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Planckian scattering of D-branes
(Elsevier BV North Holland, 1988) Das, Saurya; Dasgupta, Arundhati; Ramadevi, P.; Sarkar, Tapobrata
We consider the gravitational scattering of point particles in four dimensions, at Planckian centre of mass energy and low momentum transfer, or the eikonal approximation. The scattering amplitude can be exactly computed by modelling point particles by very generic metrics. A class of such metrics are black hole solutions obtained from dimensional reduction of p-brane solutions with one or more Ramond-Ramond charges in string theory. At weak string coupling, such black holes are replaced by a collection of wrapped D-branes. Thus, we investigate eikonal scattering at weak coupling by modelling the point particles by wrapped D-branes and show that the amplitudes exactly match the corresponding amplitude found at strong coupling. We extend the calculation for scattering of charged particles.
Electromagnetic charge-monopole versus gravitational scattering at Planckian energies
(American Physical Society, 1994) Das, Saurya; Majumdar, Parthasarathi
The amplitude for the scattering of a point magnetic monopole and a point charge, at center-of- mass energies much larger than the masses of the particles, and in the limit of low momentum transfer, is shown to be proportional to the (integer-valued) monopole strength, assuming the Dirac quantization condition for the monopole-charge system. It is demonstrated that, for small momentum transfer, charge-monopole electromagnetic effects remain comparable to those due to the gravitational interaction between the particles even at Planckian center-of-mass energies.
Electromagnetic and gravitational scattering at Planckian energies
(American Physical Society, 1995) Das, Saurya; Majumdar, Parthasarathi
The scattering of pointlike particles at a very large center-of-mass energies and fixed low momentum transfers, occurring due to both their electromagnetic and gravitational interactions, is reexamined in the particular case when one of the particles carries a magnetic charge. At Planckian center-of-mass energies, when gravitational dominance is usually expected, the presence of magnetic charge is show to produce dramatic modifications to the scattering cross section as well as to holomorphic structure of the scattering amplitude.
Shock wave mixing in Einstein and dilaton gravity
(Elsevier BV North Holland, 1995) Das, Saurya; Majumdar, Parthasarathi
We consider possible mixing of electromagnetic and gravitational shock waves, in the Planckian energy scattering of point particles in Minkowski space, By boosting a Reissner-Nordstriim black hole solution to the velocity of light, it is shown that no mixing of shock waves takes place for arbitrary finite charge carried by the black hole. However, a similar boosting procedure for a charged black hole solution in dilaton gravity yields some mixing: the wave function of even a neutral test particle, acquires a small additional phase factor depending on the dilalonic black hole charge. Possible implications for poles in the amplitudes for the dilaton gravity case are discussed
Eikonal particle scattering and dilaton gravity
(American Physical Society, 1997) Das, Saurya; Majumdar, Parthasarathi
Approximating light charged pointlike particles in terms of ~nonextremal! dilatonic black holes is shown to lead to certain pathologies in Planckian scattering in the eikonal approximation, which are traced to the presence of a ~naked! curvature singularity in the metric of these black holes. The existence of such pathologies is confirmed by analyzing the problem in an ‘‘external metric’’ formulation where an ultrarelativistic point particle scatters off a dilatonic black hole geometry at large impact parameters. The maladies disappear almost trivially upon imposing the extremal limit. Attempts to derive an effective three-dimensional ‘‘boundary’’ field theory in the eikonal limit are stymied by four-dimensional ~bulk! terms proportional to the light-cone derivatives of the dilaton field, leading to nontrivial mixing of electromagnetic and gravitational effects, in contrast with the case of general relativity. An eikonal scattering amplitude, showing decoupling of these effects, is shown to be derivable by resummation of graviton, dilaton, and photon exchange ladder diagrams in a linearized version of the theory for an asymptotic value of the dilaton field which makes the string coupling constant nonperturbative.
High energy effects on D-brane and black hole emission rates
(American Physical Society, 1997) Das, Saurya; Dasgupta, Arundhati; Sarkar, Tapobrata
We study the emission of scalar particles from a class of near-extremal five-dimensional black holes and the corresponding D-brane configuration at high energies. We show that the distribution functions and the black hole greybody factors are modified in the high energy tail of the Hawking spectrum in such a way that the emission rates exactly match. We extend the results to charged scalar emission and to four dimensions.
Aspects of Planckian scattering beyond the eikonal
(Indian Academy of Sciences, 1998) Das, Saurya; Majumdar, Parthasarathi
We discuss an approach to compute two-particle scattering amplitudes for spinless light particles colliding at Planckian centre-of-mass energies, with increasing momentum transfer away from the eikonal limit. The leading corrections to the eikonal amplitude, in our 'external metric' approach, are shown to be vanishingly small in the limit of the source particle mass going to zero. For massless charged particles, the electromagnetic and gravitational interactions decouple in the eikonal limit, hut mix non-trivially for the leading order corrections.
Black hole emission rates and the AdS/CFT correspondence
(SISSA, 1999) Das, Saurya; Dasgupta, Arundhati
We study the emission rates of scalar, spinor and vector particles from a 5 dimensional black hole for arbitrary partial waves. The solution is lifted to 6 dimensions, and the near horizon BTZ S3 geometry of the black hole solution is probed to determine the greybody factors. We show that the exact decay rates can be reproduced from a (1 + 1)-dimensional conformal eld theory which lies on the boundary of the near horizon geometry. The AdS/CFT correspondence is used to determine the dimension of the CFT operators corresponding to the bulk elds. These operators couple to plane waves incident on the CFT from in nity to produce emission in the bulk.
Statistical entropy of Schwarzschild black strings and black holes
(American Physical Society, 2000) Das, Saurya; Ghosh, Amit; Mitra, P.
The statistical entropy of a Schwarzschild black string in five dimensions is obtained by counting the black string states which form a representation of the near-horizon conformal symmetry with a central charge. The statistical entropy of the string agrees with its Bekenstein-Hawking entropy as well as that of the Schwarzschild black hole in four dimensions. The string length which gives the Virasoro algebra also reproduces the precise value of the Bekenstein-Hawking entropy and lies inside the stability bound of the string.
Conserved quantities in Kerr-anti-de Sitter spacetimes in various dimensions
(SISSA, 2000) Das, Saurya; Mann, Robert B.
We compute the conserved charges for Kerr anti-de Sitter spacetimes in various dimensions using the conformal and the counterterm prescriptions. We show that the conserved charge corresponding to the global timelike killing vector computed by the two methods di er by a constant dependent on the rotation parameter and cosmological constant in odd spacetime dimensions, whereas the charge corresponding to the rotational killing vector is the same in either approach. We comment on possible implications of our results to the AdS/CFT correspondence.
New holographic entropy bound from quantum geometry
(American Institute of Physics, 2001) Das, Saurya; Kaul, Romesh K.; Majumdar, Parthasarathi
A new entropy bound, tighter than the standard holographic bound due to Bekenstein, is derived for spacetimes with nonrotating isolated horizons from the quantum geometry approach, in which the horizon is described by the boundary degrees of freedom of a three dimensional Chern-Simons theory.
Quantum mechanics of charged black holes
(Elsevier, 2001) Barvinsky, Andrei; Das, Saurya; Kunstatter, Gabor
We quantize the spherically symmetric sector of generic charged black holes. Thermal properties are incorporated by imposing periodicity in Euclidean time, with period equal to the inverse Hawking temperature of the black hole. This leads to an exact quantization of the area (A) and charge (Q) operators. For the Reissner–Nordström black hole, A = 4πG¯h(2n + p + 1) and Q= me, for integers n,p,m. Consistency requires the fine structure constant to be quantized: e2/¯h = p/m2. Remarkably, vacuum fluctuations exclude extremal black holes from the spectrum, while near extremal black holes are highly quantum objects. We also prove that horizon area is an adiabatic invariant.
Scalar field spacetimes and the anti-de Sitter space/conformal-field theory conjecture
(American Physical Society, 2001) Das, Saurya; Gegenberg, J.; Husain, V.
We describe a class of asymptotically AdS scalar field spacetimes, and calculate the associated conserved charges for three, four and five spacetime dimensions using the conformal and counterterm prescriptions. The energy associated with the solutions in each case is proportional to AM22k2, where M is a constant and k is a scalar charge. In five spacetime dimensions, the counterterm prescription gives an additional vacuum ~Casimir! energy, which agrees with that found in the context of AdS conformal-field theory ~CFT! correspondence. We find a surprising degeneracy: the energy of the ‘‘extremal’’ scalar field solution M5k equals the energy of global AdS. This result is discussed in light of the AdS/CFT conjecture.
Adiabatic quantum computation and Deutsch's algorithm
(American Physical Society, 2002) Das, Saurya; Kobes, Randy; Kunstatter, Gabor
We show that by a suitable choice of a time-dependent Hamiltonian, Deutsch’s algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both global and local adiabatic evolutions.
Quantum mechanical spectra of charged black holes
(Elsevier, 2003) Das, Saurya; Ramadevi, P.; Yajnik, U. A.; Sule, A.
It has been argued by several authors, using different formalisms, that the quantum mechanical spectrum of black hole horizon area is discrete and uniformly spaced. Recently it was shown that two such approaches, namely the one involving quantization on a reduced phase space, and the algebraic approach of Bekenstein and Gour are equivalent for spherically symmetric, neutral black holes (hep-th/0202076). That is, the observables of one can be mapped to those of the other. Here we extend that analysis to include charged black holes. Once again, we find that the ground state of the black hole is a Planck size remnant.
Spatial variation of the cooling lines in the Orion Bar from Hersehel/PACS
(EDP Sciences, 2012) Bernard-Salas, J.; Habart, E.; Arab, H.; Abergel, A.; Dartois, E.; Martin, P.; Bontemps, S.; Joblin, C.; White, G. J.; Bernard, J.-P.; Naylor, David A.
Context. The energetics in photo-dissociation regions (PDRs) are mainly regulated by the balance between the heating from the photo-electric eﬀect acting on dust grains, and the cooling via the copious emission of photons in far-infrared lines. The Orion Bar is a luminous and nearby PDR, which presents to the observer an ideal edge-on orientation in which to study this energy balance. Spatially resolved studies of such a nearby system are essential as they enable us to characterise the physical processes that control the energetics of the regions and can serve as templates for distant systems where these processes cannot be disentangled. Aims. We characterise the emission of the far-infrared ﬁne-structure lines of [Cii](158 μm),[Oi](63and145 μm),and[Nii](122 μm) that trace the gas local conditions, via spatially resolved observations of the Orion Bar. The observed distribution and variation of the lines are discussed in relation to the underlying geometry and linked to the energetics associated with the Trapezium stars. Methods. Herschel/PACS observations are used to map the spatial distribution of these ﬁne-structure lines across the Bar, with a spatial resolution between 4 and 11 and covering a total square area of about 120 ×105 . The spatial proﬁle of the emission lines are modelled using the radiative transfer code Cloudy. Results. TheHerschel observations reveal in unprecedented detail the morphology of the Bar.The spatial distribution of the [Cii] line coincides with that of the [Oi] lines. The [Nii] line peaks closer to the ionising star than the other three lines, but with a small region of overlap. We can distinguish several knots of enhanced emission within the Bar indicating the presence of an in homogenous and structured medium. The emission proﬁles cannot be reproduced by a single PDR, clearly indicating that, besides the Bar, there is a signiﬁcant contribution from additional PDR(s)over the area studied. The combination of both the [Nii] and [Oi] 145 μm lines can be used to estimate the [Cii] emission and distinguish between it sionised or neutral origin. We have calculated how much[Cii] emission comes from the neutral and ionised region, and ﬁnd that at least ∼82% originates from the photo-dissocciation region. Together, the [Cii] 158 μm and [Oi] 63 and 145 μm lines account for∼90% of the power emitted by the main cooling lines in the Bar (including CO, H2, etc.), with [Oi] 63μm alone accounting for 72% of the total.
Physical structure of the photodissociation regions in NGC 7023: observations of gas and dust emission with Herschel*
(EDP Sciences, 2014) Kohler, M.; Habart, E.; Arab, H.; Bernard-Salas, J.; Ayasso, H.; Abergel, A.; Zavagno, A.; Polehampton, E.; van der Wiel, M.H.D.; Naylor, David A.; Makiwa, Gibion; Dassas, K.; Joblin, C.; Pilleri, P.; Berne, O.; Fuente, A.; Gerin, M.; Goicoechea, J.R.; Teyssier, D.
Context. The determination of the physical conditions in molecular clouds is a key step towards our understanding of their formation and evolution of associated star formation. We investigate the density, temperature, and column density of both dust and gas in the photodissociation regions (PDRs) located at the interface between the atomic and cold molecular gas of the NGC 7023 reflection nebula. We study how young stars a ect the gas and dust in their environment. Aims. Several Herschel Space Telescope programs provide a wealth of spatial and spectral information of dust and gas in the heart of PDRs. We focus our study on Spectral and Photometric Image Receiver (SPIRE) Fourier-Transform Spectrometer (FTS) fully sampled maps that allow us for the first time to study the bulk of cool/warm dust and warm molecular gas (CO) together. In particular, we investigate if these populations spatially coincide, if and how the medium is structured, and if strong density and temperature gradients occur, within the limits of the spatial resolution obtained with Herschel. Methods. The SPIRE FTS fully sampled maps at di erent wavelengths are analysed towards the northwest (NW) and the east (E) PDRs in NGC 7023. We study the spatial and spectral energy distribution of a wealth of intermediate rotational 12CO 4 Ju 13 and 13CO 5 Ju 10 lines. A radiative transfer code is used to assess the gas kinetic temperature, density, and column density at di erent positions in the cloud. The dust continuum emission including Spitzer, the Photoconductor Array Camera and Spectrometer (PACS), and SPIRE photometric and the Institute for Radio Astronomy in the Millimeter Range (IRAM) telescope data is also analysed. Using a single modified black body and a radiative transfer model, we derive the dust temperature, density, and column density. Results. The cloud is highly inhomogeneous, containing several irradiated dense structures. Excited 12CO and 13CO lines and warm dust grains localised at the edge of the dense structures reveal high column densities of warm/cool dense matter. Both tracers give a good agreement in the local density, column density, and physical extent, leading to the conclusion that they trace the same regions. The derived density profiles show a steep gradient at the cloud edge reaching a maximum gas density of 10^5 -10^6 cm^-3 in the PDR NGC 7023 NW and 10^4 -10^5 cm^-3 in the PDR NGC 7023 E and a subsequent decrease inside the cloud. Close to the PDR edges, the dust temperature (30 K and 20 K for the NW and E PDRs, respectively) is lower than the gas temperature derived from CO lines (65-130 K and 45-55 K, respectively). Further inside the cloud, the dust and gas temperatures are similar. The derived thermal pressure is about 10 times higher in NGC 7023NWthan in NGC 7023 E. Comparing the physical conditions to the positions of known young stellar object candidates in NGC 7023 NW, we find that protostars seem to be spatially correlated with the dense structures. Conclusions. Our approach combining both dust and gas delivers strong constraints on the physical conditions of the PDRs. We find dense and warm molecular gas of high column density in the PDRs.
Star formation relations and co spectral line energy distributions across the J-ladder and redshift
(American Astronomical Society, 2014) Greve, T. R.; Leonidaki, I.; Xilouris, E.M.; Weiss, A.; Zhang, Z.-Y.; van der Werf, P.; Aalto, S.; Armus, L.; Diaz-Santos, T.; Evans, A.S.; Fischer, J.; Gao, Y.; Gonzalez-Alfonso, E.; Harris, A.; Henkel, C.; Mekjerink, R.; Naylor, David A.; Smith, H.A.; Spaans, M.; Stacey, G.J.; Veilleux, S.; Walter, F.
We present FIR[50-300 um]-CO luminosity relations (i.e., log Lfir = a log L’co + B) for the full CO rotational ladder from J = 1 – 0 up to J = 13 -12 for a sample of 62 local (z <= 0.1) (Ultra) Luminous Infrared Galaxies (LIRGs; lIR[8-1000um > 10^11 Lo) using data from Herschel SPIRE-FTS and ground-based telescopes. We extend our sample to high redshifts (z > 1) by including 35 (sub)-millimeter selected dusty star forming galaxies from the literature with robust CO observations, and sufficiently well-sampled FIR/sub-millimeter spectral energy distributions (SEDs) so that accurate FIR luminosities can be deduced. The addition of luminous starbursts at high redshifts enlarge the range of the FIR-CO luminosity relations towards the high-IR-luminosity end while also significantly increasing the small amount of mid-J/high-J CO line data (J = 5 – 4 and higher) that was available prior to Herschel. The new data-set (both in terms of IR luminosity and J-ladder) reveals linear FIR-CO luminosity relations (i.e., a ~= 1) for J = 1 – 0 up to J = 5 – 4, with a nearly constant normalization (B ~ 2). In the simplest physical scenario this is expected from the (also) linear FIR-(molecular line) relations recently found for the dense gas tracer lines (HCN and CS), as long as the dense gas mass fraction does not vary strongly within our (merger/starburst)-dominated sample. However from J = 6 – 5 and up to the J = 13 – 12 transition we find an increasingly sub-linear slope (~ 100K) and dense (> 104 cm-3) gas component whose thermal state is unlikely to be maintained by star formation powered far-UV radiation fields (and thus is no longer directly tied to the star formation rate). We suggest that mechanical heating (e.g., supernova driven turbulence and shocks), and not cosmic rays, is the most likely source of energy for this component. The global CO spectral line energy distributions (SLEDs), which remain highly excited from J = 6 – 5 up to J = 13 – 12, are found to be a generic feature of the (U)LIRGs in our sample, and further support of the presence of this gas component.
Signatures of warm carbon monoxide in protoplanetary discs observed with Herschel SPIRE
(Oxford University Press, 2014) van der Wiel, M. H. D.; Naylor, David A.; Kamp, I.; Ménard, F.; Thi, W.-F.; Woitke, P.; Olofsson, G.; Pontoppidan, K. M.; Di Francesco, J.; Glauser, A. M.; Greaves, J. S.; Ivison, R. J.
Molecular gas constitutes the dominant mass component of protoplanetary discs. To date, these sources have not been studied comprehensively at the longest far-infrared and shortest submillimetre wavelengths. This paper presents Herschel SPIRE FTS spectroscopic observations towards 18 protoplanetary discs, covering the entire 450–1540GHz (666–195 μm) range at ν/ ν ≈ 400–1300. The spectra reveal clear detections of the dust continuum and, in six targets, a signiﬁcant amount of spectral line emission primarily attributable to 12CO rotational lines. Other targets exhibit little to no detectable spectral lines. Low signal-to-noise detections also include signatures from 13CO, [CI] and HCN. For completeness, we present upper limits of non-detected lines in all targets, including low-energy transitions of H2O and CH+ molecules. The 10 12CO lines that fall within the SPIRE FTS bands trace energy levels of ∼50–500K. Combined with lower and higher energy lines from the literature, we compare the CO rotational line energy distribution with detailed physical–chemical models, for sources where these are available and published. Our 13CO line detections in the disc around Herbig Be star HD 100546 exceed, by factors of ∼10–30, the values predicted by a model that matches a wealth of other observational constraints, including the SPIRE 12COladder. To explain the observed 12CO/13COratio, it may be necessary to consider the combined effects of optical depth and isotope selective (photo)chemical processes. Considering the full sample of 18 objects, we ﬁnd that the strongest line emission is observed in discs around Herbig Ae/Be stars, although not all show line emission. In addition, two of the six T Tauri objects exhibit detectable 12CO lines in the SPIRE range.
Calibration of the Herschel SPIRE Fourier Transform Spectrometer
(Oxford University Press, 2014) Swinyard, B. M.; Polehampton, E. T.; Hopwood, R.; Valtchanov, I.; Lu, N.; Fulton, T.; Benielli, D.; Imhof, P.; Marchili, N.; Baluteau, J.-P.; Bendo, G. J.; Ferlet, M.; Griffin, M. J.; Lim, T. L.; Makiwa, G.; Naylor, David A.; Orton, G. S.; Papageorgiou, A.; Pearson, C. P.; Schulz, B.; Sidher, S. D.; Spencer, Locke Dean; van der Wiel, M. H. D.; Wu, R.
The Herschel Spectral and Photometric REceiver (SPIRE) instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of∼450–1550GHz. In this paper, we brieﬂy review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a spatially extended source and uses the Herschel telescopeasprimarycalibrator.Conversionfromextendedtopoint-sourcecalibrationiscarried out using observations of the planet Uranus. The model of the telescope emission is shown to beaccuratetowithin6percent andrepeatable tobetterthan0.06percent and,bycomparison with models of Mars and Neptune, the Uranus model is shown to be accurate to within 3 per cent. Multiple observations of a number of point-like sources show that the repeatability of the calibration is better than 1 per cent, if the effects of the satellite absolute pointing error (APE) are corrected. The satellite APE leads to a decrement in the derived ﬂux, which can be up to∼10 per cent (1 σ) at the high-frequency end of the SPIRE range in the ﬁrst part of the mission, and∼4 per cent after Herschel operational day 1011. The lower frequency range of the SPIRE band is unaffected by this pointing error due to the larger beam size. Overall, for well-pointed, point-like sources, the absolute ﬂux calibration is better than 6 per cent, and for extended sources where mapping is required it is better than 7 per cent.

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