survey telescope. It can simultaneously perform multi-band imaging and slitless spectroscopic wide- and deep-field surveys in ten years and an ultra-deep field (UDF) survey in two years, which are suitable for cosmological studies. Here we review several CSST cosmological probes, such as weak gravitational lensing, two-dimensional (2D) and three-dimensional (3D) galaxy clustering, galaxy cluster abundance, cosmic void, Type Ia supernovae (SNe Ia), and baryonic acoustic oscillations (BAO), and explore their capabilities and prospects in discovering new physics and opportunities in cosmology. We find that CSST will measure the matter distribution from small to large scales and the expansion history of the Universe with extremely high accuracy, which can provide percent-level stringent constraints on the properties of dark energy and dark matter and precisely test the theories of gravity.

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arXiv2025

FAST drift scan survey for HI intensity mapping: simulation on Bayesian-stacking-based HI mass function estimation

This study investigates the estimation of the neutral hydrogen (HI) mass function (HIMF) using a Bayesian stacking approach with simulated data for the Five-hundred-meter Aperture Spherical radio Telescope (FAST) HI intensity mapping (HIIM) drift-scan surveys. Using data from the IllustrisTNG simulation, we construct HI sky cubes at redshift $z\sim0.1$ and the corresponding optical galaxy catalogs, simulating FAST observations under various survey strategies, including pilot, deep-field, and ultradeep-field surveys. The HIMF is measured for distinct galaxy populations -- classified by optical properties into red, blue, and bluer galaxies -- and injected with systematic effects such as observational noise and flux confusion caused by the FAST beam. The results show that Bayesian stacking significantly enhances HIMF measurements. For red and blue galaxies, the HIMF can be well constrained with pilot surveys, while deeper surveys are required for the bluer galaxy population. Our analysis also reveals that sample variance dominates over observational noise, emphasizing the importance of wide-field surveys to improve constraints. Furthermore, flux confusion shifts the HIMF toward higher masses, which we address using a transfer function for correction. Finally, we explore the effects of intrinsic sample incompleteness and propose a framework to quantify its impact. This work lays the groundwork for future \hiMF studies with FAST HIIM, addressing key challenges and enabling robust analyses of HI content across galaxy populations.

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arXiv2024

Estimating Photometric Redshifts for Galaxies from the DESI Legacy Imaging Surveys with Bayesian Neural Networks Trained by DESI EDR

We present a catalogue of photometric redshifts for galaxies from DESI Legacy Imaging Surveys, which includes $\sim0.18$ billion sources covering 14,000 ${\rm deg}^2$. The photometric redshifts, along with their uncertainties, are estimated through galaxy images in three optical bands ($g$, $r$ and $z$) from DESI and two near-infrared bands ($W1$ and $W2$) from WISE using a Bayesian Neural Network (BNN). The training of BNN is performed by above images and their corresponding spectroscopic redshifts given in DESI Early Data Release (EDR). Our results show that categorizing galaxies into individual groups based on their inherent characteristics and estimating their photo-$z$s within their group separately can effectively improve the performance. Specifically, the galaxies are categorized into four distinct groups based on DESI's target selection criteria: Bright Galaxy Sample (BGS), Luminous Red Galaxies (LRG), Emission Line Galaxies (ELG) and a group comprising the remaining sources, referred to as NON. As measured by outliers of $|Δz| > 0.15 (1 + z_{\rm true})$, accuracy $σ_{\rm NMAD}$ and mean uncertainty $\overline{E}$ for BNN, we achieve low outlier percentage, high accuracy and low uncertainty: 0.14%, 0.018 and 0.0212 for BGS and 0.45%, 0.026 and 0.0293 for LRG respectively, surpassing results without categorization. However, the photo-$z$s for ELG cannot be reliably estimated, showing result of $>15\%$, $\sim0.1$ and $\sim0.1$ irrespective of training strategy. On the other hand, NON sources can reach 1.9%, 0.039 and 0.0445 when a magnitude cut of $z<21.3$ is applied. Our findings demonstrate that estimating photo-$z$s directly from galaxy images is significantly potential, and to achieve high-quality photo-$z$ measurement for ongoing and future large-scale imaging survey, it is sensible to implement categorization of sources based on their characteristics.

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arXiv2024

Constraining the Galactic Structure using Time Domain Gravitational Wave Signal from Double White Dwarfs Detected by Space Gravitational Wave Detectors

The Gravitation Wave (GW) signals from a large number of double white dwarfs (DWDs) in the Galaxy are expected to be detected by space GW detectors, e.g., the Laser Interferometer Space Antenna (LISA), Taiji, and Tianqin in the millihertz band. In this paper, we present an alternative method by directly using the time-domain GW signal detected by space GW detectors to constrain the anisotropic structure of the Galaxy. The information of anisotropic distribution of DWDs is naturally encoded in the time-domain GW signal because of the variation of the detectors' directions and consequently the pattern functions due to their annual motion around the sun. The direct use of the time-domain GW signal enables simple calculations, such as utilizing an analytical method to assess the noise arising from the superposition of random phases of DWDs and using appropriate weights to improve the constraints. We investigate the possible constraints on the scale of the Galactic thin disk and bulge that may be obtained from LISA and Taiji by using this method with mock signals obtained from population synthesis models. We further show the different constraining capabilities of the low-frequency signal (foreground) and the high-frequency signal (resolvable-sources) via the Markov Chain Monte Carlo method, and find that the scale height and length of the Galactic thin disk and the scale radius of bulge can be constrained to a fractional accuracy of ~ 30%, 30%, 40% (or 20%, 10%, 40%) by using the low-frequency (or high-frequency) signal detected by LISA or Taiji.

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arXiv2024

HI Intensity Mapping cross-correlation with thermal SZ fluctuations: forecasted cosmological parameters estimation for FAST and Planck

The 21 cm emission from neutral hydrogen surveys holds great potential as a valuable method for exploring the large-scale structure of the Universe. In this paper, we forecast for the cross-correlation between the Thermal Sunyaev-Zel'dovich (SZ) fluctuations as probed by the Planck satellite, and fluctuations in the HI brightness temperature as probed by the ground-based Five-hundred-meter Aperture Spherical Telescope (FAST), to trace the connection between galaxy clusters and the HI large-scale structure. Assuming that the measurement is limited by instrumental noise rather than by foreground, we estimate the potential detectability of the cross-correlation signal and their improvement in the measurement of the HI cosmic density, the hydrostatic mass bias parameter, and the universal pressure profile (UPP) parameters. We obtain a constraint on the cosmic neutral hydrogen density parameter significantly to $σ(Ω_{\rm HI}) = 1.0 \times 10^{-6}$. We also find that the average halo masses contributing to the ${{\rm HI}-y}$ cross-power spectrum in the one-halo regime is $\sim 1.5\times 10^{14} M_{\odot}$. Our results also show that the HI-SZ cross-correlation has great potential to probe the distribution of neutral hydrogen (HI) within halos at low redshift.

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