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Tarun Deep Saini

Publications and source records attributed to Tarun Deep Saini.

At least 19 recordsLinked to original sources
arXiv2026

A Bayesian estimator for peculiar velocity correction in cosmological inference from supernovae data

The peculiar motion of the host galaxies introduces bias in estimating cosmological parameters from supernova data. The coherent component of the peculiar motion is usually corrected for using velocity field reconstruction based on the observed galaxy distribution, while the random component is treated statistically by inflating the magnitude uncertainty in the quadrature derived using the standard error propagation. The method of velocity field reconstruction requires assuming an underlying cosmology, which can introduce its own bias in the final inference. On the other hand, the statistical treatment of the random component assumes a locally linear approximation for the magnitude-redshift relation and a Gaussian distribution for the peculiar velocities, which can have extended tails in the non-linear regime. In this work, we present a Bayesian estimator for simultaneously correcting for peculiar motion while fitting a cosmological model to the supernova data, relaxing the assumption of linearity of the model and Gaussianity of the random peculiar motion. Our approach is based on considering the problem of fitting the magnitude-redshift relation as a non-linear model with errors in both dependent and independent variables. To this end, we develop a general method for fitting such non-linear errors-in-variables models. We then specialize it to the case of fitting the magnitude-redshift relation, validating it with simulated datasets at the precision of current and upcoming surveys, and testing it on the Pantheon sample. Our method provides an alternative approach for accounting for the peculiar velocity effects, which is a complementary method for the coherent component, as it does not require independent velocity measurements, and generalizes the treatment of the random component. Moreover, our general method is applicable to various other problems in cosmology and astronomy.

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arXiv2026

Unbiased Bayesian Inference of Peculiar Motions of Galaxies from Type Ia Supernovae Observations

The peculiar motions of galaxies are powerful cosmological probes that trace the growth of structures and the distribution of matter in the universe, providing a means to investigate the nature of dark energy and test gravity on cosmological scales. However, their direct observation is extremely challenging, as it requires independent and precise distance measurements to galaxies. We present a Bayesian approach to estimate the radial component of peculiar velocities of galaxies hosting Type Ia supernovae (SNe Ia), relying solely on the background cosmological model and the precision of the SNe Ia data. Unlike other peculiar velocity estimators based on Hubble residuals, our method does not assume local linearity of the magnitude-redshift relation or a fixed cosmology, making it unbiased even for large peculiar velocities and self-consistently avoiding bias due to a wrong cosmology. We validate our method using simulated supernova data with the precision of current and upcoming surveys, and further compare it with the linearized estimator to test its efficacy. We show that our estimator has lower bias than the standard estimator and remains consistent even for larger values of $v_{\rm p}/cz$. We also present a Bayesian derivation for the linearized estimator generalized to include the supernova magnitude covariance.

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arXiv2018

Measuring the Hubble constant: Gravitational wave observations meet galaxy clustering

We show how the distances to binary black holes measured in gravitational wave observations with ground-based interferometers can be used to constrain the redshift-distance relation and, thereby, measure the Hubble constant ($H_0$). Gravitational wave observations of stellar-mass binary black holes are not expected to be accompanied by any electro-magnetic event that may help in accessing their redshifts. We address this deficiency by using an optical catalog to get the distribution of galaxies in redshift. Assuming that the clustering of the binaries is correlated with that of the galaxies, we propose using that correlation to measure $H_0$. We show that employing this method on simulated data obtained for second-generation networks comprising at least three detectors, e.g., advanced LIGO - advanced VIRGO network, one can measure $H_0$ with an accuracy of $\sim$8% with detection of a reference population of 25 binaries, each with black holes of mass 10$M_\odot$. As expected, with third-generation detectors like the Einstein telescope (ET), which will measure distances much more accurately and to greater depths, one can obtain better estimates for $H_0$. Specifically, we show that with 25 observations, ET can constrain $H_0$ to an accuracy of $\sim$7%. This method can also be used to estimate other cosmological parameters like the matter density $Ω_m$ and the dark energy equation of state.

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arXiv2017

Effect of dark matter halo on global spiral modes in a collisionless galactic disc

Low surface brightness (LSB) galaxies are dominated by dark matter halo from the innermost radii; hence they are ideal candidates to investigate the influence of dark matter on different dynamical aspects of spiral galaxies. Here, we study the effect of dark matter halo on grand-design, m = 2, spiral modes in a galactic disk, treated as a collisionless system, by carrying out a global modal analysis within the WKB approximation. First, we study a superthin, LSB galaxy UGC 7321 and show that it does not support discrete global spiral modes when modeled as a disk-alone system or as a disk plus dark matter system. Even a moderate increase in the stellar central surface density does not yield any global spiral modes. This naturally explains the observed lack of strong large-scale spiral structure in LSBs. An earlier work (Ghosh, Saini & Jog, 2016) where the galactic disk was treated as a fluid system for simplicity had shown that the dominant halo could not arrest global modes. We found that this difference arises due to the different dispersion relation used in the two cases and which plays a crucial role in the search for global spiral modes. Thus the correct treatment of stars as a collisionless system as done here results in the suppression of global spiral modes, in agreement with the observations. We performed a similar modal analysis for the Galaxy, and found that the dark matter halo has a negligible effect on large-scale spiral structure.

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arXiv2016

Modal analysis of gravitational instabilities in nearly Keplerian, counter-rotating collisionless discs

We present a modal analysis of instabilities of counter-rotating, self-gravitating collisionless stellar discs, using the recently introduced modified WKB formulation of spiral density waves for collisionless systems (Gulati \& Saini). The discs are assumed to be axisymmetric and in coplanar orbits around a massive object at the common center of the discs. The mass in both discs is assumed to be much smaller than the mass of the central object. For each disc, the disc particles are assumed to be in near circular orbits. The two discs are coupled to each other gravitationally. The perturbed dynamics of the discs evolves on the order of the precession time scale of the discs, which is much longer than the Keplerian time scale. We present results for the azimuthal wave number $m=1$ and $m=2$, for the full range of disc mass ratio between the prograde and retrograde discs. The eigenspectra are in general complex, therefore all eigenmodes are unstable. Eigenfunctions are radially more compact for $m = 1$ as compared to $m = 2$. Pattern speed of eigenmodes is always prograde with respect to the more massive disc. The growth rate of unstable modes increases with increasing mass fraction in the retrograde disc, and decreases with $m$; therefore $m=1$ instability is likely to play the dominant role in the dynamics of such systems.

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arXiv2016

A modified WKB formulation for linear eigenmodes of a collisionless self-gravitating disc in the epicyclic approximation

The short--wave asymptotics (WKB) of spiral density waves in self-gravitating stellar discs is well suited for the study of the dynamics of tightly--wound wavepackets. But the textbook WKB theory is not well adapted to the study of the linear eigenmodes in a collisionless self-gravitating disc because of the transcendental nature of the dispersion relation. We present a modified WKB of spiral density waves, for collisionless discs in the epicyclic limit, in which the perturbed gravitational potential is related to the perturbed surface density by the Poisson integral in Kalnaj's logarithmic spiral form. An integral equation is obtained for the surface density perturbation, which is seen to also reduce to the standard WKB dispersion relation. We specialize to a low mass (or Keplerian) self-gravitating disc around a massive black hole, and derive an integral equation governing the eigenspectra and eigenfunctions of slow precessional modes. For a prograde disc, the integral kernel turns out be real and symmetric, implying that all slow modes are stable. We apply the slow mode integral equation to two unperturbed disc profiles, the Jalali--Tremaine annular discs, and the Kuzmin disc. We determine eigenvalues and eigenfunctions for both $m = 1$ and $m = 2$ slow modes for these profiles and discuss their properties. Our results compare well with those of Jalali--Tremaine.

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arXiv2015

Effect of dark matter halo on global spiral modes in galaxies

Low surface brightness (LSB) galaxies form a major class of galaxies, and are characterized by low disc surface density and low star formation rate. These are known to be dominated by dark matter halo from the innermost regions. Here we study the role of dark matter halo on the grand-design, $m=2$, spiral modes in a galactic disc by carrying out a global mode analysis in the WKB approximation. The Bohr-Sommerfeld quantization rule is used to determine how many discrete global spiral modes are permitted. First a typical superthin LSB galaxy, UGC 7321 is studied by taking only the galactic disc, modelled as fluid; and then the disc embedded in a dark matter halo. We find that both cases permit the existence of global spiral modes. This is in contrast to earlier results where the inclusion of dark matter halo was shown to nearly fully suppress local, swing-amplified spiral features. Although technically global modes are permitted in the fluid model as shown here, we argue that due to lack of tidal interactions, these are not triggered in LSB galaxies. For comparison, we carried out a similar analysis for the Galaxy, for which the dark matter halo does not dominate in the inner regions. We show that here too the dark matter halo has little effect, hence the disc embedded in a halo is also able to support global modes. The derived pattern speed of the global mode agrees fairly well with the observed value for the Galaxy.

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arXiv2015

Adiabatic black hole growth in Sérsic models of elliptical galaxies

We have examined the effect of slow growth of a central black hole on spherical galaxies that obey Sérsic or $R^{1/m}$ surface-brightness profiles. During such growth the actions of each stellar orbit are conserved, which allows us to compute the final distribution function if we assume that the initial distribution function is isotropic. We find that black-hole growth leads to a central cusp or ``excess light', in which the surface brightness varies with radius as $R^{-1.3}$ (with a weak dependence on Sérsic index $m$), the line-of-sight velocity dispersion varies as $R^{-1/2}$, and the velocity anisotropy is $β\simeq -0.24$ to $-0.28$ depending on $m$. The excess stellar mass in the cusp scales approximately linearly with the black-hole mass, and is typically 0.5--0.85 times the black-hole mass. This process may strongly influence the structure of nuclear star clusters if they contain black holes.

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arXiv2013

Reconstructing the Properties of Dark Energy using Standard Sirens

Future space-based gravity wave experiments such as the Big Bang Observatory (BBO), with their excellent projected, one sigma angular resolution, will measure the luminosity distance to a large number of gravity wave (GW) sources to high precision, and the redshift of the single galaxies in the narrow solid angles towards the sources will provide the redshifts of the gravity wave sources. One sigma BBO beams contain the actual source only in 68 per cent cases; the beams that do not contain the source may contain a spurious single galaxy, leading to misidentification. To increase the probability of the source falling within the beam, larger beams have to be considered, decreasing the chances of finding single galaxies in the beams. Saini, Sethi and Sahni (2010) argued, largely analytically, that identifying even a small number of GW source galaxies furnishes a rough distance-redshift relation, which could be used to further resolve sources that have multiple objects in the angular beam. In this work we further develop this idea by introducing a self-calibrating iterative scheme which works in conjunction with Monte-Carlo simulations to determine the luminosity distance to GW sources with progressively greater accuracy. This iterative scheme allows one to determine the equation of state of dark energy to within an accuracy of a few percent for a gravity wave experiment possessing a beam width an order of magnitude larger than BBO (and therefore having a far poorer angular resolution). This is achieved with no prior information about the nature of dark energy from other data sets such as SN Ia, BAO, CMB etc.

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arXiv2012

Unstable $m=1$ modes of counter-rotating Keplerian discs

We study the linear $m=1$ counter-rotating instability in a two-component, nearly Keplerian disc. Our goal is to understand these \emph{slow} modes in discs orbiting massive black holes in galactic nuclei. They are of interest not only because they are of large spatial scale--and can hence dominate observations--but also because they can be growing modes that are readily excited by accretion events. Self-gravity being nonlocal, the eigenvalue problem results in a pair of coupled integral equations, which we derive for a two-component softened gravity disc. We solve this integral eigenvalue problem numerically for various values of mass fraction in the counter-rotating component. The eigenvalues are in general complex, being real only in the absence of the counter-rotating component, or imaginary when both components have identical surface density profiles. Our main results are as follows: (i) the pattern speed appears to be non negative, with the growth (or damping) rate being larger for larger values of the pattern speed; (ii) for a given value of the pattern speed, the growth (or damping) rate increases as the mass in the counter-rotating component increases; (iii) the number of nodes of the eigenfunctions decreases with increasing pattern speed and growth rate. Observations of lopsided brightness distributions would then be dominated by modes with the least number of nodes, which also possess the largest pattern speeds and growth rates.

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arXiv2011

Non-Gaussianity and direction dependent systematics in HST key project data

Two new statistics, namely $Δ_χ^2$ and $Δ_χ$, based on extreme value theory, were derived in \cite{gupta08,gupta10}. We use these statistics to study direction dependence in the HST key project data which provides the most precise measurement of the Hubble constant. We also study the non-Gaussianity in this data set using these statistics. Our results for $Δ_χ^2$ show that the significance of direction dependent systematics is restricted to well below one $σ$ confidence limit, however, presence of non-Gaussian features is subtle. On the other hand $Δ_χ$ statistic, which is more sensitive to direction dependence, shows direction dependence systematics to be at slightly higher confidence level, and the presence of non-Gaussian features at a level similar to the $Δ_χ^2$ statistic.

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arXiv2011

Accretion of Chaplygin gas upon black holes: Formation of faster outflowing winds

We study the accretion of modified Chaplygin gas upon different types of black hole. Modified Chaplygin gas is one of the best candidates for a combined model of dark matter and dark energy. In addition, from a field theoretical point of view the modified Chaplygin gas model is equivalent to that of a scalar field having a self-interacting potential. We formulate the equations related to both spherical accretion and disc accretion, and respective winds. The corresponding numerical solutions of the flow, particularly of velocity, are presented and are analyzed. We show that the accretion-wind system of modified Chaplygin gas dramatically alters the wind solutions, producing faster winds, upon changes in physical parameters, while accretion solutions qualitatively remain unaffected. This implies that modified Chaplygin gas is more prone to produce outflow which is the natural consequence of the dark energy into the system.

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arXiv2010

Possible use of self-calibration to reduce systematic uncertainties in determining distance-redshift relation via gravitational radiation from merging binaries

By observing mergers of compact objects, future gravity wave experiments would measure the luminosity distance to a large number of sources to a high precision but not their redshifts. Given the directional sensitivity of an experiment, a fraction of such sources (gold plated -- GP) can be identified optically as single objects in the direction of the source. We show that if an approximate distance-redshift relation is known then it is possible to statistically resolve those sources that have multiple galaxies in the beam. We study the feasibility of using gold plated sources to iteratively resolve the unresolved sources, obtain the self-calibrated best possible distance-redshift relation and provide an analytical expression for the accuracy achievable. We derive lower limit on the total number of sources that is needed to achieve this accuracy through self-calibration. We show that this limit depends exponentially on the beam width and give estimates for various experimental parameters representative of future gravitational wave experiments DECIGO and BBO.

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arXiv2010

Direction Dependence in Supernova Data: Constraining Isotropy

We revise and extend the extreme value statistic, introduced in \cite{gup08}, to study directional dependence in the high redshift supernova data; arising either from departures from the cosmological principle or due to direction dependent statistical systematics in e data. We introduce a likelihood function that analytically marginalises over the Hubble constant, and use it to extend our previous statistic. We also introduce a new statistic that is sensitive to direction dependence arising from living off-centre inside a large void, as well as previously mentioned reasons for anisotropy. We show that for large data sets this statistic has a limiting form that can be computed analytically. We apply our statistics to the gold data sets from \cite{rie04} and \cite{rie07}, as in our previous work. Our revision and extension of previous statistic shows that 1) the effect of marginalsing over Hubble constant instead of using its best fit value has only a marginal effect on our results. However, correction of errors in our previous work reduce the level of non-Gaussianity in the 2004 gold data that was found in our earlier work. The revised results for the 2007 gold data show that the data is consistent with isotropy and Gaussianity. Our second statistic confirms these results.

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arXiv2009

Slow pressure modes in thin accretion discs

Thin accretion discs around massive compact objects can support slow pressure modes of oscillations in the linear regime that have azimuthal wavenumber $m=1$. We consider finite, flat discs composed of barotropic fluid for various surface density profiles and demonstrate--through WKB analysis and numerical solution of the eigenvalue problem--that these modes are stable and have spatial scales comparable to the size of the disc. We show that the eigenvalue equation can be mapped to a Schrödinger-like equation. Analysis of this equation shows that all eigenmodes have discrete spectra. We find that all the models we have considered support negative frequency eigenmodes; however, the positive eigenfrequency modes are only present in power law discs, albeit for physically uninteresting values of the power law index $β$ and barotropic index $γ$.

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arXiv2009

Slow m=1 instabilities of softened gravity Keplerian discs

We present the simplest model that permits a largely analytical exploration of the m=1 counter-rotating instability in a "hot" nearly Keplerian disc of collisionless self-gravitating matter. The model consists of a two-component softened gravity disc, whose linear modes are analysed using WKB. The modes are slow in the sense that their (complex) frequency is smaller than the Keplerian orbital frequency by a factor which is of order the ratio of the disc mass to the mass of the central object. Very simple analytical expressions are derived for the precession frequencies and growth rates of local modes; it is shown that a nearly Keplerian disc must be unrealistically hot to avoid an overstability. Global modes are constructed for the case of zero net rotation.

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arXiv2008

Estimation of Cosmological Parameters from HI Observations of Post-reionization Epoch

The emission from neutral hydrogen (HI) clouds in the post-reionization era (z < 6), too faint to be individually detected, is present as a diffuse background in all low frequency radio observations below 1420 MHz. The angular and frequency fluctuations of this radiation (~ 1 mK) is an important future probe of the large scale structures in the Universe. We show that such observations are a very effective probe of the background cosmological model and the perturbed Universe. In our study we focus on the possibility of determining the redshift space distortion parameter, coordinate distance and its derivative with redshift. Using reasonable estimates for the observational uncertainties and configurations representative of the ongoing and upcoming radio interferometers, we predict parameter estimation at a precision comparable with supernova Ia observations and galaxy redshift surveys, across a wide range in redshift that is only partially accessed by other probes. Future HI observations of the post-reionization era present a new technique, complementing several existing one, to probe the expansion history and to elucidate the nature of the dark energy.

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