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Proper Motions and Brightness Variations of Nonthermal X-ray Filaments in the Cassiopeia A Supernova Remnant Abstract We present Chandra ACIS X-ray observations of the Galactic supernova remnant Cassiopeia A taken in December 2007. Combining these data with previous archival Chandra observations taken in 2000, 2002, an... |
[MATH] ejecta profile running into a circumstellar wind. We further find that while the position of the reverse shock in this model is consistent with that measured in the X-rays, in order to match the forward shock velocity and radius we had to assume that [MATH] 30% of the explosion energy has gone into accelerating ... |
Subject headings: ISM: individual (Cassiopeia A) – X-rays: nonthermal emission – cosmic rays 1. Introduction Cassiopeia A (Cas A) is one of the youngest known Galactic supernova remnants (SNR) with an estimated explosion date no earlier than [MATH] |
(Fesen et al., 2006 . Optical echoes of the supernova outburst have been recently detected (Rest et al., 2008 , the spectra of which indicate Cas A is the remnant of a Type IIb supernova event (Krause et al., 2008 probably from a red supergiant in the mass range of 15–25 M that may have lost much its hydrogen envelope ... |
Viewed in X-rays, the remnant consists of a line emitting shell arising from reverse shocked ejecta rich in O, Si, Ar, Ca, and Fe |
(Fabian et al., 1980 ; Markert et al., 1983 ; Vink et al., 1996 ; Hughes et al., 2000 ; Willingale et al., 2002 2003 ; Hwang & Laming, 2003 ; Laming & Hwang, 2003 Exterior to this shell are faint X-ray filaments which mark the current position of the remnant’s forward shock front. The emission found here is nonthermal ... |
Vink et al. ( 1998 compared Einstein HRI to ROSAT HRI observations of Cas A to measure the expansion of the bright shell, finding an expansion age of |
[MATH] 500 yr, considerably less than the [MATH] 800 yr expansion age derived from 1.5 and 5.0 GHz radio observations (Anderson & Rudnick, 1995 , but similar to the 400–500 yr expansion age found by Agüeros & Green ( 1999 using data taken at 151 MHz. More recently, DeLaney & Rudnick ( 2003 using Chandra X-ray observati... |
Besides the outlying nonthermal emission filaments associated with the forward shock, some filamentary nonthermal X-ray emission is also seen in projection in the interior of the SNR (DeLaney et al., 2004 . Whether these interior filamentary emissions originate from a wrinkled forward shock seen in projection or arises... |
Comparisons of Chandra observations taken in 2000, 2002, and 2004 revealed secular changes in several X-ray thermal knots and in one nonthermal filament projected in the remnant’s interior (Patnaude & Fesen, 2007 |
Uchiyama & Aharonian ( 2008 using the same multi-epoch Chandra observations found evidence for rapid variability in many more interior nonthermal X-ray emission filaments. Motivated by similar changes seen in RX J1713-3946 (Uchiyama et al., 2007 , they measured the time variability of selected filaments to determine th... |
Such a high magnetic field strength would be consistent with equipartition field strengths inferred in observations of bright radio knots in the remnant |
(Longair, 1994 ; Wright et al., 1999 Uchiyama & Aharonian ( 2008 argue that their result points to a synchrotron origin for the emission coming from these knots, ruling out nonthermal bremsstrahlung from [MATH] 100 keV electrons (Laming, 2001 , and suggest that this is strong evidence for a hadronic origin to the TeV e... |
Here we present forward shock velocity measurements using new Chandra ACIS observations of Cas A taken in December 2007 and compare these results to models for SNR evolution with and without efficient shock acceleration. The new observations show that many nonthermal emission filaments and features have undergone subst... |
2. Observations Cas A was observed with the ACIS-S3 chip on Chandra in two 25 ksec observations taken on 5 Dec 2007 (ObsID 09117) and 8 Dec 2007 (ObsID 09773). The ACIS’s [MATH] CCD pixel scale under-samples the telescope’s [MATH] resolution. The data were reprocessed using CIAO 4.0.1 and the latest version of the Chan... |
shows the combined, exposure corrected image coded by energy. Red corresponds to 0.5–1.5 keV, green to 1.5–3.0 keV, and blue to 4.0–6.0 keV. |
For our analyses, we also made use of previous Chandra ACIS observations taken on 30 Jan 2000 (ObsID 00114; PI: Holt), 6 Feb 2002 (ObsID 01952; PI: Rudnick), and 8 Feb 2004 (ObsID 05196; PI: Hwang). These archival data were also reprocessed using the latest version of the CalDB and all four ACIS images were projected t... |
To avoid the problems with bad columns and node boundaries discussed by DeLaney & Rudnick ( 2003 , exposure corrected images for the 2000 and 2007 observations were created assuming a 1.85 keV source. We note that using a mono-energetic correction results in an artificially higher surface brightness for the forward sho... |
3. Results and Analysis 3.1. Proper Motion of the Forward Shock Front Using the ACIS 2000 and 2002 images, DeLaney & Rudnick ( 2003 estimated the proper motions of several forward shock, nonthermal filaments around the SNR. Based on their average estimated proper motion of [MATH] yr -1 , we expected the filaments to ha... |
Figure shows a Jan 2000 – Dec 2007 ACIS difference image of Cas A. The six labeled boxes correspond to regions where we measured the proper motions of the remnant’s forward shock filaments. Figure shows brightness profile plots of four forward shock filaments taken from the 2000.08 and 2007.95 ACIS images. As seen in F... |
As noted by DeLaney & Rudnick ( 2003 , a proper motion measurement using ACIS ideally should be done using images taken at the same telescope roll angle, as the telescope point spread function (PSF) varies as a function of azimuthal angle. Unfortunately, the data taken in 2000 and 2007 are at different roll angles. To ... |
[MATH] , much less than an ACIS pixel and well below the average separations shown in Figure Filament positional shifts were measured two ways. We first fitted a Gaussian plus background model to the filament profiles and then measured the difference between the resulting Gaussian centroids. This method is not strictly... |
Table lists our results for the six selected filament regions using both measurement techniques. Using the cross-correlation results, we estimate proper motions over the nearly eight year time span of 2000.08 to 2007.95 of [MATH] yr -1 to [MATH] yr -1 for the six regions around the SNR, with a typical 1 [MATH] error of... |
yr -1 In Table , we also list the 2000 – 2002 proper motion estimates reported by DeLaney & Rudnick ( 2003 along with our 2000 – 2002 measurements but using our measurement techniques. In general, we find smaller proper motions by some 15% – 20%. In view that their quoted errors are comparable or even smaller than our ... |
3.2. Cas A’s Expansion Velocity and Deceleration At a distance of 3.4 kpc, our measured proper range of [MATH] yr -1 to [MATH] yr -1 corresponds to forward shock front expansion velocities of 4200 to 5200 [MATH] km s -1 . The average expansion velocity for the six regions listed in Table is [MATH] 4900 km -1 , in good ... |
DeLaney & Rudnick ( 2003 for some two dozen regions. Vink et al. ( 1998 measured the expansion of Cas A’s main shell in X-rays by comparing ROSAT and Einstein HRI observations that were separated by 17 years. They found an expansion time-scale of 501 [MATH] 15 yr, considerably more than the [MATH] 325 yr optically deri... |
(Thorstensen et al., 2001 ; Fesen et al., 2006 , but also much less than the reported [MATH] 800 yr expansion age determined in the radio (Anderson & Rudnick, 1995 , based on 1.5 and 5.0 GHz observations. Agüeros & Green ( 1999 found an expansion age similar to Vink et al. ( 1998 , from 151 MHz observations. |
Gotthelf et al. ( 2001 measured the angular size of Cas A to be 153 [MATH] [MATH] 12 [MATH] Thorstensen et al. ( 2001 estimate an undecelerated explosion convergence date of [MATH] based on proper motion measurements on 17 outlying ejecta knots mainly using archival Palomar 5m images dating as far back as 1951, while F... |
This age yields a free expansion proper motion of [MATH] yr -1 , or, assuming a distance of 3.4 kpc, a free expansion velocity of [MATH] 7500 km -1 . We can thus calculate the deceleration parameter of the blastwave as |
[MATH] = (4900 km s -1 /7500 km s -1 [MATH] 0.65, or equivalently, using Gotthelf et al.’s angular remnant size in 2000, [MATH] yr -1 /(153 [MATH] |
[MATH] 12 [MATH] / 320 yr) [MATH] [MATH] 3.3. Cas A Expansion Models Our measurements of Cas A’s forward shock proper motion and estimated deceleration parameter can be used to model the SNR’s evolution. In ejecta–dominated remnants, the deceleration parameter is related to the self-similar evolution by [MATH] [MATH] |
(Chevalier, 1982 ; Truelove & McKee, 1999 ; Laming & Hwang, 2003 , where [MATH] is the power-law index for the ejecta density profile ( [MATH] ) and [MATH] is the power-law index for the ambient medium density profile ( [MATH] ). Generally, [MATH] corresponds to a constant density ambient medium, while [MATH] correspon... |
For remnants in the adiabatic (Sedov-Taylor) stage of expansion, the deceleration parameter [MATH] . Many young remnants, such as Tycho, Kepler, SN 1006, and Cas A, are believed to be currently transitioning between the ejecta–dominated and Sedov stage. However, our calculated deceleration parameter of 0.65 is less tha... |
However, Laming & Hwang ( 2003 estimated a much higher ejecta density profile for Cas A. Using a Lagrangian hydrodynamics model coupled to a non-equilibrium ionization code, they self-consistently modeled the density profile of Cas A’s expanding ejecta and found found that the ejecta density is well described by a powe... |
Truelove & McKee ( 1999 point out that for models for SNR evolution in which [MATH] , the bulk of the mass is concentrated at lower velocities, while the bulk of the energy is concentrated at higher velocities. Furthermore, the timescale by which a SNR enters the Sedov-Taylor phase of its evolution is set by the time t... |
In order to understand this discrepancy, we have tried to model Cas A’s expansion. At an assumed distance of 3.4 kpc and a 320 yr age in 2000, Cas A’s average forward shock radius of 153 [MATH] translates to 2.5 pc in radius and an average reverse shock radius [MATH] corresponding to [MATH] |
pc. We adopted Laming & Hwang ( 2003 estimated explosion energy of [MATH] 10 51 erg and ejecta mass of 2 M , assume that the SNR is expanding into a red giant wind (Krause et al., 2008 , and choose [MATH] |
[MATH] 10 km s -1 and [MATH] [MATH] [MATH] 10 -5 yr -1 . The results of these adopted values, summarized in Model [MATH] in Table , show that our estimated ejecta power-law index of 4.85 does not reproduce the Cas A’s measured parameters, producing a forward shock radius of 2.93 pc and velocity of 6300 km s -1 instead ... |
Given that our initial derived ejecta power-law index does not agree with that derived from spectral fits to the SNR ejecta, we explored models with ejecta profiles consistent with Laming & Hwang’s fits (Models [MATH] in Table ). We note that a similar set of parameters were also chosen by Schure et al. ( 2008 in the c... |
As shown in Table , while our Models [MATH] may be appropriate for the evolution of the SNR ejecta and the jet, they overestimate the forward shock velocity regardless of choice of the power-law index of the ejecta or progenitor wind structure. These models also do not fit the measured expansion of Cas A, producing dec... |
3.4. Cosmic Ray Acceleration at the Forward Shock As there is a great deal of evidence suggesting that shocks in SNRs are efficient generators of cosmic rays (e.g., Warren et al., 2005 we then explored the inclusion of cosmic ray modification of the forward shock as a possible solution to these poor model fits. A signa... |
In the production of cosmic rays, energy is removed from the SNR shock via particle acceleration. In doing so, the shock slows and the post-shock gas becomes more compressed. We therefore also modeled Cas A under this assumption. |
The inclusion of efficient acceleration at the forward shock should not alter the dynamics of the ejecta, and thus these models can be consistent with |
Laming & Hwang ( 2003 . We also chose to only model shock acceleration at the forward shock. Although there have been suggestions that the bulk of the particle acceleration in Cas A might be occurring at the reverse shock |
(Uchiyama & Aharonian, 2008 ; Helder & Vink, 2008 , the degree to which particle acceleration at the reverse shock is efficient remains an open question (see below). |
Starting with the parameter space explored by Laming & Hwang ( 2003 , we modeled Cas A assuming that some fraction of the explosion energy has gone into accelerating cosmic rays. These models were set up as in Ellison et al. ( 2007 |
where the nonlinear particle acceleration is tuned by an injection parameter which determines the fraction of thermal particles that are injected into the acceleration process thus determining how much of the energy of the SNR goes into cosmic rays. These models are listed as Models 8–15 in Table . The particle injecti... |
As expected and shown in Table , increasingly efficient particle acceleration leads to lower shock velocities and smaller forward shock radii, leading to smaller modeled expansion parameters. In Models 8–13, we attempted to tune the acceleration efficiency so as to match the measured forward shock expansion velocity an... |
We found that Models 11–13, with power-law indices of [MATH] , a wind velocity of [MATH] of 10 km s -1 , and a progenitor pre-SN mass loss rate of [MATH] |
[MATH] [MATH] 10 -5 yr -1 provide a good fit to our observations, where [MATH] 30% of the SN explosion energy is lost in particle acceleration. This acceleration efficiency results in a modeled forward shock velocity of [MATH] 5000 km s -1 , forward and reverse shock radii of [MATH] pc and [MATH] pc, and a deceleration... |
We also tried varying the pre-supernova wind parameters in Models 14–15 to match those of Schure et al. ( 2008 . While these models result in similar deceleration parameters and forward shock radii to Models 11–13, they significantly overestimate the forward shock velocity. |
Finally, in order to see if our results could be fit by models that do not include the effects of diffusive shock acceleration, we also explored a wider parameter space in both the ejecta mass and explosion energy. These are listed as Models [MATH] in Table , where in Models [MATH] we varied the explosion energy and ej... |
erg and 1.0–2.0 M . In Models [MATH] , we only varied the explosion energy, while fixing the other parameters as in Model 2. As seen in Table , varying the explosion energy and ejecta mass does not allow for a simultaneous fit of both the forward shock radius and velocity. For example, in Model 17 we find a suitable fi... |
Although our modeling results suggest significant cosmic ray production at the forward shock, it is uncertain whether efficient particle acceleration might also be occurring at the reverse shock as well (Ellison et al., 2005 . If efficient shock acceleration were occurring at the reverse shock, other effects of this ac... |
3.5. Brightness Variations of Nonthermal X-ray Filaments and their Origin Rapid changes in the brightness of thin, nonthermal filaments in the interior of Cas A have been noted previously via comparisons of the 2000–2004 observations (Patnaude & Fesen, 2007 ; Uchiyama & Aharonian, 2008 . A comparison of all four epoch |
Chandra ACIS images, covering nearly an eight year time span, highlights and clarifies many of these changes in filament brightness and position. This is most readily seen in an on-line movie where we show the evolution of Cas A’s X-ray emission between 2000 and 2007, of which Figure is but one frame. |
A close-up view of many of the changes exhibited by interior nonthermal emission features is presented in Figure , where we show the east-central region of Cas A in each epoch in the 4.2–6.0 keV band. In these images the remnant’s global structure of continuum emission appears not unlike that seen in the radio; that is... |
A comparison of the four frames in Figure reveals several regions where the continuum emission dramatically brightens or fades between Jan 2000 and Dec 2007. Sections of some nonthermal filaments change so substantially between images that they resemble apparent rapid proper motions [MATH] |
[MATH] yr -1 ) that are, in some places, directed inward toward the remnant center or at some random, often non-radial direction. In addition, apparent sequential brightening of small sections of some filaments can give the appearance of motion along the filament. |
Whereas the bulk of the changes in the remnant’s nonthermal emission appear to come from knots and filaments which lie inside or projected onto the interior of the SNR, a few outer forward shock front filaments can also show similar changes in brightness. One filament associated with the forward shock, shown in Figure ... |
Uchiyama & Aharonian ( 2008 argue that emission flaring of nonthermal filaments is evidence for electron acceleration while a decrease in flux corresponds to synchrotron cooling. Using the Chandra ACIS 2000–2004 data, they found such emission flaring and fading was most apparent in interior filaments, leading them to c... |
However, the addition of the new Dec 2007 observations which increases the timespan from 4 to nearly 8 years shows clear evidence for brightness variations of outer nonthermal filaments associated with the forward blastwave. As shown in Figure and listed in Table , the northeast filament brightens substantially between... |
In cases of increasing X-ray flux, the acceleration time of an X-ray emitting electron is given by [MATH] yr, where [MATH] is the electron gyro-factor, [MATH] is the shock velocity in units of 1000 km -1 , and [MATH] is the mean photon energy ( [MATH] keV). As listed in Table , the mean proper motion of this filament i... |
[MATH] yr -1 , which at a distance of 3.4 kpc corresponds to [MATH] = 4.9. Uchiyama & Aharonian ( 2008 have suggested that such brightness changes in the remnant’s interior nonthermal emission filaments originate at the remnant’s reverse shock (due to their projected interior position), a notion first suggested by |
Bleeker et al. ( 2001 based on hardness ratios for interior and outer shock filaments as measured from XMM–Newton images. Support for the interpretation that the exterior and interior nonthermal emission filaments arise from different sources is the lack of radio emission associated with the exterior X-ray forward shoc... |
Helder & Vink ( 2008 have also concluded that the interior nonthermal filaments originate from the reverse shock and not the forward shock. |
On the other hand, DeLaney et al. ( 2004 and DeLaney ( 2004 have argued that interior nonthermal filaments may merely be forward shock filaments seen in projection against the face of Cas A. In this view, interior filamentary and web-like structures arise as the forward shock interacts with a lumpy, inhomogeneous CSM, ... |
We note that a correlation between global X-ray and radio filaments is not expected, thus undermining the meaning of any correlation of nonthermal radio and X-ray emitting features. Both Cassam-Chenaï et al. ( 2005 and Ellison & Cassam-Chenaï ( 2005 showed that in the remnants of core-collapse SNe interacting with a st... |
To investigate the question of whether the nonthermal filaments projected in the interior of Cas A are associated with the reverse shock or the forward shock, we extracted spectra for six exterior forward shock filaments (including the NE filament marked in Fig. ) and 23 interior projected nonthermal filaments from our... |
Aside from obvious normalizations and differences in the absorbing column affecting the flux at lower energies, the spectra for exterior and interior nonthermal filaments are qualitatively quite similar (Fig. ). As shown in Table , while the fitted spectral indices hardly differ, interior filaments do appear to be marg... |
3.6. Magnetic Field Strength Lastly, we turn to the question of magnetic field strength in the filaments. As noted above, the northeast filament shows evidence for brightness changes over a nearly eight year timespan. If we adopt an acceleration time [MATH] |
[MATH] 2–8 yr, then this corresponds to a magnetic field strength of [MATH] [MATH] 0.1–0.3, with the lower limit corresponding to the upper limit on the acceleration time. Our results are consistent with magnetic field strengths derived from previous observations |
(Longair, 1994 ; Wright et al., 1999 ; Vink & Laming, 2003 ; Atoyan et al., 2000 ; Berezhko & Völk, 2004 as well as the recent results of Uchiyama & Aharonian ( 2008 |
Recently, Bykov et al. ( 2008 simulated the effects of magnetic field turbulence on the observed synchrotron emission in young SNRs. They showed that the structure and evolution of small clumps ( [MATH] 10 14 – 10 16 cm) can change on timescales [MATH] 1 year. The angular size of the knots and filaments seen in Figure ... |
[MATH] 10 17 cm at Cas A’s estimated a distance of 3.4 kpc. Significant flux variations on this spatial scale are seen to occur over the time period of |
[MATH] 4 yr, meaning that that yearly changes could occur over [MATH] [MATH] 10 16 cm. Bykov et al. ( 2008 argue that intensity variations on such spatial scales are consistent with localized regions of high magnetic field ( [MATH] 0.1 mG), brought about by turbulence behind the shock. Furthermore, they point out that ... |
4. Conclusions We have presented new Chandra ACIS observations of Cas A which were taken in late 2007. These new observations, when combined with previous Chandra |
data, allow us to constrain the velocity of the forward shock to be about 4900 km s -1 Combined with results from previous analyses of Cas A’s X-ray emission |
(Laming & Hwang, 2003 ; Gotthelf et al., 2001 , we present several models for the evolution of Cas A and find that it’s expansion can be well modeled by an [MATH] ejecta profile running into a circumstellar wind. We also find that the position of the reverse shock in this model is consistent with that measured by |
Gotthelf et al. ( 2001 . However, in order to match the radius of the forward shock, we found that we must assume that the forward shock is efficiently accelerating cosmic rays. |
Rapid changes in Cas A’s synchrotron emission are seen for interior and exterior projected filaments, with both showing similar nonthermal spectra as well as inferred magnetic field strengths. Based on this and the simulations presented by Bykov et al. ( 2008 , it is currently not clear whether the interior filaments a... |
Uchiyama & Aharonian ( 2008 and Helder & Vink ( 2008 Instead, we propose that the interior filaments might be forward shocks seen in projection (DeLaney, 2004 . In that case, the observed brightness variations might arise from wrinkles in front-facing, forward shock as it moves through an inhomogeneous, local circumste... |
Although we cannot rule out the possibility that interior nonthermal filaments are associated with the reverse shock, the combination of similar spectra, flaring timescale, and our fits to the remnant’s dynamics are suggestive that the observed synchrotron flaring for interior filaments arises from forward shock filame... |
We thank Don Ellison, Stephen Reynolds, and Martin Laming for many useful discussions during the preparation of this paper. We also wish to thank the anonymous referee whose many suggestions and corrections significantly improved the paper. This work was supported by NASA grant GO8-9065A which is administered by the CX... |
# Source: arxiv 0808.0735 # Title: Neutrino Astrophysics # Sections: all # Downloaded: 2026-03-02T07:59:16.565311+00:00 INT PUB 08-26 |
NEUTRINO ASTROPHYSICS W. C. Haxton Institute for Nuclear Theory and Department of Physics Box 351550 University of Washington, Seattle, WA 98195 |
email: Haxton@phys.washington.edu Introduction The neutrino is an elementary particle that scatters only through the weak interaction, and consequently rarely interacts in matter. Neutrinos are neutral, carry spin-1/2, and are members of the family of elementary particles called leptons. Thus they differ from the quark... |
[EQUATION] in which a nucleus containing N neutrons and Z protons decays to a lighter nucleus by converting a neutron to a proton, with the emission of an electron and an electron antineutrino. Indeed, it was the apparent absence of energy conservation in nuclear [MATH] decay that first lead Wolfgang Pauli, nearly 80 y... |
Neutrinos play a very special role in astrophysics . First, they are the direct byproducts of the nuclear reaction chains by which stars generate energy: each solar conversion of four protons into helium produces two neutrinos, for a total of [MATH] [MATH] 10 38 neutrinos each second. The resulting flux is observable o... |
Neutrinos also mediate important astrophysical processes. The supernova “neutrino wind,” which blows off the surface of the proto-neutron star just seconds after core collapse, is thought to produce conditions favorable for the synthesis of about half of the neutron-rich nuclear species heavier than iron, through rapid... |
Nuclear and particle physicists are exploiting astrophysical neutrino fluxes to do important tests of the standard model of particle physics. These tests include neutrino oscillations (the process by which a massive neutrino can be produced in one flavor state but detected later as a neutrino with a different flavor), ... |
Solar Neutrinos The first successful effort to detect neutrinos from the Sun began four decades ago. Ray Davis, Jr. and his collaborators constructed a 650-ton detector in the Homestake Gold Mine, one mile beneath Lead, South Dakota |
. This radiochemical detector, based on the chlorine-bearing cleaning fluid C Cl , was designed to capture about one of the approximately 10 18 high-energy neutrinos that penetrated it each day – the rest passed through the detector, without interacting. The neutrino-capture reaction was inverse-electron-capture |
[EQUATION] The product of this reaction, 37 Ar, is a noble gas isotope with a half life of about one month. It can be efficiently removed from a large volume of organic fluid by a helium gas purge, then counted in miniature gas proportional counters as 37 Ar decays back to 37 Cl. Davis typically exposed his detector fo... |
Within a few years it became apparent that the number of neutrinos detected was only about one-third that predicted by the standard solar model (SSM) |
, that is, the model of the Sun based on the standard theory of main sequence stellar evolution. Some initially attributed this “solar neutrino problem” to uncertainties in the SSM: As the flux of neutrinos most important to the Davis detector vary as [MATH] |
[MATH] , where [MATH] is the solar core temperature, a 5% theory uncertainty in [MATH] could explain the discrepancy. In fact, the correct explanation for the discrepancy proved much more profound. Davis was awarded the 2002 Nobel Prize in Physics for the Cl experiment. |
During the three-decade period of 37 Cl detector operations, five other solar neutrino experiments were constructed. The SAGE and GALLEX/GNO experiments, radiochemical detectors similar to Cl, but using 71 Ga as a target, were designed to measure the flux of neutrinos from the dominant low-energy branch of solar neutri... |
2.1 The Standard Solar Model The Sun belongs to a class of “main sequence” stars that derive their energy from burning protons to He in their cores. The SSM employs the standard theory of main-sequence stellar evolution, calibrated by the many detailed measurements only possible for the Sun, to follow the Sun from the ... |
The Sun evolves in hydrostatic equilibrium, maintaining a local balance between the gravitational force and the pressure gradient. To describe this condition in detail, one must specify the electron-gas equation of state as a function of temperature, density, and composition. |
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