text stringlengths 128 2.05k |
|---|
5.1 Neutrinos in Big-Bang Nucleosynthesis (BBN) One of the classic problems in nucleosynthesis and cosmology is accounting for the mass fraction of primordial helium of 25%, as well as the abundances of D, He, and Li. The He mass fraction shows that nuclei were synthesized from the early-universe nucleon soup at a time... |
[EQUATION] where [MATH] is the gravitational constant. This clock depends on the energy density [MATH] which, at this epoch, is dominated by relativistic particles, including the neutrinos. BBN also includes one adjustable parameter, the baryon density, which is usually given in terms of the ratio of baryons to photons... |
Detail analyses find that a consistent picture emerges. The number of neutrino species is found to be [MATH] . One can adopt the expected value of [MATH] and reproduce the abundances of both D and He at the 68% confidence level |
This standard use of BBN is now mostly of historical interest, though at one time it was the best test of the number of light neutrino species. However, there are variations of the BBN analysis that are of significant current interest, such as the consequences of a net lepton number asymmetry in the universe, or the pr... |
5.2 The Neutrino Process One of the more amusing roles for neutrinos in nucleosynthesis is found in the neutrino process, the direct synthesis of new elements through neutrino reactions. Core-collapse supernovae provide the enormous neutrino fluences necessary for such synthesis to be significant. They also eject newly... |
Among the elements that might be made primarily or partially in the [MATH] -process, the synthesis of 19 F is one of the more interesting examples |
The only stable isotope of fluorine, 19 F has an abundance [EQUATION] Ne is one of the hydrostatic burning products in massive stars, produced in great abundance and ejected in core-collapse supernovae. Thus a mechanism that converts [MATH] 0.03% of the 20 Ne in the star’s mantle into 19 F could account for the entire ... |
The Ne zone in a supernova progenitor star is typically located at a radius of [MATH] 20,000 km. A simple calculation that combines the neutrino fluence through the Ne zone with the cross section for inelastic neutrino scattering off 20 Ne shows that approximately 0.3% of the 20 Ne nuclei would interact with the neutri... |
[EQUATION] with the first reaction occurring half as frequently as the second. Thus one would expect the abundance ratio to be [MATH] , corresponding to an order of magnitude more 19 F than found in nature. |
This example shows that stars are rather complicated factories for nucleosynthesis. Implicit in the reactions above are mechanisms that also destroy 19 F. For example, about 70% of the neutrons coproduced with 19 F in the first reaction immediately recapture on 19 F, destroying the product of interest. Similarly, many ... |
23 Na(p, [MATH] Ne. Finally, some of the 19 F produced in the neon shell is destroyed when the shock wave passes through that zone: the shock wave can heat the inner portion of the Ne zone above [MATH] K, the temperature at which 19 F can be destroyed by 19 F( [MATH] N. |
If all of this physics is treated carefully in a nuclear network code, one finds that the desired 19 F/ 20 Ne [MATH] 1/3100 is achieved for a heavy-flavor neutrino temperature of about 6 MeV. This is quite consistent with the temperatures that come from supernova models. |
The neutrino process produces interesting abundances of several relatively rare, odd-A nuclei including Li, 11 B, 138 La, 180 Ta, and 15 N. Charged-current neutrino reactions on free protons can produce neutrons that, through [MATH] and [MATH] |
reactions, lead to the nucleosynthesis of the so-called “p-process” nuclei from A=92 to 126. The production of such nuclei has been a long-standing puzzle in nuclear astrophysics. |
5.3 The r-process Beyond the iron peak nuclear Coulomb barriers become so high that charged particle reactions become ineffective, leaving neutron capture as the mechanism responsible for producing the heaviest nuclei. If the neutron abundance is modest, this capture occurs in such a way that each newly synthesized nuc... |
This second process is the r- or rapid-process , which requires a neutron fluence so large that neutron capture is fast compared to [MATH] decay. In this case nuclei rapidly absorb neutrons until they approach the neutron drip line. That is, equilibrium is maintained by [MATH] , not by weak interactions. Consequently t... |
10 K), sufficient time ( [MATH] 1 second), and a ratio of neutrons to heavy seed nuclei of [MATH] 100 (so that there are enough neutrons to add to each seed nucleus). |
The path of the r-process is along neutron-rich nuclei, where the neutron Fermi sea is just [MATH] (2-3) MeV away from the neutron drip line (where no more bound neutron levels exist). After the r-process finishes (the neutron exposure ends) the nuclei decay back to the valley of stability by [MATH] |
decay. This involves conversion of neutrons into protons, and that shifts the r-process peaks from the parent-nucleus values of N [MATH] 82 and 126 to lower values for the stable daughter nuclei, off course. This effect is clearly seen in the abundance distribution – a very strong hint that many familiar heavy nuclei c... |
The role of neutrinos in the r-process is in maintaining that explosive, neutron-rich environment: while there are alternatives, perhaps the most plausible site is the neutrino-driven wind – the last ejecta blown off the neutron star – of core-collapse supernovae. This material is a hot, radiation-dominated gas contain... |
[EQUATION] to start forming heavier nuclei. The [MATH] capture continues, eventually synthesizing intermediate-mass “seed” nuclei. Once these seed nuclei are produced, if the requisite number of neutrons is available ( [MATH] 100 per seed nucleus) the synthesis of very heavy nuclei is possible. The scenario, as depicte... |
[MATH] 100 in Boltzmann units, compared to the BBN [MATH] 10 10 expand and cools, condensing into nuclei. But a detail – the neutrino wind has an excess of neutrons, while the Big Bang is proton-rich – leads to the synthesis of uranium in one case, and to termination of nucleosynthesis at He (plus a few light elements)... |
There are some very nice aspects of this site: the amount of matter ejected is [MATH] 10 [MATH] solar masses, a production per event that if integrated over the lifetime of the galaxy gives the required total abundance of r-process metals, assuming typical supernova rates. There are also a few problems, especially the ... |
Neutrino Cooling and Red Giants Several neutrino cooling scenarios have already been discussed, including cooling of the proto-neutron star produce in core collapse and cooling connected with the expansion of the early universe. Red giant cooling provides an additional example of the use of astrophysical arguments to c... |
6.1 Red Giants and Helium Ignition In a solar-like star, when the hydrogen in the central core has been exhausted, an interesting evolution ensues: |
With no further means of producing energy, the core slowly contracts, thereby increasing in temperature as gravity does work on the core. |
Matter outside the core is still hydrogen rich, and can generate energy through hydrogen burning. Thus a hydrogen-burning shell forms, generating the gas pressure supporting the outside layers of the star. As the He-rich core contracts, the matter outside the core is also pulled deeper into the gravitational potential.... |
The resulting increasing gas pressure causes the outer envelope of the star to expand by a large factor, up to a factor of 50. The increase in radius more than compensates for the increased internal energy generation, so that a cooler surface results. The star reddens. Stars of this type are called red supergiants. |
This evolution is relatively rapid, perhaps a few hundred million years: the dense core requires large energy production. The helium core is supported by its degeneracy pressure, and is characterized by densities |
[MATH] g/cm . This stage ends when the core reaches densities and temperatures that allow helium burning through the reaction [EQUATION] |
As this reaction is quite temperature dependent, the conditions for ignition are very sharply defined. This has the consequence that the core mass at the helium flash point is well determined. |
The onset of helium burning produces a new source of support for the core. The energy released elevates the temperature and the core expands: He burning, not electron degeneracy, now supports the core. The burning shell and envelope move outward, higher in the gravitational potential. Thus shell hydrogen burning slows ... |
The 3 [MATH] process involves some fascinating nuclear physics that will not be recounted here: the existence of certain nuclear resonances was predicted based on the astrophysical requirements for this process. The resulting He-burning rate exhibits a sharp temperature dependence |
[MATH] 40 in the range relevant to red giant cores. This dependence is the reason the He flash is delicately dependent on conditions in the core. |
6.2 Neutrino Magnetic Moments and He Ignition Prior to the helium flash, the degenerate He core radiates energy largely by neutrino pair emission. The process is the decay of a plasmon — which one can think of as a photon “dressed” by electron-hole excitations — thereby acquiring an effective mass of about 10 keV. The ... |
If this cooling is somehow enhanced, the degenerate helium core would not ignite at the normal time, but instead continue to grow. When the core does finally ignite, the larger core will alter the star’s subsequent evolution. |
One possible mechanism for enhanced cooling is a neutrino magnetic moment. Then the plasmon could directly couple to a neutrino pair. The strength of this coupling would depend on the size of the magnetic moment. |
A delay in the time of He ignition has several observable consequences, including changing the ratio of red giant to horizontal branch stars. Thus, using the standard theory of red giant evolution, investigators have attempted to determine what size of magnetic moment would produce unacceptable changes in the astronomy... |
on the neutrino magnetic moment of [EQUATION] This limit is two orders of magnitude more stringent than that obtained from direct laboratory tests, e.g., experiments looking for the effect of a neutrino magnetic moment in the scattering of reactor neutrinos off electrons. |
This example is just one of a number of such constraints that can be extracted from similar stellar cooling arguments. The arguments above, for example, can be repeated for neutrino electric dipole moments, or for axion emission from red giants. As noted previously, the arguments can be extended to supernovae: anomalou... |
High Energy Astrophysical Neutrinos The previous discussion focused on astrophysical neutrino sources with energies ranging from the cosmic microwave/neutrino temperature to [MATH] 10 GeV, which includes the bulk of atmospheric neutrinos. These sources are displayed in Fig. 12 |
according to their contributions to the terrestrial flux density. This figure includes sources, such as the thermal solar neutrinos of all flavors, not explicitly discussed here because of space limitations. However, the spectrum of neutrinos is believed to extend to far higher energies due to neutrino production in so... |
7.1 Neutrino Production by Cosmic Rays The ultra-high-energy cosmic ray (UHECR) spectrum – presumably protons and nuclei – is known to vary smoothly up to an energy [MATH] |
[MATH] [MATH] 10 19 eV. The spectrum just below this point is characterized by a spectral index [MATH] : the flux varies as [MATH] |
. Higher energy events are seen, but the flux drops off steeply beyond this point. This is consistent with the prediction of Greisen, Zatsepin, and Kuz’min |
of a cutoff in the spectrum above [MATH] [MATH] 10 19 eV. Above this cutoff UHECRs can loose energy by scattering off microwave photons, producing pions. This sharply reduces the mean-free path of such UHECRs. The flux drops, reflecting the reduced number of sources within a mean-free path of the Earth. |
An estimate can be made of the flux of UHE neutrinos associated with the decays of pions and other secondaries produced in the GZK scattering. Uncertainties in this estimate include the flux, spectrum, and composition of the UHECRs, the behavior of the spectrum beyond the GZK cutoff (as we are blind to these UHECRs), a... |
; another is shown in Fig. 13 These uncertainties are connected to some very interesting astrophysical issues: the maximum energies that can be reached in astrophysical accelerators; the UHECR uniformity over time (or equivalently redshift); and the role other background photon sources, such as the infrared and optical... |
As in the case of low-energy sources such as solar neutrinos, the detection of very high energy astrophysical neutrinos would open up new opportunities in both astrophysics and particle physics. Because the GZK cutoff limits the range of the UHECRs, neutrinos provide the only direct probe of nature’s most energetic ast... |
7.2 Point Sources and Neutrino Telescopes The possibility of point sources is generally considered the astrophysical “driver” for developing instruments to measure the highest energy neutrinos. There are intensely energetic sources in the sky, including active galactic nuclei (AGNs), supernovae and phenomena like [MATH... |
There are recent results that further motivate such neutrino studies. The cosmic-ray telescope Pierre Auger (see Fig. 14 ), in its studies of events near the GZK cutoff, has found correlations between clusters of events and nearby AGNs: At these energies the trajectories of protons and nuclei are not strongly perturbed... |
. Once one can attribute events to an astrophysical source, then those events become a probe of that object. In this particular case, one is then challenged to explain the mechanism by which an AGN accelerates nucleons or nuclei to, and perhaps beyond, [MATH] 10 20 eV. Were neutrinos also seen, the relative yields of h... |
The challenge in the field of UHE neutrinos is to build telescopes with the necessary sensitivity to see events, given current estimates of the fluxes (see Fig. 13 ). This requires instrumenting very large volumes. There have been ongoing efforts to use large quantities of water and ice as detectors, with experiments d... |
IceCube , a project that will extend the dimensions of such detectors to a cubic kilometer, is now under construction at the South Pole (Fig. 15 ). This telescope, when completed, will view the ice through approximately 4200 optical modules, deployed on 70 vertical strings at a depth of 1450 to 2450m. At this depth the... |
Acknowledgement This work was supported in part by the U.S. Department of Energy, Office of Nuclear Physics, under grant #DE-FG02-00ER41132. |
# Source: arxiv 0808.0757 # Title: The properties of penumbral microjets inclination # Sections: all # Downloaded: 2026-03-02T07:59:18.141733+00:00 |
The properties of penumbral microjets inclination (Received September 15, 1996; accepted March 16, 1997) Abstract Aims. We investigate the dependence of penumbral microjets inclination on the position within penumbra. |
Methods. The high cadence observations taken on 10 November 2006 with the Hinode satellite through the Ca ii H and G–band filters were analysed to determine the inclination of penumbral microjets. The results were then compared with the inclination of the magnetic field determined through the inversion of the spectropo... |
Results. The penumbral microjet inclination is increasing towards the outer edge of the penumbra. The results suggest that the penumbral microjet follows the opening magnetic field lines of a vertical flux tube that creates the sunspot. |
Key Words.: Sun: sunspots – Sun: chromosphere – Sun: photosphere – Sun: magnetic fields Introduction Katsukawa et al. ( 2007 , hereafter Paper I) reported on the existence of small jet-like features that are observed at penumbral chromospheric layers. The authors used the term penumbral microjets (PJ) and this nomencla... |
As summarised in Paper I, the PJs are highly transient events with lifetimes up to two minutes and lengths of a few thousand kilometres. The width of PJs is around 400 km for the largest ones where the smallest events are at the resolution limit of the observations. It can be expected that there are even smaller undete... |
As explained in Paper I, the three-dimensional configuration of the PJs can be estimated from the different visibilities of these events depending on the position on the solar disc. The intensity of microjets is comparable to the intensity of underlaying penumbral filaments, and the PJs can hardly be identified on obse... |
Although the observations with a cadence of four seconds can be achieved (with a limited field of view and only for a short time), the observations of penumbra with a 20 sec cadence are currently the best available measurements that can be used to study the properties of PJs. Taking the lifetimes of PJs into account, t... |
Observations and data reduction We analysed the same data set as in Paper I. These measurements were taken on 10 November 2006, and they cover a part of the sunspot in AR10923, which was located at that time at heliocentric coordinates of 6 S and 50 E. Although there are some other observations of sunspots taken with a... |
The data were taken using the Solar Optical Telescope (SOT, Tsuneta et al., 2008 onboard Hinode satellite (Kosugi et al., 2007 . The measurements are unaffected by atmospheric seeing, and the spatial resolution reaches the diffraction limit of the 50 cm telescope, i.e., 0.2 [MATH] (150 km) for the filtergram (FG) data ... |
The analysed FG data were obtained through two broadband filters, the Ca ii H (centred at 396.9 nm with bandwidth of 0.3 nm) and G–band filter (centred at 430.5 nm with bandwidth of 0.8 nm). The observations took place between 12:15 and 13:59 UT and are composed of 209 consecutive images. The data were calibrated with ... |
To determine the orientation of the magnetic field, we used the data observed by the Hinode SP. The measurements were taken in so-called normal mode; the width of the slit is equivalent to 0.16 [MATH] and comparable to the scanning step; the exposure time for one slit position is 4.8 s and results in a noise level of 1... |
Estimation of position and inclination The alignment between FG and SP data cannot be done precisely since the penumbra was slowly growing in the meantime between the observations. The alignment of the inner and outer penumbral boundaries in FG and SP data is sufficient for the purpose of our study since we do not take... |
The penumbral boundaries are approximately fitted by concentric arcs as shown in Fig. a for FG data and in Fig. b for SP data. The position of PJ in the penumbra is given by the radius of an arc that crosses the detected onset of the microjet as shown in Fig. b. |
3.1 Penumbral microjet inclination To compute the inclination angle of the PJs, we first manually determined the orientation of the microjet either directly from Ca ii H data or using running-difference images. Figures a and c show examples of four PJs. The orientations of penumbral filaments are determined from G–band... |
(Müller et al., 2002 [EQUATION] where [MATH] is the heliocentric angle, [MATH] the azimuth angle in line-of-sight (LOS) frame, and [MATH] and [MATH] represent the azimuth and inclination in the local reference frame (LRF) that is defined by the local normal line ( axis) and the orientation of the symmetry line axis). |
Our final goal is to determine the LRF inclination of the PJ ( [MATH] ). From the observations we know the heliocentric angle ( [MATH] , around 51 ) and the LOS azimuths of microjet ( [MATH] , the angle between the symmetry line and the PJ) and filament ( [MATH] , the angle between the symmetry line and the penumbral f... |
To determine the [MATH] and thus also [MATH] , we need to estimate the elevation angle of the penumbral filaments. They are not exactly horizontal since the Wilson depression must be compensated for in the penumbra. The exact value of the filaments elevation angle is unknown. We estimate it to be with respect to the lo... |
The assumption of a 5 elevation angle gives us the inclination of penumbral filament in LRF ( [MATH] ) as 85 . Thus, we know [MATH] |
[MATH] , and [MATH] , and Eq. can be used to derive the LRF azimuth value [MATH] that also represents the LRF azimuth of the PJ [MATH] ). Knowing [MATH] [MATH] , and [MATH] , Eq. |
can be used again to derive the value of [MATH] that represents the inclination of the microjet in the LRF. In Fig. c the derived values are shown for each of the four depicted jets. |
We estimate the error of individually determined inclination values to be up to 10 . This uncertainty comes from the manual estimation of the PJ and filament orientation and becomes even greater in the outer penumbra where the filament direction could be difficult to estimate from G–band images, and the microjets are l... |
The unknown value of the penumbral filament elevation, and its possible dependence on position within the penumbra causes a further increase in the error. We estimate this error to be in the order of a few degrees. No strong dependence of this value on the position within the penumbra is expected, as the absolute value... |
3.2 Magnetic field inclination The Stokes profiles observed at pixels in the marked area in Fig. b are inverted using the SIR code (Stokes Inversion based on Response functions; Ruiz Cobo & del Toro Iniesta, 1992 . Taking the high spatial resolution of the Hinode SP measurements into account, we use only a one-componen... |
The derived values of magnetic field inclination and azimuth are evaluated with respect to the LOS. After the transformation to the LRF, we determine the single value of magnetic field inclination at each pixel. As the PJs take place in the chromosphere, we want to determine the magnetic field inclination at the highes... |
The obtained curve (solid line in Fig. ) is comparable in absolute values to the inclinations of the so-called background component of the penumbral atmosphere obtained from two-component inversions (Bellot Rubio et al., 2004 ; Borrero et al., 2006 . The concept of two-components comes from the uncombed model of penumb... |
(Solanki & Montavon, 1993 ; Martínez Pillet, 2000 , where the background component has a stronger and more vertical magnetic field compared to the second component and represents the properties of a vertical flux tube that creates the sunspot. The obtained similarity between the inclination values at higher photospheri... |
Comparison of inclination In Fig. , the inclination of 209 individual PJs identified at various positions within the penumbra ( [MATH] symbols) are shown and the mean behaviour of PJs inclination (dashed line) is compared with the radial variation of the magnetic field inclination (solid line). It appears that there is... |
If we assume that these values of magnetic field inclination describe the orientation of the field lines of an vertical flux tube that creates the sunspot, then there is an apparent explanation for the more horizontal direction of PJs. Such a vertical flux tube has to be opening with height due to the pressure balance.... |
These assumptions also imply that the PJs would become more horizontal with height; i.e., the observed microjets should not be straight but instead bend towards the horizontal direction. There are only a few observed cases of PJs in the analysed data set that appear to be curved. We suppose that the rarity of curved PJ... |
Figure shows the running-difference image of a microjet (bright area, detected onset is at lower left part of the image) that appears to be bending towards the horizontal line with height in the atmosphere. A simplified sketch of a microjet is plotted in the upper left corner of Fig. There is a small change of PJ orien... |
The results shown in Fig. also imply that the field is becoming more horizontal with height along the local normal line anywhere in the penumbra. This does not agree with a simple conception of an opening flux tube that would result in approximately constant inclination values along the local normal line. Constant incl... |
Orozco Suarez et al. ( 2005 , who used the inversion of spectral lines to determine the magnetic field orientation in photosphere and chromosphere. However, the authors assume that the magnetic field inclination is constant with height in the photosphere. Thus, the obtained photospheric inclinations might by influenced... |
Conclusions We identified 209 penumbral microjets in almost two-hour long observations of the penumbra in AR10923 using the Ca ii H images taken with 30 s cadence. In combination with simultaneous G–band observations, the inclinations of these microjets (angle between the PJ and local normal line) are determined along ... |
The found radial variation in the PJ inclination resembles the change in magnetic field inclination at higher photospheric layers across the penumbra. We find the difference of 10 between the inclinations of magnetic field lines and penumbral microjets, with the former more vertical. This difference can be explained ea... |
The observed difference also implies that on average we detect the PJs at higher atmospheric layers and only rarely at the initial stage when the PJs inclination angles should be close to (or same as) the magnetic field inclination at higher photospheric layers. The scatter of individually determined values of PJs incl... |
Although our results cannot clarify the mechanism responsible for the formation of the PJs, they imply that the PJs are guided by magnetic field lines that are fanning out with height. Higher cadence observations of Ca ii H and G–band filtergrams and simultaneous SP measurements are needed to study this problem in deta... |
Acknowledgements. We thank Luis Bellot Rubio and Rolf Schlichenmaier for helpful suggestions and comments. This work was enabled thanks to the funding provided by the Japan Society for the Promotion of Science. Financial support from GA AS CR IAA30030808 is gratefully acknowledged. Hinode is a Japanese mission develope... |
# Source: arxiv 0808.0759 # Title: Rapidly spinning massive black holes in active galactic nuclei: evidence from the black hole mass function # Sections: all # Downloaded: 2026-03-02T07:59:19.349402+00:00 |
Rapidly spinning massive black holes in active galactic nuclei: evidence from the black hole mass function (Accepted 2008 August 1. Received 2008 June 16; in original form 2008 May 5) |
Abstract The comparison of the black hole mass function (BHMF) of active galactic nuclei (AGN) relics with the measured mass function of the massive black holes in galaxies provides strong evidence for the growth of massive black holes being dominated by mass accretion. We derive the Eddington ratio distributions as fu... |
[MATH] , which implies that the objects accreting at extremely high rates should be rare or such phases are very short. Using the derived Eddington ratios, we explore the cosmological evolution of massive black holes with an AGN bolometric luminosity function (LF). It is found that the resulted BHMF of AGN relics is un... |
[MATH] . We find that the BHMF of AGN relics can roughly reproduce the local BHMF of galaxies if [MATH] for [MATH] and it increases to [MATH] for [MATH] , which implies that most massive black holes ( [MATH] ) are spinning very rapidly. |
keywords: (galaxies:) quasars: general—accretion, accretion discs—black hole physics—galaxies: evolution Introduction It is believed that quasars are powered by accretion on to massive black holes, and the growth of the massive black holes could be governed by mass accretion in quasars. The massive black holes (AGN rel... |
(Ferrarese & Merritt, 2000 ; Gebhardt et al., 2000 . The black hole mass is also found to be tightly correlated with the luminosity of the spheroid component of its host galaxy (e.g., Magorrian et al., 1998 ; Marconi & Hunt, 2003 . These correlations of the black hole mass with velocity dispersion/host galaxy luminosit... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.