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Shiv Sethi

Publications and source records attributed to Shiv Sethi.

At least 19 recordsLinked to original sources
arXiv2026

X-ray polarization in magnetized neutron stars

X-ray polarimetry has opened a new window into understanding the physics around magnetized compact objects. IXPE detection of linear polarization from such systems has prompted a new spurt of theoretical modeling. Our study is based on the dominant paradigm that the observed polarization arises from the scattering of photons around highly magnetized systems. Our main focus is the dependence of the polarization of the scattered light on properties of the incoming light, i.e., geometry and the polarization state, and the determination of the spectral shape of the polarized light for a wide range of magnetic field strengths. We also analyze the impact of vacuum birefringence on photon polarization. We show that, generically, we expect a higher linear degree of polarization from magnetars as compared to normal pulsars, which is in agreement with IXPE observations. Under some conditions, our study helps to understand the observed degree of polarization from normal pulsars and low-magnetized neutron stars and their spectral dependence. However, we cannot conclusively explain the spectral shape of the observed polarization for magnetars using only a single component emission from scattering in a strong magnetic field. This probably points to the system being more complex, e.g., multi-component, than our study allows for. Upcoming X-ray polarimeters with broader energy coverage could probe some of our other predictions, e.g., the spectral shape of the polarized light close to the resonance frequency.

astro-ph.HE↗
arXiv2026

Observations of the Cosmic Dawn and Epoch of Reionization with the SKAO: Observational Lessons Learned from Precursors and Pathfinder Instruments

This chapter summarizes the observational lessons learned after two decades of observations of the Cosmic Dawn (CD) and Epoch of Reionization (EoR) with SKAO pathfinders and precursors. We will describe the effort towards building accurate simulation pipelines for actual observations and summarize the approaches that different groups have taken to calibrate and mitigate systematic effects such as sky model incompleteness, limited instrument models and antenna mutual coupling. We conclude by discussing the impact that these lessons may have on the design and analysis of upcoming SKAO observations of the Cosmic Dawn and Epoch of Reionization.

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arXiv2026

The Tracking Tapered Gridded Estimator for the 21-cm power spectrum from the Murchison Widefield Array (MWA) drift scan observations -- III. Improved upper limits at $z = 8.2$ from multiple pointings

We analyze zenith-pointing $(\delta=-26.7^{\circ})$ Murchison Widefield Array (MWA) $\nu_c=154.2 \,{\rm MHz}$ drift scan observations covering $349.0^{\circ} \le \alpha \le 70.0^{\circ}$ with 163 pointing centers (PCs) spaced by $0.5^{\circ}$. We measure $D_{\ell}$, the mean-squared angular brightness temperature fluctuations, as a function of $\alpha$. A broad peak at $\alpha \approx 50.0^{\circ}$ corresponds to the bright extended source Fornax~A in the main lobe of the primary beam. A smaller peak at $\alpha \approx 5.0^{\circ}$ possibly corresponds to Fornax~A in the first sidelobe. For $\alpha \leq 22.0^{\circ}$ and $\ell \ge 200$, we find $D_{\ell} \propto \ell^2$, which we interpret as Poisson fluctuations from point sources. We present $\Delta^2(k)$, the mean-squared 21-cm brightness temperature fluctuations from the Epoch of Reionization, as a function of $\alpha$. Fornax~A causes strong contamination near $\alpha \approx 50.5^{\circ}$, elsewhere several PCs are consistent with noise. The range $358.5^{\circ} \leq \alpha \leq 11.5^{\circ}$ is relatively foreground-free and best suited for EoR science. The PC at $\alpha = 11.0^{\circ}$ yields the best $2\sigma$ upper limit $\Delta^{2}_{\rm UL}(k) = (173.13)^{2}\,{\rm mK^{2}}$ at $k = 0.161\,{\rm Mpc^{-1}}$. We incoherently combine $23$ PCs to obtain $\Delta_{\rm UL}^2(k)=(98.67)^{2}\,{\rm mK}^{2}$ at $k=0.156\,{\rm Mpc}^{-1}$. This is the tightest upper limit from the MWA, being $\approx3$ times lower than earlier MWA limits at $z = 8.2$, but $\approx2$ and $\approx21$ times higher than the LOFAR and HERA limits, respectively, and $\approx3$ orders of magnitude above theoretical predictions.

astro-ph.CO↗
arXiv2026

GBD-DART-I : Pulsars and transient source observation between 130 MHz and 350 MHz at Gauribidanur

Gauribidanur Diamond Array Radio Telescope (GBD-DART) is a new small LPDA antenna array consisting of 64 short dipoles and associated receivers that has been custom developed and deployed at the Gauribidanur observatory (13.604 N, 77.427 E) to study bright Pulsars and Solar transients in the frequency range of 130-350 MHz. The LPDAs are arranged in a checkerboard layout, with opposite pairs combined to enable dual-polarised operation. A diamond-shaped (tilted square) array configuration was chosen to achieve high sidelobe suppression in the East-West and North-South directions. The tile measures 5.9 meters by 5.9 meters, with diagonals along both the North-South and East-West directions, each measuring about 8.4 meters. The LPDA array with one diamond-shaped tile has been fully commissioned and is operating in transit-observing mode, successfully detecting strong pulsars and solar flares over the last seven months. The present digital backend restricts the instantaneous bandwidth for observations to 16 MHz. The array operations are streamlined to facilitate remote operations. Apart from investigating Pulsar and Solar phenomena at low radio frequencies in selected sources, this work aims to provide a training platform for radio astronomy through simple-to-construct, low-cost radio telescopes. In this paper, we present details of the array, including antenna and array response studies, brief descriptions of front-end and backend instrumentation, and illustrative results from observations of both pulsars and solar flares. It will also provide brief details of future upgrade plans, particularly for the tiles and digital backend, to facilitate the observation of additional sources.

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arXiv2025

Synchrotron radiation from NGC 470 HLX1 - a hidden hyperluminous accreting neutron star?

We present the first broadband spectral analysis of NGC 470 HLX1, a hyperluminous X-ray source that exhibits significant flux variability over different epochs. We investigate the feasibility of synchrotron radiation with varying latitude from a magnetized neutron star to explain the source's spectra. Although the statistical quality of the data does not allow us to rule out simple phenomenological models, it is adequate to constrain the parameter space for this more physically motivated model. We also shed light on the particle acceleration mechanisms and maximum Lorentz factor of electrons within the neutron star magnetospheric plasma under super-Eddington accretion conditions. In our broadband spectral modeling, the detection of a blackbody-like component suggests the presence of a disk near the corotation radius or an outflow ejected from the disk. The viability of synchrotron emission in an HLX system offers new insights about the nature of these sources, motivating further sample studies to assess whether most of these sources are powered by accreting neutron stars.

astro-ph.HE↗
arXiv2025

A measurement of Galactic synchrotron emission using MWA drift scan observations

Studying the diffuse Galactic synchrotron emission (hereafter, DGSE) at arc-minute angular scale is important to remove the foregrounds for the cosmological 21-cm observations. Statistical measurements of the large-scale DGSE can also be used to constrain the magnetic field and the cosmic ray electron density of our Galaxy's interstellar medium (ISM). Here, we have used the Murchison Widefield Array (MWA) drift scan observations at $154.2 \, {\rm MHz}$ to measure the angular power spectrum $({\cal C}_{\ell})$ of the DGSE of a region of the sky from right ascension (RA) $349^{\circ}$ to $70.3^{\circ}$ at the fixed declination $-26.7^{\circ}$. In this RA range, we have chosen 24 pointing centers (PCs), for which we have removed all the bright point sources above $\sim430 \, {\rm mJy}\,(3\sigma)$, and applied the Tapered Gridded Estimator (TGE) on residual data to estimate the ${\cal C}_{\ell}$. We use the angular multipole range $65 \le \ell \le 650$ to fit the data with a model, ${\cal C}^M_{\ell}=A\times \left(\frac{1000}{\ell}\right)^{\beta}+C$, where we interpret the model as the combination of a power law $(\propto \ell^{-\beta})$ nature of the DGSE and a constant part due to the Poisson fluctuations of the residual point sources. We are able to fit the model ${\cal C}^M_{\ell}$ for six PCs centered at $\alpha=352.5^{\circ}, 353^{\circ}, 357^{\circ}, 4.5^{\circ}, 4^{\circ}$ and $1^{\circ}$. We run the Markov Chain Monte Carlo (MCMC) ensemble sampler to get the best-fit values of the parameters $A, \beta$ and $C$ for these PCs. We see that the values of $A$ vary in the range $155$ to $400$ mK$^{2}$, whereas the $\beta$ varies in the range $0.9$ to $1.7$. We find that the value of $\beta$ is consistent at $2-\sigma$ level with the earlier measurement of the DGSE at similar frequency and angular scales.

astro-ph.GA↗
arXiv2024

The Tracking Tapered Gridded Estimator for the 21-cm power spectrum from MWA drift scan observations II: The Missing Frequency Channels

Missing frequency channels pose a problem for estimating $P(k_\perp,k_\parallel)$ the redshifted 21-cm power spectrum (PS) from radio-interferometric visibility data. This is particularly severe for the Murchison Widefield Array (MWA), which has a periodic pattern of missing channels that introduce spikes along $k_\parallel$. The Tracking Tapered Gridded Estimator (TTGE) overcomes this by first correlating the visibilities in the frequency domain to estimate the multi-frequency angular power spectrum (MAPS) $C_\ell(\Delta\nu)$ that has no missing frequency separation $\Delta\nu$. We perform a Fourier transform along $\Delta\nu$ to estimate $P(k_\perp,k_\parallel)$. Considering our earlier work, simulations demonstrate that the TTGE can estimate $P(k_\perp,k_\parallel)$ without any artifacts due to the missing channels. However, the spikes were still found to persist for the actual data, which is foreground-dominated. The current work presents a detailed investigation considering both simulations and actual data. We find that the spikes arise due to a combination of the missing channels and the strong spectral dependence of the foregrounds. Based on this, we propose and demonstrate a technique to mitigate the spikes. Applying this, we find the values of $P(k_\perp,k_\parallel)$ in the region $0.004 \leq k_\perp \leq 0.048\,{\rm Mpc^{-1}}$ and $k_\parallel > 0.35 \,{\rm Mpc^{-1}}$ to be consistent with zero within the expected statistical fluctuations. We obtain the $2\sigma$ upper limit of $\Delta_{\rm UL}^2(k)=(918.17)^2\,{\rm mK^2}$ at $k=0.404\,{\rm Mpc^{-1}}$ for the mean squared brightness temperature fluctuations of the $z=8.2$ epoch of reionization (EoR) 21-cm signal. This upper limit is from just $\sim 17$ minutes of observation for a single pointing direction. We expect tighter constraints when we combine all $162$ different pointing directions of the drift scan observation.

astro-ph.CO↗
arXiv2024

The Tracking Tapered Gridded Estimator for the 21-cm power spectrum from MWA drift scan observations I: Validation and preliminary results

Drift scan observations provide the broad sky coverage and instrumental stability needed to measure the Epoch of Reionization (EoR) 21-cm signal. In such observations, the telescope's pointing center (PC) moves continuously on the sky. The Tracking Tapered Gridded Estimator (TTGE) combines observations from different PC to estimate $P(k_{\perp}, k_{\parallel})$ the 21-cm power spectrum, centered on a tracking center (TC) which remains fixed on the sky. The tapering further restricts the sky response to a small angular region around TC, thereby mitigating wide-field foregrounds. Here we consider $154.2 \, {\rm MHz}$ ($z = 8.2$) Murchison Widefield Array (MWA) drift scan observations. The periodic pattern of flagged channels, present in MWA data, is known to introduce artefacts which pose a challenge for estimating $P(k_{\perp}, k_{\parallel})$. We demonstrate that the TTGE is able to recover $P(k_{\perp}, k_{\parallel})$ without any artefacts, and estimate $P(k)$ within $5 \%$ accuracy over a large $k$-range. We also present preliminary results for a single PC, combining 9 nights of observation $(17 \, {\rm min}$ total). We find that $P(k_{\perp}, k_{\parallel})$ exhibits streaks at a fixed interval of $k_{\parallel}=0.29 \, {\rm Mpc}^{-1}$, which matches $\Delta \nu_{\rm per}=1.28 \, {\rm MHz}$ that is the period of the flagged channels. The streaks are not as pronounced at larger $k_{\parallel}$, and in some cases they do not appear to extend across the entire $k_{\perp}$ range. The rectangular region $0.05 \leq k_{\perp} \leq 0.16 \, {\rm Mpc^{-1}}$ and $0.9 \leq k_{\parallel} \leq 4.6 \, {\rm Mpc^{-1}}$ is found to be relatively free of foreground contamination and artefacts, and we have used this to place the $2\sigma$ upper limit $\Delta^2(k) < (1.85 \times 10^4)^2\, {\rm mK^2}$ on the EoR 21-cm mean squared brightness temperature fluctuations at $k=1 \,{\rm Mpc}^{-1}$.

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arXiv2023

WIMP decay as a possible Warm Dark Matter model

The Weakly Interacting Massive Particles(WIMPs) have long been the favored CDM candidate in the standard $Λ$CDM model. However, owing to great improvement in the experimental sensitivity in the past decade, some parameter space of the SUSY-based WIMP model is ruled out. In addition, WIMP as the CDM particle is also at variance with other astrophysical observables at small scales. We consider a model that addresses both these issues. In the model, the WIMP decays into a massive particle and radiation. We study the background evolution and the first order perturbation theory (coupled Einstein-Boltzmann equations) for this model and show that the dynamics can be captured by a single parameter $r=m_L/q$, which is the ratio of the lighter mass and the comoving momentum of the decay particle. We incorporate the relevant equations in the existing Boltzmann code CLASS to compute the matter power spectra and CMB angular power spectra. The decaying WIMP model is akin to a non-thermal Warm Dark Matter(WDM) model and suppresses matter power at small scales, which could alleviate several issues that plague the CDM model. We compare the predictions of the model with CMB, galaxy clustering, and high-z HI data. Both these data sets yield $r\gtrsim 10^6$, which can be translated into the bounds on other parameters. In particular, we obtain the following lower bounds on the thermally-averaged self-annihilation cross-section of WIMPs $\langle σv \rangle$, and the lighter mass $m_L$: $\langle σv \rangle \gtrsim 4.9\times 10^{-34} \, \rm cm^3 \, sec^{-1}$ and $m_L \gtrsim 2.4 \, \rm keV$. The lower limit on $m_L$ is comparable to constraints on the mass of thermally-produced WDM particle. The limit on the self-annihilation cross-section greatly expands the available parameter space as compared to the stable WIMP scenario.

astro-ph.CO↗
arXiv2023

Synchrotron cutoff in Ultraluminous X-ray sources

The origin of spectral curvature at energies $E\simeq 10$ keV in ultraluminous X-ray sources is not well understood. In this paper, we propose a novel mechanism based on synchrotron radiation to explain this cutoff. We show that relativistic plasma can give rise to observed spectral curvature for neutron star magnetic fields due to the variation in the latitude of synchrotron radiation. We analyze the NuSTAR data of two bright pulsar ULXs, NGC 5907 ULX1 and NGC 7793 P13, and provide estimates of the physical parameters of these sources. We fit the data for synchrotron emission at various latitudes and show that the spectral cutoff in these cases can be explained for a large range of acceptable physical parameters, e.g., a semi-relativistic plasma with $γ\simeq 20$ for high latitudes or a highly relativistic plasma ($γ\simeq 10^5$) for emission close to the electron's orbital plane in a typical magnetic field of $B\simeq 10^{12} \, \rm G$. We also discuss how such an emission mechanism can be distinguished from other proposed models. A corollary to our study is that most ULXs might be neutron stars as they display such a spectral cutoff.

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arXiv2023

Progression of Digital-Receiver Architecture: From MWA to SKA1-Low,and beyond

Backed by advances in digital electronics, signal processing, computation, and storage technologies, aperture arrays, which had strongly influenced the design of telescopes in the early years of radio astronomy, have made a comeback. Amid all these developments, an international effort to design and build the world's largest radio telescope, the Square Kilometre Array (SKA), is ongoing. With its vast collecting area of 1 sq-km, the SKA is envisaged to provide unsurpassed sensitivity and leverage technological advances to implement a complex receiver to provide a large field of view through multiple beams on the sky. Many pathfinders and precursor aperture array telescopes for the SKA, operating in the frequency range of 10-300 MHz, have been constructed and operationalized to obtain valuable feedback on scientific, instrumental, and functional aspects. This review article looks explicitly into the progression of digital-receiver architecture from the Murchison Widefield Array (precursor) to the SKA1-Low. It highlights the technological advances in analog-to-digital converters (ADCs),field-programmable gate arrays (FPGAs), and central processing unit-graphics processing unit (CPU-GPU) hybrid platforms around which complex digital signal processing systems implement efficient channelizers, beamformers, and correlators. The article concludes with a preview of the design of a new generation signal processing platform based on radio frequency system-on-chip (RFSoC).

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arXiv2023

High-Performance Computing for SKA Transient Search: Use of FPGA based Accelerators -- a brief review

This paper presents the High-Performance computing efforts with FPGA for the accelerated pulsar/transient search for the SKA. Case studies are presented from within SKA and pathfinder telescopes highlighting future opportunities. It reviews the scenario that has shifted from offline processing of the radio telescope data to digitizing several hundreds/thousands of antenna outputs over huge bandwidths, forming several 100s of beams, and processing the data in the SKA real-time pulsar search pipelines. A brief account of the different architectures of the accelerators, primarily the new generation Field Programmable Gate Array-based accelerators, showing their critical roles to achieve high-performance computing and in handling the enormous data volume problems of the SKA is presented here. It also presents the power-performance efficiency of this emerging technology and presents potential future scenarios.

astro-ph.IM↗
arXiv2022

The Tracking Tapered Gridded Estimator (TTGE) for the power spectrum from drift scan observations

Intensity mapping with the redshifted 21-cm line is an emerging tool in cosmology. Drift scan observations, where the antennas are fixed to the ground and the telescope's pointing center (PC) changes continuously on the sky due to earth's rotation, provide broad sky coverage and sustained instrumental stability needed for 21-cm intensity mapping. Here we present the Tracking Tapered Grided Estimator (TTGE) to quantify the power spectrum of the sky signal estimated directly from the visibilities measured in drift scan radio interferometric observations. The TTGE uses the data from the different PC to estimate the power spectrum of the signal from a small angular region located around a fixed tracking center (TC). The size of this angular region is decided by a suitably chosen tapering window function which serves to reduce the foreground contamination from bright sources located at large angles from the TC. It is possible to cover the angular footprint of the drift scan observations using multiple TC, and combine the estimated power spectra to increase the signal to noise ratio. Here we have validated the TTGE using simulations of $154 \, {\rm MHz}$ MWA drift scan observations. We show that the TTGE can recover the input model angular power spectrum $C_{\ell}$ within $20 \%$ accuracy over the $\ell$ range $40 < \ell < 700$.

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arXiv2022

HI 21-centimetre emission from an ensemble of galaxies at an average redshift of one

The baryonic processes in galaxy evolution include gas infall onto galaxies to form neutral atomic hydrogen (HI), the conversion of HI to the molecular state (H$_2$), and, finally, the conversion of H$_2$ to stars. Understanding galaxy evolution thus requires understanding the evolution of both the stars, and the neutral atomic and molecular gas, the primary fuel for star-formation, in galaxies. For the stars, the cosmic star-formation rate density is known to peak in the redshift range $z \approx 1-3$, and to decline by an order of magnitude over the next $\approx 10$ billion years; the causes of this decline are not known. For the gas, the weakness of the hyperfine HI 21cm transition, the main tracer of the HI content of galaxies, has meant that it has not hitherto been possible to measure the atomic gas mass of galaxies at redshifts higher than $\approx 0.4$; this is a critical lacuna in our understanding of galaxy evolution. Here, we report a measurement of the average HI mass of star-forming galaxies at a redshift $z \approx 1$, by stacking their individual HI 21 cm emission signals. We obtain an average HI mass similar to the average stellar mass of the sample. We also estimate the average star-formation rate of the same galaxies from the 1.4 GHz radio continuum, and find that the HI mass can fuel the observed star-formation rates for only $\approx 1-2$ billion years in the absence of fresh gas infall. This suggests that gas accretion onto galaxies at $z < 1$ may have been insufficient to sustain high star-formation rates in star-forming galaxies. This is likely to be the cause of the decline in the cosmic star-formation rate density at redshifts below 1.

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arXiv2022

Nonminimally coupled ultralight axions as cold dark matter

We consider a nonminimally coupled scalar field as a potential cold dark matter candidate. These models are natural extensions of the ultralight axion models which are based on minimally coupled scalar fields. Such ultralight scalar fields are motivated by string theory and, in particular, have been studied in the context of the axiverse scenario. For a nonminimally coupled field, the scalar-field energy density behaves as radiation at early times, which yields a bound on the coupling constant, $ξ\lesssim 10$, from the primordial nucleosynthesis theory. The first-order perturbations of the nonminimally coupled field with adiabatic initial conditions cause the gravitational potential to decay on large scales. A comparison of the cosmological data with the theoretical matter power spectrum yields the following constraint on the coupling constant: $ξ\lesssim 0.01$. We also consider isocurvature modes in our analysis. We argue that a mix of adiabatic and isocurvature initial conditions for a nonminimally coupled scalar field might allow one to obtain the usual adiabatic CDM power spectrum.

astro-ph.CO↗
arXiv2021

Giant Metrewave Radio Telescope Detection of HI 21 cm Emission from Star-forming Galaxies at $z \approx 1.3$

We report a $\approx 400$-hour Giant Metrewave Radio Telescope (GMRT) search for HI 21 cm emission from star-forming galaxies at $z = 1.18-1.39$ in seven fields of the DEEP2 Galaxy Survey. Including data from an earlier 60-hour GMRT observing run, we co-added the HI 21 cm emission signals from 2,841 blue star-forming galaxies that lie within the full-width at half-maximum of the GMRT primary beam. This yielded a $5.0σ$ detection of the average HI 21 cm signal from the 2,841 galaxies at an average redshift $\langle z \rangle \approx 1.3$, only the second detection of HI 21 cm emission at $z\ge1$. We obtain an average HI mass of $\langle {\rm M_{HI}} \rangle=(3.09 \pm 0.61) \times 10^{10}\ {\rm M}_\odot$ and an HI-to-stellar mass ratio of $2.6\pm0.5$, both significantly higher than values in galaxies with similar stellar masses in the local Universe. We also stacked the 1.4 GHz continuum emission of the galaxies to obtain a median star-formation rate (SFR) of $14.5\pm1.1\ {\rm M}_\odot \textrm{yr}^{-1}$. This implies an average HI depletion timescale of $\approx 2$ Gyr for blue star-forming galaxies at $z\approx 1.3$, a factor of $\approx 3.5$ lower than that of similar local galaxies. Our results suggest that the HI content of galaxies towards the end of the epoch of peak cosmic SFR density is insufficient to sustain their high SFR for more than $\approx 2$ Gyr. Insufficient gas accretion to replenish the HI could then explain the observed decline in the cosmic SFR density at $z< 1$.

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arXiv2021

Extracting the 21 cm EoR signal using MWA drift scan data

The detection of redshifted hyperfine line of neutral hydrogen (HI) is the most promising probe of the Epoch of Reionization (EoR). We report an analysis of 55 hours of Murchison Widefield Array (MWA) Phase II drift scan EoR data. The data correspond to a central frequency $ν_0 = 154.24 \, \rm MHz$ ($z\simeq 8.2$ for the redshifted HI hyperfine line) and bandwidth $B = 10.24 \, \rm MHz$. As one expects greater system stability in a drift scan, we test the system stability by comparing the extracted power spectra from data with noise simulations and show that the power spectra for the cleanest data behave as thermal noise. We compute the HI power spectrum as a function of time in one and two dimensions. The best upper limit on the one-dimensional power spectrum are: $Δ^2(k) \simeq (1000~\rm mK)^2$ at $k \simeq 0.2$$h~{\rm Mpc}^{-1}$ and at $k \simeq 1$$h~{\rm Mpc}^{-1}$. The cleanest modes, which might be the most suited for obtaining the optimal signal-to-noise, correspond to $k \gtrsim 1$$h~{\rm Mpc}^{-1}$. We also study the time-dependence of the foreground-dominated modes in a drift scan and compare with the expected behaviour.

astro-ph.CO↗
arXiv2020

Energy injection in pre-recombination era and EDGES detection

We study the possibility of explaining the recent EDGES detection by an energy injection in the pre-recombination era. Our aim is to show that the residue of this energy injection could give the resultant increase in the energy density at frequencies $x_e \equiv hν/(kT) \simeq 10^{-3}$, which is needed to explain the EDGES result. We consider two models of energy injection: Gaussian profile with a fixed redshift of injection and radiative decay of a non-relativistic particle. We show that the energy injection should occur in the redshift range $z\lesssim 4 \times 10^3$ to prevent free-free processes from thermalizing the injected energy. The injected energy should be nearly 200--1000 times the CMB intensity at $x_e \simeq 10^{-3}$ to obtain the requisite residue. A large fraction of the injected energy gets thermalized and therefore distorts the CMB spectrum. We compute CMB spectral distortion for both the models and show that the fractional change in CMB energy density, $Δρ_{\rm \scriptscriptstyle CMB}/ρ_{\rm \scriptscriptstyle CMB} \simeq 10^{-6}$, which might be detectable with the proposed experiment PIXIE. We also outline the implication of our proposed scenario for CMB anisotropies.

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