arXiv subjects

Yidong Xu

Publications and source records attributed to Yidong Xu.

At least 37 records · Page 2Linked to original sources

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

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

The Formation of Direct Collapse Black Holes at Cosmic Dawn and 21 cm Global Spectrum

JWST reveals numerous high-z galaxies and Supermassive Black Holes (SMBHs), suggesting that stars and SMBH seeds formation at $z \gtrsim 10$ may be more efficient than previously derived. One popular SMBH seed scenario is the Direct Collapse Black Holes (DCBHs) formed in pristine atomic-cooling halos irradiated by nearby galaxies. Therefore, the efficient star formation likely facilitates the formation of DCBH. We calculate the first critical $k_{\rm H_2}-k_{\rm H^-}$ curves for DCBH formation under the influence of X-ray radiation using the one-zone model. We then build the UV luminosity function consistent with JWST observations and incorporate it into the model that calculates the DCBH-triggering probability. We confirm that enhanced star formation promotes the DCBH formation. However, the DCBH abundance $n_{\rm DCBH}$ is significantly influenced by the X-ray radiation that is also related to star formation. Since the 21 cm global spectrum is also X-ray dependent, the 21 cm absorption depth $δT_b^{\rm trough}$ at Cosmic Dawn encodes the DCBH abundance information. We provide a tentative trend in the $n_{\rm DCBH}$ - $δT^{\rm trough}_{\rm b}$ relation, which could be a useful guide. In our fiducial model, if $δT_b^{\rm trough}\gtrsim -100$ mK, then the DCBH is rather rare; if $-150~{\rm mK} \lesssim δT_b^{\rm trough}\lesssim -100$ mK, $ n_{\rm DCBH} \sim \mathcal{O}(10^{-2}-10^{-3})$ cMpc$^{-3}$ (comoving $\rm Mpc^{-3}$), consistent with the HST/JWST observed SMBHs abundance at $z\gtrsim 6$; if $δT_b^{\rm trough}\lesssim -150$ mK, $n_{\rm DCBH}$ can largely exceed $\mathcal{O}(10^{-2})$ cMpc$^{-3}$. The 21 cm global spectrum observations will help to constrain the DCBH abundance.

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arXiv2025

The FAST HI 21-cm absorption blind survey. II. -- Statistic Exploration for Associated and Intervening systems

We present an extragalactic HI 21-cm absorption lines catalog from a blind search at z $\leqslant$ 0.35, using drift-scan data collected in 1325.6 hours by the ongoing Commensal Radio Astronomy FasT Survey (CRAFTS) and FAST All Sky HI Survey (FASHI), which spans a sky area of 6072.0 deg$^{2}$ and covers 84533 radio sources with a flux density greater than 12 mJy. 14 previously identified HI absorbers and 20 newly discovered HI absorbers were detected, comprising 15 associated systems, 10 intervening systems, and 9 systems with undetermined classifications. Through spectral stacking, the mean peak optical path, mean velocity-integrated optical path, mean FWHM and mean HI column density are measured to be 0.47 and 0.30; 27.19 and 4.36 km s$^{-1}$; 42.61 and 9.33 km s$^{-1}$; 0.49 and 0.08 T$_{s} \times$ 10$^{20}$cm$^{-2}$K$^{-1}$, for the associated and intervening samples, respectively. Statistical analysis also reveals that associated systems tend to be hosted by red ($g-r>$0.7) galaxies at lower redshifts, whereas galaxies hosting intervening HI absorption are typically found at higher redshifts and are of a bluer ($g-r\leqslant$0.7) type. A noticeable difference is observed in the positions of foregrounds, backgrounds of intervening systems, and high-redshift and low-redshift associated systems on the WISE color-color diagram. All identified foreground sources in our sample have W1-W2 magnitudes below 0.8, suggesting no Active Galactic Nuclei (AGN). In contrast, backgrounds of intervening systems tend to have W1-W2 magnitudes above 0.8, indicating AGN presence. For associated absorption, most low-redshift ($z\leqslant$0.5) systems show W1-W2 values below 0.8, while higher-redshift associated absorption ($z>$0.5) displays a broader range of W1-W2 values.

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arXiv2024

Prospects for Observing High-redshift Radio-loud Quasars in the SKA Era: Paving the Way for 21-cm Forest Observations

The 21-cm forest is a sensitive probe for the early heating process and small-scale structures during the epoch of reionization (EoR), to be realized with the upcoming Square Kilometre Array (SKA). Its detection relies on the availability of radio-bright background sources, among which the radio-loud quasars are very promising, but their abundance during the EoR is still poorly constrained due to limited observations. Here, we use a physics-driven model to forecast future radio-loud quasar observations. We fit the parameters of the model using observational data of high-redshift quasars. Assuming Eddington accretion, the model yields an average lifetime of $t_{\rm q} \sim 10^{5.3}$yr for quasars at $z\sim6$, consistent with recent results obtained from quasar proximity zone pre-study. We show that if the radio-loud fraction of quasars evolves with redshift, it will significantly reduce the abundance of observable radio-loud quasars in the SKA era, making 21-cm forest studies challenging. With a constant radio-loud fraction, our model suggests that a one-year sky survey conducted with SKA-LOW has the capability to detect approximately 20 radio-loud quasars at $z\sim 9$, with sufficient sensitivity to resolve individual 21-cm forest lines.

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arXiv2024

Large-scale Array for Radio Astronomy on the Farside

At the Royal Society meeting in 2023, we have mainly presented our lunar orbit array concept called DSL, and also briefly introduced a concept of a lunar surface array, LARAF. As the DSL concept had been presented before, in this article we introduce the LARAF. We propose to build an array in the far side of the Moon, with a master station which handles the data collection and processing, and 20 stations with maximum baseline of 10 km. Each station consists 12 membrane antenna units, and the stations are connected to the master station by power line and optical fiber. The array will make interferometric observation in the 0.1-50 MHz band during the lunar night, powered by regenerated fuel cells (RFCs). The whole array can be carried to the lunar surface with a heavy rocket mission, and deployed with a rover in 8 months. Such an array would be an important step in the long term development of lunar based ultralong wavelength radio astronomy. It has a sufficiently high sensitivity to observe many radio sources in the sky, though still short of the dark age fluctuations. We discuss the possible options in the power supply, data communication, deployment, etc.

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arXiv2024

Velocity acoustic oscillations on Cosmic Dawn 21 cm power spectrum as a probe of small-scale density fluctuations

We investigate the feasibility of using the velocity acoustic oscillations (VAO) features on the Cosmic Dawn 21 cm power spectrum to probe small-scale density fluctuations. In the standard cold dark matter (CDM) model, Pop III stars form in minihalos and affect the 21 cm signal through Ly$α$ and X-ray radiation. Such a process is modulated by the relative motion between dark matter and baryons, generating the VAO wiggles on the 21 cm power spectrum. In the fuzzy or warm dark matter models for which the number of minihalos is reduced, the VAO wiggles are weaker or even fully invisible. We investigate the wiggle features in the CDM with different astrophysical models and in different dark matter models. We find: 1) In the CDM model the relative streaming velocities can generate the VAO wiggles for broad ranges of parameters $f_*$, $ζ_X$ and $f_{\rm esc,LW}ζ_{\rm LW}$, though for different parameters the wiggles would appear at different redshifts and have different amplitudes. 2) For the axion model with $m_{\rm a} \lesssim10^{-19}$ eV, the VAO wiggles are negligible. In the mixed model, the VAO signal is sensitive to the axion fraction. For example, the wiggles almost disappear when $f_{\rm a} \gtrsim 10\%$ for $m_{\rm a}=10^{-21}$ eV. Therefore, the VAO signal can be an effective indicator for small-scale density fluctuations and a useful probe of the nature of dark matter. The SKA-low with $\sim$2000 hour observation time has the ability to detect the VAO signal and constraint dark matter models.

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arXiv2023

The 21-cm forest as a simultaneous probe of dark matter and cosmic heating history

The absorption features in spectra of high-redshift background radio sources, caused by hyperfine structure lines of hydrogen atoms in the intervening structures, are known collectively as the 21-cm forest. They provide a unique probe of small-scale structures during the epoch of reionization, and can be used to constrain the properties of the dark matter (DM) thought to govern small-scale structure formation. However, the signals are easily suppressed by heating processes that are degenerate with a warm DM model. Here we propose a probe of both the DM particle mass and the heating history of the Universe, using the one-dimensional power spectrum of the 21-cm forest. The one-dimensional power spectrum measurement not only breaks the DM model degeneracy but also increases the sensitivity, making the probe actually feasible. Making 21-cm forest observations with the upcoming Square Kilometre Array has the potential to simultaneously determine both the DM particle mass and the heating level in the early Universe, shedding light on the nature of DM and the first galaxies.

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arXiv2023

Detections of 21-cm absorption with a blind FAST survey at z $\leqslant$ 0.09

We present the early science results from a blind search of the extragalactic HI 21-cm absorption lines at z $\leqslant$ 0.09 with the drift-scan observation of the Five-hundred-meter Aperture Spherical radio Telescope (FAST). We carried out the search using the data collected in 643.8 hours by the ongoing Commensal Radio Astronomy FasT Survey (CRAFTS), which spans a sky area of 3155 deg$^{2}$ and covers 44827 radio sources with a flux density greater than 12 mJy. Due to the radio frequency interference (RFI), only the relatively clean data in the frequency range of 1.3-1.45 GHz are used in the present work. Under the assumption of $T_{s}/c_{f}$ = 100 K, the total completeness-corrected comoving absorption path length spanned by our data and sensitive to Damped Lyman $α$ Absorbers (DLAs) are $ΔX^{inv}$ = 8.33$\times10^3$ ($Δz^{inv} = 7.81\times10^{3}$) for intervening absorption. For associated absorption, the corresponding values are $ΔX^{asc}$ = 12.8 ($Δz^{asc} = 11.9$). Three known HI absorbers (UGC 00613, 3C 293 and 4C +27.14) and two new HI absorbers (towards NVSS J231240-052547 and NVSS J053118+315412) are detected blindly. We fit the HI profiles with multi-components Gaussian functions and calculate the redshift (0.063, 0.066), width, flux density, optical depth and HI column densities for each absorption. Our results demonstrate the power of FAST in blindly searching HI absorbers. For absorption towards NVSS J231240-052547, the optical counterparts are faint and currently lack existing spectra. The most likely interpretation is that a radio-loud active galactic nucleus (AGN) is faint in the optical as the background source, with a faint optical absorber in between. NVSS J053118+315412 exhibits an associated absorption with a complex profile, which may suggest unsettled gas structures or gas accretion onto the supermassive black hole (SMBH).

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arXiv2023

Reionizing islands with inhomogeneous recombinations

Observations are beginning to constrain the history of the epoch of reionization (EoR). Modeling the reionization process is indispensable to interpret the observations, to infer the properties of ionizing sources, and to probe the various astrophysical processes from the observational data. Here we present an improved version of the semi-numerical simulation islandFAST, by incorporating inhomogeneous recombinations and a corresponding inhomogeneous ionizing background, and simulate the reionization process of neutral islands during the late EoR. We find that the islands are more fragmented in models with inhomogeneous recombinations than the case with a homogeneous recombination number. In order to investigate the effects of basic assumptions in the reionization modeling, we compare the results from islandFAST with those from 21cmFAST for the same assumptions on the ionizing photon sources and sinks, to find how the morphology of the ionization field and the reionization history depend on the different treatments of these two models. Such systematic bias should be noted when interpreting the upcoming observations.

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arXiv2023

Cosmic Radio Background from Primordial Black Holes at Cosmic Dawn

The presence of an extra radio background besides the cosmic microwave background has important implications for the observation of the 21-cm signal during the cosmic Dark Ages, Cosmic Dawn, and epoch of Reionization. The strong absorption trough found in the 21-cm global spectrum measured by the EDGES experiment, which has a much greater depth than the standard model prediction, has drawn great interest to this scenario, but more generally it is still of great interest to consider such a cosmic radio background (CRB) in the early Universe. To be effective in affecting the 21-cm signal at early time, such a radio background must be produced by sources which can emit strong radio signals but modest amount of X-rays, so that the gas is not heated up too early. We investigate the scenario that such a radio background is produced by the primordial black holes (PBHs). For PBH with a single mass, we find that if the PBHs' abundance $\log(f_{\rm PBH})$ (ratio of total PBH mass density to total matter density) and mass satisfy the relation $\log(f_{\rm PBH}) \sim -1.8\log(M_\bullet/{\rm M}_{\odot})-3.5$ for $1\,{\rm M}_\odot \lesssim M_\bullet \lesssim 300 {\rm M}_\odot$, and have jet emission, they can generate a CRB required for reproducing the 21-cm absorption signal seen by the EDGES. The accretion rate can be boosted if the PBHs are surrounded by dark matter halos, which permits lower $f_{\rm PBH}$ value to satisfy the EDGES observation. In the latter scenario, since the accretion rate can evolve rapidly during the Cosmic Dawn, the frequency (redshift) and depth of the absorption trough can determine the mass and abundance of the PBHs simultaneously. For absorption trough redshift $\sim$ 17 and depth $\sim -500$ mK, it corresponds to $M_\bullet \sim 1.05\,{\rm M}_{\odot}$ and $f_{\rm PBH}\sim 1.5\times10^{-4}$.

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arXiv2022

A new method of reconstructing Galactic three-dimensional structures using ultralong-wavelength radio observations

The free-free absorption of low frequency radio waves by thermal electrons in the warm ionized medium of our Galaxy becomes very significant at $\lesssim 10$ MHz (ultralong-wavelength), and the absorption strength depends on the radio frequency. Upcoming space experiments such as the Discovering Sky at the Longest wavelength (DSL) and Farside Array for Radio Science Investigations of the Dark ages and Exoplanets (FARSIDE) will produce high-resolution multi-frequency sky maps at the ultralong-wavelength, providing a new window to observe the Universe. In this paper we propose that from these ultralong-wavelength multi-frequency maps, the three-dimensional distribution of the Galactic electrons can be reconstructed. This novel and robust reconstruction of the Galactic electron distribution will be a key science case of those space missions. Ultralong-wavelength observations will be a powerful tool for studying the astrophysics relevant to the Galactic electron distribution, for example, the impacts of supernova explosions on electron distribution, and the interaction between interstellar atoms and ionizing photons escaped from the HII regions around massive stars. An animation shows the reconstructed results using {\tt NE2001} model as input test. On ArXiv, it is given in the directory: Ancillary files. In the paper the animation is linked to Fig. 5.

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arXiv2022

Impact of the turnover in the high-z galaxy luminosity function on the 21-cm signal during Cosmic Dawn and Epoch of Reionization

The shape of the faint-end of the high-z galaxy luminosity function (LF) informs early star formation and reionization physics during the Cosmic Dawn and Epoch of Reionization. Until recently, based on the strong gravitational lensing cluster deep surveys, the Hubble Frontier Fields (HFF) has found a potential turnover in the ultraviolet (UV) LF at z$\sim$6. In this paper, we analyze the contribution of extremely faint galaxies with the magnitude larger than the turnover magnitude in LF to cosmic reionization. We apply the measurement from HFF to our suppressed star formation efficiency model, including three free parameters: halo mass threshold $M_t$, curvature parameter $β$ and a UV conversion factor $l_{\rm UV}$. According to our fit of 68\% confidence level, the high-redshift star formation in haloes smaller than $ M_t=1.82^{+2.86}_{-1.08}\times10^{10} \rm M_{\odot}$ is found to be dampened. The turnover magnitude $\rm \gtrsim -13.99-2.45$, correspondingly the halo mass $\lesssim(4.57+20.03)\times10^{9} \rm M_{\odot}$. We find that the absorption trough in the global 21-cm signal is sensitive to our SFE model parameters. Together with ($β$, $l_{\rm UV}$) = ($2.17^{+2.42}_{-1.72}$, $9.33^{+0.43}_{-0.42} \rm ~erg~yr ~s^{-1}M_{\odot}^{-1})$, the trough locates at $\sim$ $134^{+10}_{-17}$ $\rm MHz$ with an amplitude of $\sim$ $-237^{-6}_{+7}$ $\rm mK$, compared to (106\rm MHz, -212\rm mK) in the absence of turnover. Besides, we find that the star formation of faint galaxies has also an impact on the 21-cm power spectra. The best fitting peak power decreases by $\sim4\%$ and shifts towards smaller scales from $0.88 h \rm Mpc^{-1}$ to $0.91 h \rm Mpc^{-1}$. According to our calculation, such impact is distinguishable with the forthcoming Square Kilometre Array.

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arXiv2022

The Tianlai dish array low-z surveys forecasts

We present the science case for surveys with the Tianlai dish array interferometer tuned to the $\left[ 1300, 1400 \right] \mathrm{MHz}$ frequency range. Starting from a realistic generation of mock visibility data according to the survey strategy, we reconstruct a map of the sky and perform a foreground subtraction. We show that a survey of the North Celestial Polar cap during a year of observing time and covering an area of $150 \, \mathrm{deg^2}$ would reach a sensitivity of $ 1.5-2 \, \mathrm{mK} $ per $1 \, \mathrm{MHz} \times 0.25^2 \, \mathrm{deg^2 }$ voxel and be marginally impacted by mode-mixing. Tianlai would be able to detect a handful $(\sim 10)$ of nearby massive \HI clumps as well as a very strong cross-correlation signal of 21\,cm intensity maps with the North Celestial Cap Survey optical galaxies. We have also studied the performance of a mid-latitude survey, covering $\sim 1500 \, \mathrm{deg^2}$ centered on a declination of $δ=55^\circ$, which overlaps the Sloan Digital Sky Survey footprint. Despite a higher noise level for the mid-latitude survey, as well as significant distortions due to mode mixing, Tianlai would be able to detect a highly significant cross-correlation between the 21\,cm signal and the Sloan spectroscopic galaxy sample. Using the extragalactic signals from either or both of these surveys, it will be possible to assess the impact of calibration uncertainties, antenna pattern uncertainties, sources of noise, and mode mixing for future surveys requiring higher sensitivity.

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arXiv2022

Lunar Orbit Measurement of Cosmic Dawn 21 cm Global Spectrum

A redshifted 21 cm line absorption signature is commonly expected from the cosmic dawn era, when the first stars and galaxies formed. The detailed traits of this signal can provide important insight on the cosmic history. However, high precision measurement of this signal is hampered by the ionosphere refraction and absorption, as well as radio frequency interference (RFI). A space observation can solve the problem of the ionosphere, and the Moon can shield the RFI from the Earth. In this paper, we present simulations of the global spectrum measurement in the 30 -- 120 MHz frequency band on the lunar orbit, from the proposed Discovering the Sky at the Longest wavelength (DSL) project. In particular, we consider how the measured signal varies as the satellite moves along the orbit, take into account the blockage of different parts of the sky by the Moon and the antenna response. We estimate the sensitivity for such a 21 cm global spectrum experiment. An RMS noise level of $\le 0.05$ K is expected at 75 MHz after 10 orbits ($\sim$ 1 day) observation, for a frequency channel width of 0.4 MHz. We also study the influence of a frequency-dependent beam, which may generate complex spectral structures in the spectrum. Estimates of the uncertainties in the foreground and 21 cm model parameters are obtained.

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arXiv2022

Effects of Small-Scale Absorption Systems on Neutral Islands during the Late Epoch of Reionization

The reionization process is expected to be prolonged by the small-scale absorbers (SSAs) of ionizing photons, which have been seen as Lyman-limit systems in quasar absorption line observations. We use a set of semi-numerical simulations to investigate the effects of absorption systems on the reionization process, especially their impacts on the neutral islands during the late Epoch of Reionization (EoR). Three models are studied, i.e. the extreme case of no-SSA model with a high level of ionizing background, the moderate-SSA model with a relatively high level of ionizing background, and the dense-SSA model with a low level of ionizing background. We find that while the characteristic scale of neutral regions decreases during the early and middle stages of reionization, it stays nearly unchanged at about 10 comoving Mpc during the late stage for the no-SSA and moderate-SSA models. However, in the case of weak ionizing background in the dense-SSA model, the characteristic island scale shows obvious evolution, as large islands break into many small ones that are slowly ionized. The evolutionary behavior of neutral islands during the late EoR thus provides a novel way to constrain the abundance of SSAs. We discuss the 21-cm observation with the upcoming Square Kilometre Array. The different models can be distinguished by either the 21-cm imaging or the 21-cm power spectrum measurements.

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arXiv2021

Imaging sensitivity of a linear interferometer array on lunar orbit

Ground-based observation at frequencies below 30 MHz is hindered by the ionosphere of the Earth and radio frequency interference. To map the sky at these low frequencies, we have proposed the Discovering the Sky at the Longest wavelength mission (DSL, also known as the "Hongmeng" mission, which means "Primordial Universe" in Chinese) concept, which employs a linear array of micro-satellites orbiting the Moon. Such an array can be deployed to the lunar orbit by a single rocket launch, and it can make interferometric observations achieving good angular resolutions despite the small size of the antennas. However, it differs from the conventional ground-based interferometer array or even the previous orbital interferometers in many aspects, new data-processing methods need to be developed. In this work, we make a series of simulations to assess the imaging quality and sensitivity of such an array. We start with an input sky model and a simple orbit model, generate mock interferometric visibilities, and then reconstruct the sky map. We consider various observational effects and practical issues, such as the system noise, antenna response, and Moon blockage. Based on the quality of the recovered image, we quantify the imaging capability of the array for different satellite numbers and array configurations. For the first time, we make practical estimates of the point source sensitivity for such a lunar orbit array, and predict the expected number of detectable sources for the mission. Depending on the radio source number distribution which is still very uncertain at these frequencies, the proposed mission can detect $10^2 \sim 10^4$ sources during its operation.

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arXiv2021

Maximum Absorption of the Global 21 cm Spectrum in the Standard Cosmological Model

The absorption feature in the global spectrum is likely the first 21 cm observable from the cosmic dawn, which provides valuable insights into the earliest history of structure formation. We run a set of high-resolution hydrodynamic simulations of early structure formation to assess the effect of non-linear structure formation on the maximum absorption level (i.e. assuming the spin temperature coupling is saturated) of the global 21 cm spectrum in the standard cosmological framework. We ignore the star formation and feedbacks, which also tends to reduce the absorption signal, but take into account the inevitable non-linear density fluctuations in the intergalactic medium (IGM), shock heating, and Compton heating, which can reduce the absorption level. We found that the combination of these reduced the maximum absorption signal by $\sim 15\%$ at redshift 17, as compared with the homogeneous or linearly fluctuating IGM. These effects have to be carefully accounted for when interpreting the observational results, especially when considering the necessity of introducing new physics.

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