Power-law Extrapolation Research Articles

Herschel-SPIRE, far-infrared properties of millimetre-bright and -faint radio galaxies

Abstract We present the first study of the far-infrared (FIR) properties of high-redshift, radio-selected ultraluminous infrared galaxies (ULIRGs) using deep observations obtained with the Spectral and Photometric Imaging Receiver (SPIRE) from the Herschel Multi-tiered Extragalactic Survey (HerMES). These galaxies span a large range of 850-μm fluxes from submillimetre-luminous ∼10 mJy sources (SCUBA galaxies) to ∼1.5 mJy from stacked SCUBA non-detections, thus likely representing a complete distribution of ULIRG spectral energy distributions (SEDs). From Keck spectroscopic surveys in the Lockman-North field we identified a sample of 31 submillimetre galaxies (SMGs) and 37 submillimetre-faint, optically faint radio galaxies (OFRGs), all with radio-inferred IR luminosities >1012 L⊙. These galaxies were cross-identified with SPIRE 250-, 350- and 500-μm catalogues based on fluxes extracted at 24-μm positions in the SWIRE survey, yielding a sample of more than half of the galaxies well detected in at least two of the SPIRE bandpasses. By fitting greybody dust models to the SPIRE photometry together with SCUBA 850-μm measurements (for OFRGs, only 850- upper limits), we infer dust temperatures and FIR luminosities. The OFRGs detected by SPIRE have median 〈Td〉= 41 ± 5 K and the SMGs have 〈Td〉= 34 ± 5 K, both in reasonable agreement with previous (pre-Herschel) estimates, reaffirming that the local FIR/radio correlation holds (at least for this subset of high-z ULIRGs) at high redshift (we measure 〈qIR〉= 2.43 ± 0.21 using SIR derived from greybody fit coupled with a power-law extrapolation to the 24 μm). Our observations first confirm that a substantial fraction of OFRGs exhibits large infrared luminosities corresponding to SFRs of ∼400 M⊙ yr−1. The SPIRE observations secondly confirm the higher dust temperatures for these OFRGs than similarly selected SMGs, consistent with early predictions of the submillimetre-faint radio populations. Our observations also clearly confirm the large infrared luminosities of most SMGs selected with S850 μm > 5 mJy and radio and strong 24-μm detections, corresponding to SFRs of ∼700 M⊙ yr−1.

The luminosity function of the hot and cold Kuiper belt populations

We have performed an ecliptic survey of the Kuiper belt, with an areal coverage of 8.9 square degrees to a 50% limiting magnitude of r Sloan ′ = 24.7 , and have detected 88 Kuiper belt objects, roughly half of which received follow-up 1–2 months after detection. Using this survey data alone, we have measured the luminosity function of the Kuiper belt, thus avoiding any biases that might come from the inclusion of other observations. We have found that the Cold population defined as having inclinations less than 5° has a luminosity function slope α Cold = 0.82 ± 0.23, and is different from the Hot population, which has inclinations greater than 5° and a luminosity function slope α Hot = 0.35 ± 0.21. As well, we have found that those objects closer than 38 AU have virtually the same luminosity function slope as the Hot population. This result, along with similar findings of past surveys demonstrates that the dynamically Cold Kuiper belt objects likely have a steep size distribution, and are unique from all of the excited populations which have much shallower distributions. This suggests that the dynamically excited population underwent a different accretion history and achieved a more evolved state of accretion than the Cold population. As well, we discuss the similarities of the Cold and Hot populations with the size distributions of other planetesimal populations. We find that while the Jupiter family comets and the scattered disk exhibit similar size distributions, a power-law extrapolation to small sizes for the scattered disk cannot account for the observed influx of comets. As well, we have found that the Jupiter Trojan and Hot populations cannot have originated from the same parent population, a result that is difficult to reconcile with scattering models similar to the NICE model. We conclude that the similarity between the size distributions of the Cold population and the Jupiter Trojan population is a striking coincidence.

BINARY QUASARS AT HIGH REDSHIFT. II. SUB-Mpc CLUSTERING ATz∼ 3-4

We present measurements of the small-scale (0.1<~ r <~ 1 Mpc/h) quasar two-point correlation function at z>2.9, for a flux-limited (i<21) sample of 15 binary quasars compiled by Hennawi et al. (2009). The amplitude of the small-scale clustering increases from z ~ 3 to z ~ 4. The small-scale clustering amplitude is comparable to or lower than power-law extrapolations (with slope gamma=2) from the large-scale correlation function of the i<20.2 quasar sample from the Sloan Digital Sky Survey. Using simple prescriptions relating quasars to dark matter halos, we model the observed small-scale clustering with halo occupation models. Reproducing the large-scale clustering amplitude requires that the active fraction of the black holes in the central galaxies of halos is near unity, but the level of small-scale clustering favors an active fraction of black holes in satellite galaxies 0.1 <~ f_s <~ 0.5 at z >~ 3.

Impact of in situ oxygen plasma cleaning on the resistance of Ru and Au-Ru based rf microelectromechanical system contacts in vacuum

Contact resistance measurements are reported for radio frequency microelectromechanical system switches operating in an ultrahigh vacuum system equipped with in situ oxygen plasma cleaning capabilities. Ru-based contacts were prepared by means of standard sputtering techniques, sputtering followed by postdeposition oxidation, (surface RuO2) or reactive sputtering in the presence of oxygen (bulk RuO2). In situ oxygen plasma cleaning lowered the resistance of Ru contacts by two or more orders of magnitude but not lower than Au contacts, irrespective of whether the Au contacts were cleaned. The time dependence of the resistance was fit to power law extrapolations to infer contact creep properties and resistance values at t=∞. Time-dependent creep properties of mixed Au-Ru contacts were observed to be similar to those of Au-Au contacts, while the absolute value of the resistance of such contacts was more comparable to Ru-Ru contacts. Prior to, and for short oxygen plasma exposure times, bulk RuO2 resistance values exhibited much larger variations than values measured for surface RuO2. For O2 plasma exposure times exceeding about 5 min, the bulk and surface RuO2 resistance values converged, at both t=0 and t=∞, with the t=∞ values falling within experimental error of theoretical values predicted for ideal surfaces. The data strongly support prior reports in the surface science literature of oxygen plasma induced thickening of oxide layers present on Ru surfaces. In addition, they demonstrate that vacuum alone is insufficient to remove contaminants from the contact surfaces and/or prevent such contaminants from reforming after oxygen plasma exposure.

Starburst evolution: free-free absorption in the radio spectra of luminousIRASgalaxies

We describe radio observations at 244 and 610 MHz of a sample of 20 luminous and ultra-luminous IRAS galaxies. These are a sub-set of a sample of 31 objects that have well-measured radio spectra up to at least 23 GHz. The radio spectra of these objects below 1.4 GHz show a great variety of forms and are rarely a simple power-law extrapolation of the synchrotron spectra at higher frequencies. Most objects of this class have spectral turn-overs or bends in their radio spectra. We interpret these spectra in terms of free-free absorption in the starburst environment. Several objects show radio spectra with two components having free-free turn-overs at different frequencies (including Arp 220 and Arp 299), indicating that synchrotron emission originates from regions with very different emission measures. In these sources, using a simple model for the supernova rate, we estimate the time for which synchrotron emission is subject to strong free-free absorption by ionized gas, and compare this to expected HII region lifetimes. We find that the ionized gas lifetimes are an order of magnitude larger than plausible lifetimes for individual HII regions. We discuss the implications of this result and argue that those sources which have a significant radio component with strong free-free absorption are those in which the star formation rate is still increasing with time. We note that if ionization losses modify the intrinsic synchrotron spectrum so that it steepens toward higher frequencies, the often observed deficit in fluxes higher than ~10 GHz would be much reduced.

VERITAS UPPER LIMIT ON THE VERY HIGH ENERGY EMISSION FROM THE RADIO GALAXY NGC 1275

The recent detection by the Fermi gamma-ray space telescope of high-energy gamma-rays from the radio galaxy NGC 1275 makes the observation of the very high energy (VHE: E > 100 GeV) part of its broadband spectrum particularly interesting, especially for the understanding of active galactic nuclei (AGN) with misaligned multi-structured jets. The radio galaxy NGC 1275 was recently observed by VERITAS at energies above 100 GeV for about 8 hours. No VHE gamma-ray emission was detected by VERITAS from NGC 1275. A 99% confidence level upper limit of 2.1% of the Crab Nebula flux level is obtained at the decorrelation energy of approximately 340 GeV, corresponding to 19% of the power-law extrapolation of the Fermi Large Area Telescope (LAT) result.

The GeV‐TeV Connection in Galactic γ‐Ray Sources

Recent observations with atmospheric Cerenkov telescope systems such as H.E.S.S. and MAGIC have revealed a large number of new sources of very high energy (VHE) γ-rays from 100 GeV to 100 TeV, mostly concentrated along the Galactic plane. At lower energies (100 MeV to 10 GeV) the satellite-based instrument EGRET revealed a population of sources clustering along the Galactic plane. Given their adjacent energy bands, a systematic correlation study between the two source catalogs seems appropriate. Here, the populations of Galactic sources in both energy domains are characterized on observational as well as on phenomenological grounds. Surprisingly few common sources are found in terms of positional coincidence and spectral consistency. These common sources and their potential counterparts and emission mechanisms are discussed in detail. In cases of detection in only one energy band, for the first time consistent upper limits in the other energy band have been derived. The EGRET upper limits are rather unconstraining due to the sensitivity mismatch to current VHE instruments. The VHE upper limits put strong constraints on simple power-law extrapolation of several of the EGRET spectra and thus strongly suggest cutoffs in the unexplored energy range from 10 to 100 GeV. Physical reasons for the existence of cutoffs and for differences in the source population at GeV and TeV energies are discussed. Finally, predictions are derived for common GeV-TeV sources for the upcoming GLAST mission, bridging for the first time the energy gap between current GeV and TeV instruments.

MAGIC Upper Limits on the Very High Energy Emission from Gamma‐Ray Bursts

During its first data cycle, between 2005 and the beginning of 2006, the fast repositioning system of the MAGIC telescope allowed the observation of nine different gamma-ray bursts as possible sources of very high energy γ-rays. These observations were triggered by alerts from Swift, HETE-2, and INTEGRAL; they started as quickly as possible after the alerts and lasted for several minutes, with an energy threshold varying between 80 and 200 GeV, depending on the zenith angle of the burst. No evidence for gamma signals was found, and upper limits for the flux were derived for all events using the standard analysis chain of MAGIC. For the bursts with measured redshifts, the upper limits are compatible with a power-law extrapolation, when the intrinsic fluxes are evaluated taking into account the attenuation due to the scattering in the metagalactic radiation field.

Swift XRT and UVOT deep observations of the high-energy peaked BL Lacertae object PKS 0548–322 close to its brightest state

Aims. We observed the high-energy peaked BL Lac object PKS 0548-322 (BZB J0550-3216) with Swift to study the temporal and spectral properties of its synchrotron emission simultaneously in the optical, ultraviolet, and X-ray energy bands. Methods. We carried out a spectral analysis of 5 Swift XRT and UVOT observations of PKS 0548-322 taken over the period April-June 2005. Results. The X-ray flux of this BL Lac source was found to be approximately constant at a level of F (2-10 keV) ≃ 4 × 10 -11 erg cm -2 s -1 which is a factor of 2 brighter than when observed by BeppoSAX in 1999 and close to the maximum intensity reported in the Einstein Slew Survey. The very good statistics obtained in the 0.3-10 keV Swift X-ray spectrum allowed us to detect highly significant deviations from a simple power-law spectral distribution. A log-parabolic model describes the X-ray data well and gives a best-fit curvature parameter of 0.18 and a peak energy in the spectral energy distribution of about 2 keV. The UV spectral data from Swift UVOT join closely with a power-law extrapolation of the soft X-ray data points, suggesting that the same component is responsible for the observed emission in the two bands. The combination of synchrotron peak in the X-ray band and the high-intensity state confirms PKS 0548-322 as a prime target for TeV observations. X-ray monitoring and coordinated TeV campaigns are highly advisable.

Prospects for direct detection of primordial gravitational waves

We study the primordial gravitational wave background produced in models of single field inflation. Using the inflationary flow approach, we investigate the amplitude of gravitational wave spectrum in the frequency range 1 mHz - 1 Hz pertinent to future space-based laser interferometers. For models that satisfy the current observational constraint on the tensor-to-scalar ratio, r<0.36, we derive a strict upper bound of omega_{gw}<1.6 x 10^{-15}, independent of the form of the inflationary potential. Applying, in addition, the observational constraints on the spectral index and its running, omega_{gw} is expected to be considerably lower than this bound unless the shape of the potential is finely tuned. We contrast our numerical results with those based on simple power-law extrapolation of the tensor power spectrum from CMB scales. In addition to single field inflation, we summarise a number of other possible cosmological sources of primordial gravitational waves and assess what might be learnt from direct detection experiments such as LISA, Big Bang Observer and beyond.

The applicability of power-law frequency statistics to floods

Many natural hazards satisfy power-law (fractal) frequency-size statistics to a good approximation for medium and large events. Examples include earthquakes, volcanic eruptions, asteroid impacts, landslides, and forest fires. A major question is whether this is also true for floods. A number of authors have argued in favor of the applicability of power-law statistics to floods. We discuss these arguments and consider a number of examples, using both instrumental records and paleoflood studies. In our analyses we consider both annual and partial-duration flood series. We argue that use of annual floods for statistical considerations strongly biases the flood-frequency estimates, as in some years, the annual flood will be much smaller than a number of ‘statistically independent’ floods (partial-duration floods) in other years. We examine six USGS hydrologic stations with drainage areas from 41 to 95,300 km 2, representing very different climatic regions and hydrologic conditions, and with periods of records ranging from 74 to 110 water years. Excellent power-law fits to each partial-duration series are found taking Q∼ T α , with Q the discharge associated with the recurrence interval T, and the power-law exponent α ranging from 0.27 to 0.90. We also consider paleoflood estimates for Axehandle Alcove on the Colorado River and Bonza Alcove on the Paria River, and find that that power-law extrapolations based on instrumental partial-duration series for stations in each of these two areas is within a half order of magnitude when compared to their respective paleoflood estimates. Finally, we consider an alternative approach to extreme streamflows that has been proposed, examining the cumulative probability distribution of instrumental daily mean streamflows. We show that this distribution is in good agreement with the power-law correlation found using the partial-duration series.

A Modified Power Law for Creep Analysis

The creep strengths for an annealed Ni-33Fe-25Cr alloy, UNS N08120 (HAYNES® HR-120® alloy) are presented from 593°C to 1204°C at every 56°C for lives up to 30,000 hours. The creep data are used as a basis for converting the power law method (log stress versus log time at a defined temperature) to the usefulness of the Larson-Miller method for design creep analysis. A new empirical relationship was developed between stress, temperature and creep rupture life. Power Law equations were generated at each temperature using linear regression of the transformed data to obtain the best-fit constants. The constants were then plotted and a best-fit polynomial of the constants as a function of temperature was determined. The polynomial then replaced the constants in the original power law equation to obtain a single expression of stress as a function of time and temperature. Using this new Modified Power Law (MPL) equation, interpolation or extrapolation to obtain stress becomes possible for any temperature and time.

The Identification of Infrared Synchrotron Radiation from Cassiopeia A

We report the discovery of polarized flux at 2.2 μm from the bright shell of the ≈320 yr old supernova remnant Cas A. The fractional polarizations are comparable at 6 cm and 2.2 μm, and the polarization angles are similar, demonstrating that synchrotron radiation from the same relativistic plasma is being observed at these widely separated wave bands. The relativistic electrons radiating at 2.2 μm have an energy of ≈150 GeV, (γ ≈ 3 × 105), assuming an ≈500 μG magnetic field. The total intensity at 2.2 μm lies close to the power-law extrapolation from radio frequencies, showing that relativistic particle acceleration is likely an ongoing process; the infrared emitting electrons were accelerated no longer than ≈80 yr ago. There is a small but significant concave curvature to the spectrum, as expected if the accelerating shocks have been modified by the back pressure of the cosmic rays; given calibration uncertainties, this conclusion must be considered tentative at present. The 2.2 μm polarization angles and the emission-line filaments observed by the Hubble Space Telescope are both offset from the local radial direction by 10°-20°, providing evidence that the magnetic fields in Cas A are generated by Rayleigh-Taylor instabilities in the decelerating ejecta.

Comment on estimating the solar proton environment that may affect Mars missions

Estimates of the energetic proton environment for a Mars mission are generally extrapolated from the solar proton observations at 1 AU. We find that solar particle events may be divided into two general classes. Events dominated by a near-sun injection of particles onto interplanetary magnetic field lines leading to the spacecraft position represent the “classical” solar particle event associated with solar activity. This class of event will scale in radial distance by the classical power law extrapolation. The extended-interplanetary-shock source generates a maximum flux as the shock passes the detection location. This class of event typically generates maximum fluence, but in this case, the flux and fluence will not scale in the classical manner with radial distance.

Hard Pomeron enhancement of ultrahigh-energy neutrino-nucleon cross sections

An unknown small-$x$ behavior of nucleon structure functions gives appreciable uncertainties to high-energy neutrino-nucleon cross sections. We construct structure functions using at small x a Regge description inspired by Donnachie and Landshoff with soft and hard Pomerons, and employing at larger x the perturbative QCD expressions. Smooth interpolation between the two regimes for each ${Q}^{2}$ is provided with the help of simple polynomial functions. To obtain low-$x$ neutrino-nucleon structure functions ${F}_{2}^{\ensuremath{\nu}N,\overline{\ensuremath{\nu}}N}{(x,Q}^{2})$ and the singlet part of ${F}_{3}^{\ensuremath{\nu}N,\overline{\ensuremath{\nu}}N}{(x,Q}^{2})$ from the Donnachie-Landshoff function ${F}_{2}^{\mathrm{ep}}{(x,Q}^{2}),$ we use the ${Q}^{2}$-dependent ratios ${R}_{2}{(Q}^{2})$ and ${R}_{3}{(Q}^{2})$ derived from perturbative QCD calculations. The nonsinglet part of ${F}_{3}$ at low x, which is very small, is taken as a power-law extrapolation of the perturbative function at larger x. This procedure gives a full set of smooth neutrino-nucleon structure functions in the whole range of x and ${Q}^{2}$ at interest. Using these structure functions, we calculate the neutrino-nucleon cross sections and compare them with some other cross sections known in the literature. Our cross sections turn out to be the highest among them at the highest energies, which is explained by the contribution of the hard Pomeron.

Onset of ferromagnetism in Fe epitaxially grown on GaAs(001) (4×2) and (2×6)

Ultrathin Fe films were epitaxially grown at room temperature on GaAs(001) with either predominant (4×2) or (2×6) surface reconstruction. At nominal Fe coverages of tFe⩾2.8 monolayers (ML), a ferromagnetic state is observed below a certain critical temperature, TC. Surprisingly, the magnetic phase transition at TC appears even sharper than for Fe films on metallic single-crystal substrates, which were believed to be an excellent representation of two-dimensional (2D) ferromagnets. This may be due to the extremely short lateral length scale of film inhomogeneities. The critical exponent β=0.26 is close to the value expected for 2D XY systems of finite size. For tFe=3.6 ML, TC is close to room temperature. TC decreases steeply with decreasing Fe coverage, with an average slope of 270 K/ML. From a power law extrapolation, TC seems to vanish at tFe=2.5 ML. The onset of ferromagnetism at tFe=2.5 ML is interpreted as a percolation phenomenon during the coalescence process of Fe islands.

Separating Thermal and Nonthermal X‐Rays in Supernova Remnants. I. Total Fits to SN 1006 AD

The remnant of SN 1006 has an X-ray spectrum dominated by nonthermal emission, and pre-ASCA observations were well described by a synchrotron calculation with electron energies limited by escape. We describe the results of a much more stringent test: fitting spatially integrated ASCA GIS (0.6-8 keV) and RXTE PCA (3-10 keV) data with a combination of the synchrotron model SRESC newly ported to XSPEC and a new thermal shock model VPSHOCK. The new model can describe the continuum emission above 2 keV well, in both spatial distribution and spectrum. We find that the emission is dominantly nonthermal, with a small but noticeable thermal component: Mg and Si are clearly visible in the integrated spectrum. The synchrotron component rolls off smoothly from the extrapolated radio spectrum, with a characteristic rolloff frequency of 3.1E17 Hz, at which the spectrum has dropped about a factor of 6 below a powerlaw extrapolation from the radio spectrum. Comparison of TeV observations with new TeV model images and spectra based on the X-ray model fits gives a mean post-shock magnetic field strength of about 9 microGauss, implying (for a compression ratio of 4) an upstream magnetic field of 3 microGauss, and fixing the current energy content in relativistic electrons at about 7E48 ergs, resulting in a current electron-acceleration efficiency of about 5%. This total energy is about 100 times the energy in the magnetic field. Our results indicate that joint thermal and nonthermal fitting, using sophisticated models, will be required for analysis of most supernova-remnant X-ray data in the future.

Extrapolation of Galactic Dust Emission at 100 Microns to Cosmic Microwave Background Radiation Frequencies Using FIRAS

We present predicted full-sky maps of submillimeter and microwave emission from the diffuse interstellar dust in the Galaxy. These maps are extrapolated from the 100 μm emission and 100/240 μm flux ratio maps that Schlegel, Finkbeiner, & Davis generated from IRAS and COBE/DIRBE data. Results are presented for a number of physically plausible emissivity models. The correlation of COBE/FIRAS data with the simple Schlegel, Finkbeiner, & Davis (ν2 emissivity power law) extrapolation is much tighter than with other common dust templates such as H I column density or 100 μm emission. Despite the apparent success of the Schlegel, Finkbeiner, & Davis extrapolation, the assumed ν2 emissivity is inconsistent with the FIRAS data below 800 GHz. Indeed, no power-law emissivity function fits the FIRAS data from 200 to 2100 GHz. In this paper we provide a formalism for a multicomponent model for the dust emission. A two-component model with a mixture of "silicate" and "carbon-dominated" grains (motivated by Pollack et al.) provides a fit to an accuracy of ~15% to all the FIRAS data over the entire high-latitude sky. Small systematic differences are found between the atomic and molecular phases of the ISM. COBE/DMR has observed microwave emission that is correlated with thermal dust emission. However, this emission is higher than our model predicts by factors of 1.2, 2.4, and 20 at 90, 53, and 31 GHz, respectively. This provides evidence that another emission mechanism dominates dust emission at frequencies below ~60 GHz. Our predictions for the thermal (vibrational) emission from Galactic dust at ν < 3000 GHz are available for general use. These full-sky predictions can be made at the DIRBE resolution of 40' or at the higher resolution of 61 from the Schlegel, Finkbeiner, & Davis DIRBE-corrected IRAS maps.

Dynamical QCD predictions for ultrahigh energy neutrino cross sections

Neutrino-nucleon total cross sections for neutrino energies up to ultrahigh energies (UHE), E ν = 10 12, GeV, are evaluated within the framework of the dynamical (radiative) parton model. The expected uncertainties of these predictions do not exceed the level of about 20% at the highest energies where contributions of parton distributions in the yet unmeasured region around x ⋍ 10 −8, to 10 −9 are non-negligible. This is far more accurate than estimated uncertainties of about 2 ±1 due to fixed power law extrapolations of parton distributions to x < 10 −5 required for calculating UHE cosmic neutrino event rates.

Analytical and experimental assessment of mechanical borehole sealing performance in rock

This paper examines the bond strength of cement grout plugs cast in rock. The bond strength has been determined through push-out testing in which an axial load is applied to cement grout plugs emplaced in boreholes in welded tuff cylinders. The push-out tests have been performed as a function of borehole (plug) radius and plug length. The use of four different borehole radii and three different plug length-to-radius ratios enables the evaluation of size effects. A power law obeying strength decrease with increasing plug radius and decreasing plug length results. The exponents of the power law extrapolation are about 0.5 for the borehole (plug) radius size effects and about 1.1 for the size effects on plug length-to-radius ratio. The mean axial strength, mean bond strength and mean peak shear strength range from 15.0–170 MPa, 3.90–11.0 MPa and 17.0–115 MPa, respectively. The tensile stresses in and near the vicinity of an axially loaded borehole plug are analyzed. Implications of the tensile stresses and peak shear stresses on plug design are discussed. The main conclusion is a recommendation to design friction plugs in shafts, drifts, tunnels, or boreholes with a length-to-radius ratio of at least eight.