Steep Spectrum Research Articles

Signal Frequency Dependence of Ionospheric Scintillations: An Indicator of Irregularity Spectrum Characteristics

AbstractMultifrequency scintillation observations show that strong amplitude scintillations on very high frequency (VHF) signals are accompanied by weak L‐band scintillations near the dip equator and strong L‐band scintillations in equatorial ionization anomaly (EIA) region. For several decades this has been attributed to higher ambient plasma density in the EIA region. Recent work suggests that occurrence of stronger L‐band scintillations in the EIA region requires that the intermediate‐scale (~100 m to few km) ionospheric irregularity spectrum in this region be significantly shallower than that in the equatorial region. However, this has not been established so far. Signal frequency dependence of amplitude scintillations is characterized by the frequency exponent that determines the dependence on signal frequency of the S4 index: the standard deviation of normalized intensity fluctuations. In this paper, theoretical calculations of the frequency exponent for VHF and L‐band signals are carried out using different irregularity spectra and compared with observations in order to characterize power‐law irregularity spectra in different latitude zones. Intermediate‐scale irregularities in the equatorial and low‐latitude region, which are aligned with the geomagnetic field, are described by a two‐dimensional model. Model simulations show that the frequency exponent derived from S4 indices for VHF and L‐band signals is determined only by the characteristics of the irregularity spectrum and hence can be utilized to identify the nature of the power‐law irregularity spectrum. Frequency exponents computed using VHF and L‐band observations near the dip equator and EIA regions show distinct patterns, which clearly indicate steep and shallow irregularity spectra, respectively, in these regions.

A Dynamically Modulated All‐Dielectric Metasurface Doublet for Directional Harmonic Generation and Manipulation in Transmission

AbstractIn this paper, an electrically tunable all‐dielectric metasurface doublet is proposed operating at mid‐infrared frequency regime with dynamic 2π phase span in transmission mode. Each layer of the metasurface consists of a periodic array of silicon nanobars configured into p‐i‐n junctions in which the double carrier injection into the intrinsic region under forward bias allows for tuning of the silicon refractive index. The physical mechanism is based on the spectral overlap of high quality factor guided mode resonances supported by each constituent layer establishing an extreme Huygens' operation regime of nearly reflectionless transmission with steep phase spectrum. The short response time of field‐driven carrier injection in p‐i‐n junctions allows for modulation of refractive index with radio‐frequency biasing signals, yielding a stable time‐modulated all‐dielectric metasurface with directional frequency conversion and harmonic generation in transmission. A systematic approach is adopted to control the output spectrum of generated frequency harmonics through engineering the temporally modulated phase of transmitted light via adjusting the modulation waveform. Specifically, pure frequency mixing and concurrent dual‐frequency generation in transmission mode are demonstrated. Unique applications of the time‐modulated all‐dielectric metasurface are presented including wavelength‐multiplexed metalens for dual‐polarity focusing/diffusing and frequency diverse transmitarray for ultrafast spatiotemporal beam‐scanning.

An ASKAP survey for H i absorption towards dust-obscured quasars

ABSTRACT Obscuration of quasars by accreted gas and dust, or dusty intervening galaxies, can cause active galactic nuclei (AGN) to be missed in optically selected surveys. Radio observations can overcome this dust bias. In particular, radio surveys searching for H i absorption inform us on how the AGN can impact on the cold neutral gas medium within the host galaxy, or the population of intervening galaxies through the observed line of sight gas kinematics. We present the results of an H i absorption line survey at 0.4 < z < 1 towards 34 obscured quasars with the Australian SKA Pathfinder (ASKAP) commissioning array. We detect three H i absorption lines, with one of these systems previously unknown. Through optical follow-up for two sources, we find that in all detections the H i gas is associated with the AGN, and hence that these AGN are obscured by material within their host galaxies. Most of our sample are compact, and in addition, are either gigahertz peaked spectrum (GPS), or steep spectrum (CSS) sources, both thought to represent young or recently re-triggered radio AGN. The radio spectral energy distribution classifications for our sample agree with galaxy evolution models in which the obscured AGN has only recently become active. Our associated H i detection rate for GPS and compact SS sources matches those of other surveys towards such sources. We also find shallow and asymmetric H i absorption features, which agrees with previous findings that the cold neutral medium in compact radio galaxies is typically kinematically disturbed by the AGN.

Searching for signs of jet-driven negative feedback in the nearby radio galaxy UGC 05771

ABSTRACT Hydrodynamical simulations predict that the jets of young radio sources can inhibit star formation in their host galaxies by injecting heat and turbulence into the interstellar medium (ISM). To investigate jet–ISM interactions in a galaxy with a young radio source, we have carried out a multiwavelength study of the z = 0.025 Compact Steep Spectrum radio source hosted by the early-type galaxy UGC 05771. Using Keck/OSIRIS observations, we detected H2 1–0 S(1) and [Fe ii] emission at radii of 100s of parsecs, which traces shocked molecular and ionized gas being accelerated outwards by the jets to low velocities, creating a ‘stalling wind’. At kpc radii, we detected shocked ionized gas using observations from the CALIFA survey, covering an area much larger than the pc-scale radio source. We found that existing interferometric radio observations fail to recover a large fraction of the source’s total flux, indicating the likely existence of jet plasma on kpc scales, which is consistent with the extent of shocked gas in the host galaxy. To investigate the star formation efficiency in UGC 05771, we obtained IRAM CO observations to analyse the molecular gas properties. We found that UGC 05771 sits below the Kennicutt–Schmidt relation, although we were unable to definitively conclude if direct interactions from the jets are inhibiting star formation. This result shows that jets may be important in regulating star formation in the host galaxies of compact radio sources.

Spectrum of Electrons Accelerated in Supernova Remnants.

Using a semianalytic model of nonlinear diffusive shock acceleration, we model the total spectrum of cosmic ray (CR) electrons accelerated by supernova remnants (SNRs). Because electrons experience synchrotron losses in the amplified magnetic fields characteristic of SNRs, they exhibit substantially steeper spectra than protons. In particular, we find that the difference between the electron and proton spectral index (power law slope) ranges from 0.1 to 0.4. Our findings must be reckoned with theories of Galactic CR transport, which often assume that electrons and protons are injected with the same slope, and may especially have implications for the observed "positron excess".

LOFAR Discovery of a Radio Halo in the High-redshift Galaxy Cluster PSZ2 G099.86+58.45

Abstract In this Letter, we report the discovery of a radio halo in the high-redshift galaxy cluster PSZ2 G099.86+58.45 (z = 0.616) with the LOw Frequency ARray (LOFAR) at 120–168 MHz. This is one of the most distant radio halos discovered so far. The diffuse emission extends over ∼1 Mpc and has a morphology similar to that of the X-ray emission as revealed by XMM-Newton data. The halo is very faint at higher frequencies and is barely detected by follow-up 1–2 GHz Karl G. Jansky Very Large Array observations, which enable us to constrain the radio spectral index to be α ≲ 1.5–1.6, i.e., with properties between canonical and ultra-steep spectrum radio halos. Radio halos are currently explained as synchrotron radiation from relativistic electrons that are re-accelerated in the intracluster medium by turbulence driven by energetic mergers. We show that in such a framework radio halos are expected to be relatively common at ∼150 MHz (∼30%–60%) in clusters with mass and redshift similar to PSZ2 G099.86+58.45; however, at least two-thirds of these radio halos should have a steep spectrum and thus be very faint above ∼1 GHz frequencies. Furthermore, because the luminosity of radio halos at high redshift depends strongly on the magnetic field strength in the hosting clusters, future LOFAR observations will also provide vital information on the origin and amplification of magnetic fields in galaxy clusters.

A Broadband Look at the Old and New ULXs of NGC 6946

Abstract Two recent observations of the nearby galaxy NGC 6946 with NuSTAR, one simultaneous with an XMM-Newton observation, provide an opportunity to examine its population of bright accreting sources from a broadband perspective. We study the three known ultraluminous X-ray sources (ULXs) in the galaxy, and find that ULX-1 and ULX-2 have very steep power-law spectra with in both cases. Their properties are consistent with being super-Eddington accreting sources with the majority of their hard emission obscured and down-scattered. ULX-3 (NGC 6946 X-1) is significantly detected by both XMM-Newton and NuSTAR at L X = (6.5 ± 0.1) × 1039 erg s−1, and has a power-law spectrum with Γ = 2.51 ± 0.05. We are unable to identify a high-energy break in its spectrum like that found in other ULXs, but the soft spectrum likely hinders our ability to detect one. We also characterize the new source, ULX-4, which is only detected in the joint XMM-Newton and NuSTAR observation, at L X = (2.27 ± 0.07) × 1039 erg s−1, and is absent in a Chandra observation 10 days later. It has a very hard cutoff power-law spectrum with Γ = 0.7 ± 0.1 and keV. We do not detect pulsations from ULX-4, but its transient nature can be explained either as a neutron star ULX briefly leaving the propeller regime or as a micro-tidal disruption event induced by a stellar-mass compact object.

Cavity-resonator-integrated guided-mode resonance mirror with high-confinement channel structure for improvement of reflectance

A cavity-resonator-integrated guided-mode resonance mirror (CRIGM) consists of a grating coupler integrated in a waveguide cavity formed by a pair of distributed Bragg reflectors (DBRs) on a high-reflectance substrate. It is theoretically predicted that a CRIGM can give interesting characteristics of not only a narrow band-stop reflection spectrum but also flat high reflectance with steep reflection-phase spectrum according to its structure, whereas only a CRIGM with a band-stop reflection spectrum has been confirmed experimentally so far. This time, the cause of undesirable reflectance drop in a CRIGM for flat high reflectance spectrum is investigated theoretically and experimentally. It is theoretically shown that the CRIGM reflectance at the resonance wavelength is affected considerably by a slight reduction of the DBR reflectance. A CRIGM with a rib-structured channel for high lateral confinement is designed and fabricated to keep the DBR reflectance high by suppressing a propagation loss of a guided wave. The improvement of the CRIGM reflection spectrum is confirmed experimentally by measurement of the reflection spectra of the fabricated devices.

Cosmic-ray Spectrum Steepening in Supernova Remnants. I. Loss-free Self-similar Solution

Abstract The direct measurements of cosmic rays (CRs), after correction for the propagation effects in the interstellar medium, indicate that their source spectra are likely to be significantly steeper than the canonical E −2 spectrum predicted by the standard diffusive shock acceleration (DSA) mechanism. The DSA has long been held responsible for the production of galactic CRs in supernova remnant (SNR) shocks. The γ-ray “probes” of the acceleration spectra of CRs on the spot, inside the SNRs, lead to the same conclusion. We show that the steep acceleration spectrum can be attributed to the combination of (i) spherical expansion, (ii) tilting of the magnetic field along the shock surface, and (iii) shock deceleration. Because of (i) and (ii), the DSA is efficient only on two “polar caps” of a spherical shock where the local magnetic field is within ≃45° to its normal. The shock-produced spectrum observed edge-on steepens with the particle energy because the number of freshly accelerated particles with lower energies continually adds up to a growing acceleration region. We demonstrate the steepening effect by obtaining an exact self-similar solution for the particle acceleration at an expanding shock surface with an arbitrary energy dependence of particle diffusivity κ. We show that its increase toward higher energy steepens the spectrum, which deeply contrasts with the standard DSA spectrum where κ cancels out.

Signatures from a merging galaxy cluster and its AGN population: LOFAR observations of Abell 1682

We present LOFAR data from 110–180 MHz of the merging galaxy cluster Abell 1682, alongside archival optical, radio, and X-ray data. Our images of 6 arcsec in resolution at low frequencies reveal new structures associated with numerous radio galaxies in the cluster. At a resolution of 20 arcsec we see diffuse emission throughout the cluster over hundreds of kiloparsecs, indicating particle acceleration mechanisms are in play as a result of the cluster merger event and powerful active galactic nuclei. We show that a significant part of the cluster emission is from an old radio galaxy with very steep spectrum emission (having a spectral index of α < −2.5). Furthermore, we identify a new region of diffuse steep-spectrum emission (α < −1.1) as a candidate for a radio halo which is co-spatial with the centre of the cluster merger. We suggest its origin as a population of old and mildly relativistic electrons left over from radio galaxies throughout the cluster which have been re-accelerated to higher energies by shocks and turbulence induced by the cluster merger event. We also note the discovery of six new giant radio galaxies in the vicinity of Abell 1682.

Radio jet structures at ∼100 pc and larger scales of the γ-ray-emitting narrow-line Seyfert 1 galaxy PMN J0948+0022

Abstract The narrow-line Seyfert 1 (NLS1) galaxy PMN J0948+0022 is an archetype of γ-ray-emitting NLS1s in active galactic nuclei (AGNs). In this study, we investigate its radio structures using archival data obtained using the Karl G. Jansky Very Large Array (VLA) and the Very Long Baseline Array (VLBA). The new VLA images reveal an outermost radio emission separated by 9.1 arcsec. Its resolved structure and steep spectrum suggest a terminal shock in a radio lobe energized by the jet from the PMN J0948+0022 nucleus. This large-scale radio component is found at almost the same position angle as that of the pc-scale jet, indicating a stable jet direction up to ∼1 Mpc. Its apparent one-sidedness implies a moderate advancing speed (β > 0.27). The kinematic age of <1× 107 yr of the jet activity is consistent with the expected NLS1 phase of ∼107 yr in the AGN lifetime. The VLBA image reveals the jet structure at distances ranging from r = 0.82 milliarcsec to 3.5 milliarcsec, corresponding to approximately 100 pc, where superluminal motions were found. The jet width profile (∝ r1.12) and flux-density profile (∝ r−1.44) depending on the distance r along the jet suggest that the jet kinetic energy is converted to internal energy in this region. The jet is causally connected in a nearly conical streamline, which is supported by ambient pressure at 100 pc scales in the host galaxy of PMN J0948+0022.

Jet propagation velocity and environment density of giant radio sources with steep radio spectrum

Before we have determined that giant radio structure is typical for steep-spectrum sources detected with Ukrainian T-shaped Radio Telescope of model 2 (UTR-2). To estimate the jet propagation velocity and environment density of giant radio sources we consider the sample of galaxies and quasars with steep radio spectrum compiled from two regions of UTR-2 catalogue. The value of velocity of jet propagation is obtained from our estimates of linear size of radio structure and characteristic age of a source. We use the obtained values of jet propagation velocity for the estimates of density of jet environment, that is, density of environment at galaxies and quasars outskirts. We have derived that values of jet propagation velocities of examined sources are ~10e9 cm/s. The positive correlation of jet velocity and redshift of sources is displayed in our sample. On the assumption of equality of jet luminosity and corresponding kinetic luminosity we estimate the density of jet environment (radio structure environment) for galaxies (10e-26 gcm-3 to 10e-27 gcm-3) and quasars (10e-28 gcm-3). Considered steep-spectrum galaxies and quasars display strong evolution of jet propagation velocity and jet environment density. Properties of giant steep-spectrum sources are in accordance with conception of long evolution of powerful sources. The steep low-frequency spectra may be as markers of giant radio structures of galaxies and quasars.

Contrasting turbulence in stably stratified flows and thermal convection

The properties of stably stratified turbulence and turbulent thermal convection are contrasted in this paper. A key difference between theses flows is the sign of the kinetic energy feed by buoyancy, . For SST, due to its stable nature; consequently, the kinetic energy flux Πu(k) decreases with wavenumber k that leads to a steep kinetic energy spectrum, Eu(k) ∼ k−11/5. Turbulent convection is unstable, hence that leads to an increase of Πu(k) with k; this increase however, is marginal due to relatively weak buoyancy, hence Eu(k) ∼ k−5/3, similar to that in hydrodynamic turbulence. This paper also describes the conserved fluxes for the above systems.

Multi-frequency properties of an interacting narrow-angle tail radio galaxy J0037+18

We report multi-wavelength and multi-band observations of a radio galaxy, J0037+18, optical counterpart of which appears to be interacting with the galaxy J003754+182118. We present the map of J0037+18 in various radio frequencies and discuss radio properties of the source using data from the Giant Meterwave Radio Telescope and the Very Large Array. We use optical data to investigate the environment of the host. The angle between the upper lobe and the lower lobe of the radio galaxy is found to be 38 degree near the base of the jets which makes it a narrow-angle tail galaxy. Spectral index based on radio observations between $148\text{ MHz}$ and $1489\text{ MHz}$ exhibit a strong gradient along the jet with flatter spectra near the core and steeper spectra near the outer ends.

FAST ultra-wideband observation of abnormal emission-shift events of PSR B0919+06

PSR B0919+06 is known for its abnormal emission phenomenon, where the pulse emission window occasionally shifts progressively in longitude and returns afterwards. The physical mechanism behind this phenomenon is still under investigation. In this paper, we present our ultra-wideband observation of this pulsar using the Five-hundred-meter Aperture Spherical radio Telescope (FAST), with simultaneous measurements in the frequency ranges 280-780 MHz and 1250-1550 MHz. We have identified three abnormal events, each of which becomes less apparent as the frequency decreases. At 1400 MHz, the averaged profile slightly shifted after the first and third abnormal events, implying a relationship between abnormal event and profile variation. We also found a linear trend in the left-edge position of the averaged profiles between the first and third event as well as after the third event, suggesting the existence of a slow-drifting mode between the two major events. The second event has a comparatively small shift in phase and is thus categorized as a `small flare state'. During the third event, a sequence of approximately nine pulses was seen to significantly weaken in all frequency bands, likely associated with the pseudo-nulling observed at 150 MHz. A three-component de-composition analysis of the normal averaged profiles shows that the trailing component is dominant at our observing frequencies, while the centre component has a comparatively steeper spectrum. We found the overall flux density in an abnormal event to slightly differ from that in an ordinary state, and the difference shows a frequency dependence. A comparison of the normal, abnormal and dimmed averaged profile indicates that the leading component is likely to be stable in all states.

A Sino-German λ6 cm polarisation survey of the Galactic plane

Context. Large-scale radio continuum surveys provide data to get insights into the physical properties of radio sources. H II regions are prominent radio sources produced by thermal emission of ionised gas around young massive stars. Aims. We identify and analyse H II regions in the Sino-German λ6 cm polarisation survey of the Galactic plane. Methods. Objects with flat radio continuum spectra together with infrared and/or Hα emission were identified as H II regions. For H II regions with small apparent sizes, we cross-matched the λ6 cm small-diameter source catalogue with the radio H II region catalogue compiled by Paladini and the infrared H II region catalogue based on the WISE data. Effelsberg λ21 cm and λ11 cm continuum survey data were used to determine source spectra. High angular resolution data from the Canadian Galactic Plane Survey and the NRAO VLA Sky Survey were used to solve the confusion when low angular resolution observations were not sufficient. Extended H II regions were identified by eye by overlaying the Paladini and the WISE H II regions onto the λ6 cm survey images for coincidences. The TT-plot method was employed for spectral index verification. Results. A total of 401 H II regions were identified and their flux densities were determined with the Sino-German λ6 cm survey data. In the surveyed area, 76 pairs of sources are found to be duplicated in the Paladini H II region catalogue, mainly due to the non-distinction of previous observations with different angular resolutions and 78 objects in their catalogue are misclassified as H II regions, being actually planetary nebulae, supernova remnants, or extragalactic sources that have steep spectra. More than 30 H II regions and H II region candidates from our λ6 cm survey data, especially extended ones, do not have counterparts in the WISE H II region catalogue, of which 9 are identified for the first time. Our results imply that some more Galactic H II regions still await to be discovered and the combination of multi-domain observations is important for H II region identification. Based on the newly derived radio continuum spectra and the evidence of infrared emission, the previously identified SNRs G11.1−1.0, G20.4+0.1 and G16.4−0.5 are believed to be H II regions.

Jet-powered Outflows in Supermassive Black Hole Binary Candidate SDSS J1048+0055

Abstract The search and study of close pairs of supermassive black holes (SMBHs) is important in the study of galaxy mergers that can possibly trigger active galactic nucleus (AGN) activity, and in the context of their evolution into the gravitational wave emitting regime. The quasar SDSS J1048+0055 was identified as an SMBH binary (SMBHB) candidate based on the observed double-peaked [O iii] λλ4959, 5007 emission lines and two distinct radio components separated by ∼20 pc (Zhou et al. 2004). To ascertain the binary nature of this source, we analyzed multifrequency, multiepoch very long baseline interferometry (VLBI) data to investigate its parsec-scale radio properties. The source shows double components with the western feature being brighter than the eastern one. This brighter component has a brightness temperature of ∼1010 K, a spectral index of α = −0.09 ± 0.09 (flat), and is indicative of mildly relativistic beaming. In contrast, the faint component has a lower brightness temperature of ∼108−9 K and a steep spectrum. These clues are consistent with a core–jet structure; moreover, the apparent separation speed between the two components is much higher than the expected orbital motion in a binary SMBH. Thus the present study excludes the association of the two VLBI components with the cores of an SMBHB; though, the SMBHB possibility (e.g., a pair of radio-loud and radio-quiet AGNs) is not fully ruled out. In the single AGN scenario, the double-peaked optical emission lines can originate from the jet interacting with the narrow-line region as indicated by a change in the jet direction at ∼140 pc.

On the Broadband Synchrotron Spectra of Pulsar Wind Nebulae

Abstract As shown by broadband observations, pulsar wind nebulae (PWNe) are characterized by a broken power-law spectrum of synchrotron emission. Based on modern magnetohydrodynamic (MHD) turbulence theories, we investigate the reacceleration of electrons in the PWN through the adiabatic stochastic acceleration (ASA), which arises from fundamental dynamics of MHD turbulence. The ASA acts to flatten the injected energy spectrum of electrons at low energies, while synchrotron cooling results in a steep spectrum of electrons at high energies. Their dominance in different energy ranges leads to a flat radio spectrum (F ν ) and a steep X-ray spectrum. Our analytical spectral shapes generally agree well with the observed synchrotron spectra of radio- and X-ray-bright PWNe. The spectral break corresponding to the balance between the ASA and synchrotron losses provides a constraint on the acceleration timescale of the ASA and the magnetic field strength in the PWN.

Characterizing the radio emission from the binary galaxy cluster merger Abell 2146

Context. Collisions of galaxy clusters generate shocks and turbulence in the intra-cluster medium (ICM). The presence of relativistic particles and magnetic fields is inferred through the detection of extended synchrotron radio sources such as haloes and relics and implies that merger shocks and turbulence are capable of (re-)accelerating particles to relativistic energies. However, the precise relationship between merger shocks, turbulence, and extended radio emission is still unclear. Studies of the most simple binary cluster mergers are important to help understand the particle acceleration in the ICM. Aims. Our main aim is to study the properties of the extended radio emission and particle acceleration mechanism(s) associated with the generation of relativistic particles in the ICM. Methods. We measure the low-frequency radio emission from the merging galaxy cluster Abell 2146 with LOFAR at 144 MHz. We characterize the spectral properties of the radio emission by combining these data with data from archival Giant Metrewave Radio Telescope (GMRT) at 238 MHz and 612 MHz and Very Large Array (VLA) at 1.5 GHz. Results. We observe extended radio emission at 144 MHz behind the NW and SE shocks. Across the NW extended source, the spectral index steepens from −1.06 ± 0.06 to −1.29 ± 0.09 in the direction of the cluster centre. This spectral behaviour suggests that a relic is associated with the NW upstream shock. The precise nature of the SE extended emission is unclear. It may be a radio halo bounded by a shock or a superposition of a relic and halo. At 144 MHz, we detect a faint emission that was not seen with high-frequency observations, implying a steep (α < −1.3) spectrum nature of the bridge emission. Conclusions. Our results imply that the extended radio emission in Abell 2146 is probably associated with shocks and turbulence during cluster merger. The relativistic electrons in the NW and SE may originate from fossil plasma and thermal electrons, respectively.

Study on Energy Spectrum Instability in the Processes of Propagating and Breaking of Focusing Waves

Based on phase focusing theory, focusing waves with different spectral types and breaking severities were generated in a wave flume. The time series of surface elevation fluctuation along the flume were obtained by utilizing 22 wave probes mounted along the mid-stream of the flume. Based on the wave spectrum obtained using fast Fourier transform (FFT), the instability characteristics of the energy spectrum were reported in this paper. By analyzing the variation of total spectral energy, the total spectral energy after wave breaking was found to clearly decrease, and the loss value and ratio gradually increased and tended to stabilize with the enhancement of breaking severity for different spectral types. When wave breaking occurred, the energy loss was primarily in a high-frequency range of f/fp>1.0, and energy gain was primarily in a low-frequency range of f/fp<1.0. As the breaking severity increased, the energy gain-loss ratio decreased gradually, which demonstrates that the energy was mostly dissipated. For plunging waves, the energy gain-loss ratio reached 24% for the constant wave steepness (CWS) spectrum, and was slightly larger at approximately 30% for the constant wave amplitude (CWA) spectrum, and was the largest at approximately 42% for the Pierson-Moskowitz (PM) spectrum.