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A. P. Rao

Publications and source records attributed to A. P. Rao.

At least 19 recordsLinked to original sources
arXiv2025

Smoothing surfaces on fourfolds

If $\mathcal E, \mathcal F$ are vector bundles of ranks $r-1,r$ on a smooth fourfold $X$ and $\mathcal{Hom}(\mathcal E,\mathcal F)$ is globally generated, it is well known that the general map $ϕ: \mathcal E \to \mathcal F$ is injective and drops rank along a smooth surface. Chang improved on this with a filtered Bertini theorem. We strengthen these results by proving variants in which (a) $\mathcal F$ is not a vector bundle and (b) $\mathcal{Hom}(\mathcal E,\mathcal F)$ is not globally generated. As an application, we give examples of even linkage classes of surfaces on $\mathbb P^4$ in which all integral surfaces are smoothable, including the linkage classes associated with the Horrocks-Mumford surface.

math.AG↗
arXiv2022

Rank two bundles on P^n with isolated cohomology

The purpose of this paper is to study minimal monads associated to a rank two vector bundle $\mathcal E$ on $\mathbb P^n$. In particular, we study situations where $\mathcal E$ has $H^i_*(\mathcal E) =0$ for $1<i<n-1$, except for one pair of values $(k,n-k)$. We show that on $\mathbb P^8,$ if $H^3_*(\mathcal E)=H^4_*(\mathcal E)=0$, then $\mathcal E$ must be decomposable. More generally, we show that for $n\geq 4k$, there is no indecomposable bundle $\mathcal E$ for which all intermediate cohomology modules except for $H^1_*, H^k_*, H^{n-k}_*, H^{n-1}_*$ are zero.

math.AG↗
arXiv2014

Horrocks Correspondence on ACM Varieties

We describe a vector bundle $\sE$ on a smooth $n$-dimensional ACM variety in terms of its cohomological invariants $H^i_*(\sE)$, $1\leq i \leq n-1$, and certain graded modules of "socle elements" built from $\sE$. In this way we give a generalization of the Horrocks correspondence. We prove existence theorems where we construct vector bundles from these invariants and uniqueness theorems where we show that these data determine a bundle up to isomorphisms. The cases of the quadric hypersurface in $\mathbb P^{n+1}$ and the Veronese surface in $\mathbb P^5$ are considered in more detail.

math.AG↗
arXiv2013

Horrocks Correspondence on a Quadric Surface

We extend the Horrocks correspondence between vector bundles and cohomology modules on the projective plane to the product of two projective lines. We introduce a set of invariants for a vector bundle on the product of two projective lines, which includes the first cohomology module of the bundle, and prove that there is a one to one correspondence between these sets of invariants and isomorphism classes of vector bundles without line bundle summands.

math.AG↗
arXiv2010

On codimension two subvarieties in hypersurfaces

We show that for a smooth hypersurface $X\subset \bbP^n$ of degree at least 2, there exist arithmetically Cohen-Macaulay (ACM) codimension two subvarieties $Y\subset X$ which are not an intersection $X\cap{S}$ for a codimension two subvariety $S\subset\bbP^n$. We also show there exist $Y\subset X$ as above for which the normal bundle sequence for the inclusion $Y\subset X\subset\bbP^n$ does not split.

math.AG↗
arXiv2009

Nature of X-shaped sources

The nature of X-shaped sources is a matter of considerable debate: it has even been proposed that they provide evidence for black hole mergers$ / $spin reorientation, and therefore constrain the rate of strong gravitational wave events (Merritt & Ekers 2002). Based on morphological and spectral characteristics of these sources, currently a strong contender to explain the nature of these sources is the `alternative' model of Lal & Rao (2007), in which these sources consist of two pairs of jets, which are associated with two unresolved AGNs. Detailed morphological and spectral results on milliarcsecond-scales (mas) provide a crucial test of this model, and hence these sources are excellent candidates to study on mas; {\it i.e.}, to detect he presence/absence of double nuclei/AGNs, signs of helical/disrupted jets, thereby, to investigate spatially resolved/unresolved binary AGN systems and providing clues to understanding the physics of merging of AGNs on mas. We conducted a systematic study of a large sample of known X-shaped, comparison FR II radio galaxies, and newly discovered X-shaped candidate sources using Giant Metrewave Radio Telescope and Very Large Array at several radio frequencies. In our new observations of `comparison' FR II radio galaxies we find that almost all of our targets show standard spectral steepening as a function of distance from the hotspot. However, one source, 3C 321, has a low-surface-brightness extension that shows a flatter spectral index than the high-surface-brightness hotspots$ / $lobes, as found in `known' X-shaped sources.

astro-ph.CO↗
arXiv2005

GMRT observations of the field of INTEGRAL X-ray sources- II (newly discovered hard X-ray sources)

We have conducted low-frequency radio observations with the Giant Metrewave Radio Telescope (GMRT) of 40 new hard X-ray sources discovered by the INTEGRAL satellite. This survey was conducted in order, to study radio emissions from these sources, to provide precise position and to identify new microquasar candidates. From our observations we find that 24 of the X-ray sources have radio candidates within the INTEGRAL error circle. Based on the radio morphology, variability and information available from different wavelengths, we categorize them as seventeen Galactic sources (4 unresolved, 7 extended, 6 extended sources in diffuse region) and seven extragalactic sources (2 unresolved, 5 extended). Detailed account for seventeen of these sources was presented in earlier paper. Based on the radio data for the remaining sources at 0.61 GHz, and the available information from NVSS, DSS, 2MASS and NED, we have identified possible radio counterparts for the hard X-ray sources. The three unresolved sources, viz IGR J17303$-$0601, IGR J17464$-$3213, and IGR J18406$-$0539 are discussed in detail. These sources have been identified as X-ray binaries with compact central engine and variable in X-ray and in the radio, and are most likely microquasar candidates. The remaining fourteen sources have extended radio morphology and are either diffuse Galactic regions or extragalactic in origin.

astro-ph↗
arXiv2005

Simultaneous Multi-Wavelength Observations of Sgr A*

We observed Sgr A* using the Very Large Array (VLA) and the Giant Metrewave Radio Telescope (GMRT) at multiple cm and mm wavelengths on 17 June 2003. The measured flux densities of Sgr A*, together with those obtained from the Submillimeter Array (SMA) and the Keck II 10 m telescope on the same date, are used to construct a simultaneous spectrum of Sgr A* from 90 cm to 3.8 $μ$m. The simultaneous spectrum shows a spectral break at about 3.6 cm, a possible signature of synchrotron self-absorption of the strong radio outburst which occurred near epoch 17 July 2003. At 90 cm, the flux density of Sgr A* is $0.22\pm0.06$ Jy, suggesting a sharp decrease in flux density at wavelengths longer than 47 cm. The spectrum at long cm wavelengths appears to be consistent with free-free absorption by a screen of ionized gas with a cutoff $\sim$100 cm. This cutoff wavelength appears to be three times longer than that of $\sim$30 cm suggested by Davies, Walsh & Booth based on observations in 1974 and 1975. Our analysis suggests that the flux densities of Sgr A* at wavelengths longer than 30 cm could be attenuated and modulated by stellar winds from massive stars close to Sgr A*.

astro-ph↗
arXiv2005

GMRT observations of the field of INTEGRAL X-ray sources- I

The INTEGRAL observatory has discovered a variety of hard X-ray sources in the Galactic plane since its launch. Using GMRT, we have made repeated observations of these sources to search for the radio counterparts of seventeen of them at low frequencies. The source positions were taken from the various ATEL and IAUC reporting their discovery. Possible radio counterparts for seven of these sources namely, IGR J06074+2205, IGR J15479-4529, IGR J16479-4514, IGR J17091-3624, IGR J18027-1455, IGR J18539+0727 and IGR J21247+5058 were detected within 3$σ$ of the position uncertainty derived from the INTEGRAL observations. The offset in the radio position was calculated using the positions mentioned in the ATEL. We have also analyzed the available NVSS images for a few of these fields at 1.4 GHz along with our observations. In this paper we present the radio images and the best fit positions for the positive detections. The X-ray variability for few of the sources within the time scales of 100 s to 1 ks as seen in the RXTE/PCA light curves suggests their Galactic origin and possible binary nature. We discuss briefly the characteristics of these sources from the available information at different wave bands.

astro-ph↗
arXiv2005

Low frequency radio monitoring of Cygnus X-1 and Cygnus X-3

We present results of monitoring observations of the micro-quasars CygnusX-1 and Cygnus X-3 at 0.61 and 1.28 GHz. The observations were performed with Giant Meter-wave Radio Telescope, GMRT, between 2003 June and 2005 January. Variable, unresolved sources were found in both cases. Cyg X-1 was detected in about half of the observations, with a median flux density about 7 mJy at each frequency. The results show clearly that there is a break in the spectrum above 1.28 GHz. The variations in Cyg X-1 may be due to refractive interstellar scintillation. Cyg X-3 was detected in each observation, and varied by a factor of 4. For this source, models of the scintillation suggest a very long timescale (of the order of 40 yr at 1.28 GHz), and therefore we believe that the variations are intrinsic to the source.

astro-ph↗
arXiv2005

Radio, millimeter and optical monitoring of GRB030329 afterglow: Constraining the double jet model

We present radio, millimeter and optical observations of the afterglow of GRB030329. UBVR_{C}I_{C} photometry is presented for a period of 3 hours to 34 days after the burst. Radio monitoring at 1280 MHz has been carried out using the GMRT for more than a year. Simultaneous millimeter observations at 90 GHz and 230 GHz have been obtained from the Swedish-ESO Submillimeter Telescope (SEST) and the IRAM-PdB interferometer over more than a month following the burst. We use these data to constrain the double jet model proposed by Berger et al. (2003) for this afterglow. We also examine whether instead of the two jets being simultaneously present, the wider jet could result from the initially narrow jet, due to a fresh supply of energy from the central engine after the ``jet break''.

astro-ph↗
arXiv2005

Spectral properties and origin of the radio halo in A3562

We present a new detailed multiband study of the merging cluster A3562, in the core of the Shapley Concentration Supercluster. We analyzed new, low frequency radio data performed at 240 MHz, 332 MHz and 610 MHz with the Giant Metrewave Radio Telescope (GMRT). The new GMRT data allowed us to carry out a detailed study of the radio halo at the centre of A3562, as well as of the head--tail radio galaxy J1333--3141 embedded in it, and of the extended emission around the peripheral cluster galaxy J1332--3146a. Thanks to the present observations we could derive the integrated spectrum of the radio halo with five data points in the frequency range 240 MHz -- 1.4 GHz. Our data show a clear steepening of the total spectrum in this frequency range. Furthermore, by comparing the GMRT 332 MHz image with a previously published VLA 1.4 GHz image, we produced an image of the halo spectral index distribution. The image shows a very complex structure, with an average value of $α^{1.4GHz}_{332MHz} \sim 1.5$ and a number of knots steepening up to $\sim 2$. We performed a combined morphological and statistical analysis using the radio images and the quantities derived from XMM--Newton and {\it Chandra} observations. We discuss our results in the light of particle re--acceleration processes in galaxy clusters. In particular, we outline an overall picture, consistent with the available radio and X-ray data, in which the cluster merger kinematics, the injection of turbulence and B--amplification induced by the merger between A 3562 and SC 1329--313 are jointly taken into account.

astro-ph↗
arXiv2004

The simultaneous VLA observations of Sgr A* from 90 to 0.7 cm

We present a spectrum of Sgr A* observed simultaneously on June 17, 2003 at wavelengths from 90 to 0.7 cm with the VLA. In the spectrum, we also include the measurements of Sgr A* observed on the same day with the GMRT at 49 cm, the SMA at 0.89 mm and the Keck II at 3.8 $μ$m. The spectrum at the centimeter wavelengths suggests the presence of a break wavelength at 3.8 cm (8 GHz). The spectral index is alpha=0.43+-0.03 (propto nu(alpha}) at 3.8 cm and shorter wavelengths. The spectrum between 3.8 cm and 49 cm can be described by a power law with spectral index of alpha=0.10+-0.03$. We detected Sgr A* with 0.22+-0.06 Jy at 90 cm, suggesting a sharp decrease in flux density at the wavelengths longer than 49 cm. The best fit to the spectrum at the wavelengths longer than lambda_b appears to be consistent with free-free absorption by a screen of ionized gas with a turnover wavelength at nu(tau_ff}=1) = 100 cm (300 MHz). This turnover wavelength appears to be three times longer than that of 30 cm (1 GHz) as suggested by Davies et al. (1976) based on the observations in 1994 and 1995. Our analysis suggests that stellar winds from the massive stars near Sgr A* could modulate the flux density at the wavelengths longer than 30 cm (or frequencies below 1 GHz).

astro-ph↗
arXiv2004

Spectral and Timing Evolution of the Black Hole X-ray Nova 4U 1543-47 During its 2002 Outburst

We present an X-ray spectral and timing analysis of 4U 1543-47 during its 2002 outburst based on 49 pointed observations obtained using the Rossi X-ray Timing Explorer (RXTE). The outburst reached a peak intensity of 4.2 Crab in the 2-12 keV band and declined by a factor of 32 throughout the month-long observation. A 21.9 +- 0.6 mJy radio flare was detected at 1026.75 MHz two days before the X-ray maximum; the radio source was also detected late in the outburst, after the X-ray source entered the low hard state. The X-ray light curve exhibits the classic shape of a rapid rise and an exponential decay. The spectrum is soft and dominated by emission from the accretion disk. The continuum is fit with a multicolor disk blackbody (kT_{max} = 1.04 keV) and a power-law (Gamma ~ 2.7). Midway through the decay phase, a strong low-frequency QPO (nu = 7.3-8.1 Hz) was present for several days. The spectra feature a broad Fe K alpha line that is asymmetric, suggesting that the line is due to relativistic broadening rather than Comptonization. Relativistic Laor models provide much better fits to the line than non-relativistic Gaussian models, particularly near the beginning and end of our observations. The line fits yield estimates for the inner disk radius that are within 6 R_g; this result and additional evidence indicates that this black hole may have a non-zero angular momentum.

astro-ph↗
arXiv2003

New high-resolution radio observations of the SNR CTB 80

We report new high resolution and high sensitivity radio observations of the extended supernova remnant (SNR) CTB 80 (G69.0+2.7) at 240 MHz, 324 MHz, 618 MHz, and 1380 MHz. The imaging of CTB 80 at 240 MHz and 618 MHz was performed using the Giant Metrewave Radio Telescope (GMRT) in India. The observations at 324 MHz and 1380 MHz were obtained using the Very Large Array (VLA, NRAO) in its C and D configurations. The new radio images reveal faint extensions for the asymmetric arms of CTB 80. The arms are irregular with filaments and clumps of size 1' (or 0.6 pc at a distance of 2 kpc). The radio image at 1380 MHz is compared with IR and optical emission. The correspondence IR/radio is excellent along the N arm of CTB 80. Ionized gas observed in the [SII] line perfectly matches the W and N edges of CTB 80. The central nebula associated with the pulsar PSR B1951+32 was investigated with an angular resolution of 10" x 6". The new radio image obtained at 618 MHz shows with superb detail structures in the 8' x 4' E-W ``plateau'' nebula that hosts the pulsar on its western extreme. A twisted filament, about 6' in extent (~3.5 pc), trails behind the pulsar in an approximate W-E direction. In the bright ``core'' nebula (size \~45"), located to the W of the plateau, the images show a distortion in the morphology towards the W; this feature corresponds to the direction in which the pulsar escapes from the SNR with a velocity of ~240 km/s. Based on the new observations, the energetics of the SNR and of the PWN are investigated.

astro-ph↗
arXiv2001

On the association of G343.1-2.3 and PSR 1706-44

The observations of the supernova remnant G343.1-2.3 with the Mauritius Radio Telescope, the Australia Compact Array, and the Hobart Single dish are presented. With these more sensitive measurements the association with the pulsar PSR1706-44 becomes much more likely. The major points from the observations are presented.

astro-ph↗