On the contribution of nearby sources to the observed cosmic ray nuclei

The presence of nearby discrete cosmic ray (CR) sources can lead to many interesting effects on the observed properties of CRs. In this paper, we study about the possible effects on the CR primary and secondary spectra and also the subsequent effects on the CR secondary-to-primary ratios. For the study, we assume that CRs undergo diffusive propagation in the Galaxy and we neglect the effect of convection, energy losses and reacceleration. In our model, we assume that there exists a uniform and continuous distribution of CR sources in the Galaxy generating a stationary CR background at the Earth. In addition, we also consider the existence of some nearby sources which inject CRs in a discrete space–time model. Assuming a constant CR source power throughout the Galaxy, our study has found that the presence of nearby supernova remnants (SNRs) produces noticeable variations in the primary fluxes mainly above ∼100 GeV n⁻¹, if CRs are assumed to be released instantaneously after the supernova explosion. The variation reaches a value of ∼45 per cent at around 10⁵ GeV n⁻¹. Respect to earlier studies, the variation in the case of the secondaries is found to be almost negligible. We also discuss about the possible effects of the different particle release times from the SNRs. For the particle release time of ∼10⁵ yr, predicted by the diffusive shock acceleration theories in SNRs, we have found that the presence of the nearby SNRs hardly produces any significant effects on the CRs at the Earth.     

The distribution function of dark matter in massive haloes

We study the distribution function (DF) of dark matter particles in haloes of mass range  10¹⁴–10¹⁵ M_⊙  . In the numerical part of this work we measure the DF for a sample of relaxed haloes formed in the simulation of a standard Λ cold dark matter (ΛCDM) model. The DF is expressed as a function of energy E and the absolute value of the angular momentum L , a form suitable for comparison with theoretical models. By proper scaling we obtain the results that do not depend on the virial mass of the haloes. We demonstrate that the DF can be separated into energy and angular momentum components and propose a phenomenological model of the DF in the form     . This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (β₀ and  β_∞  ) and the scale of transition between them ( L ₀). The energy part   f _E ( E )  is obtained via inversion of the integral for spatial density. We provide a straightforward numerical scheme for this procedure as well as a simple analytical approximation for a typical halo formed in the simulation. The DF model is extensively compared with the simulations: using the model parameters obtained from fitting the anisotropy profile, we recover the DF from the simulation as well as the profiles of the dispersion and kurtosis of radial and tangential velocities. Finally, we show that our DF model reproduces the power-law behaviour of phase-space density   Q =ρ( r )/σ³( r )  .     

H 0 from an orientation-unbiased sample of Sunyaev–Zel'dovich and X-ray clusters

We have observed the Sunyaev–Zel'dovich (SZ) effect in a sample of five moderate-redshift clusters with the Ryle Telescope, and used them in conjunction with X-ray imaging and spectral data from ROSAT and ASCA to measure the Hubble constant. This sample was chosen with a strict X-ray flux limit using both the Bright Cluster Sample and the Northern ROSAT All-Sky Survey (RASS) cluster catalogues to be well above the surface brightness limit of the RASS, and hence to be unbiased with respect to the orientation of the cluster. This controls a major potential systematic effect in the SZ/X-ray method of measuring H ₀. Taking the weighted geometric mean of the results and including the main sources of error, namely the noise in the SZ measurement, the uncertainty in the X-ray temperatures and the unknown ellipticity and substructure of the clusters, we find   H ₀= 59⁺¹⁰₋₉ (random)⁺⁸₋₇(systematic) km s⁻¹ Mpc⁻¹  assuming a standard cold dark matter model with  Ω_M= 1.0, Ω_Λ= 0.0  or   H ₀= 66⁺¹¹₋₁₀ ⁺⁹₋₈ km  s⁻¹ Mpc⁻¹  if  Ω_M= 0.3, Ω_Λ= 0.7  .     

Wilkinson Microwave Anisotropy Probe 5-yr constraints on fnl with wavelets

We present a Gaussianity analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-yr cosmic microwave background (CMB) temperature anisotropy data maps. We use several third-order estimators based on the spherical Mexican hat wavelet. We impose constraints on the local non-linear coupling parameter f _nl using well-motivated non-Gaussian simulations. We analyse the WMAP maps at resolution of 6.9 arcmin for the Q , V , and W frequency bands. We use the KQ 75 mask recommended by the WMAP team which masks out 28 per cent of the sky. The wavelet coefficients are evaluated at 10 different scales from 6.9 to 150 arcmin. With these coefficients, we compute the third order estimators which are used to perform a  χ²  analysis. The  χ²  statistic is used to test the Gaussianity of the WMAP data as well as to constrain the f _nl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the f _nl parameter is constrained to  −8 < f _nl < +111  at 95 per cent confidence level (CL) for the combined   V + W   map. This value has been corrected for the presence of undetected point sources, which add a positive contribution of  Δ f _nl= 3 ± 5  in the   V + W   map. Our results are very similar to those obtained by the WMAP team using the bispectrum.     

Impact of cosmic rays on Population III star formation

We explore the implications of a possible cosmic-ray (CR) background generated during the first supernova explosions that end the brief lives of massive Population III stars. We show that such a CR background could have significantly influenced the cooling and collapse of primordial gas clouds in minihaloes around redshifts of   z ∼ 15–20  , provided the CR flux was sufficient to yield an ionization rate greater than about 10⁻¹⁹ s⁻¹ near the centre of the minihalo. The presence of CRs with energies  ≲10⁷  eV would indirectly enhance the molecular cooling in these regions, and we estimate that the resulting lower temperatures in these minihaloes would yield a characteristic stellar mass as low as  ∼10 M_⊙  . CRs have a less-pronounced effect on the cooling and collapse of primordial gas clouds inside more massive dark matter haloes with virial masses  ≳10⁸ M_⊙  at the later stages of cosmological structure formation around   z ∼ 10–15  . In these clouds, even without CR flux the molecular abundance is already sufficient to allow cooling to the floor set by the temperature of the cosmic microwave background.     

Ultraluminous X-ray source 1E 0953.8+6918 (M81 X-9): an intermediate-mass black hole candidate and its environs

We present a ROSAT and ASCA study of the Einstein source X-9 and its relation to a shock-heated shell-like optical nebula in a tidal arm of the M81 group of interacting galaxies. Our ASCA observation of the source shows a flat and featureless X-ray spectrum well described by a multicolour disc blackbody model. The source most likely represents an optically thick accretion disc around an intermediate-mass black hole  ( M ∼10² M_⊙)  in its high/soft state, similar to other variable ultraluminous X-ray sources observed in nearby disc galaxies. Using constraints derived from both the innermost stable orbit around a black hole and the Eddington luminosity, we find that the black hole is fast-rotating and that its mass is between ∼80 M_⊙–1.5×10² M_⊙. The inferred bolometric luminosity of the accretion disc is ∼(1.1×10⁴⁰ erg s⁻¹)/(cos  i ). Furthermore, we find that the optical nebula is very energetic and may contain large amounts of hot gas, accounting for a soft X-ray component as indicated by archival ROSAT PSPC data. The nebula is apparently associated with X-9; the latter may be powering the former and/or they could be formed in the same event (e.g. a hypernova). Such a connection, if confirmed, could have strong implications for understanding both the birth of intermediate-mass black holes and the formation of energetic interstellar structures.     

X-ray observations of the edge-on star-forming galaxy NGC 891 and its supernova SN1986J

We present XMM–Newton observations of NGC 891, a nearby edge-on spiral galaxy. We analyse the extent of the diffuse emission emitted from the disc of the galaxy, and find that it has a single-temperature profile with best-fitting temperature of 0.26 keV, though the fit of a dual-temperature plasma with temperatures of 0.08 and 0.30 keV is also acceptable. There is a considerable amount of diffuse X-ray emission protruding from the disc in the north-west direction out to approximately 6 kpc. We analyse the point-source population using a Chandra observation, using a maximum-likelihood method to find that the slope of the cumulative luminosity function of point sources in the galaxy is  −0.77^+0.13_−0.1  . Using a sample of other local galaxies, we compare the X-ray and infrared properties of NGC 891 with those of 'normal' and starburst spiral galaxies, and conclude that NGC 891 is most likely a starburst galaxy in a quiescent state. We establish that the diffuse X-ray luminosity of spirals scales with the far-infrared luminosity as   L _X∝ L ^0.87±0.07_FIR  , except for extreme starbursts, and NGC 891 does not fall in the latter category. We study the supernova SN1986J in both XMM–Newton and Chandra observations, and find that the X-ray luminosity has been declining with time more steeply than expected  ( L _X∝ t ⁻³)  .     

Quantifying the coexistence of massive black holes and dense nuclear star clusters

In large spheroidal stellar systems, such as elliptical galaxies, one invariably finds a  10⁶–10⁹ M_⊙  supermassive black hole at their centre. In contrast, within dwarf elliptical galaxies one predominantly observes a  10⁵–10⁷ M_⊙  nuclear star cluster. To date, few galaxies have been found with both types of nuclei coexisting and even less have had the masses determined for both central components. Here, we identify one dozen galaxies housing nuclear star clusters and supermassive black holes whose masses have been measured. This doubles the known number of such hermaphrodite nuclei – which are expected to be fruitful sources of gravitational radiation. Over the host spheroid (stellar) mass range  10⁸–10¹¹ M_⊙  , we find that a galaxy's nucleus-to-spheroid (baryon) mass ratio is not a constant value but decreases from a few per cent to ∼0.3 per cent such that  log[( M _BH+ M _NC)/ M _sph]=−(0.39 ± 0.07) log[ M _sph/10¹⁰ M_⊙]− (2.18 ± 0.07)  . Once dry merging commences and the nuclear star clusters disappear, this ratio is expected to become a constant value.
As a byproduct of our investigation, we have found that the projected flux from resolved nuclear star clusters is well approximated with Sérsic functions having a range of indices from ∼0.5 to ∼3, the latter index describing the Milky Way's nuclear star cluster.     

An iterative filter to reconstruct planetary transit signals in the presence of stellar variability

We report the identification, from a photometric, astrometric and spectroscopic study, of a massive white dwarf member of the nearby, approximately solar metallicity, Coma Berenices open star cluster (Melotte 111). We find the optical to near-infrared energy distribution of WD 1216+260 to be entirely consistent with that of an isolated DA and determine the effective temperature and surface gravity of this object to be   T _eff= 15 739⁺¹⁹⁷₋₁₉₆ K  and  log  g = 8.46^+0.03_−0.02  . We set tight limits on the mass of a putative cool companion,   M ≳ 0.036 M_⊙  (spatially unresolved) and   M ≳ 0.034 M_⊙  (spatially resolved and   a ≲ 2500 au  ). Based on the predictions of CO core, thick H layer evolutionary models we determine the mass and cooling time of WD 1216+260 to be   M _WD= 0.90 ± 0.04 M_⊙  and  τ_cool= 363⁺⁴⁶₋₄₁ Myr  , respectively. For an adopted cluster age of  τ= 500 ± 100 Myr  we infer the mass of its progenitor star to be   M _init= 4.77^+5.37_−0.97 M_⊙  . We briefly discuss this result in the context of the form of the stellar initial mass–final mass relation.     

The high-velocity molecular stream in W51B: a ring structure with compact H ii regions

We present ¹³ CO J  = 1 − 0 line observations of the H  ii region complex W51B located in the high-velocity (HV) stream. These observations reveal a filamentary and clumpy structure in the molecular gas. The mean local standard of rest (LSR) velocity ∼ + 65 km s⁻¹ of the molecular gas in this region is greater than the maximum velocities allowed by kinematic Galactic rotation curves. The size and mass of the molecular clouds are ∼ 48 × 17 pc² and ∼ 2.4 × 10⁵ M⊙ respectively. In a position–velocity diagram, molecular gas in the southern part comprises a redshifted ring structure with v _LSR=+ 60 to +73 km s⁻¹. The velocity gradient of this ring is ∼ 0.5 km s⁻¹ pc⁻¹, and the mass is ∼ 6.2 × 10⁴ M⊙. If we assume that the ring is expanding with a uniform velocity, the expansion velocity, radius and kinetic energy are ∼ 7 km s⁻¹, ∼ 13 pc and ∼ 3.0 × 10 ⁴⁹ erg respectively. The kinetic energy and mass spectrum of the ring could be explained by an expanding cylindrical cloud with a centrally condensed mass distribution. The locations of two compact H  ii regions, G49.0−0.3 and G48.9−0.3, coincide with the two molecular clumps in this ring. We discuss star formation, and the mechanism that produced the ring structure.     

PDS 456: an extreme accretion rate quasar?

We present quasi-simultaneous ASCA and RXTE observations of the most luminous known active galactic nucleus in the local ( z <0.3) Universe, the recently discovered quasar PDS 456. Multiwavelength observations have been conducted that show that PDS 456 has a bolometric luminosity of ∼10⁴⁷ erg s⁻¹ peaking in the ultraviolet part of the spectrum. In the X-ray band the 2–10 keV (rest-frame) luminosity is 10⁴⁵ erg s⁻¹. The broad-band X-ray spectrum obtained with ASCA and RXTE contains considerable complexity. The most striking feature observed is a very deep, ionized iron K edge, observed at 8.7 keV in the quasar rest-frame. We find that these features are consistent with reprocessing from highly ionized matter, probably the inner accretion disc. PDS 456 appeared to show a strong (factor of ∼2.1) outburst in just ∼17 ks, although non-intrinsic sources cannot be completely ruled out. If confirmed, this would be an unusual event for such a high-luminosity source, with a light-crossing-time corresponding to ∼2 R _S . The implication would be that flaring occurs within the very central regions, or else that PDS 456 is a 'super-Eddington' or relativistically beamed system. Overall we conclude on the basis of the extreme blue/UV luminosity, the rapid X-ray variability and from the imprint of highly ionized material on the X-ray spectrum, that PDS 456 is a quasar with an unusually high accretion rate.     

XMM–Newton and Chandra observations of SHEEP sources

We present Chandra and XMM–Newton observations of 12 bright  [ f (2–10 keV) > 10⁻¹³ erg cm⁻² s⁻¹]  sources from the ASCA search for the High Energy Extragalactic Population (SHEEP) survey. Most of these have been either not observed or not detected previously with the ROSAT mission, and therefore they constitute a sample biased towards hard sources. The Chandra observations are important in locating the optical counterpart of the X-ray sources with accuracy. Optical spectroscopic observations show that our sample is associated with both narrow-line (NL) (six objects) and broad-line (BL) active galactic nuclei (AGN) (five objects), with one source remaining unidentified. Our sources cover the redshift range 0.04–1.29, spanning luminosities from 10⁴² to  10⁴⁵ erg s⁻¹  (2–10 keV). The NL sources have preferentially lower redshift (and luminosity) compared to the BL ones. This can be most easily explained in a model where the NL AGN are intrinsically less luminous than the BL ones in line with the results of Steffen et al. The X-ray spectral fittings show a roughly equal number of obscured  ( N _H > 10²² cm⁻²)  and unobscured  ( N _H < 10²² cm⁻²)  sources. There is a clear tendency for obscured sources to be associated with NL AGN and unobscured sources with BL ones. However, there is a marked exception with the highest obscuring column observed at a BL AGN at a redshift of z = 0.5.     

Observations of the Sunyaev–Zel'dovich effect in the z=0.78 cluster MS 1137.5+6625

We have observed the   z =0.78  cluster MS 1137.5+6625 with the Ryle Telescope (RT) at 15 GHz. After subtraction of contaminating radio sources in the field, we find a Sunyaev–Zel'dovich flux decrement of  -421±60 μJy  on the ≈0.65 k λ baseline of the RT, spatially coincident with the optical and X-ray positions for the cluster core.
For a spherical King-profile cluster model, the best fit to our flux measurement has a core radius   θ _C=20 arcsec  , consistent with previous X-ray observations, and a central temperature decrement  Δ T =650±92 μK  .
Using this model, we calculate that the cluster has a gas mass inside a     radius of  2.9×10¹³ M_⊙  for an  Ω _M =1  universe and  1.6×10¹³ M_⊙  for  Ω _M =0.3  ,  Ω_Λ=0.7  . We compare this model with existing measurements of the total mass of the cluster, based on gravitational lensing, and estimate a gas fraction for MS 1137.5+6625 of ≈8 per cent.     

SN 2005cs in M51 – II. Complete evolution in the optical and the near-infrared

We present the results of the one-year long observational campaign of the type II plateau SN 2005cs, which exploded in the nearby spiral galaxy M51 (the Whirlpool galaxy). This extensive data set makes SN 2005cs the best observed low-luminosity, ⁵⁶Ni-poor type II plateau event so far and one of the best core-collapse supernovae ever. The optical and near-infrared spectra show narrow P-Cygni lines characteristic of this SN family, which are indicative of a very low expansion velocity (about  1000 km s⁻¹  ) of the ejected material. The optical light curves cover both the plateau phase and the late-time radioactive tail, until about 380 d after core-collapse. Numerous unfiltered observations obtained by amateur astronomers give us the rare opportunity to monitor the fast rise to maximum light, lasting about 2 d. In addition to optical observations, we also present near-infrared light curves that (together with already published ultraviolet observations) allow us to construct for the first time a reliable bolometric light curve for an object of this class. Finally, comparing the observed data with those derived from a semi-analytic model, we infer for SN 2005cs a ⁵⁶Ni mass of about  3 × 10⁻³ M_⊙  , a total ejected mass of  8–13 M_⊙  and an explosion energy of about  3 × 10⁵⁰ erg  .     

Probing the submillimetre number counts at f850 μm < 2 mJy

We have conducted a submillimetre mapping survey of faint, gravitationally lensed sources, where we have targeted 12 galaxy clusters and additionally the New Technology Telescope (NTT) Deep Field. The total area surveyed is 71.5 arcmin² in the image plane; correcting for gravitational lensing, the total area surveyed is 40 arcmin² in the source plane for a typical source redshift z ≈ 2.5. In the deepest maps, an image plane depth of 1σ rms ∼0.8 mJy is reached. This survey is the largest survey to date to reach such depths. In total 59 sources were detected, including three multiply imaged sources. The gravitational lensing makes it possible to detect sources with flux density below the blank field confusion limit. The lensing-corrected fluxes range from 0.11 to 19 mJy. After correcting for multiplicity, there are 10 sources with fluxes <2 mJy of which seven have submJy fluxes, doubling the number of such sources known. Number counts are determined below the confusion limit. At 1 mJy, the integrated number count is  ∼10⁴ deg⁻²  , and at 0.5 mJy it is  ∼2 × 10⁴ deg⁻²  . Based on the number counts, at a source plan flux limit of 0.1 mJy, essentially all of the 850-μm background emission has been resolved. The dominant contribution (>50 per cent) to the integrated background arises from sources with fluxes S ₈₅₀ between 0.4 and 2.5 mJy, while the bright sources S ₈₅₀ > 6 mJy contribute only 10 per cent.     

Unresolved emission and ionized gas in the bulge of M31

We study the origin of unresolved X-ray emission from the bulge of M31 based on archival Chandra and XMM–Newton observations. We demonstrate that three different components are present. (i) Broad-band emission from a large number of faint sources – mainly accreting white dwarfs and active binaries, associated with the old stellar population, similar to the Galactic ridge X-ray emission of the Milky Way. The X-ray to K -band luminosity ratios are compatible with those for the Milky Way and for M32; in the 2–10 keV band, the ratio is  (3.6 ± 0.2) × 10²⁷ erg s⁻¹ L⁻¹_⊙  . (ii) Soft emission from ionized gas with a temperature of about ∼300 eV and a mass of  ∼2 × 10⁶ M_⊙  . The gas distribution is significantly extended along the minor axis of the galaxy, suggesting that it may be outflowing in the direction perpendicular to the galactic disc. The mass and energy supply from evolved stars and Type Ia supernovae is sufficient to sustain the outflow. We also detect a shadow cast on the gas emission by spiral arms and the 10-kpc star-forming ring, confirming significant extent of the gas in the 'vertical' direction. (iii) Hard extended emission from spiral arms, most likely associated with young stellar objects and young stars located in the star-forming regions. The   L _X/SFR  (star formation rate) ratio equals  ∼9 × 10³⁸ (erg s⁻¹)(M_⊙ yr⁻¹)⁻¹  , which is about ∼1/3 of the high-mass X-ray binary contribution, determined earlier from Chandra observations of other nearby galaxies.     

Multiwavelength study of the nuclei of a volume-limited sample of galaxies – I. X-ray observations

We discuss ROSAT HRI X-ray observations of 33 very nearby galaxies, sensitive to X-ray sources down to a luminosity of approximately 10³⁸ erg s⁻¹. The galaxies are selected from a complete, volume-limited sample of 46 galaxies with     for which we have extensive multiwavelength data. For an almost complete subsample with     (29/31 objects) we have HRI images. Contour maps and source lists are presented within the central region of each galaxy, together with nuclear upper limits where no nuclear source was detected. Nuclear X-ray sources are found to be very common, occurring in ∼35 per cent of the sample. Nuclear X-ray luminosity is statistically connected to host galaxy luminosity – there is not a tight correlation, but the probability of a nuclear source being detected increases strongly with galaxy luminosity, and the distribution of nuclear luminosities seems to show an upper envelope that is roughly proportional to galaxy luminosity. While these sources do seem to be a genuinely nuclear phenomenon rather than nuclear examples of the general X-ray source population, it is far from obvious that they are miniature Seyfert nuclei. The more luminous nuclei are very often spatially extended, and H  ii region nuclei are detected just as often as LINERs. Finally, we also note the presence of fairly common superluminous X-ray sources in the off-nuclear population – out of 29 galaxies we find nine sources with a luminosity greater than 10³⁹ erg s⁻¹. These show no particular preference for more luminous galaxies. One is already known to be a multiple SNR system, but most have no obvious optical counterpart and their nature remains a mystery.     

Tracing gas motions in the Centaurus cluster

We apply the stochastic model of iron transport developed by Rebusco et al. to the Centaurus cluster. Using this model, we find that an effective diffusion coefficient D in the range  2 × 10²⁸–4 × 10²⁸ cm² s⁻¹  can approximately reproduce the observed abundance distribution. Reproducing the flat central profile and sharp drop around  30–70 kpc  , however, requires a diffusion coefficient that drops rapidly with radius so that   D > 4 × 10²⁸ cm² s⁻¹  only inside about  25 kpc  . Assuming that all transport is due to fully developed turbulence, which is also responsible for offsetting cooling in the cluster core, we calculate the length- and velocity-scales of energy injection. These length-scales are found to be up to a factor of ∼10 larger than expected if the turbulence is due to the inflation and rising of a bubble. We also calculate the turbulent thermal conductivity and find it is unlikely to be significant in preventing cooling.     

TeV γ-rays from old supernova remnants

We study the emission from an old supernova remnant (SNR) with an age of around 10⁵ yr and that from a giant molecular cloud (GMC) encountered by the SNR. When the SNR age is around 10⁵ yr, proton acceleration is efficient enough to emit TeV γ-rays both at the shock of the SNR and that in the GMC. The maximum energy of primarily accelerated electrons is so small that TeV γ-rays and X-rays are dominated by hadronic processes,  π⁰  -decay and synchrotron radiation from secondary electrons, respectively. However, if the SNR is older than several 10⁵ yr, there are few high-energy particles emitting TeV γ-rays because of the energy-loss effect and/or the wave-damping effect occurring at low-velocity isothermal shocks. For old SNRs or SNR–GMC interacting systems capable of generating TeV γ-ray emitting particles, we calculated the ratio of TeV γ-ray (1–10 TeV) to X-ray (2–10 keV) energy flux and found that it can be more than  ∼10²  . Such a source showing large flux ratio may be a possible origin of recently discovered unidentified TeV sources.     

Radial heating of a galactic disc by multiple spiral density waves

We consider a differentially rotating, 2D stellar disc perturbed by two steady-state spiral density waves moving at different pattern speeds. Our investigation is based on direct numerical integration of initially circular test-particle orbits. We examine a range of spiral strengths and spiral speeds and show that stars in this time-dependent gravitational field can be heated (their random motions increased). This is particularly noticeable in the simultaneous propagation of a two-armed spiral density wave near the corotation resonance (CR), and a weak four-armed one near the inner and outer 4:1 Lindblad resonances. In simulations with two spiral waves moving at different pattern speeds, we find: (i) the variance of the radial velocity,  σ² _R   , exceeds the sum of the variances measured from simulations with each individual pattern; (ii)  σ² _R   can grow with time throughout the entire simulation; (iii)  σ² _R   is increased over a wider range of radii compared to that seen with one spiral pattern; and (iv) particles diffuse radially in real space, whereas they do not when only one spiral density wave is present. Near the CR with the stronger, two-armed pattern, test-particles are observed to migrate radially. These effects take place at or near resonances of both spirals, so we interpret them as the result of stochastic motions. This provides a possible new mechanism for increasing the stellar velocity dispersion in galactic discs. If multiple spiral patterns are present in the Galaxy, we predict that there should be large variations in the stellar velocity dispersion as a function of radius.